%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP746+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:08:35 AM UTC 2025
% Result : Theorem 21.60s 21.83s
% Output : Proof 23.85s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : GRP746+1 : TPTP v9.0.0. Released v4.0.0.
% 0.04/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n012.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Jun 19 17:01:56 EDT 2025
% 0.13/0.35 % CPUTime :
% 21.60/21.83 % SZS status Theorem
% 21.60/21.83 % SZS output start Proof
% 21.60/21.83 tff(mult_type, type, (
% 21.60/21.83 mult: ( $i * $i ) > $i)).
% 21.60/21.83 tff(c_type, type, (
% 21.60/21.83 c: $i)).
% 21.60/21.83 tff(b_type, type, (
% 21.60/21.83 b: $i)).
% 21.60/21.83 tff(a_type, type, (
% 21.60/21.83 a: $i)).
% 21.60/21.83 tff(ld_type, type, (
% 21.60/21.83 ld: ( $i * $i ) > $i)).
% 21.60/21.83 tff(unit_type, type, (
% 21.60/21.83 unit: $i)).
% 21.60/21.83 tff(rd_type, type, (
% 21.60/21.83 rd: ( $i * $i ) > $i)).
% 21.60/21.83 tff(1,plain,
% 21.60/21.83 (^[B: $i, A: $i] : refl((ld(A, mult(A, B)) = B) <=> (ld(A, mult(A, B)) = B))),
% 21.60/21.83 inference(bind,[status(th)],[])).
% 21.60/21.83 tff(2,plain,
% 21.60/21.83 (![B: $i, A: $i] : (ld(A, mult(A, B)) = B) <=> ![B: $i, A: $i] : (ld(A, mult(A, B)) = B)),
% 21.60/21.83 inference(quant_intro,[status(thm)],[1])).
% 21.60/21.83 tff(3,plain,
% 21.60/21.83 (![B: $i, A: $i] : (ld(A, mult(A, B)) = B) <=> ![B: $i, A: $i] : (ld(A, mult(A, B)) = B)),
% 21.60/21.83 inference(rewrite,[status(thm)],[])).
% 21.60/21.83 tff(4,axiom,(![B: $i, A: $i] : (ld(A, mult(A, B)) = B)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','f02')).
% 21.60/21.83 tff(5,plain,
% 21.60/21.83 (![B: $i, A: $i] : (ld(A, mult(A, B)) = B)),
% 21.60/21.83 inference(modus_ponens,[status(thm)],[4, 3])).
% 21.60/21.83 tff(6,plain,(
% 21.60/21.83 ![B: $i, A: $i] : (ld(A, mult(A, B)) = B)),
% 21.60/21.83 inference(skolemize,[status(sab)],[5])).
% 21.60/21.83 tff(7,plain,
% 21.60/21.83 (![B: $i, A: $i] : (ld(A, mult(A, B)) = B)),
% 21.60/21.83 inference(modus_ponens,[status(thm)],[6, 2])).
% 21.60/21.83 tff(8,plain,
% 21.60/21.83 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(a, b), mult(mult(a, b), mult(a, mult(b, c)))) = mult(a, mult(b, c)))),
% 21.60/21.83 inference(quant_inst,[status(thm)],[])).
% 21.60/21.83 tff(9,plain,
% 21.60/21.83 (ld(mult(a, b), mult(mult(a, b), mult(a, mult(b, c)))) = mult(a, mult(b, c))),
% 21.60/21.83 inference(unit_resolution,[status(thm)],[8, 7])).
% 21.60/21.83 tff(10,plain,
% 21.60/21.83 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(c, c), mult(mult(c, c), mult(a, b))) = mult(a, b))),
% 21.60/21.83 inference(quant_inst,[status(thm)],[])).
% 21.60/21.83 tff(11,plain,
% 21.60/21.83 (ld(mult(c, c), mult(mult(c, c), mult(a, b))) = mult(a, b)),
% 21.60/21.83 inference(unit_resolution,[status(thm)],[10, 7])).
% 21.60/21.83 tff(12,assumption,(~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit))))), introduced(assumption)).
% 21.60/21.83 tff(13,plain,
% 21.60/21.83 (((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit)))))) | (mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit))))),
% 21.60/21.83 inference(tautology,[status(thm)],[])).
% 21.60/21.83 tff(14,plain,
% 21.60/21.83 ((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit)))))),
% 21.60/21.83 inference(unit_resolution,[status(thm)],[13, 12])).
% 21.60/21.83 tff(15,plain,
% 21.60/21.83 (^[X0: $i, X1: $i, X2: $i] : refl(((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1))))))) <=> ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1))))))))),
% 21.60/21.83 inference(bind,[status(th)],[])).
% 21.60/21.83 tff(16,plain,
% 21.60/21.83 (![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1))))))) <=> ![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))),
% 21.60/21.83 inference(quant_intro,[status(thm)],[15])).
% 21.60/21.83 tff(17,plain,
% 21.60/21.83 (^[X0: $i, X1: $i, X2: $i] : rewrite((((mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1)) & (mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))) | ((mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2))) & (mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1))))) <=> ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1))))))))),
% 21.60/21.83 inference(bind,[status(th)],[])).
% 21.60/21.83 tff(18,plain,
% 21.60/21.83 (![X0: $i, X1: $i, X2: $i] : (((mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1)) & (mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))) | ((mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2))) & (mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1))))) <=> ![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))),
% 21.60/21.83 inference(quant_intro,[status(thm)],[17])).
% 21.60/21.83 tff(19,plain,
% 21.60/21.83 (![X0: $i, X1: $i, X2: $i] : (((mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1)) & (mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))) | ((mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2))) & (mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1))))) <=> ![X0: $i, X1: $i, X2: $i] : (((mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1)) & (mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))) | ((mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2))) & (mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))),
% 21.60/21.83 inference(rewrite,[status(thm)],[])).
% 21.60/21.83 tff(20,plain,
% 21.60/21.83 (^[X0: $i, X1: $i, X2: $i] : rewrite((((mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2))) & (mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))) | ((mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1)) & (mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1))))) <=> (((mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1)) & (mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))) | ((mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2))) & (mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1))))))),
% 21.60/21.83 inference(bind,[status(th)],[])).
% 21.60/21.83 tff(21,plain,
% 21.60/21.83 (![X0: $i, X1: $i, X2: $i] : (((mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2))) & (mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))) | ((mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1)) & (mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1))))) <=> ![X0: $i, X1: $i, X2: $i] : (((mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1)) & (mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))) | ((mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2))) & (mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))),
% 21.60/21.83 inference(quant_intro,[status(thm)],[20])).
% 21.60/21.83 tff(22,axiom,(![X0: $i, X1: $i, X2: $i] : (((mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2))) & (mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))) | ((mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1)) & (mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','f08')).
% 21.60/21.83 tff(23,plain,
% 21.60/21.83 (![X0: $i, X1: $i, X2: $i] : (((mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1)) & (mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))) | ((mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2))) & (mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))),
% 21.60/21.83 inference(modus_ponens,[status(thm)],[22, 21])).
% 21.60/21.83 tff(24,plain,
% 21.60/21.83 (![X0: $i, X1: $i, X2: $i] : (((mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1)) & (mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))) | ((mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2))) & (mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))),
% 21.60/21.83 inference(modus_ponens,[status(thm)],[23, 19])).
% 21.60/21.83 tff(25,plain,(
% 21.60/21.83 ![X0: $i, X1: $i, X2: $i] : (((mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1)) & (mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))) | ((mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2))) & (mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))),
% 21.60/21.83 inference(skolemize,[status(sab)],[24])).
% 21.60/21.83 tff(26,plain,
% 21.60/21.83 (![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))),
% 21.60/21.83 inference(modus_ponens,[status(thm)],[25, 18])).
% 21.60/21.83 tff(27,plain,
% 21.60/21.83 (![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))),
% 21.60/21.83 inference(modus_ponens,[status(thm)],[26, 16])).
% 21.60/21.83 tff(28,plain,
% 21.60/21.83 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit))))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit))))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit))))))))),
% 21.60/21.83 inference(rewrite,[status(thm)],[])).
% 21.60/21.83 tff(29,plain,
% 21.60/21.83 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit))))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit))))))))),
% 21.60/21.83 inference(quant_inst,[status(thm)],[])).
% 21.60/21.83 tff(30,plain,
% 21.60/21.83 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit))))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit)))))))),
% 21.60/21.84 inference(modus_ponens,[status(thm)],[29, 28])).
% 21.60/21.84 tff(31,plain,
% 21.60/21.84 ((~((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit))))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit)))))))),
% 21.60/21.84 inference(unit_resolution,[status(thm)],[30, 27])).
% 21.60/21.84 tff(32,plain,
% 21.60/21.84 (~((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit))))))),
% 21.60/21.84 inference(unit_resolution,[status(thm)],[31, 14])).
% 21.60/21.84 tff(33,plain,
% 21.60/21.84 (((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit)))))) | (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit))))),
% 21.60/21.84 inference(tautology,[status(thm)],[])).
% 21.60/21.84 tff(34,plain,
% 21.60/21.84 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit)))),
% 21.60/21.84 inference(unit_resolution,[status(thm)],[33, 32])).
% 21.60/21.84 tff(35,plain,
% 21.60/21.84 (((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit)))))) | (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)))),
% 21.60/21.84 inference(tautology,[status(thm)],[])).
% 21.60/21.84 tff(36,plain,
% 21.60/21.84 (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a))),
% 21.60/21.84 inference(unit_resolution,[status(thm)],[35, 32])).
% 21.60/21.84 tff(37,plain,
% 21.60/21.84 (^[A: $i] : refl((mult(A, unit) = A) <=> (mult(A, unit) = A))),
% 21.60/21.84 inference(bind,[status(th)],[])).
% 21.60/21.84 tff(38,plain,
% 21.60/21.84 (![A: $i] : (mult(A, unit) = A) <=> ![A: $i] : (mult(A, unit) = A)),
% 21.60/21.84 inference(quant_intro,[status(thm)],[37])).
% 21.60/21.84 tff(39,plain,
% 21.60/21.84 (![A: $i] : (mult(A, unit) = A) <=> ![A: $i] : (mult(A, unit) = A)),
% 21.60/21.84 inference(rewrite,[status(thm)],[])).
% 21.60/21.84 tff(40,axiom,(![A: $i] : (mult(A, unit) = A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','f05')).
% 21.60/21.84 tff(41,plain,
% 21.60/21.84 (![A: $i] : (mult(A, unit) = A)),
% 21.60/21.84 inference(modus_ponens,[status(thm)],[40, 39])).
% 21.60/21.84 tff(42,plain,(
% 21.60/21.84 ![A: $i] : (mult(A, unit) = A)),
% 21.60/21.84 inference(skolemize,[status(sab)],[41])).
% 21.60/21.84 tff(43,plain,
% 21.60/21.84 (![A: $i] : (mult(A, unit) = A)),
% 21.60/21.84 inference(modus_ponens,[status(thm)],[42, 38])).
% 21.60/21.84 tff(44,plain,
% 21.60/21.84 ((~![A: $i] : (mult(A, unit) = A)) | (mult(mult(a, c), unit) = mult(a, c))),
% 21.60/21.84 inference(quant_inst,[status(thm)],[])).
% 21.60/21.84 tff(45,plain,
% 21.60/21.84 (mult(mult(a, c), unit) = mult(a, c)),
% 21.60/21.84 inference(unit_resolution,[status(thm)],[44, 43])).
% 21.60/21.84 tff(46,plain,
% 21.60/21.84 ((~![A: $i] : (mult(A, unit) = A)) | (mult(a, unit) = a)),
% 21.60/21.84 inference(quant_inst,[status(thm)],[])).
% 21.60/21.84 tff(47,plain,
% 21.60/21.84 (mult(a, unit) = a),
% 21.60/21.84 inference(unit_resolution,[status(thm)],[46, 43])).
% 21.60/21.84 tff(48,plain,
% 21.60/21.84 (mult(mult(a, unit), c) = mult(a, c)),
% 21.60/21.84 inference(monotonicity,[status(thm)],[47])).
% 21.60/21.84 tff(49,plain,
% 21.60/21.84 (mult(mult(mult(a, unit), c), unit) = mult(mult(a, c), unit)),
% 21.60/21.84 inference(monotonicity,[status(thm)],[48])).
% 21.60/21.84 tff(50,plain,
% 21.60/21.84 (^[C: $i, B: $i, A: $i] : refl((mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B))) <=> (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B))))),
% 21.60/21.84 inference(bind,[status(th)],[])).
% 21.60/21.84 tff(51,plain,
% 21.60/21.84 (![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B))) <=> ![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))),
% 21.60/21.84 inference(quant_intro,[status(thm)],[50])).
% 21.60/21.84 tff(52,plain,
% 21.60/21.84 (![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B))) <=> ![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))),
% 21.60/21.84 inference(rewrite,[status(thm)],[])).
% 21.60/21.84 tff(53,axiom,(![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','f07')).
% 21.60/21.84 tff(54,plain,
% 21.60/21.84 (![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))),
% 21.60/21.84 inference(modus_ponens,[status(thm)],[53, 52])).
% 21.60/21.84 tff(55,plain,(
% 21.60/21.84 ![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))),
% 21.60/21.84 inference(skolemize,[status(sab)],[54])).
% 21.60/21.84 tff(56,plain,
% 21.60/21.84 (![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))),
% 21.60/21.84 inference(modus_ponens,[status(thm)],[55, 51])).
% 21.60/21.84 tff(57,plain,
% 21.60/21.84 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(a, unit), c), unit) = mult(a, mult(mult(unit, c), unit)))),
% 21.60/21.84 inference(quant_inst,[status(thm)],[])).
% 21.60/21.84 tff(58,plain,
% 21.60/21.84 (mult(mult(mult(a, unit), c), unit) = mult(a, mult(mult(unit, c), unit))),
% 21.60/21.84 inference(unit_resolution,[status(thm)],[57, 56])).
% 21.60/21.84 tff(59,plain,
% 21.60/21.84 (mult(a, mult(mult(unit, c), unit)) = mult(mult(mult(a, unit), c), unit)),
% 21.60/21.84 inference(symmetry,[status(thm)],[58])).
% 21.60/21.84 tff(60,plain,
% 21.60/21.84 (mult(a, mult(mult(unit, c), unit)) = mult(a, c)),
% 21.60/21.84 inference(transitivity,[status(thm)],[59, 49, 45])).
% 21.60/21.84 tff(61,plain,
% 21.60/21.84 (mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit))) = mult(rd(mult(b, c), mult(a, c)), mult(a, c))),
% 21.60/21.84 inference(monotonicity,[status(thm)],[60])).
% 21.60/21.84 tff(62,plain,
% 21.60/21.84 ((~![A: $i] : (mult(A, unit) = A)) | (mult(mult(unit, c), unit) = mult(unit, c))),
% 21.60/21.84 inference(quant_inst,[status(thm)],[])).
% 21.60/21.84 tff(63,plain,
% 21.60/21.84 (mult(mult(unit, c), unit) = mult(unit, c)),
% 21.60/21.84 inference(unit_resolution,[status(thm)],[62, 43])).
% 21.60/21.84 tff(64,plain,
% 21.60/21.84 (mult(unit, c) = mult(mult(unit, c), unit)),
% 21.60/21.84 inference(symmetry,[status(thm)],[63])).
% 21.60/21.84 tff(65,plain,
% 21.60/21.84 (^[A: $i] : refl((mult(unit, A) = A) <=> (mult(unit, A) = A))),
% 21.60/21.84 inference(bind,[status(th)],[])).
% 21.60/21.84 tff(66,plain,
% 21.60/21.84 (![A: $i] : (mult(unit, A) = A) <=> ![A: $i] : (mult(unit, A) = A)),
% 21.60/21.84 inference(quant_intro,[status(thm)],[65])).
% 21.60/21.84 tff(67,plain,
% 21.60/21.84 (![A: $i] : (mult(unit, A) = A) <=> ![A: $i] : (mult(unit, A) = A)),
% 21.60/21.84 inference(rewrite,[status(thm)],[])).
% 21.60/21.84 tff(68,axiom,(![A: $i] : (mult(unit, A) = A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','f06')).
% 21.60/21.84 tff(69,plain,
% 21.60/21.84 (![A: $i] : (mult(unit, A) = A)),
% 21.60/21.84 inference(modus_ponens,[status(thm)],[68, 67])).
% 21.60/21.84 tff(70,plain,(
% 21.60/21.84 ![A: $i] : (mult(unit, A) = A)),
% 21.60/21.84 inference(skolemize,[status(sab)],[69])).
% 21.60/21.84 tff(71,plain,
% 21.60/21.84 (![A: $i] : (mult(unit, A) = A)),
% 21.60/21.84 inference(modus_ponens,[status(thm)],[70, 66])).
% 21.60/21.84 tff(72,plain,
% 21.60/21.84 ((~![A: $i] : (mult(unit, A) = A)) | (mult(unit, c) = c)),
% 21.60/21.84 inference(quant_inst,[status(thm)],[])).
% 21.60/21.84 tff(73,plain,
% 21.60/21.84 (mult(unit, c) = c),
% 21.60/21.84 inference(unit_resolution,[status(thm)],[72, 71])).
% 21.60/21.84 tff(74,plain,
% 21.60/21.84 (c = mult(unit, c)),
% 21.60/21.84 inference(symmetry,[status(thm)],[73])).
% 21.60/21.84 tff(75,plain,
% 21.60/21.84 (c = mult(mult(unit, c), unit)),
% 21.60/21.84 inference(transitivity,[status(thm)],[74, 64])).
% 21.60/21.84 tff(76,plain,
% 21.60/21.84 (mult(mult(rd(mult(b, c), mult(a, c)), a), c) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit))),
% 21.60/21.84 inference(monotonicity,[status(thm)],[75])).
% 21.60/21.84 tff(77,plain,
% 21.60/21.84 (mult(mult(rd(mult(b, c), mult(a, c)), a), c) = mult(rd(mult(b, c), mult(a, c)), mult(a, c))),
% 21.60/21.84 inference(transitivity,[status(thm)],[76, 34, 61])).
% 21.60/21.84 tff(78,plain,
% 21.60/21.84 (mult(mult(unit, c), unit) = c),
% 21.60/21.84 inference(transitivity,[status(thm)],[63, 73])).
% 21.60/21.84 tff(79,plain,
% 21.60/21.84 (mult(mult(mult(unit, c), unit), a) = mult(c, a)),
% 21.60/21.84 inference(monotonicity,[status(thm)],[78])).
% 21.60/21.84 tff(80,plain,
% 21.60/21.84 (mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(c, a))),
% 21.60/21.84 inference(monotonicity,[status(thm)],[79])).
% 21.60/21.84 tff(81,plain,
% 21.60/21.84 (mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)) = mult(rd(mult(b, c), mult(a, c)), c)),
% 21.60/21.84 inference(monotonicity,[status(thm)],[78])).
% 21.60/21.84 tff(82,plain,
% 21.60/21.84 (mult(rd(mult(b, c), mult(a, c)), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit))),
% 21.60/21.84 inference(symmetry,[status(thm)],[81])).
% 21.60/21.84 tff(83,plain,
% 21.60/21.84 (mult(mult(rd(mult(b, c), mult(a, c)), c), a) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a)),
% 21.60/21.84 inference(monotonicity,[status(thm)],[82])).
% 21.60/21.84 tff(84,plain,
% 21.60/21.84 (mult(mult(rd(mult(b, c), mult(a, c)), c), a) = mult(rd(mult(b, c), mult(a, c)), mult(c, a))),
% 21.60/21.84 inference(transitivity,[status(thm)],[83, 36, 80])).
% 21.60/21.84 tff(85,plain,
% 21.60/21.84 ((mult(mult(rd(mult(b, c), mult(a, c)), c), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), c)) <=> (mult(rd(mult(b, c), mult(a, c)), mult(c, a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, c)))),
% 21.60/21.84 inference(monotonicity,[status(thm)],[84, 77])).
% 21.60/21.84 tff(86,plain,
% 21.60/21.84 ((mult(rd(mult(b, c), mult(a, c)), mult(c, a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, c))) <=> (mult(mult(rd(mult(b, c), mult(a, c)), c), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), c))),
% 21.60/21.84 inference(symmetry,[status(thm)],[85])).
% 21.60/21.84 tff(87,plain,
% 21.60/21.84 ((~(mult(rd(mult(b, c), mult(a, c)), mult(c, a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, c)))) <=> (~(mult(mult(rd(mult(b, c), mult(a, c)), c), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), c)))),
% 21.60/21.84 inference(monotonicity,[status(thm)],[86])).
% 21.60/21.84 tff(88,plain,
% 21.60/21.84 ((mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit)))) <=> (mult(rd(mult(b, c), mult(a, c)), mult(c, a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, c)))),
% 21.60/21.84 inference(monotonicity,[status(thm)],[80, 61])).
% 21.60/21.84 tff(89,plain,
% 21.60/21.84 ((mult(rd(mult(b, c), mult(a, c)), mult(c, a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, c))) <=> (mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit))))),
% 21.60/21.84 inference(symmetry,[status(thm)],[88])).
% 21.60/21.84 tff(90,assumption,(mult(rd(mult(b, c), mult(a, c)), mult(c, a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, c))), introduced(assumption)).
% 21.60/21.84 tff(91,plain,
% 21.60/21.84 (mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit)))),
% 21.60/21.84 inference(modus_ponens,[status(thm)],[90, 89])).
% 21.60/21.84 tff(92,plain,
% 21.60/21.84 ($false),
% 21.60/21.84 inference(unit_resolution,[status(thm)],[12, 91])).
% 21.60/21.84 tff(93,plain,((mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit)))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(c, a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, c))))), inference(lemma,lemma(discharge,[]))).
% 21.60/21.84 tff(94,plain,
% 21.60/21.84 (~(mult(rd(mult(b, c), mult(a, c)), mult(c, a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, c)))),
% 21.60/21.84 inference(unit_resolution,[status(thm)],[93, 12])).
% 21.60/21.84 tff(95,plain,
% 21.60/21.84 (~(mult(mult(rd(mult(b, c), mult(a, c)), c), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), c))),
% 21.60/21.84 inference(modus_ponens,[status(thm)],[94, 87])).
% 21.60/21.84 tff(96,plain,
% 21.60/21.84 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)) = mult(mult(rd(mult(b, c), mult(a, c)), a), c)),
% 21.60/21.84 inference(symmetry,[status(thm)],[76])).
% 21.60/21.84 tff(97,assumption,(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit)))), introduced(assumption)).
% 21.60/21.84 tff(98,plain,
% 21.60/21.84 (mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit))) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit))),
% 21.68/21.84 inference(symmetry,[status(thm)],[97])).
% 21.68/21.84 tff(99,plain,
% 21.68/21.84 (mult(rd(mult(b, c), mult(a, c)), mult(a, c)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit)))),
% 21.68/21.84 inference(symmetry,[status(thm)],[61])).
% 21.68/21.84 tff(100,plain,
% 21.68/21.84 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))) = mult(a, c))),
% 21.68/21.84 inference(quant_inst,[status(thm)],[])).
% 21.68/21.84 tff(101,plain,
% 21.68/21.84 (ld(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))) = mult(a, c)),
% 21.68/21.84 inference(unit_resolution,[status(thm)],[100, 7])).
% 21.68/21.84 tff(102,assumption,(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))), introduced(assumption)).
% 21.68/21.84 tff(103,plain,
% 21.68/21.84 (ld(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a))) = ld(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 21.68/21.84 inference(monotonicity,[status(thm)],[102])).
% 21.68/21.84 tff(104,plain,
% 21.68/21.84 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a))) = mult(c, a))),
% 21.68/21.84 inference(quant_inst,[status(thm)],[])).
% 21.68/21.84 tff(105,plain,
% 21.68/21.84 (ld(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a))) = mult(c, a)),
% 21.68/21.84 inference(unit_resolution,[status(thm)],[104, 7])).
% 21.68/21.84 tff(106,plain,
% 21.68/21.84 (mult(c, a) = ld(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)))),
% 21.68/21.84 inference(symmetry,[status(thm)],[105])).
% 21.68/21.84 tff(107,plain,
% 21.68/21.84 (mult(c, a) = mult(a, c)),
% 21.68/21.84 inference(transitivity,[status(thm)],[106, 103, 101])).
% 21.68/21.84 tff(108,plain,
% 21.68/21.84 (mult(rd(mult(b, c), mult(a, c)), mult(c, a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, c))),
% 21.68/21.84 inference(monotonicity,[status(thm)],[107])).
% 21.68/21.84 tff(109,assumption,(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a))), introduced(assumption)).
% 21.68/21.84 tff(110,plain,
% 21.68/21.84 (mult(mult(rd(mult(b, c), mult(a, c)), c), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), c)),
% 21.68/21.84 inference(transitivity,[status(thm)],[83, 109, 80, 108, 99, 98, 96])).
% 21.68/21.84 tff(111,assumption,(~(mult(mult(rd(mult(b, c), mult(a, c)), c), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), c))), introduced(assumption)).
% 21.68/21.84 tff(112,plain,
% 21.68/21.84 ($false),
% 21.68/21.84 inference(unit_resolution,[status(thm)],[111, 110])).
% 21.68/21.84 tff(113,plain,((~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))) | (mult(mult(rd(mult(b, c), mult(a, c)), c), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), c)) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit)))))), inference(lemma,lemma(discharge,[]))).
% 21.68/21.84 tff(114,plain,
% 21.68/21.84 (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 21.68/21.84 inference(unit_resolution,[status(thm)],[113, 95, 36, 34])).
% 21.68/21.84 tff(115,plain,
% 21.68/21.84 (((~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))))) | (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 21.68/21.84 inference(tautology,[status(thm)],[])).
% 21.68/21.84 tff(116,plain,
% 21.68/21.84 ((~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))))),
% 21.68/21.84 inference(unit_resolution,[status(thm)],[115, 114])).
% 21.68/21.84 tff(117,plain,
% 21.68/21.84 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))))) | (~((~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)))) | (~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))))) | (~((~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)))) | (~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))))))),
% 21.68/21.84 inference(rewrite,[status(thm)],[])).
% 21.68/21.84 tff(118,plain,
% 21.68/21.84 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))))) | (~((~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)))) | (~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))))))),
% 21.68/21.84 inference(quant_inst,[status(thm)],[])).
% 21.68/21.84 tff(119,plain,
% 21.68/21.84 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))))) | (~((~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)))) | (~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))))))),
% 21.68/21.84 inference(modus_ponens,[status(thm)],[118, 117])).
% 21.68/21.84 tff(120,plain,
% 21.68/21.84 (~((~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)))) | (~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))))),
% 21.68/21.84 inference(unit_resolution,[status(thm)],[119, 27, 116])).
% 21.68/21.84 tff(121,plain,
% 21.68/21.84 (((~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)))) | (~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))))) | (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 21.68/21.85 inference(tautology,[status(thm)],[])).
% 21.68/21.85 tff(122,plain,
% 21.68/21.85 (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))),
% 21.68/21.85 inference(unit_resolution,[status(thm)],[121, 120])).
% 21.68/21.85 tff(123,plain,
% 21.68/21.85 (((~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)))) | (~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))))) | (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)))),
% 21.68/21.85 inference(tautology,[status(thm)],[])).
% 21.68/21.85 tff(124,plain,
% 21.68/21.85 (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a))),
% 21.68/21.85 inference(unit_resolution,[status(thm)],[123, 120])).
% 21.68/21.85 tff(125,plain,
% 21.68/21.85 ((mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c)) <=> (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 21.68/21.85 inference(monotonicity,[status(thm)],[124, 122])).
% 21.68/21.85 tff(126,plain,
% 21.68/21.85 ((mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))) <=> (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c))),
% 21.68/21.85 inference(symmetry,[status(thm)],[125])).
% 21.68/21.85 tff(127,plain,
% 21.68/21.85 ((~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))) <=> (~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c)))),
% 21.68/21.85 inference(monotonicity,[status(thm)],[126])).
% 21.68/21.85 tff(128,plain,
% 21.68/21.85 (~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c))),
% 21.68/21.85 inference(modus_ponens,[status(thm)],[114, 127])).
% 21.68/21.85 tff(129,plain,
% 21.68/21.85 (^[B: $i, A: $i] : refl((mult(rd(A, B), B) = A) <=> (mult(rd(A, B), B) = A))),
% 21.68/21.85 inference(bind,[status(th)],[])).
% 21.68/21.85 tff(130,plain,
% 21.68/21.85 (![B: $i, A: $i] : (mult(rd(A, B), B) = A) <=> ![B: $i, A: $i] : (mult(rd(A, B), B) = A)),
% 21.68/21.85 inference(quant_intro,[status(thm)],[129])).
% 21.68/21.85 tff(131,plain,
% 21.68/21.85 (![B: $i, A: $i] : (mult(rd(A, B), B) = A) <=> ![B: $i, A: $i] : (mult(rd(A, B), B) = A)),
% 21.68/21.85 inference(rewrite,[status(thm)],[])).
% 21.68/21.85 tff(132,axiom,(![B: $i, A: $i] : (mult(rd(A, B), B) = A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','f03')).
% 21.68/21.85 tff(133,plain,
% 21.68/21.85 (![B: $i, A: $i] : (mult(rd(A, B), B) = A)),
% 21.68/21.85 inference(modus_ponens,[status(thm)],[132, 131])).
% 21.68/21.85 tff(134,plain,(
% 21.68/21.85 ![B: $i, A: $i] : (mult(rd(A, B), B) = A)),
% 21.68/21.85 inference(skolemize,[status(sab)],[133])).
% 21.68/21.85 tff(135,plain,
% 21.68/21.85 (![B: $i, A: $i] : (mult(rd(A, B), B) = A)),
% 21.68/21.85 inference(modus_ponens,[status(thm)],[134, 130])).
% 21.68/21.85 tff(136,plain,
% 21.68/21.85 ((~![B: $i, A: $i] : (mult(rd(A, B), B) = A)) | (mult(rd(mult(b, c), mult(a, c)), mult(a, c)) = mult(b, c))),
% 21.68/21.85 inference(quant_inst,[status(thm)],[])).
% 21.68/21.85 tff(137,plain,
% 21.68/21.85 (mult(rd(mult(b, c), mult(a, c)), mult(a, c)) = mult(b, c)),
% 21.68/21.85 inference(unit_resolution,[status(thm)],[136, 135])).
% 21.68/21.85 tff(138,plain,
% 21.68/21.85 (mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c))) = mult(mult(a, c), mult(b, c))),
% 21.68/21.85 inference(monotonicity,[status(thm)],[137])).
% 21.68/21.85 tff(139,plain,
% 21.68/21.85 (mult(mult(a, c), mult(b, c)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))),
% 21.68/21.85 inference(symmetry,[status(thm)],[138])).
% 21.68/21.85 tff(140,plain,
% 21.68/21.85 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(a, mult(a, mult(b, c))) = mult(b, c))),
% 21.68/21.85 inference(quant_inst,[status(thm)],[])).
% 21.68/21.85 tff(141,plain,
% 21.68/21.85 (ld(a, mult(a, mult(b, c))) = mult(b, c)),
% 21.68/21.85 inference(unit_resolution,[status(thm)],[140, 7])).
% 21.68/21.85 tff(142,plain,
% 21.68/21.85 (mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))) = mult(a, mult(b, c))),
% 21.68/21.85 inference(monotonicity,[status(thm)],[137])).
% 21.68/21.85 tff(143,plain,
% 21.68/21.85 ((mult(a, mult(b, c)) = mult(mult(a, b), c)) <=> (mult(mult(a, b), c) = mult(a, mult(b, c)))),
% 21.68/21.85 inference(commutativity,[status(thm)],[])).
% 21.68/21.85 tff(144,plain,
% 21.68/21.85 ((~(mult(mult(a, b), c) = mult(a, mult(b, c)))) <=> (~(mult(mult(a, b), c) = mult(a, mult(b, c))))),
% 21.68/21.85 inference(rewrite,[status(thm)],[])).
% 21.68/21.85 tff(145,axiom,(~(mult(mult(a, b), c) = mult(a, mult(b, c)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goals')).
% 21.68/21.85 tff(146,plain,
% 21.68/21.85 (~(mult(mult(a, b), c) = mult(a, mult(b, c)))),
% 21.68/21.85 inference(modus_ponens,[status(thm)],[145, 144])).
% 21.68/21.85 tff(147,plain,
% 21.68/21.85 (((~(mult(mult(a, b), c) = mult(a, mult(b, c)))) | (~(mult(mult(a, c), b) = mult(a, mult(c, b))))) | (mult(mult(a, b), c) = mult(a, mult(b, c)))),
% 21.68/21.85 inference(tautology,[status(thm)],[])).
% 21.68/21.85 tff(148,plain,
% 21.68/21.85 ((~(mult(mult(a, b), c) = mult(a, mult(b, c)))) | (~(mult(mult(a, c), b) = mult(a, mult(c, b))))),
% 21.68/21.85 inference(unit_resolution,[status(thm)],[147, 146])).
% 21.68/21.85 tff(149,plain,
% 21.68/21.85 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, c), b) = mult(mult(a, b), c))) | (~(mult(a, mult(c, b)) = mult(a, mult(b, c)))))) | (~((~(mult(mult(a, b), c) = mult(a, mult(b, c)))) | (~(mult(mult(a, c), b) = mult(a, mult(c, b)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, c), b) = mult(mult(a, b), c))) | (~(mult(a, mult(c, b)) = mult(a, mult(b, c)))))) | (~((~(mult(mult(a, b), c) = mult(a, mult(b, c)))) | (~(mult(mult(a, c), b) = mult(a, mult(c, b)))))))),
% 21.68/21.85 inference(rewrite,[status(thm)],[])).
% 21.68/21.85 tff(150,plain,
% 21.68/21.85 (((~((~(mult(mult(a, c), b) = mult(mult(a, b), c))) | (~(mult(a, mult(c, b)) = mult(a, mult(b, c)))))) | (~((~(mult(mult(a, b), c) = mult(a, mult(b, c)))) | (~(mult(mult(a, c), b) = mult(a, mult(c, b))))))) <=> ((~((~(mult(mult(a, c), b) = mult(mult(a, b), c))) | (~(mult(a, mult(c, b)) = mult(a, mult(b, c)))))) | (~((~(mult(mult(a, b), c) = mult(a, mult(b, c)))) | (~(mult(mult(a, c), b) = mult(a, mult(c, b)))))))),
% 21.68/21.85 inference(rewrite,[status(thm)],[])).
% 21.68/21.85 tff(151,plain,
% 21.68/21.85 ((~((~(mult(mult(a, c), b) = mult(a, mult(c, b)))) | (~(mult(mult(a, b), c) = mult(a, mult(b, c)))))) <=> (~((~(mult(mult(a, b), c) = mult(a, mult(b, c)))) | (~(mult(mult(a, c), b) = mult(a, mult(c, b))))))),
% 21.68/21.85 inference(rewrite,[status(thm)],[])).
% 21.68/21.85 tff(152,plain,
% 21.68/21.85 ((~((~(mult(mult(a, c), b) = mult(mult(a, b), c))) | (~(mult(a, mult(c, b)) = mult(a, mult(b, c)))))) <=> (~((~(mult(mult(a, c), b) = mult(mult(a, b), c))) | (~(mult(a, mult(c, b)) = mult(a, mult(b, c))))))),
% 21.68/21.85 inference(rewrite,[status(thm)],[])).
% 21.68/21.85 tff(153,plain,
% 21.68/21.85 (((~((~(mult(mult(a, c), b) = mult(mult(a, b), c))) | (~(mult(a, mult(c, b)) = mult(a, mult(b, c)))))) | (~((~(mult(mult(a, c), b) = mult(a, mult(c, b)))) | (~(mult(mult(a, b), c) = mult(a, mult(b, c))))))) <=> ((~((~(mult(mult(a, c), b) = mult(mult(a, b), c))) | (~(mult(a, mult(c, b)) = mult(a, mult(b, c)))))) | (~((~(mult(mult(a, b), c) = mult(a, mult(b, c)))) | (~(mult(mult(a, c), b) = mult(a, mult(c, b)))))))),
% 21.68/21.85 inference(monotonicity,[status(thm)],[152, 151])).
% 21.68/21.85 tff(154,plain,
% 21.68/21.85 (((~((~(mult(mult(a, c), b) = mult(mult(a, b), c))) | (~(mult(a, mult(c, b)) = mult(a, mult(b, c)))))) | (~((~(mult(mult(a, c), b) = mult(a, mult(c, b)))) | (~(mult(mult(a, b), c) = mult(a, mult(b, c))))))) <=> ((~((~(mult(mult(a, c), b) = mult(mult(a, b), c))) | (~(mult(a, mult(c, b)) = mult(a, mult(b, c)))))) | (~((~(mult(mult(a, b), c) = mult(a, mult(b, c)))) | (~(mult(mult(a, c), b) = mult(a, mult(c, b)))))))),
% 21.68/21.85 inference(transitivity,[status(thm)],[153, 150])).
% 21.68/21.85 tff(155,plain,
% 21.68/21.85 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, c), b) = mult(mult(a, b), c))) | (~(mult(a, mult(c, b)) = mult(a, mult(b, c)))))) | (~((~(mult(mult(a, c), b) = mult(a, mult(c, b)))) | (~(mult(mult(a, b), c) = mult(a, mult(b, c)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, c), b) = mult(mult(a, b), c))) | (~(mult(a, mult(c, b)) = mult(a, mult(b, c)))))) | (~((~(mult(mult(a, b), c) = mult(a, mult(b, c)))) | (~(mult(mult(a, c), b) = mult(a, mult(c, b))))))))),
% 21.68/21.85 inference(monotonicity,[status(thm)],[154])).
% 21.68/21.85 tff(156,plain,
% 21.68/21.85 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, c), b) = mult(mult(a, b), c))) | (~(mult(a, mult(c, b)) = mult(a, mult(b, c)))))) | (~((~(mult(mult(a, c), b) = mult(a, mult(c, b)))) | (~(mult(mult(a, b), c) = mult(a, mult(b, c)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, c), b) = mult(mult(a, b), c))) | (~(mult(a, mult(c, b)) = mult(a, mult(b, c)))))) | (~((~(mult(mult(a, b), c) = mult(a, mult(b, c)))) | (~(mult(mult(a, c), b) = mult(a, mult(c, b)))))))),
% 21.68/21.85 inference(transitivity,[status(thm)],[155, 149])).
% 21.68/21.85 tff(157,plain,
% 21.68/21.85 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, c), b) = mult(mult(a, b), c))) | (~(mult(a, mult(c, b)) = mult(a, mult(b, c)))))) | (~((~(mult(mult(a, c), b) = mult(a, mult(c, b)))) | (~(mult(mult(a, b), c) = mult(a, mult(b, c)))))))),
% 21.68/21.85 inference(quant_inst,[status(thm)],[])).
% 21.68/21.85 tff(158,plain,
% 21.68/21.85 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, c), b) = mult(mult(a, b), c))) | (~(mult(a, mult(c, b)) = mult(a, mult(b, c)))))) | (~((~(mult(mult(a, b), c) = mult(a, mult(b, c)))) | (~(mult(mult(a, c), b) = mult(a, mult(c, b))))))),
% 21.68/21.85 inference(modus_ponens,[status(thm)],[157, 156])).
% 21.68/21.85 tff(159,plain,
% 21.68/21.85 (~((~(mult(mult(a, c), b) = mult(mult(a, b), c))) | (~(mult(a, mult(c, b)) = mult(a, mult(b, c)))))),
% 21.68/21.85 inference(unit_resolution,[status(thm)],[158, 27, 148])).
% 21.68/21.85 tff(160,plain,
% 21.68/21.85 (((~(mult(mult(a, c), b) = mult(mult(a, b), c))) | (~(mult(a, mult(c, b)) = mult(a, mult(b, c))))) | (mult(mult(a, c), b) = mult(mult(a, b), c))),
% 21.68/21.85 inference(tautology,[status(thm)],[])).
% 21.68/21.85 tff(161,plain,
% 21.68/21.85 (mult(mult(a, c), b) = mult(mult(a, b), c)),
% 21.68/21.85 inference(unit_resolution,[status(thm)],[160, 159])).
% 21.68/21.85 tff(162,plain,
% 21.68/21.85 (^[B: $i, A: $i] : refl((rd(mult(A, B), B) = A) <=> (rd(mult(A, B), B) = A))),
% 21.68/21.85 inference(bind,[status(th)],[])).
% 21.68/21.85 tff(163,plain,
% 21.68/21.85 (![B: $i, A: $i] : (rd(mult(A, B), B) = A) <=> ![B: $i, A: $i] : (rd(mult(A, B), B) = A)),
% 21.68/21.85 inference(quant_intro,[status(thm)],[162])).
% 21.68/21.85 tff(164,plain,
% 21.68/21.85 (![B: $i, A: $i] : (rd(mult(A, B), B) = A) <=> ![B: $i, A: $i] : (rd(mult(A, B), B) = A)),
% 21.68/21.85 inference(rewrite,[status(thm)],[])).
% 21.68/21.85 tff(165,axiom,(![B: $i, A: $i] : (rd(mult(A, B), B) = A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','f04')).
% 21.68/21.85 tff(166,plain,
% 21.68/21.85 (![B: $i, A: $i] : (rd(mult(A, B), B) = A)),
% 21.68/21.85 inference(modus_ponens,[status(thm)],[165, 164])).
% 21.68/21.85 tff(167,plain,(
% 21.68/21.85 ![B: $i, A: $i] : (rd(mult(A, B), B) = A)),
% 21.68/21.85 inference(skolemize,[status(sab)],[166])).
% 21.68/21.85 tff(168,plain,
% 21.68/21.85 (![B: $i, A: $i] : (rd(mult(A, B), B) = A)),
% 21.68/21.85 inference(modus_ponens,[status(thm)],[167, 163])).
% 21.68/21.85 tff(169,plain,
% 21.68/21.85 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(b, c), c) = b)),
% 21.68/21.85 inference(quant_inst,[status(thm)],[])).
% 21.68/21.85 tff(170,plain,
% 21.68/21.85 (rd(mult(b, c), c) = b),
% 21.68/21.85 inference(unit_resolution,[status(thm)],[169, 168])).
% 21.68/21.85 tff(171,plain,
% 21.68/21.85 (mult(mult(rd(mult(b, c), mult(a, c)), a), c) = mult(b, c)),
% 21.68/21.85 inference(transitivity,[status(thm)],[76, 97, 61, 137])).
% 21.68/21.85 tff(172,plain,
% 21.68/21.85 (rd(mult(mult(rd(mult(b, c), mult(a, c)), a), c), c) = rd(mult(b, c), c)),
% 21.68/21.85 inference(monotonicity,[status(thm)],[171])).
% 21.68/21.85 tff(173,plain,
% 21.68/21.85 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(rd(mult(b, c), mult(a, c)), a), c), c) = mult(rd(mult(b, c), mult(a, c)), a))),
% 21.68/21.85 inference(quant_inst,[status(thm)],[])).
% 21.68/21.85 tff(174,plain,
% 21.68/21.85 (rd(mult(mult(rd(mult(b, c), mult(a, c)), a), c), c) = mult(rd(mult(b, c), mult(a, c)), a)),
% 21.68/21.85 inference(unit_resolution,[status(thm)],[173, 168])).
% 21.68/21.85 tff(175,plain,
% 21.68/21.85 (mult(rd(mult(b, c), mult(a, c)), a) = rd(mult(mult(rd(mult(b, c), mult(a, c)), a), c), c)),
% 21.68/21.85 inference(symmetry,[status(thm)],[174])).
% 21.68/21.85 tff(176,plain,
% 21.68/21.85 (mult(rd(mult(b, c), mult(a, c)), a) = b),
% 21.68/21.85 inference(transitivity,[status(thm)],[175, 172, 170])).
% 21.68/21.85 tff(177,plain,
% 21.68/21.85 (mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, c), b)),
% 21.68/21.85 inference(monotonicity,[status(thm)],[176])).
% 21.68/21.85 tff(178,plain,
% 21.68/21.85 (mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, b), c)),
% 21.68/21.85 inference(transitivity,[status(thm)],[177, 161])).
% 21.68/21.85 tff(179,plain,
% 21.68/21.85 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(a, mult(b, c)), c), c) = mult(a, mult(b, c)))),
% 21.68/21.85 inference(quant_inst,[status(thm)],[])).
% 21.68/21.85 tff(180,plain,
% 21.68/21.85 (rd(mult(mult(a, mult(b, c)), c), c) = mult(a, mult(b, c))),
% 21.68/21.85 inference(unit_resolution,[status(thm)],[179, 168])).
% 21.68/21.85 tff(181,plain,
% 21.68/21.85 ((~![A: $i] : (mult(A, unit) = A)) | (mult(b, unit) = b)),
% 21.68/21.85 inference(quant_inst,[status(thm)],[])).
% 21.68/21.85 tff(182,plain,
% 21.68/21.85 (mult(b, unit) = b),
% 21.68/21.85 inference(unit_resolution,[status(thm)],[181, 43])).
% 21.68/21.85 tff(183,plain,
% 21.68/21.85 ((~![A: $i] : (mult(unit, A) = A)) | (mult(unit, b) = b)),
% 21.68/21.85 inference(quant_inst,[status(thm)],[])).
% 21.68/21.85 tff(184,plain,
% 21.68/21.85 (mult(unit, b) = b),
% 21.68/21.85 inference(unit_resolution,[status(thm)],[183, 71])).
% 21.68/21.85 tff(185,plain,
% 21.68/21.85 (mult(mult(unit, b), unit) = mult(b, unit)),
% 21.68/21.85 inference(monotonicity,[status(thm)],[184])).
% 21.68/21.85 tff(186,plain,
% 21.68/21.85 (mult(mult(unit, b), unit) = b),
% 21.68/21.85 inference(transitivity,[status(thm)],[185, 182])).
% 21.68/21.85 tff(187,plain,
% 21.68/21.85 (mult(a, mult(mult(unit, b), unit)) = mult(a, b)),
% 21.68/21.85 inference(monotonicity,[status(thm)],[186])).
% 21.68/21.85 tff(188,plain,
% 21.68/21.85 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(a, unit), b), unit) = mult(a, mult(mult(unit, b), unit)))),
% 21.68/21.85 inference(quant_inst,[status(thm)],[])).
% 21.68/21.85 tff(189,plain,
% 21.68/21.85 (mult(mult(mult(a, unit), b), unit) = mult(a, mult(mult(unit, b), unit))),
% 21.68/21.85 inference(unit_resolution,[status(thm)],[188, 56])).
% 21.68/21.85 tff(190,plain,
% 21.68/21.85 ((~![A: $i] : (mult(A, unit) = A)) | (mult(mult(mult(a, unit), b), unit) = mult(mult(a, unit), b))),
% 21.68/21.85 inference(quant_inst,[status(thm)],[])).
% 21.68/21.85 tff(191,plain,
% 21.68/21.85 (mult(mult(mult(a, unit), b), unit) = mult(mult(a, unit), b)),
% 21.68/21.85 inference(unit_resolution,[status(thm)],[190, 43])).
% 21.68/21.85 tff(192,plain,
% 21.68/21.85 (mult(a, mult(mult(unit, b), unit)) = mult(mult(mult(a, unit), b), unit)),
% 21.68/21.86 inference(symmetry,[status(thm)],[189])).
% 21.68/21.86 tff(193,plain,
% 21.68/21.86 (mult(a, b) = mult(a, mult(mult(unit, b), unit))),
% 21.68/21.86 inference(symmetry,[status(thm)],[187])).
% 21.68/21.86 tff(194,plain,
% 21.68/21.86 (mult(a, b) = mult(mult(a, unit), b)),
% 21.68/21.86 inference(transitivity,[status(thm)],[193, 192, 191])).
% 21.68/21.86 tff(195,plain,
% 21.68/21.86 (mult(mult(a, b), unit) = mult(mult(mult(a, unit), b), unit)),
% 21.68/21.86 inference(monotonicity,[status(thm)],[194])).
% 21.68/21.86 tff(196,plain,
% 21.68/21.86 (^[B: $i, A: $i] : refl((mult(A, ld(A, B)) = B) <=> (mult(A, ld(A, B)) = B))),
% 21.68/21.86 inference(bind,[status(th)],[])).
% 21.68/21.86 tff(197,plain,
% 21.68/21.86 (![B: $i, A: $i] : (mult(A, ld(A, B)) = B) <=> ![B: $i, A: $i] : (mult(A, ld(A, B)) = B)),
% 21.68/21.86 inference(quant_intro,[status(thm)],[196])).
% 21.68/21.86 tff(198,plain,
% 21.68/21.86 (![B: $i, A: $i] : (mult(A, ld(A, B)) = B) <=> ![B: $i, A: $i] : (mult(A, ld(A, B)) = B)),
% 21.68/21.86 inference(rewrite,[status(thm)],[])).
% 21.68/21.86 tff(199,axiom,(![B: $i, A: $i] : (mult(A, ld(A, B)) = B)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','f01')).
% 21.68/21.86 tff(200,plain,
% 21.68/21.86 (![B: $i, A: $i] : (mult(A, ld(A, B)) = B)),
% 21.68/21.86 inference(modus_ponens,[status(thm)],[199, 198])).
% 21.68/21.86 tff(201,plain,(
% 21.68/21.86 ![B: $i, A: $i] : (mult(A, ld(A, B)) = B)),
% 21.68/21.86 inference(skolemize,[status(sab)],[200])).
% 21.68/21.86 tff(202,plain,
% 21.68/21.86 (![B: $i, A: $i] : (mult(A, ld(A, B)) = B)),
% 21.68/21.86 inference(modus_ponens,[status(thm)],[201, 197])).
% 21.68/21.86 tff(203,plain,
% 21.68/21.86 ((~![B: $i, A: $i] : (mult(A, ld(A, B)) = B)) | (mult(c, ld(c, mult(a, b))) = mult(a, b))),
% 21.68/21.86 inference(quant_inst,[status(thm)],[])).
% 21.68/21.86 tff(204,plain,
% 21.68/21.86 (mult(c, ld(c, mult(a, b))) = mult(a, b)),
% 21.68/21.86 inference(unit_resolution,[status(thm)],[203, 202])).
% 21.68/21.86 tff(205,plain,
% 21.68/21.86 ((~![A: $i] : (mult(A, unit) = A)) | (mult(c, unit) = c)),
% 21.68/21.86 inference(quant_inst,[status(thm)],[])).
% 21.68/21.86 tff(206,plain,
% 21.68/21.86 (mult(c, unit) = c),
% 21.68/21.86 inference(unit_resolution,[status(thm)],[205, 43])).
% 21.68/21.86 tff(207,plain,
% 21.68/21.86 (mult(mult(c, unit), ld(c, mult(a, b))) = mult(c, ld(c, mult(a, b)))),
% 21.68/21.86 inference(monotonicity,[status(thm)],[206])).
% 21.68/21.86 tff(208,plain,
% 21.68/21.86 (mult(mult(c, unit), ld(c, mult(a, b))) = mult(a, b)),
% 21.68/21.86 inference(transitivity,[status(thm)],[207, 204])).
% 21.68/21.86 tff(209,plain,
% 21.68/21.86 (mult(mult(mult(c, unit), ld(c, mult(a, b))), unit) = mult(mult(a, b), unit)),
% 21.68/21.86 inference(monotonicity,[status(thm)],[208])).
% 21.68/21.86 tff(210,plain,
% 21.68/21.86 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(c, unit), ld(c, mult(a, b))), unit) = mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)))),
% 21.68/21.86 inference(quant_inst,[status(thm)],[])).
% 21.68/21.86 tff(211,plain,
% 21.68/21.86 (mult(mult(mult(c, unit), ld(c, mult(a, b))), unit) = mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))),
% 21.68/21.86 inference(unit_resolution,[status(thm)],[210, 56])).
% 21.68/21.86 tff(212,plain,
% 21.68/21.86 (mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(mult(c, unit), ld(c, mult(a, b))), unit)),
% 21.68/21.86 inference(symmetry,[status(thm)],[211])).
% 21.68/21.86 tff(213,plain,
% 21.68/21.86 (mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(a, b)),
% 21.68/21.86 inference(transitivity,[status(thm)],[212, 209, 195, 189, 187])).
% 21.68/21.86 tff(214,plain,
% 21.68/21.86 (mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(a, b), c)),
% 21.68/21.86 inference(monotonicity,[status(thm)],[213])).
% 21.68/21.86 tff(215,plain,
% 21.68/21.86 (mult(mult(a, b), c) = mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), c)),
% 21.68/21.86 inference(symmetry,[status(thm)],[214])).
% 21.68/21.86 tff(216,plain,
% 21.68/21.86 (mult(unit, mult(mult(a, b), c)) = mult(unit, mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), c))),
% 21.68/21.86 inference(monotonicity,[status(thm)],[215])).
% 21.68/21.86 tff(217,plain,
% 21.68/21.86 (mult(unit, mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), c)) = mult(unit, mult(mult(a, b), c))),
% 21.68/21.86 inference(symmetry,[status(thm)],[216])).
% 21.68/21.86 tff(218,plain,
% 21.68/21.86 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(unit, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(unit, mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), c)))),
% 21.68/21.86 inference(quant_inst,[status(thm)],[])).
% 21.68/21.86 tff(219,plain,
% 21.68/21.86 (mult(mult(mult(unit, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(unit, mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), c))),
% 21.68/21.86 inference(unit_resolution,[status(thm)],[218, 56])).
% 21.68/21.86 tff(220,plain,
% 21.68/21.86 (mult(mult(unit, c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))),
% 21.68/21.86 inference(monotonicity,[status(thm)],[73])).
% 21.68/21.86 tff(221,plain,
% 21.68/21.86 (mult(mult(unit, c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(a, b)),
% 21.68/21.86 inference(transitivity,[status(thm)],[220, 212, 209, 195, 189, 187])).
% 21.68/21.86 tff(222,plain,
% 21.68/21.86 (mult(mult(mult(unit, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(a, b), c)),
% 21.68/21.86 inference(monotonicity,[status(thm)],[221])).
% 21.68/21.86 tff(223,plain,
% 21.68/21.86 (mult(mult(a, b), c) = mult(mult(mult(unit, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c)),
% 21.68/21.86 inference(symmetry,[status(thm)],[222])).
% 21.68/21.86 tff(224,plain,
% 21.68/21.86 (mult(mult(a, b), c) = mult(unit, mult(mult(a, b), c))),
% 21.68/21.86 inference(transitivity,[status(thm)],[223, 219, 217])).
% 21.68/21.86 tff(225,plain,
% 21.68/21.86 (mult(mult(mult(a, b), c), c) = mult(mult(unit, mult(mult(a, b), c)), c)),
% 21.68/21.86 inference(monotonicity,[status(thm)],[224])).
% 21.68/21.86 tff(226,plain,
% 21.68/21.86 (mult(mult(unit, mult(mult(a, b), c)), c) = mult(mult(mult(a, b), c), c)),
% 21.68/21.86 inference(symmetry,[status(thm)],[225])).
% 21.68/21.86 tff(227,plain,
% 21.68/21.86 (mult(mult(a, b), c) = mult(mult(a, c), b)),
% 21.68/21.86 inference(symmetry,[status(thm)],[161])).
% 21.68/21.86 tff(228,plain,
% 21.68/21.86 (mult(unit, mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), c)) = mult(mult(mult(unit, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c)),
% 21.68/21.86 inference(symmetry,[status(thm)],[219])).
% 21.68/21.86 tff(229,plain,
% 21.68/21.86 (mult(unit, mult(mult(a, b), c)) = mult(mult(a, c), b)),
% 21.68/21.86 inference(transitivity,[status(thm)],[216, 228, 222, 227])).
% 21.68/21.86 tff(230,plain,
% 21.68/21.86 (mult(mult(unit, mult(mult(a, b), c)), c) = mult(mult(mult(a, c), b), c)),
% 21.68/21.86 inference(monotonicity,[status(thm)],[229])).
% 21.68/21.86 tff(231,plain,
% 21.68/21.86 (mult(mult(mult(a, c), b), c) = mult(mult(unit, mult(mult(a, b), c)), c)),
% 21.68/21.86 inference(symmetry,[status(thm)],[230])).
% 21.68/21.86 tff(232,plain,
% 21.68/21.86 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(a, c), b), c) = mult(a, mult(mult(c, b), c)))),
% 21.68/21.86 inference(quant_inst,[status(thm)],[])).
% 21.68/21.86 tff(233,plain,
% 21.68/21.86 (mult(mult(mult(a, c), b), c) = mult(a, mult(mult(c, b), c))),
% 21.68/21.86 inference(unit_resolution,[status(thm)],[232, 56])).
% 21.68/21.86 tff(234,plain,
% 21.68/21.86 (mult(a, mult(mult(c, b), c)) = mult(mult(mult(a, c), b), c)),
% 21.68/21.86 inference(symmetry,[status(thm)],[233])).
% 21.68/21.86 tff(235,plain,
% 21.68/21.86 (((~(mult(mult(a, c), b) = mult(mult(a, b), c))) | (~(mult(a, mult(c, b)) = mult(a, mult(b, c))))) | (mult(a, mult(c, b)) = mult(a, mult(b, c)))),
% 21.68/21.86 inference(tautology,[status(thm)],[])).
% 21.68/21.86 tff(236,plain,
% 21.68/21.86 (mult(a, mult(c, b)) = mult(a, mult(b, c))),
% 21.68/21.86 inference(unit_resolution,[status(thm)],[235, 159])).
% 21.68/21.86 tff(237,plain,
% 21.68/21.86 (ld(a, mult(a, mult(c, b))) = ld(a, mult(a, mult(b, c)))),
% 21.68/21.86 inference(monotonicity,[status(thm)],[236])).
% 21.68/21.86 tff(238,plain,
% 21.68/21.86 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(a, mult(a, mult(c, b))) = mult(c, b))),
% 21.68/21.86 inference(quant_inst,[status(thm)],[])).
% 21.68/21.86 tff(239,plain,
% 21.68/21.86 (ld(a, mult(a, mult(c, b))) = mult(c, b)),
% 21.68/21.86 inference(unit_resolution,[status(thm)],[238, 7])).
% 21.68/21.86 tff(240,plain,
% 21.68/21.86 (mult(c, b) = ld(a, mult(a, mult(c, b)))),
% 21.68/21.86 inference(symmetry,[status(thm)],[239])).
% 21.68/21.86 tff(241,plain,
% 21.68/21.86 (mult(c, b) = mult(b, c)),
% 21.68/21.86 inference(transitivity,[status(thm)],[240, 237, 141])).
% 21.68/21.86 tff(242,plain,
% 21.68/21.86 (mult(mult(c, b), c) = mult(mult(b, c), c)),
% 21.68/21.86 inference(monotonicity,[status(thm)],[241])).
% 21.68/21.86 tff(243,plain,
% 21.68/21.86 ((~![A: $i] : (mult(unit, A) = A)) | (mult(unit, a) = a)),
% 21.68/21.86 inference(quant_inst,[status(thm)],[])).
% 21.68/21.86 tff(244,plain,
% 21.68/21.86 (mult(unit, a) = a),
% 21.68/21.86 inference(unit_resolution,[status(thm)],[243, 71])).
% 21.68/21.86 tff(245,plain,
% 21.68/21.86 (a = mult(unit, a)),
% 21.68/21.86 inference(symmetry,[status(thm)],[244])).
% 21.68/21.86 tff(246,plain,
% 21.68/21.86 (mult(a, mult(mult(c, b), c)) = mult(mult(unit, a), mult(mult(b, c), c))),
% 21.68/21.86 inference(monotonicity,[status(thm)],[245, 242])).
% 21.68/21.86 tff(247,plain,
% 21.68/21.86 (mult(mult(unit, a), mult(mult(b, c), c)) = mult(a, mult(mult(c, b), c))),
% 21.68/21.86 inference(symmetry,[status(thm)],[246])).
% 21.68/21.86 tff(248,plain,
% 21.68/21.86 (mult(a, mult(mult(b, c), c)) = mult(mult(unit, a), mult(mult(b, c), c))),
% 21.68/21.86 inference(monotonicity,[status(thm)],[245])).
% 21.68/21.86 tff(249,assumption,(mult(mult(a, mult(b, c)), c) = mult(a, mult(mult(b, c), c))), introduced(assumption)).
% 21.68/21.86 tff(250,plain,
% 21.68/21.86 (mult(mult(a, mult(b, c)), c) = mult(mult(mult(a, b), c), c)),
% 21.68/21.86 inference(transitivity,[status(thm)],[249, 248, 247, 234, 231, 226])).
% 21.68/21.86 tff(251,plain,
% 21.68/21.86 (rd(mult(mult(a, mult(b, c)), c), c) = rd(mult(mult(mult(a, b), c), c), c)),
% 21.68/21.86 inference(monotonicity,[status(thm)],[250])).
% 21.68/21.86 tff(252,plain,
% 21.68/21.86 (rd(mult(mult(mult(a, b), c), c), c) = rd(mult(mult(a, mult(b, c)), c), c)),
% 21.68/21.86 inference(symmetry,[status(thm)],[251])).
% 21.68/21.86 tff(253,plain,
% 21.68/21.86 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(a, b), c), c), c) = mult(mult(a, b), c))),
% 21.68/21.86 inference(quant_inst,[status(thm)],[])).
% 21.68/21.86 tff(254,plain,
% 21.68/21.86 (rd(mult(mult(mult(a, b), c), c), c) = mult(mult(a, b), c)),
% 21.68/21.86 inference(unit_resolution,[status(thm)],[253, 168])).
% 21.68/21.86 tff(255,plain,
% 21.68/21.86 (mult(mult(a, b), c) = rd(mult(mult(mult(a, b), c), c), c)),
% 21.68/21.86 inference(symmetry,[status(thm)],[254])).
% 21.68/21.86 tff(256,plain,
% 21.68/21.86 (mult(mult(a, b), c) = mult(a, mult(b, c))),
% 21.68/21.86 inference(transitivity,[status(thm)],[255, 252, 180])).
% 21.68/21.86 tff(257,plain,
% 21.68/21.86 ($false),
% 21.68/21.86 inference(unit_resolution,[status(thm)],[146, 256])).
% 21.68/21.86 tff(258,plain,(~(mult(mult(a, mult(b, c)), c) = mult(a, mult(mult(b, c), c)))), inference(lemma,lemma(discharge,[]))).
% 21.68/21.86 tff(259,plain,
% 21.68/21.86 (((~(mult(mult(a, c), mult(b, c)) = mult(a, mult(c, mult(b, c))))) | (~(mult(mult(a, mult(b, c)), c) = mult(a, mult(mult(b, c), c))))) | (mult(mult(a, mult(b, c)), c) = mult(a, mult(mult(b, c), c)))),
% 21.68/21.86 inference(tautology,[status(thm)],[])).
% 21.68/21.86 tff(260,plain,
% 21.68/21.86 ((~(mult(mult(a, c), mult(b, c)) = mult(a, mult(c, mult(b, c))))) | (~(mult(mult(a, mult(b, c)), c) = mult(a, mult(mult(b, c), c))))),
% 21.68/21.86 inference(unit_resolution,[status(thm)],[259, 258])).
% 21.68/21.86 tff(261,plain,
% 21.68/21.86 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, c), mult(b, c)) = mult(mult(a, mult(b, c)), c))) | (~(mult(a, mult(c, mult(b, c))) = mult(a, mult(mult(b, c), c)))))) | (~((~(mult(mult(a, c), mult(b, c)) = mult(a, mult(c, mult(b, c))))) | (~(mult(mult(a, mult(b, c)), c) = mult(a, mult(mult(b, c), c)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, c), mult(b, c)) = mult(mult(a, mult(b, c)), c))) | (~(mult(a, mult(c, mult(b, c))) = mult(a, mult(mult(b, c), c)))))) | (~((~(mult(mult(a, c), mult(b, c)) = mult(a, mult(c, mult(b, c))))) | (~(mult(mult(a, mult(b, c)), c) = mult(a, mult(mult(b, c), c)))))))),
% 21.68/21.86 inference(rewrite,[status(thm)],[])).
% 21.68/21.86 tff(262,plain,
% 21.68/21.86 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, c), mult(b, c)) = mult(mult(a, mult(b, c)), c))) | (~(mult(a, mult(c, mult(b, c))) = mult(a, mult(mult(b, c), c)))))) | (~((~(mult(mult(a, c), mult(b, c)) = mult(a, mult(c, mult(b, c))))) | (~(mult(mult(a, mult(b, c)), c) = mult(a, mult(mult(b, c), c)))))))),
% 21.68/21.86 inference(quant_inst,[status(thm)],[])).
% 21.68/21.86 tff(263,plain,
% 21.68/21.86 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, c), mult(b, c)) = mult(mult(a, mult(b, c)), c))) | (~(mult(a, mult(c, mult(b, c))) = mult(a, mult(mult(b, c), c)))))) | (~((~(mult(mult(a, c), mult(b, c)) = mult(a, mult(c, mult(b, c))))) | (~(mult(mult(a, mult(b, c)), c) = mult(a, mult(mult(b, c), c))))))),
% 21.68/21.86 inference(modus_ponens,[status(thm)],[262, 261])).
% 21.68/21.86 tff(264,plain,
% 21.68/21.86 (~((~(mult(mult(a, c), mult(b, c)) = mult(mult(a, mult(b, c)), c))) | (~(mult(a, mult(c, mult(b, c))) = mult(a, mult(mult(b, c), c)))))),
% 21.68/21.86 inference(unit_resolution,[status(thm)],[263, 27, 260])).
% 21.68/21.86 tff(265,plain,
% 21.68/21.86 (((~(mult(mult(a, c), mult(b, c)) = mult(mult(a, mult(b, c)), c))) | (~(mult(a, mult(c, mult(b, c))) = mult(a, mult(mult(b, c), c))))) | (mult(mult(a, c), mult(b, c)) = mult(mult(a, mult(b, c)), c))),
% 21.68/21.86 inference(tautology,[status(thm)],[])).
% 21.68/21.86 tff(266,plain,
% 21.68/21.86 (mult(mult(a, c), mult(b, c)) = mult(mult(a, mult(b, c)), c)),
% 21.68/21.86 inference(unit_resolution,[status(thm)],[265, 264])).
% 21.68/21.86 tff(267,plain,
% 21.68/21.86 (mult(b, c) = mult(rd(mult(b, c), mult(a, c)), mult(a, c))),
% 21.68/21.86 inference(symmetry,[status(thm)],[137])).
% 21.68/21.86 tff(268,plain,
% 21.68/21.86 (mult(mult(a, c), mult(b, c)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))),
% 21.68/21.86 inference(monotonicity,[status(thm)],[267])).
% 21.68/21.86 tff(269,plain,
% 21.68/21.86 (mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c))) = mult(mult(a, c), mult(b, c))),
% 21.68/21.86 inference(symmetry,[status(thm)],[268])).
% 21.68/21.86 tff(270,assumption,(~(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))), introduced(assumption)).
% 21.68/21.86 tff(271,plain,
% 21.68/21.86 (((~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))) | (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))),
% 21.68/21.86 inference(tautology,[status(thm)],[])).
% 21.68/21.86 tff(272,plain,
% 21.68/21.86 ((~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))),
% 21.68/21.86 inference(unit_resolution,[status(thm)],[271, 270])).
% 21.68/21.86 tff(273,plain,
% 21.68/21.86 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))) | (~((~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))) | (~((~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))))),
% 21.68/21.86 inference(rewrite,[status(thm)],[])).
% 21.68/21.86 tff(274,plain,
% 21.68/21.86 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))) | (~((~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))))),
% 21.68/21.86 inference(quant_inst,[status(thm)],[])).
% 21.68/21.86 tff(275,plain,
% 21.68/21.86 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))) | (~((~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))))),
% 21.68/21.86 inference(modus_ponens,[status(thm)],[274, 273])).
% 21.68/21.86 tff(276,plain,
% 21.68/21.86 ((~((~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))) | (~((~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))))),
% 21.68/21.86 inference(unit_resolution,[status(thm)],[275, 27])).
% 21.68/21.86 tff(277,plain,
% 21.68/21.86 (~((~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))),
% 21.68/21.86 inference(unit_resolution,[status(thm)],[276, 272])).
% 21.68/21.86 tff(278,plain,
% 21.68/21.86 (((~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))) | (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))),
% 21.68/21.86 inference(tautology,[status(thm)],[])).
% 21.68/21.86 tff(279,plain,
% 21.68/21.86 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))),
% 21.68/21.86 inference(unit_resolution,[status(thm)],[278, 277])).
% 21.68/21.86 tff(280,plain,
% 21.68/21.86 (((~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))) | (mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 21.68/21.86 inference(tautology,[status(thm)],[])).
% 21.68/21.86 tff(281,plain,
% 21.68/21.86 (mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 21.68/21.86 inference(unit_resolution,[status(thm)],[280, 277])).
% 21.68/21.86 tff(282,plain,
% 21.68/21.86 ((mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))) <=> (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))),
% 21.68/21.86 inference(monotonicity,[status(thm)],[281, 279])).
% 21.68/21.86 tff(283,plain,
% 21.68/21.86 ((mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))) <=> (mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 21.68/21.86 inference(symmetry,[status(thm)],[282])).
% 21.68/21.86 tff(284,plain,
% 21.68/21.86 ((~(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) <=> (~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))))),
% 21.68/21.87 inference(monotonicity,[status(thm)],[283])).
% 21.68/21.87 tff(285,plain,
% 21.68/21.87 (~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 21.68/21.87 inference(modus_ponens,[status(thm)],[270, 284])).
% 21.68/21.87 tff(286,assumption,(mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))), introduced(assumption)).
% 21.68/21.87 tff(287,assumption,(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))), introduced(assumption)).
% 21.68/21.87 tff(288,plain,
% 21.68/21.87 (mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))),
% 21.68/21.87 inference(symmetry,[status(thm)],[287])).
% 21.68/21.87 tff(289,plain,
% 21.68/21.87 (mult(a, mult(b, c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))),
% 21.68/21.87 inference(symmetry,[status(thm)],[142])).
% 21.68/21.87 tff(290,plain,
% 21.68/21.87 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(a, c), mult(mult(a, c), mult(b, c))) = mult(b, c))),
% 21.68/21.87 inference(quant_inst,[status(thm)],[])).
% 21.68/21.87 tff(291,plain,
% 21.68/21.87 (ld(mult(a, c), mult(mult(a, c), mult(b, c))) = mult(b, c)),
% 21.68/21.87 inference(unit_resolution,[status(thm)],[290, 7])).
% 21.68/21.87 tff(292,plain,
% 21.68/21.87 (mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(b, c))),
% 21.68/21.87 inference(transitivity,[status(thm)],[286, 138])).
% 21.68/21.87 tff(293,plain,
% 21.68/21.87 (ld(mult(a, c), mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c))))) = ld(mult(a, c), mult(mult(a, c), mult(b, c)))),
% 21.68/21.87 inference(monotonicity,[status(thm)],[292])).
% 21.68/21.87 tff(294,plain,
% 21.68/21.87 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(a, c), mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c))))) = mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 21.68/21.87 inference(quant_inst,[status(thm)],[])).
% 21.68/21.87 tff(295,plain,
% 21.68/21.87 (ld(mult(a, c), mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c))))) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))),
% 21.68/21.87 inference(unit_resolution,[status(thm)],[294, 7])).
% 21.68/21.87 tff(296,plain,
% 21.68/21.87 (mult(mult(a, c), rd(mult(b, c), mult(a, c))) = ld(mult(a, c), mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 21.68/21.87 inference(symmetry,[status(thm)],[295])).
% 21.68/21.87 tff(297,plain,
% 21.68/21.87 (mult(mult(a, c), rd(mult(b, c), mult(a, c))) = mult(b, c)),
% 21.68/21.87 inference(transitivity,[status(thm)],[296, 293, 291])).
% 21.68/21.87 tff(298,plain,
% 21.68/21.87 (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(b, c))),
% 21.68/21.87 inference(monotonicity,[status(thm)],[297])).
% 21.68/21.87 tff(299,assumption,(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))), introduced(assumption)).
% 21.68/21.87 tff(300,plain,
% 21.68/21.87 (mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))),
% 21.68/21.87 inference(transitivity,[status(thm)],[299, 298, 289, 288])).
% 21.68/21.87 tff(301,assumption,(~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))), introduced(assumption)).
% 21.68/21.87 tff(302,plain,
% 21.68/21.87 ($false),
% 21.68/21.87 inference(unit_resolution,[status(thm)],[301, 300])).
% 21.68/21.87 tff(303,plain,((~(mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))) | (~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))), inference(lemma,lemma(discharge,[]))).
% 21.68/21.87 tff(304,plain,
% 21.68/21.87 (mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))),
% 21.68/21.87 inference(unit_resolution,[status(thm)],[303, 281, 286, 279])).
% 21.68/21.87 tff(305,plain,
% 21.68/21.87 ($false),
% 21.68/21.87 inference(unit_resolution,[status(thm)],[304, 285])).
% 21.68/21.87 tff(306,plain,((mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))) | (~(mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))), inference(lemma,lemma(discharge,[]))).
% 21.68/21.87 tff(307,plain,
% 21.68/21.87 (~(mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))),
% 21.68/21.87 inference(unit_resolution,[status(thm)],[306, 270])).
% 21.68/21.87 tff(308,plain,
% 21.68/21.87 (((~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))) | (mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))),
% 21.68/21.87 inference(tautology,[status(thm)],[])).
% 21.68/21.87 tff(309,plain,
% 21.68/21.87 ((~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))),
% 21.68/21.87 inference(unit_resolution,[status(thm)],[308, 307])).
% 21.68/21.87 tff(310,plain,
% 21.68/21.87 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))) | (~((~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))) | (~((~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))))),
% 21.68/21.87 inference(rewrite,[status(thm)],[])).
% 21.68/21.87 tff(311,plain,
% 21.68/21.87 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))) | (~((~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))))),
% 21.68/21.87 inference(quant_inst,[status(thm)],[])).
% 21.68/21.87 tff(312,plain,
% 21.68/21.87 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))) | (~((~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))))),
% 21.68/21.87 inference(modus_ponens,[status(thm)],[311, 310])).
% 21.68/21.87 tff(313,plain,
% 21.68/21.87 ((~((~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))) | (~((~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))))),
% 21.68/21.87 inference(unit_resolution,[status(thm)],[312, 27])).
% 21.68/21.87 tff(314,plain,
% 21.68/21.87 (~((~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))),
% 21.68/21.87 inference(unit_resolution,[status(thm)],[313, 309])).
% 21.68/21.87 tff(315,plain,
% 21.68/21.87 (((~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))) | (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))),
% 21.68/21.87 inference(tautology,[status(thm)],[])).
% 21.68/21.87 tff(316,plain,
% 21.68/21.87 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))),
% 21.68/21.87 inference(unit_resolution,[status(thm)],[315, 314])).
% 21.68/21.87 tff(317,assumption,(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))), introduced(assumption)).
% 21.68/21.87 tff(318,plain,
% 21.68/21.87 (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(a, mult(b, c)), c)),
% 21.68/21.87 inference(transitivity,[status(thm)],[317, 316, 269, 266])).
% 21.68/21.87 tff(319,plain,
% 21.68/21.87 (rd(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c), c) = rd(mult(mult(a, mult(b, c)), c), c)),
% 21.68/21.87 inference(monotonicity,[status(thm)],[318])).
% 21.68/21.87 tff(320,plain,
% 21.68/21.87 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))),
% 21.68/21.87 inference(quant_inst,[status(thm)],[])).
% 21.68/21.87 tff(321,plain,
% 21.68/21.87 (rd(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)),
% 21.68/21.87 inference(unit_resolution,[status(thm)],[320, 168])).
% 21.68/21.87 tff(322,plain,
% 21.68/21.87 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = rd(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c), c)),
% 21.68/21.87 inference(symmetry,[status(thm)],[321])).
% 21.68/21.87 tff(323,plain,
% 21.68/21.87 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(a, mult(b, c))),
% 21.68/21.87 inference(transitivity,[status(thm)],[322, 319, 180])).
% 21.68/21.87 tff(324,plain,
% 21.68/21.87 ((mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))) <=> (mult(a, mult(b, c)) = mult(mult(a, b), c))),
% 21.68/21.87 inference(monotonicity,[status(thm)],[323, 178])).
% 21.68/21.87 tff(325,plain,
% 21.68/21.87 ((mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))) <=> (mult(mult(a, b), c) = mult(a, mult(b, c)))),
% 21.68/21.87 inference(transitivity,[status(thm)],[324, 143])).
% 21.68/21.88 tff(326,plain,
% 21.68/21.88 ((mult(mult(a, b), c) = mult(a, mult(b, c))) <=> (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))),
% 21.68/21.88 inference(symmetry,[status(thm)],[325])).
% 21.68/21.88 tff(327,plain,
% 21.68/21.88 ((~(mult(mult(a, b), c) = mult(a, mult(b, c)))) <=> (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))))),
% 21.68/21.88 inference(monotonicity,[status(thm)],[326])).
% 21.68/21.88 tff(328,plain,
% 21.68/21.88 (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))),
% 21.68/21.88 inference(modus_ponens,[status(thm)],[146, 327])).
% 21.68/21.88 tff(329,assumption,(~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))), introduced(assumption)).
% 21.68/21.88 tff(330,assumption,(~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))), introduced(assumption)).
% 21.68/21.88 tff(331,plain,
% 21.68/21.88 (((~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))) | (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))))) | (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))),
% 21.68/21.88 inference(tautology,[status(thm)],[])).
% 21.68/21.88 tff(332,plain,
% 21.68/21.88 ((~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))) | (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))))),
% 21.68/21.88 inference(unit_resolution,[status(thm)],[331, 330])).
% 21.68/21.88 tff(333,plain,
% 21.68/21.88 (((~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))))) | (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))),
% 21.68/21.88 inference(tautology,[status(thm)],[])).
% 21.68/21.88 tff(334,plain,
% 21.68/21.88 ((~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))))),
% 21.68/21.88 inference(unit_resolution,[status(thm)],[333, 329])).
% 21.68/21.88 tff(335,assumption,((~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))) | (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))))), introduced(assumption)).
% 21.68/21.88 tff(336,plain,
% 21.68/21.88 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))) | (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))))) | (~((~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))) | (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))))) | (~((~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))))))),
% 21.68/21.88 inference(rewrite,[status(thm)],[])).
% 21.68/21.88 tff(337,plain,
% 21.68/21.88 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))) | (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))))) | (~((~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))))))),
% 21.68/21.88 inference(quant_inst,[status(thm)],[])).
% 21.68/21.88 tff(338,plain,
% 21.68/21.88 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))) | (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))))) | (~((~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))))))),
% 21.68/21.88 inference(modus_ponens,[status(thm)],[337, 336])).
% 21.68/21.88 tff(339,plain,
% 21.68/21.88 ($false),
% 21.68/21.88 inference(unit_resolution,[status(thm)],[338, 27, 335, 334])).
% 21.68/21.88 tff(340,plain,((~((~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))) | (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))))) | (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))), inference(lemma,lemma(discharge,[]))).
% 21.68/21.88 tff(341,plain,
% 21.68/21.88 ($false),
% 21.68/21.88 inference(unit_resolution,[status(thm)],[340, 332, 329])).
% 21.68/21.88 tff(342,plain,((mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))) | (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))), inference(lemma,lemma(discharge,[]))).
% 21.68/21.88 tff(343,plain,
% 21.68/21.88 (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))),
% 21.68/21.88 inference(unit_resolution,[status(thm)],[342, 328])).
% 21.68/21.88 tff(344,plain,
% 21.68/21.88 (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, b), c)),
% 21.68/21.88 inference(transitivity,[status(thm)],[343, 177, 161])).
% 21.68/21.88 tff(345,plain,
% 21.68/21.88 (~((~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))) | (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))))),
% 21.68/21.88 inference(unit_resolution,[status(thm)],[340, 328])).
% 21.68/21.88 tff(346,plain,
% 21.68/21.88 (((~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))) | (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))))) | (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))),
% 21.68/21.88 inference(tautology,[status(thm)],[])).
% 21.68/21.88 tff(347,plain,
% 21.68/21.88 (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)),
% 21.68/21.88 inference(unit_resolution,[status(thm)],[346, 345])).
% 21.68/21.88 tff(348,plain,
% 21.68/21.88 (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(a, mult(b, c))),
% 21.68/21.88 inference(transitivity,[status(thm)],[347, 322, 319, 180])).
% 21.72/21.88 tff(349,plain,
% 21.72/21.88 ((mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) <=> (mult(a, mult(b, c)) = mult(mult(a, b), c))),
% 21.72/21.88 inference(monotonicity,[status(thm)],[348, 344])).
% 21.72/21.88 tff(350,plain,
% 21.72/21.88 ((mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) <=> (mult(mult(a, b), c) = mult(a, mult(b, c)))),
% 21.72/21.88 inference(transitivity,[status(thm)],[349, 143])).
% 21.72/21.88 tff(351,plain,
% 21.72/21.88 ((mult(mult(a, b), c) = mult(a, mult(b, c))) <=> (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))),
% 21.72/21.88 inference(symmetry,[status(thm)],[350])).
% 21.72/21.88 tff(352,plain,
% 21.72/21.88 ((~(mult(mult(a, b), c) = mult(a, mult(b, c)))) <=> (~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))))),
% 21.72/21.88 inference(monotonicity,[status(thm)],[351])).
% 21.72/21.88 tff(353,plain,
% 21.72/21.88 (~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))),
% 21.72/21.88 inference(modus_ponens,[status(thm)],[146, 352])).
% 21.72/21.88 tff(354,assumption,(~(mult(rd(mult(b, c), mult(a, c)), mult(c, a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, c)))), introduced(assumption)).
% 21.72/21.88 tff(355,plain,
% 21.72/21.88 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))) = mult(a, c))),
% 21.72/21.88 inference(quant_inst,[status(thm)],[])).
% 21.72/21.88 tff(356,plain,
% 21.72/21.88 (ld(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))) = mult(a, c)),
% 21.72/21.88 inference(unit_resolution,[status(thm)],[355, 7])).
% 21.72/21.88 tff(357,plain,
% 21.72/21.88 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(a, c), mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = mult(a, rd(mult(b, c), mult(a, c))))),
% 21.72/21.88 inference(quant_inst,[status(thm)],[])).
% 21.72/21.88 tff(358,plain,
% 21.72/21.88 (ld(mult(a, c), mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = mult(a, rd(mult(b, c), mult(a, c)))),
% 21.72/21.88 inference(unit_resolution,[status(thm)],[357, 7])).
% 21.72/21.88 tff(359,assumption,(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))), introduced(assumption)).
% 21.72/21.88 tff(360,plain,
% 21.72/21.88 (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), b)),
% 21.72/21.88 inference(transitivity,[status(thm)],[359, 177])).
% 21.72/21.88 tff(361,plain,
% 21.72/21.88 (ld(mult(a, c), mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = ld(mult(a, c), mult(mult(a, c), b))),
% 21.72/21.88 inference(monotonicity,[status(thm)],[360])).
% 21.72/21.88 tff(362,plain,
% 21.72/21.88 (ld(mult(a, c), mult(mult(a, c), b)) = ld(mult(a, c), mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))),
% 21.72/21.88 inference(symmetry,[status(thm)],[361])).
% 21.72/21.88 tff(363,plain,
% 21.72/21.88 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(a, c), mult(mult(a, c), b)) = b)),
% 21.72/21.88 inference(quant_inst,[status(thm)],[])).
% 21.72/21.88 tff(364,plain,
% 21.72/21.88 (ld(mult(a, c), mult(mult(a, c), b)) = b),
% 21.72/21.88 inference(unit_resolution,[status(thm)],[363, 7])).
% 21.72/21.88 tff(365,plain,
% 21.72/21.88 (b = ld(mult(a, c), mult(mult(a, c), b))),
% 21.72/21.88 inference(symmetry,[status(thm)],[364])).
% 21.72/21.88 tff(366,plain,
% 21.72/21.88 (b = mult(a, rd(mult(b, c), mult(a, c)))),
% 21.72/21.88 inference(transitivity,[status(thm)],[365, 362, 358])).
% 21.72/21.88 tff(367,plain,
% 21.72/21.88 (mult(b, mult(a, c)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))),
% 21.72/21.88 inference(monotonicity,[status(thm)],[366])).
% 21.72/21.88 tff(368,assumption,(mult(b, mult(c, a)) = mult(b, mult(a, c))), introduced(assumption)).
% 21.72/21.88 tff(369,plain,
% 21.72/21.88 (mult(b, mult(c, a)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))),
% 21.72/21.88 inference(transitivity,[status(thm)],[368, 367])).
% 21.72/21.88 tff(370,plain,
% 21.72/21.88 (ld(b, mult(b, mult(c, a))) = ld(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 21.72/21.88 inference(monotonicity,[status(thm)],[366, 369])).
% 21.72/21.88 tff(371,plain,
% 21.72/21.88 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(b, mult(b, mult(c, a))) = mult(c, a))),
% 21.72/21.88 inference(quant_inst,[status(thm)],[])).
% 21.72/21.88 tff(372,plain,
% 21.72/21.88 (ld(b, mult(b, mult(c, a))) = mult(c, a)),
% 21.72/21.88 inference(unit_resolution,[status(thm)],[371, 7])).
% 21.72/21.88 tff(373,plain,
% 21.72/21.88 (mult(c, a) = ld(b, mult(b, mult(c, a)))),
% 21.72/21.88 inference(symmetry,[status(thm)],[372])).
% 21.72/21.88 tff(374,plain,
% 21.72/21.88 (mult(c, a) = mult(a, c)),
% 21.72/21.88 inference(transitivity,[status(thm)],[373, 370, 356])).
% 21.72/21.88 tff(375,plain,
% 21.72/21.88 (mult(rd(mult(b, c), mult(a, c)), mult(c, a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, c))),
% 21.72/21.88 inference(monotonicity,[status(thm)],[374])).
% 21.72/21.88 tff(376,plain,
% 21.72/21.88 ($false),
% 21.72/21.88 inference(unit_resolution,[status(thm)],[354, 375])).
% 21.72/21.88 tff(377,plain,((~(mult(b, mult(c, a)) = mult(b, mult(a, c)))) | (mult(rd(mult(b, c), mult(a, c)), mult(c, a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, c))) | (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit)))))), inference(lemma,lemma(discharge,[]))).
% 21.72/21.88 tff(378,plain,
% 21.72/21.88 (~(mult(b, mult(c, a)) = mult(b, mult(a, c)))),
% 21.72/21.88 inference(unit_resolution,[status(thm)],[377, 343, 354, 97])).
% 21.72/21.88 tff(379,plain,
% 21.72/21.88 (((~(mult(mult(b, c), a) = mult(mult(b, a), c))) | (~(mult(b, mult(c, a)) = mult(b, mult(a, c))))) | (mult(b, mult(c, a)) = mult(b, mult(a, c)))),
% 21.72/21.88 inference(tautology,[status(thm)],[])).
% 21.72/21.88 tff(380,plain,
% 21.72/21.88 ((~(mult(mult(b, c), a) = mult(mult(b, a), c))) | (~(mult(b, mult(c, a)) = mult(b, mult(a, c))))),
% 21.72/21.88 inference(unit_resolution,[status(thm)],[379, 378])).
% 21.72/21.88 tff(381,plain,
% 21.72/21.88 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(b, c), a) = mult(mult(b, a), c))) | (~(mult(b, mult(c, a)) = mult(b, mult(a, c)))))) | (~((~(mult(mult(b, c), a) = mult(b, mult(c, a)))) | (~(mult(mult(b, a), c) = mult(b, mult(a, c)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(b, c), a) = mult(mult(b, a), c))) | (~(mult(b, mult(c, a)) = mult(b, mult(a, c)))))) | (~((~(mult(mult(b, c), a) = mult(b, mult(c, a)))) | (~(mult(mult(b, a), c) = mult(b, mult(a, c)))))))),
% 21.72/21.88 inference(rewrite,[status(thm)],[])).
% 21.72/21.88 tff(382,plain,
% 21.72/21.88 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(b, c), a) = mult(mult(b, a), c))) | (~(mult(b, mult(c, a)) = mult(b, mult(a, c)))))) | (~((~(mult(mult(b, c), a) = mult(b, mult(c, a)))) | (~(mult(mult(b, a), c) = mult(b, mult(a, c)))))))),
% 21.72/21.88 inference(quant_inst,[status(thm)],[])).
% 21.72/21.88 tff(383,plain,
% 21.72/21.88 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(b, c), a) = mult(mult(b, a), c))) | (~(mult(b, mult(c, a)) = mult(b, mult(a, c)))))) | (~((~(mult(mult(b, c), a) = mult(b, mult(c, a)))) | (~(mult(mult(b, a), c) = mult(b, mult(a, c))))))),
% 21.72/21.88 inference(modus_ponens,[status(thm)],[382, 381])).
% 21.72/21.88 tff(384,plain,
% 21.72/21.88 ((~((~(mult(mult(b, c), a) = mult(mult(b, a), c))) | (~(mult(b, mult(c, a)) = mult(b, mult(a, c)))))) | (~((~(mult(mult(b, c), a) = mult(b, mult(c, a)))) | (~(mult(mult(b, a), c) = mult(b, mult(a, c))))))),
% 21.72/21.88 inference(unit_resolution,[status(thm)],[383, 27])).
% 21.72/21.88 tff(385,plain,
% 21.72/21.88 (~((~(mult(mult(b, c), a) = mult(b, mult(c, a)))) | (~(mult(mult(b, a), c) = mult(b, mult(a, c)))))),
% 21.72/21.88 inference(unit_resolution,[status(thm)],[384, 380])).
% 21.72/21.88 tff(386,plain,
% 21.72/21.88 (((~(mult(mult(b, c), a) = mult(b, mult(c, a)))) | (~(mult(mult(b, a), c) = mult(b, mult(a, c))))) | (mult(mult(b, a), c) = mult(b, mult(a, c)))),
% 21.72/21.88 inference(tautology,[status(thm)],[])).
% 21.72/21.88 tff(387,plain,
% 21.72/21.88 (mult(mult(b, a), c) = mult(b, mult(a, c))),
% 21.72/21.88 inference(unit_resolution,[status(thm)],[386, 385])).
% 21.72/21.88 tff(388,assumption,(mult(mult(b, a), c) = mult(b, mult(a, c))), introduced(assumption)).
% 21.72/21.88 tff(389,plain,
% 21.72/21.88 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(b, mult(b, mult(b, a))) = mult(b, a))),
% 21.72/21.88 inference(quant_inst,[status(thm)],[])).
% 21.72/21.88 tff(390,plain,
% 21.72/21.88 (ld(b, mult(b, mult(b, a))) = mult(b, a)),
% 21.72/21.88 inference(unit_resolution,[status(thm)],[389, 7])).
% 21.72/21.88 tff(391,assumption,(mult(b, mult(a, b)) = mult(b, mult(b, a))), introduced(assumption)).
% 21.72/21.88 tff(392,plain,
% 21.72/21.88 (mult(b, mult(b, a)) = mult(b, mult(a, b))),
% 21.72/21.88 inference(symmetry,[status(thm)],[391])).
% 21.72/21.88 tff(393,plain,
% 21.72/21.88 (ld(b, mult(b, mult(b, a))) = ld(b, mult(b, mult(a, b)))),
% 21.72/21.88 inference(monotonicity,[status(thm)],[392])).
% 21.72/21.88 tff(394,plain,
% 21.72/21.88 (ld(b, mult(b, mult(a, b))) = ld(b, mult(b, mult(b, a)))),
% 21.72/21.88 inference(symmetry,[status(thm)],[393])).
% 21.72/21.88 tff(395,plain,
% 21.72/21.88 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(b, mult(b, mult(a, b))) = mult(a, b))),
% 21.72/21.88 inference(quant_inst,[status(thm)],[])).
% 21.72/21.88 tff(396,plain,
% 21.72/21.88 (ld(b, mult(b, mult(a, b))) = mult(a, b)),
% 21.72/21.88 inference(unit_resolution,[status(thm)],[395, 7])).
% 21.72/21.88 tff(397,plain,
% 21.72/21.88 (mult(a, b) = ld(b, mult(b, mult(a, b)))),
% 21.72/21.88 inference(symmetry,[status(thm)],[396])).
% 21.72/21.88 tff(398,plain,
% 21.72/21.88 (mult(a, b) = mult(b, a)),
% 21.72/21.88 inference(transitivity,[status(thm)],[397, 394, 390])).
% 21.72/21.88 tff(399,plain,
% 21.72/21.88 (mult(mult(a, b), c) = mult(mult(b, a), c)),
% 21.72/21.88 inference(monotonicity,[status(thm)],[398])).
% 21.72/21.88 tff(400,plain,
% 21.72/21.88 (mult(mult(a, b), c) = mult(a, mult(b, c))),
% 21.72/21.88 inference(transitivity,[status(thm)],[399, 388, 367, 287, 142])).
% 21.72/21.88 tff(401,plain,
% 21.72/21.88 ($false),
% 21.72/21.88 inference(unit_resolution,[status(thm)],[146, 400])).
% 21.72/21.88 tff(402,plain,((~(mult(b, mult(a, b)) = mult(b, mult(b, a)))) | (~(mult(mult(b, a), c) = mult(b, mult(a, c)))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit)))))), inference(lemma,lemma(discharge,[]))).
% 21.72/21.88 tff(403,plain,
% 21.72/21.88 (~(mult(b, mult(a, b)) = mult(b, mult(b, a)))),
% 21.72/21.88 inference(unit_resolution,[status(thm)],[402, 387, 279, 97, 343])).
% 21.72/21.88 tff(404,plain,
% 21.72/21.88 (mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))),
% 21.72/21.88 inference(symmetry,[status(thm)],[359])).
% 21.72/21.88 tff(405,plain,
% 21.72/21.88 (mult(mult(a, c), b) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))),
% 21.72/21.88 inference(symmetry,[status(thm)],[177])).
% 21.72/21.88 tff(406,plain,
% 21.72/21.88 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(a, b), c), a), a) = mult(mult(a, b), c))),
% 21.72/21.88 inference(quant_inst,[status(thm)],[])).
% 21.72/21.88 tff(407,plain,
% 21.72/21.88 (rd(mult(mult(mult(a, b), c), a), a) = mult(mult(a, b), c)),
% 21.72/21.88 inference(unit_resolution,[status(thm)],[406, 168])).
% 21.72/21.88 tff(408,plain,
% 21.72/21.88 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(mult(a, b), c), a), rd(mult(b, c), mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, b), c), a))),
% 21.72/21.88 inference(quant_inst,[status(thm)],[])).
% 21.72/21.88 tff(409,plain,
% 21.72/21.88 (rd(mult(mult(mult(mult(a, b), c), a), rd(mult(b, c), mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, b), c), a)),
% 21.72/21.88 inference(unit_resolution,[status(thm)],[408, 168])).
% 21.72/21.88 tff(410,plain,
% 21.72/21.88 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(mult(mult(a, b), c), a), rd(mult(b, c), mult(a, c))), a), a) = mult(mult(mult(mult(a, b), c), a), rd(mult(b, c), mult(a, c))))),
% 21.72/21.88 inference(quant_inst,[status(thm)],[])).
% 21.72/21.88 tff(411,plain,
% 21.72/21.88 (rd(mult(mult(mult(mult(mult(a, b), c), a), rd(mult(b, c), mult(a, c))), a), a) = mult(mult(mult(mult(a, b), c), a), rd(mult(b, c), mult(a, c)))),
% 21.72/21.89 inference(unit_resolution,[status(thm)],[410, 168])).
% 21.72/21.89 tff(412,assumption,(~(mult(b, mult(a, b)) = mult(b, mult(b, a)))), introduced(assumption)).
% 21.72/21.89 tff(413,plain,
% 21.72/21.89 (((~(mult(mult(b, a), b) = mult(mult(b, b), a))) | (~(mult(b, mult(a, b)) = mult(b, mult(b, a))))) | (mult(b, mult(a, b)) = mult(b, mult(b, a)))),
% 21.72/21.89 inference(tautology,[status(thm)],[])).
% 21.72/21.89 tff(414,plain,
% 21.72/21.89 ((~(mult(mult(b, a), b) = mult(mult(b, b), a))) | (~(mult(b, mult(a, b)) = mult(b, mult(b, a))))),
% 21.72/21.89 inference(unit_resolution,[status(thm)],[413, 412])).
% 21.72/21.89 tff(415,plain,
% 21.72/21.89 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(b, a), b) = mult(mult(b, b), a))) | (~(mult(b, mult(a, b)) = mult(b, mult(b, a)))))) | (~((~(mult(mult(b, a), b) = mult(b, mult(a, b)))) | (~(mult(mult(b, b), a) = mult(b, mult(b, a)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(b, a), b) = mult(mult(b, b), a))) | (~(mult(b, mult(a, b)) = mult(b, mult(b, a)))))) | (~((~(mult(mult(b, a), b) = mult(b, mult(a, b)))) | (~(mult(mult(b, b), a) = mult(b, mult(b, a)))))))),
% 21.72/21.89 inference(rewrite,[status(thm)],[])).
% 21.72/21.89 tff(416,plain,
% 21.72/21.89 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(b, a), b) = mult(mult(b, b), a))) | (~(mult(b, mult(a, b)) = mult(b, mult(b, a)))))) | (~((~(mult(mult(b, a), b) = mult(b, mult(a, b)))) | (~(mult(mult(b, b), a) = mult(b, mult(b, a)))))))),
% 21.72/21.89 inference(quant_inst,[status(thm)],[])).
% 21.72/21.89 tff(417,plain,
% 21.72/21.89 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(b, a), b) = mult(mult(b, b), a))) | (~(mult(b, mult(a, b)) = mult(b, mult(b, a)))))) | (~((~(mult(mult(b, a), b) = mult(b, mult(a, b)))) | (~(mult(mult(b, b), a) = mult(b, mult(b, a))))))),
% 21.72/21.89 inference(modus_ponens,[status(thm)],[416, 415])).
% 21.72/21.89 tff(418,plain,
% 21.72/21.89 ((~((~(mult(mult(b, a), b) = mult(mult(b, b), a))) | (~(mult(b, mult(a, b)) = mult(b, mult(b, a)))))) | (~((~(mult(mult(b, a), b) = mult(b, mult(a, b)))) | (~(mult(mult(b, b), a) = mult(b, mult(b, a))))))),
% 21.72/21.89 inference(unit_resolution,[status(thm)],[417, 27])).
% 21.72/21.89 tff(419,plain,
% 21.72/21.89 (~((~(mult(mult(b, a), b) = mult(b, mult(a, b)))) | (~(mult(mult(b, b), a) = mult(b, mult(b, a)))))),
% 21.72/21.89 inference(unit_resolution,[status(thm)],[418, 414])).
% 21.72/21.89 tff(420,plain,
% 21.72/21.89 (((~(mult(mult(b, a), b) = mult(b, mult(a, b)))) | (~(mult(mult(b, b), a) = mult(b, mult(b, a))))) | (mult(mult(b, a), b) = mult(b, mult(a, b)))),
% 21.72/21.89 inference(tautology,[status(thm)],[])).
% 21.72/21.89 tff(421,plain,
% 21.72/21.89 (mult(mult(b, a), b) = mult(b, mult(a, b))),
% 21.72/21.89 inference(unit_resolution,[status(thm)],[420, 419])).
% 21.72/21.89 tff(422,plain,
% 21.72/21.89 (((~(mult(mult(b, a), b) = mult(b, mult(a, b)))) | (~(mult(mult(b, b), a) = mult(b, mult(b, a))))) | (mult(mult(b, b), a) = mult(b, mult(b, a)))),
% 21.72/21.89 inference(tautology,[status(thm)],[])).
% 21.72/21.89 tff(423,plain,
% 21.72/21.89 (mult(mult(b, b), a) = mult(b, mult(b, a))),
% 21.72/21.89 inference(unit_resolution,[status(thm)],[422, 419])).
% 21.72/21.89 tff(424,assumption,(~(ld(mult(a, c), mult(mult(a, c), mult(unit, mult(mult(mult(b, unit), b), a)))) = mult(unit, mult(mult(mult(b, unit), b), a)))), introduced(assumption)).
% 21.72/21.89 tff(425,plain,
% 21.72/21.89 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(a, c), mult(mult(a, c), mult(unit, mult(mult(mult(b, unit), b), a)))) = mult(unit, mult(mult(mult(b, unit), b), a)))),
% 21.72/21.89 inference(quant_inst,[status(thm)],[])).
% 21.72/21.89 tff(426,plain,
% 21.72/21.89 ($false),
% 21.72/21.89 inference(unit_resolution,[status(thm)],[425, 7, 424])).
% 21.72/21.89 tff(427,plain,(ld(mult(a, c), mult(mult(a, c), mult(unit, mult(mult(mult(b, unit), b), a)))) = mult(unit, mult(mult(mult(b, unit), b), a))), inference(lemma,lemma(discharge,[]))).
% 21.72/21.89 tff(428,plain,
% 21.72/21.89 ((~![A: $i] : (mult(unit, A) = A)) | (mult(unit, mult(mult(b, unit), b)) = mult(mult(b, unit), b))),
% 21.72/21.89 inference(quant_inst,[status(thm)],[])).
% 21.72/21.89 tff(429,plain,
% 21.72/21.89 (mult(unit, mult(mult(b, unit), b)) = mult(mult(b, unit), b)),
% 21.72/21.89 inference(unit_resolution,[status(thm)],[428, 71])).
% 21.72/21.89 tff(430,plain,
% 21.72/21.89 (mult(mult(b, unit), b) = mult(unit, mult(mult(b, unit), b))),
% 21.72/21.89 inference(symmetry,[status(thm)],[429])).
% 21.72/21.89 tff(431,plain,
% 21.72/21.89 (b = mult(b, unit)),
% 21.72/21.89 inference(symmetry,[status(thm)],[182])).
% 21.72/21.89 tff(432,plain,
% 21.72/21.89 (mult(b, b) = mult(mult(b, unit), b)),
% 21.72/21.89 inference(monotonicity,[status(thm)],[431])).
% 21.72/21.89 tff(433,plain,
% 21.72/21.89 (mult(b, b) = mult(unit, mult(mult(b, unit), b))),
% 21.72/21.89 inference(transitivity,[status(thm)],[432, 430])).
% 21.72/21.89 tff(434,plain,
% 21.72/21.89 (mult(mult(b, b), a) = mult(mult(unit, mult(mult(b, unit), b)), a)),
% 21.72/21.89 inference(monotonicity,[status(thm)],[433])).
% 21.72/21.89 tff(435,plain,
% 21.72/21.89 (mult(mult(unit, mult(mult(b, unit), b)), a) = mult(mult(b, b), a)),
% 21.72/21.89 inference(symmetry,[status(thm)],[434])).
% 21.72/21.89 tff(436,plain,
% 21.72/21.89 (mult(mult(unit, a), mult(mult(b, unit), b)) = mult(a, mult(mult(b, unit), b))),
% 21.72/21.89 inference(monotonicity,[status(thm)],[244])).
% 21.72/21.89 tff(437,plain,
% 21.72/21.89 (mult(a, mult(mult(b, unit), b)) = mult(mult(unit, a), mult(mult(b, unit), b))),
% 21.72/21.89 inference(symmetry,[status(thm)],[436])).
% 21.72/21.89 tff(438,plain,
% 21.72/21.89 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(a, b), unit), b) = mult(a, mult(mult(b, unit), b)))),
% 21.72/21.89 inference(quant_inst,[status(thm)],[])).
% 21.72/21.89 tff(439,plain,
% 21.72/21.89 (mult(mult(mult(a, b), unit), b) = mult(a, mult(mult(b, unit), b))),
% 21.72/21.89 inference(unit_resolution,[status(thm)],[438, 56])).
% 21.72/21.89 tff(440,plain,
% 21.72/21.89 (mult(mult(a, b), unit) = mult(a, b)),
% 21.72/21.89 inference(transitivity,[status(thm)],[195, 189, 187])).
% 21.72/21.89 tff(441,plain,
% 21.72/21.89 (mult(mult(mult(a, b), unit), b) = mult(mult(a, b), b)),
% 21.72/21.89 inference(monotonicity,[status(thm)],[440])).
% 21.72/21.89 tff(442,plain,
% 21.72/21.89 (mult(mult(a, b), b) = mult(mult(mult(a, b), unit), b)),
% 21.72/21.89 inference(symmetry,[status(thm)],[441])).
% 21.72/21.89 tff(443,plain,
% 21.72/21.89 ((~![A: $i] : (mult(unit, A) = A)) | (mult(unit, mult(mult(a, b), b)) = mult(mult(a, b), b))),
% 21.72/21.89 inference(quant_inst,[status(thm)],[])).
% 21.72/21.89 tff(444,plain,
% 21.72/21.89 (mult(unit, mult(mult(a, b), b)) = mult(mult(a, b), b)),
% 21.72/21.89 inference(unit_resolution,[status(thm)],[443, 71])).
% 21.72/21.89 tff(445,plain,
% 21.72/21.89 (mult(a, mult(mult(b, unit), b)) = mult(mult(mult(a, b), unit), b)),
% 21.72/21.89 inference(symmetry,[status(thm)],[439])).
% 21.72/21.89 tff(446,plain,
% 21.72/21.89 (mult(a, mult(mult(b, unit), b)) = mult(mult(a, b), b)),
% 21.72/21.89 inference(transitivity,[status(thm)],[445, 441])).
% 21.72/21.89 tff(447,plain,
% 21.72/21.89 (mult(unit, mult(a, mult(mult(b, unit), b))) = mult(unit, mult(mult(a, b), b))),
% 21.72/21.89 inference(monotonicity,[status(thm)],[446])).
% 21.72/21.89 tff(448,assumption,(~(mult(mult(unit, mult(mult(b, unit), b)), a) = mult(unit, mult(mult(mult(b, unit), b), a)))), introduced(assumption)).
% 21.72/21.89 tff(449,plain,
% 21.72/21.89 (((~(mult(mult(unit, mult(mult(b, unit), b)), a) = mult(unit, mult(mult(mult(b, unit), b), a)))) | (~(mult(mult(unit, a), mult(mult(b, unit), b)) = mult(unit, mult(a, mult(mult(b, unit), b)))))) | (mult(mult(unit, mult(mult(b, unit), b)), a) = mult(unit, mult(mult(mult(b, unit), b), a)))),
% 21.72/21.89 inference(tautology,[status(thm)],[])).
% 21.72/21.89 tff(450,plain,
% 21.72/21.89 ((~(mult(mult(unit, mult(mult(b, unit), b)), a) = mult(unit, mult(mult(mult(b, unit), b), a)))) | (~(mult(mult(unit, a), mult(mult(b, unit), b)) = mult(unit, mult(a, mult(mult(b, unit), b)))))),
% 21.72/21.89 inference(unit_resolution,[status(thm)],[449, 448])).
% 21.72/21.89 tff(451,plain,
% 21.72/21.89 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(unit, mult(mult(b, unit), b)), a) = mult(mult(unit, a), mult(mult(b, unit), b)))) | (~(mult(unit, mult(mult(mult(b, unit), b), a)) = mult(unit, mult(a, mult(mult(b, unit), b))))))) | (~((~(mult(mult(unit, mult(mult(b, unit), b)), a) = mult(unit, mult(mult(mult(b, unit), b), a)))) | (~(mult(mult(unit, a), mult(mult(b, unit), b)) = mult(unit, mult(a, mult(mult(b, unit), b))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(unit, mult(mult(b, unit), b)), a) = mult(mult(unit, a), mult(mult(b, unit), b)))) | (~(mult(unit, mult(mult(mult(b, unit), b), a)) = mult(unit, mult(a, mult(mult(b, unit), b))))))) | (~((~(mult(mult(unit, mult(mult(b, unit), b)), a) = mult(unit, mult(mult(mult(b, unit), b), a)))) | (~(mult(mult(unit, a), mult(mult(b, unit), b)) = mult(unit, mult(a, mult(mult(b, unit), b))))))))),
% 21.72/21.89 inference(rewrite,[status(thm)],[])).
% 21.72/21.89 tff(452,plain,
% 21.72/21.89 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(unit, mult(mult(b, unit), b)), a) = mult(mult(unit, a), mult(mult(b, unit), b)))) | (~(mult(unit, mult(mult(mult(b, unit), b), a)) = mult(unit, mult(a, mult(mult(b, unit), b))))))) | (~((~(mult(mult(unit, mult(mult(b, unit), b)), a) = mult(unit, mult(mult(mult(b, unit), b), a)))) | (~(mult(mult(unit, a), mult(mult(b, unit), b)) = mult(unit, mult(a, mult(mult(b, unit), b))))))))),
% 21.72/21.89 inference(quant_inst,[status(thm)],[])).
% 21.72/21.89 tff(453,plain,
% 21.72/21.89 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(unit, mult(mult(b, unit), b)), a) = mult(mult(unit, a), mult(mult(b, unit), b)))) | (~(mult(unit, mult(mult(mult(b, unit), b), a)) = mult(unit, mult(a, mult(mult(b, unit), b))))))) | (~((~(mult(mult(unit, mult(mult(b, unit), b)), a) = mult(unit, mult(mult(mult(b, unit), b), a)))) | (~(mult(mult(unit, a), mult(mult(b, unit), b)) = mult(unit, mult(a, mult(mult(b, unit), b)))))))),
% 21.72/21.89 inference(modus_ponens,[status(thm)],[452, 451])).
% 21.72/21.89 tff(454,plain,
% 21.72/21.89 ((~((~(mult(mult(unit, mult(mult(b, unit), b)), a) = mult(mult(unit, a), mult(mult(b, unit), b)))) | (~(mult(unit, mult(mult(mult(b, unit), b), a)) = mult(unit, mult(a, mult(mult(b, unit), b))))))) | (~((~(mult(mult(unit, mult(mult(b, unit), b)), a) = mult(unit, mult(mult(mult(b, unit), b), a)))) | (~(mult(mult(unit, a), mult(mult(b, unit), b)) = mult(unit, mult(a, mult(mult(b, unit), b)))))))),
% 21.72/21.89 inference(unit_resolution,[status(thm)],[453, 27])).
% 21.72/21.89 tff(455,plain,
% 21.72/21.89 (~((~(mult(mult(unit, mult(mult(b, unit), b)), a) = mult(mult(unit, a), mult(mult(b, unit), b)))) | (~(mult(unit, mult(mult(mult(b, unit), b), a)) = mult(unit, mult(a, mult(mult(b, unit), b))))))),
% 21.72/21.89 inference(unit_resolution,[status(thm)],[454, 450])).
% 21.72/21.89 tff(456,plain,
% 21.72/21.89 (((~(mult(mult(unit, mult(mult(b, unit), b)), a) = mult(mult(unit, a), mult(mult(b, unit), b)))) | (~(mult(unit, mult(mult(mult(b, unit), b), a)) = mult(unit, mult(a, mult(mult(b, unit), b)))))) | (mult(unit, mult(mult(mult(b, unit), b), a)) = mult(unit, mult(a, mult(mult(b, unit), b))))),
% 21.72/21.89 inference(tautology,[status(thm)],[])).
% 21.72/21.89 tff(457,plain,
% 21.72/21.89 (mult(unit, mult(mult(mult(b, unit), b), a)) = mult(unit, mult(a, mult(mult(b, unit), b)))),
% 21.72/21.89 inference(unit_resolution,[status(thm)],[456, 455])).
% 21.72/21.89 tff(458,plain,
% 21.72/21.89 (mult(unit, mult(mult(mult(b, unit), b), a)) = mult(mult(unit, a), mult(mult(b, unit), b))),
% 21.72/21.89 inference(transitivity,[status(thm)],[457, 447, 444, 442, 439, 437])).
% 21.72/21.89 tff(459,plain,
% 21.72/21.89 ((mult(mult(unit, mult(mult(b, unit), b)), a) = mult(unit, mult(mult(mult(b, unit), b), a))) <=> (mult(mult(unit, mult(mult(b, unit), b)), a) = mult(mult(unit, a), mult(mult(b, unit), b)))),
% 21.72/21.89 inference(monotonicity,[status(thm)],[458])).
% 21.72/21.89 tff(460,plain,
% 21.72/21.89 ((mult(mult(unit, mult(mult(b, unit), b)), a) = mult(mult(unit, a), mult(mult(b, unit), b))) <=> (mult(mult(unit, mult(mult(b, unit), b)), a) = mult(unit, mult(mult(mult(b, unit), b), a)))),
% 21.72/21.89 inference(symmetry,[status(thm)],[459])).
% 21.72/21.89 tff(461,plain,
% 21.72/21.89 (((~(mult(mult(unit, mult(mult(b, unit), b)), a) = mult(mult(unit, a), mult(mult(b, unit), b)))) | (~(mult(unit, mult(mult(mult(b, unit), b), a)) = mult(unit, mult(a, mult(mult(b, unit), b)))))) | (mult(mult(unit, mult(mult(b, unit), b)), a) = mult(mult(unit, a), mult(mult(b, unit), b)))),
% 21.72/21.89 inference(tautology,[status(thm)],[])).
% 21.72/21.89 tff(462,plain,
% 21.72/21.89 (mult(mult(unit, mult(mult(b, unit), b)), a) = mult(mult(unit, a), mult(mult(b, unit), b))),
% 21.72/21.89 inference(unit_resolution,[status(thm)],[461, 455])).
% 21.72/21.89 tff(463,plain,
% 21.72/21.89 (mult(mult(unit, mult(mult(b, unit), b)), a) = mult(unit, mult(mult(mult(b, unit), b), a))),
% 21.72/21.89 inference(modus_ponens,[status(thm)],[462, 460])).
% 21.72/21.89 tff(464,plain,
% 21.72/21.89 ($false),
% 21.72/21.89 inference(unit_resolution,[status(thm)],[448, 463])).
% 21.72/21.89 tff(465,plain,(mult(mult(unit, mult(mult(b, unit), b)), a) = mult(unit, mult(mult(mult(b, unit), b), a))), inference(lemma,lemma(discharge,[]))).
% 21.72/21.89 tff(466,plain,
% 21.72/21.89 (mult(unit, mult(mult(mult(b, unit), b), a)) = mult(mult(unit, mult(mult(b, unit), b)), a)),
% 21.72/21.89 inference(symmetry,[status(thm)],[465])).
% 21.72/21.89 tff(467,assumption,(ld(mult(a, c), mult(mult(a, c), mult(unit, mult(mult(mult(b, unit), b), a)))) = mult(unit, mult(mult(mult(b, unit), b), a))), introduced(assumption)).
% 21.72/21.89 tff(468,plain,
% 21.72/21.89 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), a)))),
% 21.72/21.89 inference(quant_inst,[status(thm)],[])).
% 21.72/21.89 tff(469,plain,
% 21.72/21.89 (mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), a))),
% 21.72/21.89 inference(unit_resolution,[status(thm)],[468, 56])).
% 21.72/21.89 tff(470,plain,
% 21.72/21.89 (mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), a)) = mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a)),
% 21.72/21.89 inference(symmetry,[status(thm)],[469])).
% 21.72/21.89 tff(471,plain,
% 21.72/21.89 (mult(a, rd(mult(b, c), mult(a, c))) = ld(mult(a, c), mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))),
% 21.72/21.89 inference(symmetry,[status(thm)],[358])).
% 21.72/21.89 tff(472,plain,
% 21.72/21.89 (mult(a, rd(mult(b, c), mult(a, c))) = b),
% 21.72/21.89 inference(transitivity,[status(thm)],[471, 361, 364])).
% 21.72/21.89 tff(473,plain,
% 21.72/21.89 (mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(b, a)),
% 21.72/21.89 inference(monotonicity,[status(thm)],[472])).
% 21.72/21.89 tff(474,plain,
% 21.72/21.89 (mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), a)) = mult(b, mult(b, a))),
% 21.72/21.89 inference(monotonicity,[status(thm)],[473])).
% 21.72/21.89 tff(475,plain,
% 21.72/21.89 (mult(b, mult(b, a)) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), a))),
% 21.72/21.89 inference(symmetry,[status(thm)],[474])).
% 21.72/21.89 tff(476,plain,
% 21.72/21.89 (mult(unit, mult(mult(mult(b, unit), b), a)) = mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a)),
% 21.72/21.89 inference(transitivity,[status(thm)],[466, 435, 423, 475, 470])).
% 21.72/21.89 tff(477,plain,
% 21.72/21.89 (mult(mult(a, c), mult(unit, mult(mult(mult(b, unit), b), a))) = mult(mult(a, c), mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a))),
% 21.72/21.89 inference(monotonicity,[status(thm)],[476])).
% 21.72/21.89 tff(478,plain,
% 21.72/21.89 (mult(mult(a, c), mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a)) = mult(mult(a, c), mult(unit, mult(mult(mult(b, unit), b), a)))),
% 21.72/21.89 inference(symmetry,[status(thm)],[477])).
% 21.72/21.89 tff(479,plain,
% 21.72/21.89 ((mult(b, mult(b, a)) = mult(b, mult(a, b))) <=> (mult(b, mult(a, b)) = mult(b, mult(b, a)))),
% 21.72/21.89 inference(commutativity,[status(thm)],[])).
% 21.72/21.89 tff(480,plain,
% 21.72/21.89 (mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(b, a), b)),
% 21.72/21.89 inference(monotonicity,[status(thm)],[176])).
% 21.72/21.89 tff(481,plain,
% 21.72/21.89 (mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), a)) = mult(b, mult(a, b))),
% 21.72/21.90 inference(transitivity,[status(thm)],[480, 421])).
% 21.72/21.90 tff(482,plain,
% 21.72/21.90 (mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a) = mult(b, mult(b, a))),
% 21.72/21.90 inference(transitivity,[status(thm)],[469, 474])).
% 21.72/21.90 tff(483,plain,
% 21.72/21.90 ((mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), a))) <=> (mult(b, mult(b, a)) = mult(b, mult(a, b)))),
% 21.72/21.90 inference(monotonicity,[status(thm)],[482, 481])).
% 21.72/21.90 tff(484,plain,
% 21.72/21.90 ((mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), a))) <=> (mult(b, mult(a, b)) = mult(b, mult(b, a)))),
% 21.72/21.90 inference(transitivity,[status(thm)],[483, 479])).
% 21.72/21.90 tff(485,plain,
% 21.72/21.90 ((mult(b, mult(a, b)) = mult(b, mult(b, a))) <=> (mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), a)))),
% 21.72/21.90 inference(symmetry,[status(thm)],[484])).
% 21.72/21.90 tff(486,plain,
% 21.72/21.90 ((~(mult(b, mult(a, b)) = mult(b, mult(b, a)))) <=> (~(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), a))))),
% 21.72/21.90 inference(monotonicity,[status(thm)],[485])).
% 21.72/21.90 tff(487,plain,
% 21.72/21.90 (~(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), a)))),
% 21.72/21.90 inference(modus_ponens,[status(thm)],[412, 486])).
% 21.72/21.90 tff(488,plain,
% 21.72/21.90 (((~(mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c))) = mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), a))))) | (mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), a)))),
% 21.72/21.90 inference(tautology,[status(thm)],[])).
% 21.72/21.90 tff(489,plain,
% 21.72/21.90 ((~(mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c))) = mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), a))))),
% 21.72/21.90 inference(unit_resolution,[status(thm)],[488, 487])).
% 21.72/21.90 tff(490,plain,
% 21.72/21.90 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c))) = mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), a)))))) | (~((~(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c))))) | (~(mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c))) = mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), a)))))) | (~((~(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c))))) | (~(mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))))))))),
% 21.72/21.90 inference(rewrite,[status(thm)],[])).
% 21.72/21.90 tff(491,plain,
% 21.72/21.90 (((~((~(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c))))) | (~(mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c))) = mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), a))))))) <=> ((~((~(mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c))) = mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), a)))))) | (~((~(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c))))) | (~(mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))))))))),
% 21.72/21.90 inference(rewrite,[status(thm)],[])).
% 21.72/21.90 tff(492,plain,
% 21.72/21.90 ((~((~(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c))) = mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))))))) <=> (~((~(mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c))) = mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), a))))))),
% 21.72/21.90 inference(rewrite,[status(thm)],[])).
% 21.72/21.90 tff(493,plain,
% 21.72/21.90 ((~((~(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c))))) | (~(mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))))))) <=> (~((~(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c))))) | (~(mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c))))))))),
% 21.72/21.90 inference(rewrite,[status(thm)],[])).
% 21.72/21.90 tff(494,plain,
% 21.72/21.90 (((~((~(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c))))) | (~(mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c))) = mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c))))))))) <=> ((~((~(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c))))) | (~(mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c))) = mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), a)))))))),
% 21.72/21.90 inference(monotonicity,[status(thm)],[493, 492])).
% 21.72/21.90 tff(495,plain,
% 21.72/21.90 (((~((~(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c))))) | (~(mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c))) = mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c))))))))) <=> ((~((~(mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c))) = mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), a)))))) | (~((~(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c))))) | (~(mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))))))))),
% 21.72/21.90 inference(transitivity,[status(thm)],[494, 491])).
% 21.72/21.90 tff(496,plain,
% 21.72/21.90 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c))))) | (~(mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c))) = mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c))) = mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), a)))))) | (~((~(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c))))) | (~(mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c))))))))))),
% 21.72/21.90 inference(monotonicity,[status(thm)],[495])).
% 21.72/21.90 tff(497,plain,
% 21.72/21.90 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c))))) | (~(mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c))) = mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c))) = mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), a)))))) | (~((~(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c))))) | (~(mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))))))))),
% 21.72/21.90 inference(transitivity,[status(thm)],[496, 490])).
% 21.72/21.90 tff(498,plain,
% 21.72/21.90 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c))))) | (~(mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c))) = mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))))))))),
% 21.72/21.90 inference(quant_inst,[status(thm)],[])).
% 21.72/21.90 tff(499,plain,
% 21.72/21.90 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c))) = mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), a)))))) | (~((~(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c))))) | (~(mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c))))))))),
% 21.72/21.90 inference(modus_ponens,[status(thm)],[498, 497])).
% 21.72/21.90 tff(500,plain,
% 21.72/21.90 ((~((~(mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c))) = mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), a)))))) | (~((~(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c))))) | (~(mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c))))))))),
% 21.72/21.90 inference(unit_resolution,[status(thm)],[499, 27])).
% 21.72/21.90 tff(501,plain,
% 21.72/21.90 (~((~(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c))))) | (~(mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))))))),
% 21.72/21.90 inference(unit_resolution,[status(thm)],[500, 489])).
% 21.72/21.90 tff(502,plain,
% 21.72/21.90 (((~(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c))))) | (~(mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c))))))) | (mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c))))),
% 21.72/21.90 inference(tautology,[status(thm)],[])).
% 21.72/21.90 tff(503,plain,
% 21.72/21.90 (mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c)))),
% 21.72/21.90 inference(unit_resolution,[status(thm)],[502, 501])).
% 21.72/21.90 tff(504,plain,
% 21.72/21.90 (mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a)),
% 21.72/21.90 inference(symmetry,[status(thm)],[503])).
% 21.72/21.90 tff(505,plain,
% 21.72/21.90 ((~![A: $i] : (mult(A, unit) = A)) | (mult(mult(unit, a), unit) = mult(unit, a))),
% 21.72/21.90 inference(quant_inst,[status(thm)],[])).
% 21.72/21.90 tff(506,plain,
% 21.72/21.90 (mult(mult(unit, a), unit) = mult(unit, a)),
% 21.72/21.90 inference(unit_resolution,[status(thm)],[505, 43])).
% 21.72/21.90 tff(507,plain,
% 21.72/21.90 (mult(mult(unit, a), unit) = a),
% 21.72/21.90 inference(transitivity,[status(thm)],[506, 244])).
% 21.72/21.90 tff(508,plain,
% 21.72/21.90 (mult(b, mult(mult(unit, a), unit)) = mult(b, a)),
% 21.72/21.90 inference(monotonicity,[status(thm)],[507])).
% 21.72/21.90 tff(509,plain,
% 21.72/21.90 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(b, unit), a), unit) = mult(b, mult(mult(unit, a), unit)))),
% 21.72/21.90 inference(quant_inst,[status(thm)],[])).
% 21.72/21.90 tff(510,plain,
% 21.72/21.90 (mult(mult(mult(b, unit), a), unit) = mult(b, mult(mult(unit, a), unit))),
% 21.72/21.90 inference(unit_resolution,[status(thm)],[509, 56])).
% 21.72/21.90 tff(511,plain,
% 21.72/21.90 (mult(mult(b, unit), a) = mult(b, a)),
% 21.72/21.90 inference(monotonicity,[status(thm)],[182])).
% 21.72/21.90 tff(512,plain,
% 21.72/21.90 (mult(b, a) = mult(mult(b, unit), a)),
% 21.72/21.90 inference(symmetry,[status(thm)],[511])).
% 21.72/21.90 tff(513,plain,
% 21.72/21.90 (mult(mult(b, a), unit) = mult(mult(mult(b, unit), a), unit)),
% 21.72/21.90 inference(monotonicity,[status(thm)],[512])).
% 21.72/21.90 tff(514,plain,
% 21.72/21.90 (mult(mult(b, a), unit) = mult(b, a)),
% 21.72/21.90 inference(transitivity,[status(thm)],[513, 510, 508])).
% 21.72/21.90 tff(515,plain,
% 21.72/21.90 (mult(mult(mult(b, a), unit), a) = mult(mult(b, a), a)),
% 21.72/21.90 inference(monotonicity,[status(thm)],[514])).
% 21.72/21.90 tff(516,plain,
% 21.72/21.90 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(b, a), unit), a) = mult(b, mult(mult(a, unit), a)))),
% 21.72/21.90 inference(quant_inst,[status(thm)],[])).
% 21.72/21.90 tff(517,plain,
% 21.72/21.90 (mult(mult(mult(b, a), unit), a) = mult(b, mult(mult(a, unit), a))),
% 21.72/21.90 inference(unit_resolution,[status(thm)],[516, 56])).
% 21.72/21.90 tff(518,plain,
% 21.72/21.90 (mult(b, mult(mult(a, unit), a)) = mult(mult(mult(b, a), unit), a)),
% 21.72/21.90 inference(symmetry,[status(thm)],[517])).
% 21.72/21.90 tff(519,plain,
% 21.72/21.90 (mult(mult(a, unit), a) = mult(a, a)),
% 21.72/21.90 inference(monotonicity,[status(thm)],[47])).
% 21.72/21.90 tff(520,plain,
% 21.72/21.90 (mult(a, a) = mult(mult(a, unit), a)),
% 21.72/21.91 inference(symmetry,[status(thm)],[519])).
% 21.72/21.91 tff(521,plain,
% 21.72/21.91 (mult(b, mult(a, a)) = mult(b, mult(mult(a, unit), a))),
% 21.72/21.91 inference(monotonicity,[status(thm)],[520])).
% 21.72/21.91 tff(522,plain,
% 21.72/21.91 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(b, mult(a, a))),
% 21.72/21.91 inference(monotonicity,[status(thm)],[472])).
% 21.72/21.91 tff(523,plain,
% 21.72/21.91 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(mult(b, a), a)),
% 21.72/21.91 inference(transitivity,[status(thm)],[522, 521, 518, 515])).
% 21.72/21.91 tff(524,plain,
% 21.72/21.91 (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, a)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c)))),
% 21.72/21.91 inference(monotonicity,[status(thm)],[523])).
% 21.72/21.91 tff(525,plain,
% 21.72/21.91 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, a)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), mult(a, a)), rd(mult(b, c), mult(a, c)))))),
% 21.72/21.91 inference(quant_inst,[status(thm)],[])).
% 21.72/21.91 tff(526,plain,
% 21.72/21.91 (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, a)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), mult(a, a)), rd(mult(b, c), mult(a, c))))),
% 21.72/21.91 inference(unit_resolution,[status(thm)],[525, 56])).
% 21.72/21.91 tff(527,plain,
% 21.72/21.91 (mult(a, mult(mult(rd(mult(b, c), mult(a, c)), mult(a, a)), rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, a)), rd(mult(b, c), mult(a, c)))),
% 21.72/21.91 inference(symmetry,[status(thm)],[526])).
% 21.72/21.91 tff(528,plain,
% 21.72/21.91 (mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, a), unit)) = mult(rd(mult(b, c), mult(a, c)), a)),
% 21.72/21.91 inference(monotonicity,[status(thm)],[507])).
% 21.72/21.91 tff(529,plain,
% 21.72/21.91 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(rd(mult(b, c), mult(a, c)), unit), a), unit) = mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, a), unit)))),
% 21.72/21.91 inference(quant_inst,[status(thm)],[])).
% 21.72/21.91 tff(530,plain,
% 21.72/21.91 (mult(mult(mult(rd(mult(b, c), mult(a, c)), unit), a), unit) = mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, a), unit))),
% 21.72/21.91 inference(unit_resolution,[status(thm)],[529, 56])).
% 21.72/21.91 tff(531,plain,
% 21.72/21.91 ((~![A: $i] : (mult(A, unit) = A)) | (mult(rd(mult(b, c), mult(a, c)), unit) = rd(mult(b, c), mult(a, c)))),
% 21.72/21.91 inference(quant_inst,[status(thm)],[])).
% 21.72/21.91 tff(532,plain,
% 21.72/21.91 (mult(rd(mult(b, c), mult(a, c)), unit) = rd(mult(b, c), mult(a, c))),
% 21.72/21.91 inference(unit_resolution,[status(thm)],[531, 43])).
% 21.72/21.91 tff(533,plain,
% 21.72/21.91 (mult(mult(rd(mult(b, c), mult(a, c)), unit), a) = mult(rd(mult(b, c), mult(a, c)), a)),
% 21.72/21.91 inference(monotonicity,[status(thm)],[532])).
% 21.72/21.91 tff(534,plain,
% 21.72/21.91 (mult(rd(mult(b, c), mult(a, c)), a) = mult(mult(rd(mult(b, c), mult(a, c)), unit), a)),
% 21.72/21.91 inference(symmetry,[status(thm)],[533])).
% 21.72/21.91 tff(535,plain,
% 21.72/21.91 (mult(mult(rd(mult(b, c), mult(a, c)), a), unit) = mult(mult(mult(rd(mult(b, c), mult(a, c)), unit), a), unit)),
% 21.72/21.91 inference(monotonicity,[status(thm)],[534])).
% 21.72/21.91 tff(536,plain,
% 21.72/21.91 (mult(mult(rd(mult(b, c), mult(a, c)), a), unit) = b),
% 21.72/21.91 inference(transitivity,[status(thm)],[535, 530, 528, 175, 172, 170])).
% 21.72/21.91 tff(537,plain,
% 21.72/21.91 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), unit), a) = mult(b, a)),
% 21.72/21.91 inference(monotonicity,[status(thm)],[536])).
% 21.72/21.91 tff(538,plain,
% 21.72/21.91 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), unit), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, unit), a)))),
% 21.72/21.91 inference(quant_inst,[status(thm)],[])).
% 21.72/21.91 tff(539,plain,
% 21.72/21.91 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), unit), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, unit), a))),
% 21.72/21.91 inference(unit_resolution,[status(thm)],[538, 56])).
% 21.72/21.91 tff(540,plain,
% 21.72/21.91 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, unit), a)) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), unit), a)),
% 21.72/21.91 inference(symmetry,[status(thm)],[539])).
% 21.72/21.91 tff(541,plain,
% 21.72/21.91 (mult(rd(mult(b, c), mult(a, c)), mult(a, a)) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, unit), a))),
% 21.72/21.91 inference(monotonicity,[status(thm)],[520])).
% 21.72/21.91 tff(542,plain,
% 21.72/21.91 (mult(rd(mult(b, c), mult(a, c)), mult(a, a)) = mult(b, a)),
% 21.72/21.91 inference(transitivity,[status(thm)],[541, 540, 537])).
% 21.72/21.91 tff(543,plain,
% 21.72/21.91 (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, a)), rd(mult(b, c), mult(a, c))) = mult(mult(b, a), rd(mult(b, c), mult(a, c)))),
% 21.72/21.91 inference(monotonicity,[status(thm)],[542])).
% 21.72/21.91 tff(544,plain,
% 21.72/21.91 (mult(mult(b, a), rd(mult(b, c), mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, a)), rd(mult(b, c), mult(a, c)))),
% 21.72/21.91 inference(symmetry,[status(thm)],[543])).
% 21.72/21.91 tff(545,plain,
% 21.72/21.91 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a), a) = mult(mult(b, a), rd(mult(b, c), mult(a, c))))),
% 21.72/21.91 inference(quant_inst,[status(thm)],[])).
% 21.72/21.91 tff(546,plain,
% 21.72/21.91 (rd(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a), a) = mult(mult(b, a), rd(mult(b, c), mult(a, c)))),
% 21.72/21.91 inference(unit_resolution,[status(thm)],[545, 168])).
% 21.72/21.91 tff(547,plain,
% 21.72/21.91 (mult(b, mult(b, a)) = mult(mult(b, b), a)),
% 21.72/21.91 inference(symmetry,[status(thm)],[423])).
% 21.72/21.91 tff(548,plain,
% 21.72/21.91 (mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(unit, mult(mult(b, unit), b)), a)),
% 21.72/21.91 inference(transitivity,[status(thm)],[469, 474, 547, 434])).
% 21.72/21.91 tff(549,plain,
% 21.72/21.91 (rd(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a), a) = rd(mult(mult(unit, mult(mult(b, unit), b)), a), a)),
% 21.72/21.91 inference(monotonicity,[status(thm)],[548])).
% 21.72/21.91 tff(550,plain,
% 21.72/21.91 (rd(mult(mult(unit, mult(mult(b, unit), b)), a), a) = rd(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a), a)),
% 21.72/21.91 inference(symmetry,[status(thm)],[549])).
% 21.72/21.91 tff(551,plain,
% 21.72/21.91 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(unit, mult(mult(b, unit), b)), a), a) = mult(unit, mult(mult(b, unit), b)))),
% 21.72/21.91 inference(quant_inst,[status(thm)],[])).
% 21.72/21.91 tff(552,plain,
% 21.72/21.91 (rd(mult(mult(unit, mult(mult(b, unit), b)), a), a) = mult(unit, mult(mult(b, unit), b))),
% 21.72/21.91 inference(unit_resolution,[status(thm)],[551, 168])).
% 21.72/21.91 tff(553,plain,
% 21.72/21.91 (mult(unit, mult(mult(b, unit), b)) = rd(mult(mult(unit, mult(mult(b, unit), b)), a), a)),
% 21.72/21.91 inference(symmetry,[status(thm)],[552])).
% 21.72/21.91 tff(554,plain,
% 21.72/21.91 (mult(mult(b, unit), b) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, a)), rd(mult(b, c), mult(a, c)))),
% 21.72/21.91 inference(transitivity,[status(thm)],[430, 553, 550, 546, 544])).
% 21.72/21.91 tff(555,plain,
% 21.72/21.91 (mult(mult(unit, a), mult(mult(b, unit), b)) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), mult(a, a)), rd(mult(b, c), mult(a, c))))),
% 21.72/21.91 inference(monotonicity,[status(thm)],[244, 554])).
% 21.72/21.91 tff(556,plain,
% 21.72/21.91 (mult(a, mult(mult(b, unit), b)) = mult(mult(unit, a), mult(mult(b, unit), b))),
% 21.72/21.91 inference(monotonicity,[status(thm)],[245])).
% 21.72/21.91 tff(557,plain,
% 21.72/21.91 (mult(mult(mult(a, unit), b), unit) = mult(mult(a, b), unit)),
% 21.72/21.91 inference(symmetry,[status(thm)],[195])).
% 21.72/21.91 tff(558,plain,
% 21.72/21.91 (mult(a, b) = mult(mult(a, b), unit)),
% 21.72/21.91 inference(transitivity,[status(thm)],[193, 192, 557])).
% 21.72/21.91 tff(559,plain,
% 21.72/21.91 (mult(mult(a, b), b) = mult(mult(mult(a, b), unit), b)),
% 21.72/21.91 inference(monotonicity,[status(thm)],[558])).
% 21.72/21.91 tff(560,plain,
% 21.72/21.91 (mult(mult(a, b), b) = mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a)),
% 21.72/21.91 inference(transitivity,[status(thm)],[559, 439, 556, 555, 527, 524, 504])).
% 21.72/21.91 tff(561,plain,
% 21.72/21.91 (mult(mult(a, c), mult(mult(a, b), b)) = mult(mult(a, c), mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a))),
% 21.72/21.91 inference(monotonicity,[status(thm)],[560])).
% 21.72/21.91 tff(562,assumption,(mult(mult(a, c), mult(b, mult(a, b))) = mult(mult(a, c), mult(mult(a, b), b))), introduced(assumption)).
% 21.72/21.91 tff(563,plain,
% 21.72/21.91 (mult(mult(a, c), mult(b, mult(a, b))) = mult(mult(a, c), mult(unit, mult(mult(mult(b, unit), b), a)))),
% 21.72/21.91 inference(transitivity,[status(thm)],[562, 561, 478])).
% 21.72/21.91 tff(564,plain,
% 21.72/21.91 (ld(mult(a, c), mult(mult(a, c), mult(b, mult(a, b)))) = ld(mult(a, c), mult(mult(a, c), mult(unit, mult(mult(mult(b, unit), b), a))))),
% 21.72/21.91 inference(monotonicity,[status(thm)],[563])).
% 21.72/21.91 tff(565,plain,
% 21.72/21.91 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(a, c), mult(mult(a, c), mult(b, mult(a, b)))) = mult(b, mult(a, b)))),
% 21.72/21.91 inference(quant_inst,[status(thm)],[])).
% 21.72/21.91 tff(566,plain,
% 21.72/21.91 (ld(mult(a, c), mult(mult(a, c), mult(b, mult(a, b)))) = mult(b, mult(a, b))),
% 21.72/21.91 inference(unit_resolution,[status(thm)],[565, 7])).
% 21.72/21.91 tff(567,plain,
% 21.72/21.91 (mult(b, mult(a, b)) = ld(mult(a, c), mult(mult(a, c), mult(b, mult(a, b))))),
% 21.72/21.91 inference(symmetry,[status(thm)],[566])).
% 21.72/21.91 tff(568,plain,
% 21.72/21.91 (mult(b, mult(a, b)) = mult(b, mult(b, a))),
% 21.72/21.91 inference(transitivity,[status(thm)],[567, 564, 467, 466, 435, 423])).
% 21.72/21.91 tff(569,plain,
% 21.72/21.91 ($false),
% 21.72/21.91 inference(unit_resolution,[status(thm)],[412, 568])).
% 21.72/21.91 tff(570,plain,((~(ld(mult(a, c), mult(mult(a, c), mult(unit, mult(mult(mult(b, unit), b), a)))) = mult(unit, mult(mult(mult(b, unit), b), a)))) | (mult(b, mult(a, b)) = mult(b, mult(b, a))) | (~(mult(mult(a, c), mult(b, mult(a, b))) = mult(mult(a, c), mult(mult(a, b), b)))) | (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit)))))), inference(lemma,lemma(discharge,[]))).
% 21.72/21.91 tff(571,plain,
% 21.72/21.91 ((mult(b, mult(a, b)) = mult(b, mult(b, a))) | (~(mult(mult(a, c), mult(b, mult(a, b))) = mult(mult(a, c), mult(mult(a, b), b)))) | (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit)))))),
% 21.72/21.91 inference(unit_resolution,[status(thm)],[570, 427])).
% 21.72/21.91 tff(572,plain,
% 21.72/21.91 (~(mult(mult(a, c), mult(b, mult(a, b))) = mult(mult(a, c), mult(mult(a, b), b)))),
% 21.72/21.91 inference(unit_resolution,[status(thm)],[571, 412, 359, 97])).
% 21.72/21.91 tff(573,plain,
% 21.72/21.91 ((mult(mult(mult(a, c), mult(a, b)), b) = mult(mult(mult(a, c), b), mult(a, b))) <=> (mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(mult(a, c), mult(a, b)), b))),
% 21.72/21.91 inference(commutativity,[status(thm)],[])).
% 21.72/21.91 tff(574,plain,
% 21.72/21.91 (mult(mult(mult(a, b), c), mult(a, b)) = mult(mult(mult(a, c), b), mult(a, b))),
% 21.72/21.91 inference(monotonicity,[status(thm)],[227])).
% 21.72/21.91 tff(575,assumption,(~(mult(mult(a, c), mult(b, mult(a, b))) = mult(mult(a, c), mult(mult(a, b), b)))), introduced(assumption)).
% 21.72/21.91 tff(576,plain,
% 21.72/21.91 (((~(mult(mult(a, c), mult(b, mult(a, b))) = mult(mult(a, c), mult(mult(a, b), b)))) | (~(mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(mult(a, c), mult(a, b)), b)))) | (mult(mult(a, c), mult(b, mult(a, b))) = mult(mult(a, c), mult(mult(a, b), b)))),
% 21.72/21.91 inference(tautology,[status(thm)],[])).
% 21.72/21.91 tff(577,plain,
% 21.72/21.91 ((~(mult(mult(a, c), mult(b, mult(a, b))) = mult(mult(a, c), mult(mult(a, b), b)))) | (~(mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(mult(a, c), mult(a, b)), b)))),
% 21.72/21.91 inference(unit_resolution,[status(thm)],[576, 575])).
% 21.72/21.91 tff(578,plain,
% 21.72/21.91 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, c), mult(b, mult(a, b))) = mult(mult(a, c), mult(mult(a, b), b)))) | (~(mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(mult(a, c), mult(a, b)), b))))) | (~((~(mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(a, c), mult(b, mult(a, b))))) | (~(mult(mult(mult(a, c), mult(a, b)), b) = mult(mult(a, c), mult(mult(a, b), b)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, c), mult(b, mult(a, b))) = mult(mult(a, c), mult(mult(a, b), b)))) | (~(mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(mult(a, c), mult(a, b)), b))))) | (~((~(mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(a, c), mult(b, mult(a, b))))) | (~(mult(mult(mult(a, c), mult(a, b)), b) = mult(mult(a, c), mult(mult(a, b), b)))))))),
% 21.72/21.91 inference(rewrite,[status(thm)],[])).
% 21.72/21.91 tff(579,plain,
% 21.72/21.91 (((~((~(mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(mult(a, c), mult(a, b)), b))) | (~(mult(mult(a, c), mult(b, mult(a, b))) = mult(mult(a, c), mult(mult(a, b), b)))))) | (~((~(mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(a, c), mult(b, mult(a, b))))) | (~(mult(mult(mult(a, c), mult(a, b)), b) = mult(mult(a, c), mult(mult(a, b), b))))))) <=> ((~((~(mult(mult(a, c), mult(b, mult(a, b))) = mult(mult(a, c), mult(mult(a, b), b)))) | (~(mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(mult(a, c), mult(a, b)), b))))) | (~((~(mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(a, c), mult(b, mult(a, b))))) | (~(mult(mult(mult(a, c), mult(a, b)), b) = mult(mult(a, c), mult(mult(a, b), b)))))))),
% 21.72/21.91 inference(rewrite,[status(thm)],[])).
% 21.72/21.91 tff(580,plain,
% 21.72/21.91 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(mult(a, c), mult(a, b)), b))) | (~(mult(mult(a, c), mult(b, mult(a, b))) = mult(mult(a, c), mult(mult(a, b), b)))))) | (~((~(mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(a, c), mult(b, mult(a, b))))) | (~(mult(mult(mult(a, c), mult(a, b)), b) = mult(mult(a, c), mult(mult(a, b), b)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, c), mult(b, mult(a, b))) = mult(mult(a, c), mult(mult(a, b), b)))) | (~(mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(mult(a, c), mult(a, b)), b))))) | (~((~(mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(a, c), mult(b, mult(a, b))))) | (~(mult(mult(mult(a, c), mult(a, b)), b) = mult(mult(a, c), mult(mult(a, b), b))))))))),
% 21.72/21.91 inference(monotonicity,[status(thm)],[579])).
% 21.72/21.91 tff(581,plain,
% 21.72/21.91 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(mult(a, c), mult(a, b)), b))) | (~(mult(mult(a, c), mult(b, mult(a, b))) = mult(mult(a, c), mult(mult(a, b), b)))))) | (~((~(mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(a, c), mult(b, mult(a, b))))) | (~(mult(mult(mult(a, c), mult(a, b)), b) = mult(mult(a, c), mult(mult(a, b), b)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, c), mult(b, mult(a, b))) = mult(mult(a, c), mult(mult(a, b), b)))) | (~(mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(mult(a, c), mult(a, b)), b))))) | (~((~(mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(a, c), mult(b, mult(a, b))))) | (~(mult(mult(mult(a, c), mult(a, b)), b) = mult(mult(a, c), mult(mult(a, b), b)))))))),
% 21.72/21.91 inference(transitivity,[status(thm)],[580, 578])).
% 21.72/21.91 tff(582,plain,
% 21.72/21.91 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(mult(a, c), mult(a, b)), b))) | (~(mult(mult(a, c), mult(b, mult(a, b))) = mult(mult(a, c), mult(mult(a, b), b)))))) | (~((~(mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(a, c), mult(b, mult(a, b))))) | (~(mult(mult(mult(a, c), mult(a, b)), b) = mult(mult(a, c), mult(mult(a, b), b)))))))),
% 21.72/21.92 inference(quant_inst,[status(thm)],[])).
% 21.72/21.92 tff(583,plain,
% 21.72/21.92 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, c), mult(b, mult(a, b))) = mult(mult(a, c), mult(mult(a, b), b)))) | (~(mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(mult(a, c), mult(a, b)), b))))) | (~((~(mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(a, c), mult(b, mult(a, b))))) | (~(mult(mult(mult(a, c), mult(a, b)), b) = mult(mult(a, c), mult(mult(a, b), b))))))),
% 21.72/21.92 inference(modus_ponens,[status(thm)],[582, 581])).
% 21.72/21.92 tff(584,plain,
% 21.72/21.92 ((~((~(mult(mult(a, c), mult(b, mult(a, b))) = mult(mult(a, c), mult(mult(a, b), b)))) | (~(mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(mult(a, c), mult(a, b)), b))))) | (~((~(mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(a, c), mult(b, mult(a, b))))) | (~(mult(mult(mult(a, c), mult(a, b)), b) = mult(mult(a, c), mult(mult(a, b), b))))))),
% 21.72/21.92 inference(unit_resolution,[status(thm)],[583, 27])).
% 21.72/21.92 tff(585,plain,
% 21.72/21.92 (~((~(mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(a, c), mult(b, mult(a, b))))) | (~(mult(mult(mult(a, c), mult(a, b)), b) = mult(mult(a, c), mult(mult(a, b), b)))))),
% 21.72/21.92 inference(unit_resolution,[status(thm)],[584, 577])).
% 21.72/21.92 tff(586,plain,
% 21.72/21.92 (((~(mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(a, c), mult(b, mult(a, b))))) | (~(mult(mult(mult(a, c), mult(a, b)), b) = mult(mult(a, c), mult(mult(a, b), b))))) | (mult(mult(mult(a, c), mult(a, b)), b) = mult(mult(a, c), mult(mult(a, b), b)))),
% 21.72/21.92 inference(tautology,[status(thm)],[])).
% 21.72/21.92 tff(587,plain,
% 21.72/21.92 (mult(mult(mult(a, c), mult(a, b)), b) = mult(mult(a, c), mult(mult(a, b), b))),
% 21.72/21.92 inference(unit_resolution,[status(thm)],[586, 585])).
% 21.72/21.92 tff(588,plain,
% 21.72/21.92 (mult(mult(a, c), mult(mult(a, b), b)) = mult(mult(mult(a, c), mult(a, b)), b)),
% 21.72/21.92 inference(symmetry,[status(thm)],[587])).
% 21.72/21.92 tff(589,assumption,(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c)))), introduced(assumption)).
% 21.72/21.92 tff(590,plain,
% 21.72/21.92 (mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a)),
% 21.72/21.92 inference(symmetry,[status(thm)],[589])).
% 21.72/21.92 tff(591,assumption,(mult(mult(b, b), a) = mult(b, mult(b, a))), introduced(assumption)).
% 21.72/21.92 tff(592,plain,
% 21.72/21.92 (mult(b, mult(b, a)) = mult(mult(b, b), a)),
% 21.72/21.92 inference(symmetry,[status(thm)],[591])).
% 21.72/21.92 tff(593,plain,
% 21.72/21.92 (mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(unit, mult(mult(b, unit), b)), a)),
% 21.72/21.92 inference(transitivity,[status(thm)],[469, 474, 592, 434])).
% 21.72/21.92 tff(594,plain,
% 21.72/21.92 (rd(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a), a) = rd(mult(mult(unit, mult(mult(b, unit), b)), a), a)),
% 21.72/21.92 inference(monotonicity,[status(thm)],[593])).
% 21.72/21.92 tff(595,plain,
% 21.72/21.92 (rd(mult(mult(unit, mult(mult(b, unit), b)), a), a) = rd(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a), a)),
% 21.72/21.92 inference(symmetry,[status(thm)],[594])).
% 21.72/21.92 tff(596,plain,
% 21.72/21.92 (mult(mult(b, unit), b) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, a)), rd(mult(b, c), mult(a, c)))),
% 21.72/21.92 inference(transitivity,[status(thm)],[430, 553, 595, 546, 544])).
% 21.72/21.92 tff(597,plain,
% 21.72/21.92 (mult(mult(unit, a), mult(mult(b, unit), b)) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), mult(a, a)), rd(mult(b, c), mult(a, c))))),
% 21.72/21.92 inference(monotonicity,[status(thm)],[244, 596])).
% 21.72/21.92 tff(598,plain,
% 21.72/21.92 (mult(mult(a, b), b) = mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a)),
% 21.72/21.92 inference(transitivity,[status(thm)],[559, 439, 556, 597, 527, 524, 590])).
% 21.72/21.92 tff(599,plain,
% 21.72/21.92 (mult(mult(a, c), mult(mult(a, b), b)) = mult(mult(a, c), mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a))),
% 21.72/21.92 inference(monotonicity,[status(thm)],[598])).
% 21.72/21.92 tff(600,plain,
% 21.72/21.92 (mult(mult(a, c), mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a)) = mult(mult(a, c), mult(mult(a, b), b))),
% 21.72/21.92 inference(symmetry,[status(thm)],[599])).
% 21.72/21.92 tff(601,plain,
% 21.72/21.92 (mult(b, mult(b, a)) = mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a)),
% 21.72/21.92 inference(transitivity,[status(thm)],[475, 470])).
% 21.72/21.92 tff(602,plain,
% 21.72/21.92 (mult(mult(a, c), mult(b, mult(b, a))) = mult(mult(a, c), mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a))),
% 21.72/21.92 inference(monotonicity,[status(thm)],[601])).
% 21.72/21.92 tff(603,plain,
% 21.72/21.92 (mult(mult(a, c), mult(b, mult(b, a))) = mult(mult(mult(a, c), mult(a, b)), b)),
% 21.72/21.92 inference(transitivity,[status(thm)],[602, 600, 588])).
% 21.72/21.92 tff(604,plain,
% 21.72/21.92 (((~(mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(a, c), mult(b, mult(a, b))))) | (~(mult(mult(mult(a, c), mult(a, b)), b) = mult(mult(a, c), mult(mult(a, b), b))))) | (mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(a, c), mult(b, mult(a, b))))),
% 21.72/21.92 inference(tautology,[status(thm)],[])).
% 21.72/21.92 tff(605,plain,
% 21.72/21.92 (mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(a, c), mult(b, mult(a, b)))),
% 21.72/21.92 inference(unit_resolution,[status(thm)],[604, 585])).
% 21.72/21.92 tff(606,plain,
% 21.72/21.92 (mult(mult(a, c), mult(b, mult(a, b))) = mult(mult(mult(a, c), b), mult(a, b))),
% 21.72/21.92 inference(symmetry,[status(thm)],[605])).
% 21.72/21.92 tff(607,assumption,(mult(mult(b, a), b) = mult(b, mult(a, b))), introduced(assumption)).
% 21.72/21.92 tff(608,plain,
% 21.72/21.92 (mult(mult(a, c), mult(mult(b, a), b)) = mult(mult(a, c), mult(b, mult(a, b)))),
% 21.72/21.92 inference(monotonicity,[status(thm)],[607])).
% 21.72/21.92 tff(609,plain,
% 21.72/21.92 (mult(mult(a, c), mult(mult(b, a), b)) = mult(mult(mult(a, c), b), mult(a, b))),
% 21.72/21.92 inference(transitivity,[status(thm)],[608, 606])).
% 21.72/21.92 tff(610,plain,
% 21.72/21.92 ((mult(mult(a, c), mult(mult(b, a), b)) = mult(mult(a, c), mult(b, mult(b, a)))) <=> (mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(mult(a, c), mult(a, b)), b))),
% 21.72/21.92 inference(monotonicity,[status(thm)],[609, 603])).
% 21.72/21.92 tff(611,plain,
% 21.72/21.92 ((mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(mult(a, c), mult(a, b)), b)) <=> (mult(mult(a, c), mult(mult(b, a), b)) = mult(mult(a, c), mult(b, mult(b, a))))),
% 21.72/21.92 inference(symmetry,[status(thm)],[610])).
% 21.72/21.92 tff(612,plain,
% 21.72/21.92 ((~(mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(mult(a, c), mult(a, b)), b))) <=> (~(mult(mult(a, c), mult(mult(b, a), b)) = mult(mult(a, c), mult(b, mult(b, a)))))),
% 21.72/21.92 inference(monotonicity,[status(thm)],[611])).
% 21.72/21.92 tff(613,plain,
% 21.72/21.92 ((mult(mult(a, c), mult(b, mult(a, b))) = mult(mult(a, c), mult(mult(a, b), b))) <=> (mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(mult(a, c), mult(a, b)), b))),
% 21.72/21.92 inference(monotonicity,[status(thm)],[606, 588])).
% 21.72/21.92 tff(614,plain,
% 21.72/21.92 ((~(mult(mult(a, c), mult(b, mult(a, b))) = mult(mult(a, c), mult(mult(a, b), b)))) <=> (~(mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(mult(a, c), mult(a, b)), b)))),
% 21.72/21.92 inference(monotonicity,[status(thm)],[613])).
% 21.72/21.92 tff(615,plain,
% 21.72/21.92 (~(mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(mult(a, c), mult(a, b)), b))),
% 21.72/21.92 inference(modus_ponens,[status(thm)],[575, 614])).
% 21.72/21.92 tff(616,plain,
% 21.72/21.92 (~(mult(mult(a, c), mult(mult(b, a), b)) = mult(mult(a, c), mult(b, mult(b, a))))),
% 21.72/21.92 inference(modus_ponens,[status(thm)],[615, 612])).
% 21.72/21.92 tff(617,plain,
% 21.72/21.92 (((~(mult(mult(mult(a, c), mult(b, a)), b) = mult(mult(mult(a, c), b), mult(b, a)))) | (~(mult(mult(a, c), mult(mult(b, a), b)) = mult(mult(a, c), mult(b, mult(b, a)))))) | (mult(mult(a, c), mult(mult(b, a), b)) = mult(mult(a, c), mult(b, mult(b, a))))),
% 21.72/21.92 inference(tautology,[status(thm)],[])).
% 21.72/21.92 tff(618,plain,
% 21.72/21.92 ((~(mult(mult(mult(a, c), mult(b, a)), b) = mult(mult(mult(a, c), b), mult(b, a)))) | (~(mult(mult(a, c), mult(mult(b, a), b)) = mult(mult(a, c), mult(b, mult(b, a)))))),
% 21.72/21.92 inference(unit_resolution,[status(thm)],[617, 616])).
% 21.72/21.92 tff(619,plain,
% 21.72/21.92 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, c), mult(b, a)), b) = mult(mult(mult(a, c), b), mult(b, a)))) | (~(mult(mult(a, c), mult(mult(b, a), b)) = mult(mult(a, c), mult(b, mult(b, a))))))) | (~((~(mult(mult(mult(a, c), mult(b, a)), b) = mult(mult(a, c), mult(mult(b, a), b)))) | (~(mult(mult(mult(a, c), b), mult(b, a)) = mult(mult(a, c), mult(b, mult(b, a))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(a, c), mult(b, a)), b) = mult(mult(mult(a, c), b), mult(b, a)))) | (~(mult(mult(a, c), mult(mult(b, a), b)) = mult(mult(a, c), mult(b, mult(b, a))))))) | (~((~(mult(mult(mult(a, c), mult(b, a)), b) = mult(mult(a, c), mult(mult(b, a), b)))) | (~(mult(mult(mult(a, c), b), mult(b, a)) = mult(mult(a, c), mult(b, mult(b, a))))))))),
% 21.72/21.92 inference(rewrite,[status(thm)],[])).
% 21.72/21.92 tff(620,plain,
% 21.72/21.92 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, c), mult(b, a)), b) = mult(mult(mult(a, c), b), mult(b, a)))) | (~(mult(mult(a, c), mult(mult(b, a), b)) = mult(mult(a, c), mult(b, mult(b, a))))))) | (~((~(mult(mult(mult(a, c), mult(b, a)), b) = mult(mult(a, c), mult(mult(b, a), b)))) | (~(mult(mult(mult(a, c), b), mult(b, a)) = mult(mult(a, c), mult(b, mult(b, a))))))))),
% 21.72/21.92 inference(quant_inst,[status(thm)],[])).
% 21.72/21.92 tff(621,plain,
% 21.72/21.92 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(a, c), mult(b, a)), b) = mult(mult(mult(a, c), b), mult(b, a)))) | (~(mult(mult(a, c), mult(mult(b, a), b)) = mult(mult(a, c), mult(b, mult(b, a))))))) | (~((~(mult(mult(mult(a, c), mult(b, a)), b) = mult(mult(a, c), mult(mult(b, a), b)))) | (~(mult(mult(mult(a, c), b), mult(b, a)) = mult(mult(a, c), mult(b, mult(b, a)))))))),
% 21.72/21.92 inference(modus_ponens,[status(thm)],[620, 619])).
% 21.72/21.92 tff(622,plain,
% 21.72/21.92 ((~((~(mult(mult(mult(a, c), mult(b, a)), b) = mult(mult(mult(a, c), b), mult(b, a)))) | (~(mult(mult(a, c), mult(mult(b, a), b)) = mult(mult(a, c), mult(b, mult(b, a))))))) | (~((~(mult(mult(mult(a, c), mult(b, a)), b) = mult(mult(a, c), mult(mult(b, a), b)))) | (~(mult(mult(mult(a, c), b), mult(b, a)) = mult(mult(a, c), mult(b, mult(b, a)))))))),
% 21.72/21.92 inference(unit_resolution,[status(thm)],[621, 27])).
% 21.72/21.92 tff(623,plain,
% 21.72/21.92 (~((~(mult(mult(mult(a, c), mult(b, a)), b) = mult(mult(a, c), mult(mult(b, a), b)))) | (~(mult(mult(mult(a, c), b), mult(b, a)) = mult(mult(a, c), mult(b, mult(b, a))))))),
% 21.72/21.92 inference(unit_resolution,[status(thm)],[622, 618])).
% 21.72/21.92 tff(624,plain,
% 21.72/21.92 (((~(mult(mult(mult(a, c), mult(b, a)), b) = mult(mult(a, c), mult(mult(b, a), b)))) | (~(mult(mult(mult(a, c), b), mult(b, a)) = mult(mult(a, c), mult(b, mult(b, a)))))) | (mult(mult(mult(a, c), b), mult(b, a)) = mult(mult(a, c), mult(b, mult(b, a))))),
% 21.72/21.92 inference(tautology,[status(thm)],[])).
% 21.72/21.92 tff(625,plain,
% 21.72/21.92 (mult(mult(mult(a, c), b), mult(b, a)) = mult(mult(a, c), mult(b, mult(b, a)))),
% 21.72/21.92 inference(unit_resolution,[status(thm)],[624, 623])).
% 21.72/21.92 tff(626,plain,
% 21.72/21.92 (mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, c), b), mult(b, a))),
% 21.72/21.92 inference(monotonicity,[status(thm)],[227])).
% 21.72/21.92 tff(627,plain,
% 21.72/21.92 (mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, c), mult(a, b)), b)),
% 21.72/21.92 inference(transitivity,[status(thm)],[626, 625, 602, 600, 588])).
% 21.72/21.92 tff(628,plain,
% 21.72/21.92 ((mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(a, b))) <=> (mult(mult(mult(a, c), mult(a, b)), b) = mult(mult(mult(a, c), b), mult(a, b)))),
% 21.72/21.92 inference(monotonicity,[status(thm)],[627, 574])).
% 21.72/21.92 tff(629,plain,
% 21.72/21.92 ((mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(a, b))) <=> (mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(mult(a, c), mult(a, b)), b))),
% 21.72/21.92 inference(transitivity,[status(thm)],[628, 573])).
% 21.72/21.92 tff(630,plain,
% 21.72/21.92 ((mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(mult(a, c), mult(a, b)), b)) <=> (mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(a, b)))),
% 21.72/21.92 inference(symmetry,[status(thm)],[629])).
% 21.72/21.92 tff(631,plain,
% 21.72/21.92 ((~(mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(mult(a, c), mult(a, b)), b))) <=> (~(mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(a, b))))),
% 21.72/21.92 inference(monotonicity,[status(thm)],[630])).
% 21.72/21.92 tff(632,plain,
% 21.72/21.92 (~(mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(a, b)))),
% 21.72/21.92 inference(modus_ponens,[status(thm)],[615, 631])).
% 21.72/21.92 tff(633,assumption,(mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(a, b))), introduced(assumption)).
% 21.72/21.92 tff(634,plain,
% 21.72/21.92 ($false),
% 21.72/21.92 inference(unit_resolution,[status(thm)],[633, 632])).
% 21.72/21.92 tff(635,plain,((mult(mult(a, c), mult(b, mult(a, b))) = mult(mult(a, c), mult(mult(a, b), b))) | (~(mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(a, b)))) | (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit))))) | (~(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c))))) | (~(mult(mult(b, b), a) = mult(b, mult(b, a)))) | (~(mult(mult(b, a), b) = mult(b, mult(a, b))))), inference(lemma,lemma(discharge,[]))).
% 21.72/21.92 tff(636,plain,
% 21.72/21.92 (~(mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(a, b)))),
% 21.72/21.92 inference(unit_resolution,[status(thm)],[635, 503, 359, 97, 572, 423, 421])).
% 21.72/21.92 tff(637,plain,
% 21.72/21.92 (((~(mult(mult(mult(mult(a, b), c), b), a) = mult(mult(mult(mult(a, b), c), a), b))) | (~(mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(a, b))))) | (mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(a, b)))),
% 21.72/21.92 inference(tautology,[status(thm)],[])).
% 21.72/21.92 tff(638,plain,
% 21.72/21.92 ((~(mult(mult(mult(mult(a, b), c), b), a) = mult(mult(mult(mult(a, b), c), a), b))) | (~(mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(a, b))))),
% 21.72/21.92 inference(unit_resolution,[status(thm)],[637, 636])).
% 21.72/21.92 tff(639,plain,
% 21.72/21.92 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(mult(a, b), c), b), a) = mult(mult(mult(mult(a, b), c), a), b))) | (~(mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(a, b)))))) | (~((~(mult(mult(mult(mult(a, b), c), b), a) = mult(mult(mult(a, b), c), mult(b, a)))) | (~(mult(mult(mult(mult(a, b), c), a), b) = mult(mult(mult(a, b), c), mult(a, b)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(mult(a, b), c), b), a) = mult(mult(mult(mult(a, b), c), a), b))) | (~(mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(a, b)))))) | (~((~(mult(mult(mult(mult(a, b), c), b), a) = mult(mult(mult(a, b), c), mult(b, a)))) | (~(mult(mult(mult(mult(a, b), c), a), b) = mult(mult(mult(a, b), c), mult(a, b)))))))),
% 21.72/21.92 inference(rewrite,[status(thm)],[])).
% 21.72/21.92 tff(640,plain,
% 21.72/21.92 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(mult(a, b), c), b), a) = mult(mult(mult(mult(a, b), c), a), b))) | (~(mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(a, b)))))) | (~((~(mult(mult(mult(mult(a, b), c), b), a) = mult(mult(mult(a, b), c), mult(b, a)))) | (~(mult(mult(mult(mult(a, b), c), a), b) = mult(mult(mult(a, b), c), mult(a, b)))))))),
% 21.72/21.93 inference(quant_inst,[status(thm)],[])).
% 21.72/21.93 tff(641,plain,
% 21.72/21.93 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(mult(a, b), c), b), a) = mult(mult(mult(mult(a, b), c), a), b))) | (~(mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(a, b)))))) | (~((~(mult(mult(mult(mult(a, b), c), b), a) = mult(mult(mult(a, b), c), mult(b, a)))) | (~(mult(mult(mult(mult(a, b), c), a), b) = mult(mult(mult(a, b), c), mult(a, b))))))),
% 21.72/21.93 inference(modus_ponens,[status(thm)],[640, 639])).
% 21.72/21.93 tff(642,plain,
% 21.72/21.93 ((~((~(mult(mult(mult(mult(a, b), c), b), a) = mult(mult(mult(mult(a, b), c), a), b))) | (~(mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(a, b)))))) | (~((~(mult(mult(mult(mult(a, b), c), b), a) = mult(mult(mult(a, b), c), mult(b, a)))) | (~(mult(mult(mult(mult(a, b), c), a), b) = mult(mult(mult(a, b), c), mult(a, b))))))),
% 21.72/21.93 inference(unit_resolution,[status(thm)],[641, 27])).
% 21.72/21.93 tff(643,plain,
% 21.72/21.93 (~((~(mult(mult(mult(mult(a, b), c), b), a) = mult(mult(mult(a, b), c), mult(b, a)))) | (~(mult(mult(mult(mult(a, b), c), a), b) = mult(mult(mult(a, b), c), mult(a, b)))))),
% 21.72/21.93 inference(unit_resolution,[status(thm)],[642, 638])).
% 21.72/21.93 tff(644,plain,
% 21.72/21.93 (((~(mult(mult(mult(mult(a, b), c), b), a) = mult(mult(mult(a, b), c), mult(b, a)))) | (~(mult(mult(mult(mult(a, b), c), a), b) = mult(mult(mult(a, b), c), mult(a, b))))) | (mult(mult(mult(mult(a, b), c), b), a) = mult(mult(mult(a, b), c), mult(b, a)))),
% 21.72/21.93 inference(tautology,[status(thm)],[])).
% 21.72/21.93 tff(645,plain,
% 21.72/21.93 (mult(mult(mult(mult(a, b), c), b), a) = mult(mult(mult(a, b), c), mult(b, a))),
% 21.72/21.93 inference(unit_resolution,[status(thm)],[644, 643])).
% 21.72/21.93 tff(646,plain,
% 21.72/21.93 (mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(mult(a, b), c), b), a)),
% 21.72/21.93 inference(symmetry,[status(thm)],[645])).
% 21.72/21.93 tff(647,plain,
% 21.72/21.93 (mult(mult(mult(a, b), c), mult(mult(a, rd(mult(b, c), mult(a, c))), a)) = mult(mult(mult(a, b), c), mult(b, a))),
% 21.72/21.93 inference(monotonicity,[status(thm)],[473])).
% 21.72/21.93 tff(648,plain,
% 21.72/21.93 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(mult(a, b), c), a), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(a, b), c), mult(mult(a, rd(mult(b, c), mult(a, c))), a)))),
% 21.72/21.93 inference(quant_inst,[status(thm)],[])).
% 21.72/21.93 tff(649,plain,
% 21.72/21.93 (mult(mult(mult(mult(mult(a, b), c), a), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(a, b), c), mult(mult(a, rd(mult(b, c), mult(a, c))), a))),
% 21.72/21.93 inference(unit_resolution,[status(thm)],[648, 56])).
% 21.72/21.93 tff(650,plain,
% 21.72/21.93 (mult(mult(mult(mult(mult(a, b), c), a), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(mult(a, b), c), b), a)),
% 21.72/21.93 inference(transitivity,[status(thm)],[649, 647, 646])).
% 21.72/21.93 tff(651,plain,
% 21.72/21.93 (rd(mult(mult(mult(mult(mult(a, b), c), a), rd(mult(b, c), mult(a, c))), a), a) = rd(mult(mult(mult(mult(a, b), c), b), a), a)),
% 21.72/21.93 inference(monotonicity,[status(thm)],[650])).
% 21.72/21.93 tff(652,plain,
% 21.72/21.93 (rd(mult(mult(mult(mult(a, b), c), b), a), a) = rd(mult(mult(mult(mult(mult(a, b), c), a), rd(mult(b, c), mult(a, c))), a), a)),
% 21.72/21.93 inference(symmetry,[status(thm)],[651])).
% 21.72/21.93 tff(653,plain,
% 21.72/21.93 (mult(mult(mult(a, c), b), mult(b, a)) = mult(mult(mult(a, b), c), mult(b, a))),
% 21.72/21.93 inference(symmetry,[status(thm)],[626])).
% 21.72/21.93 tff(654,plain,
% 21.72/21.93 ((~(mult(mult(a, c), mult(b, mult(a, b))) = mult(mult(a, c), mult(mult(a, b), b)))) | (~(mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(mult(a, c), mult(a, b)), b)))),
% 21.72/21.93 inference(unit_resolution,[status(thm)],[576, 572])).
% 21.72/21.93 tff(655,plain,
% 21.72/21.93 (~((~(mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(a, c), mult(b, mult(a, b))))) | (~(mult(mult(mult(a, c), mult(a, b)), b) = mult(mult(a, c), mult(mult(a, b), b)))))),
% 21.72/21.93 inference(unit_resolution,[status(thm)],[584, 654])).
% 21.72/21.93 tff(656,plain,
% 21.72/21.93 (mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(a, c), mult(b, mult(a, b)))),
% 21.72/21.93 inference(unit_resolution,[status(thm)],[604, 655])).
% 21.72/21.93 tff(657,plain,
% 21.72/21.93 (mult(mult(a, c), mult(b, mult(a, b))) = mult(mult(mult(a, c), b), mult(a, b))),
% 21.72/21.93 inference(symmetry,[status(thm)],[656])).
% 21.72/21.93 tff(658,plain,
% 21.72/21.93 (mult(mult(a, c), mult(mult(b, a), b)) = mult(mult(a, c), mult(b, mult(a, b)))),
% 21.72/21.93 inference(monotonicity,[status(thm)],[421])).
% 21.72/21.93 tff(659,plain,
% 21.72/21.93 (mult(mult(a, c), mult(mult(b, a), b)) = mult(mult(mult(a, c), b), mult(a, b))),
% 21.72/21.93 inference(transitivity,[status(thm)],[658, 657])).
% 21.72/21.93 tff(660,plain,
% 21.72/21.93 (mult(mult(mult(a, c), mult(a, b)), b) = mult(mult(a, c), mult(mult(a, b), b))),
% 21.72/21.93 inference(unit_resolution,[status(thm)],[586, 655])).
% 21.72/21.93 tff(661,plain,
% 21.72/21.93 (mult(mult(a, c), mult(mult(a, b), b)) = mult(mult(mult(a, c), mult(a, b)), b)),
% 21.72/21.93 inference(symmetry,[status(thm)],[660])).
% 21.72/21.93 tff(662,plain,
% 21.72/21.93 (mult(mult(mult(a, b), unit), b) = mult(mult(a, b), b)),
% 21.72/21.93 inference(symmetry,[status(thm)],[559])).
% 21.72/21.93 tff(663,plain,
% 21.72/21.93 (mult(mult(unit, a), mult(mult(b, unit), b)) = mult(a, mult(mult(b, unit), b))),
% 21.72/21.93 inference(symmetry,[status(thm)],[556])).
% 21.72/21.93 tff(664,plain,
% 21.72/21.93 (mult(a, mult(mult(rd(mult(b, c), mult(a, c)), mult(a, a)), rd(mult(b, c), mult(a, c)))) = mult(mult(unit, a), mult(mult(b, unit), b))),
% 21.72/21.93 inference(symmetry,[status(thm)],[555])).
% 21.72/21.93 tff(665,plain,
% 21.72/21.93 (mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, a)), rd(mult(b, c), mult(a, c)))),
% 21.72/21.93 inference(symmetry,[status(thm)],[524])).
% 21.72/21.93 tff(666,plain,
% 21.72/21.93 (mult(unit, mult(mult(mult(b, unit), b), a)) = mult(mult(a, b), b)),
% 21.72/21.93 inference(transitivity,[status(thm)],[466, 435, 423, 475, 470, 503, 665, 526, 664, 663, 445, 662])).
% 21.72/21.93 tff(667,plain,
% 21.72/21.93 (mult(mult(a, c), mult(unit, mult(mult(mult(b, unit), b), a))) = mult(mult(a, c), mult(mult(a, b), b))),
% 21.72/21.93 inference(monotonicity,[status(thm)],[666])).
% 21.72/21.93 tff(668,plain,
% 21.72/21.93 (mult(b, mult(b, a)) = mult(unit, mult(mult(mult(b, unit), b), a))),
% 21.72/21.93 inference(transitivity,[status(thm)],[547, 434, 465])).
% 21.72/21.93 tff(669,plain,
% 21.72/21.93 (mult(mult(a, c), mult(b, mult(b, a))) = mult(mult(a, c), mult(unit, mult(mult(mult(b, unit), b), a)))),
% 21.72/21.93 inference(monotonicity,[status(thm)],[668])).
% 21.72/21.93 tff(670,plain,
% 21.72/21.93 (mult(mult(a, c), mult(b, mult(b, a))) = mult(mult(mult(a, c), mult(a, b)), b)),
% 21.72/21.93 inference(transitivity,[status(thm)],[669, 667, 661])).
% 21.72/21.93 tff(671,plain,
% 21.72/21.93 ((mult(mult(a, c), mult(b, mult(b, a))) = mult(mult(a, c), mult(mult(b, a), b))) <=> (mult(mult(mult(a, c), mult(a, b)), b) = mult(mult(mult(a, c), b), mult(a, b)))),
% 21.72/21.93 inference(monotonicity,[status(thm)],[670, 659])).
% 21.72/21.93 tff(672,plain,
% 21.72/21.93 ((mult(mult(a, c), mult(b, mult(b, a))) = mult(mult(a, c), mult(mult(b, a), b))) <=> (mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(mult(a, c), mult(a, b)), b))),
% 21.72/21.93 inference(transitivity,[status(thm)],[671, 573])).
% 21.72/21.93 tff(673,plain,
% 21.72/21.93 ((mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(mult(a, c), mult(a, b)), b)) <=> (mult(mult(a, c), mult(b, mult(b, a))) = mult(mult(a, c), mult(mult(b, a), b)))),
% 21.72/21.93 inference(symmetry,[status(thm)],[672])).
% 21.72/21.93 tff(674,plain,
% 21.72/21.93 ((~(mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(mult(a, c), mult(a, b)), b))) <=> (~(mult(mult(a, c), mult(b, mult(b, a))) = mult(mult(a, c), mult(mult(b, a), b))))),
% 21.72/21.93 inference(monotonicity,[status(thm)],[673])).
% 21.72/21.93 tff(675,plain,
% 21.72/21.93 ((mult(mult(a, c), mult(b, mult(a, b))) = mult(mult(a, c), mult(mult(a, b), b))) <=> (mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(mult(a, c), mult(a, b)), b))),
% 21.72/21.93 inference(monotonicity,[status(thm)],[657, 661])).
% 21.72/21.93 tff(676,plain,
% 21.72/21.93 ((~(mult(mult(a, c), mult(b, mult(a, b))) = mult(mult(a, c), mult(mult(a, b), b)))) <=> (~(mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(mult(a, c), mult(a, b)), b)))),
% 21.72/21.93 inference(monotonicity,[status(thm)],[675])).
% 21.72/21.93 tff(677,plain,
% 21.72/21.93 (~(mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(mult(a, c), mult(a, b)), b))),
% 21.72/21.93 inference(modus_ponens,[status(thm)],[572, 676])).
% 21.72/21.93 tff(678,plain,
% 21.72/21.93 (~(mult(mult(a, c), mult(b, mult(b, a))) = mult(mult(a, c), mult(mult(b, a), b)))),
% 21.72/21.93 inference(modus_ponens,[status(thm)],[677, 674])).
% 21.72/21.93 tff(679,plain,
% 21.72/21.93 (((~(mult(mult(mult(a, c), b), mult(b, a)) = mult(mult(mult(a, c), mult(b, a)), b))) | (~(mult(mult(a, c), mult(b, mult(b, a))) = mult(mult(a, c), mult(mult(b, a), b))))) | (mult(mult(a, c), mult(b, mult(b, a))) = mult(mult(a, c), mult(mult(b, a), b)))),
% 21.72/21.93 inference(tautology,[status(thm)],[])).
% 21.72/21.93 tff(680,plain,
% 21.72/21.93 ((~(mult(mult(mult(a, c), b), mult(b, a)) = mult(mult(mult(a, c), mult(b, a)), b))) | (~(mult(mult(a, c), mult(b, mult(b, a))) = mult(mult(a, c), mult(mult(b, a), b))))),
% 21.72/21.93 inference(unit_resolution,[status(thm)],[679, 678])).
% 21.72/21.93 tff(681,plain,
% 21.72/21.93 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, c), b), mult(b, a)) = mult(mult(mult(a, c), mult(b, a)), b))) | (~(mult(mult(a, c), mult(b, mult(b, a))) = mult(mult(a, c), mult(mult(b, a), b)))))) | (~((~(mult(mult(mult(a, c), b), mult(b, a)) = mult(mult(a, c), mult(b, mult(b, a))))) | (~(mult(mult(mult(a, c), mult(b, a)), b) = mult(mult(a, c), mult(mult(b, a), b)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(a, c), b), mult(b, a)) = mult(mult(mult(a, c), mult(b, a)), b))) | (~(mult(mult(a, c), mult(b, mult(b, a))) = mult(mult(a, c), mult(mult(b, a), b)))))) | (~((~(mult(mult(mult(a, c), b), mult(b, a)) = mult(mult(a, c), mult(b, mult(b, a))))) | (~(mult(mult(mult(a, c), mult(b, a)), b) = mult(mult(a, c), mult(mult(b, a), b)))))))),
% 21.72/21.93 inference(rewrite,[status(thm)],[])).
% 21.72/21.93 tff(682,plain,
% 21.72/21.93 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, c), b), mult(b, a)) = mult(mult(mult(a, c), mult(b, a)), b))) | (~(mult(mult(a, c), mult(b, mult(b, a))) = mult(mult(a, c), mult(mult(b, a), b)))))) | (~((~(mult(mult(mult(a, c), b), mult(b, a)) = mult(mult(a, c), mult(b, mult(b, a))))) | (~(mult(mult(mult(a, c), mult(b, a)), b) = mult(mult(a, c), mult(mult(b, a), b)))))))),
% 21.72/21.93 inference(quant_inst,[status(thm)],[])).
% 21.72/21.93 tff(683,plain,
% 21.72/21.93 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(a, c), b), mult(b, a)) = mult(mult(mult(a, c), mult(b, a)), b))) | (~(mult(mult(a, c), mult(b, mult(b, a))) = mult(mult(a, c), mult(mult(b, a), b)))))) | (~((~(mult(mult(mult(a, c), b), mult(b, a)) = mult(mult(a, c), mult(b, mult(b, a))))) | (~(mult(mult(mult(a, c), mult(b, a)), b) = mult(mult(a, c), mult(mult(b, a), b))))))),
% 21.72/21.93 inference(modus_ponens,[status(thm)],[682, 681])).
% 21.72/21.93 tff(684,plain,
% 21.72/21.93 ((~((~(mult(mult(mult(a, c), b), mult(b, a)) = mult(mult(mult(a, c), mult(b, a)), b))) | (~(mult(mult(a, c), mult(b, mult(b, a))) = mult(mult(a, c), mult(mult(b, a), b)))))) | (~((~(mult(mult(mult(a, c), b), mult(b, a)) = mult(mult(a, c), mult(b, mult(b, a))))) | (~(mult(mult(mult(a, c), mult(b, a)), b) = mult(mult(a, c), mult(mult(b, a), b))))))),
% 21.72/21.93 inference(unit_resolution,[status(thm)],[683, 27])).
% 21.72/21.93 tff(685,plain,
% 21.72/21.93 (~((~(mult(mult(mult(a, c), b), mult(b, a)) = mult(mult(a, c), mult(b, mult(b, a))))) | (~(mult(mult(mult(a, c), mult(b, a)), b) = mult(mult(a, c), mult(mult(b, a), b)))))),
% 21.72/21.93 inference(unit_resolution,[status(thm)],[684, 680])).
% 21.72/21.93 tff(686,plain,
% 21.72/21.93 (((~(mult(mult(mult(a, c), b), mult(b, a)) = mult(mult(a, c), mult(b, mult(b, a))))) | (~(mult(mult(mult(a, c), mult(b, a)), b) = mult(mult(a, c), mult(mult(b, a), b))))) | (mult(mult(mult(a, c), b), mult(b, a)) = mult(mult(a, c), mult(b, mult(b, a))))),
% 21.77/21.93 inference(tautology,[status(thm)],[])).
% 21.77/21.93 tff(687,plain,
% 21.77/21.93 (mult(mult(mult(a, c), b), mult(b, a)) = mult(mult(a, c), mult(b, mult(b, a)))),
% 21.77/21.93 inference(unit_resolution,[status(thm)],[686, 685])).
% 21.77/21.93 tff(688,plain,
% 21.77/21.93 (mult(mult(a, c), mult(b, mult(b, a))) = mult(mult(mult(a, c), b), mult(b, a))),
% 21.77/21.93 inference(symmetry,[status(thm)],[687])).
% 21.77/21.93 tff(689,plain,
% 21.77/21.93 (mult(mult(a, c), mult(unit, mult(mult(mult(b, unit), b), a))) = mult(mult(a, c), mult(b, mult(b, a)))),
% 21.77/21.93 inference(symmetry,[status(thm)],[669])).
% 21.77/21.93 tff(690,plain,
% 21.77/21.93 (mult(mult(b, a), rd(mult(b, c), mult(a, c))) = rd(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a), a)),
% 21.77/21.93 inference(symmetry,[status(thm)],[546])).
% 21.77/21.93 tff(691,plain,
% 21.77/21.93 (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), rd(mult(b, c), mult(a, c))) = mult(mult(b, a), rd(mult(b, c), mult(a, c)))),
% 21.77/21.93 inference(monotonicity,[status(thm)],[473])).
% 21.77/21.93 tff(692,plain,
% 21.77/21.93 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), rd(mult(b, c), mult(a, c)))))),
% 21.77/21.93 inference(quant_inst,[status(thm)],[])).
% 21.77/21.93 tff(693,plain,
% 21.77/21.93 (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), rd(mult(b, c), mult(a, c))))),
% 21.77/21.93 inference(unit_resolution,[status(thm)],[692, 56])).
% 21.77/21.93 tff(694,plain,
% 21.77/21.93 (mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), rd(mult(b, c), mult(a, c)))),
% 21.77/21.93 inference(symmetry,[status(thm)],[693])).
% 21.77/21.93 tff(695,plain,
% 21.77/21.93 (mult(mult(rd(mult(b, c), mult(a, c)), a), rd(mult(b, c), mult(a, c))) = mult(b, rd(mult(b, c), mult(a, c)))),
% 21.77/21.93 inference(monotonicity,[status(thm)],[176])).
% 21.77/21.93 tff(696,plain,
% 21.77/21.93 (mult(b, rd(mult(b, c), mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), a), rd(mult(b, c), mult(a, c)))),
% 21.77/21.93 inference(symmetry,[status(thm)],[695])).
% 21.77/21.93 tff(697,plain,
% 21.77/21.93 (mult(a, mult(b, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), rd(mult(b, c), mult(a, c))))),
% 21.77/21.93 inference(monotonicity,[status(thm)],[696])).
% 21.77/21.93 tff(698,plain,
% 21.77/21.93 (mult(a, mult(b, rd(mult(b, c), mult(a, c)))) = mult(unit, mult(mult(b, unit), b))),
% 21.77/21.93 inference(transitivity,[status(thm)],[697, 694, 691, 690, 549, 552])).
% 21.77/21.93 tff(699,plain,
% 21.77/21.93 (mult(mult(a, mult(b, rd(mult(b, c), mult(a, c)))), a) = mult(mult(unit, mult(mult(b, unit), b)), a)),
% 21.77/21.93 inference(monotonicity,[status(thm)],[698])).
% 21.77/21.93 tff(700,plain,
% 21.77/21.93 (mult(mult(a, mult(b, rd(mult(b, c), mult(a, c)))), a) = mult(unit, mult(mult(mult(b, unit), b), a))),
% 21.77/21.93 inference(transitivity,[status(thm)],[699, 465])).
% 21.77/21.93 tff(701,plain,
% 21.77/21.93 (mult(mult(a, c), mult(mult(a, mult(b, rd(mult(b, c), mult(a, c)))), a)) = mult(mult(a, c), mult(unit, mult(mult(mult(b, unit), b), a)))),
% 21.77/21.93 inference(monotonicity,[status(thm)],[700])).
% 21.77/21.93 tff(702,plain,
% 21.77/21.93 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(a, c), a), mult(b, rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, c), mult(mult(a, mult(b, rd(mult(b, c), mult(a, c)))), a)))),
% 21.77/21.93 inference(quant_inst,[status(thm)],[])).
% 21.77/21.93 tff(703,plain,
% 21.77/21.93 (mult(mult(mult(mult(a, c), a), mult(b, rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, c), mult(mult(a, mult(b, rd(mult(b, c), mult(a, c)))), a))),
% 21.77/21.93 inference(unit_resolution,[status(thm)],[702, 56])).
% 21.77/21.93 tff(704,plain,
% 21.77/21.93 (mult(mult(mult(mult(a, c), a), mult(b, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(mult(a, b), c), b), a)),
% 21.77/21.93 inference(transitivity,[status(thm)],[703, 701, 689, 688, 653, 646])).
% 21.77/21.93 tff(705,plain,
% 21.77/21.93 (rd(mult(mult(mult(mult(a, c), a), mult(b, rd(mult(b, c), mult(a, c)))), a), a) = rd(mult(mult(mult(mult(a, b), c), b), a), a)),
% 21.77/21.93 inference(monotonicity,[status(thm)],[704])).
% 21.77/21.94 tff(706,plain,
% 21.77/21.94 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(mult(a, c), a), mult(b, rd(mult(b, c), mult(a, c)))), a), a) = mult(mult(mult(a, c), a), mult(b, rd(mult(b, c), mult(a, c)))))),
% 21.77/21.94 inference(quant_inst,[status(thm)],[])).
% 21.77/21.94 tff(707,plain,
% 21.77/21.94 (rd(mult(mult(mult(mult(a, c), a), mult(b, rd(mult(b, c), mult(a, c)))), a), a) = mult(mult(mult(a, c), a), mult(b, rd(mult(b, c), mult(a, c))))),
% 21.77/21.94 inference(unit_resolution,[status(thm)],[706, 168])).
% 21.77/21.94 tff(708,plain,
% 21.77/21.94 (mult(mult(mult(a, c), a), mult(b, rd(mult(b, c), mult(a, c)))) = rd(mult(mult(mult(mult(a, c), a), mult(b, rd(mult(b, c), mult(a, c)))), a), a)),
% 21.77/21.94 inference(symmetry,[status(thm)],[707])).
% 21.77/21.94 tff(709,plain,
% 21.77/21.94 (mult(mult(mult(a, c), a), mult(mult(rd(mult(b, c), mult(a, c)), a), rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, c), a), mult(b, rd(mult(b, c), mult(a, c))))),
% 21.77/21.94 inference(monotonicity,[status(thm)],[695])).
% 21.77/21.94 tff(710,plain,
% 21.77/21.94 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), a), mult(mult(rd(mult(b, c), mult(a, c)), a), rd(mult(b, c), mult(a, c)))))),
% 21.77/21.94 inference(quant_inst,[status(thm)],[])).
% 21.77/21.94 tff(711,plain,
% 21.77/21.94 (mult(mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), a), mult(mult(rd(mult(b, c), mult(a, c)), a), rd(mult(b, c), mult(a, c))))),
% 21.77/21.94 inference(unit_resolution,[status(thm)],[710, 56])).
% 21.77/21.94 tff(712,plain,
% 21.77/21.94 (mult(mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(mult(a, b), c), a), rd(mult(b, c), mult(a, c)))),
% 21.77/21.94 inference(transitivity,[status(thm)],[711, 709, 708, 705, 652, 411])).
% 21.77/21.94 tff(713,plain,
% 21.77/21.94 (rd(mult(mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), a), rd(mult(b, c), mult(a, c))), rd(mult(b, c), mult(a, c))) = rd(mult(mult(mult(mult(a, b), c), a), rd(mult(b, c), mult(a, c))), rd(mult(b, c), mult(a, c)))),
% 21.77/21.94 inference(monotonicity,[status(thm)],[712])).
% 21.77/21.94 tff(714,plain,
% 21.77/21.94 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), a), rd(mult(b, c), mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), a))),
% 21.77/21.94 inference(quant_inst,[status(thm)],[])).
% 21.77/21.94 tff(715,plain,
% 21.77/21.94 (rd(mult(mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), a), rd(mult(b, c), mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), a)),
% 21.77/21.94 inference(unit_resolution,[status(thm)],[714, 168])).
% 21.77/21.94 tff(716,plain,
% 21.77/21.94 (mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), a) = rd(mult(mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), a), rd(mult(b, c), mult(a, c))), rd(mult(b, c), mult(a, c)))),
% 21.77/21.94 inference(symmetry,[status(thm)],[715])).
% 21.77/21.94 tff(717,plain,
% 21.77/21.94 (mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(a, b), c), a)),
% 21.77/21.94 inference(transitivity,[status(thm)],[716, 713, 409])).
% 21.77/21.94 tff(718,plain,
% 21.77/21.94 (rd(mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), a), a) = rd(mult(mult(mult(a, b), c), a), a)),
% 21.77/21.94 inference(monotonicity,[status(thm)],[717])).
% 21.77/21.94 tff(719,plain,
% 21.77/21.94 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), a), a) = mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))))),
% 21.77/21.94 inference(quant_inst,[status(thm)],[])).
% 21.77/21.94 tff(720,plain,
% 21.77/21.94 (rd(mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), a), a) = mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))),
% 21.77/21.94 inference(unit_resolution,[status(thm)],[719, 168])).
% 21.77/21.94 tff(721,plain,
% 21.77/21.94 (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = rd(mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), a), a)),
% 21.77/21.94 inference(symmetry,[status(thm)],[720])).
% 21.77/21.94 tff(722,plain,
% 21.77/21.94 (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))),
% 21.77/21.94 inference(transitivity,[status(thm)],[721, 718, 407, 227, 405, 404])).
% 21.77/21.94 tff(723,assumption,(~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))), introduced(assumption)).
% 21.77/21.94 tff(724,plain,
% 21.77/21.94 ($false),
% 21.77/21.94 inference(unit_resolution,[status(thm)],[723, 722])).
% 21.77/21.94 tff(725,plain,((mult(b, mult(a, b)) = mult(b, mult(b, a))) | (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) | (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit)))))), inference(lemma,lemma(discharge,[]))).
% 21.77/21.94 tff(726,plain,
% 21.77/21.94 (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))),
% 21.77/21.94 inference(unit_resolution,[status(thm)],[725, 403, 343, 97])).
% 21.77/21.94 tff(727,plain,
% 21.77/21.94 ($false),
% 21.77/21.94 inference(unit_resolution,[status(thm)],[726, 353])).
% 21.77/21.94 tff(728,plain,((mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit))))) | (~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))) | (mult(rd(mult(b, c), mult(a, c)), mult(c, a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, c)))), inference(lemma,lemma(discharge,[]))).
% 21.77/21.94 tff(729,plain,
% 21.77/21.94 (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))),
% 21.77/21.94 inference(unit_resolution,[status(thm)],[728, 34, 122, 94])).
% 21.77/21.94 tff(730,plain,
% 21.77/21.94 (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(b, c))),
% 21.77/21.94 inference(transitivity,[status(thm)],[729, 142])).
% 21.77/21.94 tff(731,plain,
% 21.77/21.94 (ld(a, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))) = ld(a, mult(a, mult(b, c)))),
% 21.77/21.94 inference(monotonicity,[status(thm)],[730])).
% 21.77/21.94 tff(732,plain,
% 21.77/21.94 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(a, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))) = mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 21.77/21.94 inference(quant_inst,[status(thm)],[])).
% 21.77/21.94 tff(733,plain,
% 21.77/21.94 (ld(a, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))),
% 21.77/21.94 inference(unit_resolution,[status(thm)],[732, 7])).
% 21.77/21.94 tff(734,plain,
% 21.77/21.94 (mult(mult(a, c), rd(mult(b, c), mult(a, c))) = ld(a, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 21.77/21.94 inference(symmetry,[status(thm)],[733])).
% 21.77/21.94 tff(735,plain,
% 21.77/21.94 (mult(mult(a, c), rd(mult(b, c), mult(a, c))) = mult(b, c)),
% 21.77/21.94 inference(transitivity,[status(thm)],[734, 731, 141])).
% 21.77/21.94 tff(736,plain,
% 21.77/21.94 (mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(b, c))),
% 21.77/21.94 inference(monotonicity,[status(thm)],[735])).
% 21.77/21.94 tff(737,plain,
% 21.77/21.94 (mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))),
% 21.77/21.94 inference(transitivity,[status(thm)],[736, 139])).
% 21.77/21.94 tff(738,plain,
% 21.77/21.94 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c)),
% 21.77/21.94 inference(symmetry,[status(thm)],[317])).
% 21.77/21.94 tff(739,plain,
% 21.77/21.94 (ld(mult(a, c), mult(mult(a, c), mult(b, c))) = ld(mult(a, c), mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 21.77/21.94 inference(symmetry,[status(thm)],[293])).
% 21.77/21.94 tff(740,plain,
% 21.77/21.94 (mult(b, c) = ld(mult(a, c), mult(mult(a, c), mult(b, c)))),
% 21.77/21.94 inference(symmetry,[status(thm)],[291])).
% 21.77/21.94 tff(741,plain,
% 21.77/21.94 (mult(b, c) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))),
% 21.77/21.94 inference(transitivity,[status(thm)],[740, 739, 295])).
% 21.77/21.94 tff(742,plain,
% 21.77/21.94 (mult(mult(b, c), mult(a, c)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))),
% 21.77/21.94 inference(monotonicity,[status(thm)],[741])).
% 21.77/21.94 tff(743,assumption,(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))), introduced(assumption)).
% 21.77/21.94 tff(744,plain,
% 21.77/21.94 (ld(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, a))) = ld(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 21.77/21.94 inference(monotonicity,[status(thm)],[743])).
% 21.77/21.94 tff(745,plain,
% 21.77/21.94 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, a))) = mult(c, a))),
% 21.77/21.94 inference(quant_inst,[status(thm)],[])).
% 21.77/21.94 tff(746,plain,
% 21.77/21.94 (ld(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, a))) = mult(c, a)),
% 21.77/21.94 inference(unit_resolution,[status(thm)],[745, 7])).
% 21.77/21.94 tff(747,plain,
% 21.77/21.94 (mult(c, a) = ld(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, a)))),
% 21.77/21.94 inference(symmetry,[status(thm)],[746])).
% 21.77/21.94 tff(748,plain,
% 21.77/21.94 (mult(c, a) = mult(a, c)),
% 21.77/21.94 inference(transitivity,[status(thm)],[747, 744, 356])).
% 21.77/21.94 tff(749,plain,
% 21.77/21.94 (mult(mult(b, c), mult(c, a)) = mult(mult(b, c), mult(a, c))),
% 21.77/21.94 inference(monotonicity,[status(thm)],[748])).
% 21.77/21.94 tff(750,plain,
% 21.77/21.94 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(b, c), mult(c, a))),
% 21.77/21.94 inference(monotonicity,[status(thm)],[297])).
% 21.77/21.94 tff(751,assumption,(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a))), introduced(assumption)).
% 21.77/21.94 tff(752,plain,
% 21.77/21.94 (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c)),
% 21.77/21.94 inference(transitivity,[status(thm)],[751, 750, 749, 742, 738])).
% 21.77/21.94 tff(753,assumption,(~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c))), introduced(assumption)).
% 21.77/21.94 tff(754,plain,
% 21.77/21.94 ($false),
% 21.77/21.94 inference(unit_resolution,[status(thm)],[753, 752])).
% 21.77/21.94 tff(755,plain,((~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))) | (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c)) | (~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)))) | (~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))), inference(lemma,lemma(discharge,[]))).
% 21.77/21.94 tff(756,plain,
% 21.77/21.94 (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 21.77/21.94 inference(unit_resolution,[status(thm)],[755, 737, 124, 122, 128])).
% 21.77/21.94 tff(757,plain,
% 21.77/21.94 (((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), c))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))))) | (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 21.77/21.94 inference(tautology,[status(thm)],[])).
% 21.77/21.94 tff(758,plain,
% 21.77/21.94 ((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), c))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))))),
% 21.77/21.94 inference(unit_resolution,[status(thm)],[757, 756])).
% 21.77/21.94 tff(759,plain,
% 21.77/21.94 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), c))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))))) | (~((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), a) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, a)))) | (~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), c) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), c))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))))) | (~((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), a) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, a)))) | (~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), c) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))))))),
% 21.77/21.94 inference(rewrite,[status(thm)],[])).
% 21.77/21.94 tff(760,plain,
% 21.77/21.94 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), c))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))))) | (~((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), a) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, a)))) | (~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), c) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))))))),
% 21.77/21.94 inference(quant_inst,[status(thm)],[])).
% 21.77/21.94 tff(761,plain,
% 21.77/21.94 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), c))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))))) | (~((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), a) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, a)))) | (~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), c) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))))))),
% 21.77/21.94 inference(modus_ponens,[status(thm)],[760, 759])).
% 21.77/21.94 tff(762,plain,
% 21.77/21.94 ((~((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), c))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))))) | (~((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), a) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, a)))) | (~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), c) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))))))),
% 21.77/21.94 inference(unit_resolution,[status(thm)],[761, 27])).
% 21.77/21.94 tff(763,plain,
% 21.77/21.94 (~((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), a) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, a)))) | (~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), c) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))))),
% 21.77/21.94 inference(unit_resolution,[status(thm)],[762, 758])).
% 21.77/21.94 tff(764,plain,
% 21.77/21.94 (((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), a) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, a)))) | (~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), c) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))))) | (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), c) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 21.77/21.94 inference(tautology,[status(thm)],[])).
% 21.77/21.94 tff(765,plain,
% 21.77/21.95 (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), c) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))),
% 21.77/21.95 inference(unit_resolution,[status(thm)],[764, 763])).
% 21.77/21.95 tff(766,plain,
% 21.77/21.95 (mult(mult(rd(mult(b, c), mult(a, c)), a), c) = mult(b, c)),
% 21.77/21.95 inference(transitivity,[status(thm)],[76, 34, 61, 137])).
% 21.77/21.95 tff(767,plain,
% 21.77/21.95 (rd(mult(mult(rd(mult(b, c), mult(a, c)), a), c), c) = rd(mult(b, c), c)),
% 21.77/21.95 inference(monotonicity,[status(thm)],[766])).
% 21.77/21.95 tff(768,plain,
% 21.77/21.95 (mult(rd(mult(b, c), mult(a, c)), a) = b),
% 21.77/21.95 inference(transitivity,[status(thm)],[175, 767, 170])).
% 21.77/21.95 tff(769,plain,
% 21.77/21.95 (mult(a, mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, b)),
% 21.77/21.95 inference(monotonicity,[status(thm)],[768])).
% 21.77/21.95 tff(770,plain,
% 21.77/21.95 (mult(mult(unit, b), c) = mult(b, c)),
% 21.77/21.95 inference(monotonicity,[status(thm)],[184])).
% 21.77/21.95 tff(771,plain,
% 21.77/21.95 (mult(mult(mult(unit, b), c), b) = mult(mult(b, c), b)),
% 21.77/21.95 inference(monotonicity,[status(thm)],[770])).
% 21.77/21.95 tff(772,plain,
% 21.77/21.95 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(unit, b), c), b) = mult(unit, mult(mult(b, c), b)))),
% 21.77/21.95 inference(quant_inst,[status(thm)],[])).
% 21.77/21.95 tff(773,plain,
% 21.77/21.95 (mult(mult(mult(unit, b), c), b) = mult(unit, mult(mult(b, c), b))),
% 21.77/21.95 inference(unit_resolution,[status(thm)],[772, 56])).
% 21.77/21.95 tff(774,plain,
% 21.77/21.95 (mult(unit, mult(mult(b, c), b)) = mult(mult(mult(unit, b), c), b)),
% 21.77/21.95 inference(symmetry,[status(thm)],[773])).
% 21.77/21.95 tff(775,plain,
% 21.77/21.95 (mult(unit, mult(mult(b, c), b)) = mult(mult(b, c), b)),
% 21.77/21.95 inference(transitivity,[status(thm)],[774, 771])).
% 21.77/21.95 tff(776,plain,
% 21.77/21.95 (mult(mult(unit, mult(mult(b, c), b)), a) = mult(mult(mult(b, c), b), a)),
% 21.77/21.95 inference(monotonicity,[status(thm)],[775])).
% 21.77/21.95 tff(777,plain,
% 21.77/21.95 (mult(mult(mult(b, c), b), a) = mult(mult(unit, mult(mult(b, c), b)), a)),
% 21.77/21.95 inference(symmetry,[status(thm)],[776])).
% 21.77/21.95 tff(778,plain,
% 21.77/21.95 (mult(mult(unit, a), mult(mult(b, c), b)) = mult(a, mult(mult(b, c), b))),
% 21.77/21.95 inference(monotonicity,[status(thm)],[244])).
% 21.77/21.95 tff(779,plain,
% 21.77/21.95 (mult(a, mult(mult(b, c), b)) = mult(mult(unit, a), mult(mult(b, c), b))),
% 21.77/21.95 inference(symmetry,[status(thm)],[778])).
% 21.77/21.95 tff(780,plain,
% 21.77/21.95 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(a, b), c), b) = mult(a, mult(mult(b, c), b)))),
% 21.77/21.95 inference(quant_inst,[status(thm)],[])).
% 21.77/21.95 tff(781,plain,
% 21.77/21.95 (mult(mult(mult(a, b), c), b) = mult(a, mult(mult(b, c), b))),
% 21.77/21.95 inference(unit_resolution,[status(thm)],[780, 56])).
% 21.77/21.95 tff(782,plain,
% 21.77/21.95 ((mult(mult(a, b), mult(c, b)) = mult(mult(mult(a, b), c), b)) <=> (mult(mult(mult(a, b), c), b) = mult(mult(a, b), mult(c, b)))),
% 21.77/21.95 inference(commutativity,[status(thm)],[])).
% 21.77/21.95 tff(783,plain,
% 21.77/21.95 (mult(a, mult(mult(b, c), b)) = mult(mult(mult(a, b), c), b)),
% 21.77/21.95 inference(symmetry,[status(thm)],[781])).
% 21.77/21.95 tff(784,plain,
% 21.77/21.95 (mult(mult(a, b), mult(c, b)) = mult(mult(a, b), mult(b, c))),
% 21.77/21.95 inference(monotonicity,[status(thm)],[241])).
% 21.77/21.95 tff(785,plain,
% 21.77/21.95 (mult(mult(a, b), mult(b, c)) = mult(mult(a, b), mult(c, b))),
% 21.77/21.95 inference(symmetry,[status(thm)],[784])).
% 21.77/21.95 tff(786,plain,
% 21.77/21.95 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(a, mult(b, c)), b), b) = mult(a, mult(b, c)))),
% 21.77/21.95 inference(quant_inst,[status(thm)],[])).
% 21.77/21.95 tff(787,plain,
% 21.77/21.95 (rd(mult(mult(a, mult(b, c)), b), b) = mult(a, mult(b, c))),
% 21.77/21.95 inference(unit_resolution,[status(thm)],[786, 168])).
% 21.77/21.95 tff(788,assumption,(mult(mult(a, mult(b, c)), b) = mult(a, mult(mult(b, c), b))), introduced(assumption)).
% 21.77/21.95 tff(789,plain,
% 21.77/21.95 (mult(mult(a, mult(b, c)), b) = mult(mult(mult(a, b), c), b)),
% 21.77/21.95 inference(transitivity,[status(thm)],[788, 783])).
% 21.77/21.95 tff(790,plain,
% 21.77/21.95 (rd(mult(mult(a, mult(b, c)), b), b) = rd(mult(mult(mult(a, b), c), b), b)),
% 21.77/21.95 inference(monotonicity,[status(thm)],[789])).
% 21.77/21.95 tff(791,plain,
% 21.77/21.95 (rd(mult(mult(mult(a, b), c), b), b) = rd(mult(mult(a, mult(b, c)), b), b)),
% 21.77/21.95 inference(symmetry,[status(thm)],[790])).
% 21.77/21.95 tff(792,plain,
% 21.77/21.95 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(a, b), c), b), b) = mult(mult(a, b), c))),
% 21.77/21.95 inference(quant_inst,[status(thm)],[])).
% 21.77/21.95 tff(793,plain,
% 21.77/21.95 (rd(mult(mult(mult(a, b), c), b), b) = mult(mult(a, b), c)),
% 21.77/21.95 inference(unit_resolution,[status(thm)],[792, 168])).
% 21.77/21.95 tff(794,plain,
% 21.77/21.95 (mult(mult(a, b), c) = rd(mult(mult(mult(a, b), c), b), b)),
% 21.77/21.95 inference(symmetry,[status(thm)],[793])).
% 21.77/21.95 tff(795,plain,
% 21.77/21.95 (mult(mult(a, b), c) = mult(a, mult(b, c))),
% 21.77/21.95 inference(transitivity,[status(thm)],[794, 791, 787])).
% 21.77/21.95 tff(796,plain,
% 21.77/21.95 ($false),
% 21.77/21.95 inference(unit_resolution,[status(thm)],[146, 795])).
% 21.77/21.95 tff(797,plain,(~(mult(mult(a, mult(b, c)), b) = mult(a, mult(mult(b, c), b)))), inference(lemma,lemma(discharge,[]))).
% 21.77/21.95 tff(798,plain,
% 21.77/21.95 (((~(mult(mult(a, b), mult(b, c)) = mult(a, mult(b, mult(b, c))))) | (~(mult(mult(a, mult(b, c)), b) = mult(a, mult(mult(b, c), b))))) | (mult(mult(a, mult(b, c)), b) = mult(a, mult(mult(b, c), b)))),
% 21.77/21.95 inference(tautology,[status(thm)],[])).
% 21.77/21.95 tff(799,plain,
% 21.77/21.95 ((~(mult(mult(a, b), mult(b, c)) = mult(a, mult(b, mult(b, c))))) | (~(mult(mult(a, mult(b, c)), b) = mult(a, mult(mult(b, c), b))))),
% 21.77/21.95 inference(unit_resolution,[status(thm)],[798, 797])).
% 21.77/21.95 tff(800,plain,
% 21.77/21.95 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, b), mult(b, c)) = mult(mult(a, mult(b, c)), b))) | (~(mult(a, mult(b, mult(b, c))) = mult(a, mult(mult(b, c), b)))))) | (~((~(mult(mult(a, b), mult(b, c)) = mult(a, mult(b, mult(b, c))))) | (~(mult(mult(a, mult(b, c)), b) = mult(a, mult(mult(b, c), b)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, b), mult(b, c)) = mult(mult(a, mult(b, c)), b))) | (~(mult(a, mult(b, mult(b, c))) = mult(a, mult(mult(b, c), b)))))) | (~((~(mult(mult(a, b), mult(b, c)) = mult(a, mult(b, mult(b, c))))) | (~(mult(mult(a, mult(b, c)), b) = mult(a, mult(mult(b, c), b)))))))),
% 21.77/21.95 inference(rewrite,[status(thm)],[])).
% 21.77/21.95 tff(801,plain,
% 21.77/21.95 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, b), mult(b, c)) = mult(mult(a, mult(b, c)), b))) | (~(mult(a, mult(b, mult(b, c))) = mult(a, mult(mult(b, c), b)))))) | (~((~(mult(mult(a, b), mult(b, c)) = mult(a, mult(b, mult(b, c))))) | (~(mult(mult(a, mult(b, c)), b) = mult(a, mult(mult(b, c), b)))))))),
% 21.77/21.95 inference(quant_inst,[status(thm)],[])).
% 21.77/21.95 tff(802,plain,
% 21.77/21.95 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, b), mult(b, c)) = mult(mult(a, mult(b, c)), b))) | (~(mult(a, mult(b, mult(b, c))) = mult(a, mult(mult(b, c), b)))))) | (~((~(mult(mult(a, b), mult(b, c)) = mult(a, mult(b, mult(b, c))))) | (~(mult(mult(a, mult(b, c)), b) = mult(a, mult(mult(b, c), b))))))),
% 21.77/21.95 inference(modus_ponens,[status(thm)],[801, 800])).
% 21.77/21.95 tff(803,plain,
% 21.77/21.95 (~((~(mult(mult(a, b), mult(b, c)) = mult(mult(a, mult(b, c)), b))) | (~(mult(a, mult(b, mult(b, c))) = mult(a, mult(mult(b, c), b)))))),
% 21.77/21.95 inference(unit_resolution,[status(thm)],[802, 27, 799])).
% 21.77/21.95 tff(804,plain,
% 21.77/21.95 (((~(mult(mult(a, b), mult(b, c)) = mult(mult(a, mult(b, c)), b))) | (~(mult(a, mult(b, mult(b, c))) = mult(a, mult(mult(b, c), b))))) | (mult(mult(a, b), mult(b, c)) = mult(mult(a, mult(b, c)), b))),
% 21.77/21.95 inference(tautology,[status(thm)],[])).
% 21.77/21.95 tff(805,plain,
% 21.77/21.95 (mult(mult(a, b), mult(b, c)) = mult(mult(a, mult(b, c)), b)),
% 21.77/21.95 inference(unit_resolution,[status(thm)],[804, 803])).
% 21.77/21.95 tff(806,plain,
% 21.79/21.95 (mult(mult(a, mult(b, c)), b) = mult(mult(a, b), mult(b, c))),
% 21.79/21.95 inference(symmetry,[status(thm)],[805])).
% 21.79/21.95 tff(807,plain,
% 21.79/21.95 (mult(mult(a, mult(b, c)), b) = mult(mult(a, b), mult(c, b))),
% 21.79/21.95 inference(transitivity,[status(thm)],[806, 785])).
% 21.79/21.95 tff(808,plain,
% 21.79/21.95 ((mult(mult(a, mult(b, c)), b) = mult(a, mult(mult(b, c), b))) <=> (mult(mult(a, b), mult(c, b)) = mult(mult(mult(a, b), c), b))),
% 21.79/21.95 inference(monotonicity,[status(thm)],[807, 783])).
% 21.79/21.95 tff(809,plain,
% 21.79/21.95 ((mult(mult(a, mult(b, c)), b) = mult(a, mult(mult(b, c), b))) <=> (mult(mult(mult(a, b), c), b) = mult(mult(a, b), mult(c, b)))),
% 21.79/21.95 inference(transitivity,[status(thm)],[808, 782])).
% 21.79/21.95 tff(810,plain,
% 21.79/21.95 ((~(mult(mult(a, mult(b, c)), b) = mult(a, mult(mult(b, c), b)))) <=> (~(mult(mult(mult(a, b), c), b) = mult(mult(a, b), mult(c, b))))),
% 21.79/21.95 inference(monotonicity,[status(thm)],[809])).
% 21.79/21.95 tff(811,plain,
% 21.79/21.95 (~(mult(mult(mult(a, b), c), b) = mult(mult(a, b), mult(c, b)))),
% 21.79/21.95 inference(modus_ponens,[status(thm)],[797, 810])).
% 21.79/21.95 tff(812,plain,
% 21.79/21.95 (((~(mult(mult(mult(a, b), b), c) = mult(mult(a, b), mult(b, c)))) | (~(mult(mult(mult(a, b), c), b) = mult(mult(a, b), mult(c, b))))) | (mult(mult(mult(a, b), c), b) = mult(mult(a, b), mult(c, b)))),
% 21.79/21.95 inference(tautology,[status(thm)],[])).
% 21.79/21.95 tff(813,plain,
% 21.79/21.95 ((~(mult(mult(mult(a, b), b), c) = mult(mult(a, b), mult(b, c)))) | (~(mult(mult(mult(a, b), c), b) = mult(mult(a, b), mult(c, b))))),
% 21.79/21.95 inference(unit_resolution,[status(thm)],[812, 811])).
% 21.79/21.95 tff(814,plain,
% 21.79/21.95 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, b), b), c) = mult(mult(a, b), mult(b, c)))) | (~(mult(mult(mult(a, b), c), b) = mult(mult(a, b), mult(c, b)))))) | (~((~(mult(mult(mult(a, b), c), b) = mult(mult(mult(a, b), b), c))) | (~(mult(mult(a, b), mult(c, b)) = mult(mult(a, b), mult(b, c)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(a, b), b), c) = mult(mult(a, b), mult(b, c)))) | (~(mult(mult(mult(a, b), c), b) = mult(mult(a, b), mult(c, b)))))) | (~((~(mult(mult(mult(a, b), c), b) = mult(mult(mult(a, b), b), c))) | (~(mult(mult(a, b), mult(c, b)) = mult(mult(a, b), mult(b, c)))))))),
% 21.79/21.95 inference(rewrite,[status(thm)],[])).
% 21.79/21.95 tff(815,plain,
% 21.79/21.95 (((~((~(mult(mult(mult(a, b), c), b) = mult(mult(mult(a, b), b), c))) | (~(mult(mult(a, b), mult(c, b)) = mult(mult(a, b), mult(b, c)))))) | (~((~(mult(mult(mult(a, b), b), c) = mult(mult(a, b), mult(b, c)))) | (~(mult(mult(mult(a, b), c), b) = mult(mult(a, b), mult(c, b))))))) <=> ((~((~(mult(mult(mult(a, b), b), c) = mult(mult(a, b), mult(b, c)))) | (~(mult(mult(mult(a, b), c), b) = mult(mult(a, b), mult(c, b)))))) | (~((~(mult(mult(mult(a, b), c), b) = mult(mult(mult(a, b), b), c))) | (~(mult(mult(a, b), mult(c, b)) = mult(mult(a, b), mult(b, c)))))))),
% 21.79/21.95 inference(rewrite,[status(thm)],[])).
% 21.79/21.95 tff(816,plain,
% 21.79/21.95 ((~((~(mult(mult(mult(a, b), c), b) = mult(mult(a, b), mult(c, b)))) | (~(mult(mult(mult(a, b), b), c) = mult(mult(a, b), mult(b, c)))))) <=> (~((~(mult(mult(mult(a, b), b), c) = mult(mult(a, b), mult(b, c)))) | (~(mult(mult(mult(a, b), c), b) = mult(mult(a, b), mult(c, b))))))),
% 21.79/21.95 inference(rewrite,[status(thm)],[])).
% 21.79/21.95 tff(817,plain,
% 21.79/21.95 ((~((~(mult(mult(mult(a, b), c), b) = mult(mult(mult(a, b), b), c))) | (~(mult(mult(a, b), mult(c, b)) = mult(mult(a, b), mult(b, c)))))) <=> (~((~(mult(mult(mult(a, b), c), b) = mult(mult(mult(a, b), b), c))) | (~(mult(mult(a, b), mult(c, b)) = mult(mult(a, b), mult(b, c))))))),
% 21.79/21.95 inference(rewrite,[status(thm)],[])).
% 21.79/21.95 tff(818,plain,
% 21.79/21.95 (((~((~(mult(mult(mult(a, b), c), b) = mult(mult(mult(a, b), b), c))) | (~(mult(mult(a, b), mult(c, b)) = mult(mult(a, b), mult(b, c)))))) | (~((~(mult(mult(mult(a, b), c), b) = mult(mult(a, b), mult(c, b)))) | (~(mult(mult(mult(a, b), b), c) = mult(mult(a, b), mult(b, c))))))) <=> ((~((~(mult(mult(mult(a, b), c), b) = mult(mult(mult(a, b), b), c))) | (~(mult(mult(a, b), mult(c, b)) = mult(mult(a, b), mult(b, c)))))) | (~((~(mult(mult(mult(a, b), b), c) = mult(mult(a, b), mult(b, c)))) | (~(mult(mult(mult(a, b), c), b) = mult(mult(a, b), mult(c, b)))))))),
% 21.79/21.95 inference(monotonicity,[status(thm)],[817, 816])).
% 21.79/21.95 tff(819,plain,
% 21.79/21.95 (((~((~(mult(mult(mult(a, b), c), b) = mult(mult(mult(a, b), b), c))) | (~(mult(mult(a, b), mult(c, b)) = mult(mult(a, b), mult(b, c)))))) | (~((~(mult(mult(mult(a, b), c), b) = mult(mult(a, b), mult(c, b)))) | (~(mult(mult(mult(a, b), b), c) = mult(mult(a, b), mult(b, c))))))) <=> ((~((~(mult(mult(mult(a, b), b), c) = mult(mult(a, b), mult(b, c)))) | (~(mult(mult(mult(a, b), c), b) = mult(mult(a, b), mult(c, b)))))) | (~((~(mult(mult(mult(a, b), c), b) = mult(mult(mult(a, b), b), c))) | (~(mult(mult(a, b), mult(c, b)) = mult(mult(a, b), mult(b, c)))))))),
% 21.79/21.95 inference(transitivity,[status(thm)],[818, 815])).
% 21.79/21.95 tff(820,plain,
% 21.79/21.95 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, b), c), b) = mult(mult(mult(a, b), b), c))) | (~(mult(mult(a, b), mult(c, b)) = mult(mult(a, b), mult(b, c)))))) | (~((~(mult(mult(mult(a, b), c), b) = mult(mult(a, b), mult(c, b)))) | (~(mult(mult(mult(a, b), b), c) = mult(mult(a, b), mult(b, c)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, b), b), c) = mult(mult(a, b), mult(b, c)))) | (~(mult(mult(mult(a, b), c), b) = mult(mult(a, b), mult(c, b)))))) | (~((~(mult(mult(mult(a, b), c), b) = mult(mult(mult(a, b), b), c))) | (~(mult(mult(a, b), mult(c, b)) = mult(mult(a, b), mult(b, c))))))))),
% 21.79/21.95 inference(monotonicity,[status(thm)],[819])).
% 21.79/21.95 tff(821,plain,
% 21.79/21.95 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, b), c), b) = mult(mult(mult(a, b), b), c))) | (~(mult(mult(a, b), mult(c, b)) = mult(mult(a, b), mult(b, c)))))) | (~((~(mult(mult(mult(a, b), c), b) = mult(mult(a, b), mult(c, b)))) | (~(mult(mult(mult(a, b), b), c) = mult(mult(a, b), mult(b, c)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(a, b), b), c) = mult(mult(a, b), mult(b, c)))) | (~(mult(mult(mult(a, b), c), b) = mult(mult(a, b), mult(c, b)))))) | (~((~(mult(mult(mult(a, b), c), b) = mult(mult(mult(a, b), b), c))) | (~(mult(mult(a, b), mult(c, b)) = mult(mult(a, b), mult(b, c)))))))),
% 21.79/21.95 inference(transitivity,[status(thm)],[820, 814])).
% 21.79/21.95 tff(822,plain,
% 21.79/21.95 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, b), c), b) = mult(mult(mult(a, b), b), c))) | (~(mult(mult(a, b), mult(c, b)) = mult(mult(a, b), mult(b, c)))))) | (~((~(mult(mult(mult(a, b), c), b) = mult(mult(a, b), mult(c, b)))) | (~(mult(mult(mult(a, b), b), c) = mult(mult(a, b), mult(b, c)))))))),
% 21.79/21.95 inference(quant_inst,[status(thm)],[])).
% 21.79/21.95 tff(823,plain,
% 21.79/21.95 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(a, b), b), c) = mult(mult(a, b), mult(b, c)))) | (~(mult(mult(mult(a, b), c), b) = mult(mult(a, b), mult(c, b)))))) | (~((~(mult(mult(mult(a, b), c), b) = mult(mult(mult(a, b), b), c))) | (~(mult(mult(a, b), mult(c, b)) = mult(mult(a, b), mult(b, c))))))),
% 21.79/21.96 inference(modus_ponens,[status(thm)],[822, 821])).
% 21.79/21.96 tff(824,plain,
% 21.79/21.96 ((~((~(mult(mult(mult(a, b), b), c) = mult(mult(a, b), mult(b, c)))) | (~(mult(mult(mult(a, b), c), b) = mult(mult(a, b), mult(c, b)))))) | (~((~(mult(mult(mult(a, b), c), b) = mult(mult(mult(a, b), b), c))) | (~(mult(mult(a, b), mult(c, b)) = mult(mult(a, b), mult(b, c))))))),
% 21.79/21.96 inference(unit_resolution,[status(thm)],[823, 27])).
% 21.79/21.96 tff(825,plain,
% 21.79/21.96 (~((~(mult(mult(mult(a, b), c), b) = mult(mult(mult(a, b), b), c))) | (~(mult(mult(a, b), mult(c, b)) = mult(mult(a, b), mult(b, c)))))),
% 21.79/21.96 inference(unit_resolution,[status(thm)],[824, 813])).
% 21.79/21.96 tff(826,plain,
% 21.79/21.96 (((~(mult(mult(mult(a, b), c), b) = mult(mult(mult(a, b), b), c))) | (~(mult(mult(a, b), mult(c, b)) = mult(mult(a, b), mult(b, c))))) | (mult(mult(mult(a, b), c), b) = mult(mult(mult(a, b), b), c))),
% 21.79/21.96 inference(tautology,[status(thm)],[])).
% 21.79/21.96 tff(827,plain,
% 21.79/21.96 (mult(mult(mult(a, b), c), b) = mult(mult(mult(a, b), b), c)),
% 21.79/21.96 inference(unit_resolution,[status(thm)],[826, 825])).
% 21.79/21.96 tff(828,plain,
% 21.79/21.96 (mult(mult(mult(a, b), b), c) = mult(mult(mult(a, b), c), b)),
% 21.79/21.96 inference(symmetry,[status(thm)],[827])).
% 21.79/21.96 tff(829,plain,
% 21.79/21.96 (mult(a, mult(unit, mult(mult(b, unit), b))) = mult(mult(unit, a), mult(mult(b, unit), b))),
% 21.79/21.96 inference(monotonicity,[status(thm)],[245, 429])).
% 21.79/21.96 tff(830,plain,
% 21.79/21.96 (mult(mult(unit, a), mult(mult(b, unit), b)) = mult(a, mult(unit, mult(mult(b, unit), b)))),
% 21.79/21.96 inference(symmetry,[status(thm)],[829])).
% 21.79/21.96 tff(831,plain,
% 21.79/21.96 (mult(mult(a, b), b) = mult(a, mult(unit, mult(mult(b, unit), b)))),
% 21.79/21.96 inference(transitivity,[status(thm)],[559, 439, 556, 830])).
% 21.79/21.96 tff(832,plain,
% 21.79/21.96 (mult(mult(mult(a, b), b), c) = mult(mult(a, mult(unit, mult(mult(b, unit), b))), c)),
% 21.79/21.96 inference(monotonicity,[status(thm)],[831])).
% 21.79/21.96 tff(833,plain,
% 21.79/21.96 (mult(mult(a, mult(unit, mult(mult(b, unit), b))), c) = mult(mult(mult(a, b), b), c)),
% 21.79/21.96 inference(symmetry,[status(thm)],[832])).
% 21.79/21.96 tff(834,plain,
% 21.79/21.96 ((mult(a, mult(c, mult(unit, mult(mult(b, unit), b)))) = mult(a, mult(mult(unit, mult(mult(b, unit), b)), c))) <=> (mult(a, mult(mult(unit, mult(mult(b, unit), b)), c)) = mult(a, mult(c, mult(unit, mult(mult(b, unit), b)))))),
% 21.79/21.96 inference(commutativity,[status(thm)],[])).
% 21.79/21.96 tff(835,plain,
% 21.79/21.96 (mult(c, mult(mult(unit, b), unit)) = mult(c, b)),
% 21.79/21.96 inference(monotonicity,[status(thm)],[186])).
% 21.79/21.96 tff(836,plain,
% 21.79/21.96 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(c, unit), b), unit) = mult(c, mult(mult(unit, b), unit)))),
% 21.79/21.96 inference(quant_inst,[status(thm)],[])).
% 21.79/21.96 tff(837,plain,
% 21.79/21.96 (mult(mult(mult(c, unit), b), unit) = mult(c, mult(mult(unit, b), unit))),
% 21.79/21.96 inference(unit_resolution,[status(thm)],[836, 56])).
% 21.79/21.96 tff(838,plain,
% 21.79/21.96 ((~![A: $i] : (mult(A, unit) = A)) | (mult(mult(mult(c, unit), b), unit) = mult(mult(c, unit), b))),
% 21.79/21.96 inference(quant_inst,[status(thm)],[])).
% 21.79/21.96 tff(839,plain,
% 21.79/21.96 (mult(mult(mult(c, unit), b), unit) = mult(mult(c, unit), b)),
% 21.79/21.96 inference(unit_resolution,[status(thm)],[838, 43])).
% 21.79/21.96 tff(840,plain,
% 21.79/21.96 (mult(c, mult(mult(unit, b), unit)) = mult(mult(mult(c, unit), b), unit)),
% 21.79/21.96 inference(symmetry,[status(thm)],[837])).
% 21.79/21.96 tff(841,plain,
% 21.79/21.96 (mult(c, b) = mult(c, mult(mult(unit, b), unit))),
% 21.79/21.96 inference(symmetry,[status(thm)],[835])).
% 21.79/21.96 tff(842,plain,
% 21.79/21.96 (ld(a, mult(a, mult(b, c))) = ld(a, mult(a, mult(c, b)))),
% 21.79/21.96 inference(symmetry,[status(thm)],[237])).
% 21.79/21.96 tff(843,plain,
% 21.79/21.96 (mult(b, c) = ld(a, mult(a, mult(b, c)))),
% 21.79/21.96 inference(symmetry,[status(thm)],[141])).
% 21.79/21.96 tff(844,plain,
% 21.79/21.96 (mult(b, c) = mult(mult(c, unit), b)),
% 21.79/21.96 inference(transitivity,[status(thm)],[843, 842, 239, 841, 840, 839])).
% 21.79/21.96 tff(845,plain,
% 21.79/21.96 (mult(mult(b, c), unit) = mult(mult(mult(c, unit), b), unit)),
% 21.79/21.96 inference(monotonicity,[status(thm)],[844])).
% 21.79/21.96 tff(846,plain,
% 21.79/21.96 (mult(mult(c, b), unit) = mult(mult(b, c), unit)),
% 21.79/21.96 inference(monotonicity,[status(thm)],[241])).
% 21.79/21.96 tff(847,plain,
% 21.79/21.96 (mult(mult(c, b), unit) = mult(b, c)),
% 21.79/21.96 inference(transitivity,[status(thm)],[846, 845, 837, 835, 240, 237, 141])).
% 21.79/21.96 tff(848,plain,
% 21.79/21.96 (mult(mult(mult(c, b), unit), b) = mult(mult(b, c), b)),
% 21.79/21.96 inference(monotonicity,[status(thm)],[847])).
% 21.79/21.96 tff(849,plain,
% 21.79/21.96 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(c, b), unit), b) = mult(c, mult(mult(b, unit), b)))),
% 21.79/21.96 inference(quant_inst,[status(thm)],[])).
% 21.79/21.96 tff(850,plain,
% 21.79/21.96 (mult(mult(mult(c, b), unit), b) = mult(c, mult(mult(b, unit), b))),
% 21.79/21.96 inference(unit_resolution,[status(thm)],[849, 56])).
% 21.79/21.96 tff(851,plain,
% 21.79/21.96 (mult(c, mult(mult(b, unit), b)) = mult(mult(mult(c, b), unit), b)),
% 21.79/21.96 inference(symmetry,[status(thm)],[850])).
% 21.79/21.96 tff(852,plain,
% 21.79/21.96 (mult(c, mult(unit, mult(mult(b, unit), b))) = mult(c, mult(mult(b, unit), b))),
% 21.79/21.96 inference(monotonicity,[status(thm)],[429])).
% 21.79/21.96 tff(853,plain,
% 21.79/21.96 (mult(c, mult(unit, mult(mult(b, unit), b))) = mult(mult(b, c), b)),
% 21.79/21.96 inference(transitivity,[status(thm)],[852, 851, 848])).
% 21.79/21.96 tff(854,plain,
% 21.79/21.96 (mult(a, mult(c, mult(unit, mult(mult(b, unit), b)))) = mult(mult(unit, a), mult(mult(b, c), b))),
% 21.79/21.96 inference(monotonicity,[status(thm)],[245, 853])).
% 21.79/21.96 tff(855,plain,
% 21.79/21.96 (mult(mult(unit, a), mult(mult(b, c), b)) = mult(a, mult(c, mult(unit, mult(mult(b, unit), b))))),
% 21.79/21.96 inference(symmetry,[status(thm)],[854])).
% 21.79/21.96 tff(856,plain,
% 21.79/21.96 (mult(mult(a, c), mult(mult(unit, b), unit)) = mult(mult(a, c), b)),
% 21.79/21.96 inference(monotonicity,[status(thm)],[186])).
% 21.79/21.96 tff(857,plain,
% 21.79/21.96 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(a, c), unit), b), unit) = mult(mult(a, c), mult(mult(unit, b), unit)))),
% 21.79/21.96 inference(quant_inst,[status(thm)],[])).
% 21.79/21.96 tff(858,plain,
% 21.79/21.96 (mult(mult(mult(mult(a, c), unit), b), unit) = mult(mult(a, c), mult(mult(unit, b), unit))),
% 21.79/21.96 inference(unit_resolution,[status(thm)],[857, 56])).
% 21.79/21.96 tff(859,plain,
% 21.79/21.96 ((~![A: $i] : (mult(A, unit) = A)) | (mult(mult(mult(mult(a, c), unit), b), unit) = mult(mult(mult(a, c), unit), b))),
% 21.79/21.96 inference(quant_inst,[status(thm)],[])).
% 21.79/21.96 tff(860,plain,
% 21.79/21.96 (mult(mult(mult(mult(a, c), unit), b), unit) = mult(mult(mult(a, c), unit), b)),
% 21.79/21.96 inference(unit_resolution,[status(thm)],[859, 43])).
% 21.79/21.96 tff(861,plain,
% 21.79/21.96 (mult(mult(a, c), mult(mult(unit, b), unit)) = mult(mult(mult(mult(a, c), unit), b), unit)),
% 21.79/21.96 inference(symmetry,[status(thm)],[858])).
% 21.79/21.96 tff(862,plain,
% 21.79/21.96 (mult(mult(a, c), b) = mult(mult(a, c), mult(mult(unit, b), unit))),
% 21.79/21.96 inference(symmetry,[status(thm)],[856])).
% 21.79/21.96 tff(863,plain,
% 21.79/21.96 (mult(mult(a, c), b) = mult(mult(mult(a, c), unit), b)),
% 21.79/21.96 inference(transitivity,[status(thm)],[862, 861, 860])).
% 21.79/21.96 tff(864,plain,
% 21.79/21.96 (mult(mult(mult(a, c), b), unit) = mult(mult(mult(mult(a, c), unit), b), unit)),
% 21.79/21.96 inference(monotonicity,[status(thm)],[863])).
% 21.79/21.96 tff(865,plain,
% 21.79/21.96 (mult(mult(mult(a, c), b), unit) = mult(mult(a, b), c)),
% 21.79/21.96 inference(transitivity,[status(thm)],[864, 858, 856, 161])).
% 21.79/21.96 tff(866,plain,
% 21.79/21.96 (mult(mult(mult(mult(a, c), b), unit), b) = mult(mult(mult(a, b), c), b)),
% 21.79/21.96 inference(monotonicity,[status(thm)],[865])).
% 21.79/21.96 tff(867,plain,
% 21.79/21.96 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(a, c), b), unit), b) = mult(mult(a, c), mult(mult(b, unit), b)))),
% 21.79/21.96 inference(quant_inst,[status(thm)],[])).
% 21.79/21.96 tff(868,plain,
% 21.79/21.96 (mult(mult(mult(mult(a, c), b), unit), b) = mult(mult(a, c), mult(mult(b, unit), b))),
% 21.79/21.96 inference(unit_resolution,[status(thm)],[867, 56])).
% 21.79/21.96 tff(869,plain,
% 21.79/21.96 (mult(mult(a, c), mult(mult(b, unit), b)) = mult(mult(mult(mult(a, c), b), unit), b)),
% 21.79/21.96 inference(symmetry,[status(thm)],[868])).
% 21.79/21.96 tff(870,plain,
% 21.79/21.96 (mult(mult(a, c), mult(unit, mult(mult(b, unit), b))) = mult(mult(a, c), mult(mult(b, unit), b))),
% 21.79/21.96 inference(monotonicity,[status(thm)],[429])).
% 21.79/21.96 tff(871,assumption,(~(mult(mult(a, mult(unit, mult(mult(b, unit), b))), c) = mult(a, mult(mult(unit, mult(mult(b, unit), b)), c)))), introduced(assumption)).
% 21.79/21.96 tff(872,plain,
% 21.79/21.96 (((~(mult(mult(a, mult(unit, mult(mult(b, unit), b))), c) = mult(a, mult(mult(unit, mult(mult(b, unit), b)), c)))) | (~(mult(mult(a, c), mult(unit, mult(mult(b, unit), b))) = mult(a, mult(c, mult(unit, mult(mult(b, unit), b))))))) | (mult(mult(a, mult(unit, mult(mult(b, unit), b))), c) = mult(a, mult(mult(unit, mult(mult(b, unit), b)), c)))),
% 21.79/21.96 inference(tautology,[status(thm)],[])).
% 21.79/21.96 tff(873,plain,
% 21.79/21.96 ((~(mult(mult(a, mult(unit, mult(mult(b, unit), b))), c) = mult(a, mult(mult(unit, mult(mult(b, unit), b)), c)))) | (~(mult(mult(a, c), mult(unit, mult(mult(b, unit), b))) = mult(a, mult(c, mult(unit, mult(mult(b, unit), b))))))),
% 21.79/21.96 inference(unit_resolution,[status(thm)],[872, 871])).
% 21.79/21.96 tff(874,plain,
% 21.79/21.96 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(a, mult(mult(unit, mult(mult(b, unit), b)), c)) = mult(a, mult(c, mult(unit, mult(mult(b, unit), b)))))) | (~(mult(mult(a, mult(unit, mult(mult(b, unit), b))), c) = mult(mult(a, c), mult(unit, mult(mult(b, unit), b))))))) | (~((~(mult(mult(a, mult(unit, mult(mult(b, unit), b))), c) = mult(a, mult(mult(unit, mult(mult(b, unit), b)), c)))) | (~(mult(mult(a, c), mult(unit, mult(mult(b, unit), b))) = mult(a, mult(c, mult(unit, mult(mult(b, unit), b)))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(a, mult(mult(unit, mult(mult(b, unit), b)), c)) = mult(a, mult(c, mult(unit, mult(mult(b, unit), b)))))) | (~(mult(mult(a, mult(unit, mult(mult(b, unit), b))), c) = mult(mult(a, c), mult(unit, mult(mult(b, unit), b))))))) | (~((~(mult(mult(a, mult(unit, mult(mult(b, unit), b))), c) = mult(a, mult(mult(unit, mult(mult(b, unit), b)), c)))) | (~(mult(mult(a, c), mult(unit, mult(mult(b, unit), b))) = mult(a, mult(c, mult(unit, mult(mult(b, unit), b)))))))))),
% 21.79/21.96 inference(rewrite,[status(thm)],[])).
% 21.79/21.96 tff(875,plain,
% 21.79/21.96 (((~((~(mult(mult(a, mult(unit, mult(mult(b, unit), b))), c) = mult(mult(a, c), mult(unit, mult(mult(b, unit), b))))) | (~(mult(a, mult(mult(unit, mult(mult(b, unit), b)), c)) = mult(a, mult(c, mult(unit, mult(mult(b, unit), b)))))))) | (~((~(mult(mult(a, mult(unit, mult(mult(b, unit), b))), c) = mult(a, mult(mult(unit, mult(mult(b, unit), b)), c)))) | (~(mult(mult(a, c), mult(unit, mult(mult(b, unit), b))) = mult(a, mult(c, mult(unit, mult(mult(b, unit), b))))))))) <=> ((~((~(mult(a, mult(mult(unit, mult(mult(b, unit), b)), c)) = mult(a, mult(c, mult(unit, mult(mult(b, unit), b)))))) | (~(mult(mult(a, mult(unit, mult(mult(b, unit), b))), c) = mult(mult(a, c), mult(unit, mult(mult(b, unit), b))))))) | (~((~(mult(mult(a, mult(unit, mult(mult(b, unit), b))), c) = mult(a, mult(mult(unit, mult(mult(b, unit), b)), c)))) | (~(mult(mult(a, c), mult(unit, mult(mult(b, unit), b))) = mult(a, mult(c, mult(unit, mult(mult(b, unit), b)))))))))),
% 21.79/21.96 inference(rewrite,[status(thm)],[])).
% 21.79/21.96 tff(876,plain,
% 21.79/21.96 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, mult(unit, mult(mult(b, unit), b))), c) = mult(mult(a, c), mult(unit, mult(mult(b, unit), b))))) | (~(mult(a, mult(mult(unit, mult(mult(b, unit), b)), c)) = mult(a, mult(c, mult(unit, mult(mult(b, unit), b)))))))) | (~((~(mult(mult(a, mult(unit, mult(mult(b, unit), b))), c) = mult(a, mult(mult(unit, mult(mult(b, unit), b)), c)))) | (~(mult(mult(a, c), mult(unit, mult(mult(b, unit), b))) = mult(a, mult(c, mult(unit, mult(mult(b, unit), b)))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(a, mult(mult(unit, mult(mult(b, unit), b)), c)) = mult(a, mult(c, mult(unit, mult(mult(b, unit), b)))))) | (~(mult(mult(a, mult(unit, mult(mult(b, unit), b))), c) = mult(mult(a, c), mult(unit, mult(mult(b, unit), b))))))) | (~((~(mult(mult(a, mult(unit, mult(mult(b, unit), b))), c) = mult(a, mult(mult(unit, mult(mult(b, unit), b)), c)))) | (~(mult(mult(a, c), mult(unit, mult(mult(b, unit), b))) = mult(a, mult(c, mult(unit, mult(mult(b, unit), b))))))))))),
% 21.79/21.96 inference(monotonicity,[status(thm)],[875])).
% 21.79/21.96 tff(877,plain,
% 21.79/21.96 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, mult(unit, mult(mult(b, unit), b))), c) = mult(mult(a, c), mult(unit, mult(mult(b, unit), b))))) | (~(mult(a, mult(mult(unit, mult(mult(b, unit), b)), c)) = mult(a, mult(c, mult(unit, mult(mult(b, unit), b)))))))) | (~((~(mult(mult(a, mult(unit, mult(mult(b, unit), b))), c) = mult(a, mult(mult(unit, mult(mult(b, unit), b)), c)))) | (~(mult(mult(a, c), mult(unit, mult(mult(b, unit), b))) = mult(a, mult(c, mult(unit, mult(mult(b, unit), b)))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(a, mult(mult(unit, mult(mult(b, unit), b)), c)) = mult(a, mult(c, mult(unit, mult(mult(b, unit), b)))))) | (~(mult(mult(a, mult(unit, mult(mult(b, unit), b))), c) = mult(mult(a, c), mult(unit, mult(mult(b, unit), b))))))) | (~((~(mult(mult(a, mult(unit, mult(mult(b, unit), b))), c) = mult(a, mult(mult(unit, mult(mult(b, unit), b)), c)))) | (~(mult(mult(a, c), mult(unit, mult(mult(b, unit), b))) = mult(a, mult(c, mult(unit, mult(mult(b, unit), b)))))))))),
% 21.79/21.96 inference(transitivity,[status(thm)],[876, 874])).
% 21.79/21.96 tff(878,plain,
% 21.79/21.96 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, mult(unit, mult(mult(b, unit), b))), c) = mult(mult(a, c), mult(unit, mult(mult(b, unit), b))))) | (~(mult(a, mult(mult(unit, mult(mult(b, unit), b)), c)) = mult(a, mult(c, mult(unit, mult(mult(b, unit), b)))))))) | (~((~(mult(mult(a, mult(unit, mult(mult(b, unit), b))), c) = mult(a, mult(mult(unit, mult(mult(b, unit), b)), c)))) | (~(mult(mult(a, c), mult(unit, mult(mult(b, unit), b))) = mult(a, mult(c, mult(unit, mult(mult(b, unit), b)))))))))),
% 21.79/21.96 inference(quant_inst,[status(thm)],[])).
% 21.79/21.96 tff(879,plain,
% 21.79/21.96 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(a, mult(mult(unit, mult(mult(b, unit), b)), c)) = mult(a, mult(c, mult(unit, mult(mult(b, unit), b)))))) | (~(mult(mult(a, mult(unit, mult(mult(b, unit), b))), c) = mult(mult(a, c), mult(unit, mult(mult(b, unit), b))))))) | (~((~(mult(mult(a, mult(unit, mult(mult(b, unit), b))), c) = mult(a, mult(mult(unit, mult(mult(b, unit), b)), c)))) | (~(mult(mult(a, c), mult(unit, mult(mult(b, unit), b))) = mult(a, mult(c, mult(unit, mult(mult(b, unit), b))))))))),
% 21.79/21.96 inference(modus_ponens,[status(thm)],[878, 877])).
% 21.79/21.96 tff(880,plain,
% 21.79/21.96 ((~((~(mult(a, mult(mult(unit, mult(mult(b, unit), b)), c)) = mult(a, mult(c, mult(unit, mult(mult(b, unit), b)))))) | (~(mult(mult(a, mult(unit, mult(mult(b, unit), b))), c) = mult(mult(a, c), mult(unit, mult(mult(b, unit), b))))))) | (~((~(mult(mult(a, mult(unit, mult(mult(b, unit), b))), c) = mult(a, mult(mult(unit, mult(mult(b, unit), b)), c)))) | (~(mult(mult(a, c), mult(unit, mult(mult(b, unit), b))) = mult(a, mult(c, mult(unit, mult(mult(b, unit), b))))))))),
% 21.79/21.96 inference(unit_resolution,[status(thm)],[879, 27])).
% 21.79/21.96 tff(881,plain,
% 21.79/21.96 (~((~(mult(a, mult(mult(unit, mult(mult(b, unit), b)), c)) = mult(a, mult(c, mult(unit, mult(mult(b, unit), b)))))) | (~(mult(mult(a, mult(unit, mult(mult(b, unit), b))), c) = mult(mult(a, c), mult(unit, mult(mult(b, unit), b))))))),
% 21.79/21.96 inference(unit_resolution,[status(thm)],[880, 873])).
% 21.79/21.96 tff(882,plain,
% 21.79/21.96 (((~(mult(a, mult(mult(unit, mult(mult(b, unit), b)), c)) = mult(a, mult(c, mult(unit, mult(mult(b, unit), b)))))) | (~(mult(mult(a, mult(unit, mult(mult(b, unit), b))), c) = mult(mult(a, c), mult(unit, mult(mult(b, unit), b)))))) | (mult(mult(a, mult(unit, mult(mult(b, unit), b))), c) = mult(mult(a, c), mult(unit, mult(mult(b, unit), b))))),
% 21.79/21.96 inference(tautology,[status(thm)],[])).
% 21.79/21.96 tff(883,plain,
% 21.79/21.96 (mult(mult(a, mult(unit, mult(mult(b, unit), b))), c) = mult(mult(a, c), mult(unit, mult(mult(b, unit), b)))),
% 21.79/21.96 inference(unit_resolution,[status(thm)],[882, 881])).
% 21.79/21.96 tff(884,plain,
% 21.79/21.96 (mult(mult(a, mult(unit, mult(mult(b, unit), b))), c) = mult(a, mult(c, mult(unit, mult(mult(b, unit), b))))),
% 21.79/21.96 inference(transitivity,[status(thm)],[883, 870, 869, 866, 781, 779, 855])).
% 21.79/21.96 tff(885,plain,
% 21.79/21.96 ((mult(mult(a, mult(unit, mult(mult(b, unit), b))), c) = mult(a, mult(mult(unit, mult(mult(b, unit), b)), c))) <=> (mult(a, mult(c, mult(unit, mult(mult(b, unit), b)))) = mult(a, mult(mult(unit, mult(mult(b, unit), b)), c)))),
% 21.79/21.96 inference(monotonicity,[status(thm)],[884])).
% 21.79/21.96 tff(886,plain,
% 21.79/21.96 ((mult(mult(a, mult(unit, mult(mult(b, unit), b))), c) = mult(a, mult(mult(unit, mult(mult(b, unit), b)), c))) <=> (mult(a, mult(mult(unit, mult(mult(b, unit), b)), c)) = mult(a, mult(c, mult(unit, mult(mult(b, unit), b)))))),
% 21.79/21.96 inference(transitivity,[status(thm)],[885, 834])).
% 21.79/21.96 tff(887,plain,
% 21.79/21.96 ((mult(a, mult(mult(unit, mult(mult(b, unit), b)), c)) = mult(a, mult(c, mult(unit, mult(mult(b, unit), b))))) <=> (mult(mult(a, mult(unit, mult(mult(b, unit), b))), c) = mult(a, mult(mult(unit, mult(mult(b, unit), b)), c)))),
% 21.79/21.96 inference(symmetry,[status(thm)],[886])).
% 21.79/21.96 tff(888,plain,
% 21.79/21.96 (((~(mult(a, mult(mult(unit, mult(mult(b, unit), b)), c)) = mult(a, mult(c, mult(unit, mult(mult(b, unit), b)))))) | (~(mult(mult(a, mult(unit, mult(mult(b, unit), b))), c) = mult(mult(a, c), mult(unit, mult(mult(b, unit), b)))))) | (mult(a, mult(mult(unit, mult(mult(b, unit), b)), c)) = mult(a, mult(c, mult(unit, mult(mult(b, unit), b)))))),
% 21.79/21.96 inference(tautology,[status(thm)],[])).
% 21.79/21.96 tff(889,plain,
% 21.79/21.96 (mult(a, mult(mult(unit, mult(mult(b, unit), b)), c)) = mult(a, mult(c, mult(unit, mult(mult(b, unit), b))))),
% 21.79/21.96 inference(unit_resolution,[status(thm)],[888, 881])).
% 21.79/21.96 tff(890,plain,
% 21.79/21.96 (mult(mult(a, mult(unit, mult(mult(b, unit), b))), c) = mult(a, mult(mult(unit, mult(mult(b, unit), b)), c))),
% 21.79/21.96 inference(modus_ponens,[status(thm)],[889, 887])).
% 21.79/21.96 tff(891,plain,
% 21.79/21.96 ($false),
% 21.79/21.96 inference(unit_resolution,[status(thm)],[871, 890])).
% 21.79/21.96 tff(892,plain,(mult(mult(a, mult(unit, mult(mult(b, unit), b))), c) = mult(a, mult(mult(unit, mult(mult(b, unit), b)), c))), inference(lemma,lemma(discharge,[]))).
% 21.79/21.96 tff(893,plain,
% 21.79/21.96 (mult(a, mult(mult(unit, mult(mult(b, unit), b)), c)) = mult(mult(a, mult(unit, mult(mult(b, unit), b))), c)),
% 21.79/21.96 inference(symmetry,[status(thm)],[892])).
% 21.79/21.96 tff(894,plain,
% 21.79/21.96 (mult(a, mult(mult(unit, mult(mult(b, unit), b)), c)) = mult(mult(mult(a, b), c), b)),
% 21.79/21.96 inference(transitivity,[status(thm)],[893, 833, 828])).
% 21.79/21.96 tff(895,plain,
% 21.79/21.96 (mult(mult(a, mult(mult(unit, mult(mult(b, unit), b)), c)), a) = mult(mult(mult(mult(a, b), c), b), a)),
% 21.79/21.97 inference(monotonicity,[status(thm)],[894])).
% 21.79/21.97 tff(896,plain,
% 21.79/21.97 (mult(mult(mult(mult(a, b), c), b), a) = mult(mult(a, mult(mult(unit, mult(mult(b, unit), b)), c)), a)),
% 21.79/21.97 inference(symmetry,[status(thm)],[895])).
% 21.79/21.97 tff(897,plain,
% 21.79/21.97 ((mult(mult(mult(a, b), c), mult(a, b)) = mult(mult(mult(a, b), c), mult(b, a))) <=> (mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(a, b)))),
% 21.79/21.97 inference(commutativity,[status(thm)],[])).
% 21.79/21.97 tff(898,assumption,(~(mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a)))), introduced(assumption)).
% 21.79/21.97 tff(899,plain,
% 21.79/21.97 (((~(mult(mult(a, a), rd(mult(b, c), mult(a, c))) = mult(a, mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a))))) | (mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a)))),
% 21.79/21.97 inference(tautology,[status(thm)],[])).
% 21.79/21.97 tff(900,plain,
% 21.79/21.97 ((~(mult(mult(a, a), rd(mult(b, c), mult(a, c))) = mult(a, mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a))))),
% 21.79/21.97 inference(unit_resolution,[status(thm)],[899, 898])).
% 21.79/21.97 tff(901,assumption,((~(mult(mult(a, a), rd(mult(b, c), mult(a, c))) = mult(a, mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a))))), introduced(assumption)).
% 21.79/21.97 tff(902,assumption,((~(mult(mult(a, a), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), a))) | (~(mult(a, mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), a))))), introduced(assumption)).
% 21.79/21.97 tff(903,plain,
% 21.79/21.97 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, a), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), a))) | (~(mult(a, mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), a)))))) | (~((~(mult(mult(a, a), rd(mult(b, c), mult(a, c))) = mult(a, mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, a), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), a))) | (~(mult(a, mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), a)))))) | (~((~(mult(mult(a, a), rd(mult(b, c), mult(a, c))) = mult(a, mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a)))))))),
% 21.79/21.97 inference(rewrite,[status(thm)],[])).
% 21.79/21.97 tff(904,plain,
% 21.79/21.97 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, a), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), a))) | (~(mult(a, mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), a)))))) | (~((~(mult(mult(a, a), rd(mult(b, c), mult(a, c))) = mult(a, mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a)))))))),
% 21.79/21.97 inference(quant_inst,[status(thm)],[])).
% 21.79/21.97 tff(905,plain,
% 21.79/21.97 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, a), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), a))) | (~(mult(a, mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), a)))))) | (~((~(mult(mult(a, a), rd(mult(b, c), mult(a, c))) = mult(a, mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a))))))),
% 21.79/21.97 inference(modus_ponens,[status(thm)],[904, 903])).
% 21.79/21.97 tff(906,plain,
% 21.79/21.97 ($false),
% 21.79/21.97 inference(unit_resolution,[status(thm)],[905, 27, 902, 901])).
% 21.79/21.97 tff(907,plain,((~((~(mult(mult(a, a), rd(mult(b, c), mult(a, c))) = mult(a, mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a)))))) | (~((~(mult(mult(a, a), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), a))) | (~(mult(a, mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), a))))))), inference(lemma,lemma(discharge,[]))).
% 21.79/21.97 tff(908,plain,
% 21.79/21.97 (~((~(mult(mult(a, a), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), a))) | (~(mult(a, mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), a)))))),
% 21.79/21.97 inference(unit_resolution,[status(thm)],[907, 900])).
% 21.79/21.97 tff(909,plain,
% 21.79/21.97 (((~(mult(mult(a, a), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), a))) | (~(mult(a, mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), a))))) | (mult(a, mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), a)))),
% 21.79/21.97 inference(tautology,[status(thm)],[])).
% 21.79/21.97 tff(910,plain,
% 21.79/21.97 (mult(a, mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), a))),
% 21.79/21.97 inference(unit_resolution,[status(thm)],[909, 908])).
% 21.79/21.97 tff(911,plain,
% 21.79/21.97 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(a, mult(a, b)) = b)),
% 21.79/21.97 inference(quant_inst,[status(thm)],[])).
% 21.79/21.97 tff(912,plain,
% 21.79/21.97 (ld(a, mult(a, b)) = b),
% 21.79/21.97 inference(unit_resolution,[status(thm)],[911, 7])).
% 21.79/21.97 tff(913,plain,
% 21.79/21.97 (mult(a, mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, b)),
% 21.79/21.97 inference(monotonicity,[status(thm)],[176])).
% 21.79/21.97 tff(914,assumption,(mult(a, mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), a))), introduced(assumption)).
% 21.79/21.97 tff(915,plain,
% 21.79/21.97 (mult(a, mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, b)),
% 21.79/21.97 inference(transitivity,[status(thm)],[914, 913])).
% 21.79/21.97 tff(916,plain,
% 21.79/21.97 (ld(a, mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = ld(a, mult(a, b))),
% 21.79/21.97 inference(monotonicity,[status(thm)],[915])).
% 21.79/21.97 tff(917,plain,
% 21.79/21.97 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(a, mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(a, rd(mult(b, c), mult(a, c))))),
% 21.79/21.97 inference(quant_inst,[status(thm)],[])).
% 21.79/21.97 tff(918,plain,
% 21.79/21.97 (ld(a, mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(a, rd(mult(b, c), mult(a, c)))),
% 21.79/21.97 inference(unit_resolution,[status(thm)],[917, 7])).
% 21.79/21.97 tff(919,plain,
% 21.79/21.97 (mult(a, rd(mult(b, c), mult(a, c))) = ld(a, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))),
% 21.79/21.97 inference(symmetry,[status(thm)],[918])).
% 21.79/21.97 tff(920,plain,
% 21.79/21.97 (mult(a, rd(mult(b, c), mult(a, c))) = b),
% 21.79/21.97 inference(transitivity,[status(thm)],[919, 916, 912])).
% 21.79/21.97 tff(921,plain,
% 21.79/21.97 (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), b)),
% 21.79/21.97 inference(monotonicity,[status(thm)],[920])).
% 21.79/21.97 tff(922,plain,
% 21.79/21.97 (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))),
% 21.79/21.97 inference(transitivity,[status(thm)],[921, 405])).
% 21.79/21.97 tff(923,plain,
% 21.79/21.97 ($false),
% 21.79/21.97 inference(unit_resolution,[status(thm)],[330, 922])).
% 21.79/21.97 tff(924,plain,((~(mult(a, mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), a)))) | (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit)))))), inference(lemma,lemma(discharge,[]))).
% 21.79/21.97 tff(925,plain,
% 21.79/21.97 (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))),
% 21.79/21.97 inference(unit_resolution,[status(thm)],[924, 910, 97])).
% 21.79/21.97 tff(926,plain,
% 21.79/21.97 (mult(mult(unit, a), b) = mult(a, b)),
% 21.79/21.97 inference(monotonicity,[status(thm)],[244])).
% 21.79/21.97 tff(927,plain,
% 21.79/21.97 (mult(a, b) = mult(mult(unit, a), b)),
% 21.79/21.97 inference(symmetry,[status(thm)],[926])).
% 21.79/21.97 tff(928,plain,
% 21.79/21.97 (mult(a, mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(unit, a), b)),
% 21.79/21.97 inference(transitivity,[status(thm)],[913, 927])).
% 21.79/21.97 tff(929,plain,
% 21.79/21.97 (mult(mult(unit, b), a) = mult(b, a)),
% 21.79/21.97 inference(monotonicity,[status(thm)],[184])).
% 21.79/21.97 tff(930,plain,
% 21.79/21.97 (mult(b, a) = mult(mult(unit, b), a)),
% 21.79/21.97 inference(symmetry,[status(thm)],[929])).
% 21.79/21.97 tff(931,plain,
% 21.79/21.97 (mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(mult(unit, b), a)),
% 21.79/21.97 inference(transitivity,[status(thm)],[473, 930])).
% 21.79/21.97 tff(932,plain,
% 21.79/21.97 ((mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a))) <=> (mult(mult(unit, b), a) = mult(mult(unit, a), b))),
% 21.79/21.97 inference(monotonicity,[status(thm)],[931, 928])).
% 21.79/21.97 tff(933,plain,
% 21.79/21.97 ((mult(mult(unit, b), a) = mult(mult(unit, a), b)) <=> (mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a)))),
% 21.79/21.97 inference(symmetry,[status(thm)],[932])).
% 21.79/21.97 tff(934,assumption,(mult(mult(unit, b), a) = mult(mult(unit, a), b)), introduced(assumption)).
% 21.79/21.97 tff(935,plain,
% 21.79/21.97 (mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a))),
% 21.79/21.97 inference(modus_ponens,[status(thm)],[934, 933])).
% 21.79/21.97 tff(936,plain,
% 21.79/21.97 ($false),
% 21.79/21.97 inference(unit_resolution,[status(thm)],[898, 935])).
% 21.79/21.97 tff(937,plain,((~(mult(mult(unit, b), a) = mult(mult(unit, a), b))) | (mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit))))) | (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))))), inference(lemma,lemma(discharge,[]))).
% 21.79/21.97 tff(938,plain,
% 21.79/21.97 (~(mult(mult(unit, b), a) = mult(mult(unit, a), b))),
% 21.79/21.97 inference(unit_resolution,[status(thm)],[937, 925, 898, 97])).
% 21.79/21.97 tff(939,plain,
% 21.79/21.97 (mult(b, a) = ld(b, mult(b, mult(b, a)))),
% 21.79/21.97 inference(symmetry,[status(thm)],[390])).
% 21.79/21.97 tff(940,plain,
% 21.79/21.97 (mult(mult(unit, b), a) = mult(mult(unit, a), b)),
% 21.79/21.97 inference(transitivity,[status(thm)],[929, 939, 393, 396, 927])).
% 21.79/21.97 tff(941,assumption,(~(mult(mult(unit, b), a) = mult(mult(unit, a), b))), introduced(assumption)).
% 21.79/21.97 tff(942,plain,
% 21.79/21.97 ($false),
% 21.79/21.97 inference(unit_resolution,[status(thm)],[941, 940])).
% 21.79/21.97 tff(943,plain,((~(mult(b, mult(a, b)) = mult(b, mult(b, a)))) | (mult(mult(unit, b), a) = mult(mult(unit, a), b))), inference(lemma,lemma(discharge,[]))).
% 21.79/21.97 tff(944,plain,
% 21.79/21.97 (~(mult(b, mult(a, b)) = mult(b, mult(b, a)))),
% 21.79/21.97 inference(unit_resolution,[status(thm)],[943, 938])).
% 21.79/21.97 tff(945,plain,
% 21.79/21.97 (~(mult(mult(a, c), mult(b, mult(a, b))) = mult(mult(a, c), mult(mult(a, b), b)))),
% 21.79/21.97 inference(unit_resolution,[status(thm)],[571, 944, 925, 97])).
% 21.79/21.97 tff(946,plain,
% 21.79/21.97 ((~(mult(mult(a, c), mult(b, mult(a, b))) = mult(mult(a, c), mult(mult(a, b), b)))) | (~(mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(mult(a, c), mult(a, b)), b)))),
% 21.79/21.97 inference(unit_resolution,[status(thm)],[576, 945])).
% 21.79/21.97 tff(947,plain,
% 21.79/21.97 (~((~(mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(a, c), mult(b, mult(a, b))))) | (~(mult(mult(mult(a, c), mult(a, b)), b) = mult(mult(a, c), mult(mult(a, b), b)))))),
% 21.79/21.97 inference(unit_resolution,[status(thm)],[584, 946])).
% 21.79/21.97 tff(948,plain,
% 21.79/21.97 (mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(a, c), mult(b, mult(a, b)))),
% 21.79/21.97 inference(unit_resolution,[status(thm)],[604, 947])).
% 21.79/21.97 tff(949,plain,
% 21.79/21.97 (mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(mult(a, b), c), mult(a, b))),
% 21.79/21.97 inference(symmetry,[status(thm)],[574])).
% 21.79/21.97 tff(950,plain,
% 21.79/21.97 (mult(mult(a, c), mult(b, mult(a, b))) = mult(mult(mult(a, c), b), mult(a, b))),
% 21.79/21.97 inference(symmetry,[status(thm)],[948])).
% 21.79/21.97 tff(951,plain,
% 21.79/21.97 ((~(mult(mult(b, a), b) = mult(mult(b, b), a))) | (~(mult(b, mult(a, b)) = mult(b, mult(b, a))))),
% 21.79/21.97 inference(unit_resolution,[status(thm)],[413, 944])).
% 21.79/21.97 tff(952,plain,
% 21.79/21.97 (~((~(mult(mult(b, a), b) = mult(b, mult(a, b)))) | (~(mult(mult(b, b), a) = mult(b, mult(b, a)))))),
% 21.79/21.97 inference(unit_resolution,[status(thm)],[418, 951])).
% 21.79/21.97 tff(953,plain,
% 21.79/21.97 (mult(mult(b, a), b) = mult(b, mult(a, b))),
% 21.79/21.97 inference(unit_resolution,[status(thm)],[420, 952])).
% 21.79/21.97 tff(954,plain,
% 21.79/21.97 (mult(mult(a, c), mult(mult(b, a), b)) = mult(mult(a, c), mult(b, mult(a, b)))),
% 21.79/21.97 inference(monotonicity,[status(thm)],[953])).
% 21.79/21.97 tff(955,plain,
% 21.79/21.97 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(a, c), b), a), b) = mult(mult(a, c), mult(mult(b, a), b)))),
% 21.79/21.97 inference(quant_inst,[status(thm)],[])).
% 21.79/21.97 tff(956,plain,
% 21.79/21.97 (mult(mult(mult(mult(a, c), b), a), b) = mult(mult(a, c), mult(mult(b, a), b))),
% 21.79/21.97 inference(unit_resolution,[status(thm)],[955, 56])).
% 21.79/21.97 tff(957,plain,
% 21.79/21.97 (mult(mult(mult(a, c), b), a) = mult(mult(mult(a, b), c), a)),
% 21.79/21.97 inference(monotonicity,[status(thm)],[161])).
% 21.79/21.97 tff(958,plain,
% 21.79/21.97 (mult(mult(mult(a, b), c), a) = mult(mult(mult(a, c), b), a)),
% 21.79/21.97 inference(symmetry,[status(thm)],[957])).
% 21.79/21.97 tff(959,plain,
% 21.79/21.97 (mult(mult(mult(mult(a, b), c), a), b) = mult(mult(mult(mult(a, c), b), a), b)),
% 21.79/21.97 inference(monotonicity,[status(thm)],[958])).
% 21.79/21.97 tff(960,plain,
% 21.79/21.97 (mult(mult(mult(mult(a, b), c), a), b) = mult(mult(mult(a, b), c), mult(a, b))),
% 21.79/21.97 inference(transitivity,[status(thm)],[959, 956, 954, 950, 949])).
% 21.79/21.97 tff(961,assumption,(mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(a, c), mult(b, mult(a, b)))), introduced(assumption)).
% 21.79/21.97 tff(962,assumption,(mult(mult(mult(mult(a, b), c), a), b) = mult(mult(mult(a, b), c), mult(a, b))), introduced(assumption)).
% 21.79/21.97 tff(963,plain,
% 21.79/21.97 (mult(mult(mult(mult(a, c), b), a), b) = mult(mult(mult(mult(a, b), c), a), b)),
% 21.79/21.97 inference(monotonicity,[status(thm)],[957])).
% 21.79/21.97 tff(964,plain,
% 21.79/21.97 (mult(mult(a, c), mult(mult(b, a), b)) = mult(mult(mult(mult(a, c), b), a), b)),
% 21.79/21.97 inference(symmetry,[status(thm)],[956])).
% 21.79/21.97 tff(965,assumption,(mult(mult(a, c), mult(mult(b, a), b)) = mult(mult(a, c), mult(b, mult(b, a)))), introduced(assumption)).
% 21.79/21.97 tff(966,plain,
% 21.79/21.97 (mult(mult(a, c), mult(b, mult(b, a))) = mult(mult(a, c), mult(mult(b, a), b))),
% 21.79/21.97 inference(symmetry,[status(thm)],[965])).
% 21.79/21.97 tff(967,plain,
% 21.79/21.97 (mult(unit, mult(mult(mult(b, unit), b), a)) = mult(b, mult(b, a))),
% 21.79/21.97 inference(transitivity,[status(thm)],[466, 435, 423])).
% 21.79/21.97 tff(968,plain,
% 21.79/21.97 (mult(mult(a, c), mult(unit, mult(mult(mult(b, unit), b), a))) = mult(mult(a, c), mult(b, mult(b, a)))),
% 21.79/21.97 inference(monotonicity,[status(thm)],[967])).
% 21.79/21.97 tff(969,plain,
% 21.79/21.97 (mult(mult(a, c), mult(unit, mult(mult(mult(b, unit), b), a))) = mult(mult(a, c), mult(b, mult(a, b)))),
% 21.79/21.97 inference(transitivity,[status(thm)],[968, 966, 964, 963, 962, 574, 961])).
% 21.79/21.97 tff(970,plain,
% 21.79/21.97 (ld(mult(a, c), mult(mult(a, c), mult(unit, mult(mult(mult(b, unit), b), a)))) = ld(mult(a, c), mult(mult(a, c), mult(b, mult(a, b))))),
% 21.79/21.97 inference(monotonicity,[status(thm)],[969])).
% 21.79/21.97 tff(971,plain,
% 21.79/21.97 (ld(mult(a, c), mult(mult(a, c), mult(b, mult(a, b)))) = ld(mult(a, c), mult(mult(a, c), mult(unit, mult(mult(mult(b, unit), b), a))))),
% 21.79/21.97 inference(symmetry,[status(thm)],[970])).
% 21.79/21.97 tff(972,plain,
% 21.79/21.97 (mult(b, mult(a, b)) = mult(b, mult(b, a))),
% 21.79/21.97 inference(transitivity,[status(thm)],[567, 971, 427, 466, 435, 423])).
% 21.79/21.97 tff(973,plain,
% 21.79/21.97 ($false),
% 21.79/21.97 inference(unit_resolution,[status(thm)],[412, 972])).
% 21.79/21.97 tff(974,plain,((~(mult(mult(a, c), mult(mult(b, a), b)) = mult(mult(a, c), mult(b, mult(b, a))))) | (mult(b, mult(a, b)) = mult(b, mult(b, a))) | (~(mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(a, c), mult(b, mult(a, b))))) | (~(mult(mult(mult(mult(a, b), c), a), b) = mult(mult(mult(a, b), c), mult(a, b))))), inference(lemma,lemma(discharge,[]))).
% 21.79/21.97 tff(975,plain,
% 21.79/21.97 (~(mult(mult(a, c), mult(mult(b, a), b)) = mult(mult(a, c), mult(b, mult(b, a))))),
% 21.79/21.98 inference(unit_resolution,[status(thm)],[974, 960, 948, 944])).
% 21.79/21.98 tff(976,plain,
% 21.79/21.98 ((~(mult(mult(mult(a, c), mult(b, a)), b) = mult(mult(mult(a, c), b), mult(b, a)))) | (~(mult(mult(a, c), mult(mult(b, a), b)) = mult(mult(a, c), mult(b, mult(b, a)))))),
% 21.79/21.98 inference(unit_resolution,[status(thm)],[617, 975])).
% 21.79/21.98 tff(977,plain,
% 21.79/21.98 (~((~(mult(mult(mult(a, c), mult(b, a)), b) = mult(mult(a, c), mult(mult(b, a), b)))) | (~(mult(mult(mult(a, c), b), mult(b, a)) = mult(mult(a, c), mult(b, mult(b, a))))))),
% 21.79/21.98 inference(unit_resolution,[status(thm)],[622, 976])).
% 21.79/21.98 tff(978,plain,
% 21.79/21.98 (mult(mult(mult(a, c), b), mult(b, a)) = mult(mult(a, c), mult(b, mult(b, a)))),
% 21.79/21.98 inference(unit_resolution,[status(thm)],[624, 977])).
% 21.79/21.98 tff(979,plain,
% 21.79/21.98 (mult(mult(a, c), mult(b, mult(b, a))) = mult(mult(mult(a, c), b), mult(b, a))),
% 21.79/21.98 inference(symmetry,[status(thm)],[978])).
% 21.79/21.98 tff(980,plain,
% 21.79/21.98 (mult(mult(a, c), mult(b, mult(b, a))) = mult(mult(mult(a, b), c), mult(b, a))),
% 21.79/21.98 inference(transitivity,[status(thm)],[979, 653])).
% 21.79/21.98 tff(981,plain,
% 21.79/21.98 (mult(mult(a, c), mult(mult(b, a), b)) = mult(mult(mult(a, b), c), mult(a, b))),
% 21.79/21.98 inference(transitivity,[status(thm)],[954, 950, 949])).
% 21.79/21.98 tff(982,plain,
% 21.79/21.98 ((mult(mult(a, c), mult(mult(b, a), b)) = mult(mult(a, c), mult(b, mult(b, a)))) <=> (mult(mult(mult(a, b), c), mult(a, b)) = mult(mult(mult(a, b), c), mult(b, a)))),
% 21.79/21.98 inference(monotonicity,[status(thm)],[981, 980])).
% 21.79/21.98 tff(983,plain,
% 21.79/21.98 ((mult(mult(a, c), mult(mult(b, a), b)) = mult(mult(a, c), mult(b, mult(b, a)))) <=> (mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(a, b)))),
% 21.79/21.98 inference(transitivity,[status(thm)],[982, 897])).
% 21.79/21.98 tff(984,plain,
% 21.79/21.98 ((~(mult(mult(a, c), mult(mult(b, a), b)) = mult(mult(a, c), mult(b, mult(b, a))))) <=> (~(mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(a, b))))),
% 21.79/21.98 inference(monotonicity,[status(thm)],[983])).
% 21.79/21.98 tff(985,plain,
% 21.79/21.98 (~(mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(a, b)))),
% 21.79/21.98 inference(modus_ponens,[status(thm)],[975, 984])).
% 21.79/21.98 tff(986,plain,
% 21.79/21.98 ((~(mult(mult(mult(mult(a, b), c), b), a) = mult(mult(mult(mult(a, b), c), a), b))) | (~(mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(a, b))))),
% 21.79/21.98 inference(unit_resolution,[status(thm)],[637, 985])).
% 21.79/21.98 tff(987,plain,
% 21.79/21.98 (~((~(mult(mult(mult(mult(a, b), c), b), a) = mult(mult(mult(a, b), c), mult(b, a)))) | (~(mult(mult(mult(mult(a, b), c), a), b) = mult(mult(mult(a, b), c), mult(a, b)))))),
% 21.79/21.98 inference(unit_resolution,[status(thm)],[642, 986])).
% 21.79/21.98 tff(988,plain,
% 21.79/21.98 (mult(mult(mult(mult(a, b), c), b), a) = mult(mult(mult(a, b), c), mult(b, a))),
% 21.79/21.98 inference(unit_resolution,[status(thm)],[644, 987])).
% 21.79/21.98 tff(989,plain,
% 21.79/21.98 (mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(mult(a, b), c), b), a)),
% 21.79/21.98 inference(symmetry,[status(thm)],[988])).
% 21.79/21.98 tff(990,plain,
% 21.79/21.98 (mult(a, mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, b)),
% 21.79/21.98 inference(transitivity,[status(thm)],[910, 913])).
% 21.79/21.98 tff(991,plain,
% 21.79/21.98 (ld(a, mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = ld(a, mult(a, b))),
% 21.79/21.98 inference(monotonicity,[status(thm)],[990])).
% 21.79/21.98 tff(992,plain,
% 21.79/21.98 (mult(a, rd(mult(b, c), mult(a, c))) = b),
% 21.79/21.98 inference(transitivity,[status(thm)],[919, 991, 912])).
% 21.79/21.98 tff(993,plain,
% 21.79/21.98 (mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(b, a)),
% 21.79/21.98 inference(monotonicity,[status(thm)],[992])).
% 21.79/21.98 tff(994,plain,
% 21.79/21.98 (mult(mult(mult(a, b), c), mult(mult(a, rd(mult(b, c), mult(a, c))), a)) = mult(mult(mult(a, b), c), mult(b, a))),
% 21.79/21.98 inference(monotonicity,[status(thm)],[993])).
% 21.79/21.98 tff(995,plain,
% 21.79/21.98 (mult(mult(mult(mult(mult(a, b), c), a), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, mult(mult(unit, mult(mult(b, unit), b)), c)), a)),
% 21.79/21.98 inference(transitivity,[status(thm)],[649, 994, 989, 896])).
% 21.79/21.98 tff(996,plain,
% 21.79/21.98 (rd(mult(mult(mult(mult(mult(a, b), c), a), rd(mult(b, c), mult(a, c))), a), a) = rd(mult(mult(a, mult(mult(unit, mult(mult(b, unit), b)), c)), a), a)),
% 21.79/21.98 inference(monotonicity,[status(thm)],[995])).
% 21.79/21.98 tff(997,plain,
% 21.79/21.98 (rd(mult(mult(a, mult(mult(unit, mult(mult(b, unit), b)), c)), a), a) = rd(mult(mult(mult(mult(mult(a, b), c), a), rd(mult(b, c), mult(a, c))), a), a)),
% 21.79/21.98 inference(symmetry,[status(thm)],[996])).
% 21.79/21.98 tff(998,plain,
% 21.79/21.98 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(a, mult(mult(unit, mult(mult(b, unit), b)), c)), a), a) = mult(a, mult(mult(unit, mult(mult(b, unit), b)), c)))),
% 21.79/21.98 inference(quant_inst,[status(thm)],[])).
% 21.79/21.98 tff(999,plain,
% 21.79/21.98 (rd(mult(mult(a, mult(mult(unit, mult(mult(b, unit), b)), c)), a), a) = mult(a, mult(mult(unit, mult(mult(b, unit), b)), c))),
% 21.79/21.98 inference(unit_resolution,[status(thm)],[998, 168])).
% 21.79/21.98 tff(1000,plain,
% 21.79/21.98 (mult(a, mult(mult(unit, mult(mult(b, unit), b)), c)) = rd(mult(mult(a, mult(mult(unit, mult(mult(b, unit), b)), c)), a), a)),
% 21.79/21.98 inference(symmetry,[status(thm)],[999])).
% 21.79/21.98 tff(1001,plain,
% 21.79/21.98 (mult(mult(b, b), a) = mult(b, mult(b, a))),
% 21.79/21.98 inference(unit_resolution,[status(thm)],[422, 952])).
% 21.79/21.98 tff(1002,plain,
% 21.79/21.98 (mult(b, mult(b, a)) = mult(mult(b, b), a)),
% 21.79/21.98 inference(symmetry,[status(thm)],[1001])).
% 21.79/21.98 tff(1003,plain,
% 21.79/21.98 (mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), a)) = mult(b, mult(b, a))),
% 21.79/21.98 inference(monotonicity,[status(thm)],[993])).
% 21.79/21.98 tff(1004,plain,
% 21.79/21.98 (mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(unit, mult(mult(b, unit), b)), a)),
% 21.79/21.98 inference(transitivity,[status(thm)],[469, 1003, 1002, 434])).
% 21.79/21.98 tff(1005,plain,
% 21.79/21.98 (rd(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a), a) = rd(mult(mult(unit, mult(mult(b, unit), b)), a), a)),
% 21.79/21.98 inference(monotonicity,[status(thm)],[1004])).
% 21.79/21.98 tff(1006,plain,
% 21.79/21.98 (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, a)), rd(mult(b, c), mult(a, c))) = mult(unit, mult(mult(b, unit), b))),
% 21.79/21.98 inference(transitivity,[status(thm)],[543, 690, 1005, 552])).
% 21.79/21.98 tff(1007,plain,
% 21.79/21.98 (mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), mult(a, a)), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(unit, mult(mult(b, unit), b)))),
% 21.79/21.98 inference(monotonicity,[status(thm)],[1006])).
% 21.79/21.98 tff(1008,plain,
% 21.79/21.98 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, a)), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), mult(a, a)), rd(mult(b, c), mult(a, c)))))),
% 21.79/21.98 inference(quant_inst,[status(thm)],[])).
% 21.79/21.98 tff(1009,plain,
% 21.79/21.98 (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, a)), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), mult(a, a)), rd(mult(b, c), mult(a, c))))),
% 21.79/21.98 inference(unit_resolution,[status(thm)],[1008, 56])).
% 21.79/21.98 tff(1010,plain,
% 21.79/21.98 (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, a)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(mult(a, b), c), a), rd(mult(b, c), mult(a, c)))),
% 21.79/21.98 inference(transitivity,[status(thm)],[1009, 1007, 870, 869, 866, 827, 832, 892, 1000, 997, 411])).
% 21.79/21.98 tff(1011,plain,
% 21.79/21.98 (rd(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, a)), rd(mult(b, c), mult(a, c))), rd(mult(b, c), mult(a, c))) = rd(mult(mult(mult(mult(a, b), c), a), rd(mult(b, c), mult(a, c))), rd(mult(b, c), mult(a, c)))),
% 21.79/21.98 inference(monotonicity,[status(thm)],[1010])).
% 21.79/21.98 tff(1012,plain,
% 21.79/21.98 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, a)), rd(mult(b, c), mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, a)))),
% 21.79/21.98 inference(quant_inst,[status(thm)],[])).
% 21.79/21.98 tff(1013,plain,
% 21.79/21.98 (rd(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, a)), rd(mult(b, c), mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, a))),
% 21.79/21.98 inference(unit_resolution,[status(thm)],[1012, 168])).
% 21.79/21.98 tff(1014,plain,
% 21.79/21.98 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, a)) = rd(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, a)), rd(mult(b, c), mult(a, c))), rd(mult(b, c), mult(a, c)))),
% 21.79/21.98 inference(symmetry,[status(thm)],[1013])).
% 21.79/21.98 tff(1015,plain,
% 21.79/21.98 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(mult(a, unit), a)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, a))),
% 21.79/21.98 inference(monotonicity,[status(thm)],[519])).
% 21.79/21.98 tff(1016,plain,
% 21.79/21.98 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), unit), a) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(mult(a, unit), a)))),
% 21.79/21.98 inference(quant_inst,[status(thm)],[])).
% 21.79/21.98 tff(1017,plain,
% 21.79/21.98 (mult(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), unit), a) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(mult(a, unit), a))),
% 21.79/21.98 inference(unit_resolution,[status(thm)],[1016, 56])).
% 21.79/21.98 tff(1018,plain,
% 21.79/21.98 (mult(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), unit), a) = mult(mult(mult(a, b), c), a)),
% 21.79/21.98 inference(transitivity,[status(thm)],[1017, 1015, 1014, 1011, 409])).
% 21.79/21.98 tff(1019,plain,
% 21.79/21.98 (rd(mult(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), unit), a), a) = rd(mult(mult(mult(a, b), c), a), a)),
% 21.79/21.98 inference(monotonicity,[status(thm)],[1018])).
% 21.79/21.98 tff(1020,plain,
% 21.79/21.98 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), unit), a), a) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), unit))),
% 21.79/21.98 inference(quant_inst,[status(thm)],[])).
% 21.79/21.98 tff(1021,plain,
% 21.79/21.98 (rd(mult(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), unit), a), a) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), unit)),
% 21.79/21.98 inference(unit_resolution,[status(thm)],[1020, 168])).
% 21.79/21.98 tff(1022,plain,
% 21.79/21.98 (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), unit) = rd(mult(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), unit), a), a)),
% 21.79/21.98 inference(symmetry,[status(thm)],[1021])).
% 21.79/21.98 tff(1023,plain,
% 21.79/21.98 ((~![A: $i] : (mult(A, unit) = A)) | (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), unit) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))),
% 21.79/21.98 inference(quant_inst,[status(thm)],[])).
% 21.79/21.98 tff(1024,plain,
% 21.79/21.98 (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), unit) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)),
% 21.79/21.98 inference(unit_resolution,[status(thm)],[1023, 43])).
% 21.79/21.98 tff(1025,plain,
% 21.79/21.98 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), unit)),
% 21.79/21.98 inference(symmetry,[status(thm)],[1024])).
% 21.79/21.98 tff(1026,assumption,(~(ld(mult(a, c), mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c))))) = mult(mult(a, c), rd(mult(b, c), mult(a, c))))), introduced(assumption)).
% 21.79/21.98 tff(1027,plain,
% 21.79/21.98 ($false),
% 21.79/21.98 inference(unit_resolution,[status(thm)],[294, 7, 1026])).
% 21.79/21.98 tff(1028,plain,(ld(mult(a, c), mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c))))) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))), inference(lemma,lemma(discharge,[]))).
% 21.79/21.98 tff(1029,assumption,(~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))), introduced(assumption)).
% 21.79/21.98 tff(1030,plain,
% 21.79/21.98 ((~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))))),
% 21.79/21.98 inference(unit_resolution,[status(thm)],[115, 1029])).
% 21.79/21.98 tff(1031,plain,
% 21.79/21.98 (~((~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)))) | (~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))))),
% 21.79/21.98 inference(unit_resolution,[status(thm)],[119, 27, 1030])).
% 21.79/21.98 tff(1032,plain,
% 21.79/21.98 (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))),
% 21.79/21.98 inference(unit_resolution,[status(thm)],[121, 1031])).
% 21.79/21.98 tff(1033,plain,
% 21.79/21.98 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(a, mult(b, c)), a), a) = mult(a, mult(b, c)))),
% 21.79/21.98 inference(quant_inst,[status(thm)],[])).
% 21.79/21.98 tff(1034,plain,
% 21.79/21.98 (rd(mult(mult(a, mult(b, c)), a), a) = mult(a, mult(b, c))),
% 21.79/21.98 inference(unit_resolution,[status(thm)],[1033, 168])).
% 21.79/21.98 tff(1035,plain,
% 21.79/21.98 (mult(mult(c, unit), b) = mult(mult(mult(c, unit), b), unit)),
% 21.79/21.98 inference(symmetry,[status(thm)],[839])).
% 21.79/21.98 tff(1036,plain,
% 21.79/21.98 (mult(mult(c, unit), b) = mult(b, c)),
% 21.79/21.98 inference(transitivity,[status(thm)],[1035, 837, 835, 240, 237, 141])).
% 21.79/21.98 tff(1037,plain,
% 21.79/21.98 (mult(a, mult(mult(c, unit), b)) = mult(a, mult(b, c))),
% 21.79/21.98 inference(monotonicity,[status(thm)],[1036])).
% 21.79/21.98 tff(1038,plain,
% 21.79/21.98 (mult(a, mult(b, c)) = mult(a, mult(mult(c, unit), b))),
% 21.79/21.98 inference(symmetry,[status(thm)],[1037])).
% 21.79/21.98 tff(1039,assumption,(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))), introduced(assumption)).
% 21.79/21.98 tff(1040,plain,
% 21.79/21.98 (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(a, mult(b, c)), c)),
% 21.79/21.98 inference(transitivity,[status(thm)],[317, 1039, 138, 266])).
% 21.79/21.98 tff(1041,plain,
% 21.79/21.98 (rd(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c), c) = rd(mult(mult(a, mult(b, c)), c), c)),
% 21.79/21.98 inference(monotonicity,[status(thm)],[1040])).
% 21.79/21.98 tff(1042,plain,
% 21.79/21.98 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(a, mult(mult(c, unit), b))),
% 21.79/21.98 inference(transitivity,[status(thm)],[322, 1041, 180, 1038])).
% 21.79/21.98 tff(1043,plain,
% 21.79/21.98 (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), unit) = mult(mult(a, mult(mult(c, unit), b)), unit)),
% 21.79/21.98 inference(monotonicity,[status(thm)],[1042])).
% 21.79/21.98 tff(1044,plain,
% 21.79/21.98 (mult(mult(a, mult(mult(c, unit), b)), unit) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), unit)),
% 21.79/21.98 inference(symmetry,[status(thm)],[1043])).
% 21.79/21.98 tff(1045,plain,
% 21.79/21.98 (mult(mult(a, unit), mult(b, c)) = mult(a, mult(b, c))),
% 21.79/21.98 inference(monotonicity,[status(thm)],[47])).
% 21.79/21.98 tff(1046,plain,
% 21.79/21.98 (mult(a, mult(b, c)) = mult(mult(a, unit), mult(b, c))),
% 21.79/21.98 inference(symmetry,[status(thm)],[1045])).
% 21.79/21.98 tff(1047,plain,
% 21.79/21.98 (mult(a, mult(mult(c, unit), b)) = mult(mult(a, unit), mult(b, c))),
% 21.79/21.98 inference(transitivity,[status(thm)],[1037, 1046])).
% 21.79/21.98 tff(1048,plain,
% 21.79/21.98 (mult(mult(a, mult(mult(c, unit), b)), unit) = mult(mult(mult(a, unit), mult(b, c)), unit)),
% 21.79/21.98 inference(monotonicity,[status(thm)],[1047])).
% 21.79/21.98 tff(1049,plain,
% 21.79/21.98 (mult(mult(mult(a, unit), mult(b, c)), unit) = mult(mult(a, mult(mult(c, unit), b)), unit)),
% 21.79/21.98 inference(symmetry,[status(thm)],[1048])).
% 21.79/21.98 tff(1050,plain,
% 21.79/21.98 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(a, unit), mult(b, c)), unit) = mult(a, mult(mult(unit, mult(b, c)), unit)))),
% 21.79/21.98 inference(quant_inst,[status(thm)],[])).
% 21.79/21.98 tff(1051,plain,
% 21.79/21.98 (mult(mult(mult(a, unit), mult(b, c)), unit) = mult(a, mult(mult(unit, mult(b, c)), unit))),
% 21.79/21.98 inference(unit_resolution,[status(thm)],[1050, 56])).
% 21.79/21.98 tff(1052,plain,
% 21.79/21.98 (mult(a, mult(mult(unit, mult(b, c)), unit)) = mult(mult(mult(a, unit), mult(b, c)), unit)),
% 21.79/21.98 inference(symmetry,[status(thm)],[1051])).
% 21.79/21.98 tff(1053,plain,
% 21.79/21.98 ((~![A: $i] : (mult(unit, A) = A)) | (mult(unit, mult(b, c)) = mult(b, c))),
% 21.79/21.98 inference(quant_inst,[status(thm)],[])).
% 21.79/21.98 tff(1054,plain,
% 21.79/21.98 (mult(unit, mult(b, c)) = mult(b, c)),
% 21.79/21.98 inference(unit_resolution,[status(thm)],[1053, 71])).
% 21.79/21.98 tff(1055,plain,
% 21.79/21.98 (mult(mult(unit, mult(b, c)), unit) = mult(mult(b, c), unit)),
% 21.79/21.98 inference(monotonicity,[status(thm)],[1054])).
% 21.79/21.98 tff(1056,plain,
% 21.79/21.98 (mult(mult(unit, mult(b, c)), unit) = mult(b, c)),
% 21.79/21.98 inference(transitivity,[status(thm)],[1055, 845, 837, 835, 240, 237, 141])).
% 21.79/21.98 tff(1057,plain,
% 21.79/21.98 (mult(a, mult(mult(unit, mult(b, c)), unit)) = mult(a, mult(b, c))),
% 21.79/21.98 inference(monotonicity,[status(thm)],[1056])).
% 21.79/21.98 tff(1058,plain,
% 21.79/21.98 (mult(a, mult(b, c)) = mult(a, mult(mult(unit, mult(b, c)), unit))),
% 21.79/21.98 inference(symmetry,[status(thm)],[1057])).
% 21.79/21.98 tff(1059,plain,
% 21.79/21.98 (mult(a, mult(b, c)) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), unit)),
% 21.79/21.99 inference(transitivity,[status(thm)],[1058, 1052, 1049, 1044])).
% 21.79/21.99 tff(1060,plain,
% 21.79/21.99 (mult(mult(a, mult(b, c)), a) = mult(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), unit), a)),
% 21.79/21.99 inference(monotonicity,[status(thm)],[1059])).
% 21.79/21.99 tff(1061,plain,
% 21.79/21.99 (mult(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), unit), a) = mult(mult(a, mult(b, c)), a)),
% 21.79/21.99 inference(symmetry,[status(thm)],[1060])).
% 21.79/21.99 tff(1062,plain,
% 21.79/21.99 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(mult(a, unit), a)) = mult(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), unit), a)),
% 21.79/21.99 inference(symmetry,[status(thm)],[1017])).
% 21.79/21.99 tff(1063,plain,
% 21.79/21.99 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(mult(a, unit), a))),
% 21.79/21.99 inference(symmetry,[status(thm)],[1015])).
% 21.79/21.99 tff(1064,assumption,(~(mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(a, b)))), introduced(assumption)).
% 21.79/21.99 tff(1065,plain,
% 21.79/21.99 ((~(mult(mult(mult(mult(a, b), c), b), a) = mult(mult(mult(mult(a, b), c), a), b))) | (~(mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(a, b))))),
% 21.79/21.99 inference(unit_resolution,[status(thm)],[637, 1064])).
% 21.79/21.99 tff(1066,plain,
% 21.79/21.99 (~((~(mult(mult(mult(mult(a, b), c), b), a) = mult(mult(mult(a, b), c), mult(b, a)))) | (~(mult(mult(mult(mult(a, b), c), a), b) = mult(mult(mult(a, b), c), mult(a, b)))))),
% 21.79/21.99 inference(unit_resolution,[status(thm)],[641, 27, 1065])).
% 21.79/21.99 tff(1067,plain,
% 21.79/21.99 (mult(mult(mult(mult(a, b), c), b), a) = mult(mult(mult(a, b), c), mult(b, a))),
% 21.79/21.99 inference(unit_resolution,[status(thm)],[644, 1066])).
% 21.79/21.99 tff(1068,plain,
% 21.79/21.99 (mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(mult(a, b), c), b), a)),
% 21.79/21.99 inference(symmetry,[status(thm)],[1067])).
% 21.79/21.99 tff(1069,plain,
% 21.79/21.99 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(a, mult(b, c))),
% 21.79/21.99 inference(transitivity,[status(thm)],[322, 1041, 180])).
% 21.79/21.99 tff(1070,plain,
% 21.79/21.99 ((mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))) <=> (mult(a, mult(b, c)) = mult(mult(a, b), c))),
% 21.79/21.99 inference(monotonicity,[status(thm)],[1069, 178])).
% 21.79/21.99 tff(1071,plain,
% 21.79/21.99 ((mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))) <=> (mult(mult(a, b), c) = mult(a, mult(b, c)))),
% 21.79/21.99 inference(transitivity,[status(thm)],[1070, 143])).
% 21.79/21.99 tff(1072,plain,
% 21.79/21.99 ((mult(mult(a, b), c) = mult(a, mult(b, c))) <=> (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))),
% 21.79/21.99 inference(symmetry,[status(thm)],[1071])).
% 21.79/21.99 tff(1073,plain,
% 21.79/21.99 ((~(mult(mult(a, b), c) = mult(a, mult(b, c)))) <=> (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))))),
% 21.79/21.99 inference(monotonicity,[status(thm)],[1072])).
% 21.79/21.99 tff(1074,plain,
% 21.79/21.99 (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))),
% 21.79/21.99 inference(modus_ponens,[status(thm)],[146, 1073])).
% 21.79/21.99 tff(1075,plain,
% 21.79/21.99 ((~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))))),
% 21.79/21.99 inference(unit_resolution,[status(thm)],[333, 1074])).
% 21.79/21.99 tff(1076,plain,
% 21.79/21.99 ((~((~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))) | (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))))) | (~((~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))))))),
% 21.79/21.99 inference(unit_resolution,[status(thm)],[338, 27])).
% 21.79/21.99 tff(1077,plain,
% 21.79/21.99 (~((~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))) | (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))))),
% 21.79/21.99 inference(unit_resolution,[status(thm)],[1076, 1075])).
% 21.79/21.99 tff(1078,plain,
% 21.79/21.99 (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))),
% 21.79/21.99 inference(unit_resolution,[status(thm)],[331, 1077])).
% 21.79/21.99 tff(1079,plain,
% 21.79/21.99 (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), b)),
% 21.79/21.99 inference(transitivity,[status(thm)],[1078, 177])).
% 21.79/21.99 tff(1080,plain,
% 21.79/21.99 (ld(mult(a, c), mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = ld(mult(a, c), mult(mult(a, c), b))),
% 21.79/21.99 inference(monotonicity,[status(thm)],[1079])).
% 21.79/21.99 tff(1081,plain,
% 21.79/21.99 (mult(a, rd(mult(b, c), mult(a, c))) = b),
% 21.79/21.99 inference(transitivity,[status(thm)],[471, 1080, 364])).
% 21.79/21.99 tff(1082,plain,
% 21.79/21.99 (mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(b, a)),
% 21.79/21.99 inference(monotonicity,[status(thm)],[1081])).
% 21.79/21.99 tff(1083,plain,
% 21.79/21.99 (mult(mult(mult(a, b), c), mult(mult(a, rd(mult(b, c), mult(a, c))), a)) = mult(mult(mult(a, b), c), mult(b, a))),
% 21.79/21.99 inference(monotonicity,[status(thm)],[1082])).
% 21.79/21.99 tff(1084,plain,
% 21.79/21.99 (mult(mult(mult(mult(mult(a, b), c), a), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(mult(a, b), c), b), a)),
% 21.79/21.99 inference(transitivity,[status(thm)],[649, 1083, 1068])).
% 21.79/21.99 tff(1085,plain,
% 21.79/21.99 (rd(mult(mult(mult(mult(mult(a, b), c), a), rd(mult(b, c), mult(a, c))), a), a) = rd(mult(mult(mult(mult(a, b), c), b), a), a)),
% 21.79/21.99 inference(monotonicity,[status(thm)],[1084])).
% 21.79/21.99 tff(1086,plain,
% 21.79/21.99 (rd(mult(mult(mult(mult(a, b), c), b), a), a) = rd(mult(mult(mult(mult(mult(a, b), c), a), rd(mult(b, c), mult(a, c))), a), a)),
% 21.79/21.99 inference(symmetry,[status(thm)],[1085])).
% 21.79/21.99 tff(1087,plain,
% 21.79/21.99 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(mult(a, b), c), b), a), a) = mult(mult(mult(a, b), c), b))),
% 21.79/21.99 inference(quant_inst,[status(thm)],[])).
% 21.79/21.99 tff(1088,plain,
% 21.79/21.99 (rd(mult(mult(mult(mult(a, b), c), b), a), a) = mult(mult(mult(a, b), c), b)),
% 21.79/21.99 inference(unit_resolution,[status(thm)],[1087, 168])).
% 21.79/21.99 tff(1089,plain,
% 21.79/21.99 (mult(mult(mult(a, b), c), b) = rd(mult(mult(mult(mult(a, b), c), b), a), a)),
% 21.79/21.99 inference(symmetry,[status(thm)],[1088])).
% 21.79/21.99 tff(1090,assumption,(mult(mult(mult(a, c), mult(a, b)), b) = mult(mult(a, c), mult(mult(a, b), b))), introduced(assumption)).
% 21.79/21.99 tff(1091,plain,
% 21.79/21.99 (mult(mult(a, c), mult(mult(a, b), b)) = mult(mult(mult(a, c), mult(a, b)), b)),
% 21.79/21.99 inference(symmetry,[status(thm)],[1090])).
% 21.79/21.99 tff(1092,plain,
% 21.79/21.99 (mult(a, mult(unit, mult(mult(b, unit), b))) = mult(mult(a, b), b)),
% 21.79/21.99 inference(transitivity,[status(thm)],[829, 663, 445, 662])).
% 21.79/21.99 tff(1093,plain,
% 21.79/21.99 (mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b)))) = mult(mult(a, c), mult(mult(a, b), b))),
% 21.79/21.99 inference(monotonicity,[status(thm)],[1092])).
% 21.79/21.99 tff(1094,plain,
% 21.79/21.99 (mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b)))) = mult(mult(mult(a, c), mult(a, b)), b)),
% 21.79/21.99 inference(transitivity,[status(thm)],[1093, 1091])).
% 21.79/21.99 tff(1095,plain,
% 21.79/21.99 (mult(mult(a, c), mult(b, mult(a, b))) = mult(mult(mult(a, c), b), mult(a, b))),
% 21.79/21.99 inference(symmetry,[status(thm)],[961])).
% 21.79/21.99 tff(1096,plain,
% 21.79/21.99 (((~(mult(mult(mult(mult(a, b), c), b), a) = mult(mult(mult(a, b), c), mult(b, a)))) | (~(mult(mult(mult(mult(a, b), c), a), b) = mult(mult(mult(a, b), c), mult(a, b))))) | (mult(mult(mult(mult(a, b), c), a), b) = mult(mult(mult(a, b), c), mult(a, b)))),
% 21.79/21.99 inference(tautology,[status(thm)],[])).
% 21.79/21.99 tff(1097,plain,
% 21.79/21.99 (mult(mult(mult(mult(a, b), c), a), b) = mult(mult(mult(a, b), c), mult(a, b))),
% 21.79/21.99 inference(unit_resolution,[status(thm)],[1096, 1066])).
% 21.79/21.99 tff(1098,plain,
% 21.79/21.99 (mult(mult(a, c), mult(mult(b, a), b)) = mult(mult(a, c), mult(b, mult(a, b)))),
% 21.79/21.99 inference(transitivity,[status(thm)],[964, 963, 1097, 574, 961])).
% 21.79/21.99 tff(1099,plain,
% 21.79/21.99 (ld(mult(a, c), mult(mult(a, c), mult(mult(b, a), b))) = ld(mult(a, c), mult(mult(a, c), mult(b, mult(a, b))))),
% 21.79/21.99 inference(monotonicity,[status(thm)],[1098])).
% 21.79/21.99 tff(1100,plain,
% 21.79/21.99 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(a, c), mult(mult(a, c), mult(mult(b, a), b))) = mult(mult(b, a), b))),
% 21.79/21.99 inference(quant_inst,[status(thm)],[])).
% 21.79/21.99 tff(1101,plain,
% 21.79/21.99 (ld(mult(a, c), mult(mult(a, c), mult(mult(b, a), b))) = mult(mult(b, a), b)),
% 21.79/21.99 inference(unit_resolution,[status(thm)],[1100, 7])).
% 21.79/21.99 tff(1102,plain,
% 21.79/21.99 (mult(mult(b, a), b) = ld(mult(a, c), mult(mult(a, c), mult(mult(b, a), b)))),
% 21.79/21.99 inference(symmetry,[status(thm)],[1101])).
% 21.79/21.99 tff(1103,assumption,(mult(mult(b, a), b) = mult(mult(b, b), a)), introduced(assumption)).
% 21.79/21.99 tff(1104,plain,
% 21.79/21.99 (mult(mult(b, b), a) = mult(mult(b, a), b)),
% 21.79/21.99 inference(symmetry,[status(thm)],[1103])).
% 21.79/21.99 tff(1105,plain,
% 21.79/21.99 (mult(mult(b, unit), b) = mult(b, b)),
% 21.79/21.99 inference(symmetry,[status(thm)],[432])).
% 21.79/21.99 tff(1106,plain,
% 21.79/21.99 (mult(unit, mult(mult(b, unit), b)) = mult(b, b)),
% 21.79/21.99 inference(transitivity,[status(thm)],[429, 1105])).
% 21.79/21.99 tff(1107,plain,
% 21.79/21.99 (mult(mult(unit, mult(mult(b, unit), b)), a) = mult(mult(b, b), a)),
% 21.79/21.99 inference(monotonicity,[status(thm)],[1106])).
% 21.79/21.99 tff(1108,plain,
% 21.79/21.99 (mult(mult(unit, mult(mult(b, unit), b)), a) = mult(b, mult(a, b))),
% 21.79/21.99 inference(transitivity,[status(thm)],[1107, 1104, 1102, 1099, 566])).
% 21.79/21.99 tff(1109,plain,
% 21.79/21.99 (mult(mult(a, c), mult(mult(unit, mult(mult(b, unit), b)), a)) = mult(mult(a, c), mult(b, mult(a, b)))),
% 21.79/21.99 inference(monotonicity,[status(thm)],[1108])).
% 21.79/21.99 tff(1110,plain,
% 21.79/21.99 (mult(mult(a, c), mult(mult(unit, mult(mult(b, unit), b)), a)) = mult(mult(mult(a, c), b), mult(a, b))),
% 21.79/21.99 inference(transitivity,[status(thm)],[1109, 1095])).
% 21.79/21.99 tff(1111,plain,
% 21.79/21.99 ((mult(mult(a, c), mult(mult(unit, mult(mult(b, unit), b)), a)) = mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b))))) <=> (mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(mult(a, c), mult(a, b)), b))),
% 21.79/21.99 inference(monotonicity,[status(thm)],[1110, 1094])).
% 21.79/21.99 tff(1112,plain,
% 21.79/21.99 ((mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(mult(a, c), mult(a, b)), b)) <=> (mult(mult(a, c), mult(mult(unit, mult(mult(b, unit), b)), a)) = mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b)))))),
% 21.79/21.99 inference(symmetry,[status(thm)],[1111])).
% 21.79/21.99 tff(1113,plain,
% 21.79/21.99 ((~(mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(mult(a, c), mult(a, b)), b))) <=> (~(mult(mult(a, c), mult(mult(unit, mult(mult(b, unit), b)), a)) = mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b))))))),
% 21.79/21.99 inference(monotonicity,[status(thm)],[1112])).
% 21.79/21.99 tff(1114,assumption,(~(mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(mult(a, c), mult(a, b)), b))), introduced(assumption)).
% 21.79/21.99 tff(1115,plain,
% 21.79/21.99 (~(mult(mult(a, c), mult(mult(unit, mult(mult(b, unit), b)), a)) = mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b)))))),
% 21.79/21.99 inference(modus_ponens,[status(thm)],[1114, 1113])).
% 21.79/21.99 tff(1116,plain,
% 21.79/21.99 (((~(mult(mult(mult(a, c), mult(unit, mult(mult(b, unit), b))), a) = mult(mult(mult(a, c), a), mult(unit, mult(mult(b, unit), b))))) | (~(mult(mult(a, c), mult(mult(unit, mult(mult(b, unit), b)), a)) = mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b))))))) | (mult(mult(a, c), mult(mult(unit, mult(mult(b, unit), b)), a)) = mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b)))))),
% 21.79/21.99 inference(tautology,[status(thm)],[])).
% 21.79/21.99 tff(1117,plain,
% 21.79/21.99 ((~(mult(mult(mult(a, c), mult(unit, mult(mult(b, unit), b))), a) = mult(mult(mult(a, c), a), mult(unit, mult(mult(b, unit), b))))) | (~(mult(mult(a, c), mult(mult(unit, mult(mult(b, unit), b)), a)) = mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b))))))),
% 21.79/21.99 inference(unit_resolution,[status(thm)],[1116, 1115])).
% 21.79/21.99 tff(1118,plain,
% 21.79/21.99 (mult(mult(a, c), mult(mult(unit, mult(mult(b, unit), b)), a)) = mult(mult(mult(a, b), c), mult(a, b))),
% 21.79/21.99 inference(transitivity,[status(thm)],[1109, 1095, 949])).
% 21.79/21.99 tff(1119,plain,
% 21.79/21.99 (mult(mult(a, c), mult(unit, mult(mult(b, unit), b))) = mult(mult(mult(a, b), c), b)),
% 21.79/21.99 inference(transitivity,[status(thm)],[870, 869, 866])).
% 21.79/21.99 tff(1120,plain,
% 21.79/21.99 (mult(mult(mult(a, c), mult(unit, mult(mult(b, unit), b))), a) = mult(mult(mult(mult(a, b), c), b), a)),
% 21.79/21.99 inference(monotonicity,[status(thm)],[1119])).
% 21.79/21.99 tff(1121,plain,
% 21.79/21.99 (mult(mult(mult(a, c), mult(unit, mult(mult(b, unit), b))), a) = mult(mult(mult(a, b), c), mult(b, a))),
% 21.79/21.99 inference(transitivity,[status(thm)],[1120, 1067])).
% 21.79/21.99 tff(1122,plain,
% 21.79/21.99 ((mult(mult(mult(a, c), mult(unit, mult(mult(b, unit), b))), a) = mult(mult(a, c), mult(mult(unit, mult(mult(b, unit), b)), a))) <=> (mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(a, b)))),
% 21.79/21.99 inference(monotonicity,[status(thm)],[1121, 1118])).
% 21.79/21.99 tff(1123,plain,
% 21.79/21.99 ((mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(a, b))) <=> (mult(mult(mult(a, c), mult(unit, mult(mult(b, unit), b))), a) = mult(mult(a, c), mult(mult(unit, mult(mult(b, unit), b)), a)))),
% 21.79/21.99 inference(symmetry,[status(thm)],[1122])).
% 21.79/21.99 tff(1124,plain,
% 21.79/21.99 ((~(mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(a, b)))) <=> (~(mult(mult(mult(a, c), mult(unit, mult(mult(b, unit), b))), a) = mult(mult(a, c), mult(mult(unit, mult(mult(b, unit), b)), a))))),
% 21.79/21.99 inference(monotonicity,[status(thm)],[1123])).
% 21.79/21.99 tff(1125,plain,
% 21.79/21.99 (~(mult(mult(mult(a, c), mult(unit, mult(mult(b, unit), b))), a) = mult(mult(a, c), mult(mult(unit, mult(mult(b, unit), b)), a)))),
% 21.79/21.99 inference(modus_ponens,[status(thm)],[1064, 1124])).
% 21.79/21.99 tff(1126,plain,
% 21.79/21.99 (((~(mult(mult(mult(a, c), mult(unit, mult(mult(b, unit), b))), a) = mult(mult(a, c), mult(mult(unit, mult(mult(b, unit), b)), a)))) | (~(mult(mult(mult(a, c), a), mult(unit, mult(mult(b, unit), b))) = mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b))))))) | (mult(mult(mult(a, c), mult(unit, mult(mult(b, unit), b))), a) = mult(mult(a, c), mult(mult(unit, mult(mult(b, unit), b)), a)))),
% 21.79/21.99 inference(tautology,[status(thm)],[])).
% 21.79/21.99 tff(1127,plain,
% 21.79/21.99 ((~(mult(mult(mult(a, c), mult(unit, mult(mult(b, unit), b))), a) = mult(mult(a, c), mult(mult(unit, mult(mult(b, unit), b)), a)))) | (~(mult(mult(mult(a, c), a), mult(unit, mult(mult(b, unit), b))) = mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b))))))),
% 21.79/21.99 inference(unit_resolution,[status(thm)],[1126, 1125])).
% 21.79/21.99 tff(1128,plain,
% 21.79/21.99 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, c), mult(unit, mult(mult(b, unit), b))), a) = mult(mult(mult(a, c), a), mult(unit, mult(mult(b, unit), b))))) | (~(mult(mult(a, c), mult(mult(unit, mult(mult(b, unit), b)), a)) = mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b)))))))) | (~((~(mult(mult(mult(a, c), mult(unit, mult(mult(b, unit), b))), a) = mult(mult(a, c), mult(mult(unit, mult(mult(b, unit), b)), a)))) | (~(mult(mult(mult(a, c), a), mult(unit, mult(mult(b, unit), b))) = mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b)))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(a, c), mult(unit, mult(mult(b, unit), b))), a) = mult(mult(mult(a, c), a), mult(unit, mult(mult(b, unit), b))))) | (~(mult(mult(a, c), mult(mult(unit, mult(mult(b, unit), b)), a)) = mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b)))))))) | (~((~(mult(mult(mult(a, c), mult(unit, mult(mult(b, unit), b))), a) = mult(mult(a, c), mult(mult(unit, mult(mult(b, unit), b)), a)))) | (~(mult(mult(mult(a, c), a), mult(unit, mult(mult(b, unit), b))) = mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b)))))))))),
% 21.79/21.99 inference(rewrite,[status(thm)],[])).
% 21.79/21.99 tff(1129,plain,
% 21.79/21.99 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, c), mult(unit, mult(mult(b, unit), b))), a) = mult(mult(mult(a, c), a), mult(unit, mult(mult(b, unit), b))))) | (~(mult(mult(a, c), mult(mult(unit, mult(mult(b, unit), b)), a)) = mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b)))))))) | (~((~(mult(mult(mult(a, c), mult(unit, mult(mult(b, unit), b))), a) = mult(mult(a, c), mult(mult(unit, mult(mult(b, unit), b)), a)))) | (~(mult(mult(mult(a, c), a), mult(unit, mult(mult(b, unit), b))) = mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b)))))))))),
% 21.79/22.00 inference(quant_inst,[status(thm)],[])).
% 21.79/22.00 tff(1130,plain,
% 21.79/22.00 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(a, c), mult(unit, mult(mult(b, unit), b))), a) = mult(mult(mult(a, c), a), mult(unit, mult(mult(b, unit), b))))) | (~(mult(mult(a, c), mult(mult(unit, mult(mult(b, unit), b)), a)) = mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b)))))))) | (~((~(mult(mult(mult(a, c), mult(unit, mult(mult(b, unit), b))), a) = mult(mult(a, c), mult(mult(unit, mult(mult(b, unit), b)), a)))) | (~(mult(mult(mult(a, c), a), mult(unit, mult(mult(b, unit), b))) = mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b))))))))),
% 21.79/22.00 inference(modus_ponens,[status(thm)],[1129, 1128])).
% 21.79/22.00 tff(1131,plain,
% 21.79/22.00 ((~((~(mult(mult(mult(a, c), mult(unit, mult(mult(b, unit), b))), a) = mult(mult(mult(a, c), a), mult(unit, mult(mult(b, unit), b))))) | (~(mult(mult(a, c), mult(mult(unit, mult(mult(b, unit), b)), a)) = mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b)))))))) | (~((~(mult(mult(mult(a, c), mult(unit, mult(mult(b, unit), b))), a) = mult(mult(a, c), mult(mult(unit, mult(mult(b, unit), b)), a)))) | (~(mult(mult(mult(a, c), a), mult(unit, mult(mult(b, unit), b))) = mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b))))))))),
% 21.79/22.00 inference(unit_resolution,[status(thm)],[1130, 27])).
% 21.79/22.00 tff(1132,plain,
% 21.79/22.00 ($false),
% 21.79/22.00 inference(unit_resolution,[status(thm)],[1131, 1127, 1117])).
% 21.79/22.00 tff(1133,plain,((~(mult(mult(b, a), b) = mult(mult(b, b), a))) | (mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(a, b))) | (~(mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(a, c), mult(b, mult(a, b))))) | (mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(mult(a, c), mult(a, b)), b)) | (~(mult(mult(mult(a, c), mult(a, b)), b) = mult(mult(a, c), mult(mult(a, b), b))))), inference(lemma,lemma(discharge,[]))).
% 21.79/22.00 tff(1134,plain,
% 21.79/22.00 (~(mult(mult(b, a), b) = mult(mult(b, b), a))),
% 21.79/22.00 inference(unit_resolution,[status(thm)],[1133, 605, 1064, 615, 587])).
% 21.79/22.00 tff(1135,plain,
% 21.79/22.00 (((~(mult(mult(b, a), b) = mult(mult(b, b), a))) | (~(mult(b, mult(a, b)) = mult(b, mult(b, a))))) | (mult(mult(b, a), b) = mult(mult(b, b), a))),
% 21.79/22.00 inference(tautology,[status(thm)],[])).
% 21.79/22.00 tff(1136,plain,
% 21.79/22.00 ((~(mult(mult(b, a), b) = mult(mult(b, b), a))) | (~(mult(b, mult(a, b)) = mult(b, mult(b, a))))),
% 21.79/22.00 inference(unit_resolution,[status(thm)],[1135, 1134])).
% 21.79/22.00 tff(1137,plain,
% 21.79/22.00 (~((~(mult(mult(b, a), b) = mult(b, mult(a, b)))) | (~(mult(mult(b, b), a) = mult(b, mult(b, a)))))),
% 21.79/22.00 inference(unit_resolution,[status(thm)],[418, 1136])).
% 21.79/22.00 tff(1138,plain,
% 21.79/22.00 (mult(mult(b, b), a) = mult(b, mult(b, a))),
% 21.79/22.00 inference(unit_resolution,[status(thm)],[422, 1137])).
% 21.79/22.00 tff(1139,plain,
% 21.79/22.00 (mult(b, mult(b, a)) = mult(mult(b, b), a)),
% 21.79/22.00 inference(symmetry,[status(thm)],[1138])).
% 21.79/22.00 tff(1140,plain,
% 21.79/22.00 (mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), a)) = mult(b, mult(b, a))),
% 21.79/22.00 inference(monotonicity,[status(thm)],[1082])).
% 21.79/22.00 tff(1141,plain,
% 21.79/22.00 (mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(unit, mult(mult(b, unit), b)), a)),
% 21.79/22.00 inference(transitivity,[status(thm)],[469, 1140, 1139, 434])).
% 21.79/22.00 tff(1142,plain,
% 21.79/22.00 (rd(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a), a) = rd(mult(mult(unit, mult(mult(b, unit), b)), a), a)),
% 21.79/22.00 inference(monotonicity,[status(thm)],[1141])).
% 21.79/22.00 tff(1143,plain,
% 21.79/22.00 (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, a)), rd(mult(b, c), mult(a, c))) = mult(mult(b, unit), b)),
% 21.79/22.00 inference(transitivity,[status(thm)],[543, 690, 1142, 552, 429])).
% 21.79/22.00 tff(1144,plain,
% 21.79/22.00 (mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), mult(a, a)), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(mult(b, unit), b))),
% 21.79/22.00 inference(monotonicity,[status(thm)],[1143])).
% 21.79/22.00 tff(1145,plain,
% 21.79/22.00 (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, a)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(mult(a, b), c), a), rd(mult(b, c), mult(a, c)))),
% 21.79/22.00 inference(transitivity,[status(thm)],[1009, 1144, 869, 866, 1089, 1086, 411])).
% 21.79/22.00 tff(1146,plain,
% 21.79/22.00 (rd(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, a)), rd(mult(b, c), mult(a, c))), rd(mult(b, c), mult(a, c))) = rd(mult(mult(mult(mult(a, b), c), a), rd(mult(b, c), mult(a, c))), rd(mult(b, c), mult(a, c)))),
% 21.79/22.00 inference(monotonicity,[status(thm)],[1145])).
% 21.79/22.00 tff(1147,plain,
% 21.79/22.00 (rd(mult(mult(mult(mult(a, b), c), a), rd(mult(b, c), mult(a, c))), rd(mult(b, c), mult(a, c))) = rd(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, a)), rd(mult(b, c), mult(a, c))), rd(mult(b, c), mult(a, c)))),
% 21.79/22.00 inference(symmetry,[status(thm)],[1146])).
% 21.79/22.00 tff(1148,plain,
% 21.79/22.00 (mult(mult(mult(a, b), c), a) = rd(mult(mult(mult(mult(a, b), c), a), rd(mult(b, c), mult(a, c))), rd(mult(b, c), mult(a, c)))),
% 21.79/22.00 inference(symmetry,[status(thm)],[409])).
% 21.79/22.00 tff(1149,plain,
% 21.79/22.00 (mult(mult(mult(a, b), c), a) = mult(mult(a, mult(b, c)), a)),
% 21.79/22.00 inference(transitivity,[status(thm)],[1148, 1147, 1013, 1063, 1062, 1061])).
% 21.79/22.00 tff(1150,plain,
% 21.79/22.00 (rd(mult(mult(mult(a, b), c), a), a) = rd(mult(mult(a, mult(b, c)), a), a)),
% 21.79/22.00 inference(monotonicity,[status(thm)],[1149])).
% 21.79/22.00 tff(1151,plain,
% 21.79/22.00 (mult(mult(a, b), c) = rd(mult(mult(mult(a, b), c), a), a)),
% 21.79/22.00 inference(symmetry,[status(thm)],[407])).
% 21.79/22.00 tff(1152,plain,
% 21.79/22.00 (mult(mult(a, b), c) = mult(a, mult(b, c))),
% 21.79/22.00 inference(transitivity,[status(thm)],[1151, 1150, 1034])).
% 21.79/22.00 tff(1153,plain,
% 21.79/22.00 ($false),
% 21.79/22.00 inference(unit_resolution,[status(thm)],[146, 1152])).
% 21.79/22.00 tff(1154,plain,((mult(mult(a, c), mult(b, mult(a, b))) = mult(mult(a, c), mult(mult(a, b), b))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit))))) | (~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(a, b)))), inference(lemma,lemma(discharge,[]))).
% 21.79/22.00 tff(1155,plain,
% 21.79/22.00 (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))),
% 21.79/22.00 inference(unit_resolution,[status(thm)],[1154, 1032, 97, 945, 985])).
% 21.79/22.00 tff(1156,plain,
% 21.79/22.00 ((~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))),
% 21.79/22.00 inference(unit_resolution,[status(thm)],[315, 1155])).
% 21.79/22.00 tff(1157,plain,
% 21.79/22.00 (~((~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))),
% 21.79/22.00 inference(unit_resolution,[status(thm)],[313, 1156])).
% 21.79/22.00 tff(1158,plain,
% 21.79/22.00 (mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))),
% 21.79/22.00 inference(unit_resolution,[status(thm)],[308, 1157])).
% 21.79/22.00 tff(1159,plain,
% 21.79/22.00 (mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(b, c))),
% 21.79/22.00 inference(transitivity,[status(thm)],[1158, 138])).
% 21.79/22.00 tff(1160,plain,
% 21.79/22.00 (ld(mult(a, c), mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c))))) = ld(mult(a, c), mult(mult(a, c), mult(b, c)))),
% 21.79/22.00 inference(monotonicity,[status(thm)],[1159])).
% 21.79/22.00 tff(1161,plain,
% 21.79/22.00 (ld(mult(a, c), mult(mult(a, c), mult(b, c))) = ld(mult(a, c), mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 21.79/22.00 inference(symmetry,[status(thm)],[1160])).
% 21.79/22.00 tff(1162,plain,
% 21.79/22.00 (mult(b, c) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))),
% 21.79/22.00 inference(transitivity,[status(thm)],[740, 1161, 1028])).
% 21.79/22.00 tff(1163,plain,
% 21.79/22.00 (mult(mult(b, c), a) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)),
% 21.79/22.00 inference(monotonicity,[status(thm)],[1162])).
% 21.79/22.00 tff(1164,plain,
% 21.79/22.00 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a) = mult(mult(b, c), a)),
% 21.79/22.00 inference(monotonicity,[status(thm)],[171])).
% 21.79/22.00 tff(1165,assumption,(~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))), introduced(assumption)).
% 21.79/22.00 tff(1166,plain,
% 21.79/22.00 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))),
% 21.79/22.00 inference(quant_inst,[status(thm)],[])).
% 21.79/22.00 tff(1167,plain,
% 21.79/22.00 ($false),
% 21.79/22.00 inference(unit_resolution,[status(thm)],[1166, 56, 1165])).
% 21.79/22.00 tff(1168,plain,(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))), inference(lemma,lemma(discharge,[]))).
% 21.79/22.00 tff(1169,plain,
% 21.79/22.00 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a)),
% 21.79/22.00 inference(symmetry,[status(thm)],[1168])).
% 21.79/22.00 tff(1170,plain,
% 21.79/22.00 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)) = mult(mult(a, b), c)),
% 21.79/22.00 inference(transitivity,[status(thm)],[1169, 1164, 1163, 1025, 1022, 1019, 407])).
% 21.79/22.00 tff(1171,plain,
% 21.79/22.00 (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), b) = mult(mult(mult(a, b), c), b)),
% 21.79/22.00 inference(monotonicity,[status(thm)],[1170])).
% 21.79/22.00 tff(1172,plain,
% 21.79/22.00 (mult(mult(b, c), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a)),
% 21.79/22.00 inference(symmetry,[status(thm)],[1164])).
% 21.79/22.00 tff(1173,plain,
% 21.79/22.00 (mult(mult(b, c), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))),
% 21.79/22.00 inference(transitivity,[status(thm)],[1172, 1168])).
% 21.79/22.00 tff(1174,plain,
% 21.79/22.00 (mult(mult(mult(b, c), a), b) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), b)),
% 21.79/22.00 inference(monotonicity,[status(thm)],[1173])).
% 21.79/22.00 tff(1175,plain,
% 21.79/22.00 (mult(mult(mult(b, c), a), b) = mult(mult(unit, a), mult(mult(b, c), b))),
% 21.79/22.00 inference(transitivity,[status(thm)],[1174, 1171, 781, 779])).
% 21.79/22.00 tff(1176,plain,
% 21.79/22.00 ((mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a)) <=> (mult(mult(unit, a), mult(mult(b, c), b)) = mult(mult(unit, mult(mult(b, c), b)), a))),
% 21.79/22.00 inference(monotonicity,[status(thm)],[1175, 777])).
% 21.79/22.00 tff(1177,plain,
% 21.79/22.00 ((mult(mult(unit, a), mult(mult(b, c), b)) = mult(mult(unit, mult(mult(b, c), b)), a)) <=> (mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a))),
% 21.79/22.00 inference(symmetry,[status(thm)],[1176])).
% 21.79/22.00 tff(1178,plain,
% 21.79/22.00 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(b, c), mult(mult(b, c), mult(b, a))) = mult(b, a))),
% 21.79/22.00 inference(quant_inst,[status(thm)],[])).
% 21.79/22.00 tff(1179,plain,
% 21.79/22.00 (ld(mult(b, c), mult(mult(b, c), mult(b, a))) = mult(b, a)),
% 21.79/22.00 inference(unit_resolution,[status(thm)],[1178, 7])).
% 21.79/22.00 tff(1180,assumption,(mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a))), introduced(assumption)).
% 21.79/22.00 tff(1181,plain,
% 21.79/22.00 (mult(mult(b, c), mult(b, a)) = mult(mult(b, c), mult(a, b))),
% 21.79/22.00 inference(symmetry,[status(thm)],[1180])).
% 21.79/22.00 tff(1182,plain,
% 21.79/22.00 (ld(mult(b, c), mult(mult(b, c), mult(b, a))) = ld(mult(b, c), mult(mult(b, c), mult(a, b)))),
% 21.79/22.00 inference(monotonicity,[status(thm)],[1181])).
% 21.79/22.00 tff(1183,plain,
% 21.79/22.00 (ld(mult(b, c), mult(mult(b, c), mult(a, b))) = ld(mult(b, c), mult(mult(b, c), mult(b, a)))),
% 21.79/22.00 inference(symmetry,[status(thm)],[1182])).
% 21.79/22.00 tff(1184,plain,
% 21.79/22.00 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(b, c), mult(mult(b, c), mult(a, b))) = mult(a, b))),
% 21.79/22.00 inference(quant_inst,[status(thm)],[])).
% 21.79/22.00 tff(1185,plain,
% 21.79/22.00 (ld(mult(b, c), mult(mult(b, c), mult(a, b))) = mult(a, b)),
% 21.79/22.00 inference(unit_resolution,[status(thm)],[1184, 7])).
% 21.79/22.00 tff(1186,plain,
% 21.79/22.00 (mult(a, b) = ld(mult(b, c), mult(mult(b, c), mult(a, b)))),
% 21.79/22.00 inference(symmetry,[status(thm)],[1185])).
% 21.79/22.00 tff(1187,plain,
% 21.79/22.00 (mult(a, b) = mult(b, a)),
% 21.79/22.00 inference(transitivity,[status(thm)],[1186, 1183, 1179])).
% 21.79/22.00 tff(1188,plain,
% 21.79/22.00 (mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(mult(a, b), c), mult(b, a))),
% 21.79/22.00 inference(monotonicity,[status(thm)],[161, 1187])).
% 21.79/22.00 tff(1189,plain,
% 21.79/22.00 (mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, c), b), mult(a, b))),
% 21.79/22.00 inference(symmetry,[status(thm)],[1188])).
% 21.79/22.00 tff(1190,plain,
% 21.79/22.00 (mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(a, b))),
% 21.79/22.00 inference(transitivity,[status(thm)],[1189, 949])).
% 21.79/22.00 tff(1191,plain,
% 21.79/22.00 ($false),
% 21.79/22.00 inference(unit_resolution,[status(thm)],[1064, 1190])).
% 21.79/22.00 tff(1192,plain,((~(mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a)))) | (mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(a, b)))), inference(lemma,lemma(discharge,[]))).
% 21.79/22.00 tff(1193,plain,
% 21.79/22.00 (~(mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a)))),
% 21.79/22.00 inference(unit_resolution,[status(thm)],[1192, 985])).
% 21.79/22.00 tff(1194,plain,
% 21.79/22.00 (((~(mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a))) | (~(mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a))))) | (mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a)))),
% 21.79/22.00 inference(tautology,[status(thm)],[])).
% 21.79/22.00 tff(1195,plain,
% 21.79/22.00 ((~(mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a))) | (~(mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a))))),
% 21.79/22.00 inference(unit_resolution,[status(thm)],[1194, 1193])).
% 21.79/22.00 tff(1196,plain,
% 21.79/22.00 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(b, c), a), b) = mult(mult(b, c), mult(a, b)))) | (~(mult(mult(mult(b, c), b), a) = mult(mult(b, c), mult(b, a)))))) | (~((~(mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a))) | (~(mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(b, c), a), b) = mult(mult(b, c), mult(a, b)))) | (~(mult(mult(mult(b, c), b), a) = mult(mult(b, c), mult(b, a)))))) | (~((~(mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a))) | (~(mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a)))))))),
% 21.79/22.00 inference(rewrite,[status(thm)],[])).
% 21.79/22.00 tff(1197,plain,
% 21.79/22.00 (((~((~(mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a))) | (~(mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a)))))) | (~((~(mult(mult(mult(b, c), a), b) = mult(mult(b, c), mult(a, b)))) | (~(mult(mult(mult(b, c), b), a) = mult(mult(b, c), mult(b, a))))))) <=> ((~((~(mult(mult(mult(b, c), a), b) = mult(mult(b, c), mult(a, b)))) | (~(mult(mult(mult(b, c), b), a) = mult(mult(b, c), mult(b, a)))))) | (~((~(mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a))) | (~(mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a)))))))),
% 21.79/22.00 inference(rewrite,[status(thm)],[])).
% 21.79/22.00 tff(1198,plain,
% 21.79/22.00 ((~((~(mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a))) | (~(mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a)))))) <=> (~((~(mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a))) | (~(mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a))))))),
% 21.79/22.00 inference(rewrite,[status(thm)],[])).
% 21.79/22.00 tff(1199,plain,
% 21.79/22.00 (((~((~(mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a))) | (~(mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a)))))) | (~((~(mult(mult(mult(b, c), a), b) = mult(mult(b, c), mult(a, b)))) | (~(mult(mult(mult(b, c), b), a) = mult(mult(b, c), mult(b, a))))))) <=> ((~((~(mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a))) | (~(mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a)))))) | (~((~(mult(mult(mult(b, c), a), b) = mult(mult(b, c), mult(a, b)))) | (~(mult(mult(mult(b, c), b), a) = mult(mult(b, c), mult(b, a)))))))),
% 21.79/22.01 inference(monotonicity,[status(thm)],[1198])).
% 21.79/22.01 tff(1200,plain,
% 21.79/22.01 (((~((~(mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a))) | (~(mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a)))))) | (~((~(mult(mult(mult(b, c), a), b) = mult(mult(b, c), mult(a, b)))) | (~(mult(mult(mult(b, c), b), a) = mult(mult(b, c), mult(b, a))))))) <=> ((~((~(mult(mult(mult(b, c), a), b) = mult(mult(b, c), mult(a, b)))) | (~(mult(mult(mult(b, c), b), a) = mult(mult(b, c), mult(b, a)))))) | (~((~(mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a))) | (~(mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a)))))))),
% 21.79/22.01 inference(transitivity,[status(thm)],[1199, 1197])).
% 21.79/22.01 tff(1201,plain,
% 21.79/22.01 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a))) | (~(mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a)))))) | (~((~(mult(mult(mult(b, c), a), b) = mult(mult(b, c), mult(a, b)))) | (~(mult(mult(mult(b, c), b), a) = mult(mult(b, c), mult(b, a)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(b, c), a), b) = mult(mult(b, c), mult(a, b)))) | (~(mult(mult(mult(b, c), b), a) = mult(mult(b, c), mult(b, a)))))) | (~((~(mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a))) | (~(mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a))))))))),
% 21.79/22.01 inference(monotonicity,[status(thm)],[1200])).
% 21.79/22.01 tff(1202,plain,
% 21.79/22.01 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a))) | (~(mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a)))))) | (~((~(mult(mult(mult(b, c), a), b) = mult(mult(b, c), mult(a, b)))) | (~(mult(mult(mult(b, c), b), a) = mult(mult(b, c), mult(b, a)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(b, c), a), b) = mult(mult(b, c), mult(a, b)))) | (~(mult(mult(mult(b, c), b), a) = mult(mult(b, c), mult(b, a)))))) | (~((~(mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a))) | (~(mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a)))))))),
% 21.79/22.01 inference(transitivity,[status(thm)],[1201, 1196])).
% 21.79/22.01 tff(1203,plain,
% 21.79/22.01 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a))) | (~(mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a)))))) | (~((~(mult(mult(mult(b, c), a), b) = mult(mult(b, c), mult(a, b)))) | (~(mult(mult(mult(b, c), b), a) = mult(mult(b, c), mult(b, a)))))))),
% 21.79/22.01 inference(quant_inst,[status(thm)],[])).
% 21.79/22.01 tff(1204,plain,
% 21.79/22.01 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(b, c), a), b) = mult(mult(b, c), mult(a, b)))) | (~(mult(mult(mult(b, c), b), a) = mult(mult(b, c), mult(b, a)))))) | (~((~(mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a))) | (~(mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a))))))),
% 21.79/22.01 inference(modus_ponens,[status(thm)],[1203, 1202])).
% 21.79/22.01 tff(1205,plain,
% 21.79/22.01 ((~((~(mult(mult(mult(b, c), a), b) = mult(mult(b, c), mult(a, b)))) | (~(mult(mult(mult(b, c), b), a) = mult(mult(b, c), mult(b, a)))))) | (~((~(mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a))) | (~(mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a))))))),
% 21.79/22.01 inference(unit_resolution,[status(thm)],[1204, 27])).
% 21.79/22.01 tff(1206,plain,
% 21.79/22.01 (~((~(mult(mult(mult(b, c), a), b) = mult(mult(b, c), mult(a, b)))) | (~(mult(mult(mult(b, c), b), a) = mult(mult(b, c), mult(b, a)))))),
% 21.79/22.01 inference(unit_resolution,[status(thm)],[1205, 1195])).
% 21.79/22.01 tff(1207,plain,
% 21.79/22.01 (((~(mult(mult(mult(b, c), a), b) = mult(mult(b, c), mult(a, b)))) | (~(mult(mult(mult(b, c), b), a) = mult(mult(b, c), mult(b, a))))) | (mult(mult(mult(b, c), b), a) = mult(mult(b, c), mult(b, a)))),
% 21.79/22.01 inference(tautology,[status(thm)],[])).
% 21.79/22.01 tff(1208,plain,
% 21.79/22.01 (mult(mult(mult(b, c), b), a) = mult(mult(b, c), mult(b, a))),
% 21.79/22.01 inference(unit_resolution,[status(thm)],[1207, 1206])).
% 21.79/22.01 tff(1209,plain,
% 21.79/22.01 (mult(mult(b, c), mult(b, a)) = mult(mult(mult(b, c), b), a)),
% 21.79/22.01 inference(symmetry,[status(thm)],[1208])).
% 21.79/22.01 tff(1210,plain,
% 21.79/22.01 (mult(b, a) = mult(mult(a, rd(mult(b, c), mult(a, c))), a)),
% 21.79/22.01 inference(symmetry,[status(thm)],[993])).
% 21.79/22.01 tff(1211,plain,
% 21.79/22.01 (mult(mult(b, c), mult(b, a)) = mult(mult(b, c), mult(mult(a, rd(mult(b, c), mult(a, c))), a))),
% 21.79/22.01 inference(monotonicity,[status(thm)],[1210])).
% 21.79/22.01 tff(1212,plain,
% 21.79/22.01 (mult(mult(b, c), mult(mult(a, rd(mult(b, c), mult(a, c))), a)) = mult(mult(b, c), mult(b, a))),
% 21.79/22.01 inference(symmetry,[status(thm)],[1211])).
% 21.79/22.01 tff(1213,plain,
% 21.79/22.01 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(b, c), a), rd(mult(b, c), mult(a, c))), a) = mult(mult(b, c), mult(mult(a, rd(mult(b, c), mult(a, c))), a)))),
% 21.79/22.01 inference(quant_inst,[status(thm)],[])).
% 21.79/22.01 tff(1214,plain,
% 21.79/22.01 (mult(mult(mult(mult(b, c), a), rd(mult(b, c), mult(a, c))), a) = mult(mult(b, c), mult(mult(a, rd(mult(b, c), mult(a, c))), a))),
% 21.79/22.01 inference(unit_resolution,[status(thm)],[1213, 56])).
% 21.79/22.01 tff(1215,plain,
% 21.79/22.01 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)) = mult(mult(b, c), a)),
% 21.79/22.01 inference(transitivity,[status(thm)],[1169, 1164])).
% 21.79/22.01 tff(1216,plain,
% 21.79/22.01 (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(b, c), a), rd(mult(b, c), mult(a, c)))),
% 21.79/22.01 inference(monotonicity,[status(thm)],[1215])).
% 21.79/22.01 tff(1217,plain,
% 21.79/22.01 (mult(mult(mult(b, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c)))),
% 21.79/22.01 inference(symmetry,[status(thm)],[1216])).
% 21.79/22.01 tff(1218,plain,
% 21.79/22.01 (mult(mult(mult(mult(b, c), a), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))), a)),
% 21.79/22.01 inference(monotonicity,[status(thm)],[1217])).
% 21.79/22.01 tff(1219,plain,
% 21.79/22.01 (mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(mult(b, c), a), rd(mult(b, c), mult(a, c))), a)),
% 21.79/22.01 inference(symmetry,[status(thm)],[1218])).
% 21.79/22.01 tff(1220,plain,
% 21.79/22.01 ((mult(mult(mult(b, c), b), a) = mult(mult(mult(b, c), a), b)) <=> (mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a))),
% 21.79/22.01 inference(commutativity,[status(thm)],[])).
% 21.79/22.01 tff(1221,plain,
% 21.79/22.01 (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), b) = mult(mult(mult(b, c), a), b)),
% 21.79/22.01 inference(symmetry,[status(thm)],[1174])).
% 21.79/22.01 tff(1222,plain,
% 21.79/22.01 (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), b)),
% 21.79/22.01 inference(monotonicity,[status(thm)],[176])).
% 21.79/22.01 tff(1223,plain,
% 21.79/22.01 (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(b, c), a), b)),
% 21.79/22.01 inference(transitivity,[status(thm)],[1222, 1221])).
% 21.79/22.01 tff(1224,plain,
% 21.79/22.01 (mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(b, c), b), a)),
% 21.79/22.01 inference(transitivity,[status(thm)],[1219, 1214, 1212, 1209])).
% 21.79/22.01 tff(1225,plain,
% 21.79/22.01 ((mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))), a) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(rd(mult(b, c), mult(a, c)), a))) <=> (mult(mult(mult(b, c), b), a) = mult(mult(mult(b, c), a), b))),
% 21.79/22.01 inference(monotonicity,[status(thm)],[1224, 1223])).
% 21.79/22.01 tff(1226,plain,
% 21.79/22.01 ((mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))), a) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(rd(mult(b, c), mult(a, c)), a))) <=> (mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a))),
% 21.79/22.01 inference(transitivity,[status(thm)],[1225, 1220])).
% 21.79/22.01 tff(1227,plain,
% 21.79/22.01 ((mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a)) <=> (mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))), a) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(rd(mult(b, c), mult(a, c)), a)))),
% 21.79/22.01 inference(symmetry,[status(thm)],[1226])).
% 21.79/22.01 tff(1228,plain,
% 21.79/22.01 ((~(mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a))) <=> (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))), a) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(rd(mult(b, c), mult(a, c)), a))))),
% 21.79/22.01 inference(monotonicity,[status(thm)],[1227])).
% 21.79/22.01 tff(1229,plain,
% 21.79/22.01 (((~(mult(mult(mult(b, c), a), b) = mult(mult(b, c), mult(a, b)))) | (~(mult(mult(mult(b, c), b), a) = mult(mult(b, c), mult(b, a))))) | (mult(mult(mult(b, c), a), b) = mult(mult(b, c), mult(a, b)))),
% 21.79/22.01 inference(tautology,[status(thm)],[])).
% 21.79/22.01 tff(1230,plain,
% 21.79/22.01 (mult(mult(mult(b, c), a), b) = mult(mult(b, c), mult(a, b))),
% 21.79/22.01 inference(unit_resolution,[status(thm)],[1229, 1206])).
% 21.79/22.01 tff(1231,plain,
% 21.79/22.01 (mult(mult(b, c), mult(a, b)) = mult(mult(mult(b, c), a), b)),
% 21.79/22.01 inference(symmetry,[status(thm)],[1230])).
% 21.79/22.01 tff(1232,plain,
% 21.79/22.01 ((mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a))) <=> (mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a))),
% 21.79/22.01 inference(monotonicity,[status(thm)],[1231, 1209])).
% 21.79/22.01 tff(1233,plain,
% 21.79/22.01 ((~(mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a)))) <=> (~(mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a)))),
% 21.79/22.01 inference(monotonicity,[status(thm)],[1232])).
% 21.79/22.01 tff(1234,plain,
% 21.79/22.01 (~(mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a))),
% 21.79/22.01 inference(modus_ponens,[status(thm)],[1193, 1233])).
% 21.79/22.01 tff(1235,plain,
% 21.79/22.01 (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))), a) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(rd(mult(b, c), mult(a, c)), a)))),
% 21.79/22.01 inference(modus_ponens,[status(thm)],[1234, 1228])).
% 21.79/22.01 tff(1236,plain,
% 21.79/22.01 (((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))), a) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(rd(mult(b, c), mult(a, c)), a))))) | (mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))), a) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(rd(mult(b, c), mult(a, c)), a)))),
% 21.79/22.01 inference(tautology,[status(thm)],[])).
% 21.79/22.01 tff(1237,plain,
% 21.79/22.01 ((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))), a) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(rd(mult(b, c), mult(a, c)), a))))),
% 21.79/22.01 inference(unit_resolution,[status(thm)],[1236, 1235])).
% 21.79/22.01 tff(1238,plain,
% 21.79/22.01 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))), a) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(rd(mult(b, c), mult(a, c)), a)))))) | (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))), a))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(rd(mult(b, c), mult(a, c)), a)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))), a) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(rd(mult(b, c), mult(a, c)), a)))))) | (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))), a))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(rd(mult(b, c), mult(a, c)), a)))))))),
% 21.79/22.01 inference(rewrite,[status(thm)],[])).
% 21.79/22.01 tff(1239,plain,
% 21.79/22.01 (((~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))), a))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(rd(mult(b, c), mult(a, c)), a)))))) | (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))), a) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(rd(mult(b, c), mult(a, c)), a))))))) <=> ((~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))), a) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(rd(mult(b, c), mult(a, c)), a)))))) | (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))), a))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(rd(mult(b, c), mult(a, c)), a)))))))),
% 21.79/22.02 inference(rewrite,[status(thm)],[])).
% 21.79/22.02 tff(1240,plain,
% 21.79/22.02 ((~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))), a))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(rd(mult(b, c), mult(a, c)), a)))))) <=> (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))), a))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(rd(mult(b, c), mult(a, c)), a))))))),
% 21.79/22.02 inference(rewrite,[status(thm)],[])).
% 21.79/22.02 tff(1241,plain,
% 21.79/22.02 (((~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))), a))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(rd(mult(b, c), mult(a, c)), a)))))) | (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))), a) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(rd(mult(b, c), mult(a, c)), a))))))) <=> ((~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))), a))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(rd(mult(b, c), mult(a, c)), a)))))) | (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))), a) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(rd(mult(b, c), mult(a, c)), a)))))))),
% 21.79/22.02 inference(monotonicity,[status(thm)],[1240])).
% 21.79/22.02 tff(1242,plain,
% 21.79/22.02 (((~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))), a))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(rd(mult(b, c), mult(a, c)), a)))))) | (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))), a) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(rd(mult(b, c), mult(a, c)), a))))))) <=> ((~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))), a) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(rd(mult(b, c), mult(a, c)), a)))))) | (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))), a))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(rd(mult(b, c), mult(a, c)), a)))))))),
% 21.79/22.02 inference(transitivity,[status(thm)],[1241, 1239])).
% 21.79/22.02 tff(1243,plain,
% 21.79/22.02 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))), a))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(rd(mult(b, c), mult(a, c)), a)))))) | (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))), a) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(rd(mult(b, c), mult(a, c)), a)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))), a) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(rd(mult(b, c), mult(a, c)), a)))))) | (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))), a))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(rd(mult(b, c), mult(a, c)), a))))))))),
% 21.79/22.02 inference(monotonicity,[status(thm)],[1242])).
% 21.79/22.02 tff(1244,plain,
% 21.79/22.02 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))), a))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(rd(mult(b, c), mult(a, c)), a)))))) | (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))), a) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(rd(mult(b, c), mult(a, c)), a)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))), a) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(rd(mult(b, c), mult(a, c)), a)))))) | (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))), a))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(rd(mult(b, c), mult(a, c)), a)))))))),
% 21.79/22.02 inference(transitivity,[status(thm)],[1243, 1238])).
% 21.79/22.02 tff(1245,plain,
% 21.79/22.02 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))), a))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(rd(mult(b, c), mult(a, c)), a)))))) | (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))), a) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(rd(mult(b, c), mult(a, c)), a)))))))),
% 21.79/22.02 inference(quant_inst,[status(thm)],[])).
% 21.79/22.02 tff(1246,plain,
% 21.79/22.02 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))), a) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(rd(mult(b, c), mult(a, c)), a)))))) | (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))), a))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(rd(mult(b, c), mult(a, c)), a))))))),
% 21.79/22.02 inference(modus_ponens,[status(thm)],[1245, 1244])).
% 21.79/22.02 tff(1247,plain,
% 21.79/22.02 ((~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))), a) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(rd(mult(b, c), mult(a, c)), a)))))) | (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))), a))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(rd(mult(b, c), mult(a, c)), a))))))),
% 21.79/22.03 inference(unit_resolution,[status(thm)],[1246, 27])).
% 21.79/22.03 tff(1248,plain,
% 21.79/22.03 (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))), a))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(rd(mult(b, c), mult(a, c)), a)))))),
% 21.79/22.03 inference(unit_resolution,[status(thm)],[1247, 1237])).
% 21.79/22.03 tff(1249,plain,
% 21.79/22.03 (((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))), a))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(rd(mult(b, c), mult(a, c)), a))))) | (mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))), a))),
% 21.79/22.03 inference(tautology,[status(thm)],[])).
% 21.79/22.03 tff(1250,plain,
% 21.79/22.03 (mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))), a)),
% 21.79/22.03 inference(unit_resolution,[status(thm)],[1249, 1248])).
% 21.79/22.03 tff(1251,plain,
% 21.79/22.03 (mult(mult(b, c), mult(a, a)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, a))),
% 21.79/22.03 inference(monotonicity,[status(thm)],[1162])).
% 21.79/22.03 tff(1252,plain,
% 21.79/22.03 (mult(mult(b, c), mult(mult(a, unit), a)) = mult(mult(b, c), mult(a, a))),
% 21.79/22.03 inference(monotonicity,[status(thm)],[519])).
% 21.79/22.03 tff(1253,plain,
% 21.79/22.03 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(b, c), a), unit), a) = mult(mult(b, c), mult(mult(a, unit), a)))),
% 21.79/22.03 inference(quant_inst,[status(thm)],[])).
% 21.79/22.03 tff(1254,plain,
% 21.79/22.03 (mult(mult(mult(mult(b, c), a), unit), a) = mult(mult(b, c), mult(mult(a, unit), a))),
% 21.79/22.03 inference(unit_resolution,[status(thm)],[1253, 56])).
% 21.79/22.03 tff(1255,plain,
% 21.79/22.03 (mult(mult(b, c), unit) = mult(b, c)),
% 21.79/22.03 inference(transitivity,[status(thm)],[845, 837, 835, 240, 237, 141])).
% 21.79/22.03 tff(1256,plain,
% 21.79/22.03 (mult(mult(mult(b, c), unit), a) = mult(mult(b, c), a)),
% 21.79/22.03 inference(monotonicity,[status(thm)],[1255])).
% 21.79/22.03 tff(1257,plain,
% 21.79/22.03 (mult(mult(b, c), a) = mult(mult(mult(b, c), unit), a)),
% 21.79/22.03 inference(symmetry,[status(thm)],[1256])).
% 21.79/22.03 tff(1258,plain,
% 21.79/22.03 (mult(mult(mult(b, c), a), unit) = mult(mult(mult(mult(b, c), unit), a), unit)),
% 21.79/22.03 inference(monotonicity,[status(thm)],[1257])).
% 21.79/22.03 tff(1259,plain,
% 21.79/22.03 (mult(mult(mult(mult(b, c), unit), a), unit) = mult(mult(mult(b, c), a), unit)),
% 21.79/22.03 inference(symmetry,[status(thm)],[1258])).
% 21.79/22.03 tff(1260,plain,
% 21.79/22.03 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(b, c), unit), a), unit) = mult(mult(b, c), mult(mult(unit, a), unit)))),
% 21.79/22.03 inference(quant_inst,[status(thm)],[])).
% 21.79/22.03 tff(1261,plain,
% 21.79/22.03 (mult(mult(mult(mult(b, c), unit), a), unit) = mult(mult(b, c), mult(mult(unit, a), unit))),
% 21.79/22.03 inference(unit_resolution,[status(thm)],[1260, 56])).
% 21.79/22.03 tff(1262,plain,
% 21.79/22.03 (mult(mult(b, c), mult(mult(unit, a), unit)) = mult(mult(mult(mult(b, c), unit), a), unit)),
% 21.79/22.03 inference(symmetry,[status(thm)],[1261])).
% 21.79/22.03 tff(1263,plain,
% 21.79/22.03 (mult(mult(b, c), mult(mult(unit, a), unit)) = mult(mult(b, c), a)),
% 21.79/22.03 inference(monotonicity,[status(thm)],[507])).
% 21.79/22.03 tff(1264,plain,
% 21.79/22.03 (mult(mult(b, c), a) = mult(mult(b, c), mult(mult(unit, a), unit))),
% 21.79/22.03 inference(symmetry,[status(thm)],[1263])).
% 21.79/22.03 tff(1265,plain,
% 21.79/22.03 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)) = mult(mult(mult(b, c), a), unit)),
% 21.79/22.03 inference(transitivity,[status(thm)],[1169, 1164, 1264, 1262, 1259])).
% 21.79/22.03 tff(1266,plain,
% 21.79/22.03 (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a) = mult(mult(mult(mult(b, c), a), unit), a)),
% 21.79/22.03 inference(monotonicity,[status(thm)],[1265])).
% 21.79/22.03 tff(1267,plain,
% 21.79/22.03 (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a) = mult(mult(mult(a, b), c), a)),
% 21.79/22.03 inference(transitivity,[status(thm)],[1266, 1254, 1252, 1251, 1014, 1011, 409])).
% 21.79/22.03 tff(1268,plain,
% 21.79/22.03 (mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(mult(a, b), c), a), rd(mult(b, c), mult(a, c)))),
% 21.79/22.03 inference(monotonicity,[status(thm)],[1267])).
% 21.79/22.03 tff(1269,plain,
% 21.79/22.03 (mult(mult(mult(mult(a, b), c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c)))),
% 21.79/22.03 inference(symmetry,[status(thm)],[1268])).
% 21.79/22.03 tff(1270,plain,
% 21.79/22.03 (mult(mult(unit, a), mult(mult(b, c), b)) = mult(mult(unit, mult(mult(b, c), b)), a)),
% 21.79/22.03 inference(transitivity,[status(thm)],[778, 783, 827, 832, 892, 1000, 997, 411, 1269, 1250, 1219, 1214, 1212, 1209, 777])).
% 21.79/22.03 tff(1271,plain,
% 21.79/22.03 (mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a)),
% 21.79/22.03 inference(modus_ponens,[status(thm)],[1270, 1177])).
% 21.79/22.03 tff(1272,plain,
% 21.79/22.03 ($false),
% 21.79/22.03 inference(unit_resolution,[status(thm)],[1234, 1271])).
% 21.79/22.03 tff(1273,plain,((mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit))))) | (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))), inference(lemma,lemma(discharge,[]))).
% 21.79/22.03 tff(1274,plain,
% 21.79/22.03 (mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a))),
% 21.79/22.03 inference(unit_resolution,[status(thm)],[1273, 34, 114])).
% 21.79/22.03 tff(1275,plain,
% 21.79/22.03 (mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, b)),
% 21.79/22.03 inference(transitivity,[status(thm)],[1274, 769])).
% 21.79/22.03 tff(1276,plain,
% 21.79/22.03 (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), c) = mult(mult(a, b), c)),
% 21.79/22.03 inference(monotonicity,[status(thm)],[1275])).
% 21.79/22.03 tff(1277,plain,
% 21.79/22.03 (mult(mult(a, b), c) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), c)),
% 21.79/22.03 inference(symmetry,[status(thm)],[1276])).
% 21.79/22.03 tff(1278,plain,
% 21.79/22.03 (mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, c), b)),
% 21.79/22.03 inference(monotonicity,[status(thm)],[768])).
% 21.79/22.03 tff(1279,plain,
% 21.79/22.03 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(a, mult(a, mult(mult(a, b), mult(b, c)))) = mult(mult(a, b), mult(b, c)))),
% 21.79/22.03 inference(quant_inst,[status(thm)],[])).
% 21.79/22.03 tff(1280,plain,
% 21.79/22.03 (ld(a, mult(a, mult(mult(a, b), mult(b, c)))) = mult(mult(a, b), mult(b, c))),
% 21.79/22.03 inference(unit_resolution,[status(thm)],[1279, 7])).
% 21.79/22.03 tff(1281,plain,
% 21.79/22.03 (mult(mult(a, b), b) = mult(a, mult(unit, mult(mult(b, unit), b)))),
% 21.79/22.03 inference(transitivity,[status(thm)],[442, 439, 437, 830])).
% 21.79/22.03 tff(1282,plain,
% 21.79/22.03 (mult(mult(mult(a, b), b), c) = mult(mult(a, mult(unit, mult(mult(b, unit), b))), c)),
% 21.79/22.03 inference(monotonicity,[status(thm)],[1281])).
% 21.79/22.03 tff(1283,plain,
% 21.79/22.03 (mult(mult(a, mult(unit, mult(mult(b, unit), b))), c) = mult(mult(mult(a, b), b), c)),
% 21.79/22.03 inference(symmetry,[status(thm)],[1282])).
% 21.79/22.03 tff(1284,plain,
% 21.79/22.03 (mult(a, mult(mult(unit, mult(mult(b, unit), b)), c)) = mult(mult(mult(a, b), b), c)),
% 21.79/22.03 inference(transitivity,[status(thm)],[893, 1283])).
% 21.79/22.03 tff(1285,plain,
% 21.79/22.03 (mult(a, mult(a, mult(mult(unit, mult(mult(b, unit), b)), c))) = mult(a, mult(mult(mult(a, b), b), c))),
% 21.79/22.03 inference(monotonicity,[status(thm)],[1284])).
% 21.79/22.03 tff(1286,plain,
% 21.79/22.03 (mult(a, mult(mult(mult(a, b), b), c)) = mult(a, mult(a, mult(mult(unit, mult(mult(b, unit), b)), c)))),
% 21.79/22.03 inference(symmetry,[status(thm)],[1285])).
% 21.79/22.03 tff(1287,assumption,(mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a))), introduced(assumption)).
% 21.79/22.03 tff(1288,plain,
% 21.79/22.03 (mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, b)),
% 21.79/22.03 inference(transitivity,[status(thm)],[1287, 913])).
% 21.79/22.03 tff(1289,plain,
% 21.79/22.03 (mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), a)) = mult(b, mult(a, b))),
% 21.79/22.03 inference(monotonicity,[status(thm)],[1288])).
% 21.79/22.03 tff(1290,plain,
% 21.79/22.03 (mult(b, mult(a, b)) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), a))),
% 21.79/22.03 inference(symmetry,[status(thm)],[1289])).
% 21.79/22.03 tff(1291,assumption,(~(mult(mult(mult(b, c), a), mult(a, b)) = mult(mult(b, c), mult(a, mult(a, b))))), introduced(assumption)).
% 21.79/22.03 tff(1292,assumption,(~(mult(mult(mult(mult(b, c), a), b), a) = mult(mult(b, c), mult(mult(a, b), a)))), introduced(assumption)).
% 21.79/22.03 tff(1293,plain,
% 21.79/22.03 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(b, c), a), b), a) = mult(mult(b, c), mult(mult(a, b), a)))),
% 21.79/22.03 inference(quant_inst,[status(thm)],[])).
% 21.79/22.03 tff(1294,plain,
% 21.79/22.03 ($false),
% 21.79/22.03 inference(unit_resolution,[status(thm)],[1293, 56, 1292])).
% 21.79/22.03 tff(1295,plain,(mult(mult(mult(mult(b, c), a), b), a) = mult(mult(b, c), mult(mult(a, b), a))), inference(lemma,lemma(discharge,[]))).
% 21.79/22.03 tff(1296,plain,
% 21.79/22.03 (((~(mult(mult(mult(b, c), mult(a, b)), a) = mult(mult(b, c), mult(mult(a, b), a)))) | (~(mult(mult(mult(b, c), a), mult(a, b)) = mult(mult(b, c), mult(a, mult(a, b)))))) | (mult(mult(mult(b, c), a), mult(a, b)) = mult(mult(b, c), mult(a, mult(a, b))))),
% 21.79/22.03 inference(tautology,[status(thm)],[])).
% 21.79/22.03 tff(1297,plain,
% 21.79/22.03 ((~(mult(mult(mult(b, c), mult(a, b)), a) = mult(mult(b, c), mult(mult(a, b), a)))) | (~(mult(mult(mult(b, c), a), mult(a, b)) = mult(mult(b, c), mult(a, mult(a, b)))))),
% 21.79/22.03 inference(unit_resolution,[status(thm)],[1296, 1291])).
% 21.79/22.03 tff(1298,assumption,((~(mult(mult(b, c), mult(mult(a, b), a)) = mult(mult(b, c), mult(a, mult(a, b))))) | (~(mult(mult(mult(b, c), mult(a, b)), a) = mult(mult(mult(b, c), a), mult(a, b))))), introduced(assumption)).
% 21.79/22.03 tff(1299,plain,
% 21.79/22.03 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(b, c), mult(mult(a, b), a)) = mult(mult(b, c), mult(a, mult(a, b))))) | (~(mult(mult(mult(b, c), mult(a, b)), a) = mult(mult(mult(b, c), a), mult(a, b)))))) | (~((~(mult(mult(mult(b, c), mult(a, b)), a) = mult(mult(b, c), mult(mult(a, b), a)))) | (~(mult(mult(mult(b, c), a), mult(a, b)) = mult(mult(b, c), mult(a, mult(a, b))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(b, c), mult(mult(a, b), a)) = mult(mult(b, c), mult(a, mult(a, b))))) | (~(mult(mult(mult(b, c), mult(a, b)), a) = mult(mult(mult(b, c), a), mult(a, b)))))) | (~((~(mult(mult(mult(b, c), mult(a, b)), a) = mult(mult(b, c), mult(mult(a, b), a)))) | (~(mult(mult(mult(b, c), a), mult(a, b)) = mult(mult(b, c), mult(a, mult(a, b))))))))),
% 21.79/22.03 inference(rewrite,[status(thm)],[])).
% 21.79/22.03 tff(1300,plain,
% 21.79/22.03 (((~((~(mult(mult(mult(b, c), mult(a, b)), a) = mult(mult(mult(b, c), a), mult(a, b)))) | (~(mult(mult(b, c), mult(mult(a, b), a)) = mult(mult(b, c), mult(a, mult(a, b))))))) | (~((~(mult(mult(mult(b, c), mult(a, b)), a) = mult(mult(b, c), mult(mult(a, b), a)))) | (~(mult(mult(mult(b, c), a), mult(a, b)) = mult(mult(b, c), mult(a, mult(a, b)))))))) <=> ((~((~(mult(mult(b, c), mult(mult(a, b), a)) = mult(mult(b, c), mult(a, mult(a, b))))) | (~(mult(mult(mult(b, c), mult(a, b)), a) = mult(mult(mult(b, c), a), mult(a, b)))))) | (~((~(mult(mult(mult(b, c), mult(a, b)), a) = mult(mult(b, c), mult(mult(a, b), a)))) | (~(mult(mult(mult(b, c), a), mult(a, b)) = mult(mult(b, c), mult(a, mult(a, b))))))))),
% 21.79/22.03 inference(rewrite,[status(thm)],[])).
% 21.79/22.03 tff(1301,plain,
% 21.79/22.03 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(b, c), mult(a, b)), a) = mult(mult(mult(b, c), a), mult(a, b)))) | (~(mult(mult(b, c), mult(mult(a, b), a)) = mult(mult(b, c), mult(a, mult(a, b))))))) | (~((~(mult(mult(mult(b, c), mult(a, b)), a) = mult(mult(b, c), mult(mult(a, b), a)))) | (~(mult(mult(mult(b, c), a), mult(a, b)) = mult(mult(b, c), mult(a, mult(a, b))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(b, c), mult(mult(a, b), a)) = mult(mult(b, c), mult(a, mult(a, b))))) | (~(mult(mult(mult(b, c), mult(a, b)), a) = mult(mult(mult(b, c), a), mult(a, b)))))) | (~((~(mult(mult(mult(b, c), mult(a, b)), a) = mult(mult(b, c), mult(mult(a, b), a)))) | (~(mult(mult(mult(b, c), a), mult(a, b)) = mult(mult(b, c), mult(a, mult(a, b)))))))))),
% 21.87/22.03 inference(monotonicity,[status(thm)],[1300])).
% 21.87/22.03 tff(1302,plain,
% 21.87/22.03 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(b, c), mult(a, b)), a) = mult(mult(mult(b, c), a), mult(a, b)))) | (~(mult(mult(b, c), mult(mult(a, b), a)) = mult(mult(b, c), mult(a, mult(a, b))))))) | (~((~(mult(mult(mult(b, c), mult(a, b)), a) = mult(mult(b, c), mult(mult(a, b), a)))) | (~(mult(mult(mult(b, c), a), mult(a, b)) = mult(mult(b, c), mult(a, mult(a, b))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(b, c), mult(mult(a, b), a)) = mult(mult(b, c), mult(a, mult(a, b))))) | (~(mult(mult(mult(b, c), mult(a, b)), a) = mult(mult(mult(b, c), a), mult(a, b)))))) | (~((~(mult(mult(mult(b, c), mult(a, b)), a) = mult(mult(b, c), mult(mult(a, b), a)))) | (~(mult(mult(mult(b, c), a), mult(a, b)) = mult(mult(b, c), mult(a, mult(a, b))))))))),
% 21.87/22.03 inference(transitivity,[status(thm)],[1301, 1299])).
% 21.87/22.03 tff(1303,plain,
% 21.87/22.03 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(b, c), mult(a, b)), a) = mult(mult(mult(b, c), a), mult(a, b)))) | (~(mult(mult(b, c), mult(mult(a, b), a)) = mult(mult(b, c), mult(a, mult(a, b))))))) | (~((~(mult(mult(mult(b, c), mult(a, b)), a) = mult(mult(b, c), mult(mult(a, b), a)))) | (~(mult(mult(mult(b, c), a), mult(a, b)) = mult(mult(b, c), mult(a, mult(a, b))))))))),
% 21.87/22.03 inference(quant_inst,[status(thm)],[])).
% 21.87/22.03 tff(1304,plain,
% 21.87/22.03 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(b, c), mult(mult(a, b), a)) = mult(mult(b, c), mult(a, mult(a, b))))) | (~(mult(mult(mult(b, c), mult(a, b)), a) = mult(mult(mult(b, c), a), mult(a, b)))))) | (~((~(mult(mult(mult(b, c), mult(a, b)), a) = mult(mult(b, c), mult(mult(a, b), a)))) | (~(mult(mult(mult(b, c), a), mult(a, b)) = mult(mult(b, c), mult(a, mult(a, b)))))))),
% 21.87/22.03 inference(modus_ponens,[status(thm)],[1303, 1302])).
% 21.87/22.03 tff(1305,plain,
% 21.87/22.03 ($false),
% 21.87/22.03 inference(unit_resolution,[status(thm)],[1304, 27, 1298, 1297])).
% 21.87/22.03 tff(1306,plain,((~((~(mult(mult(b, c), mult(mult(a, b), a)) = mult(mult(b, c), mult(a, mult(a, b))))) | (~(mult(mult(mult(b, c), mult(a, b)), a) = mult(mult(mult(b, c), a), mult(a, b)))))) | (mult(mult(mult(b, c), a), mult(a, b)) = mult(mult(b, c), mult(a, mult(a, b))))), inference(lemma,lemma(discharge,[]))).
% 21.87/22.03 tff(1307,plain,
% 21.87/22.03 (~((~(mult(mult(b, c), mult(mult(a, b), a)) = mult(mult(b, c), mult(a, mult(a, b))))) | (~(mult(mult(mult(b, c), mult(a, b)), a) = mult(mult(mult(b, c), a), mult(a, b)))))),
% 21.87/22.04 inference(unit_resolution,[status(thm)],[1306, 1291])).
% 21.87/22.04 tff(1308,plain,
% 21.87/22.04 (((~(mult(mult(b, c), mult(mult(a, b), a)) = mult(mult(b, c), mult(a, mult(a, b))))) | (~(mult(mult(mult(b, c), mult(a, b)), a) = mult(mult(mult(b, c), a), mult(a, b))))) | (mult(mult(b, c), mult(mult(a, b), a)) = mult(mult(b, c), mult(a, mult(a, b))))),
% 21.87/22.04 inference(tautology,[status(thm)],[])).
% 21.87/22.04 tff(1309,plain,
% 21.87/22.04 (mult(mult(b, c), mult(mult(a, b), a)) = mult(mult(b, c), mult(a, mult(a, b)))),
% 21.87/22.04 inference(unit_resolution,[status(thm)],[1308, 1307])).
% 21.87/22.04 tff(1310,assumption,(mult(mult(mult(mult(b, c), a), b), a) = mult(mult(b, c), mult(mult(a, b), a))), introduced(assumption)).
% 21.87/22.04 tff(1311,assumption,(mult(mult(mult(b, c), a), b) = mult(mult(b, c), mult(a, b))), introduced(assumption)).
% 21.87/22.04 tff(1312,plain,
% 21.87/22.04 (mult(mult(b, c), mult(a, b)) = mult(mult(mult(b, c), a), b)),
% 21.87/22.04 inference(symmetry,[status(thm)],[1311])).
% 21.87/22.04 tff(1313,plain,
% 21.87/22.04 (mult(mult(mult(b, c), mult(a, b)), a) = mult(mult(mult(mult(b, c), a), b), a)),
% 21.87/22.04 inference(monotonicity,[status(thm)],[1312])).
% 21.87/22.04 tff(1314,plain,
% 21.87/22.04 (((~(mult(mult(b, c), mult(mult(a, b), a)) = mult(mult(b, c), mult(a, mult(a, b))))) | (~(mult(mult(mult(b, c), mult(a, b)), a) = mult(mult(mult(b, c), a), mult(a, b))))) | (mult(mult(mult(b, c), mult(a, b)), a) = mult(mult(mult(b, c), a), mult(a, b)))),
% 21.87/22.04 inference(tautology,[status(thm)],[])).
% 21.87/22.04 tff(1315,plain,
% 21.87/22.04 (mult(mult(mult(b, c), mult(a, b)), a) = mult(mult(mult(b, c), a), mult(a, b))),
% 21.87/22.04 inference(unit_resolution,[status(thm)],[1314, 1307])).
% 21.87/22.04 tff(1316,plain,
% 21.87/22.04 (mult(mult(mult(b, c), a), mult(a, b)) = mult(mult(mult(b, c), mult(a, b)), a)),
% 21.87/22.04 inference(symmetry,[status(thm)],[1315])).
% 21.87/22.04 tff(1317,plain,
% 21.87/22.04 (mult(mult(mult(b, c), a), mult(a, b)) = mult(mult(b, c), mult(a, mult(a, b)))),
% 21.87/22.04 inference(transitivity,[status(thm)],[1316, 1313, 1310, 1309])).
% 21.87/22.04 tff(1318,plain,
% 21.87/22.04 ($false),
% 21.87/22.04 inference(unit_resolution,[status(thm)],[1291, 1317])).
% 21.87/22.04 tff(1319,plain,((~(mult(mult(mult(mult(b, c), a), b), a) = mult(mult(b, c), mult(mult(a, b), a)))) | (mult(mult(mult(b, c), a), mult(a, b)) = mult(mult(b, c), mult(a, mult(a, b)))) | (~(mult(mult(mult(b, c), a), b) = mult(mult(b, c), mult(a, b))))), inference(lemma,lemma(discharge,[]))).
% 21.87/22.04 tff(1320,plain,
% 21.87/22.04 ((mult(mult(mult(b, c), a), mult(a, b)) = mult(mult(b, c), mult(a, mult(a, b)))) | (~(mult(mult(mult(b, c), a), b) = mult(mult(b, c), mult(a, b))))),
% 21.87/22.04 inference(unit_resolution,[status(thm)],[1319, 1295])).
% 21.87/22.04 tff(1321,plain,
% 21.87/22.04 (~(mult(mult(mult(b, c), a), b) = mult(mult(b, c), mult(a, b)))),
% 21.87/22.04 inference(unit_resolution,[status(thm)],[1320, 1291])).
% 21.87/22.04 tff(1322,plain,
% 21.87/22.04 ((~(mult(mult(mult(b, c), a), b) = mult(mult(b, c), mult(a, b)))) | (~(mult(mult(mult(b, c), b), a) = mult(mult(b, c), mult(b, a))))),
% 21.87/22.04 inference(unit_resolution,[status(thm)],[1229, 1321])).
% 21.87/22.04 tff(1323,plain,
% 21.87/22.04 (~((~(mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a))) | (~(mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a)))))),
% 21.87/22.04 inference(unit_resolution,[status(thm)],[1205, 1322])).
% 21.87/22.04 tff(1324,plain,
% 21.87/22.04 (mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a))),
% 21.87/22.04 inference(unit_resolution,[status(thm)],[1194, 1323])).
% 21.87/22.04 tff(1325,plain,
% 21.87/22.04 (mult(mult(b, c), mult(b, a)) = mult(mult(b, c), mult(a, b))),
% 21.87/22.04 inference(symmetry,[status(thm)],[1324])).
% 21.87/22.04 tff(1326,plain,
% 21.87/22.04 (ld(mult(b, c), mult(mult(b, c), mult(b, a))) = ld(mult(b, c), mult(mult(b, c), mult(a, b)))),
% 21.87/22.04 inference(monotonicity,[status(thm)],[1325])).
% 21.87/22.04 tff(1327,plain,
% 21.87/22.04 (ld(mult(b, c), mult(mult(b, c), mult(a, b))) = ld(mult(b, c), mult(mult(b, c), mult(b, a)))),
% 21.87/22.04 inference(symmetry,[status(thm)],[1326])).
% 21.87/22.04 tff(1328,plain,
% 21.87/22.04 (mult(a, b) = mult(b, a)),
% 21.87/22.04 inference(transitivity,[status(thm)],[1186, 1327, 1179])).
% 21.87/22.04 tff(1329,plain,
% 21.87/22.04 (mult(b, mult(a, b)) = mult(b, mult(b, a))),
% 21.87/22.04 inference(monotonicity,[status(thm)],[1328])).
% 21.87/22.04 tff(1330,plain,
% 21.87/22.04 (mult(b, mult(b, a)) = mult(b, mult(a, b))),
% 21.87/22.04 inference(symmetry,[status(thm)],[1329])).
% 21.87/22.04 tff(1331,plain,
% 21.87/22.04 ((mult(mult(b, a), c) = mult(mult(b, c), a)) <=> (mult(mult(b, c), a) = mult(mult(b, a), c))),
% 21.87/22.04 inference(commutativity,[status(thm)],[])).
% 21.87/22.04 tff(1332,plain,
% 21.87/22.04 (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(mult(b, c), a)),
% 21.87/22.04 inference(monotonicity,[status(thm)],[137])).
% 21.87/22.04 tff(1333,plain,
% 21.87/22.04 ((mult(mult(a, a), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), a)) <=> (mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(mult(a, a), rd(mult(b, c), mult(a, c))))),
% 21.87/22.04 inference(commutativity,[status(thm)],[])).
% 21.87/22.04 tff(1334,plain,
% 21.87/22.04 (mult(a, mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, rd(mult(b, c), mult(a, c))), a)),
% 21.87/22.04 inference(symmetry,[status(thm)],[1287])).
% 21.87/22.04 tff(1335,assumption,(~(mult(mult(a, a), rd(mult(b, c), mult(a, c))) = mult(a, mult(a, rd(mult(b, c), mult(a, c)))))), introduced(assumption)).
% 21.87/22.04 tff(1336,plain,
% 21.87/22.04 (((~(mult(mult(a, a), rd(mult(b, c), mult(a, c))) = mult(a, mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a))))) | (mult(mult(a, a), rd(mult(b, c), mult(a, c))) = mult(a, mult(a, rd(mult(b, c), mult(a, c)))))),
% 21.87/22.04 inference(tautology,[status(thm)],[])).
% 21.87/22.04 tff(1337,plain,
% 21.87/22.04 ((~(mult(mult(a, a), rd(mult(b, c), mult(a, c))) = mult(a, mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a))))),
% 21.87/22.04 inference(unit_resolution,[status(thm)],[1336, 1335])).
% 21.87/22.04 tff(1338,plain,
% 21.87/22.04 (~((~(mult(mult(a, a), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), a))) | (~(mult(a, mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), a)))))),
% 21.87/22.04 inference(unit_resolution,[status(thm)],[907, 1337])).
% 21.87/22.04 tff(1339,plain,
% 21.87/22.04 (mult(a, mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), a))),
% 21.87/22.04 inference(unit_resolution,[status(thm)],[909, 1338])).
% 21.87/22.04 tff(1340,plain,
% 21.87/22.04 (mult(a, mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, rd(mult(b, c), mult(a, c))), a)),
% 21.87/22.04 inference(transitivity,[status(thm)],[1339, 1334])).
% 21.87/22.04 tff(1341,plain,
% 21.87/22.04 ((mult(mult(a, a), rd(mult(b, c), mult(a, c))) = mult(a, mult(a, rd(mult(b, c), mult(a, c))))) <=> (mult(mult(a, a), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), a))),
% 21.87/22.04 inference(monotonicity,[status(thm)],[1340])).
% 21.87/22.04 tff(1342,plain,
% 21.87/22.04 ((mult(mult(a, a), rd(mult(b, c), mult(a, c))) = mult(a, mult(a, rd(mult(b, c), mult(a, c))))) <=> (mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(mult(a, a), rd(mult(b, c), mult(a, c))))),
% 21.87/22.04 inference(transitivity,[status(thm)],[1341, 1333])).
% 21.87/22.04 tff(1343,plain,
% 21.87/22.04 ((mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(mult(a, a), rd(mult(b, c), mult(a, c)))) <=> (mult(mult(a, a), rd(mult(b, c), mult(a, c))) = mult(a, mult(a, rd(mult(b, c), mult(a, c)))))),
% 21.87/22.04 inference(symmetry,[status(thm)],[1342])).
% 21.87/22.04 tff(1344,plain,
% 21.87/22.04 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, a), rd(mult(b, c), mult(a, c))) = mult(a, mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a)))))) | (~((~(mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(mult(a, a), rd(mult(b, c), mult(a, c))))) | (~(mult(a, mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, a), rd(mult(b, c), mult(a, c))) = mult(a, mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a)))))) | (~((~(mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(mult(a, a), rd(mult(b, c), mult(a, c))))) | (~(mult(a, mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))))),
% 21.87/22.04 inference(rewrite,[status(thm)],[])).
% 21.87/22.04 tff(1345,plain,
% 21.87/22.04 (((~((~(mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(mult(a, a), rd(mult(b, c), mult(a, c))))) | (~(mult(a, mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(a, a), rd(mult(b, c), mult(a, c))) = mult(a, mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a))))))) <=> ((~((~(mult(mult(a, a), rd(mult(b, c), mult(a, c))) = mult(a, mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a)))))) | (~((~(mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(mult(a, a), rd(mult(b, c), mult(a, c))))) | (~(mult(a, mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))))),
% 21.87/22.04 inference(rewrite,[status(thm)],[])).
% 21.87/22.04 tff(1346,plain,
% 21.87/22.04 ((~((~(mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(a, a), rd(mult(b, c), mult(a, c))) = mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))) <=> (~((~(mult(mult(a, a), rd(mult(b, c), mult(a, c))) = mult(a, mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a))))))),
% 21.87/22.04 inference(rewrite,[status(thm)],[])).
% 21.87/22.04 tff(1347,plain,
% 21.87/22.04 ((~((~(mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(mult(a, a), rd(mult(b, c), mult(a, c))))) | (~(mult(a, mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))) <=> (~((~(mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(mult(a, a), rd(mult(b, c), mult(a, c))))) | (~(mult(a, mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(a, rd(mult(b, c), mult(a, c))))))))),
% 21.87/22.04 inference(rewrite,[status(thm)],[])).
% 21.87/22.04 tff(1348,plain,
% 21.87/22.04 (((~((~(mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(mult(a, a), rd(mult(b, c), mult(a, c))))) | (~(mult(a, mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(a, a), rd(mult(b, c), mult(a, c))) = mult(a, mult(a, rd(mult(b, c), mult(a, c))))))))) <=> ((~((~(mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(mult(a, a), rd(mult(b, c), mult(a, c))))) | (~(mult(a, mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(a, a), rd(mult(b, c), mult(a, c))) = mult(a, mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a)))))))),
% 21.87/22.04 inference(monotonicity,[status(thm)],[1347, 1346])).
% 21.87/22.04 tff(1349,plain,
% 21.87/22.04 (((~((~(mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(mult(a, a), rd(mult(b, c), mult(a, c))))) | (~(mult(a, mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(a, a), rd(mult(b, c), mult(a, c))) = mult(a, mult(a, rd(mult(b, c), mult(a, c))))))))) <=> ((~((~(mult(mult(a, a), rd(mult(b, c), mult(a, c))) = mult(a, mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a)))))) | (~((~(mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(mult(a, a), rd(mult(b, c), mult(a, c))))) | (~(mult(a, mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))))),
% 21.87/22.04 inference(transitivity,[status(thm)],[1348, 1345])).
% 21.87/22.04 tff(1350,plain,
% 21.87/22.04 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(mult(a, a), rd(mult(b, c), mult(a, c))))) | (~(mult(a, mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(a, a), rd(mult(b, c), mult(a, c))) = mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, a), rd(mult(b, c), mult(a, c))) = mult(a, mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a)))))) | (~((~(mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(mult(a, a), rd(mult(b, c), mult(a, c))))) | (~(mult(a, mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(a, rd(mult(b, c), mult(a, c))))))))))),
% 21.87/22.04 inference(monotonicity,[status(thm)],[1349])).
% 21.87/22.04 tff(1351,plain,
% 21.87/22.04 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(mult(a, a), rd(mult(b, c), mult(a, c))))) | (~(mult(a, mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(a, a), rd(mult(b, c), mult(a, c))) = mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, a), rd(mult(b, c), mult(a, c))) = mult(a, mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a)))))) | (~((~(mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(mult(a, a), rd(mult(b, c), mult(a, c))))) | (~(mult(a, mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))))),
% 21.87/22.04 inference(transitivity,[status(thm)],[1350, 1344])).
% 21.87/22.04 tff(1352,plain,
% 21.87/22.04 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(mult(a, a), rd(mult(b, c), mult(a, c))))) | (~(mult(a, mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(a, a), rd(mult(b, c), mult(a, c))) = mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))))),
% 21.87/22.04 inference(quant_inst,[status(thm)],[])).
% 21.87/22.04 tff(1353,plain,
% 21.87/22.04 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, a), rd(mult(b, c), mult(a, c))) = mult(a, mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a)))))) | (~((~(mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(mult(a, a), rd(mult(b, c), mult(a, c))))) | (~(mult(a, mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(a, rd(mult(b, c), mult(a, c))))))))),
% 21.87/22.04 inference(modus_ponens,[status(thm)],[1352, 1351])).
% 21.87/22.05 tff(1354,plain,
% 21.87/22.05 ((~((~(mult(mult(a, a), rd(mult(b, c), mult(a, c))) = mult(a, mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a)))))) | (~((~(mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(mult(a, a), rd(mult(b, c), mult(a, c))))) | (~(mult(a, mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(a, rd(mult(b, c), mult(a, c))))))))),
% 21.87/22.05 inference(unit_resolution,[status(thm)],[1353, 27])).
% 21.87/22.05 tff(1355,plain,
% 21.87/22.05 (~((~(mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(mult(a, a), rd(mult(b, c), mult(a, c))))) | (~(mult(a, mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))),
% 21.87/22.05 inference(unit_resolution,[status(thm)],[1354, 1337])).
% 21.87/22.05 tff(1356,plain,
% 21.87/22.05 (((~(mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(mult(a, a), rd(mult(b, c), mult(a, c))))) | (~(mult(a, mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) | (mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(mult(a, a), rd(mult(b, c), mult(a, c))))),
% 21.87/22.05 inference(tautology,[status(thm)],[])).
% 21.87/22.05 tff(1357,plain,
% 21.87/22.05 (mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(mult(a, a), rd(mult(b, c), mult(a, c)))),
% 21.87/22.05 inference(unit_resolution,[status(thm)],[1356, 1355])).
% 21.87/22.05 tff(1358,plain,
% 21.87/22.05 (mult(mult(a, a), rd(mult(b, c), mult(a, c))) = mult(a, mult(a, rd(mult(b, c), mult(a, c))))),
% 21.87/22.05 inference(modus_ponens,[status(thm)],[1357, 1343])).
% 21.87/22.05 tff(1359,plain,
% 21.87/22.05 ($false),
% 21.87/22.05 inference(unit_resolution,[status(thm)],[1335, 1358])).
% 21.87/22.05 tff(1360,plain,((mult(mult(a, a), rd(mult(b, c), mult(a, c))) = mult(a, mult(a, rd(mult(b, c), mult(a, c))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a))))), inference(lemma,lemma(discharge,[]))).
% 21.87/22.05 tff(1361,plain,
% 21.87/22.05 (mult(mult(a, a), rd(mult(b, c), mult(a, c))) = mult(a, mult(a, rd(mult(b, c), mult(a, c))))),
% 21.87/22.05 inference(unit_resolution,[status(thm)],[1360, 1287])).
% 21.87/22.05 tff(1362,assumption,(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))), introduced(assumption)).
% 21.87/22.05 tff(1363,plain,
% 21.87/22.05 (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))),
% 21.87/22.05 inference(transitivity,[status(thm)],[1332, 1172, 1362])).
% 21.87/22.05 tff(1364,assumption,(~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))), introduced(assumption)).
% 21.87/22.05 tff(1365,plain,
% 21.87/22.05 ($false),
% 21.87/22.05 inference(unit_resolution,[status(thm)],[1364, 1363])).
% 21.87/22.05 tff(1366,plain,((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) | (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit)))))), inference(lemma,lemma(discharge,[]))).
% 21.87/22.05 tff(1367,plain,
% 21.87/22.05 ((mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit)))))),
% 21.87/22.05 inference(unit_resolution,[status(thm)],[1366, 1168])).
% 21.87/22.05 tff(1368,plain,
% 21.87/22.05 (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))),
% 21.87/22.05 inference(unit_resolution,[status(thm)],[1367, 97])).
% 21.87/22.05 tff(1369,plain,
% 21.87/22.05 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(b, c), a), a) = mult(b, c))),
% 21.87/22.05 inference(quant_inst,[status(thm)],[])).
% 21.87/22.05 tff(1370,plain,
% 21.87/22.05 (rd(mult(mult(b, c), a), a) = mult(b, c)),
% 21.87/22.05 inference(unit_resolution,[status(thm)],[1369, 168])).
% 21.87/22.05 tff(1371,assumption,(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))), introduced(assumption)).
% 21.87/22.05 tff(1372,plain,
% 21.87/22.05 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a)),
% 21.87/22.05 inference(symmetry,[status(thm)],[1371])).
% 21.87/22.05 tff(1373,plain,
% 21.87/22.05 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a) = mult(mult(b, c), a)),
% 21.87/22.05 inference(transitivity,[status(thm)],[1168, 1372, 1332])).
% 21.87/22.05 tff(1374,plain,
% 21.87/22.05 (rd(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a), a) = rd(mult(mult(b, c), a), a)),
% 21.87/22.05 inference(monotonicity,[status(thm)],[1373])).
% 21.87/22.05 tff(1375,plain,
% 21.87/22.05 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), c))),
% 21.87/22.05 inference(quant_inst,[status(thm)],[])).
% 21.87/22.05 tff(1376,plain,
% 21.87/22.05 (rd(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), c)),
% 21.87/22.05 inference(unit_resolution,[status(thm)],[1375, 168])).
% 21.87/22.05 tff(1377,plain,
% 21.87/22.05 (mult(mult(rd(mult(b, c), mult(a, c)), a), c) = rd(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a), a)),
% 21.87/22.05 inference(symmetry,[status(thm)],[1376])).
% 21.87/22.05 tff(1378,plain,
% 21.87/22.05 (mult(mult(rd(mult(b, c), mult(a, c)), a), c) = mult(b, c)),
% 21.87/22.05 inference(transitivity,[status(thm)],[1377, 1374, 1370])).
% 21.87/22.05 tff(1379,plain,
% 21.87/22.05 (rd(mult(mult(rd(mult(b, c), mult(a, c)), a), c), c) = rd(mult(b, c), c)),
% 21.87/22.05 inference(monotonicity,[status(thm)],[1378])).
% 21.87/22.05 tff(1380,plain,
% 21.87/22.05 (mult(rd(mult(b, c), mult(a, c)), a) = b),
% 21.87/22.05 inference(transitivity,[status(thm)],[175, 1379, 170])).
% 21.87/22.05 tff(1381,plain,
% 21.87/22.05 (mult(a, mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, b)),
% 21.87/22.05 inference(monotonicity,[status(thm)],[1380])).
% 21.87/22.05 tff(1382,plain,
% 21.87/22.05 (mult(a, b) = mult(a, mult(rd(mult(b, c), mult(a, c)), a))),
% 21.87/22.05 inference(symmetry,[status(thm)],[1381])).
% 21.87/22.05 tff(1383,plain,
% 21.87/22.05 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(a, b), a), a) = mult(a, b))),
% 21.87/22.05 inference(quant_inst,[status(thm)],[])).
% 21.87/22.05 tff(1384,plain,
% 21.87/22.05 (rd(mult(mult(a, b), a), a) = mult(a, b)),
% 21.87/22.05 inference(unit_resolution,[status(thm)],[1383, 168])).
% 21.87/22.05 tff(1385,plain,
% 21.87/22.05 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(b, c), mult(mult(b, c), mult(mult(a, b), a))) = mult(mult(a, b), a))),
% 21.87/22.05 inference(quant_inst,[status(thm)],[])).
% 21.87/22.05 tff(1386,plain,
% 21.87/22.05 (ld(mult(b, c), mult(mult(b, c), mult(mult(a, b), a))) = mult(mult(a, b), a)),
% 21.87/22.05 inference(unit_resolution,[status(thm)],[1385, 7])).
% 21.87/22.05 tff(1387,plain,
% 21.87/22.05 ((~((~(mult(mult(b, c), mult(mult(a, b), a)) = mult(mult(b, c), mult(a, mult(a, b))))) | (~(mult(mult(mult(b, c), mult(a, b)), a) = mult(mult(mult(b, c), a), mult(a, b)))))) | (~((~(mult(mult(mult(b, c), mult(a, b)), a) = mult(mult(b, c), mult(mult(a, b), a)))) | (~(mult(mult(mult(b, c), a), mult(a, b)) = mult(mult(b, c), mult(a, mult(a, b)))))))),
% 21.87/22.05 inference(unit_resolution,[status(thm)],[1304, 27])).
% 21.87/22.05 tff(1388,plain,
% 21.87/22.05 (~((~(mult(mult(b, c), mult(mult(a, b), a)) = mult(mult(b, c), mult(a, mult(a, b))))) | (~(mult(mult(mult(b, c), mult(a, b)), a) = mult(mult(mult(b, c), a), mult(a, b)))))),
% 21.87/22.05 inference(unit_resolution,[status(thm)],[1387, 1297])).
% 21.87/22.05 tff(1389,plain,
% 21.87/22.05 (mult(mult(b, c), mult(mult(a, b), a)) = mult(mult(b, c), mult(a, mult(a, b)))),
% 21.87/22.05 inference(unit_resolution,[status(thm)],[1308, 1388])).
% 21.87/22.05 tff(1390,plain,
% 21.87/22.05 (mult(mult(b, c), mult(a, mult(a, b))) = mult(mult(b, c), mult(mult(a, b), a))),
% 21.87/22.05 inference(symmetry,[status(thm)],[1389])).
% 21.87/22.05 tff(1391,assumption,(mult(mult(a, a), rd(mult(b, c), mult(a, c))) = mult(a, mult(a, rd(mult(b, c), mult(a, c))))), introduced(assumption)).
% 21.87/22.05 tff(1392,plain,
% 21.87/22.05 (mult(mult(mult(a, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), a)),
% 21.87/22.05 inference(monotonicity,[status(thm)],[1391])).
% 21.87/22.05 tff(1393,plain,
% 21.87/22.05 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(a, a), rd(mult(b, c), mult(a, c))), a) = mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), a)))),
% 21.87/22.05 inference(quant_inst,[status(thm)],[])).
% 21.87/22.05 tff(1394,plain,
% 21.87/22.05 (mult(mult(mult(a, a), rd(mult(b, c), mult(a, c))), a) = mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), a))),
% 21.87/22.05 inference(unit_resolution,[status(thm)],[1393, 56])).
% 21.87/22.05 tff(1395,plain,
% 21.87/22.05 (mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), a)) = mult(mult(mult(a, a), rd(mult(b, c), mult(a, c))), a)),
% 21.87/22.05 inference(symmetry,[status(thm)],[1394])).
% 21.87/22.05 tff(1396,plain,
% 21.87/22.05 (mult(a, b) = mult(mult(a, rd(mult(b, c), mult(a, c))), a)),
% 21.87/22.05 inference(transitivity,[status(thm)],[1382, 1334])).
% 21.87/22.05 tff(1397,plain,
% 21.87/22.05 (mult(a, mult(a, b)) = mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), a))),
% 21.87/22.05 inference(monotonicity,[status(thm)],[1396])).
% 21.87/22.05 tff(1398,plain,
% 21.87/22.05 (mult(a, mult(a, b)) = mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), a)),
% 21.87/22.05 inference(transitivity,[status(thm)],[1397, 1395, 1392])).
% 21.87/22.05 tff(1399,plain,
% 21.87/22.05 (mult(b, c) = mult(c, b)),
% 21.87/22.05 inference(transitivity,[status(thm)],[843, 842, 239])).
% 21.87/22.05 tff(1400,plain,
% 21.87/22.05 (mult(mult(b, c), mult(a, mult(a, b))) = mult(mult(c, b), mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), a))),
% 21.87/22.05 inference(monotonicity,[status(thm)],[1399, 1398])).
% 21.87/22.05 tff(1401,plain,
% 21.87/22.05 (mult(mult(c, b), mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), a)) = mult(mult(b, c), mult(a, mult(a, b)))),
% 21.87/22.05 inference(symmetry,[status(thm)],[1400])).
% 21.87/22.05 tff(1402,plain,
% 21.87/22.05 (mult(mult(c, b), mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), a)) = mult(mult(b, c), mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), a))),
% 21.87/22.05 inference(monotonicity,[status(thm)],[241])).
% 21.87/22.05 tff(1403,plain,
% 21.87/22.05 (mult(mult(b, c), mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), a)) = mult(mult(c, b), mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), a))),
% 21.87/22.05 inference(symmetry,[status(thm)],[1402])).
% 21.87/22.05 tff(1404,plain,
% 21.87/22.05 (mult(mult(b, c), mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), a)) = mult(mult(b, c), mult(mult(a, b), a))),
% 21.87/22.05 inference(transitivity,[status(thm)],[1403, 1401, 1390])).
% 21.87/22.05 tff(1405,plain,
% 21.87/22.05 (ld(mult(b, c), mult(mult(b, c), mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), a))) = ld(mult(b, c), mult(mult(b, c), mult(mult(a, b), a)))),
% 21.87/22.05 inference(monotonicity,[status(thm)],[1404])).
% 21.87/22.05 tff(1406,plain,
% 21.87/22.05 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(b, c), mult(mult(b, c), mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), a))) = mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), a))),
% 21.87/22.05 inference(quant_inst,[status(thm)],[])).
% 21.87/22.05 tff(1407,plain,
% 21.87/22.05 (ld(mult(b, c), mult(mult(b, c), mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), a))) = mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), a)),
% 21.87/22.05 inference(unit_resolution,[status(thm)],[1406, 7])).
% 21.87/22.05 tff(1408,plain,
% 21.87/22.05 (mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), a) = ld(mult(b, c), mult(mult(b, c), mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), a)))),
% 21.87/22.05 inference(symmetry,[status(thm)],[1407])).
% 21.87/22.05 tff(1409,plain,
% 21.87/22.05 (mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, b), a)),
% 21.87/22.05 inference(transitivity,[status(thm)],[1408, 1405, 1386])).
% 21.87/22.05 tff(1410,plain,
% 21.87/22.05 (rd(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), a), a) = rd(mult(mult(a, b), a), a)),
% 21.87/22.05 inference(monotonicity,[status(thm)],[1409])).
% 21.87/22.05 tff(1411,plain,
% 21.87/22.05 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), a), a) = mult(a, mult(a, rd(mult(b, c), mult(a, c)))))),
% 21.87/22.05 inference(quant_inst,[status(thm)],[])).
% 21.87/22.05 tff(1412,plain,
% 21.87/22.05 (rd(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), a), a) = mult(a, mult(a, rd(mult(b, c), mult(a, c))))),
% 21.87/22.05 inference(unit_resolution,[status(thm)],[1411, 168])).
% 21.87/22.05 tff(1413,plain,
% 21.87/22.05 (mult(a, mult(a, rd(mult(b, c), mult(a, c)))) = rd(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), a), a)),
% 21.87/22.05 inference(symmetry,[status(thm)],[1412])).
% 21.87/22.05 tff(1414,plain,
% 21.87/22.05 (mult(a, mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), a))),
% 21.87/22.05 inference(transitivity,[status(thm)],[1413, 1410, 1384, 1382])).
% 21.87/22.05 tff(1415,assumption,(~(mult(a, mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), a)))), introduced(assumption)).
% 21.87/22.05 tff(1416,plain,
% 21.87/22.05 ($false),
% 21.87/22.05 inference(unit_resolution,[status(thm)],[1415, 1414])).
% 21.87/22.05 tff(1417,plain,((mult(mult(mult(b, c), a), mult(a, b)) = mult(mult(b, c), mult(a, mult(a, b)))) | (mult(a, mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), a))) | (~(mult(mult(a, a), rd(mult(b, c), mult(a, c))) = mult(a, mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))), inference(lemma,lemma(discharge,[]))).
% 21.87/22.05 tff(1418,plain,
% 21.87/22.05 (mult(a, mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), a))),
% 21.87/22.05 inference(unit_resolution,[status(thm)],[1417, 1291, 1368, 1287, 1361])).
% 21.87/22.05 tff(1419,plain,
% 21.87/22.05 (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))),
% 21.87/22.05 inference(unit_resolution,[status(thm)],[924, 1418, 97])).
% 21.87/22.05 tff(1420,plain,
% 21.87/22.05 (~(mult(b, mult(c, a)) = mult(b, mult(a, c)))),
% 21.87/22.05 inference(unit_resolution,[status(thm)],[377, 1419, 354, 97])).
% 21.87/22.05 tff(1421,plain,
% 21.87/22.05 ((~(mult(mult(b, c), a) = mult(mult(b, a), c))) | (~(mult(b, mult(c, a)) = mult(b, mult(a, c))))),
% 21.87/22.05 inference(unit_resolution,[status(thm)],[379, 1420])).
% 21.87/22.05 tff(1422,plain,
% 21.87/22.05 (~((~(mult(mult(b, c), a) = mult(b, mult(c, a)))) | (~(mult(mult(b, a), c) = mult(b, mult(a, c)))))),
% 21.87/22.05 inference(unit_resolution,[status(thm)],[384, 1421])).
% 21.87/22.05 tff(1423,plain,
% 21.87/22.05 (mult(mult(b, a), c) = mult(b, mult(a, c))),
% 21.87/22.05 inference(unit_resolution,[status(thm)],[386, 1422])).
% 21.87/22.05 tff(1424,plain,
% 21.87/22.05 (mult(b, mult(a, c)) = mult(mult(b, a), c)),
% 21.87/22.05 inference(symmetry,[status(thm)],[1423])).
% 21.87/22.05 tff(1425,plain,
% 21.87/22.05 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(b, mult(a, c))),
% 21.87/22.05 inference(monotonicity,[status(thm)],[176])).
% 21.87/22.05 tff(1426,plain,
% 21.87/22.05 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(b, a), c)),
% 21.87/22.05 inference(transitivity,[status(thm)],[1425, 1424])).
% 21.87/22.05 tff(1427,plain,
% 21.87/22.05 ((mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a)) <=> (mult(mult(b, a), c) = mult(mult(b, c), a))),
% 21.87/22.05 inference(monotonicity,[status(thm)],[1426, 1332])).
% 21.87/22.05 tff(1428,plain,
% 21.87/22.05 ((mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a)) <=> (mult(mult(b, c), a) = mult(mult(b, a), c))),
% 21.87/22.05 inference(transitivity,[status(thm)],[1427, 1331])).
% 21.87/22.05 tff(1429,plain,
% 21.87/22.05 ((mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c))) <=> (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a))),
% 21.87/22.05 inference(commutativity,[status(thm)],[])).
% 21.87/22.05 tff(1430,plain,
% 21.87/22.05 (mult(b, mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c))),
% 21.87/22.05 inference(symmetry,[status(thm)],[1425])).
% 21.87/22.05 tff(1431,plain,
% 21.87/22.05 (mult(mult(b, c), a) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a)),
% 21.87/22.05 inference(symmetry,[status(thm)],[1332])).
% 21.87/22.05 tff(1432,plain,
% 21.87/22.05 (((~(mult(mult(b, c), a) = mult(b, mult(c, a)))) | (~(mult(mult(b, a), c) = mult(b, mult(a, c))))) | (mult(mult(b, c), a) = mult(b, mult(c, a)))),
% 21.87/22.05 inference(tautology,[status(thm)],[])).
% 21.87/22.05 tff(1433,plain,
% 21.87/22.05 (mult(mult(b, c), a) = mult(b, mult(c, a))),
% 21.87/22.05 inference(unit_resolution,[status(thm)],[1432, 1422])).
% 21.87/22.05 tff(1434,plain,
% 21.87/22.05 (mult(b, mult(c, a)) = mult(mult(b, c), a)),
% 21.87/22.05 inference(symmetry,[status(thm)],[1433])).
% 21.87/22.05 tff(1435,plain,
% 21.87/22.05 (mult(b, mult(c, a)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a)),
% 21.87/22.05 inference(transitivity,[status(thm)],[1434, 1431])).
% 21.87/22.05 tff(1436,plain,
% 21.87/22.05 ((mult(b, mult(c, a)) = mult(b, mult(a, c))) <=> (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)))),
% 21.87/22.05 inference(monotonicity,[status(thm)],[1435, 1430])).
% 21.87/22.05 tff(1437,plain,
% 21.87/22.05 ((mult(b, mult(c, a)) = mult(b, mult(a, c))) <=> (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a))),
% 21.87/22.05 inference(transitivity,[status(thm)],[1436, 1429])).
% 21.87/22.05 tff(1438,plain,
% 21.87/22.05 ((mult(b, mult(c, a)) = mult(b, mult(a, c))) <=> (mult(mult(b, c), a) = mult(mult(b, a), c))),
% 21.87/22.06 inference(transitivity,[status(thm)],[1437, 1428])).
% 21.87/22.06 tff(1439,plain,
% 21.87/22.06 ((~(mult(b, mult(c, a)) = mult(b, mult(a, c)))) <=> (~(mult(mult(b, c), a) = mult(mult(b, a), c)))),
% 21.87/22.06 inference(monotonicity,[status(thm)],[1438])).
% 21.87/22.06 tff(1440,plain,
% 21.87/22.06 (~(mult(mult(b, c), a) = mult(mult(b, a), c))),
% 21.87/22.06 inference(modus_ponens,[status(thm)],[1420, 1439])).
% 21.87/22.06 tff(1441,plain,
% 21.87/22.06 (mult(a, b) = mult(c, ld(c, mult(a, b)))),
% 21.87/22.06 inference(symmetry,[status(thm)],[204])).
% 21.87/22.06 tff(1442,plain,
% 21.87/22.06 (mult(c, mult(a, b)) = mult(c, mult(c, ld(c, mult(a, b))))),
% 21.87/22.06 inference(monotonicity,[status(thm)],[1441])).
% 21.87/22.06 tff(1443,plain,
% 21.87/22.06 (mult(c, mult(c, ld(c, mult(a, b)))) = mult(c, mult(a, b))),
% 21.87/22.06 inference(symmetry,[status(thm)],[1442])).
% 21.87/22.06 tff(1444,plain,
% 21.87/22.06 (mult(b, a) = ld(mult(b, c), mult(mult(b, c), mult(b, a)))),
% 21.87/22.06 inference(symmetry,[status(thm)],[1179])).
% 21.87/22.06 tff(1445,plain,
% 21.87/22.06 (mult(b, a) = mult(c, ld(c, mult(a, b)))),
% 21.87/22.06 inference(transitivity,[status(thm)],[1444, 1326, 1185, 1441])).
% 21.87/22.06 tff(1446,plain,
% 21.87/22.06 (mult(c, mult(b, a)) = mult(c, mult(c, ld(c, mult(a, b))))),
% 21.87/22.06 inference(monotonicity,[status(thm)],[1445])).
% 21.87/22.06 tff(1447,plain,
% 21.87/22.06 (mult(c, mult(b, a)) = mult(c, mult(a, b))),
% 21.87/22.06 inference(transitivity,[status(thm)],[1446, 1443])).
% 21.87/22.06 tff(1448,plain,
% 21.87/22.06 (mult(b, a) = mult(a, b)),
% 21.87/22.06 inference(transitivity,[status(thm)],[1444, 1326, 1185])).
% 21.87/22.06 tff(1449,plain,
% 21.87/22.06 (mult(mult(b, a), c) = mult(mult(a, b), c)),
% 21.87/22.06 inference(monotonicity,[status(thm)],[1448])).
% 21.87/22.06 tff(1450,plain,
% 21.87/22.06 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(b, a), a) = b)),
% 21.87/22.06 inference(quant_inst,[status(thm)],[])).
% 21.87/22.06 tff(1451,plain,
% 21.87/22.06 (rd(mult(b, a), a) = b),
% 21.87/22.06 inference(unit_resolution,[status(thm)],[1450, 168])).
% 21.87/22.06 tff(1452,plain,
% 21.87/22.06 (mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(b, a)),
% 21.87/22.06 inference(transitivity,[status(thm)],[1287, 913, 1186, 1327, 1179])).
% 21.87/22.06 tff(1453,plain,
% 21.87/22.06 (rd(mult(mult(a, rd(mult(b, c), mult(a, c))), a), a) = rd(mult(b, a), a)),
% 21.87/22.06 inference(monotonicity,[status(thm)],[1452])).
% 21.87/22.06 tff(1454,plain,
% 21.87/22.06 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(a, rd(mult(b, c), mult(a, c))), a), a) = mult(a, rd(mult(b, c), mult(a, c))))),
% 21.87/22.06 inference(quant_inst,[status(thm)],[])).
% 21.87/22.06 tff(1455,plain,
% 21.87/22.06 (rd(mult(mult(a, rd(mult(b, c), mult(a, c))), a), a) = mult(a, rd(mult(b, c), mult(a, c)))),
% 21.87/22.06 inference(unit_resolution,[status(thm)],[1454, 168])).
% 21.87/22.06 tff(1456,plain,
% 21.87/22.06 (mult(a, rd(mult(b, c), mult(a, c))) = rd(mult(mult(a, rd(mult(b, c), mult(a, c))), a), a)),
% 21.87/22.06 inference(symmetry,[status(thm)],[1455])).
% 21.87/22.06 tff(1457,plain,
% 21.87/22.06 (mult(a, rd(mult(b, c), mult(a, c))) = b),
% 21.87/22.06 inference(transitivity,[status(thm)],[1456, 1453, 1451])).
% 21.87/22.06 tff(1458,plain,
% 21.87/22.06 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(b, mult(a, c))),
% 21.87/22.06 inference(monotonicity,[status(thm)],[1457])).
% 21.87/22.06 tff(1459,plain,
% 21.87/22.06 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, b), c)),
% 21.87/22.06 inference(transitivity,[status(thm)],[1458, 1424, 1449])).
% 21.87/22.06 tff(1460,plain,
% 21.87/22.06 ((mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))) <=> (mult(mult(a, b), c) = mult(a, mult(b, c)))),
% 21.87/22.06 inference(monotonicity,[status(thm)],[1459, 142])).
% 21.87/22.06 tff(1461,plain,
% 21.87/22.06 ((mult(mult(a, b), c) = mult(a, mult(b, c))) <=> (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))),
% 21.87/22.06 inference(symmetry,[status(thm)],[1460])).
% 21.87/22.06 tff(1462,plain,
% 21.87/22.06 ((~(mult(mult(a, b), c) = mult(a, mult(b, c)))) <=> (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))),
% 21.87/22.06 inference(monotonicity,[status(thm)],[1461])).
% 21.87/22.06 tff(1463,plain,
% 21.87/22.06 (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))),
% 21.87/22.06 inference(modus_ponens,[status(thm)],[146, 1462])).
% 21.87/22.06 tff(1464,plain,
% 21.87/22.06 ((~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))),
% 21.87/22.06 inference(unit_resolution,[status(thm)],[278, 1463])).
% 21.87/22.06 tff(1465,plain,
% 21.87/22.06 (~((~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))),
% 21.87/22.06 inference(unit_resolution,[status(thm)],[276, 1464])).
% 21.87/22.06 tff(1466,plain,
% 21.87/22.06 (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))),
% 21.87/22.06 inference(unit_resolution,[status(thm)],[271, 1465])).
% 21.87/22.06 tff(1467,plain,
% 21.87/22.06 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(c, mult(c, mult(a, b))) = mult(a, b))),
% 21.87/22.06 inference(quant_inst,[status(thm)],[])).
% 21.87/22.06 tff(1468,plain,
% 21.87/22.06 (ld(c, mult(c, mult(a, b))) = mult(a, b)),
% 21.87/22.06 inference(unit_resolution,[status(thm)],[1467, 7])).
% 21.87/22.06 tff(1469,assumption,(mult(c, mult(b, a)) = mult(c, mult(a, b))), introduced(assumption)).
% 21.87/22.06 tff(1470,plain,
% 21.87/22.06 (ld(c, mult(c, mult(b, a))) = ld(c, mult(c, mult(a, b)))),
% 21.87/22.06 inference(monotonicity,[status(thm)],[1469])).
% 21.87/22.06 tff(1471,plain,
% 21.87/22.06 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(c, mult(c, mult(b, a))) = mult(b, a))),
% 21.87/22.06 inference(quant_inst,[status(thm)],[])).
% 21.87/22.06 tff(1472,plain,
% 21.87/22.06 (ld(c, mult(c, mult(b, a))) = mult(b, a)),
% 21.87/22.06 inference(unit_resolution,[status(thm)],[1471, 7])).
% 21.87/22.06 tff(1473,plain,
% 21.87/22.06 (mult(b, a) = ld(c, mult(c, mult(b, a)))),
% 21.87/22.06 inference(symmetry,[status(thm)],[1472])).
% 21.87/22.06 tff(1474,plain,
% 21.87/22.06 (mult(b, a) = mult(a, b)),
% 21.87/22.06 inference(transitivity,[status(thm)],[1473, 1470, 1468])).
% 21.87/22.06 tff(1475,plain,
% 21.87/22.06 (mult(mult(b, a), c) = mult(mult(a, b), c)),
% 21.87/22.06 inference(monotonicity,[status(thm)],[1474])).
% 21.87/22.06 tff(1476,plain,
% 21.87/22.06 (mult(mult(a, b), c) = mult(mult(b, a), c)),
% 21.87/22.06 inference(symmetry,[status(thm)],[1475])).
% 21.87/22.06 tff(1477,plain,
% 21.87/22.06 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(mult(a, b), c), a), b), b) = mult(mult(mult(a, b), c), a))),
% 21.87/22.06 inference(quant_inst,[status(thm)],[])).
% 21.87/22.06 tff(1478,plain,
% 21.87/22.06 (rd(mult(mult(mult(mult(a, b), c), a), b), b) = mult(mult(mult(a, b), c), a)),
% 21.87/22.06 inference(unit_resolution,[status(thm)],[1477, 168])).
% 21.87/22.06 tff(1479,plain,
% 21.87/22.06 (mult(mult(b, a), b) = mult(mult(a, b), b)),
% 21.87/22.06 inference(monotonicity,[status(thm)],[1474])).
% 21.87/22.06 tff(1480,plain,
% 21.87/22.06 (mult(mult(a, c), mult(mult(b, a), b)) = mult(mult(a, c), mult(mult(a, b), b))),
% 21.87/22.06 inference(monotonicity,[status(thm)],[1479])).
% 21.87/22.06 tff(1481,plain,
% 21.87/22.06 (mult(mult(mult(mult(a, b), c), a), b) = mult(mult(mult(a, c), mult(a, b)), b)),
% 21.87/22.06 inference(transitivity,[status(thm)],[959, 956, 1480, 1091])).
% 21.87/22.06 tff(1482,plain,
% 21.87/22.06 (rd(mult(mult(mult(mult(a, b), c), a), b), b) = rd(mult(mult(mult(a, c), mult(a, b)), b), b)),
% 21.87/22.06 inference(monotonicity,[status(thm)],[1481])).
% 21.87/22.06 tff(1483,plain,
% 21.87/22.06 (rd(mult(mult(mult(a, c), mult(a, b)), b), b) = rd(mult(mult(mult(mult(a, b), c), a), b), b)),
% 21.87/22.06 inference(symmetry,[status(thm)],[1482])).
% 21.87/22.06 tff(1484,plain,
% 21.87/22.06 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(a, c), mult(a, b)), b), b) = mult(mult(a, c), mult(a, b)))),
% 21.87/22.06 inference(quant_inst,[status(thm)],[])).
% 21.87/22.06 tff(1485,plain,
% 21.87/22.06 (rd(mult(mult(mult(a, c), mult(a, b)), b), b) = mult(mult(a, c), mult(a, b))),
% 21.87/22.06 inference(unit_resolution,[status(thm)],[1484, 168])).
% 21.87/22.06 tff(1486,plain,
% 21.87/22.06 (mult(mult(a, c), mult(a, b)) = rd(mult(mult(mult(a, c), mult(a, b)), b), b)),
% 21.87/22.06 inference(symmetry,[status(thm)],[1485])).
% 21.87/22.06 tff(1487,plain,
% 21.87/22.06 (mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(b, a), c)),
% 21.87/22.06 inference(transitivity,[status(thm)],[177, 161, 1476])).
% 21.87/22.06 tff(1488,assumption,(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))), introduced(assumption)).
% 21.87/22.06 tff(1489,plain,
% 21.87/22.06 (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(b, c))),
% 21.87/22.06 inference(transitivity,[status(thm)],[1488, 142])).
% 21.87/22.06 tff(1490,plain,
% 21.87/22.06 (ld(a, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))) = ld(a, mult(a, mult(b, c)))),
% 21.87/22.06 inference(monotonicity,[status(thm)],[1489])).
% 21.87/22.06 tff(1491,plain,
% 21.87/22.06 (mult(mult(a, c), rd(mult(b, c), mult(a, c))) = mult(b, c)),
% 21.87/22.06 inference(transitivity,[status(thm)],[734, 1490, 141])).
% 21.87/22.06 tff(1492,plain,
% 21.87/22.06 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(b, c), a)),
% 21.87/22.06 inference(monotonicity,[status(thm)],[1491])).
% 21.87/22.06 tff(1493,plain,
% 21.87/22.06 ((mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))) <=> (mult(mult(b, c), a) = mult(mult(b, a), c))),
% 21.87/22.06 inference(monotonicity,[status(thm)],[1492, 1487])).
% 21.87/22.06 tff(1494,plain,
% 21.87/22.06 ((mult(mult(b, c), a) = mult(mult(b, a), c)) <=> (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))),
% 21.87/22.06 inference(symmetry,[status(thm)],[1493])).
% 21.87/22.06 tff(1495,plain,
% 21.87/22.06 ((~(mult(mult(b, c), a) = mult(mult(b, a), c))) <=> (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))))),
% 21.87/22.06 inference(monotonicity,[status(thm)],[1494])).
% 21.87/22.06 tff(1496,assumption,(~(mult(mult(b, c), a) = mult(mult(b, a), c))), introduced(assumption)).
% 21.87/22.06 tff(1497,plain,
% 21.87/22.06 (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))),
% 21.87/22.06 inference(modus_ponens,[status(thm)],[1496, 1495])).
% 21.87/22.06 tff(1498,plain,
% 21.87/22.06 ((~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))))),
% 21.87/22.06 inference(unit_resolution,[status(thm)],[333, 1497])).
% 21.87/22.06 tff(1499,plain,
% 21.87/22.06 (~((~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))) | (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))))),
% 21.87/22.06 inference(unit_resolution,[status(thm)],[1076, 1498])).
% 21.87/22.06 tff(1500,plain,
% 21.87/22.06 (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))),
% 21.87/22.06 inference(unit_resolution,[status(thm)],[331, 1499])).
% 21.87/22.06 tff(1501,plain,
% 21.87/22.06 (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), b)),
% 21.87/22.06 inference(transitivity,[status(thm)],[1500, 177])).
% 21.87/22.06 tff(1502,plain,
% 21.87/22.06 (ld(mult(a, c), mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = ld(mult(a, c), mult(mult(a, c), b))),
% 21.87/22.06 inference(monotonicity,[status(thm)],[1501])).
% 21.87/22.06 tff(1503,plain,
% 21.87/22.06 (mult(a, rd(mult(b, c), mult(a, c))) = b),
% 21.87/22.06 inference(transitivity,[status(thm)],[471, 1502, 364])).
% 21.87/22.06 tff(1504,plain,
% 21.87/22.06 (mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(b, a)),
% 21.87/22.06 inference(monotonicity,[status(thm)],[1503])).
% 21.87/22.06 tff(1505,plain,
% 21.87/22.06 (mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, b)),
% 21.87/22.06 inference(transitivity,[status(thm)],[1504, 1473, 1470, 1468])).
% 21.87/22.06 tff(1506,plain,
% 21.87/22.06 (mult(mult(a, c), mult(mult(a, rd(mult(b, c), mult(a, c))), a)) = mult(mult(a, c), mult(a, b))),
% 21.87/22.06 inference(monotonicity,[status(thm)],[1505])).
% 21.87/22.06 tff(1507,plain,
% 21.87/22.06 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(mult(a, rd(mult(b, c), mult(a, c))), a)))),
% 21.87/22.06 inference(quant_inst,[status(thm)],[])).
% 21.87/22.06 tff(1508,plain,
% 21.87/22.06 (mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(mult(a, rd(mult(b, c), mult(a, c))), a))),
% 21.87/22.06 inference(unit_resolution,[status(thm)],[1507, 56])).
% 21.87/22.06 tff(1509,plain,
% 21.87/22.06 (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)),
% 21.87/22.06 inference(unit_resolution,[status(thm)],[346, 1499])).
% 21.87/22.06 tff(1510,plain,
% 21.87/22.06 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))),
% 21.87/22.06 inference(symmetry,[status(thm)],[1509])).
% 21.87/22.06 tff(1511,plain,
% 21.87/22.06 (mult(mult(b, c), a) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)),
% 21.87/22.06 inference(symmetry,[status(thm)],[1492])).
% 21.87/22.06 tff(1512,plain,
% 21.87/22.06 (mult(mult(b, c), a) = mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))),
% 21.87/22.06 inference(transitivity,[status(thm)],[1511, 1510])).
% 21.87/22.06 tff(1513,plain,
% 21.87/22.06 (mult(mult(mult(b, c), a), a) = mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), a)),
% 21.87/22.06 inference(monotonicity,[status(thm)],[1512])).
% 21.87/22.06 tff(1514,plain,
% 21.87/22.06 (mult(mult(mult(b, c), a), a) = mult(mult(mult(a, b), c), a)),
% 21.87/22.06 inference(transitivity,[status(thm)],[1513, 1508, 1506, 1486, 1483, 1478])).
% 21.87/22.06 tff(1515,plain,
% 21.87/22.06 (rd(mult(mult(mult(b, c), a), a), a) = rd(mult(mult(mult(a, b), c), a), a)),
% 21.87/22.06 inference(monotonicity,[status(thm)],[1514])).
% 21.87/22.06 tff(1516,plain,
% 21.87/22.06 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(b, c), a), a), a) = mult(mult(b, c), a))),
% 21.87/22.06 inference(quant_inst,[status(thm)],[])).
% 21.87/22.06 tff(1517,plain,
% 21.87/22.06 (rd(mult(mult(mult(b, c), a), a), a) = mult(mult(b, c), a)),
% 21.87/22.06 inference(unit_resolution,[status(thm)],[1516, 168])).
% 21.87/22.06 tff(1518,plain,
% 21.87/22.06 (mult(mult(b, c), a) = rd(mult(mult(mult(b, c), a), a), a)),
% 21.87/22.06 inference(symmetry,[status(thm)],[1517])).
% 21.87/22.06 tff(1519,plain,
% 21.87/22.06 (mult(mult(b, c), a) = mult(mult(b, a), c)),
% 21.87/22.06 inference(transitivity,[status(thm)],[1518, 1515, 407, 1476])).
% 21.87/22.06 tff(1520,plain,
% 21.87/22.06 ($false),
% 21.87/22.06 inference(unit_resolution,[status(thm)],[1496, 1519])).
% 21.87/22.06 tff(1521,plain,((~(mult(mult(mult(a, c), mult(a, b)), b) = mult(mult(a, c), mult(mult(a, b), b)))) | (mult(mult(b, c), a) = mult(mult(b, a), c)) | (~(mult(c, mult(b, a)) = mult(c, mult(a, b)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit))))) | (~(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))), inference(lemma,lemma(discharge,[]))).
% 21.87/22.06 tff(1522,plain,
% 21.87/22.06 (~(mult(mult(mult(a, c), mult(a, b)), b) = mult(mult(a, c), mult(mult(a, b), b)))),
% 21.87/22.06 inference(unit_resolution,[status(thm)],[1521, 1466, 97, 1447, 1440])).
% 21.87/22.06 tff(1523,plain,
% 21.87/22.06 ((~(mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(a, c), mult(b, mult(a, b))))) | (~(mult(mult(mult(a, c), mult(a, b)), b) = mult(mult(a, c), mult(mult(a, b), b))))),
% 21.87/22.06 inference(unit_resolution,[status(thm)],[586, 1522])).
% 21.87/22.06 tff(1524,plain,
% 21.87/22.06 (~((~(mult(mult(a, c), mult(b, mult(a, b))) = mult(mult(a, c), mult(mult(a, b), b)))) | (~(mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(mult(a, c), mult(a, b)), b))))),
% 21.87/22.06 inference(unit_resolution,[status(thm)],[584, 1523])).
% 21.87/22.06 tff(1525,plain,
% 21.87/22.06 (mult(mult(a, c), mult(b, mult(a, b))) = mult(mult(a, c), mult(mult(a, b), b))),
% 21.87/22.06 inference(unit_resolution,[status(thm)],[576, 1524])).
% 21.87/22.06 tff(1526,assumption,(~(mult(mult(b, b), a) = mult(b, mult(b, a)))), introduced(assumption)).
% 21.87/22.06 tff(1527,plain,
% 21.87/22.06 (mult(mult(a, b), b) = mult(mult(b, a), b)),
% 21.87/22.06 inference(monotonicity,[status(thm)],[398])).
% 21.87/22.06 tff(1528,plain,
% 21.87/22.06 (mult(a, mult(unit, mult(mult(b, unit), b))) = mult(unit, mult(mult(mult(b, unit), b), a))),
% 21.87/22.06 inference(transitivity,[status(thm)],[829, 436, 445, 441, 1527, 1103, 434, 465])).
% 21.87/22.06 tff(1529,plain,
% 21.87/22.06 (mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b)))) = mult(mult(a, c), mult(unit, mult(mult(mult(b, unit), b), a)))),
% 21.87/22.06 inference(monotonicity,[status(thm)],[1528])).
% 21.87/22.06 tff(1530,plain,
% 21.87/22.06 (mult(mult(a, c), mult(mult(a, b), b)) = mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b))))),
% 21.87/22.06 inference(monotonicity,[status(thm)],[1281])).
% 21.87/22.06 tff(1531,plain,
% 21.87/22.06 (mult(mult(a, c), mult(b, mult(a, b))) = mult(mult(a, c), mult(unit, mult(mult(mult(b, unit), b), a)))),
% 21.87/22.06 inference(transitivity,[status(thm)],[562, 1530, 1529])).
% 21.87/22.06 tff(1532,plain,
% 21.87/22.06 (ld(mult(a, c), mult(mult(a, c), mult(b, mult(a, b)))) = ld(mult(a, c), mult(mult(a, c), mult(unit, mult(mult(mult(b, unit), b), a))))),
% 21.87/22.06 inference(monotonicity,[status(thm)],[1531])).
% 21.87/22.06 tff(1533,plain,
% 21.87/22.06 (ld(mult(a, c), mult(mult(a, c), mult(unit, mult(mult(mult(b, unit), b), a)))) = ld(mult(a, c), mult(mult(a, c), mult(b, mult(a, b))))),
% 21.87/22.06 inference(symmetry,[status(thm)],[1532])).
% 21.87/22.06 tff(1534,plain,
% 21.87/22.06 (mult(unit, mult(mult(mult(b, unit), b), a)) = ld(mult(a, c), mult(mult(a, c), mult(unit, mult(mult(mult(b, unit), b), a))))),
% 21.87/22.06 inference(symmetry,[status(thm)],[427])).
% 21.87/22.06 tff(1535,plain,
% 21.87/22.06 (mult(mult(b, b), a) = mult(b, mult(b, a))),
% 21.87/22.06 inference(transitivity,[status(thm)],[434, 465, 1534, 1533, 566, 391])).
% 21.87/22.06 tff(1536,plain,
% 21.87/22.06 ($false),
% 21.87/22.06 inference(unit_resolution,[status(thm)],[1526, 1535])).
% 21.87/22.06 tff(1537,plain,((~(mult(mult(a, c), mult(b, mult(a, b))) = mult(mult(a, c), mult(mult(a, b), b)))) | (mult(mult(b, b), a) = mult(b, mult(b, a))) | (~(mult(b, mult(a, b)) = mult(b, mult(b, a)))) | (~(mult(mult(b, a), b) = mult(mult(b, b), a)))), inference(lemma,lemma(discharge,[]))).
% 21.87/22.06 tff(1538,plain,
% 21.87/22.06 (~(mult(mult(b, a), b) = mult(mult(b, b), a))),
% 21.87/22.06 inference(unit_resolution,[status(thm)],[1537, 1526, 391, 562])).
% 21.87/22.06 tff(1539,plain,
% 21.87/22.06 ((~(mult(mult(b, a), b) = mult(b, mult(a, b)))) | (~(mult(mult(b, b), a) = mult(b, mult(b, a))))),
% 21.87/22.06 inference(unit_resolution,[status(thm)],[422, 1526])).
% 21.87/22.06 tff(1540,plain,
% 21.87/22.06 (~((~(mult(mult(b, a), b) = mult(mult(b, b), a))) | (~(mult(b, mult(a, b)) = mult(b, mult(b, a)))))),
% 21.87/22.06 inference(unit_resolution,[status(thm)],[418, 1539])).
% 21.87/22.06 tff(1541,plain,
% 21.87/22.06 ($false),
% 21.87/22.06 inference(unit_resolution,[status(thm)],[1135, 1540, 1538])).
% 21.87/22.06 tff(1542,plain,((mult(mult(b, b), a) = mult(b, mult(b, a))) | (~(mult(b, mult(a, b)) = mult(b, mult(b, a)))) | (~(mult(mult(a, c), mult(b, mult(a, b))) = mult(mult(a, c), mult(mult(a, b), b))))), inference(lemma,lemma(discharge,[]))).
% 21.87/22.06 tff(1543,plain,
% 21.87/22.06 (mult(mult(b, b), a) = mult(b, mult(b, a))),
% 21.87/22.06 inference(unit_resolution,[status(thm)],[1542, 1525, 1329])).
% 21.87/22.06 tff(1544,plain,
% 21.87/22.06 (mult(mult(unit, mult(mult(b, unit), b)), a) = mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a)),
% 21.87/22.06 inference(transitivity,[status(thm)],[435, 1543, 1330, 1290, 470])).
% 21.87/22.06 tff(1545,plain,
% 21.87/22.06 (rd(mult(mult(unit, mult(mult(b, unit), b)), a), a) = rd(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a), a)),
% 21.87/22.06 inference(monotonicity,[status(thm)],[1544])).
% 21.87/22.06 tff(1546,plain,
% 21.87/22.06 (rd(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a), a) = rd(mult(mult(unit, mult(mult(b, unit), b)), a), a)),
% 21.87/22.06 inference(symmetry,[status(thm)],[1545])).
% 21.87/22.06 tff(1547,plain,
% 21.87/22.06 (mult(mult(b, a), rd(mult(b, c), mult(a, c))) = mult(unit, mult(mult(b, unit), b))),
% 21.87/22.06 inference(transitivity,[status(thm)],[690, 1546, 552])).
% 21.87/22.06 tff(1548,plain,
% 21.87/22.06 ((~![A: $i] : (mult(unit, A) = A)) | (mult(unit, mult(a, c)) = mult(a, c))),
% 21.87/22.06 inference(quant_inst,[status(thm)],[])).
% 21.87/22.06 tff(1549,plain,
% 21.87/22.06 (mult(unit, mult(a, c)) = mult(a, c)),
% 21.87/22.06 inference(unit_resolution,[status(thm)],[1548, 71])).
% 21.87/22.06 tff(1550,plain,
% 21.87/22.06 (mult(mult(unit, mult(a, c)), mult(mult(b, a), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(unit, mult(mult(b, unit), b)))),
% 21.87/22.06 inference(monotonicity,[status(thm)],[1549, 1547])).
% 21.87/22.06 tff(1551,plain,
% 21.87/22.06 (mult(a, c) = mult(unit, mult(a, c))),
% 21.87/22.06 inference(symmetry,[status(thm)],[1549])).
% 21.87/22.06 tff(1552,plain,
% 21.87/22.06 (mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), mult(a, a)), rd(mult(b, c), mult(a, c)))) = mult(mult(unit, mult(a, c)), mult(mult(b, a), rd(mult(b, c), mult(a, c))))),
% 21.87/22.06 inference(monotonicity,[status(thm)],[1551, 543])).
% 21.87/22.06 tff(1553,plain,
% 21.87/22.06 (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(b, c))),
% 21.87/22.06 inference(transitivity,[status(thm)],[1466, 142])).
% 21.87/22.06 tff(1554,plain,
% 21.87/22.06 (ld(a, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))) = ld(a, mult(a, mult(b, c)))),
% 21.87/22.06 inference(monotonicity,[status(thm)],[1553])).
% 21.87/22.06 tff(1555,plain,
% 21.87/22.06 (mult(mult(a, c), rd(mult(b, c), mult(a, c))) = mult(b, c)),
% 21.87/22.06 inference(transitivity,[status(thm)],[734, 1554, 141])).
% 21.87/22.06 tff(1556,plain,
% 21.87/22.06 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(mult(b, c), mult(a, a))),
% 21.87/22.06 inference(monotonicity,[status(thm)],[1555])).
% 21.87/22.06 tff(1557,plain,
% 21.87/22.06 (mult(mult(b, c), mult(a, a)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, a))),
% 21.87/22.06 inference(symmetry,[status(thm)],[1556])).
% 21.87/22.06 tff(1558,plain,
% 21.87/22.06 (mult(mult(b, c), mult(a, a)) = mult(mult(b, c), mult(mult(a, unit), a))),
% 21.87/22.06 inference(monotonicity,[status(thm)],[520])).
% 21.87/22.07 tff(1559,plain,
% 21.87/22.07 (mult(mult(b, c), mult(mult(a, unit), a)) = mult(mult(b, c), mult(a, a))),
% 21.87/22.07 inference(symmetry,[status(thm)],[1558])).
% 21.87/22.07 tff(1560,plain,
% 21.87/22.07 (mult(b, c) = mult(mult(rd(mult(b, c), mult(a, c)), a), c)),
% 21.87/22.07 inference(transitivity,[status(thm)],[267, 99, 98, 96])).
% 21.87/22.07 tff(1561,plain,
% 21.87/22.07 (mult(mult(b, c), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a)),
% 21.87/22.07 inference(monotonicity,[status(thm)],[1560])).
% 21.87/22.07 tff(1562,plain,
% 21.87/22.07 (mult(mult(mult(b, c), a), unit) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))),
% 21.87/22.07 inference(transitivity,[status(thm)],[1258, 1261, 1263, 1561, 1168])).
% 21.87/22.07 tff(1563,plain,
% 21.87/22.07 (mult(mult(mult(mult(b, c), a), unit), a) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a)),
% 21.87/22.07 inference(monotonicity,[status(thm)],[1562])).
% 21.87/22.07 tff(1564,plain,
% 21.87/22.07 (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a) = mult(mult(mult(mult(b, c), a), unit), a)),
% 21.87/22.07 inference(symmetry,[status(thm)],[1563])).
% 21.87/22.07 tff(1565,plain,
% 21.87/22.07 (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, a))),
% 21.87/22.07 inference(transitivity,[status(thm)],[1564, 1254, 1559, 1557])).
% 21.87/22.07 tff(1566,plain,
% 21.87/22.07 (mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, a)), rd(mult(b, c), mult(a, c)))),
% 21.87/22.07 inference(monotonicity,[status(thm)],[1565])).
% 21.87/22.07 tff(1567,plain,
% 21.87/22.07 ((mult(mult(b, c), mult(b, a)) = mult(mult(mult(b, c), b), a)) <=> (mult(mult(mult(b, c), b), a) = mult(mult(b, c), mult(b, a)))),
% 21.87/22.07 inference(commutativity,[status(thm)],[])).
% 21.87/22.07 tff(1568,plain,
% 21.87/22.07 (((~(mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a))) | (~(mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a))))) | (mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a))),
% 21.87/22.07 inference(tautology,[status(thm)],[])).
% 21.87/22.07 tff(1569,plain,
% 21.87/22.07 (mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a)),
% 21.87/22.07 inference(unit_resolution,[status(thm)],[1568, 1323])).
% 21.87/22.07 tff(1570,plain,
% 21.87/22.07 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a) = mult(mult(b, c), a)),
% 21.87/22.07 inference(symmetry,[status(thm)],[1561])).
% 21.87/22.07 tff(1571,plain,
% 21.87/22.07 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)) = mult(mult(b, c), a)),
% 21.87/22.07 inference(transitivity,[status(thm)],[1169, 1570])).
% 21.87/22.07 tff(1572,plain,
% 21.87/22.07 (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), b) = mult(mult(mult(b, c), a), b)),
% 21.87/22.07 inference(monotonicity,[status(thm)],[1571])).
% 21.87/22.07 tff(1573,plain,
% 21.87/22.07 (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(b, c), b), a)),
% 21.87/22.07 inference(transitivity,[status(thm)],[1222, 1572, 1569])).
% 21.87/22.07 tff(1574,plain,
% 21.87/22.07 (mult(a, b) = mult(a, mult(rd(mult(b, c), mult(a, c)), a))),
% 21.87/22.07 inference(symmetry,[status(thm)],[913])).
% 21.87/22.07 tff(1575,plain,
% 21.87/22.07 (mult(a, b) = mult(mult(a, rd(mult(b, c), mult(a, c))), a)),
% 21.87/22.07 inference(transitivity,[status(thm)],[1574, 1334])).
% 21.87/22.07 tff(1576,plain,
% 21.87/22.07 (mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(mult(a, rd(mult(b, c), mult(a, c))), a))),
% 21.87/22.07 inference(monotonicity,[status(thm)],[1575])).
% 21.87/22.07 tff(1577,plain,
% 21.87/22.07 (mult(mult(b, c), mult(mult(a, rd(mult(b, c), mult(a, c))), a)) = mult(mult(b, c), mult(a, b))),
% 21.87/22.07 inference(symmetry,[status(thm)],[1576])).
% 21.87/22.07 tff(1578,plain,
% 21.87/22.07 (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(b, c), a), rd(mult(b, c), mult(a, c)))),
% 21.87/22.07 inference(monotonicity,[status(thm)],[1571])).
% 21.87/22.07 tff(1579,plain,
% 21.87/22.07 (mult(mult(mult(b, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c)))),
% 21.87/22.07 inference(symmetry,[status(thm)],[1578])).
% 21.87/22.07 tff(1580,plain,
% 21.87/22.07 (mult(mult(mult(mult(b, c), a), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))), a)),
% 21.87/22.07 inference(monotonicity,[status(thm)],[1579])).
% 21.87/22.07 tff(1581,plain,
% 21.87/22.07 (mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(mult(b, c), a), rd(mult(b, c), mult(a, c))), a)),
% 21.87/22.07 inference(symmetry,[status(thm)],[1580])).
% 21.87/22.07 tff(1582,plain,
% 21.87/22.07 (mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))), a) = mult(mult(b, c), mult(b, a))),
% 21.87/22.07 inference(transitivity,[status(thm)],[1581, 1214, 1577, 1324])).
% 21.87/22.07 tff(1583,plain,
% 21.87/22.07 ((mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))), a) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(rd(mult(b, c), mult(a, c)), a))) <=> (mult(mult(b, c), mult(b, a)) = mult(mult(mult(b, c), b), a))),
% 21.87/22.07 inference(monotonicity,[status(thm)],[1582, 1573])).
% 21.87/22.07 tff(1584,plain,
% 21.87/22.07 ((mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))), a) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(rd(mult(b, c), mult(a, c)), a))) <=> (mult(mult(mult(b, c), b), a) = mult(mult(b, c), mult(b, a)))),
% 21.87/22.07 inference(transitivity,[status(thm)],[1583, 1567])).
% 21.87/22.07 tff(1585,plain,
% 21.87/22.07 ((mult(mult(mult(b, c), b), a) = mult(mult(b, c), mult(b, a))) <=> (mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))), a) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(rd(mult(b, c), mult(a, c)), a)))),
% 21.87/22.07 inference(symmetry,[status(thm)],[1584])).
% 21.87/22.07 tff(1586,plain,
% 21.87/22.07 ((~(mult(mult(mult(b, c), b), a) = mult(mult(b, c), mult(b, a)))) <=> (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))), a) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(rd(mult(b, c), mult(a, c)), a))))),
% 21.87/22.07 inference(monotonicity,[status(thm)],[1585])).
% 21.87/22.07 tff(1587,plain,
% 21.87/22.07 ((mult(mult(mult(b, c), a), b) = mult(mult(b, c), mult(a, b))) <=> (mult(mult(mult(b, c), b), a) = mult(mult(b, c), mult(b, a)))),
% 21.87/22.07 inference(monotonicity,[status(thm)],[1569, 1324])).
% 21.87/22.07 tff(1588,plain,
% 21.87/22.07 ((~(mult(mult(mult(b, c), a), b) = mult(mult(b, c), mult(a, b)))) <=> (~(mult(mult(mult(b, c), b), a) = mult(mult(b, c), mult(b, a))))),
% 21.87/22.07 inference(monotonicity,[status(thm)],[1587])).
% 21.87/22.07 tff(1589,plain,
% 21.87/22.07 (~(mult(mult(mult(b, c), b), a) = mult(mult(b, c), mult(b, a)))),
% 21.87/22.07 inference(modus_ponens,[status(thm)],[1321, 1588])).
% 21.87/22.07 tff(1590,plain,
% 21.87/22.07 (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))), a) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(rd(mult(b, c), mult(a, c)), a)))),
% 21.87/22.07 inference(modus_ponens,[status(thm)],[1589, 1586])).
% 21.87/22.07 tff(1591,plain,
% 21.87/22.07 ((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))), a) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(rd(mult(b, c), mult(a, c)), a))))),
% 21.87/22.07 inference(unit_resolution,[status(thm)],[1236, 1590])).
% 21.87/22.07 tff(1592,plain,
% 21.87/22.07 (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))), a))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(rd(mult(b, c), mult(a, c)), a)))))),
% 21.87/22.07 inference(unit_resolution,[status(thm)],[1247, 1591])).
% 21.87/22.07 tff(1593,plain,
% 21.87/22.07 (mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))), a)),
% 21.87/22.07 inference(unit_resolution,[status(thm)],[1249, 1592])).
% 21.87/22.07 tff(1594,plain,
% 21.87/22.07 (mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c)))),
% 21.87/22.07 inference(symmetry,[status(thm)],[1593])).
% 21.87/22.07 tff(1595,plain,
% 21.87/22.07 (mult(mult(mult(mult(b, c), a), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(a, b), b), c)),
% 21.87/22.07 inference(transitivity,[status(thm)],[1580, 1594, 1566, 1009, 1552, 1550, 870, 869, 866, 827])).
% 21.87/22.07 tff(1596,plain,
% 21.87/22.07 (mult(a, mult(mult(mult(mult(b, c), a), rd(mult(b, c), mult(a, c))), a)) = mult(a, mult(mult(mult(a, b), b), c))),
% 21.87/22.07 inference(monotonicity,[status(thm)],[1595])).
% 21.87/22.07 tff(1597,plain,
% 21.87/22.07 (mult(mult(b, c), mult(mult(a, rd(mult(b, c), mult(a, c))), a)) = mult(mult(mult(mult(b, c), a), rd(mult(b, c), mult(a, c))), a)),
% 21.87/22.07 inference(symmetry,[status(thm)],[1214])).
% 21.87/22.07 tff(1598,plain,
% 21.87/22.07 (mult(mult(b, c), mult(a, b)) = mult(mult(mult(mult(b, c), a), rd(mult(b, c), mult(a, c))), a)),
% 21.87/22.07 inference(transitivity,[status(thm)],[1576, 1597])).
% 21.87/22.07 tff(1599,plain,
% 21.87/22.07 (mult(a, mult(mult(b, c), mult(a, b))) = mult(a, mult(mult(mult(mult(b, c), a), rd(mult(b, c), mult(a, c))), a))),
% 21.87/22.07 inference(monotonicity,[status(thm)],[1598])).
% 21.87/22.07 tff(1600,plain,
% 21.87/22.07 (mult(mult(a, b), c) = mult(mult(b, a), c)),
% 21.87/22.07 inference(symmetry,[status(thm)],[1449])).
% 21.87/22.07 tff(1601,plain,
% 21.87/22.07 (mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c))),
% 21.87/22.07 inference(transitivity,[status(thm)],[177, 161, 1600, 1423, 1430])).
% 21.87/22.07 tff(1602,plain,
% 21.87/22.07 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(b, c), a)),
% 21.87/22.07 inference(monotonicity,[status(thm)],[1555])).
% 21.87/22.07 tff(1603,plain,
% 21.87/22.07 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a)),
% 21.87/22.07 inference(transitivity,[status(thm)],[1602, 1431])).
% 21.87/22.07 tff(1604,plain,
% 21.87/22.07 ((mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))) <=> (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)))),
% 21.87/22.07 inference(monotonicity,[status(thm)],[1603, 1601])).
% 21.87/22.07 tff(1605,plain,
% 21.87/22.07 ((mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))) <=> (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a))),
% 21.87/22.07 inference(transitivity,[status(thm)],[1604, 1429])).
% 21.87/22.07 tff(1606,plain,
% 21.87/22.07 ((mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a)) <=> (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))),
% 21.87/22.07 inference(symmetry,[status(thm)],[1605])).
% 21.87/22.07 tff(1607,plain,
% 21.87/22.07 ((~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a))) <=> (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))))),
% 21.87/22.07 inference(monotonicity,[status(thm)],[1606])).
% 21.87/22.07 tff(1608,plain,
% 21.87/22.07 ((~(mult(b, mult(c, a)) = mult(b, mult(a, c)))) <=> (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a)))),
% 21.87/22.07 inference(monotonicity,[status(thm)],[1437])).
% 21.87/22.07 tff(1609,plain,
% 21.87/22.07 (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a))),
% 21.87/22.07 inference(modus_ponens,[status(thm)],[1420, 1608])).
% 21.87/22.07 tff(1610,plain,
% 21.87/22.07 (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))),
% 21.87/22.07 inference(modus_ponens,[status(thm)],[1609, 1607])).
% 21.87/22.07 tff(1611,plain,
% 21.87/22.07 (~((~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))) | (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))))),
% 21.87/22.07 inference(unit_resolution,[status(thm)],[340, 1610])).
% 21.87/22.07 tff(1612,plain,
% 21.87/22.07 (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)),
% 21.87/22.07 inference(unit_resolution,[status(thm)],[346, 1611])).
% 21.87/22.07 tff(1613,plain,
% 21.87/22.07 (mult(mult(b, b), a) = mult(mult(unit, mult(mult(b, unit), b)), a)),
% 21.87/22.07 inference(symmetry,[status(thm)],[1107])).
% 21.87/22.07 tff(1614,assumption,(~(mult(mult(b, a), b) = mult(b, mult(a, b)))), introduced(assumption)).
% 21.87/22.07 tff(1615,plain,
% 21.87/22.07 ((~(mult(mult(b, a), b) = mult(b, mult(a, b)))) | (~(mult(mult(b, b), a) = mult(b, mult(b, a))))),
% 21.87/22.07 inference(unit_resolution,[status(thm)],[420, 1614])).
% 21.87/22.07 tff(1616,plain,
% 21.87/22.07 (~((~(mult(mult(b, a), b) = mult(mult(b, b), a))) | (~(mult(b, mult(a, b)) = mult(b, mult(b, a)))))),
% 21.87/22.07 inference(unit_resolution,[status(thm)],[418, 1615])).
% 21.87/22.07 tff(1617,plain,
% 21.87/22.07 (mult(mult(b, a), b) = mult(mult(b, b), a)),
% 21.87/22.07 inference(unit_resolution,[status(thm)],[1135, 1616])).
% 21.87/22.07 tff(1618,plain,
% 21.87/22.07 (mult(mult(a, b), b) = mult(mult(b, a), b)),
% 21.87/22.07 inference(symmetry,[status(thm)],[1479])).
% 21.87/22.07 tff(1619,plain,
% 21.87/22.07 (mult(a, mult(unit, mult(mult(b, unit), b))) = mult(unit, mult(mult(mult(b, unit), b), a))),
% 21.87/22.07 inference(transitivity,[status(thm)],[829, 663, 445, 662, 1618, 1617, 1613, 465])).
% 21.87/22.07 tff(1620,plain,
% 21.87/22.07 (mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b)))) = mult(mult(a, c), mult(unit, mult(mult(mult(b, unit), b), a)))),
% 21.87/22.07 inference(monotonicity,[status(thm)],[1619])).
% 21.87/22.07 tff(1621,plain,
% 21.87/22.07 (mult(mult(a, c), mult(mult(a, b), b)) = mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b))))),
% 21.87/22.07 inference(monotonicity,[status(thm)],[831])).
% 21.87/22.07 tff(1622,plain,
% 21.87/22.07 (mult(mult(a, c), mult(b, mult(a, b))) = mult(mult(a, c), mult(unit, mult(mult(mult(b, unit), b), a)))),
% 21.87/22.07 inference(transitivity,[status(thm)],[562, 1621, 1620])).
% 21.87/22.07 tff(1623,plain,
% 21.87/22.07 (ld(mult(a, c), mult(mult(a, c), mult(b, mult(a, b)))) = ld(mult(a, c), mult(mult(a, c), mult(unit, mult(mult(mult(b, unit), b), a))))),
% 21.87/22.07 inference(monotonicity,[status(thm)],[1622])).
% 21.87/22.07 tff(1624,plain,
% 21.87/22.07 (ld(mult(a, c), mult(mult(a, c), mult(unit, mult(mult(mult(b, unit), b), a)))) = ld(mult(a, c), mult(mult(a, c), mult(b, mult(a, b))))),
% 21.87/22.07 inference(symmetry,[status(thm)],[1623])).
% 21.87/22.07 tff(1625,plain,
% 21.87/22.07 (mult(mult(b, a), b) = mult(b, mult(a, b))),
% 21.87/22.07 inference(transitivity,[status(thm)],[1617, 1613, 465, 1534, 1624, 566])).
% 21.87/22.07 tff(1626,plain,
% 21.87/22.07 ($false),
% 21.87/22.07 inference(unit_resolution,[status(thm)],[1614, 1625])).
% 21.87/22.07 tff(1627,plain,((~(mult(mult(a, c), mult(b, mult(a, b))) = mult(mult(a, c), mult(mult(a, b), b)))) | (mult(mult(b, a), b) = mult(b, mult(a, b))) | (~(mult(c, mult(b, a)) = mult(c, mult(a, b))))), inference(lemma,lemma(discharge,[]))).
% 21.87/22.07 tff(1628,plain,
% 21.87/22.07 (mult(mult(b, a), b) = mult(b, mult(a, b))),
% 21.87/22.07 inference(unit_resolution,[status(thm)],[1627, 1525, 1447])).
% 21.87/22.07 tff(1629,plain,
% 21.87/22.07 (mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(b, c))),
% 21.87/22.07 inference(monotonicity,[status(thm)],[1555])).
% 21.87/22.07 tff(1630,plain,
% 21.87/22.07 (mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))),
% 21.87/22.07 inference(transitivity,[status(thm)],[1629, 139])).
% 21.87/22.07 tff(1631,plain,
% 21.87/22.07 (mult(b, c) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))),
% 21.87/22.07 inference(transitivity,[status(thm)],[740, 739, 1028])).
% 21.87/22.07 tff(1632,plain,
% 21.87/22.07 (mult(mult(b, c), mult(a, c)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))),
% 21.87/22.07 inference(monotonicity,[status(thm)],[1631])).
% 21.87/22.07 tff(1633,plain,
% 21.87/22.07 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(a, c))) = mult(a, c))),
% 21.87/22.07 inference(quant_inst,[status(thm)],[])).
% 21.87/22.07 tff(1634,plain,
% 21.87/22.07 (ld(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(a, c))) = mult(a, c)),
% 21.87/22.07 inference(unit_resolution,[status(thm)],[1633, 7])).
% 21.87/22.07 tff(1635,assumption,(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(a, c))), introduced(assumption)).
% 21.87/22.07 tff(1636,plain,
% 21.87/22.07 (ld(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(c, a))) = ld(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 21.87/22.07 inference(monotonicity,[status(thm)],[1635])).
% 21.87/22.08 tff(1637,plain,
% 21.87/22.08 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(c, a))) = mult(c, a))),
% 21.87/22.08 inference(quant_inst,[status(thm)],[])).
% 21.87/22.08 tff(1638,plain,
% 21.87/22.08 (ld(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(c, a))) = mult(c, a)),
% 21.87/22.08 inference(unit_resolution,[status(thm)],[1637, 7])).
% 21.87/22.08 tff(1639,plain,
% 21.87/22.08 (mult(c, a) = ld(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(c, a)))),
% 21.87/22.08 inference(symmetry,[status(thm)],[1638])).
% 21.87/22.08 tff(1640,plain,
% 21.87/22.08 (mult(c, a) = mult(a, c)),
% 21.87/22.08 inference(transitivity,[status(thm)],[1639, 1636, 1634])).
% 21.87/22.08 tff(1641,plain,
% 21.87/22.08 (mult(mult(b, c), mult(c, a)) = mult(mult(b, c), mult(a, c))),
% 21.87/22.08 inference(monotonicity,[status(thm)],[1640])).
% 21.87/22.08 tff(1642,plain,
% 21.87/22.08 (mult(mult(a, c), rd(mult(b, c), mult(a, c))) = ld(mult(a, c), mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 21.87/22.08 inference(symmetry,[status(thm)],[1028])).
% 21.87/22.08 tff(1643,plain,
% 21.87/22.08 (mult(mult(a, c), rd(mult(b, c), mult(a, c))) = mult(b, c)),
% 21.87/22.08 inference(transitivity,[status(thm)],[1642, 293, 291])).
% 21.87/22.08 tff(1644,plain,
% 21.87/22.08 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(b, c), mult(c, a))),
% 21.87/22.08 inference(monotonicity,[status(thm)],[1643])).
% 21.87/22.08 tff(1645,plain,
% 21.87/22.08 (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c)),
% 21.87/22.08 inference(transitivity,[status(thm)],[751, 1644, 1641, 1632, 738])).
% 21.87/22.08 tff(1646,plain,
% 21.87/22.08 ($false),
% 21.87/22.08 inference(unit_resolution,[status(thm)],[753, 1645])).
% 21.87/22.08 tff(1647,plain,((~(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(a, c)))) | (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c)) | (~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)))) | (~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))), inference(lemma,lemma(discharge,[]))).
% 21.92/22.08 tff(1648,plain,
% 21.92/22.08 (~(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 21.92/22.08 inference(unit_resolution,[status(thm)],[1647, 1630, 751, 317, 753])).
% 21.92/22.08 tff(1649,plain,
% 21.92/22.08 (((~(mult(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a), c))) | (~(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(a, c))))) | (mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 21.92/22.08 inference(tautology,[status(thm)],[])).
% 21.92/22.08 tff(1650,plain,
% 21.92/22.08 ((~(mult(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a), c))) | (~(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(a, c))))),
% 21.92/22.08 inference(unit_resolution,[status(thm)],[1649, 1648])).
% 21.92/22.08 tff(1651,plain,
% 21.92/22.08 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a), c))) | (~(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(a, c)))))) | (~((~(mult(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(c, a)))) | (~(mult(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(a, c)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a), c))) | (~(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(a, c)))))) | (~((~(mult(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(c, a)))) | (~(mult(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(a, c)))))))),
% 21.92/22.08 inference(rewrite,[status(thm)],[])).
% 21.92/22.08 tff(1652,plain,
% 21.92/22.08 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a), c))) | (~(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(a, c)))))) | (~((~(mult(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(c, a)))) | (~(mult(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(a, c)))))))),
% 21.92/22.08 inference(quant_inst,[status(thm)],[])).
% 21.92/22.08 tff(1653,plain,
% 21.92/22.08 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a), c))) | (~(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(a, c)))))) | (~((~(mult(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(c, a)))) | (~(mult(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(a, c))))))),
% 21.92/22.08 inference(modus_ponens,[status(thm)],[1652, 1651])).
% 21.92/22.08 tff(1654,plain,
% 21.92/22.08 ((~((~(mult(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a), c))) | (~(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(a, c)))))) | (~((~(mult(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(c, a)))) | (~(mult(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(a, c))))))),
% 21.92/22.08 inference(unit_resolution,[status(thm)],[1653, 27])).
% 21.92/22.08 tff(1655,plain,
% 21.92/22.08 (~((~(mult(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(c, a)))) | (~(mult(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(a, c)))))),
% 21.92/22.08 inference(unit_resolution,[status(thm)],[1654, 1650])).
% 21.92/22.08 tff(1656,plain,
% 21.92/22.08 (((~(mult(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(c, a)))) | (~(mult(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(a, c))))) | (mult(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 21.92/22.08 inference(tautology,[status(thm)],[])).
% 21.92/22.08 tff(1657,plain,
% 21.92/22.08 (mult(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(a, c))),
% 21.92/22.08 inference(unit_resolution,[status(thm)],[1656, 1655])).
% 21.92/22.08 tff(1658,plain,
% 21.92/22.08 (((~(mult(mult(a, c), mult(b, mult(a, b))) = mult(mult(a, c), mult(mult(a, b), b)))) | (~(mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(mult(a, c), mult(a, b)), b)))) | (mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(mult(a, c), mult(a, b)), b))),
% 21.92/22.08 inference(tautology,[status(thm)],[])).
% 21.92/22.08 tff(1659,plain,
% 21.92/22.08 (mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(mult(a, c), mult(a, b)), b)),
% 21.92/22.08 inference(unit_resolution,[status(thm)],[1658, 1524])).
% 21.92/22.08 tff(1660,plain,
% 21.92/22.08 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(a, mult(b, c)), mult(a, b)), mult(a, b)) = mult(a, mult(b, c)))),
% 21.92/22.08 inference(quant_inst,[status(thm)],[])).
% 21.92/22.08 tff(1661,plain,
% 21.92/22.08 (rd(mult(mult(a, mult(b, c)), mult(a, b)), mult(a, b)) = mult(a, mult(b, c))),
% 21.92/22.08 inference(unit_resolution,[status(thm)],[1660, 168])).
% 21.92/22.08 tff(1662,assumption,(mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(mult(a, c), mult(a, b)), b)), introduced(assumption)).
% 21.92/22.08 tff(1663,plain,
% 21.92/22.08 (mult(mult(mult(a, c), mult(a, b)), b) = mult(mult(mult(a, c), b), mult(a, b))),
% 21.92/22.08 inference(symmetry,[status(thm)],[1662])).
% 21.92/22.08 tff(1664,plain,
% 21.92/22.08 (mult(b, a) = mult(a, b)),
% 21.92/22.08 inference(transitivity,[status(thm)],[1444, 1182, 1185])).
% 21.92/22.08 tff(1665,plain,
% 21.92/22.08 (mult(mult(b, a), c) = mult(mult(a, b), c)),
% 21.92/22.08 inference(monotonicity,[status(thm)],[1664])).
% 21.92/22.08 tff(1666,plain,
% 21.92/22.08 (mult(b, mult(a, c)) = mult(mult(b, a), c)),
% 21.92/22.08 inference(symmetry,[status(thm)],[388])).
% 21.92/22.08 tff(1667,plain,
% 21.92/22.08 (mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(b, a)),
% 21.92/22.08 inference(transitivity,[status(thm)],[1287, 913, 1186, 1183, 1179])).
% 21.92/22.08 tff(1668,plain,
% 21.92/22.08 (rd(mult(mult(a, rd(mult(b, c), mult(a, c))), a), a) = rd(mult(b, a), a)),
% 21.92/22.08 inference(monotonicity,[status(thm)],[1667])).
% 21.92/22.08 tff(1669,plain,
% 21.92/22.08 (mult(a, rd(mult(b, c), mult(a, c))) = b),
% 21.92/22.08 inference(transitivity,[status(thm)],[1456, 1668, 1451])).
% 21.92/22.08 tff(1670,plain,
% 21.92/22.08 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(b, mult(a, c))),
% 21.92/22.08 inference(monotonicity,[status(thm)],[1669])).
% 21.92/22.08 tff(1671,plain,
% 21.92/22.08 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, b), c)),
% 21.92/22.08 inference(transitivity,[status(thm)],[1670, 1666, 1665])).
% 21.92/22.08 tff(1672,plain,
% 21.92/22.08 ((mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))) <=> (mult(mult(a, b), c) = mult(a, mult(b, c)))),
% 21.92/22.08 inference(monotonicity,[status(thm)],[1671, 142])).
% 21.92/22.08 tff(1673,plain,
% 21.92/22.08 ((mult(mult(a, b), c) = mult(a, mult(b, c))) <=> (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))),
% 21.92/22.08 inference(symmetry,[status(thm)],[1672])).
% 21.92/22.08 tff(1674,plain,
% 21.92/22.08 ((~(mult(mult(a, b), c) = mult(a, mult(b, c)))) <=> (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))),
% 21.92/22.08 inference(monotonicity,[status(thm)],[1673])).
% 21.92/22.08 tff(1675,plain,
% 21.92/22.08 (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))),
% 21.92/22.08 inference(modus_ponens,[status(thm)],[146, 1674])).
% 21.92/22.08 tff(1676,plain,
% 21.92/22.08 ((~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))),
% 21.92/22.08 inference(unit_resolution,[status(thm)],[278, 1675])).
% 21.92/22.08 tff(1677,plain,
% 21.92/22.08 (~((~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))),
% 21.92/22.08 inference(unit_resolution,[status(thm)],[276, 1676])).
% 21.92/22.08 tff(1678,plain,
% 21.92/22.08 (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))),
% 21.92/22.08 inference(unit_resolution,[status(thm)],[271, 1677])).
% 21.92/22.08 tff(1679,plain,
% 21.92/22.08 (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(b, c))),
% 21.92/22.08 inference(transitivity,[status(thm)],[1678, 142])).
% 21.92/22.08 tff(1680,plain,
% 21.92/22.08 (ld(a, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))) = ld(a, mult(a, mult(b, c)))),
% 21.92/22.08 inference(monotonicity,[status(thm)],[1679])).
% 21.92/22.08 tff(1681,plain,
% 21.92/22.08 (mult(mult(a, c), rd(mult(b, c), mult(a, c))) = mult(b, c)),
% 21.92/22.08 inference(transitivity,[status(thm)],[734, 1680, 141])).
% 21.92/22.08 tff(1682,plain,
% 21.92/22.08 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(b, c), a)),
% 21.92/22.08 inference(monotonicity,[status(thm)],[1681])).
% 21.92/22.08 tff(1683,assumption,(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)), introduced(assumption)).
% 21.92/22.09 tff(1684,plain,
% 21.92/22.09 (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))),
% 21.92/22.09 inference(transitivity,[status(thm)],[1683, 1682, 1561, 1168])).
% 21.92/22.09 tff(1685,plain,
% 21.92/22.09 (mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), a) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a)),
% 21.92/22.09 inference(monotonicity,[status(thm)],[1684])).
% 21.92/22.09 tff(1686,plain,
% 21.92/22.09 (mult(mult(a, c), mult(mult(a, rd(mult(b, c), mult(a, c))), a)) = mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), a)),
% 21.92/22.09 inference(symmetry,[status(thm)],[1508])).
% 21.92/22.09 tff(1687,plain,
% 21.92/22.09 (mult(mult(a, c), mult(a, b)) = mult(mult(a, c), mult(mult(a, rd(mult(b, c), mult(a, c))), a))),
% 21.92/22.09 inference(monotonicity,[status(thm)],[1575])).
% 21.92/22.09 tff(1688,plain,
% 21.92/22.09 (mult(mult(a, c), mult(a, b)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a)),
% 21.92/22.09 inference(transitivity,[status(thm)],[1687, 1686, 1685])).
% 21.92/22.09 tff(1689,plain,
% 21.92/22.09 (mult(mult(mult(a, c), mult(a, b)), b) = mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), b)),
% 21.92/22.09 inference(monotonicity,[status(thm)],[1688])).
% 21.92/22.09 tff(1690,plain,
% 21.92/22.09 (mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), b) = mult(mult(mult(a, c), mult(a, b)), b)),
% 21.92/22.09 inference(symmetry,[status(thm)],[1689])).
% 21.92/22.09 tff(1691,plain,
% 21.92/22.09 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a))),
% 21.92/22.09 inference(quant_inst,[status(thm)],[])).
% 21.92/22.09 tff(1692,plain,
% 21.92/22.09 (rd(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a)),
% 21.92/22.09 inference(unit_resolution,[status(thm)],[1691, 168])).
% 21.92/22.09 tff(1693,plain,
% 21.92/22.09 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(mult(b, c), mult(a, a))),
% 21.92/22.09 inference(monotonicity,[status(thm)],[1681])).
% 21.92/22.09 tff(1694,plain,
% 21.92/22.09 (mult(mult(b, c), mult(a, a)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, a))),
% 21.92/22.09 inference(symmetry,[status(thm)],[1693])).
% 21.92/22.09 tff(1695,plain,
% 21.92/22.09 (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, a))),
% 21.92/22.09 inference(transitivity,[status(thm)],[1564, 1254, 1559, 1694])).
% 21.92/22.09 tff(1696,plain,
% 21.92/22.09 (mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, a)), rd(mult(b, c), mult(a, c)))),
% 21.92/22.09 inference(monotonicity,[status(thm)],[1695])).
% 21.92/22.09 tff(1697,plain,
% 21.92/22.09 (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, a)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c)))),
% 21.92/22.09 inference(symmetry,[status(thm)],[1696])).
% 21.92/22.09 tff(1698,plain,
% 21.92/22.09 (mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), mult(a, a)), rd(mult(b, c), mult(a, c)))) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, a)), rd(mult(b, c), mult(a, c)))),
% 21.92/22.09 inference(symmetry,[status(thm)],[1009])).
% 21.92/22.09 tff(1699,plain,
% 21.92/22.09 (mult(mult(unit, mult(a, c)), mult(mult(b, a), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), mult(a, a)), rd(mult(b, c), mult(a, c))))),
% 21.92/22.09 inference(symmetry,[status(thm)],[1552])).
% 21.92/22.09 tff(1700,plain,
% 21.92/22.09 (mult(b, mult(a, b)) = mult(b, mult(b, a))),
% 21.92/22.09 inference(monotonicity,[status(thm)],[1187])).
% 21.92/22.09 tff(1701,plain,
% 21.92/22.09 (mult(b, mult(b, a)) = mult(b, mult(a, b))),
% 21.92/22.09 inference(symmetry,[status(thm)],[1700])).
% 21.92/22.09 tff(1702,plain,
% 21.92/22.09 (mult(mult(unit, mult(mult(b, unit), b)), a) = mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a)),
% 21.92/22.09 inference(transitivity,[status(thm)],[435, 591, 1701, 1290, 470])).
% 21.92/22.09 tff(1703,plain,
% 21.92/22.09 (rd(mult(mult(unit, mult(mult(b, unit), b)), a), a) = rd(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a), a)),
% 21.92/22.09 inference(monotonicity,[status(thm)],[1702])).
% 21.92/22.09 tff(1704,plain,
% 21.92/22.09 (rd(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a), a) = rd(mult(mult(unit, mult(mult(b, unit), b)), a), a)),
% 21.92/22.09 inference(symmetry,[status(thm)],[1703])).
% 21.92/22.09 tff(1705,plain,
% 21.92/22.09 (mult(mult(b, a), rd(mult(b, c), mult(a, c))) = mult(unit, mult(mult(b, unit), b))),
% 21.92/22.09 inference(transitivity,[status(thm)],[690, 1704, 552])).
% 21.92/22.09 tff(1706,plain,
% 21.92/22.09 (mult(mult(unit, mult(a, c)), mult(mult(b, a), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(unit, mult(mult(b, unit), b)))),
% 21.92/22.09 inference(monotonicity,[status(thm)],[1549, 1705])).
% 21.92/22.09 tff(1707,plain,
% 21.92/22.09 (mult(mult(a, c), mult(unit, mult(mult(b, unit), b))) = mult(mult(unit, mult(a, c)), mult(mult(b, a), rd(mult(b, c), mult(a, c))))),
% 21.92/22.09 inference(symmetry,[status(thm)],[1706])).
% 21.92/22.09 tff(1708,plain,
% 21.92/22.09 (mult(mult(a, c), mult(mult(b, unit), b)) = mult(mult(a, c), mult(unit, mult(mult(b, unit), b)))),
% 21.92/22.09 inference(symmetry,[status(thm)],[870])).
% 21.92/22.09 tff(1709,plain,
% 21.92/22.09 (mult(mult(mult(a, b), c), b) = mult(mult(mult(mult(a, c), b), unit), b)),
% 21.92/22.09 inference(symmetry,[status(thm)],[866])).
% 21.92/22.09 tff(1710,plain,
% 21.92/22.09 (mult(mult(a, b), b) = mult(mult(b, a), b)),
% 21.92/22.09 inference(monotonicity,[status(thm)],[1187])).
% 21.92/22.09 tff(1711,plain,
% 21.92/22.09 (mult(mult(b, a), b) = mult(mult(a, b), b)),
% 21.92/22.09 inference(symmetry,[status(thm)],[1710])).
% 21.92/22.09 tff(1712,plain,
% 21.92/22.09 (mult(b, mult(a, b)) = mult(mult(b, a), b)),
% 21.92/22.09 inference(symmetry,[status(thm)],[607])).
% 21.92/22.09 tff(1713,plain,
% 21.92/22.09 (mult(unit, mult(mult(mult(b, unit), b), a)) = mult(a, mult(unit, mult(mult(b, unit), b)))),
% 21.92/22.09 inference(transitivity,[status(thm)],[466, 435, 591, 1701, 1712, 1711, 442, 439, 437, 830])).
% 21.92/22.09 tff(1714,plain,
% 21.92/22.09 (mult(mult(unit, mult(mult(mult(b, unit), b), a)), c) = mult(mult(a, mult(unit, mult(mult(b, unit), b))), c)),
% 21.92/22.09 inference(monotonicity,[status(thm)],[1713])).
% 21.92/22.09 tff(1715,plain,
% 21.92/22.09 (mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a) = mult(unit, mult(mult(mult(b, unit), b), a))),
% 21.92/22.09 inference(transitivity,[status(thm)],[469, 1289, 1700, 592, 434, 465])).
% 21.92/22.09 tff(1716,plain,
% 21.92/22.09 (mult(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(unit, mult(mult(mult(b, unit), b), a)), c)),
% 21.92/22.09 inference(monotonicity,[status(thm)],[1715])).
% 21.92/22.09 tff(1717,assumption,(mult(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(a, c))), introduced(assumption)).
% 21.92/22.09 tff(1718,plain,
% 21.92/22.09 (mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a), c)),
% 21.92/22.09 inference(symmetry,[status(thm)],[1717])).
% 21.92/22.09 tff(1719,plain,
% 21.92/22.09 (mult(mult(a, b), rd(mult(b, c), mult(a, c))) = mult(mult(b, a), rd(mult(b, c), mult(a, c)))),
% 21.92/22.09 inference(monotonicity,[status(thm)],[1187])).
% 21.92/22.09 tff(1720,plain,
% 21.92/22.09 (mult(mult(mult(a, b), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(a, c))),
% 21.92/22.09 inference(monotonicity,[status(thm)],[1719])).
% 21.92/22.09 tff(1721,plain,
% 21.92/22.09 (mult(mult(a, b), mult(rd(mult(b, c), mult(a, c)), mult(a, c))) = mult(mult(a, b), mult(b, c))),
% 21.92/22.09 inference(monotonicity,[status(thm)],[137])).
% 21.92/22.09 tff(1722,plain,
% 21.92/22.09 (mult(mult(mult(a, b), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(mult(a, b), b), c)),
% 21.92/22.09 inference(transitivity,[status(thm)],[1720, 1718, 1716, 1714, 1283])).
% 21.92/22.09 tff(1723,plain,
% 21.92/22.09 ((mult(mult(mult(a, b), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, b), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))) <=> (mult(mult(mult(a, b), b), c) = mult(mult(a, b), mult(b, c)))),
% 21.92/22.09 inference(monotonicity,[status(thm)],[1722, 1721])).
% 21.92/22.09 tff(1724,plain,
% 21.92/22.09 ((mult(mult(mult(a, b), b), c) = mult(mult(a, b), mult(b, c))) <=> (mult(mult(mult(a, b), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, b), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))),
% 21.92/22.09 inference(symmetry,[status(thm)],[1723])).
% 21.92/22.09 tff(1725,plain,
% 21.92/22.09 ((~(mult(mult(mult(a, b), b), c) = mult(mult(a, b), mult(b, c)))) <=> (~(mult(mult(mult(a, b), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, b), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))),
% 21.92/22.09 inference(monotonicity,[status(thm)],[1724])).
% 21.92/22.09 tff(1726,plain,
% 21.92/22.09 ((mult(mult(mult(a, b), b), c) = mult(mult(a, b), mult(b, c))) <=> (mult(mult(mult(a, b), c), b) = mult(mult(a, b), mult(c, b)))),
% 21.92/22.09 inference(monotonicity,[status(thm)],[828, 785])).
% 21.92/22.09 tff(1727,plain,
% 21.92/22.09 ((mult(mult(mult(a, b), c), b) = mult(mult(a, b), mult(c, b))) <=> (mult(mult(mult(a, b), b), c) = mult(mult(a, b), mult(b, c)))),
% 21.92/22.09 inference(symmetry,[status(thm)],[1726])).
% 21.92/22.09 tff(1728,plain,
% 21.92/22.09 ((~(mult(mult(mult(a, b), c), b) = mult(mult(a, b), mult(c, b)))) <=> (~(mult(mult(mult(a, b), b), c) = mult(mult(a, b), mult(b, c))))),
% 21.92/22.09 inference(monotonicity,[status(thm)],[1727])).
% 21.92/22.09 tff(1729,plain,
% 21.92/22.09 (~(mult(mult(mult(a, b), b), c) = mult(mult(a, b), mult(b, c)))),
% 21.92/22.09 inference(modus_ponens,[status(thm)],[811, 1728])).
% 21.92/22.09 tff(1730,plain,
% 21.92/22.09 (~(mult(mult(mult(a, b), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, b), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))),
% 21.92/22.09 inference(modus_ponens,[status(thm)],[1729, 1725])).
% 21.92/22.09 tff(1731,plain,
% 21.92/22.09 (((~(mult(mult(mult(a, b), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, b), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, b), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, b), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))) | (mult(mult(mult(a, b), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, b), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))),
% 21.92/22.09 inference(tautology,[status(thm)],[])).
% 21.92/22.09 tff(1732,plain,
% 21.92/22.09 ((~(mult(mult(mult(a, b), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, b), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, b), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, b), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))),
% 21.92/22.09 inference(unit_resolution,[status(thm)],[1731, 1730])).
% 21.92/22.09 tff(1733,plain,
% 21.92/22.09 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, b), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, b), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, b), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, b), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))) | (~((~(mult(mult(mult(a, b), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, b), rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(mult(a, b), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, b), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(a, b), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, b), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, b), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, b), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))) | (~((~(mult(mult(mult(a, b), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, b), rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(mult(a, b), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, b), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))))),
% 21.92/22.09 inference(rewrite,[status(thm)],[])).
% 21.92/22.09 tff(1734,plain,
% 21.92/22.09 (((~((~(mult(mult(mult(a, b), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, b), rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(mult(a, b), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, b), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))) | (~((~(mult(mult(mult(a, b), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, b), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, b), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, b), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))))) <=> ((~((~(mult(mult(mult(a, b), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, b), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, b), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, b), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))) | (~((~(mult(mult(mult(a, b), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, b), rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(mult(a, b), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, b), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))))),
% 21.92/22.09 inference(rewrite,[status(thm)],[])).
% 21.92/22.09 tff(1735,plain,
% 21.92/22.09 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, b), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, b), rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(mult(a, b), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, b), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))) | (~((~(mult(mult(mult(a, b), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, b), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, b), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, b), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, b), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, b), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, b), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, b), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))) | (~((~(mult(mult(mult(a, b), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, b), rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(mult(a, b), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, b), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))))))),
% 21.92/22.09 inference(monotonicity,[status(thm)],[1734])).
% 21.92/22.09 tff(1736,plain,
% 21.92/22.09 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, b), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, b), rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(mult(a, b), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, b), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))) | (~((~(mult(mult(mult(a, b), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, b), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, b), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, b), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(a, b), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, b), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, b), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, b), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))) | (~((~(mult(mult(mult(a, b), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, b), rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(mult(a, b), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, b), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))))),
% 21.92/22.10 inference(transitivity,[status(thm)],[1735, 1733])).
% 21.92/22.10 tff(1737,plain,
% 21.92/22.10 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, b), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, b), rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(mult(a, b), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, b), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))) | (~((~(mult(mult(mult(a, b), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, b), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, b), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, b), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))))),
% 21.92/22.10 inference(quant_inst,[status(thm)],[])).
% 21.92/22.10 tff(1738,plain,
% 21.92/22.10 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(a, b), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, b), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, b), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, b), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))) | (~((~(mult(mult(mult(a, b), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, b), rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(mult(a, b), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, b), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))))),
% 21.92/22.10 inference(modus_ponens,[status(thm)],[1737, 1736])).
% 21.92/22.10 tff(1739,plain,
% 21.92/22.10 ((~((~(mult(mult(mult(a, b), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, b), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, b), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, b), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))) | (~((~(mult(mult(mult(a, b), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, b), rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(mult(a, b), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, b), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))))),
% 21.92/22.10 inference(unit_resolution,[status(thm)],[1738, 27])).
% 21.92/22.10 tff(1740,plain,
% 21.92/22.10 (~((~(mult(mult(mult(a, b), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, b), rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(mult(a, b), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, b), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))),
% 21.92/22.10 inference(unit_resolution,[status(thm)],[1739, 1732])).
% 21.92/22.10 tff(1741,plain,
% 21.92/22.10 (((~(mult(mult(mult(a, b), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, b), rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(mult(a, b), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, b), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))) | (mult(mult(mult(a, b), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, b), rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 21.92/22.10 inference(tautology,[status(thm)],[])).
% 21.92/22.10 tff(1742,plain,
% 21.92/22.10 (mult(mult(mult(a, b), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, b), rd(mult(b, c), mult(a, c))), mult(a, c))),
% 21.92/22.10 inference(unit_resolution,[status(thm)],[1741, 1740])).
% 21.92/22.10 tff(1743,plain,
% 21.92/22.10 (mult(mult(mult(a, b), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c)))),
% 21.92/22.10 inference(transitivity,[status(thm)],[1742, 1720, 1718, 1716, 1714, 1283, 828, 1709, 868, 1708, 1707, 1699, 1698, 1697])).
% 21.92/22.10 tff(1744,plain,
% 21.92/22.10 (rd(mult(mult(mult(a, b), mult(a, c)), rd(mult(b, c), mult(a, c))), rd(mult(b, c), mult(a, c))) = rd(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c))), rd(mult(b, c), mult(a, c)))),
% 21.92/22.10 inference(monotonicity,[status(thm)],[1743])).
% 21.92/22.10 tff(1745,plain,
% 21.92/22.10 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(a, b), mult(a, c)), rd(mult(b, c), mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(a, b), mult(a, c)))),
% 21.92/22.10 inference(quant_inst,[status(thm)],[])).
% 21.92/22.10 tff(1746,plain,
% 21.92/22.10 (rd(mult(mult(mult(a, b), mult(a, c)), rd(mult(b, c), mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(a, b), mult(a, c))),
% 21.92/22.10 inference(unit_resolution,[status(thm)],[1745, 168])).
% 21.92/22.10 tff(1747,plain,
% 21.92/22.10 (mult(mult(a, b), mult(a, c)) = rd(mult(mult(mult(a, b), mult(a, c)), rd(mult(b, c), mult(a, c))), rd(mult(b, c), mult(a, c)))),
% 21.92/22.10 inference(symmetry,[status(thm)],[1746])).
% 21.92/22.10 tff(1748,plain,
% 21.92/22.10 (mult(mult(a, b), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a)),
% 21.92/22.10 inference(transitivity,[status(thm)],[1747, 1744, 1692])).
% 21.92/22.10 tff(1749,plain,
% 21.92/22.10 (mult(mult(mult(a, b), mult(a, c)), b) = mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), b)),
% 21.92/22.10 inference(monotonicity,[status(thm)],[1748])).
% 21.92/22.10 tff(1750,plain,
% 21.92/22.10 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(a, b), mult(a, c)), b) = mult(a, mult(mult(b, mult(a, c)), b)))),
% 21.92/22.10 inference(quant_inst,[status(thm)],[])).
% 21.92/22.10 tff(1751,plain,
% 21.92/22.10 (mult(mult(mult(a, b), mult(a, c)), b) = mult(a, mult(mult(b, mult(a, c)), b))),
% 21.92/22.10 inference(unit_resolution,[status(thm)],[1750, 56])).
% 21.92/22.10 tff(1752,plain,
% 21.92/22.10 (mult(a, mult(mult(b, mult(a, c)), b)) = mult(mult(mult(a, b), mult(a, c)), b)),
% 21.92/22.10 inference(symmetry,[status(thm)],[1751])).
% 21.92/22.10 tff(1753,plain,
% 21.92/22.10 (mult(b, mult(a, c)) = mult(mult(a, b), c)),
% 21.92/22.10 inference(transitivity,[status(thm)],[1666, 1665])).
% 21.92/22.10 tff(1754,plain,
% 21.92/22.10 (mult(mult(b, mult(a, c)), b) = mult(mult(mult(a, b), c), b)),
% 21.92/22.10 inference(monotonicity,[status(thm)],[1753])).
% 21.92/22.10 tff(1755,plain,
% 21.92/22.10 (mult(mult(mult(a, b), c), b) = mult(mult(b, mult(a, c)), b)),
% 21.92/22.10 inference(symmetry,[status(thm)],[1754])).
% 21.92/22.10 tff(1756,plain,
% 21.92/22.10 (mult(mult(mult(a, b), b), c) = mult(mult(b, mult(a, c)), b)),
% 21.92/22.10 inference(transitivity,[status(thm)],[828, 1755])).
% 21.92/22.10 tff(1757,plain,
% 21.92/22.10 (mult(a, mult(mult(mult(a, b), b), c)) = mult(a, mult(mult(b, mult(a, c)), b))),
% 21.92/22.10 inference(monotonicity,[status(thm)],[1756])).
% 21.92/22.10 tff(1758,assumption,(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))), a)), introduced(assumption)).
% 21.92/22.10 tff(1759,plain,
% 21.92/22.10 (mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c)))),
% 21.92/22.10 inference(symmetry,[status(thm)],[1758])).
% 21.92/22.10 tff(1760,plain,
% 21.92/22.10 (mult(mult(mult(mult(b, c), a), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(a, b), b), c)),
% 21.92/22.10 inference(transitivity,[status(thm)],[1580, 1759, 1696, 1009, 1552, 1706, 870, 869, 866, 827])).
% 21.92/22.10 tff(1761,plain,
% 21.92/22.10 (mult(a, mult(mult(mult(mult(b, c), a), rd(mult(b, c), mult(a, c))), a)) = mult(a, mult(mult(mult(a, b), b), c))),
% 21.92/22.10 inference(monotonicity,[status(thm)],[1760])).
% 21.92/22.10 tff(1762,assumption,(mult(mult(a, mult(b, c)), mult(a, b)) = mult(a, mult(mult(b, c), mult(a, b)))), introduced(assumption)).
% 21.92/22.10 tff(1763,plain,
% 21.92/22.10 (mult(mult(a, mult(b, c)), mult(a, b)) = mult(mult(mult(a, b), c), mult(a, b))),
% 21.92/22.10 inference(transitivity,[status(thm)],[1762, 1599, 1761, 1757, 1752, 1749, 1690, 1663, 949])).
% 21.92/22.10 tff(1764,plain,
% 21.92/22.10 (rd(mult(mult(a, mult(b, c)), mult(a, b)), mult(a, b)) = rd(mult(mult(mult(a, b), c), mult(a, b)), mult(a, b))),
% 21.92/22.10 inference(monotonicity,[status(thm)],[1763])).
% 21.92/22.10 tff(1765,plain,
% 21.92/22.10 (rd(mult(mult(mult(a, b), c), mult(a, b)), mult(a, b)) = rd(mult(mult(a, mult(b, c)), mult(a, b)), mult(a, b))),
% 21.92/22.10 inference(symmetry,[status(thm)],[1764])).
% 21.92/22.10 tff(1766,plain,
% 21.92/22.10 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(a, b), c), mult(a, b)), mult(a, b)) = mult(mult(a, b), c))),
% 21.92/22.10 inference(quant_inst,[status(thm)],[])).
% 21.92/22.10 tff(1767,plain,
% 21.92/22.10 (rd(mult(mult(mult(a, b), c), mult(a, b)), mult(a, b)) = mult(mult(a, b), c)),
% 21.92/22.10 inference(unit_resolution,[status(thm)],[1766, 168])).
% 21.92/22.10 tff(1768,plain,
% 21.92/22.10 (mult(mult(a, b), c) = rd(mult(mult(mult(a, b), c), mult(a, b)), mult(a, b))),
% 21.92/22.10 inference(symmetry,[status(thm)],[1767])).
% 21.92/22.10 tff(1769,plain,
% 21.92/22.10 (mult(mult(a, b), c) = mult(a, mult(b, c))),
% 21.92/22.10 inference(transitivity,[status(thm)],[1768, 1765, 1661])).
% 21.92/22.10 tff(1770,plain,
% 21.92/22.10 ($false),
% 21.92/22.10 inference(unit_resolution,[status(thm)],[146, 1769])).
% 21.92/22.10 tff(1771,plain,((~(mult(mult(a, mult(b, c)), mult(a, b)) = mult(a, mult(mult(b, c), mult(a, b))))) | (~(mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(mult(a, c), mult(a, b)), b))) | (~(mult(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(mult(b, a), b) = mult(b, mult(a, b)))) | (~(mult(mult(b, b), a) = mult(b, mult(b, a)))) | (~(mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a)))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit))))) | (~(mult(mult(b, a), c) = mult(b, mult(a, c)))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))), a))) | (~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)))), inference(lemma,lemma(discharge,[]))).
% 21.92/22.10 tff(1772,plain,
% 21.92/22.10 (~(mult(mult(a, mult(b, c)), mult(a, b)) = mult(a, mult(mult(b, c), mult(a, b))))),
% 21.92/22.10 inference(unit_resolution,[status(thm)],[1771, 1659, 1657, 1628, 1543, 1324, 1287, 97, 1423, 1593, 1612])).
% 21.92/22.10 tff(1773,plain,
% 21.92/22.10 (((~(mult(mult(a, mult(a, b)), mult(b, c)) = mult(a, mult(mult(a, b), mult(b, c))))) | (~(mult(mult(a, mult(b, c)), mult(a, b)) = mult(a, mult(mult(b, c), mult(a, b)))))) | (mult(mult(a, mult(b, c)), mult(a, b)) = mult(a, mult(mult(b, c), mult(a, b))))),
% 21.92/22.10 inference(tautology,[status(thm)],[])).
% 21.92/22.10 tff(1774,plain,
% 21.92/22.10 ((~(mult(mult(a, mult(a, b)), mult(b, c)) = mult(a, mult(mult(a, b), mult(b, c))))) | (~(mult(mult(a, mult(b, c)), mult(a, b)) = mult(a, mult(mult(b, c), mult(a, b)))))),
% 21.92/22.10 inference(unit_resolution,[status(thm)],[1773, 1772])).
% 21.92/22.10 tff(1775,plain,
% 21.92/22.10 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, mult(a, b)), mult(b, c)) = mult(a, mult(mult(a, b), mult(b, c))))) | (~(mult(mult(a, mult(b, c)), mult(a, b)) = mult(a, mult(mult(b, c), mult(a, b))))))) | (~((~(mult(mult(a, mult(a, b)), mult(b, c)) = mult(mult(a, mult(b, c)), mult(a, b)))) | (~(mult(a, mult(mult(a, b), mult(b, c))) = mult(a, mult(mult(b, c), mult(a, b))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, mult(a, b)), mult(b, c)) = mult(a, mult(mult(a, b), mult(b, c))))) | (~(mult(mult(a, mult(b, c)), mult(a, b)) = mult(a, mult(mult(b, c), mult(a, b))))))) | (~((~(mult(mult(a, mult(a, b)), mult(b, c)) = mult(mult(a, mult(b, c)), mult(a, b)))) | (~(mult(a, mult(mult(a, b), mult(b, c))) = mult(a, mult(mult(b, c), mult(a, b))))))))),
% 21.92/22.10 inference(rewrite,[status(thm)],[])).
% 21.92/22.10 tff(1776,plain,
% 21.92/22.10 (((~((~(mult(mult(a, mult(a, b)), mult(b, c)) = mult(mult(a, mult(b, c)), mult(a, b)))) | (~(mult(a, mult(mult(a, b), mult(b, c))) = mult(a, mult(mult(b, c), mult(a, b))))))) | (~((~(mult(mult(a, mult(a, b)), mult(b, c)) = mult(a, mult(mult(a, b), mult(b, c))))) | (~(mult(mult(a, mult(b, c)), mult(a, b)) = mult(a, mult(mult(b, c), mult(a, b)))))))) <=> ((~((~(mult(mult(a, mult(a, b)), mult(b, c)) = mult(a, mult(mult(a, b), mult(b, c))))) | (~(mult(mult(a, mult(b, c)), mult(a, b)) = mult(a, mult(mult(b, c), mult(a, b))))))) | (~((~(mult(mult(a, mult(a, b)), mult(b, c)) = mult(mult(a, mult(b, c)), mult(a, b)))) | (~(mult(a, mult(mult(a, b), mult(b, c))) = mult(a, mult(mult(b, c), mult(a, b))))))))),
% 21.92/22.10 inference(rewrite,[status(thm)],[])).
% 21.92/22.10 tff(1777,plain,
% 21.92/22.10 ((~((~(mult(mult(a, mult(a, b)), mult(b, c)) = mult(mult(a, mult(b, c)), mult(a, b)))) | (~(mult(a, mult(mult(a, b), mult(b, c))) = mult(a, mult(mult(b, c), mult(a, b))))))) <=> (~((~(mult(mult(a, mult(a, b)), mult(b, c)) = mult(mult(a, mult(b, c)), mult(a, b)))) | (~(mult(a, mult(mult(a, b), mult(b, c))) = mult(a, mult(mult(b, c), mult(a, b)))))))),
% 21.92/22.10 inference(rewrite,[status(thm)],[])).
% 21.92/22.10 tff(1778,plain,
% 21.92/22.10 (((~((~(mult(mult(a, mult(a, b)), mult(b, c)) = mult(mult(a, mult(b, c)), mult(a, b)))) | (~(mult(a, mult(mult(a, b), mult(b, c))) = mult(a, mult(mult(b, c), mult(a, b))))))) | (~((~(mult(mult(a, mult(a, b)), mult(b, c)) = mult(a, mult(mult(a, b), mult(b, c))))) | (~(mult(mult(a, mult(b, c)), mult(a, b)) = mult(a, mult(mult(b, c), mult(a, b)))))))) <=> ((~((~(mult(mult(a, mult(a, b)), mult(b, c)) = mult(mult(a, mult(b, c)), mult(a, b)))) | (~(mult(a, mult(mult(a, b), mult(b, c))) = mult(a, mult(mult(b, c), mult(a, b))))))) | (~((~(mult(mult(a, mult(a, b)), mult(b, c)) = mult(a, mult(mult(a, b), mult(b, c))))) | (~(mult(mult(a, mult(b, c)), mult(a, b)) = mult(a, mult(mult(b, c), mult(a, b))))))))),
% 21.92/22.10 inference(monotonicity,[status(thm)],[1777])).
% 21.92/22.10 tff(1779,plain,
% 21.92/22.10 (((~((~(mult(mult(a, mult(a, b)), mult(b, c)) = mult(mult(a, mult(b, c)), mult(a, b)))) | (~(mult(a, mult(mult(a, b), mult(b, c))) = mult(a, mult(mult(b, c), mult(a, b))))))) | (~((~(mult(mult(a, mult(a, b)), mult(b, c)) = mult(a, mult(mult(a, b), mult(b, c))))) | (~(mult(mult(a, mult(b, c)), mult(a, b)) = mult(a, mult(mult(b, c), mult(a, b)))))))) <=> ((~((~(mult(mult(a, mult(a, b)), mult(b, c)) = mult(a, mult(mult(a, b), mult(b, c))))) | (~(mult(mult(a, mult(b, c)), mult(a, b)) = mult(a, mult(mult(b, c), mult(a, b))))))) | (~((~(mult(mult(a, mult(a, b)), mult(b, c)) = mult(mult(a, mult(b, c)), mult(a, b)))) | (~(mult(a, mult(mult(a, b), mult(b, c))) = mult(a, mult(mult(b, c), mult(a, b))))))))),
% 21.92/22.10 inference(transitivity,[status(thm)],[1778, 1776])).
% 21.92/22.10 tff(1780,plain,
% 21.92/22.10 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, mult(a, b)), mult(b, c)) = mult(mult(a, mult(b, c)), mult(a, b)))) | (~(mult(a, mult(mult(a, b), mult(b, c))) = mult(a, mult(mult(b, c), mult(a, b))))))) | (~((~(mult(mult(a, mult(a, b)), mult(b, c)) = mult(a, mult(mult(a, b), mult(b, c))))) | (~(mult(mult(a, mult(b, c)), mult(a, b)) = mult(a, mult(mult(b, c), mult(a, b))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, mult(a, b)), mult(b, c)) = mult(a, mult(mult(a, b), mult(b, c))))) | (~(mult(mult(a, mult(b, c)), mult(a, b)) = mult(a, mult(mult(b, c), mult(a, b))))))) | (~((~(mult(mult(a, mult(a, b)), mult(b, c)) = mult(mult(a, mult(b, c)), mult(a, b)))) | (~(mult(a, mult(mult(a, b), mult(b, c))) = mult(a, mult(mult(b, c), mult(a, b)))))))))),
% 21.92/22.11 inference(monotonicity,[status(thm)],[1779])).
% 21.92/22.11 tff(1781,plain,
% 21.92/22.11 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, mult(a, b)), mult(b, c)) = mult(mult(a, mult(b, c)), mult(a, b)))) | (~(mult(a, mult(mult(a, b), mult(b, c))) = mult(a, mult(mult(b, c), mult(a, b))))))) | (~((~(mult(mult(a, mult(a, b)), mult(b, c)) = mult(a, mult(mult(a, b), mult(b, c))))) | (~(mult(mult(a, mult(b, c)), mult(a, b)) = mult(a, mult(mult(b, c), mult(a, b))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, mult(a, b)), mult(b, c)) = mult(a, mult(mult(a, b), mult(b, c))))) | (~(mult(mult(a, mult(b, c)), mult(a, b)) = mult(a, mult(mult(b, c), mult(a, b))))))) | (~((~(mult(mult(a, mult(a, b)), mult(b, c)) = mult(mult(a, mult(b, c)), mult(a, b)))) | (~(mult(a, mult(mult(a, b), mult(b, c))) = mult(a, mult(mult(b, c), mult(a, b))))))))),
% 21.92/22.11 inference(transitivity,[status(thm)],[1780, 1775])).
% 21.92/22.11 tff(1782,plain,
% 21.92/22.11 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, mult(a, b)), mult(b, c)) = mult(mult(a, mult(b, c)), mult(a, b)))) | (~(mult(a, mult(mult(a, b), mult(b, c))) = mult(a, mult(mult(b, c), mult(a, b))))))) | (~((~(mult(mult(a, mult(a, b)), mult(b, c)) = mult(a, mult(mult(a, b), mult(b, c))))) | (~(mult(mult(a, mult(b, c)), mult(a, b)) = mult(a, mult(mult(b, c), mult(a, b))))))))),
% 21.92/22.11 inference(quant_inst,[status(thm)],[])).
% 21.92/22.11 tff(1783,plain,
% 21.92/22.11 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, mult(a, b)), mult(b, c)) = mult(a, mult(mult(a, b), mult(b, c))))) | (~(mult(mult(a, mult(b, c)), mult(a, b)) = mult(a, mult(mult(b, c), mult(a, b))))))) | (~((~(mult(mult(a, mult(a, b)), mult(b, c)) = mult(mult(a, mult(b, c)), mult(a, b)))) | (~(mult(a, mult(mult(a, b), mult(b, c))) = mult(a, mult(mult(b, c), mult(a, b)))))))),
% 21.92/22.11 inference(modus_ponens,[status(thm)],[1782, 1781])).
% 21.92/22.11 tff(1784,plain,
% 21.92/22.11 ((~((~(mult(mult(a, mult(a, b)), mult(b, c)) = mult(a, mult(mult(a, b), mult(b, c))))) | (~(mult(mult(a, mult(b, c)), mult(a, b)) = mult(a, mult(mult(b, c), mult(a, b))))))) | (~((~(mult(mult(a, mult(a, b)), mult(b, c)) = mult(mult(a, mult(b, c)), mult(a, b)))) | (~(mult(a, mult(mult(a, b), mult(b, c))) = mult(a, mult(mult(b, c), mult(a, b)))))))),
% 21.92/22.11 inference(unit_resolution,[status(thm)],[1783, 27])).
% 21.92/22.11 tff(1785,plain,
% 21.92/22.11 (~((~(mult(mult(a, mult(a, b)), mult(b, c)) = mult(mult(a, mult(b, c)), mult(a, b)))) | (~(mult(a, mult(mult(a, b), mult(b, c))) = mult(a, mult(mult(b, c), mult(a, b))))))),
% 21.92/22.11 inference(unit_resolution,[status(thm)],[1784, 1774])).
% 21.92/22.11 tff(1786,plain,
% 21.92/22.11 (((~(mult(mult(a, mult(a, b)), mult(b, c)) = mult(mult(a, mult(b, c)), mult(a, b)))) | (~(mult(a, mult(mult(a, b), mult(b, c))) = mult(a, mult(mult(b, c), mult(a, b)))))) | (mult(a, mult(mult(a, b), mult(b, c))) = mult(a, mult(mult(b, c), mult(a, b))))),
% 21.92/22.11 inference(tautology,[status(thm)],[])).
% 21.92/22.11 tff(1787,plain,
% 21.92/22.11 (mult(a, mult(mult(a, b), mult(b, c))) = mult(a, mult(mult(b, c), mult(a, b)))),
% 21.92/22.11 inference(unit_resolution,[status(thm)],[1786, 1785])).
% 21.92/22.11 tff(1788,plain,
% 21.92/22.11 (mult(a, mult(mult(a, b), mult(b, c))) = mult(a, mult(a, mult(mult(unit, mult(mult(b, unit), b)), c)))),
% 21.92/22.11 inference(transitivity,[status(thm)],[1787, 1599, 1596, 1286])).
% 21.92/22.11 tff(1789,plain,
% 21.92/22.11 (ld(a, mult(a, mult(mult(a, b), mult(b, c)))) = ld(a, mult(a, mult(a, mult(mult(unit, mult(mult(b, unit), b)), c))))),
% 21.92/22.11 inference(monotonicity,[status(thm)],[1788])).
% 21.92/22.11 tff(1790,plain,
% 21.92/22.11 (ld(a, mult(a, mult(a, mult(mult(unit, mult(mult(b, unit), b)), c)))) = ld(a, mult(a, mult(mult(a, b), mult(b, c))))),
% 21.92/22.11 inference(symmetry,[status(thm)],[1789])).
% 21.92/22.11 tff(1791,plain,
% 21.92/22.11 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(a, mult(a, mult(a, mult(mult(unit, mult(mult(b, unit), b)), c)))) = mult(a, mult(mult(unit, mult(mult(b, unit), b)), c)))),
% 21.92/22.11 inference(quant_inst,[status(thm)],[])).
% 21.92/22.11 tff(1792,plain,
% 21.92/22.11 (ld(a, mult(a, mult(a, mult(mult(unit, mult(mult(b, unit), b)), c)))) = mult(a, mult(mult(unit, mult(mult(b, unit), b)), c))),
% 21.92/22.11 inference(unit_resolution,[status(thm)],[1791, 7])).
% 21.92/22.11 tff(1793,plain,
% 21.92/22.11 (mult(a, mult(mult(unit, mult(mult(b, unit), b)), c)) = ld(a, mult(a, mult(a, mult(mult(unit, mult(mult(b, unit), b)), c))))),
% 21.92/22.11 inference(symmetry,[status(thm)],[1792])).
% 21.92/22.11 tff(1794,plain,
% 21.92/22.11 (mult(mult(mult(a, b), b), c) = mult(mult(a, b), mult(b, c))),
% 21.92/22.11 inference(transitivity,[status(thm)],[1282, 892, 1793, 1790, 1280])).
% 21.92/22.11 tff(1795,plain,
% 21.92/22.11 ($false),
% 21.92/22.11 inference(unit_resolution,[status(thm)],[1729, 1794])).
% 21.92/22.11 tff(1796,plain,((mult(mult(mult(b, c), a), mult(a, b)) = mult(mult(b, c), mult(a, mult(a, b)))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit))))) | (~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)))) | (~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))) | (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c)) | (mult(rd(mult(b, c), mult(a, c)), mult(c, a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, c)))), inference(lemma,lemma(discharge,[]))).
% 21.92/22.11 tff(1797,plain,
% 21.92/22.11 (mult(mult(mult(b, c), a), mult(a, b)) = mult(mult(b, c), mult(a, mult(a, b)))),
% 21.92/22.11 inference(unit_resolution,[status(thm)],[1796, 1274, 34, 124, 122, 128, 94])).
% 21.92/22.11 tff(1798,plain,
% 21.92/22.11 (mult(mult(mult(mult(a, b), c), a), b) = mult(mult(mult(mult(a, c), b), a), b)),
% 21.92/22.11 inference(symmetry,[status(thm)],[963])).
% 21.92/22.11 tff(1799,assumption,(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))), introduced(assumption)).
% 21.92/22.11 tff(1800,plain,
% 21.92/22.11 (mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)),
% 21.92/22.11 inference(symmetry,[status(thm)],[1799])).
% 21.92/22.11 tff(1801,plain,
% 21.92/22.11 (((~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))))) | (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))),
% 21.92/22.11 inference(tautology,[status(thm)],[])).
% 21.92/22.11 tff(1802,plain,
% 21.92/22.11 ((~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))))),
% 21.92/22.11 inference(unit_resolution,[status(thm)],[1801, 723])).
% 21.92/22.11 tff(1803,assumption,((~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))))), introduced(assumption)).
% 21.92/22.11 tff(1804,plain,
% 21.92/22.11 ($false),
% 21.92/22.11 inference(unit_resolution,[status(thm)],[338, 27, 335, 1803])).
% 21.92/22.11 tff(1805,plain,((~((~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))))) | (~((~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))) | (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))))))), inference(lemma,lemma(discharge,[]))).
% 21.92/22.11 tff(1806,plain,
% 21.92/22.11 (~((~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))) | (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))))),
% 21.92/22.11 inference(unit_resolution,[status(thm)],[1805, 1802])).
% 21.92/22.11 tff(1807,plain,
% 21.92/22.11 (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))),
% 21.92/22.11 inference(unit_resolution,[status(thm)],[331, 1806])).
% 21.92/22.11 tff(1808,plain,
% 21.92/22.11 (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)),
% 21.92/22.11 inference(transitivity,[status(thm)],[1807, 1800])).
% 21.92/22.11 tff(1809,plain,
% 21.92/22.11 ((mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) <=> (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))),
% 21.92/22.11 inference(monotonicity,[status(thm)],[1808])).
% 21.92/22.11 tff(1810,plain,
% 21.92/22.11 ((mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)) <=> (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))),
% 21.92/22.11 inference(symmetry,[status(thm)],[1809])).
% 21.92/22.11 tff(1811,plain,
% 21.92/22.11 (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)),
% 21.92/22.11 inference(unit_resolution,[status(thm)],[346, 1806])).
% 21.92/22.11 tff(1812,plain,
% 21.92/22.11 (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))),
% 21.92/22.11 inference(modus_ponens,[status(thm)],[1811, 1810])).
% 21.92/22.11 tff(1813,plain,
% 21.92/22.11 ($false),
% 21.92/22.11 inference(unit_resolution,[status(thm)],[723, 1812])).
% 21.92/22.11 tff(1814,plain,((mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))))), inference(lemma,lemma(discharge,[]))).
% 21.92/22.11 tff(1815,plain,
% 21.92/22.11 (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))),
% 21.92/22.11 inference(unit_resolution,[status(thm)],[1814, 723])).
% 21.92/22.11 tff(1816,plain,
% 21.92/22.11 (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))),
% 21.92/22.11 inference(unit_resolution,[status(thm)],[342, 1815])).
% 21.92/22.11 tff(1817,plain,
% 21.92/22.11 (~(mult(b, mult(c, a)) = mult(b, mult(a, c)))),
% 21.92/22.11 inference(unit_resolution,[status(thm)],[377, 1816, 354, 97])).
% 21.92/22.11 tff(1818,plain,
% 21.92/22.11 ((~(mult(mult(b, c), a) = mult(mult(b, a), c))) | (~(mult(b, mult(c, a)) = mult(b, mult(a, c))))),
% 21.92/22.11 inference(unit_resolution,[status(thm)],[379, 1817])).
% 21.92/22.11 tff(1819,plain,
% 21.92/22.11 (~((~(mult(mult(b, c), a) = mult(b, mult(c, a)))) | (~(mult(mult(b, a), c) = mult(b, mult(a, c)))))),
% 21.92/22.11 inference(unit_resolution,[status(thm)],[384, 1818])).
% 21.92/22.11 tff(1820,plain,
% 21.92/22.11 (mult(mult(b, a), c) = mult(b, mult(a, c))),
% 21.92/22.11 inference(unit_resolution,[status(thm)],[386, 1819])).
% 21.92/22.11 tff(1821,plain,
% 21.92/22.11 (mult(b, mult(a, c)) = mult(mult(b, a), c)),
% 21.92/22.11 inference(symmetry,[status(thm)],[1820])).
% 21.92/22.11 tff(1822,plain,
% 21.92/22.11 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(b, a), c)),
% 21.92/22.11 inference(transitivity,[status(thm)],[1425, 1821])).
% 21.92/22.11 tff(1823,plain,
% 21.92/22.11 ((mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a)) <=> (mult(mult(b, a), c) = mult(mult(b, c), a))),
% 21.92/22.11 inference(monotonicity,[status(thm)],[1822, 1332])).
% 21.92/22.11 tff(1824,plain,
% 21.92/22.11 ((mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a)) <=> (mult(mult(b, c), a) = mult(mult(b, a), c))),
% 21.92/22.11 inference(transitivity,[status(thm)],[1823, 1331])).
% 21.92/22.11 tff(1825,plain,
% 21.92/22.11 (mult(mult(b, c), a) = mult(b, mult(c, a))),
% 21.92/22.11 inference(unit_resolution,[status(thm)],[1432, 1819])).
% 21.92/22.11 tff(1826,plain,
% 21.92/22.11 (mult(b, mult(c, a)) = mult(mult(b, c), a)),
% 21.92/22.11 inference(symmetry,[status(thm)],[1825])).
% 21.92/22.11 tff(1827,plain,
% 21.92/22.11 (mult(b, mult(c, a)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a)),
% 21.92/22.11 inference(transitivity,[status(thm)],[1826, 1431])).
% 21.92/22.11 tff(1828,plain,
% 21.92/22.11 ((mult(b, mult(c, a)) = mult(b, mult(a, c))) <=> (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)))),
% 21.92/22.11 inference(monotonicity,[status(thm)],[1827, 1430])).
% 21.92/22.11 tff(1829,plain,
% 21.92/22.11 ((mult(b, mult(c, a)) = mult(b, mult(a, c))) <=> (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a))),
% 21.92/22.11 inference(transitivity,[status(thm)],[1828, 1429])).
% 21.92/22.11 tff(1830,plain,
% 21.92/22.11 ((mult(b, mult(c, a)) = mult(b, mult(a, c))) <=> (mult(mult(b, c), a) = mult(mult(b, a), c))),
% 21.92/22.11 inference(transitivity,[status(thm)],[1829, 1824])).
% 21.92/22.11 tff(1831,plain,
% 21.92/22.11 ((~(mult(b, mult(c, a)) = mult(b, mult(a, c)))) <=> (~(mult(mult(b, c), a) = mult(mult(b, a), c)))),
% 21.92/22.11 inference(monotonicity,[status(thm)],[1830])).
% 21.92/22.11 tff(1832,plain,
% 21.92/22.11 (~(mult(mult(b, c), a) = mult(mult(b, a), c))),
% 21.92/22.11 inference(modus_ponens,[status(thm)],[1817, 1831])).
% 21.92/22.11 tff(1833,plain,
% 21.92/22.11 (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), b)),
% 21.92/22.11 inference(transitivity,[status(thm)],[1816, 177])).
% 21.92/22.11 tff(1834,plain,
% 21.92/22.11 (ld(mult(a, c), mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = ld(mult(a, c), mult(mult(a, c), b))),
% 21.92/22.11 inference(monotonicity,[status(thm)],[1833])).
% 21.92/22.11 tff(1835,plain,
% 21.92/22.11 (ld(mult(a, c), mult(mult(a, c), b)) = ld(mult(a, c), mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))),
% 21.92/22.11 inference(symmetry,[status(thm)],[1834])).
% 21.92/22.11 tff(1836,plain,
% 21.92/22.11 (b = mult(a, rd(mult(b, c), mult(a, c)))),
% 21.92/22.11 inference(transitivity,[status(thm)],[365, 1835, 358])).
% 21.92/22.11 tff(1837,plain,
% 21.92/22.11 (mult(b, a) = mult(mult(a, rd(mult(b, c), mult(a, c))), a)),
% 21.92/22.11 inference(monotonicity,[status(thm)],[1836])).
% 21.92/22.11 tff(1838,plain,
% 21.92/22.11 (mult(b, a) = mult(c, ld(c, mult(a, b)))),
% 21.92/22.11 inference(transitivity,[status(thm)],[1837, 1287, 913, 1441])).
% 21.92/22.11 tff(1839,plain,
% 21.92/22.11 (mult(c, mult(b, a)) = mult(c, mult(c, ld(c, mult(a, b))))),
% 21.92/22.11 inference(monotonicity,[status(thm)],[1838])).
% 21.92/22.11 tff(1840,plain,
% 21.92/22.11 (mult(c, mult(b, a)) = mult(c, mult(a, b))),
% 21.92/22.11 inference(transitivity,[status(thm)],[1839, 1443])).
% 21.92/22.11 tff(1841,plain,
% 21.92/22.11 (~(mult(mult(mult(a, c), mult(a, b)), b) = mult(mult(a, c), mult(mult(a, b), b)))),
% 21.92/22.11 inference(unit_resolution,[status(thm)],[1521, 1840, 97, 1488, 1832])).
% 21.92/22.11 tff(1842,plain,
% 21.92/22.11 ((~(mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(a, c), mult(b, mult(a, b))))) | (~(mult(mult(mult(a, c), mult(a, b)), b) = mult(mult(a, c), mult(mult(a, b), b))))),
% 21.92/22.11 inference(unit_resolution,[status(thm)],[586, 1841])).
% 21.92/22.11 tff(1843,plain,
% 21.92/22.11 (~((~(mult(mult(a, c), mult(b, mult(a, b))) = mult(mult(a, c), mult(mult(a, b), b)))) | (~(mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(mult(a, c), mult(a, b)), b))))),
% 21.92/22.11 inference(unit_resolution,[status(thm)],[584, 1842])).
% 21.92/22.11 tff(1844,plain,
% 21.92/22.11 (mult(mult(a, c), mult(b, mult(a, b))) = mult(mult(a, c), mult(mult(a, b), b))),
% 21.92/22.11 inference(unit_resolution,[status(thm)],[576, 1843])).
% 21.92/22.11 tff(1845,plain,
% 21.92/22.11 (mult(mult(b, a), b) = mult(b, mult(a, b))),
% 21.92/22.11 inference(unit_resolution,[status(thm)],[1627, 1844, 1840])).
% 21.92/22.11 tff(1846,plain,
% 21.92/22.11 (mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(mult(a, c), mult(a, b)), b)),
% 21.92/22.11 inference(unit_resolution,[status(thm)],[1658, 1843])).
% 21.92/22.11 tff(1847,plain,
% 21.92/22.11 (ld(mult(a, c), mult(mult(a, c), mult(b, mult(a, b)))) = ld(mult(a, c), mult(mult(a, c), mult(mult(a, b), b)))),
% 21.92/22.11 inference(monotonicity,[status(thm)],[562])).
% 21.92/22.11 tff(1848,plain,
% 21.92/22.11 (ld(mult(a, c), mult(mult(a, c), mult(mult(a, b), b))) = ld(mult(a, c), mult(mult(a, c), mult(b, mult(a, b))))),
% 21.92/22.11 inference(symmetry,[status(thm)],[1847])).
% 21.92/22.11 tff(1849,plain,
% 21.92/22.11 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(a, c), mult(mult(a, c), mult(mult(a, b), b))) = mult(mult(a, b), b))),
% 21.92/22.11 inference(quant_inst,[status(thm)],[])).
% 21.92/22.11 tff(1850,plain,
% 21.92/22.11 (ld(mult(a, c), mult(mult(a, c), mult(mult(a, b), b))) = mult(mult(a, b), b)),
% 21.92/22.11 inference(unit_resolution,[status(thm)],[1849, 7])).
% 21.92/22.11 tff(1851,plain,
% 21.92/22.11 (mult(mult(a, b), b) = ld(mult(a, c), mult(mult(a, c), mult(mult(a, b), b)))),
% 21.92/22.11 inference(symmetry,[status(thm)],[1850])).
% 21.92/22.11 tff(1852,plain,
% 21.92/22.11 (mult(mult(a, b), b) = mult(mult(b, a), b)),
% 21.92/22.11 inference(transitivity,[status(thm)],[1851, 1848, 566, 1712])).
% 21.92/22.11 tff(1853,plain,
% 21.92/22.11 (mult(mult(a, c), mult(mult(a, b), b)) = mult(mult(a, c), mult(mult(b, a), b))),
% 21.92/22.11 inference(monotonicity,[status(thm)],[1852])).
% 21.92/22.11 tff(1854,plain,
% 21.92/22.11 (mult(mult(a, c), mult(mult(b, a), b)) = mult(mult(a, c), mult(mult(a, b), b))),
% 21.92/22.11 inference(symmetry,[status(thm)],[1853])).
% 21.92/22.11 tff(1855,plain,
% 21.92/22.11 (mult(mult(mult(a, b), c), mult(a, b)) = mult(mult(mult(mult(a, b), c), a), b)),
% 21.92/22.11 inference(symmetry,[status(thm)],[962])).
% 21.92/22.11 tff(1856,plain,
% 21.92/22.11 (mult(mult(mult(a, c), mult(a, b)), b) = mult(mult(a, c), mult(mult(a, b), b))),
% 21.92/22.11 inference(transitivity,[status(thm)],[1663, 949, 1855, 1798, 956, 1854])).
% 21.92/22.11 tff(1857,assumption,(~(mult(mult(mult(a, c), mult(a, b)), b) = mult(mult(a, c), mult(mult(a, b), b)))), introduced(assumption)).
% 21.92/22.11 tff(1858,plain,
% 21.92/22.11 ($false),
% 21.92/22.11 inference(unit_resolution,[status(thm)],[1857, 1856])).
% 21.92/22.11 tff(1859,plain,((~(mult(mult(b, a), b) = mult(b, mult(a, b)))) | (mult(mult(mult(a, c), mult(a, b)), b) = mult(mult(a, c), mult(mult(a, b), b))) | (~(mult(mult(mult(mult(a, b), c), a), b) = mult(mult(mult(a, b), c), mult(a, b)))) | (~(mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(mult(a, c), mult(a, b)), b))) | (~(mult(mult(a, c), mult(b, mult(a, b))) = mult(mult(a, c), mult(mult(a, b), b))))), inference(lemma,lemma(discharge,[]))).
% 21.92/22.12 tff(1860,plain,
% 21.92/22.12 (~(mult(mult(mult(mult(a, b), c), a), b) = mult(mult(mult(a, b), c), mult(a, b)))),
% 21.92/22.12 inference(unit_resolution,[status(thm)],[1859, 1846, 1845, 1844, 1841])).
% 21.92/22.12 tff(1861,plain,
% 21.92/22.12 ((~(mult(mult(mult(mult(a, b), c), b), a) = mult(mult(mult(a, b), c), mult(b, a)))) | (~(mult(mult(mult(mult(a, b), c), a), b) = mult(mult(mult(a, b), c), mult(a, b))))),
% 21.92/22.12 inference(unit_resolution,[status(thm)],[1096, 1860])).
% 21.92/22.12 tff(1862,plain,
% 21.92/22.12 (~((~(mult(mult(mult(mult(a, b), c), b), a) = mult(mult(mult(mult(a, b), c), a), b))) | (~(mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(a, b)))))),
% 21.92/22.12 inference(unit_resolution,[status(thm)],[641, 27, 1861])).
% 21.92/22.12 tff(1863,plain,
% 21.92/22.12 (((~(mult(mult(mult(mult(a, b), c), b), a) = mult(mult(mult(mult(a, b), c), a), b))) | (~(mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(a, b))))) | (mult(mult(mult(mult(a, b), c), b), a) = mult(mult(mult(mult(a, b), c), a), b))),
% 21.92/22.12 inference(tautology,[status(thm)],[])).
% 21.92/22.12 tff(1864,plain,
% 21.92/22.12 (mult(mult(mult(mult(a, b), c), b), a) = mult(mult(mult(mult(a, b), c), a), b)),
% 21.92/22.12 inference(unit_resolution,[status(thm)],[1863, 1862])).
% 21.92/22.12 tff(1865,plain,
% 21.92/22.12 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), unit), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), a), mult(mult(rd(mult(b, c), mult(a, c)), unit), rd(mult(b, c), mult(a, c)))))),
% 21.92/22.12 inference(quant_inst,[status(thm)],[])).
% 21.92/22.12 tff(1866,plain,
% 21.92/22.12 (mult(mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), unit), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), a), mult(mult(rd(mult(b, c), mult(a, c)), unit), rd(mult(b, c), mult(a, c))))),
% 21.92/22.12 inference(unit_resolution,[status(thm)],[1865, 56])).
% 21.92/22.12 tff(1867,plain,
% 21.92/22.12 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), mult(mult(unit, a), unit)) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a)),
% 21.92/22.12 inference(monotonicity,[status(thm)],[507])).
% 21.92/22.12 tff(1868,plain,
% 21.92/22.12 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), unit), a), unit) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), mult(mult(unit, a), unit)))),
% 21.92/22.12 inference(quant_inst,[status(thm)],[])).
% 21.92/22.12 tff(1869,plain,
% 21.92/22.12 (mult(mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), unit), a), unit) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), mult(mult(unit, a), unit))),
% 21.92/22.12 inference(unit_resolution,[status(thm)],[1868, 56])).
% 21.92/22.12 tff(1870,plain,
% 21.92/22.12 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), unit), c), unit) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)))),
% 21.92/22.12 inference(quant_inst,[status(thm)],[])).
% 21.92/22.12 tff(1871,plain,
% 21.92/22.12 (mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), unit), c), unit) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit))),
% 21.92/22.12 inference(unit_resolution,[status(thm)],[1870, 56])).
% 21.92/22.12 tff(1872,plain,
% 21.92/22.12 (mult(mult(rd(mult(b, c), mult(a, c)), a), unit) = mult(rd(mult(b, c), mult(a, c)), a)),
% 21.92/22.12 inference(transitivity,[status(thm)],[535, 530, 528])).
% 21.92/22.12 tff(1873,plain,
% 21.92/22.12 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), unit), c) = mult(mult(rd(mult(b, c), mult(a, c)), a), c)),
% 21.92/22.12 inference(monotonicity,[status(thm)],[1872])).
% 21.92/22.12 tff(1874,plain,
% 21.92/22.12 (mult(mult(rd(mult(b, c), mult(a, c)), a), c) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), unit), c)),
% 21.92/22.12 inference(symmetry,[status(thm)],[1873])).
% 21.92/22.12 tff(1875,plain,
% 21.92/22.12 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), unit) = mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), unit), c), unit)),
% 21.92/22.12 inference(monotonicity,[status(thm)],[1874])).
% 21.92/22.12 tff(1876,plain,
% 21.92/22.12 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), unit) = mult(mult(rd(mult(b, c), mult(a, c)), a), c)),
% 21.92/22.12 inference(transitivity,[status(thm)],[1875, 1871, 96])).
% 21.92/22.12 tff(1877,plain,
% 21.92/22.12 (mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), unit), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a)),
% 21.92/22.12 inference(monotonicity,[status(thm)],[1876])).
% 21.92/22.12 tff(1878,plain,
% 21.92/22.12 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a) = mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), unit), a)),
% 21.92/22.12 inference(symmetry,[status(thm)],[1877])).
% 21.92/22.12 tff(1879,plain,
% 21.92/22.12 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)) = mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), unit), a)),
% 21.92/22.12 inference(transitivity,[status(thm)],[1169, 1878])).
% 21.92/22.12 tff(1880,plain,
% 21.92/22.12 (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), unit) = mult(mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), unit), a), unit)),
% 21.92/22.12 inference(monotonicity,[status(thm)],[1879])).
% 21.92/22.12 tff(1881,plain,
% 21.92/22.12 (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))),
% 21.92/22.12 inference(transitivity,[status(thm)],[1811, 1492, 1561, 1168])).
% 21.92/22.12 tff(1882,plain,
% 21.92/22.12 (mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), unit) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), unit)),
% 21.92/22.12 inference(monotonicity,[status(thm)],[1881])).
% 21.92/22.12 tff(1883,plain,
% 21.92/22.12 (mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), unit) = mult(mult(b, c), a)),
% 21.92/22.12 inference(transitivity,[status(thm)],[1882, 1880, 1869, 1867, 1570])).
% 21.92/22.12 tff(1884,plain,
% 21.92/22.12 (mult(mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), unit), rd(mult(b, c), mult(a, c))) = mult(mult(mult(b, c), a), rd(mult(b, c), mult(a, c)))),
% 21.92/22.12 inference(monotonicity,[status(thm)],[1883])).
% 21.92/22.12 tff(1885,plain,
% 21.92/22.12 (mult(mult(mult(b, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), unit), rd(mult(b, c), mult(a, c)))),
% 21.92/22.12 inference(symmetry,[status(thm)],[1884])).
% 21.92/22.12 tff(1886,plain,
% 21.92/22.12 (mult(mult(mult(b, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), a), mult(mult(rd(mult(b, c), mult(a, c)), unit), rd(mult(b, c), mult(a, c))))),
% 21.92/22.12 inference(transitivity,[status(thm)],[1885, 1866])).
% 21.92/22.12 tff(1887,plain,
% 21.92/22.12 (mult(mult(mult(mult(b, c), a), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(mult(a, c), a), mult(mult(rd(mult(b, c), mult(a, c)), unit), rd(mult(b, c), mult(a, c)))), a)),
% 21.92/22.12 inference(monotonicity,[status(thm)],[1886])).
% 21.92/22.12 tff(1888,plain,
% 21.92/22.12 (mult(mult(mult(mult(a, c), a), mult(mult(rd(mult(b, c), mult(a, c)), unit), rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(mult(b, c), a), rd(mult(b, c), mult(a, c))), a)),
% 21.92/22.12 inference(symmetry,[status(thm)],[1887])).
% 21.92/22.12 tff(1889,plain,
% 21.92/22.12 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(a, c), a), mult(mult(rd(mult(b, c), mult(a, c)), unit), rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, c), mult(mult(a, mult(mult(rd(mult(b, c), mult(a, c)), unit), rd(mult(b, c), mult(a, c)))), a)))),
% 21.92/22.12 inference(quant_inst,[status(thm)],[])).
% 21.92/22.12 tff(1890,plain,
% 21.92/22.12 (mult(mult(mult(mult(a, c), a), mult(mult(rd(mult(b, c), mult(a, c)), unit), rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, c), mult(mult(a, mult(mult(rd(mult(b, c), mult(a, c)), unit), rd(mult(b, c), mult(a, c)))), a))),
% 21.92/22.12 inference(unit_resolution,[status(thm)],[1889, 56])).
% 21.92/22.12 tff(1891,plain,
% 21.92/22.12 (mult(mult(a, c), mult(mult(a, mult(mult(rd(mult(b, c), mult(a, c)), unit), rd(mult(b, c), mult(a, c)))), a)) = mult(mult(mult(mult(a, c), a), mult(mult(rd(mult(b, c), mult(a, c)), unit), rd(mult(b, c), mult(a, c)))), a)),
% 21.92/22.12 inference(symmetry,[status(thm)],[1890])).
% 21.92/22.12 tff(1892,plain,
% 21.92/22.12 ((~![A: $i] : (mult(unit, A) = A)) | (mult(unit, rd(mult(b, c), mult(a, c))) = rd(mult(b, c), mult(a, c)))),
% 21.92/22.12 inference(quant_inst,[status(thm)],[])).
% 21.92/22.12 tff(1893,plain,
% 21.92/22.12 (mult(unit, rd(mult(b, c), mult(a, c))) = rd(mult(b, c), mult(a, c))),
% 21.92/22.12 inference(unit_resolution,[status(thm)],[1892, 71])).
% 21.92/22.12 tff(1894,plain,
% 21.92/22.12 ((~![A: $i] : (mult(A, unit) = A)) | (mult(mult(unit, rd(mult(b, c), mult(a, c))), unit) = mult(unit, rd(mult(b, c), mult(a, c))))),
% 21.92/22.12 inference(quant_inst,[status(thm)],[])).
% 21.92/22.12 tff(1895,plain,
% 21.92/22.12 (mult(mult(unit, rd(mult(b, c), mult(a, c))), unit) = mult(unit, rd(mult(b, c), mult(a, c)))),
% 21.92/22.12 inference(unit_resolution,[status(thm)],[1894, 43])).
% 21.92/22.12 tff(1896,plain,
% 21.92/22.12 (mult(mult(unit, rd(mult(b, c), mult(a, c))), unit) = rd(mult(b, c), mult(a, c))),
% 21.92/22.12 inference(transitivity,[status(thm)],[1895, 1893])).
% 21.92/22.12 tff(1897,plain,
% 21.92/22.12 (mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(a, rd(mult(b, c), mult(a, c)))),
% 21.92/22.12 inference(monotonicity,[status(thm)],[1896])).
% 21.92/22.12 tff(1898,plain,
% 21.92/22.12 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(a, unit), rd(mult(b, c), mult(a, c))), unit) = mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))),
% 21.92/22.12 inference(quant_inst,[status(thm)],[])).
% 21.92/22.12 tff(1899,plain,
% 21.92/22.12 (mult(mult(mult(a, unit), rd(mult(b, c), mult(a, c))), unit) = mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))),
% 21.92/22.12 inference(unit_resolution,[status(thm)],[1898, 56])).
% 21.92/22.12 tff(1900,plain,
% 21.92/22.12 (mult(mult(a, unit), rd(mult(b, c), mult(a, c))) = mult(a, rd(mult(b, c), mult(a, c)))),
% 21.92/22.12 inference(monotonicity,[status(thm)],[47])).
% 21.92/22.12 tff(1901,plain,
% 21.92/22.12 (mult(a, rd(mult(b, c), mult(a, c))) = mult(mult(a, unit), rd(mult(b, c), mult(a, c)))),
% 21.92/22.12 inference(symmetry,[status(thm)],[1900])).
% 21.92/22.12 tff(1902,plain,
% 21.92/22.12 (mult(mult(a, rd(mult(b, c), mult(a, c))), unit) = mult(mult(mult(a, unit), rd(mult(b, c), mult(a, c))), unit)),
% 21.92/22.12 inference(monotonicity,[status(thm)],[1901])).
% 21.92/22.12 tff(1903,plain,
% 21.92/22.12 (mult(mult(a, rd(mult(b, c), mult(a, c))), unit) = b),
% 21.92/22.12 inference(transitivity,[status(thm)],[1902, 1899, 1897, 471, 1834, 364])).
% 21.92/22.12 tff(1904,plain,
% 21.92/22.12 (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), unit), rd(mult(b, c), mult(a, c))) = mult(b, rd(mult(b, c), mult(a, c)))),
% 21.92/22.12 inference(monotonicity,[status(thm)],[1903])).
% 21.92/22.12 tff(1905,plain,
% 21.92/22.12 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), unit), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), unit), rd(mult(b, c), mult(a, c)))))),
% 21.92/22.12 inference(quant_inst,[status(thm)],[])).
% 21.92/22.12 tff(1906,plain,
% 21.92/22.12 (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), unit), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), unit), rd(mult(b, c), mult(a, c))))),
% 21.92/22.12 inference(unit_resolution,[status(thm)],[1905, 56])).
% 21.92/22.12 tff(1907,plain,
% 21.92/22.12 (mult(a, mult(mult(rd(mult(b, c), mult(a, c)), unit), rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), unit), rd(mult(b, c), mult(a, c)))),
% 21.92/22.12 inference(symmetry,[status(thm)],[1906])).
% 21.92/22.12 tff(1908,plain,
% 21.92/22.12 (mult(a, mult(mult(rd(mult(b, c), mult(a, c)), unit), rd(mult(b, c), mult(a, c)))) = mult(b, rd(mult(b, c), mult(a, c)))),
% 21.92/22.12 inference(transitivity,[status(thm)],[1907, 1904])).
% 21.92/22.12 tff(1909,plain,
% 21.92/22.12 (mult(mult(a, mult(mult(rd(mult(b, c), mult(a, c)), unit), rd(mult(b, c), mult(a, c)))), a) = mult(mult(b, rd(mult(b, c), mult(a, c))), a)),
% 21.92/22.12 inference(monotonicity,[status(thm)],[1908])).
% 21.92/22.12 tff(1910,plain,
% 21.92/22.12 (mult(mult(a, c), mult(mult(a, mult(mult(rd(mult(b, c), mult(a, c)), unit), rd(mult(b, c), mult(a, c)))), a)) = mult(mult(a, c), mult(mult(b, rd(mult(b, c), mult(a, c))), a))),
% 21.92/22.12 inference(monotonicity,[status(thm)],[1909])).
% 21.92/22.12 tff(1911,plain,
% 21.92/22.12 (mult(mult(a, c), mult(mult(b, rd(mult(b, c), mult(a, c))), a)) = mult(mult(a, c), mult(mult(a, mult(mult(rd(mult(b, c), mult(a, c)), unit), rd(mult(b, c), mult(a, c)))), a))),
% 21.92/22.12 inference(symmetry,[status(thm)],[1910])).
% 21.92/22.12 tff(1912,plain,
% 21.92/22.12 (mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(b, a)),
% 21.92/22.12 inference(symmetry,[status(thm)],[1837])).
% 21.92/22.12 tff(1913,plain,
% 21.92/22.12 (mult(a, b) = mult(b, a)),
% 21.92/22.12 inference(transitivity,[status(thm)],[1574, 1334, 1912])).
% 21.92/22.12 tff(1914,plain,
% 21.92/22.12 (mult(b, mult(a, b)) = mult(b, mult(b, a))),
% 21.92/22.12 inference(monotonicity,[status(thm)],[1913])).
% 21.92/22.12 tff(1915,plain,
% 21.92/22.12 (mult(b, mult(b, a)) = mult(b, mult(a, b))),
% 21.92/22.12 inference(symmetry,[status(thm)],[1914])).
% 21.92/22.12 tff(1916,plain,
% 21.92/22.12 (mult(b, mult(a, b)) = mult(b, mult(b, a))),
% 21.92/22.12 inference(unit_resolution,[status(thm)],[413, 1540])).
% 21.92/22.12 tff(1917,plain,
% 21.92/22.12 (mult(b, mult(b, a)) = mult(b, mult(a, b))),
% 21.92/22.12 inference(symmetry,[status(thm)],[1916])).
% 21.92/22.12 tff(1918,plain,
% 21.92/22.12 (ld(b, mult(b, mult(b, a))) = ld(b, mult(b, mult(a, b)))),
% 21.92/22.12 inference(monotonicity,[status(thm)],[1917])).
% 21.92/22.12 tff(1919,plain,
% 21.92/22.12 (ld(b, mult(b, mult(a, b))) = ld(b, mult(b, mult(b, a)))),
% 21.92/22.12 inference(symmetry,[status(thm)],[1918])).
% 21.92/22.12 tff(1920,plain,
% 21.92/22.12 (mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(b, a)),
% 21.92/22.12 inference(transitivity,[status(thm)],[1287, 913, 397, 1919, 390])).
% 21.92/22.12 tff(1921,plain,
% 21.92/22.12 (rd(mult(mult(a, rd(mult(b, c), mult(a, c))), a), a) = rd(mult(b, a), a)),
% 21.92/22.12 inference(monotonicity,[status(thm)],[1920])).
% 21.92/22.12 tff(1922,plain,
% 21.92/22.12 (mult(a, rd(mult(b, c), mult(a, c))) = b),
% 21.92/22.12 inference(transitivity,[status(thm)],[1456, 1921, 1451])).
% 21.92/22.12 tff(1923,plain,
% 21.92/22.12 (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), b)),
% 21.92/22.12 inference(monotonicity,[status(thm)],[1922])).
% 21.92/22.12 tff(1924,plain,
% 21.92/22.12 (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))),
% 21.92/22.12 inference(transitivity,[status(thm)],[1923, 405])).
% 21.92/22.12 tff(1925,plain,
% 21.92/22.12 (~(mult(b, mult(c, a)) = mult(b, mult(a, c)))),
% 21.92/22.12 inference(unit_resolution,[status(thm)],[377, 1924, 354, 97])).
% 21.92/22.12 tff(1926,plain,
% 21.92/22.12 ((~(mult(mult(b, c), a) = mult(mult(b, a), c))) | (~(mult(b, mult(c, a)) = mult(b, mult(a, c))))),
% 21.92/22.12 inference(unit_resolution,[status(thm)],[379, 1925])).
% 21.92/22.12 tff(1927,plain,
% 21.92/22.12 (~((~(mult(mult(b, c), a) = mult(b, mult(c, a)))) | (~(mult(mult(b, a), c) = mult(b, mult(a, c)))))),
% 21.92/22.12 inference(unit_resolution,[status(thm)],[384, 1926])).
% 21.92/22.12 tff(1928,plain,
% 21.92/22.12 (mult(mult(b, a), c) = mult(b, mult(a, c))),
% 21.92/22.12 inference(unit_resolution,[status(thm)],[386, 1927])).
% 21.92/22.12 tff(1929,plain,
% 21.92/22.12 (mult(b, mult(a, c)) = mult(mult(b, a), c)),
% 21.92/22.12 inference(symmetry,[status(thm)],[1928])).
% 21.92/22.12 tff(1930,plain,
% 21.92/22.12 (mult(mult(b, c), a) = mult(b, mult(c, a))),
% 21.92/22.12 inference(unit_resolution,[status(thm)],[1432, 1927])).
% 21.92/22.12 tff(1931,plain,
% 21.92/22.12 (mult(b, mult(c, a)) = mult(mult(b, c), a)),
% 21.92/22.12 inference(symmetry,[status(thm)],[1930])).
% 21.92/22.12 tff(1932,plain,
% 21.92/22.12 ((mult(b, mult(c, a)) = mult(b, mult(a, c))) <=> (mult(mult(b, c), a) = mult(mult(b, a), c))),
% 21.92/22.12 inference(monotonicity,[status(thm)],[1931, 1929])).
% 21.92/22.12 tff(1933,plain,
% 21.92/22.12 ((mult(mult(b, c), a) = mult(mult(b, a), c)) <=> (mult(b, mult(c, a)) = mult(b, mult(a, c)))),
% 21.92/22.12 inference(symmetry,[status(thm)],[1932])).
% 21.92/22.12 tff(1934,plain,
% 21.92/22.12 (mult(b, a) = mult(c, ld(c, mult(a, b)))),
% 21.92/22.12 inference(transitivity,[status(thm)],[939, 1918, 396, 1441])).
% 21.92/22.12 tff(1935,plain,
% 21.92/22.12 (mult(c, mult(b, a)) = mult(c, mult(c, ld(c, mult(a, b))))),
% 21.92/22.12 inference(monotonicity,[status(thm)],[1934])).
% 21.92/22.12 tff(1936,plain,
% 21.92/22.12 (mult(c, mult(b, a)) = mult(c, mult(a, b))),
% 21.92/22.12 inference(transitivity,[status(thm)],[1935, 1443])).
% 21.92/22.12 tff(1937,plain,
% 21.92/22.12 (mult(mult(b, a), b) = mult(mult(b, b), a)),
% 21.92/22.12 inference(unit_resolution,[status(thm)],[1135, 1540])).
% 21.92/22.12 tff(1938,plain,
% 21.92/22.12 (~(mult(mult(a, c), mult(b, mult(a, b))) = mult(mult(a, c), mult(mult(a, b), b)))),
% 21.92/22.12 inference(unit_resolution,[status(thm)],[1537, 1916, 1526, 1937])).
% 21.92/22.12 tff(1939,plain,
% 21.92/22.12 ((~(mult(mult(a, c), mult(b, mult(a, b))) = mult(mult(a, c), mult(mult(a, b), b)))) | (~(mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(mult(a, c), mult(a, b)), b)))),
% 21.92/22.12 inference(unit_resolution,[status(thm)],[576, 1938])).
% 21.92/22.12 tff(1940,plain,
% 21.92/22.12 (~((~(mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(a, c), mult(b, mult(a, b))))) | (~(mult(mult(mult(a, c), mult(a, b)), b) = mult(mult(a, c), mult(mult(a, b), b)))))),
% 21.92/22.12 inference(unit_resolution,[status(thm)],[584, 1939])).
% 21.92/22.12 tff(1941,plain,
% 21.92/22.12 (mult(mult(mult(a, c), mult(a, b)), b) = mult(mult(a, c), mult(mult(a, b), b))),
% 21.92/22.12 inference(unit_resolution,[status(thm)],[586, 1940])).
% 21.92/22.12 tff(1942,plain,
% 21.92/22.12 (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))),
% 21.92/22.12 inference(unit_resolution,[status(thm)],[402, 1928, 1916, 97, 1924])).
% 21.92/22.12 tff(1943,plain,
% 21.92/22.12 ((~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))),
% 21.92/22.12 inference(unit_resolution,[status(thm)],[278, 1942])).
% 21.92/22.12 tff(1944,plain,
% 21.92/22.12 (~((~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))),
% 21.92/22.12 inference(unit_resolution,[status(thm)],[276, 1943])).
% 21.92/22.12 tff(1945,plain,
% 21.92/22.12 (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))),
% 21.92/22.12 inference(unit_resolution,[status(thm)],[271, 1944])).
% 21.92/22.12 tff(1946,plain,
% 21.92/22.12 (mult(mult(b, c), a) = mult(mult(b, a), c)),
% 21.92/22.12 inference(unit_resolution,[status(thm)],[1521, 1945, 97, 1941, 1936])).
% 21.92/22.12 tff(1947,plain,
% 21.92/22.12 (mult(b, mult(c, a)) = mult(b, mult(a, c))),
% 21.92/22.12 inference(modus_ponens,[status(thm)],[1946, 1933])).
% 21.92/22.12 tff(1948,plain,
% 21.92/22.12 ($false),
% 21.92/22.12 inference(unit_resolution,[status(thm)],[1925, 1947])).
% 21.92/22.12 tff(1949,plain,((mult(mult(b, b), a) = mult(b, mult(b, a))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit))))) | (mult(rd(mult(b, c), mult(a, c)), mult(c, a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, c))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a))))), inference(lemma,lemma(discharge,[]))).
% 21.92/22.12 tff(1950,plain,
% 21.92/22.12 (mult(mult(b, b), a) = mult(b, mult(b, a))),
% 21.92/22.12 inference(unit_resolution,[status(thm)],[1949, 97, 354, 1287])).
% 21.92/22.12 tff(1951,plain,
% 21.92/22.12 (mult(mult(unit, mult(mult(b, unit), b)), a) = mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a)),
% 21.92/22.12 inference(transitivity,[status(thm)],[435, 1950, 1915, 1290, 470])).
% 21.92/22.12 tff(1952,plain,
% 21.92/22.12 (rd(mult(mult(unit, mult(mult(b, unit), b)), a), a) = rd(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a), a)),
% 21.92/22.13 inference(monotonicity,[status(thm)],[1951])).
% 21.92/22.13 tff(1953,plain,
% 21.92/22.13 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(a, mult(a, mult(unit, mult(mult(b, unit), b)))) = mult(unit, mult(mult(b, unit), b)))),
% 21.92/22.13 inference(quant_inst,[status(thm)],[])).
% 21.92/22.13 tff(1954,plain,
% 21.92/22.13 (ld(a, mult(a, mult(unit, mult(mult(b, unit), b)))) = mult(unit, mult(mult(b, unit), b))),
% 21.92/22.13 inference(unit_resolution,[status(thm)],[1953, 7])).
% 21.92/22.13 tff(1955,plain,
% 21.92/22.13 (mult(mult(a, b), b) = mult(mult(b, a), b)),
% 21.92/22.13 inference(monotonicity,[status(thm)],[1913])).
% 21.92/22.13 tff(1956,plain,
% 21.92/22.13 (mult(mult(b, a), b) = mult(mult(a, b), b)),
% 21.92/22.13 inference(symmetry,[status(thm)],[1955])).
% 21.92/22.13 tff(1957,plain,
% 21.92/22.13 (mult(b, mult(a, b)) = mult(mult(b, a), b)),
% 21.92/22.13 inference(symmetry,[status(thm)],[1845])).
% 21.92/22.13 tff(1958,plain,
% 21.92/22.13 (mult(mult(a, b), rd(mult(b, c), mult(a, c))) = mult(mult(b, a), rd(mult(b, c), mult(a, c)))),
% 21.92/22.13 inference(monotonicity,[status(thm)],[1913])).
% 21.92/22.13 tff(1959,plain,
% 21.92/22.13 (mult(a, rd(mult(b, c), mult(a, c))) = b),
% 21.92/22.13 inference(transitivity,[status(thm)],[471, 1834, 364])).
% 21.92/22.13 tff(1960,plain,
% 21.92/22.13 (mult(a, mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, b)),
% 21.92/22.13 inference(monotonicity,[status(thm)],[1959])).
% 21.92/22.13 tff(1961,plain,
% 21.92/22.13 (mult(mult(a, a), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(mult(a, a), rd(mult(b, c), mult(a, c)))),
% 21.92/22.13 inference(monotonicity,[status(thm)],[1896])).
% 21.92/22.13 tff(1962,plain,
% 21.92/22.13 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(a, a), unit), rd(mult(b, c), mult(a, c))), unit) = mult(mult(a, a), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))),
% 21.92/22.13 inference(quant_inst,[status(thm)],[])).
% 21.92/22.13 tff(1963,plain,
% 21.92/22.13 (mult(mult(mult(mult(a, a), unit), rd(mult(b, c), mult(a, c))), unit) = mult(mult(a, a), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))),
% 21.92/22.13 inference(unit_resolution,[status(thm)],[1962, 56])).
% 21.92/22.13 tff(1964,plain,
% 21.92/22.13 (mult(a, mult(mult(unit, a), unit)) = mult(a, a)),
% 21.92/22.13 inference(monotonicity,[status(thm)],[507])).
% 21.92/22.13 tff(1965,plain,
% 21.92/22.13 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(a, unit), a), unit) = mult(a, mult(mult(unit, a), unit)))),
% 21.92/22.13 inference(quant_inst,[status(thm)],[])).
% 21.92/22.13 tff(1966,plain,
% 21.92/22.13 (mult(mult(mult(a, unit), a), unit) = mult(a, mult(mult(unit, a), unit))),
% 21.92/22.13 inference(unit_resolution,[status(thm)],[1965, 56])).
% 21.92/22.13 tff(1967,plain,
% 21.92/22.13 (mult(mult(a, a), unit) = mult(mult(mult(a, unit), a), unit)),
% 21.92/22.13 inference(monotonicity,[status(thm)],[520])).
% 21.92/22.13 tff(1968,plain,
% 21.92/22.13 (mult(mult(a, a), unit) = mult(a, a)),
% 21.92/22.13 inference(transitivity,[status(thm)],[1967, 1966, 1964])).
% 21.92/22.13 tff(1969,plain,
% 21.92/22.13 (mult(mult(mult(a, a), unit), rd(mult(b, c), mult(a, c))) = mult(mult(a, a), rd(mult(b, c), mult(a, c)))),
% 21.92/22.13 inference(monotonicity,[status(thm)],[1968])).
% 21.92/22.13 tff(1970,plain,
% 21.92/22.13 (mult(mult(a, a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, a), unit), rd(mult(b, c), mult(a, c)))),
% 21.92/22.13 inference(symmetry,[status(thm)],[1969])).
% 21.92/22.13 tff(1971,plain,
% 21.92/22.13 (mult(a, mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, a), rd(mult(b, c), mult(a, c)))),
% 21.92/22.13 inference(symmetry,[status(thm)],[1361])).
% 21.92/22.13 tff(1972,plain,
% 21.92/22.13 (mult(a, mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, a), unit), rd(mult(b, c), mult(a, c)))),
% 21.92/22.13 inference(transitivity,[status(thm)],[1971, 1970])).
% 21.92/22.13 tff(1973,plain,
% 21.92/22.13 (mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), unit) = mult(mult(mult(mult(a, a), unit), rd(mult(b, c), mult(a, c))), unit)),
% 21.92/22.13 inference(monotonicity,[status(thm)],[1972])).
% 21.92/22.13 tff(1974,plain,
% 21.92/22.13 (mult(mult(mult(a, a), rd(mult(b, c), mult(a, c))), unit) = mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), unit)),
% 21.92/22.13 inference(monotonicity,[status(thm)],[1361])).
% 21.92/22.13 tff(1975,plain,
% 21.92/22.13 (mult(mult(mult(a, a), rd(mult(b, c), mult(a, c))), unit) = mult(a, b)),
% 21.92/22.13 inference(transitivity,[status(thm)],[1974, 1973, 1963, 1961, 1361, 1960])).
% 21.92/22.13 tff(1976,plain,
% 21.92/22.13 (mult(mult(mult(mult(a, a), rd(mult(b, c), mult(a, c))), unit), rd(mult(b, c), mult(a, c))) = mult(mult(a, b), rd(mult(b, c), mult(a, c)))),
% 21.92/22.13 inference(monotonicity,[status(thm)],[1975])).
% 21.92/22.13 tff(1977,plain,
% 21.92/22.13 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(a, a), rd(mult(b, c), mult(a, c))), unit), rd(mult(b, c), mult(a, c))) = mult(mult(a, a), mult(mult(rd(mult(b, c), mult(a, c)), unit), rd(mult(b, c), mult(a, c)))))),
% 21.92/22.13 inference(quant_inst,[status(thm)],[])).
% 21.92/22.13 tff(1978,plain,
% 21.92/22.13 (mult(mult(mult(mult(a, a), rd(mult(b, c), mult(a, c))), unit), rd(mult(b, c), mult(a, c))) = mult(mult(a, a), mult(mult(rd(mult(b, c), mult(a, c)), unit), rd(mult(b, c), mult(a, c))))),
% 21.92/22.13 inference(unit_resolution,[status(thm)],[1977, 56])).
% 21.92/22.13 tff(1979,plain,
% 21.92/22.13 (mult(mult(a, a), mult(mult(rd(mult(b, c), mult(a, c)), unit), rd(mult(b, c), mult(a, c)))) = mult(mult(mult(mult(a, a), rd(mult(b, c), mult(a, c))), unit), rd(mult(b, c), mult(a, c)))),
% 21.92/22.13 inference(symmetry,[status(thm)],[1978])).
% 21.92/22.13 tff(1980,plain,
% 21.92/22.13 (mult(mult(a, a), mult(mult(rd(mult(b, c), mult(a, c)), unit), rd(mult(b, c), mult(a, c)))) = mult(mult(b, a), rd(mult(b, c), mult(a, c)))),
% 21.92/22.13 inference(transitivity,[status(thm)],[1979, 1976, 1958])).
% 21.92/22.13 tff(1981,plain,
% 21.92/22.13 (mult(mult(mult(a, a), mult(mult(rd(mult(b, c), mult(a, c)), unit), rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a)),
% 21.92/22.13 inference(monotonicity,[status(thm)],[1980])).
% 21.92/22.13 tff(1982,plain,
% 21.92/22.13 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(a, a), mult(mult(rd(mult(b, c), mult(a, c)), unit), rd(mult(b, c), mult(a, c)))), a) = mult(a, mult(mult(a, mult(mult(rd(mult(b, c), mult(a, c)), unit), rd(mult(b, c), mult(a, c)))), a)))),
% 21.92/22.13 inference(quant_inst,[status(thm)],[])).
% 21.92/22.13 tff(1983,plain,
% 21.92/22.13 (mult(mult(mult(a, a), mult(mult(rd(mult(b, c), mult(a, c)), unit), rd(mult(b, c), mult(a, c)))), a) = mult(a, mult(mult(a, mult(mult(rd(mult(b, c), mult(a, c)), unit), rd(mult(b, c), mult(a, c)))), a))),
% 21.92/22.13 inference(unit_resolution,[status(thm)],[1982, 56])).
% 21.92/22.13 tff(1984,plain,
% 21.92/22.13 (mult(a, mult(mult(a, mult(mult(rd(mult(b, c), mult(a, c)), unit), rd(mult(b, c), mult(a, c)))), a)) = mult(mult(mult(a, a), mult(mult(rd(mult(b, c), mult(a, c)), unit), rd(mult(b, c), mult(a, c)))), a)),
% 21.92/22.13 inference(symmetry,[status(thm)],[1983])).
% 21.92/22.13 tff(1985,plain,
% 21.92/22.13 (mult(mult(b, rd(mult(b, c), mult(a, c))), a) = mult(mult(a, mult(mult(rd(mult(b, c), mult(a, c)), unit), rd(mult(b, c), mult(a, c)))), a)),
% 21.92/22.13 inference(symmetry,[status(thm)],[1909])).
% 21.92/22.13 tff(1986,plain,
% 21.92/22.13 (mult(a, mult(mult(b, rd(mult(b, c), mult(a, c))), a)) = mult(a, mult(mult(a, mult(mult(rd(mult(b, c), mult(a, c)), unit), rd(mult(b, c), mult(a, c)))), a))),
% 21.92/22.13 inference(monotonicity,[status(thm)],[1985])).
% 21.92/22.13 tff(1987,plain,
% 21.92/22.13 (mult(a, mult(mult(b, rd(mult(b, c), mult(a, c))), a)) = mult(a, mult(unit, mult(mult(b, unit), b)))),
% 21.92/22.13 inference(transitivity,[status(thm)],[1986, 1984, 1981, 469, 1289, 1957, 1956, 442, 439, 437, 830])).
% 21.92/22.13 tff(1988,plain,
% 21.92/22.13 (ld(a, mult(a, mult(mult(b, rd(mult(b, c), mult(a, c))), a))) = ld(a, mult(a, mult(unit, mult(mult(b, unit), b))))),
% 21.92/22.13 inference(monotonicity,[status(thm)],[1987])).
% 21.92/22.13 tff(1989,plain,
% 21.92/22.13 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(a, mult(a, mult(mult(b, rd(mult(b, c), mult(a, c))), a))) = mult(mult(b, rd(mult(b, c), mult(a, c))), a))),
% 21.92/22.13 inference(quant_inst,[status(thm)],[])).
% 21.92/22.13 tff(1990,plain,
% 21.92/22.13 (ld(a, mult(a, mult(mult(b, rd(mult(b, c), mult(a, c))), a))) = mult(mult(b, rd(mult(b, c), mult(a, c))), a)),
% 21.92/22.13 inference(unit_resolution,[status(thm)],[1989, 7])).
% 21.92/22.13 tff(1991,plain,
% 21.92/22.13 (mult(mult(b, rd(mult(b, c), mult(a, c))), a) = ld(a, mult(a, mult(mult(b, rd(mult(b, c), mult(a, c))), a)))),
% 21.92/22.13 inference(symmetry,[status(thm)],[1990])).
% 21.92/22.13 tff(1992,plain,
% 21.92/22.13 (mult(mult(b, rd(mult(b, c), mult(a, c))), a) = mult(mult(b, a), rd(mult(b, c), mult(a, c)))),
% 21.92/22.13 inference(transitivity,[status(thm)],[1991, 1988, 1954, 553, 1952, 546])).
% 21.92/22.13 tff(1993,plain,
% 21.92/22.13 (mult(mult(a, c), mult(mult(b, rd(mult(b, c), mult(a, c))), a)) = mult(mult(unit, mult(a, c)), mult(mult(b, a), rd(mult(b, c), mult(a, c))))),
% 21.92/22.13 inference(monotonicity,[status(thm)],[1551, 1992])).
% 21.92/22.13 tff(1994,plain,
% 21.92/22.13 (mult(mult(unit, mult(a, c)), mult(mult(b, a), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(mult(b, rd(mult(b, c), mult(a, c))), a))),
% 21.92/22.13 inference(symmetry,[status(thm)],[1993])).
% 21.92/22.13 tff(1995,plain,
% 21.92/22.13 (rd(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a), a) = rd(mult(mult(unit, mult(mult(b, unit), b)), a), a)),
% 21.92/22.13 inference(symmetry,[status(thm)],[1952])).
% 21.92/22.13 tff(1996,plain,
% 21.92/22.13 (mult(mult(b, a), rd(mult(b, c), mult(a, c))) = mult(unit, mult(mult(b, unit), b))),
% 21.92/22.13 inference(transitivity,[status(thm)],[690, 1995, 552])).
% 21.92/22.13 tff(1997,plain,
% 21.92/22.13 (mult(mult(unit, mult(a, c)), mult(mult(b, a), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(unit, mult(mult(b, unit), b)))),
% 21.92/22.13 inference(monotonicity,[status(thm)],[1549, 1996])).
% 21.92/22.13 tff(1998,plain,
% 21.92/22.13 (mult(mult(a, c), mult(unit, mult(mult(b, unit), b))) = mult(mult(unit, mult(a, c)), mult(mult(b, a), rd(mult(b, c), mult(a, c))))),
% 21.92/22.13 inference(symmetry,[status(thm)],[1997])).
% 21.92/22.13 tff(1999,plain,
% 21.92/22.13 (mult(mult(mult(a, b), c), b) = mult(mult(b, c), mult(a, b))),
% 21.92/22.13 inference(transitivity,[status(thm)],[1709, 868, 1708, 1998, 1994, 1911, 1891, 1888, 1214, 1577])).
% 21.92/22.13 tff(2000,plain,
% 21.92/22.13 (mult(mult(mult(mult(a, b), c), b), a) = mult(mult(mult(b, c), mult(a, b)), a)),
% 21.92/22.13 inference(monotonicity,[status(thm)],[1999])).
% 21.92/22.13 tff(2001,plain,
% 21.92/22.13 (mult(mult(mult(b, c), mult(a, b)), a) = mult(mult(mult(mult(a, b), c), b), a)),
% 21.92/22.13 inference(symmetry,[status(thm)],[2000])).
% 21.92/22.13 tff(2002,plain,
% 21.92/22.13 ((mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), a))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(mult(a, b), a))) <=> (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(mult(a, b), a)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), a))))),
% 21.92/22.13 inference(commutativity,[status(thm)],[])).
% 21.92/22.13 tff(2003,plain,
% 21.92/22.13 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(mult(a, b), a)) = mult(mult(b, c), mult(mult(a, b), a))),
% 21.92/22.13 inference(monotonicity,[status(thm)],[1491])).
% 21.92/22.13 tff(2004,plain,
% 21.92/22.13 (mult(mult(b, c), mult(mult(a, b), a)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(mult(a, b), a))),
% 21.92/22.13 inference(symmetry,[status(thm)],[2003])).
% 21.92/22.13 tff(2005,plain,
% 21.92/22.13 (mult(rd(mult(b, c), mult(a, c)), a) = mult(b, unit)),
% 21.92/22.13 inference(transitivity,[status(thm)],[175, 172, 170, 431])).
% 21.92/22.13 tff(2006,plain,
% 21.92/22.13 (mult(mult(rd(mult(b, c), mult(a, c)), a), b) = mult(mult(b, unit), b)),
% 21.92/22.13 inference(monotonicity,[status(thm)],[2005])).
% 21.92/22.13 tff(2007,plain,
% 21.92/22.13 (mult(mult(rd(mult(b, c), mult(a, c)), a), b) = mult(unit, mult(mult(b, unit), b))),
% 21.92/22.13 inference(transitivity,[status(thm)],[2006, 430])).
% 21.92/22.13 tff(2008,plain,
% 21.92/22.13 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), b), a) = mult(mult(unit, mult(mult(b, unit), b)), a)),
% 21.92/22.13 inference(monotonicity,[status(thm)],[2007])).
% 21.92/22.13 tff(2009,plain,
% 21.92/22.13 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), b), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), a)))),
% 21.92/22.13 inference(quant_inst,[status(thm)],[])).
% 21.92/22.13 tff(2010,plain,
% 21.92/22.13 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), b), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), a))),
% 21.92/22.13 inference(unit_resolution,[status(thm)],[2009, 56])).
% 21.92/22.13 tff(2011,plain,
% 21.92/22.13 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), a)) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), b), a)),
% 21.92/22.13 inference(symmetry,[status(thm)],[2010])).
% 21.92/22.13 tff(2012,plain,
% 21.92/22.13 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), a)) = mult(unit, mult(mult(mult(b, unit), b), a))),
% 21.92/22.13 inference(transitivity,[status(thm)],[2011, 2008, 465])).
% 21.92/22.13 tff(2013,plain,
% 21.92/22.13 (mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), a))) = mult(mult(a, c), mult(unit, mult(mult(mult(b, unit), b), a)))),
% 21.92/22.13 inference(monotonicity,[status(thm)],[2012])).
% 21.92/22.13 tff(2014,plain,
% 21.92/22.13 (mult(mult(a, c), mult(unit, mult(mult(mult(b, unit), b), a))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), a)))),
% 21.92/22.13 inference(symmetry,[status(thm)],[2013])).
% 21.92/22.13 tff(2015,plain,
% 21.92/22.13 (mult(unit, mult(mult(mult(b, unit), b), a)) = mult(b, mult(a, b))),
% 21.92/22.13 inference(transitivity,[status(thm)],[466, 435, 1950, 1915])).
% 21.92/22.13 tff(2016,plain,
% 21.92/22.13 (mult(mult(a, c), mult(unit, mult(mult(mult(b, unit), b), a))) = mult(mult(a, c), mult(b, mult(a, b)))),
% 21.92/22.13 inference(monotonicity,[status(thm)],[2015])).
% 21.92/22.13 tff(2017,plain,
% 21.92/22.13 (mult(mult(a, c), mult(b, mult(a, b))) = mult(mult(a, c), mult(unit, mult(mult(mult(b, unit), b), a)))),
% 21.92/22.13 inference(symmetry,[status(thm)],[2016])).
% 21.92/22.13 tff(2018,plain,
% 21.92/22.13 (mult(mult(a, c), mult(mult(a, b), b)) = mult(mult(a, c), mult(b, mult(a, b)))),
% 21.92/22.13 inference(symmetry,[status(thm)],[1844])).
% 21.92/22.13 tff(2019,plain,
% 21.92/22.13 (mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b)))) = mult(mult(a, c), mult(mult(a, b), b))),
% 21.92/22.13 inference(symmetry,[status(thm)],[1530])).
% 21.92/22.13 tff(2020,plain,
% 21.92/22.13 (mult(a, mult(unit, mult(mult(b, unit), b))) = mult(mult(b, a), b)),
% 21.92/22.13 inference(transitivity,[status(thm)],[829, 436, 445, 441, 1955])).
% 21.92/22.13 tff(2021,plain,
% 21.92/22.13 (mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b)))) = mult(mult(a, c), mult(mult(b, a), b))),
% 21.92/22.13 inference(monotonicity,[status(thm)],[2020])).
% 21.92/22.13 tff(2022,plain,
% 21.92/22.13 (mult(mult(a, c), mult(mult(b, a), b)) = mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b))))),
% 21.92/22.13 inference(symmetry,[status(thm)],[2021])).
% 21.92/22.13 tff(2023,plain,
% 21.92/22.13 (mult(mult(mult(b, c), mult(a, b)), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), a)))),
% 21.92/22.13 inference(transitivity,[status(thm)],[2001, 1864, 1798, 956, 2022, 2019, 2018, 2017, 2014])).
% 21.92/22.13 tff(2024,plain,
% 21.92/22.13 ((mult(mult(mult(b, c), mult(a, b)), a) = mult(mult(b, c), mult(mult(a, b), a))) <=> (mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), a))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(mult(a, b), a)))),
% 21.92/22.13 inference(monotonicity,[status(thm)],[2023, 2004])).
% 21.92/22.13 tff(2025,plain,
% 21.92/22.13 ((mult(mult(mult(b, c), mult(a, b)), a) = mult(mult(b, c), mult(mult(a, b), a))) <=> (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(mult(a, b), a)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), a))))),
% 21.92/22.13 inference(transitivity,[status(thm)],[2024, 2002])).
% 21.92/22.13 tff(2026,plain,
% 21.92/22.13 ((mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(mult(a, b), a)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), a)))) <=> (mult(mult(mult(b, c), mult(a, b)), a) = mult(mult(b, c), mult(mult(a, b), a)))),
% 21.92/22.13 inference(symmetry,[status(thm)],[2025])).
% 21.92/22.13 tff(2027,plain,
% 21.92/22.13 (mult(mult(b, c), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))),
% 21.92/22.13 inference(transitivity,[status(thm)],[1561, 1168])).
% 21.92/22.13 tff(2028,plain,
% 21.92/22.13 (mult(mult(mult(b, c), a), mult(b, a)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(b, a))),
% 21.92/22.13 inference(monotonicity,[status(thm)],[2027])).
% 21.92/22.13 tff(2029,plain,
% 21.92/22.13 (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(b, a)) = mult(mult(mult(b, c), a), mult(b, a))),
% 21.92/22.13 inference(symmetry,[status(thm)],[2028])).
% 21.92/22.13 tff(2030,plain,
% 21.92/22.13 (mult(b, a) = mult(a, b)),
% 21.92/22.13 inference(transitivity,[status(thm)],[1837, 1287, 913])).
% 21.92/22.13 tff(2031,plain,
% 21.92/22.13 (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(b, a)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(a, b))),
% 21.92/22.13 inference(monotonicity,[status(thm)],[2030])).
% 21.92/22.13 tff(2032,plain,
% 21.92/22.13 (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(a, b)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(b, a))),
% 21.92/22.13 inference(symmetry,[status(thm)],[2031])).
% 21.92/22.13 tff(2033,plain,
% 21.92/22.13 (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(a, b)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(mult(a, rd(mult(b, c), mult(a, c))), a))),
% 21.92/22.13 inference(monotonicity,[status(thm)],[1575])).
% 21.92/22.13 tff(2034,plain,
% 21.92/22.13 (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(mult(a, rd(mult(b, c), mult(a, c))), a)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(a, b))),
% 21.92/22.14 inference(symmetry,[status(thm)],[2033])).
% 21.92/22.14 tff(2035,plain,
% 21.92/22.14 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c))), a) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(mult(a, rd(mult(b, c), mult(a, c))), a)))),
% 21.92/22.14 inference(quant_inst,[status(thm)],[])).
% 21.92/22.14 tff(2036,plain,
% 21.92/22.14 (mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c))), a) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(mult(a, rd(mult(b, c), mult(a, c))), a))),
% 21.92/22.14 inference(unit_resolution,[status(thm)],[2035, 56])).
% 21.92/22.14 tff(2037,plain,
% 21.92/22.14 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(mult(b, c), mult(a, a))),
% 21.92/22.14 inference(monotonicity,[status(thm)],[1491])).
% 21.92/22.14 tff(2038,plain,
% 21.92/22.14 (mult(mult(b, c), mult(a, a)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, a))),
% 21.92/22.14 inference(symmetry,[status(thm)],[2037])).
% 21.92/22.14 tff(2039,plain,
% 21.92/22.14 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))),
% 21.92/22.14 inference(symmetry,[status(thm)],[1811])).
% 21.92/22.14 tff(2040,plain,
% 21.92/22.14 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)) = mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))),
% 21.92/22.14 inference(transitivity,[status(thm)],[1169, 1570, 1511, 2039])).
% 21.92/22.14 tff(2041,plain,
% 21.92/22.14 (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a) = mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), a)),
% 21.92/22.14 inference(monotonicity,[status(thm)],[2040])).
% 21.92/22.14 tff(2042,plain,
% 21.92/22.14 (mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), a) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a)),
% 21.92/22.14 inference(symmetry,[status(thm)],[2041])).
% 21.92/22.14 tff(2043,plain,
% 21.92/22.14 (mult(mult(a, c), mult(mult(a, rd(mult(b, c), mult(a, c))), a)) = mult(mult(a, c), mult(a, b))),
% 21.92/22.14 inference(monotonicity,[status(thm)],[1288])).
% 21.92/22.14 tff(2044,plain,
% 21.92/22.14 (mult(mult(a, c), mult(a, b)) = mult(mult(a, c), mult(mult(a, rd(mult(b, c), mult(a, c))), a))),
% 21.92/22.14 inference(symmetry,[status(thm)],[2043])).
% 21.92/22.14 tff(2045,plain,
% 21.92/22.14 (mult(mult(a, c), mult(a, b)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, a))),
% 21.92/22.14 inference(transitivity,[status(thm)],[2044, 1686, 2042, 1564, 1254, 1559, 2038])).
% 21.92/22.14 tff(2046,plain,
% 21.92/22.14 (mult(mult(mult(a, c), mult(a, b)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, a)), rd(mult(b, c), mult(a, c)))),
% 21.92/22.14 inference(monotonicity,[status(thm)],[2045])).
% 21.92/22.14 tff(2047,plain,
% 21.92/22.14 (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a) = mult(mult(a, c), mult(a, b))),
% 21.92/22.14 inference(transitivity,[status(thm)],[2041, 1508, 2043])).
% 21.92/22.14 tff(2048,plain,
% 21.92/22.14 (mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), mult(a, b)), rd(mult(b, c), mult(a, c)))),
% 21.92/22.14 inference(monotonicity,[status(thm)],[2047])).
% 21.92/22.14 tff(2049,plain,
% 21.92/22.14 (mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, b), c), b)),
% 21.92/22.14 inference(transitivity,[status(thm)],[2048, 2046, 1009, 1552, 1997, 870, 869, 866])).
% 21.92/22.14 tff(2050,plain,
% 21.92/22.14 (mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(mult(a, b), c), b), a)),
% 21.92/22.14 inference(monotonicity,[status(thm)],[2049])).
% 21.92/22.14 tff(2051,plain,
% 21.92/22.14 (mult(mult(mult(mult(a, b), c), b), a) = mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c))), a)),
% 21.92/22.14 inference(symmetry,[status(thm)],[2050])).
% 21.92/22.14 tff(2052,plain,
% 21.92/22.14 (mult(mult(mult(mult(a, b), c), a), b) = mult(mult(mult(mult(a, b), c), b), a)),
% 21.92/22.14 inference(symmetry,[status(thm)],[1864])).
% 21.92/22.14 tff(2053,plain,
% 21.92/22.14 (mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), a))) = mult(mult(mult(b, c), a), mult(b, a))),
% 21.92/22.14 inference(transitivity,[status(thm)],[2013, 2016, 1844, 1530, 2021, 964, 963, 2052, 2051, 2036, 2034, 2032, 2029])).
% 21.92/22.14 tff(2054,plain,
% 21.92/22.14 (mult(mult(b, c), mult(mult(a, b), a)) = mult(mult(mult(mult(b, c), a), b), a)),
% 21.92/22.14 inference(symmetry,[status(thm)],[1295])).
% 21.92/22.14 tff(2055,plain,
% 21.92/22.14 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(mult(a, b), a)) = mult(mult(mult(mult(b, c), a), b), a)),
% 21.92/22.14 inference(transitivity,[status(thm)],[2003, 2054])).
% 21.92/22.14 tff(2056,plain,
% 21.92/22.14 ((mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(mult(a, b), a)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), a)))) <=> (mult(mult(mult(mult(b, c), a), b), a) = mult(mult(mult(b, c), a), mult(b, a)))),
% 21.92/22.14 inference(monotonicity,[status(thm)],[2055, 2053])).
% 21.92/22.14 tff(2057,plain,
% 21.92/22.14 ((mult(mult(mult(mult(b, c), a), b), a) = mult(mult(mult(b, c), a), mult(b, a))) <=> (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(mult(a, b), a)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), a))))),
% 21.92/22.14 inference(symmetry,[status(thm)],[2056])).
% 21.92/22.14 tff(2058,plain,
% 21.92/22.14 ((mult(mult(mult(mult(b, c), a), b), a) = mult(mult(mult(b, c), a), mult(b, a))) <=> (mult(mult(mult(b, c), mult(a, b)), a) = mult(mult(b, c), mult(mult(a, b), a)))),
% 21.92/22.14 inference(transitivity,[status(thm)],[2057, 2026])).
% 21.92/22.14 tff(2059,plain,
% 21.92/22.14 ((mult(mult(mult(b, c), a), mult(b, a)) = mult(mult(mult(mult(b, c), a), b), a)) <=> (mult(mult(mult(mult(b, c), a), b), a) = mult(mult(mult(b, c), a), mult(b, a)))),
% 21.92/22.14 inference(commutativity,[status(thm)],[])).
% 21.92/22.14 tff(2060,plain,
% 21.92/22.14 (mult(mult(a, a), rd(mult(b, c), mult(a, c))) = mult(a, b)),
% 21.92/22.14 inference(transitivity,[status(thm)],[1361, 1960])).
% 21.92/22.14 tff(2061,plain,
% 21.92/22.14 (mult(mult(mult(a, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, b), a)),
% 21.92/22.14 inference(monotonicity,[status(thm)],[2060])).
% 21.92/22.14 tff(2062,plain,
% 21.92/22.14 (mult(a, mult(a, b)) = mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), a))),
% 21.92/22.14 inference(monotonicity,[status(thm)],[1575])).
% 21.92/22.14 tff(2063,plain,
% 21.92/22.14 (mult(a, mult(a, b)) = mult(mult(a, b), a)),
% 21.92/22.14 inference(transitivity,[status(thm)],[2062, 1395, 2061])).
% 21.92/22.14 tff(2064,plain,
% 21.92/22.14 (mult(mult(b, c), mult(a, mult(a, b))) = mult(mult(b, c), mult(mult(a, b), a))),
% 21.92/22.14 inference(monotonicity,[status(thm)],[2063])).
% 21.92/22.14 tff(2065,plain,
% 21.92/22.14 (mult(mult(b, c), mult(a, mult(a, b))) = mult(mult(mult(mult(b, c), a), b), a)),
% 21.92/22.14 inference(transitivity,[status(thm)],[2064, 2054])).
% 21.92/22.14 tff(2066,plain,
% 21.92/22.14 (mult(mult(mult(b, c), a), mult(a, b)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(a, b))),
% 21.92/22.14 inference(monotonicity,[status(thm)],[2027])).
% 21.92/22.14 tff(2067,plain,
% 21.92/22.14 (mult(mult(mult(b, c), a), mult(a, b)) = mult(mult(mult(b, c), a), mult(b, a))),
% 21.92/22.14 inference(transitivity,[status(thm)],[2066, 2032, 2029])).
% 21.92/22.14 tff(2068,plain,
% 21.92/22.14 ((mult(mult(mult(b, c), a), mult(a, b)) = mult(mult(b, c), mult(a, mult(a, b)))) <=> (mult(mult(mult(b, c), a), mult(b, a)) = mult(mult(mult(mult(b, c), a), b), a))),
% 21.92/22.14 inference(monotonicity,[status(thm)],[2067, 2065])).
% 21.92/22.14 tff(2069,plain,
% 21.92/22.14 ((mult(mult(mult(b, c), a), mult(a, b)) = mult(mult(b, c), mult(a, mult(a, b)))) <=> (mult(mult(mult(mult(b, c), a), b), a) = mult(mult(mult(b, c), a), mult(b, a)))),
% 21.92/22.14 inference(transitivity,[status(thm)],[2068, 2059])).
% 21.92/22.14 tff(2070,assumption,(mult(mult(mult(b, c), a), mult(a, b)) = mult(mult(b, c), mult(a, mult(a, b)))), introduced(assumption)).
% 21.92/22.14 tff(2071,plain,
% 21.92/22.14 (mult(mult(mult(mult(b, c), a), b), a) = mult(mult(mult(b, c), a), mult(b, a))),
% 21.92/22.14 inference(modus_ponens,[status(thm)],[2070, 2069])).
% 21.92/22.14 tff(2072,plain,
% 21.92/22.14 (mult(mult(mult(b, c), mult(a, b)), a) = mult(mult(b, c), mult(mult(a, b), a))),
% 21.92/22.14 inference(modus_ponens,[status(thm)],[2071, 2058])).
% 21.92/22.14 tff(2073,plain,
% 21.92/22.14 (mult(mult(b, c), mult(mult(a, b), a)) = mult(mult(mult(b, c), mult(a, b)), a)),
% 21.92/22.14 inference(symmetry,[status(thm)],[2072])).
% 21.92/22.14 tff(2074,plain,
% 21.92/22.14 (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(mult(a, rd(mult(b, c), mult(a, c))), a)) = mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c))), a)),
% 21.92/22.14 inference(symmetry,[status(thm)],[2036])).
% 21.92/22.14 tff(2075,plain,
% 21.92/22.14 (mult(mult(mult(b, c), a), mult(a, b)) = mult(mult(a, c), mult(mult(b, a), b))),
% 21.92/22.14 inference(transitivity,[status(thm)],[2066, 2033, 2074, 2050, 1864, 1798, 956])).
% 21.92/22.14 tff(2076,plain,
% 21.92/22.14 (mult(mult(a, c), mult(b, a)) = mult(mult(a, c), mult(a, b))),
% 21.92/22.14 inference(monotonicity,[status(thm)],[2030])).
% 21.92/22.14 tff(2077,plain,
% 21.92/22.14 (mult(mult(mult(a, c), mult(b, a)), b) = mult(mult(mult(a, c), mult(a, b)), b)),
% 21.92/22.14 inference(monotonicity,[status(thm)],[2076])).
% 21.92/22.14 tff(2078,plain,
% 21.92/22.14 (mult(mult(mult(a, c), mult(a, b)), b) = mult(mult(mult(a, c), mult(b, a)), b)),
% 21.92/22.14 inference(symmetry,[status(thm)],[2077])).
% 21.92/22.14 tff(2079,plain,
% 21.92/22.14 (mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), b) = mult(mult(mult(a, c), mult(a, b)), b)),
% 21.92/22.14 inference(monotonicity,[status(thm)],[2047])).
% 21.92/22.14 tff(2080,plain,
% 21.92/22.14 (mult(mult(mult(b, c), a), a) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a)),
% 21.92/22.14 inference(monotonicity,[status(thm)],[2027])).
% 21.92/22.14 tff(2081,plain,
% 21.92/22.14 (mult(mult(mult(mult(b, c), a), a), b) = mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), b)),
% 21.92/22.14 inference(monotonicity,[status(thm)],[2080])).
% 21.92/22.14 tff(2082,plain,
% 21.92/22.14 (mult(mult(mult(mult(b, c), a), a), b) = mult(mult(mult(a, c), mult(b, a)), b)),
% 21.92/22.14 inference(transitivity,[status(thm)],[2081, 2079, 2078])).
% 21.92/22.14 tff(2083,plain,
% 21.92/22.14 ((mult(mult(mult(mult(b, c), a), a), b) = mult(mult(mult(b, c), a), mult(a, b))) <=> (mult(mult(mult(a, c), mult(b, a)), b) = mult(mult(a, c), mult(mult(b, a), b)))),
% 21.92/22.14 inference(monotonicity,[status(thm)],[2082, 2075])).
% 21.92/22.14 tff(2084,plain,
% 21.92/22.14 ((mult(mult(mult(a, c), mult(b, a)), b) = mult(mult(a, c), mult(mult(b, a), b))) <=> (mult(mult(mult(mult(b, c), a), a), b) = mult(mult(mult(b, c), a), mult(a, b)))),
% 21.92/22.14 inference(symmetry,[status(thm)],[2083])).
% 21.92/22.14 tff(2085,plain,
% 21.92/22.14 ((~(mult(mult(mult(a, c), mult(b, a)), b) = mult(mult(a, c), mult(mult(b, a), b)))) <=> (~(mult(mult(mult(mult(b, c), a), a), b) = mult(mult(mult(b, c), a), mult(a, b))))),
% 21.92/22.14 inference(monotonicity,[status(thm)],[2084])).
% 21.92/22.14 tff(2086,plain,
% 21.92/22.14 ((mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(mult(a, b), c), b), a)) <=> (mult(mult(mult(mult(a, b), c), b), a) = mult(mult(mult(a, b), c), mult(b, a)))),
% 21.92/22.14 inference(commutativity,[status(thm)],[])).
% 21.92/22.14 tff(2087,plain,
% 21.92/22.14 (mult(mult(a, c), mult(mult(b, a), b)) = mult(mult(mult(mult(a, b), c), b), a)),
% 21.92/22.14 inference(transitivity,[status(thm)],[964, 963, 2052])).
% 21.92/22.14 tff(2088,plain,
% 21.92/22.14 (mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, c), b), mult(a, b))),
% 21.92/22.14 inference(monotonicity,[status(thm)],[227, 2030])).
% 21.92/22.14 tff(2089,plain,
% 21.92/22.14 (mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(mult(a, b), c), mult(b, a))),
% 21.92/22.14 inference(symmetry,[status(thm)],[2088])).
% 21.92/22.14 tff(2090,plain,
% 21.92/22.14 (mult(mult(mult(a, c), mult(a, b)), b) = mult(mult(mult(a, c), b), mult(a, b))),
% 21.92/22.14 inference(symmetry,[status(thm)],[1846])).
% 21.92/22.14 tff(2091,plain,
% 21.92/22.14 (mult(mult(mult(a, c), mult(b, a)), b) = mult(mult(mult(a, b), c), mult(b, a))),
% 21.92/22.14 inference(transitivity,[status(thm)],[2077, 2090, 2089])).
% 21.92/22.14 tff(2092,plain,
% 21.92/22.14 ((mult(mult(mult(a, c), mult(b, a)), b) = mult(mult(a, c), mult(mult(b, a), b))) <=> (mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(mult(a, b), c), b), a))),
% 21.92/22.14 inference(monotonicity,[status(thm)],[2091, 2087])).
% 21.92/22.14 tff(2093,plain,
% 21.92/22.14 ((mult(mult(mult(a, c), mult(b, a)), b) = mult(mult(a, c), mult(mult(b, a), b))) <=> (mult(mult(mult(mult(a, b), c), b), a) = mult(mult(mult(a, b), c), mult(b, a)))),
% 21.92/22.14 inference(transitivity,[status(thm)],[2092, 2086])).
% 21.92/22.14 tff(2094,plain,
% 21.92/22.14 ((mult(mult(mult(mult(a, b), c), b), a) = mult(mult(mult(a, b), c), mult(b, a))) <=> (mult(mult(mult(a, c), mult(b, a)), b) = mult(mult(a, c), mult(mult(b, a), b)))),
% 21.92/22.14 inference(symmetry,[status(thm)],[2093])).
% 21.92/22.14 tff(2095,plain,
% 21.92/22.14 ((~(mult(mult(mult(mult(a, b), c), b), a) = mult(mult(mult(a, b), c), mult(b, a)))) <=> (~(mult(mult(mult(a, c), mult(b, a)), b) = mult(mult(a, c), mult(mult(b, a), b))))),
% 21.92/22.14 inference(monotonicity,[status(thm)],[2094])).
% 21.92/22.14 tff(2096,plain,
% 21.92/22.14 (mult(mult(mult(a, b), c), mult(a, b)) = mult(mult(mult(a, b), c), mult(b, a))),
% 21.92/22.14 inference(transitivity,[status(thm)],[574, 2089])).
% 21.92/22.14 tff(2097,plain,
% 21.92/22.14 ((mult(mult(mult(mult(a, b), c), a), b) = mult(mult(mult(a, b), c), mult(a, b))) <=> (mult(mult(mult(mult(a, b), c), b), a) = mult(mult(mult(a, b), c), mult(b, a)))),
% 21.92/22.14 inference(monotonicity,[status(thm)],[2052, 2096])).
% 21.92/22.14 tff(2098,plain,
% 21.92/22.14 ((~(mult(mult(mult(mult(a, b), c), a), b) = mult(mult(mult(a, b), c), mult(a, b)))) <=> (~(mult(mult(mult(mult(a, b), c), b), a) = mult(mult(mult(a, b), c), mult(b, a))))),
% 21.92/22.14 inference(monotonicity,[status(thm)],[2097])).
% 21.92/22.14 tff(2099,plain,
% 21.92/22.14 (~(mult(mult(mult(mult(a, b), c), b), a) = mult(mult(mult(a, b), c), mult(b, a)))),
% 21.92/22.14 inference(modus_ponens,[status(thm)],[1860, 2098])).
% 21.92/22.14 tff(2100,plain,
% 21.92/22.14 (~(mult(mult(mult(a, c), mult(b, a)), b) = mult(mult(a, c), mult(mult(b, a), b)))),
% 21.92/22.14 inference(modus_ponens,[status(thm)],[2099, 2095])).
% 21.92/22.14 tff(2101,plain,
% 21.92/22.14 (~(mult(mult(mult(mult(b, c), a), a), b) = mult(mult(mult(b, c), a), mult(a, b)))),
% 21.92/22.14 inference(modus_ponens,[status(thm)],[2100, 2085])).
% 21.92/22.14 tff(2102,assumption,(~(mult(mult(mult(mult(b, c), a), a), b) = mult(mult(mult(b, c), a), mult(a, b)))), introduced(assumption)).
% 21.92/22.14 tff(2103,plain,
% 21.92/22.14 (((~(mult(mult(mult(mult(b, c), a), b), a) = mult(mult(mult(b, c), a), mult(b, a)))) | (~(mult(mult(mult(mult(b, c), a), a), b) = mult(mult(mult(b, c), a), mult(a, b))))) | (mult(mult(mult(mult(b, c), a), a), b) = mult(mult(mult(b, c), a), mult(a, b)))),
% 21.92/22.14 inference(tautology,[status(thm)],[])).
% 21.92/22.14 tff(2104,plain,
% 21.92/22.14 ((~(mult(mult(mult(mult(b, c), a), b), a) = mult(mult(mult(b, c), a), mult(b, a)))) | (~(mult(mult(mult(mult(b, c), a), a), b) = mult(mult(mult(b, c), a), mult(a, b))))),
% 21.92/22.14 inference(unit_resolution,[status(thm)],[2103, 2102])).
% 21.92/22.14 tff(2105,assumption,((~(mult(mult(mult(mult(b, c), a), b), a) = mult(mult(mult(mult(b, c), a), a), b))) | (~(mult(mult(mult(b, c), a), mult(b, a)) = mult(mult(mult(b, c), a), mult(a, b))))), introduced(assumption)).
% 21.92/22.14 tff(2106,plain,
% 21.92/22.14 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(mult(b, c), a), b), a) = mult(mult(mult(mult(b, c), a), a), b))) | (~(mult(mult(mult(b, c), a), mult(b, a)) = mult(mult(mult(b, c), a), mult(a, b)))))) | (~((~(mult(mult(mult(mult(b, c), a), b), a) = mult(mult(mult(b, c), a), mult(b, a)))) | (~(mult(mult(mult(mult(b, c), a), a), b) = mult(mult(mult(b, c), a), mult(a, b)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(mult(b, c), a), b), a) = mult(mult(mult(mult(b, c), a), a), b))) | (~(mult(mult(mult(b, c), a), mult(b, a)) = mult(mult(mult(b, c), a), mult(a, b)))))) | (~((~(mult(mult(mult(mult(b, c), a), b), a) = mult(mult(mult(b, c), a), mult(b, a)))) | (~(mult(mult(mult(mult(b, c), a), a), b) = mult(mult(mult(b, c), a), mult(a, b)))))))),
% 21.92/22.14 inference(rewrite,[status(thm)],[])).
% 21.92/22.14 tff(2107,plain,
% 21.92/22.14 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(mult(b, c), a), b), a) = mult(mult(mult(mult(b, c), a), a), b))) | (~(mult(mult(mult(b, c), a), mult(b, a)) = mult(mult(mult(b, c), a), mult(a, b)))))) | (~((~(mult(mult(mult(mult(b, c), a), b), a) = mult(mult(mult(b, c), a), mult(b, a)))) | (~(mult(mult(mult(mult(b, c), a), a), b) = mult(mult(mult(b, c), a), mult(a, b)))))))),
% 21.92/22.14 inference(quant_inst,[status(thm)],[])).
% 21.92/22.14 tff(2108,plain,
% 21.92/22.14 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(mult(b, c), a), b), a) = mult(mult(mult(mult(b, c), a), a), b))) | (~(mult(mult(mult(b, c), a), mult(b, a)) = mult(mult(mult(b, c), a), mult(a, b)))))) | (~((~(mult(mult(mult(mult(b, c), a), b), a) = mult(mult(mult(b, c), a), mult(b, a)))) | (~(mult(mult(mult(mult(b, c), a), a), b) = mult(mult(mult(b, c), a), mult(a, b))))))),
% 21.92/22.15 inference(modus_ponens,[status(thm)],[2107, 2106])).
% 21.92/22.15 tff(2109,plain,
% 21.92/22.15 ($false),
% 21.92/22.15 inference(unit_resolution,[status(thm)],[2108, 27, 2105, 2104])).
% 21.92/22.15 tff(2110,plain,((~((~(mult(mult(mult(mult(b, c), a), b), a) = mult(mult(mult(mult(b, c), a), a), b))) | (~(mult(mult(mult(b, c), a), mult(b, a)) = mult(mult(mult(b, c), a), mult(a, b)))))) | (mult(mult(mult(mult(b, c), a), a), b) = mult(mult(mult(b, c), a), mult(a, b)))), inference(lemma,lemma(discharge,[]))).
% 21.92/22.15 tff(2111,plain,
% 21.92/22.15 (~((~(mult(mult(mult(mult(b, c), a), b), a) = mult(mult(mult(mult(b, c), a), a), b))) | (~(mult(mult(mult(b, c), a), mult(b, a)) = mult(mult(mult(b, c), a), mult(a, b)))))),
% 21.92/22.15 inference(unit_resolution,[status(thm)],[2110, 2101])).
% 21.92/22.15 tff(2112,plain,
% 21.92/22.15 (((~(mult(mult(mult(mult(b, c), a), b), a) = mult(mult(mult(mult(b, c), a), a), b))) | (~(mult(mult(mult(b, c), a), mult(b, a)) = mult(mult(mult(b, c), a), mult(a, b))))) | (mult(mult(mult(mult(b, c), a), b), a) = mult(mult(mult(mult(b, c), a), a), b))),
% 21.92/22.15 inference(tautology,[status(thm)],[])).
% 21.92/22.15 tff(2113,plain,
% 21.92/22.15 (mult(mult(mult(mult(b, c), a), b), a) = mult(mult(mult(mult(b, c), a), a), b)),
% 21.92/22.15 inference(unit_resolution,[status(thm)],[2112, 2111])).
% 21.92/22.15 tff(2114,plain,
% 21.92/22.15 (mult(mult(mult(mult(b, c), a), a), b) = mult(mult(mult(mult(b, c), a), b), a)),
% 21.92/22.15 inference(symmetry,[status(thm)],[2113])).
% 21.92/22.15 tff(2115,plain,
% 21.92/22.15 (mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), b) = mult(mult(mult(mult(b, c), a), a), b)),
% 21.92/22.15 inference(symmetry,[status(thm)],[2081])).
% 21.92/22.15 tff(2116,plain,
% 21.92/22.15 (mult(mult(mult(a, c), mult(a, b)), b) = mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), b)),
% 21.92/22.15 inference(symmetry,[status(thm)],[2079])).
% 21.92/22.15 tff(2117,plain,
% 21.92/22.15 (mult(mult(mult(a, c), mult(b, a)), b) = mult(mult(a, c), mult(mult(b, a), b))),
% 21.92/22.15 inference(transitivity,[status(thm)],[2077, 2116, 2115, 2114, 1295, 2073, 2001, 1864, 1798, 956])).
% 21.92/22.15 tff(2118,plain,
% 21.92/22.15 ($false),
% 21.92/22.15 inference(unit_resolution,[status(thm)],[2100, 2117])).
% 21.92/22.15 tff(2119,plain,((mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit))))) | (~(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (~(mult(mult(mult(b, c), a), mult(a, b)) = mult(mult(b, c), mult(a, mult(a, b))))) | (mult(rd(mult(b, c), mult(a, c)), mult(c, a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, c)))), inference(lemma,lemma(discharge,[]))).
% 21.92/22.15 tff(2120,plain,
% 21.92/22.15 (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))),
% 21.92/22.15 inference(unit_resolution,[status(thm)],[2119, 1274, 34, 729, 1797, 94])).
% 21.92/22.15 tff(2121,plain,
% 21.92/22.15 (mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a))),
% 21.92/22.15 inference(unit_resolution,[status(thm)],[1273, 97, 1029])).
% 21.92/22.15 tff(2122,plain,
% 21.92/22.15 (mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, b)),
% 21.92/22.15 inference(transitivity,[status(thm)],[2121, 913])).
% 21.92/22.15 tff(2123,plain,
% 21.92/22.15 (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(mult(a, rd(mult(b, c), mult(a, c))), a)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(a, b))),
% 21.92/22.15 inference(monotonicity,[status(thm)],[2122])).
% 21.92/22.15 tff(2124,plain,
% 21.92/22.15 (ld(a, mult(a, mult(b, c))) = ld(a, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 21.92/22.15 inference(symmetry,[status(thm)],[1490])).
% 21.92/22.15 tff(2125,plain,
% 21.92/22.15 (mult(b, c) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))),
% 21.92/22.15 inference(transitivity,[status(thm)],[843, 2124, 733])).
% 21.92/22.15 tff(2126,plain,
% 21.92/22.15 (mult(mult(b, c), a) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)),
% 21.92/22.15 inference(monotonicity,[status(thm)],[2125])).
% 21.92/22.15 tff(2127,plain,
% 21.92/22.15 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(b, c), a)),
% 21.92/22.15 inference(symmetry,[status(thm)],[2126])).
% 21.92/22.15 tff(2128,plain,
% 21.92/22.15 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))),
% 21.92/22.15 inference(unit_resolution,[status(thm)],[342, 330])).
% 21.92/22.15 tff(2129,plain,
% 21.92/22.15 (mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)),
% 21.92/22.15 inference(symmetry,[status(thm)],[2128])).
% 21.92/22.15 tff(2130,plain,
% 21.92/22.15 (mult(mult(a, b), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))),
% 21.92/22.15 inference(transitivity,[status(thm)],[227, 405, 2129, 2127, 1172, 1168])).
% 21.92/22.15 tff(2131,plain,
% 21.92/22.15 (mult(mult(mult(a, b), c), a) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a)),
% 21.92/22.15 inference(monotonicity,[status(thm)],[2130])).
% 21.92/22.15 tff(2132,plain,
% 21.92/22.15 (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), c) = mult(mult(a, b), c)),
% 21.92/22.15 inference(monotonicity,[status(thm)],[2122])).
% 21.92/22.15 tff(2133,plain,
% 21.92/22.15 (mult(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), c), a) = mult(mult(mult(a, b), c), a)),
% 21.92/22.15 inference(monotonicity,[status(thm)],[2132])).
% 21.92/22.15 tff(2134,plain,
% 21.92/22.15 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), c), a) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)))),
% 21.92/22.15 inference(quant_inst,[status(thm)],[])).
% 21.92/22.15 tff(2135,plain,
% 21.92/22.15 (mult(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), c), a) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a))),
% 21.92/22.15 inference(unit_resolution,[status(thm)],[2134, 56])).
% 21.92/22.15 tff(2136,plain,
% 21.92/22.15 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), c), a)),
% 21.92/22.15 inference(symmetry,[status(thm)],[2135])).
% 21.92/22.15 tff(2137,plain,
% 21.92/22.15 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a)),
% 21.92/22.15 inference(transitivity,[status(thm)],[2136, 2133, 2131])).
% 21.92/22.15 tff(2138,plain,
% 21.92/22.15 (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c)))),
% 21.92/22.15 inference(monotonicity,[status(thm)],[2137])).
% 21.92/22.15 tff(2139,plain,
% 21.92/22.15 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c)))))),
% 21.92/22.15 inference(quant_inst,[status(thm)],[])).
% 21.92/22.15 tff(2140,plain,
% 21.92/22.15 (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))))),
% 21.92/22.15 inference(unit_resolution,[status(thm)],[2139, 56])).
% 21.92/22.15 tff(2141,plain,
% 21.92/22.15 (mult(a, mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c)))),
% 21.92/22.15 inference(symmetry,[status(thm)],[2140])).
% 21.92/22.15 tff(2142,plain,
% 21.92/22.15 (mult(a, mult(mult(mult(b, c), a), rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))))),
% 21.92/22.15 inference(monotonicity,[status(thm)],[1217])).
% 21.92/22.15 tff(2143,plain,
% 21.92/22.15 (mult(mult(b, c), a) = mult(mult(a, b), c)),
% 21.92/22.15 inference(transitivity,[status(thm)],[2126, 2128, 177, 161])).
% 21.92/22.15 tff(2144,plain,
% 21.92/22.15 (mult(mult(mult(b, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))),
% 21.92/22.15 inference(monotonicity,[status(thm)],[2143])).
% 21.92/22.15 tff(2145,plain,
% 21.92/22.15 (mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))) = mult(mult(mult(b, c), a), rd(mult(b, c), mult(a, c)))),
% 21.92/22.15 inference(symmetry,[status(thm)],[2144])).
% 21.92/22.15 tff(2146,plain,
% 21.92/22.15 (mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(mult(b, c), a), rd(mult(b, c), mult(a, c))))),
% 21.92/22.15 inference(monotonicity,[status(thm)],[2145])).
% 21.92/22.15 tff(2147,plain,
% 21.92/22.15 (mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))) = mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c)))),
% 21.92/22.15 inference(transitivity,[status(thm)],[2146, 2142, 2141, 2138])).
% 21.92/22.15 tff(2148,plain,
% 21.92/22.15 (mult(mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c))), a)),
% 21.92/22.15 inference(monotonicity,[status(thm)],[2147])).
% 21.92/22.15 tff(2149,plain,
% 21.92/22.15 ((mult(mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, a), mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))))) <=> (mult(mult(a, a), mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))), a))),
% 21.92/22.15 inference(commutativity,[status(thm)],[])).
% 21.92/22.15 tff(2150,plain,
% 21.92/22.15 ((mult(mult(a, a), mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))), a)) <=> (mult(mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, a), mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))))),
% 21.92/22.15 inference(symmetry,[status(thm)],[2149])).
% 21.92/22.15 tff(2151,plain,
% 21.92/22.15 (mult(a, mult(mult(mult(b, c), a), rd(mult(b, c), mult(a, c)))) = mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c)))),
% 21.92/22.15 inference(transitivity,[status(thm)],[2142, 2141, 2138])).
% 21.92/22.15 tff(2152,plain,
% 21.92/22.15 (mult(mult(a, mult(mult(mult(b, c), a), rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c))), a)),
% 21.92/22.15 inference(monotonicity,[status(thm)],[2151])).
% 21.92/22.15 tff(2153,plain,
% 21.92/22.15 (mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, mult(mult(mult(b, c), a), rd(mult(b, c), mult(a, c)))), a)),
% 21.92/22.15 inference(symmetry,[status(thm)],[2152])).
% 21.92/22.15 tff(2154,plain,
% 21.92/22.15 (mult(mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, mult(mult(mult(b, c), a), rd(mult(b, c), mult(a, c)))), a)),
% 21.92/22.15 inference(transitivity,[status(thm)],[2148, 2153])).
% 21.92/22.15 tff(2155,plain,
% 21.92/22.15 (mult(mult(a, a), mult(mult(mult(b, c), a), rd(mult(b, c), mult(a, c)))) = mult(mult(a, a), mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))))),
% 21.92/22.15 inference(monotonicity,[status(thm)],[2144])).
% 21.92/22.15 tff(2156,plain,
% 21.92/22.15 (mult(mult(a, a), mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, a), mult(mult(mult(b, c), a), rd(mult(b, c), mult(a, c))))),
% 21.92/22.15 inference(symmetry,[status(thm)],[2155])).
% 21.92/22.15 tff(2157,plain,
% 21.92/22.15 ((mult(mult(a, a), mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))), a)) <=> (mult(mult(a, a), mult(mult(mult(b, c), a), rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(mult(mult(b, c), a), rd(mult(b, c), mult(a, c)))), a))),
% 21.92/22.15 inference(monotonicity,[status(thm)],[2156, 2154])).
% 21.92/22.15 tff(2158,plain,
% 21.92/22.15 ((mult(mult(a, a), mult(mult(mult(b, c), a), rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(mult(mult(b, c), a), rd(mult(b, c), mult(a, c)))), a)) <=> (mult(mult(a, a), mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))), a))),
% 21.92/22.15 inference(symmetry,[status(thm)],[2157])).
% 21.92/22.15 tff(2159,plain,
% 21.92/22.15 (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(a, b)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(mult(a, rd(mult(b, c), mult(a, c))), a))),
% 21.92/22.15 inference(symmetry,[status(thm)],[2123])).
% 21.92/22.15 tff(2160,plain,
% 21.92/22.15 (mult(mult(a, c), b) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))),
% 21.92/22.15 inference(transitivity,[status(thm)],[405, 2129, 2127, 1172, 1168])).
% 21.92/22.15 tff(2161,plain,
% 21.92/22.15 (mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(a, b))),
% 21.92/22.15 inference(monotonicity,[status(thm)],[2160])).
% 21.92/22.15 tff(2162,plain,
% 21.92/22.15 (mult(mult(mult(a, c), unit), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))),
% 21.92/22.15 inference(monotonicity,[status(thm)],[45])).
% 21.92/22.15 tff(2163,plain,
% 21.92/22.15 ((mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), unit) = mult(mult(mult(a, c), unit), rd(mult(b, c), mult(a, c)))) <=> (mult(mult(mult(a, c), unit), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), unit))),
% 21.92/22.15 inference(commutativity,[status(thm)],[])).
% 21.92/22.15 tff(2164,plain,
% 21.92/22.15 ((~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), unit) = mult(mult(mult(a, c), unit), rd(mult(b, c), mult(a, c))))) <=> (~(mult(mult(mult(a, c), unit), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), unit)))),
% 21.92/22.15 inference(monotonicity,[status(thm)],[2163])).
% 21.92/22.15 tff(2165,assumption,(~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), unit) = mult(mult(mult(a, c), unit), rd(mult(b, c), mult(a, c))))), introduced(assumption)).
% 21.92/22.15 tff(2166,plain,
% 21.92/22.15 (~(mult(mult(mult(a, c), unit), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), unit))),
% 21.92/22.15 inference(modus_ponens,[status(thm)],[2165, 2164])).
% 21.92/22.15 tff(2167,plain,
% 21.92/22.15 (mult(mult(a, c), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), unit), rd(mult(b, c), mult(a, c)))),
% 21.92/22.15 inference(symmetry,[status(thm)],[2162])).
% 21.92/22.15 tff(2168,plain,
% 21.92/22.15 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), unit) = mult(mult(mult(mult(a, c), unit), rd(mult(b, c), mult(a, c))), unit)),
% 21.92/22.15 inference(monotonicity,[status(thm)],[2167])).
% 21.92/22.15 tff(2169,plain,
% 21.92/22.15 (mult(mult(mult(mult(a, c), unit), rd(mult(b, c), mult(a, c))), unit) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), unit)),
% 21.92/22.15 inference(symmetry,[status(thm)],[2168])).
% 21.92/22.15 tff(2170,plain,
% 21.92/22.15 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(a, c), unit), rd(mult(b, c), mult(a, c))), unit) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))),
% 21.92/22.15 inference(quant_inst,[status(thm)],[])).
% 21.92/22.15 tff(2171,plain,
% 21.92/22.15 (mult(mult(mult(mult(a, c), unit), rd(mult(b, c), mult(a, c))), unit) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))),
% 21.92/22.15 inference(unit_resolution,[status(thm)],[2170, 56])).
% 21.92/22.15 tff(2172,plain,
% 21.92/22.15 (mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(mult(mult(mult(a, c), unit), rd(mult(b, c), mult(a, c))), unit)),
% 21.92/22.15 inference(symmetry,[status(thm)],[2171])).
% 21.92/22.15 tff(2173,plain,
% 21.92/22.15 (mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))),
% 21.92/22.15 inference(monotonicity,[status(thm)],[1896])).
% 21.92/22.15 tff(2174,plain,
% 21.92/22.15 (mult(mult(a, c), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))),
% 21.92/22.15 inference(symmetry,[status(thm)],[2173])).
% 21.92/22.15 tff(2175,plain,
% 21.92/22.15 (mult(mult(mult(a, c), unit), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), unit)),
% 21.92/22.15 inference(transitivity,[status(thm)],[2162, 2174, 2172, 2169])).
% 21.92/22.15 tff(2176,plain,
% 21.92/22.15 ($false),
% 21.92/22.15 inference(unit_resolution,[status(thm)],[2175, 2166])).
% 21.92/22.15 tff(2177,plain,(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), unit) = mult(mult(mult(a, c), unit), rd(mult(b, c), mult(a, c)))), inference(lemma,lemma(discharge,[]))).
% 21.92/22.15 tff(2178,plain,
% 21.92/22.15 (mult(mult(mult(mult(a, c), unit), rd(mult(b, c), mult(a, c))), unit) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), unit)),
% 21.92/22.15 inference(monotonicity,[status(thm)],[2162])).
% 21.92/22.15 tff(2179,plain,
% 21.92/22.15 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))),
% 21.92/22.15 inference(unit_resolution,[status(thm)],[1166, 56])).
% 21.92/22.15 tff(2180,plain,
% 21.92/22.15 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a) = mult(mult(b, c), a)),
% 21.92/22.16 inference(transitivity,[status(thm)],[2179, 1372, 1332])).
% 21.92/22.16 tff(2181,plain,
% 21.92/22.16 (rd(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a), a) = rd(mult(mult(b, c), a), a)),
% 21.92/22.16 inference(monotonicity,[status(thm)],[2180])).
% 21.92/22.16 tff(2182,plain,
% 21.92/22.16 (mult(mult(rd(mult(b, c), mult(a, c)), a), c) = mult(b, c)),
% 21.92/22.16 inference(transitivity,[status(thm)],[1377, 2181, 1370])).
% 21.92/22.16 tff(2183,plain,
% 21.92/22.16 (rd(mult(mult(rd(mult(b, c), mult(a, c)), a), c), c) = rd(mult(b, c), c)),
% 21.92/22.16 inference(monotonicity,[status(thm)],[2182])).
% 21.92/22.16 tff(2184,plain,
% 21.92/22.16 (mult(rd(mult(b, c), mult(a, c)), a) = b),
% 21.92/22.16 inference(transitivity,[status(thm)],[175, 2183, 170])).
% 21.92/22.16 tff(2185,plain,
% 21.92/22.16 (mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, c), b)),
% 21.92/22.16 inference(monotonicity,[status(thm)],[2184])).
% 21.92/22.16 tff(2186,plain,
% 21.92/22.16 (mult(mult(a, c), b) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))),
% 21.92/22.16 inference(symmetry,[status(thm)],[2185])).
% 21.92/22.16 tff(2187,assumption,(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))), introduced(assumption)).
% 21.92/22.16 tff(2188,plain,
% 21.92/22.16 (mult(a, rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))),
% 21.92/22.16 inference(symmetry,[status(thm)],[1897])).
% 21.92/22.16 tff(2189,plain,
% 21.92/22.16 (mult(mult(a, rd(mult(b, c), mult(a, c))), c) = mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c)),
% 21.92/22.16 inference(monotonicity,[status(thm)],[2188])).
% 21.92/22.16 tff(2190,plain,
% 21.92/22.16 (mult(mult(a, rd(mult(b, c), mult(a, c))), c) = mult(b, c)),
% 21.92/22.16 inference(transitivity,[status(thm)],[2189, 2187, 2172, 2178, 2177, 2162, 734, 1490, 141])).
% 21.92/22.16 tff(2191,plain,
% 21.92/22.16 (rd(mult(mult(a, rd(mult(b, c), mult(a, c))), c), c) = rd(mult(b, c), c)),
% 21.92/22.16 inference(monotonicity,[status(thm)],[2190])).
% 21.92/22.16 tff(2192,plain,
% 21.92/22.16 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(a, rd(mult(b, c), mult(a, c))), c), c) = mult(a, rd(mult(b, c), mult(a, c))))),
% 21.92/22.16 inference(quant_inst,[status(thm)],[])).
% 21.92/22.16 tff(2193,plain,
% 21.92/22.16 (rd(mult(mult(a, rd(mult(b, c), mult(a, c))), c), c) = mult(a, rd(mult(b, c), mult(a, c)))),
% 21.92/22.16 inference(unit_resolution,[status(thm)],[2192, 168])).
% 21.92/22.16 tff(2194,plain,
% 21.92/22.16 (mult(a, rd(mult(b, c), mult(a, c))) = rd(mult(mult(a, rd(mult(b, c), mult(a, c))), c), c)),
% 21.92/22.16 inference(symmetry,[status(thm)],[2193])).
% 21.92/22.16 tff(2195,plain,
% 21.92/22.16 (mult(a, rd(mult(b, c), mult(a, c))) = b),
% 21.92/22.16 inference(transitivity,[status(thm)],[2194, 2191, 170])).
% 21.92/22.16 tff(2196,plain,
% 21.92/22.16 (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), b)),
% 21.92/22.16 inference(monotonicity,[status(thm)],[2195])).
% 21.92/22.16 tff(2197,plain,
% 21.92/22.16 (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))),
% 21.92/22.16 inference(transitivity,[status(thm)],[2196, 2186])).
% 21.92/22.16 tff(2198,plain,
% 21.92/22.16 ($false),
% 21.92/22.16 inference(unit_resolution,[status(thm)],[330, 2197])).
% 21.92/22.16 tff(2199,plain,((~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))) | (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))) | (~(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))), inference(lemma,lemma(discharge,[]))).
% 21.92/22.16 tff(2200,plain,
% 21.92/22.16 (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))),
% 21.92/22.16 inference(unit_resolution,[status(thm)],[2199, 330, 1488, 1368])).
% 21.92/22.16 tff(2201,plain,
% 21.92/22.16 (((~(mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))),
% 21.92/22.16 inference(tautology,[status(thm)],[])).
% 21.92/22.16 tff(2202,plain,
% 21.92/22.16 ((~(mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))),
% 21.92/22.16 inference(unit_resolution,[status(thm)],[2201, 2200])).
% 21.92/22.16 tff(2203,plain,
% 21.92/22.16 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)))))) | (~((~(mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)))))) | (~((~(mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))))))),
% 21.92/22.16 inference(rewrite,[status(thm)],[])).
% 21.92/22.16 tff(2204,plain,
% 21.92/22.16 (((~((~(mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))))) | (~((~(mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c))))))) <=> ((~((~(mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)))))) | (~((~(mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))))))),
% 21.92/22.16 inference(rewrite,[status(thm)],[])).
% 21.92/22.16 tff(2205,plain,
% 21.92/22.16 ((~((~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)))) | (~(mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))))) <=> (~((~(mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c))))))),
% 22.00/22.16 inference(rewrite,[status(thm)],[])).
% 22.00/22.16 tff(2206,plain,
% 22.00/22.16 ((~((~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))) | (~(mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))))) <=> (~((~(mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))))),
% 22.00/22.16 inference(rewrite,[status(thm)],[])).
% 22.00/22.16 tff(2207,plain,
% 22.00/22.16 (((~((~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))) | (~(mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))))) | (~((~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)))) | (~(mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))))))) <=> ((~((~(mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))))) | (~((~(mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)))))))),
% 22.00/22.16 inference(monotonicity,[status(thm)],[2206, 2205])).
% 22.00/22.16 tff(2208,plain,
% 22.00/22.16 (((~((~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))) | (~(mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))))) | (~((~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)))) | (~(mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))))))) <=> ((~((~(mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)))))) | (~((~(mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))))))),
% 22.00/22.16 inference(transitivity,[status(thm)],[2207, 2204])).
% 22.00/22.16 tff(2209,plain,
% 22.00/22.16 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))) | (~(mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))))) | (~((~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)))) | (~(mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)))))) | (~((~(mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))))))),
% 22.00/22.16 inference(monotonicity,[status(thm)],[2208])).
% 22.00/22.16 tff(2210,plain,
% 22.00/22.16 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))) | (~(mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))))) | (~((~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)))) | (~(mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)))))) | (~((~(mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))))))),
% 22.00/22.16 inference(transitivity,[status(thm)],[2209, 2203])).
% 22.00/22.16 tff(2211,plain,
% 22.00/22.16 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))) | (~(mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))))) | (~((~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)))) | (~(mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))))))),
% 22.00/22.16 inference(quant_inst,[status(thm)],[])).
% 22.00/22.16 tff(2212,plain,
% 22.00/22.16 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)))))) | (~((~(mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))))),
% 22.00/22.17 inference(modus_ponens,[status(thm)],[2211, 2210])).
% 22.00/22.17 tff(2213,plain,
% 22.00/22.17 ((~((~(mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)))))) | (~((~(mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))))),
% 22.00/22.17 inference(unit_resolution,[status(thm)],[2212, 27])).
% 22.00/22.17 tff(2214,plain,
% 22.00/22.17 (~((~(mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)))))),
% 22.00/22.17 inference(unit_resolution,[status(thm)],[2213, 2202])).
% 22.00/22.17 tff(2215,plain,
% 22.00/22.17 (((~(mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c))))) | (mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))),
% 22.00/22.17 inference(tautology,[status(thm)],[])).
% 22.00/22.17 tff(2216,plain,
% 22.00/22.17 (mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))),
% 22.00/22.17 inference(unit_resolution,[status(thm)],[2215, 2214])).
% 22.00/22.17 tff(2217,plain,
% 22.00/22.17 (mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))),
% 22.00/22.17 inference(symmetry,[status(thm)],[2216])).
% 22.00/22.17 tff(2218,plain,
% 22.00/22.17 (mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(c, rd(mult(b, c), mult(a, c)))),
% 22.00/22.17 inference(monotonicity,[status(thm)],[1896])).
% 22.00/22.17 tff(2219,plain,
% 22.00/22.17 (mult(c, rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))),
% 22.00/22.17 inference(symmetry,[status(thm)],[2218])).
% 22.00/22.17 tff(2220,plain,
% 22.00/22.17 (mult(a, mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))),
% 22.00/22.17 inference(monotonicity,[status(thm)],[2219])).
% 22.00/22.17 tff(2221,plain,
% 22.00/22.17 (mult(a, mult(c, rd(mult(b, c), mult(a, c)))) = mult(b, c)),
% 22.00/22.17 inference(transitivity,[status(thm)],[2220, 2217, 2172, 2178, 2177, 2162, 734, 1490, 141])).
% 22.00/22.17 tff(2222,plain,
% 22.00/22.17 (mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(b, c), a)),
% 22.00/22.17 inference(monotonicity,[status(thm)],[2221])).
% 22.00/22.17 tff(2223,plain,
% 22.00/22.17 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(b, c), c), c) = mult(b, c))),
% 22.00/22.17 inference(quant_inst,[status(thm)],[])).
% 22.00/22.17 tff(2224,plain,
% 22.00/22.17 (rd(mult(mult(b, c), c), c) = mult(b, c)),
% 22.00/22.17 inference(unit_resolution,[status(thm)],[2223, 168])).
% 22.00/22.17 tff(2225,plain,
% 22.00/22.17 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(b, c), c)),
% 22.00/22.17 inference(monotonicity,[status(thm)],[1491])).
% 22.00/22.17 tff(2226,plain,
% 22.00/22.17 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a), a) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c))),
% 22.00/22.17 inference(quant_inst,[status(thm)],[])).
% 22.00/22.17 tff(2227,plain,
% 22.00/22.17 (rd(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a), a) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)),
% 22.00/22.17 inference(unit_resolution,[status(thm)],[2226, 168])).
% 22.00/22.17 tff(2228,plain,
% 22.00/22.17 (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a))),
% 22.00/22.17 inference(unit_resolution,[status(thm)],[123, 1031])).
% 22.00/22.17 tff(2229,plain,
% 22.00/22.17 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a)),
% 22.00/22.17 inference(symmetry,[status(thm)],[2228])).
% 22.00/22.17 tff(2230,plain,
% 22.00/22.17 (mult(mult(b, c), mult(c, a)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a))),
% 22.00/22.17 inference(monotonicity,[status(thm)],[2125])).
% 22.00/22.17 tff(2231,plain,
% 22.00/22.17 (mult(mult(c, b), mult(c, a)) = mult(mult(b, c), mult(c, a))),
% 22.00/22.17 inference(monotonicity,[status(thm)],[241])).
% 22.00/22.17 tff(2232,plain,
% 22.00/22.17 (mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, c), b)),
% 22.00/22.17 inference(monotonicity,[status(thm)],[1380])).
% 22.00/22.17 tff(2233,plain,
% 22.00/22.17 (mult(mult(a, c), b) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))),
% 22.00/22.17 inference(symmetry,[status(thm)],[2232])).
% 22.00/22.17 tff(2234,plain,
% 22.00/22.17 (ld(c, mult(c, mult(a, b))) = ld(c, mult(c, mult(b, a)))),
% 22.00/22.17 inference(symmetry,[status(thm)],[1470])).
% 22.00/22.17 tff(2235,plain,
% 22.00/22.17 (mult(a, b) = ld(c, mult(c, mult(a, b)))),
% 22.00/22.17 inference(symmetry,[status(thm)],[1468])).
% 22.00/22.17 tff(2236,plain,
% 22.00/22.17 (mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(b, a)),
% 22.00/22.17 inference(transitivity,[status(thm)],[1287, 1381, 2235, 2234, 1472])).
% 22.00/22.17 tff(2237,plain,
% 22.00/22.17 (rd(mult(mult(a, rd(mult(b, c), mult(a, c))), a), a) = rd(mult(b, a), a)),
% 22.00/22.17 inference(monotonicity,[status(thm)],[2236])).
% 22.00/22.17 tff(2238,plain,
% 22.00/22.17 (mult(a, rd(mult(b, c), mult(a, c))) = b),
% 22.00/22.17 inference(transitivity,[status(thm)],[1456, 2237, 1451])).
% 22.00/22.17 tff(2239,plain,
% 22.00/22.17 (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), b)),
% 22.00/22.17 inference(monotonicity,[status(thm)],[2238])).
% 22.00/22.17 tff(2240,plain,
% 22.00/22.17 (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))),
% 22.00/22.17 inference(transitivity,[status(thm)],[2239, 2233])).
% 22.00/22.17 tff(2241,plain,
% 22.00/22.17 ($false),
% 22.00/22.17 inference(unit_resolution,[status(thm)],[330, 2240])).
% 22.00/22.17 tff(2242,plain,((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) | (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(c, mult(b, a)) = mult(c, mult(a, b))))), inference(lemma,lemma(discharge,[]))).
% 22.00/22.17 tff(2243,plain,
% 22.00/22.17 (~(mult(c, mult(b, a)) = mult(c, mult(a, b)))),
% 22.00/22.17 inference(unit_resolution,[status(thm)],[2242, 330, 1368, 2121])).
% 22.00/22.17 tff(2244,plain,
% 22.00/22.17 (((~(mult(mult(c, b), a) = mult(mult(c, a), b))) | (~(mult(c, mult(b, a)) = mult(c, mult(a, b))))) | (mult(c, mult(b, a)) = mult(c, mult(a, b)))),
% 22.00/22.17 inference(tautology,[status(thm)],[])).
% 22.00/22.17 tff(2245,plain,
% 22.00/22.17 ((~(mult(mult(c, b), a) = mult(mult(c, a), b))) | (~(mult(c, mult(b, a)) = mult(c, mult(a, b))))),
% 22.00/22.17 inference(unit_resolution,[status(thm)],[2244, 2243])).
% 22.00/22.17 tff(2246,plain,
% 22.00/22.17 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(c, b), a) = mult(mult(c, a), b))) | (~(mult(c, mult(b, a)) = mult(c, mult(a, b)))))) | (~((~(mult(mult(c, b), a) = mult(c, mult(b, a)))) | (~(mult(mult(c, a), b) = mult(c, mult(a, b)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(c, b), a) = mult(mult(c, a), b))) | (~(mult(c, mult(b, a)) = mult(c, mult(a, b)))))) | (~((~(mult(mult(c, b), a) = mult(c, mult(b, a)))) | (~(mult(mult(c, a), b) = mult(c, mult(a, b)))))))),
% 22.00/22.17 inference(rewrite,[status(thm)],[])).
% 22.00/22.17 tff(2247,plain,
% 22.00/22.17 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(c, b), a) = mult(mult(c, a), b))) | (~(mult(c, mult(b, a)) = mult(c, mult(a, b)))))) | (~((~(mult(mult(c, b), a) = mult(c, mult(b, a)))) | (~(mult(mult(c, a), b) = mult(c, mult(a, b)))))))),
% 22.00/22.17 inference(quant_inst,[status(thm)],[])).
% 22.00/22.17 tff(2248,plain,
% 22.00/22.17 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(c, b), a) = mult(mult(c, a), b))) | (~(mult(c, mult(b, a)) = mult(c, mult(a, b)))))) | (~((~(mult(mult(c, b), a) = mult(c, mult(b, a)))) | (~(mult(mult(c, a), b) = mult(c, mult(a, b))))))),
% 22.00/22.17 inference(modus_ponens,[status(thm)],[2247, 2246])).
% 22.00/22.17 tff(2249,plain,
% 22.00/22.17 ((~((~(mult(mult(c, b), a) = mult(mult(c, a), b))) | (~(mult(c, mult(b, a)) = mult(c, mult(a, b)))))) | (~((~(mult(mult(c, b), a) = mult(c, mult(b, a)))) | (~(mult(mult(c, a), b) = mult(c, mult(a, b))))))),
% 22.00/22.17 inference(unit_resolution,[status(thm)],[2248, 27])).
% 22.00/22.17 tff(2250,plain,
% 22.00/22.17 (~((~(mult(mult(c, b), a) = mult(c, mult(b, a)))) | (~(mult(mult(c, a), b) = mult(c, mult(a, b)))))),
% 22.00/22.17 inference(unit_resolution,[status(thm)],[2249, 2245])).
% 22.00/22.17 tff(2251,plain,
% 22.00/22.17 (((~(mult(mult(c, b), a) = mult(c, mult(b, a)))) | (~(mult(mult(c, a), b) = mult(c, mult(a, b))))) | (mult(mult(c, b), a) = mult(c, mult(b, a)))),
% 22.00/22.17 inference(tautology,[status(thm)],[])).
% 22.00/22.17 tff(2252,plain,
% 22.00/22.17 (mult(mult(c, b), a) = mult(c, mult(b, a))),
% 22.00/22.17 inference(unit_resolution,[status(thm)],[2251, 2250])).
% 22.00/22.17 tff(2253,plain,
% 22.00/22.17 ((mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c)) <=> (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 22.00/22.17 inference(monotonicity,[status(thm)],[2228, 1032])).
% 22.00/22.17 tff(2254,plain,
% 22.00/22.17 ((mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))) <=> (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c))),
% 22.00/22.17 inference(symmetry,[status(thm)],[2253])).
% 22.00/22.17 tff(2255,plain,
% 22.00/22.17 ((~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))) <=> (~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c)))),
% 22.00/22.17 inference(monotonicity,[status(thm)],[2254])).
% 22.00/22.17 tff(2256,plain,
% 22.00/22.17 (~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c))),
% 22.00/22.17 inference(modus_ponens,[status(thm)],[1029, 2255])).
% 22.00/22.17 tff(2257,plain,
% 22.00/22.17 (mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(b, c))),
% 22.00/22.17 inference(monotonicity,[status(thm)],[1491])).
% 22.00/22.17 tff(2258,plain,
% 22.00/22.17 (mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))),
% 22.00/22.17 inference(transitivity,[status(thm)],[2257, 139])).
% 22.00/22.17 tff(2259,plain,
% 22.00/22.17 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(b, mult(b, mult(a, c))) = mult(a, c))),
% 22.00/22.17 inference(quant_inst,[status(thm)],[])).
% 22.00/22.17 tff(2260,plain,
% 22.00/22.17 (ld(b, mult(b, mult(a, c))) = mult(a, c)),
% 22.00/22.17 inference(unit_resolution,[status(thm)],[2259, 7])).
% 22.00/22.17 tff(2261,assumption,(mult(b, mult(a, c)) = mult(b, mult(c, a))), introduced(assumption)).
% 22.00/22.17 tff(2262,plain,
% 22.00/22.17 (mult(b, mult(c, a)) = mult(b, mult(a, c))),
% 22.00/22.17 inference(symmetry,[status(thm)],[2261])).
% 22.00/22.17 tff(2263,plain,
% 22.00/22.17 (ld(b, mult(b, mult(c, a))) = ld(b, mult(b, mult(a, c)))),
% 22.00/22.17 inference(monotonicity,[status(thm)],[2262])).
% 22.00/22.17 tff(2264,plain,
% 22.00/22.17 (mult(c, a) = mult(a, c)),
% 22.00/22.17 inference(transitivity,[status(thm)],[373, 2263, 2260])).
% 22.00/22.17 tff(2265,plain,
% 22.00/22.17 (mult(mult(b, c), mult(c, a)) = mult(mult(b, c), mult(a, c))),
% 22.00/22.17 inference(monotonicity,[status(thm)],[2264])).
% 22.00/22.17 tff(2266,plain,
% 22.00/22.17 (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c)),
% 22.00/22.17 inference(transitivity,[status(thm)],[751, 750, 2265, 742, 738])).
% 22.00/22.17 tff(2267,plain,
% 22.00/22.17 ($false),
% 22.00/22.17 inference(unit_resolution,[status(thm)],[753, 2266])).
% 22.00/22.17 tff(2268,plain,((~(mult(b, mult(a, c)) = mult(b, mult(c, a)))) | (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c)) | (~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)))) | (~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))), inference(lemma,lemma(discharge,[]))).
% 22.00/22.17 tff(2269,plain,
% 22.00/22.17 (~(mult(b, mult(a, c)) = mult(b, mult(c, a)))),
% 22.00/22.17 inference(unit_resolution,[status(thm)],[2268, 2258, 2228, 1032, 2256])).
% 22.00/22.17 tff(2270,plain,
% 22.00/22.17 (((~(mult(mult(b, a), c) = mult(mult(b, c), a))) | (~(mult(b, mult(a, c)) = mult(b, mult(c, a))))) | (mult(b, mult(a, c)) = mult(b, mult(c, a)))),
% 22.00/22.17 inference(tautology,[status(thm)],[])).
% 22.00/22.17 tff(2271,plain,
% 22.00/22.17 ((~(mult(mult(b, a), c) = mult(mult(b, c), a))) | (~(mult(b, mult(a, c)) = mult(b, mult(c, a))))),
% 22.00/22.17 inference(unit_resolution,[status(thm)],[2270, 2269])).
% 22.00/22.17 tff(2272,plain,
% 22.00/22.17 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(b, a), c) = mult(mult(b, c), a))) | (~(mult(b, mult(a, c)) = mult(b, mult(c, a)))))) | (~((~(mult(mult(b, a), c) = mult(b, mult(a, c)))) | (~(mult(mult(b, c), a) = mult(b, mult(c, a)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(b, a), c) = mult(mult(b, c), a))) | (~(mult(b, mult(a, c)) = mult(b, mult(c, a)))))) | (~((~(mult(mult(b, a), c) = mult(b, mult(a, c)))) | (~(mult(mult(b, c), a) = mult(b, mult(c, a)))))))),
% 22.00/22.17 inference(rewrite,[status(thm)],[])).
% 22.00/22.17 tff(2273,plain,
% 22.00/22.17 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(b, a), c) = mult(mult(b, c), a))) | (~(mult(b, mult(a, c)) = mult(b, mult(c, a)))))) | (~((~(mult(mult(b, a), c) = mult(b, mult(a, c)))) | (~(mult(mult(b, c), a) = mult(b, mult(c, a)))))))),
% 22.00/22.17 inference(quant_inst,[status(thm)],[])).
% 22.00/22.17 tff(2274,plain,
% 22.00/22.17 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(b, a), c) = mult(mult(b, c), a))) | (~(mult(b, mult(a, c)) = mult(b, mult(c, a)))))) | (~((~(mult(mult(b, a), c) = mult(b, mult(a, c)))) | (~(mult(mult(b, c), a) = mult(b, mult(c, a))))))),
% 22.00/22.17 inference(modus_ponens,[status(thm)],[2273, 2272])).
% 22.00/22.18 tff(2275,plain,
% 22.00/22.18 ((~((~(mult(mult(b, a), c) = mult(mult(b, c), a))) | (~(mult(b, mult(a, c)) = mult(b, mult(c, a)))))) | (~((~(mult(mult(b, a), c) = mult(b, mult(a, c)))) | (~(mult(mult(b, c), a) = mult(b, mult(c, a))))))),
% 22.00/22.18 inference(unit_resolution,[status(thm)],[2274, 27])).
% 22.00/22.18 tff(2276,plain,
% 22.00/22.18 (~((~(mult(mult(b, a), c) = mult(b, mult(a, c)))) | (~(mult(mult(b, c), a) = mult(b, mult(c, a)))))),
% 22.00/22.18 inference(unit_resolution,[status(thm)],[2275, 2271])).
% 22.00/22.18 tff(2277,plain,
% 22.00/22.18 (((~(mult(mult(b, a), c) = mult(b, mult(a, c)))) | (~(mult(mult(b, c), a) = mult(b, mult(c, a))))) | (mult(mult(b, c), a) = mult(b, mult(c, a)))),
% 22.00/22.18 inference(tautology,[status(thm)],[])).
% 22.00/22.18 tff(2278,plain,
% 22.00/22.18 (mult(mult(b, c), a) = mult(b, mult(c, a))),
% 22.00/22.18 inference(unit_resolution,[status(thm)],[2277, 2276])).
% 22.00/22.18 tff(2279,plain,
% 22.00/22.18 (((~(mult(mult(c, b), a) = mult(c, mult(b, a)))) | (~(mult(mult(c, a), b) = mult(c, mult(a, b))))) | (mult(mult(c, a), b) = mult(c, mult(a, b)))),
% 22.00/22.18 inference(tautology,[status(thm)],[])).
% 22.00/22.18 tff(2280,plain,
% 22.00/22.18 (mult(mult(c, a), b) = mult(c, mult(a, b))),
% 22.00/22.18 inference(unit_resolution,[status(thm)],[2279, 2250])).
% 22.00/22.18 tff(2281,plain,
% 22.00/22.18 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(c, mult(c, mult(c, mult(c, ld(c, mult(a, b)))))) = mult(c, mult(c, ld(c, mult(a, b)))))),
% 22.00/22.18 inference(quant_inst,[status(thm)],[])).
% 22.00/22.18 tff(2282,plain,
% 22.00/22.18 (ld(c, mult(c, mult(c, mult(c, ld(c, mult(a, b)))))) = mult(c, mult(c, ld(c, mult(a, b))))),
% 22.00/22.18 inference(unit_resolution,[status(thm)],[2281, 7])).
% 22.00/22.18 tff(2283,assumption,(mult(mult(b, c), a) = mult(b, mult(c, a))), introduced(assumption)).
% 22.00/22.18 tff(2284,plain,
% 22.00/22.18 (mult(c, mult(mult(b, c), a)) = mult(c, mult(b, mult(c, a)))),
% 22.00/22.18 inference(monotonicity,[status(thm)],[2283])).
% 22.00/22.18 tff(2285,plain,
% 22.00/22.18 (mult(c, mult(b, mult(c, a))) = mult(c, mult(mult(b, c), a))),
% 22.00/22.18 inference(symmetry,[status(thm)],[2284])).
% 22.00/22.18 tff(2286,assumption,(mult(c, mult(b, mult(c, a))) = mult(c, mult(mult(c, a), b))), introduced(assumption)).
% 22.00/22.18 tff(2287,plain,
% 22.00/22.18 (mult(c, mult(mult(c, a), b)) = mult(c, mult(b, mult(c, a)))),
% 22.00/22.18 inference(symmetry,[status(thm)],[2286])).
% 22.00/22.18 tff(2288,assumption,(mult(mult(c, a), b) = mult(c, mult(a, b))), introduced(assumption)).
% 22.00/22.18 tff(2289,plain,
% 22.00/22.18 (mult(c, mult(mult(c, a), b)) = mult(c, mult(c, mult(a, b)))),
% 22.00/22.18 inference(monotonicity,[status(thm)],[2288])).
% 22.00/22.18 tff(2290,plain,
% 22.00/22.18 (mult(c, mult(c, mult(a, b))) = mult(c, mult(mult(c, a), b))),
% 22.00/22.18 inference(symmetry,[status(thm)],[2289])).
% 22.00/22.18 tff(2291,plain,
% 22.00/22.18 (mult(c, mult(c, mult(c, ld(c, mult(a, b))))) = mult(c, mult(c, mult(a, b)))),
% 22.00/22.18 inference(monotonicity,[status(thm)],[1443])).
% 22.00/22.18 tff(2292,plain,
% 22.00/22.18 (mult(c, mult(c, mult(c, ld(c, mult(a, b))))) = mult(c, mult(mult(b, c), a))),
% 22.00/22.18 inference(transitivity,[status(thm)],[2291, 2290, 2287, 2285])).
% 22.00/22.18 tff(2293,plain,
% 22.00/22.18 (ld(c, mult(c, mult(c, mult(c, ld(c, mult(a, b)))))) = ld(c, mult(c, mult(mult(b, c), a)))),
% 22.00/22.18 inference(monotonicity,[status(thm)],[2292])).
% 22.00/22.18 tff(2294,plain,
% 22.00/22.18 (ld(c, mult(c, mult(mult(b, c), a))) = ld(c, mult(c, mult(c, mult(c, ld(c, mult(a, b))))))),
% 22.00/22.18 inference(symmetry,[status(thm)],[2293])).
% 22.00/22.18 tff(2295,plain,
% 22.00/22.18 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(c, mult(c, mult(mult(b, c), a))) = mult(mult(b, c), a))),
% 22.00/22.18 inference(quant_inst,[status(thm)],[])).
% 22.00/22.18 tff(2296,plain,
% 22.00/22.18 (ld(c, mult(c, mult(mult(b, c), a))) = mult(mult(b, c), a)),
% 22.00/22.18 inference(unit_resolution,[status(thm)],[2295, 7])).
% 22.00/22.18 tff(2297,plain,
% 22.00/22.18 (mult(mult(b, c), a) = ld(c, mult(c, mult(mult(b, c), a)))),
% 22.00/22.18 inference(symmetry,[status(thm)],[2296])).
% 22.00/22.18 tff(2298,plain,
% 22.00/22.18 (mult(mult(c, b), a) = mult(mult(b, c), a)),
% 22.00/22.18 inference(monotonicity,[status(thm)],[241])).
% 22.00/22.18 tff(2299,assumption,(mult(mult(c, b), a) = mult(c, mult(b, a))), introduced(assumption)).
% 22.00/22.18 tff(2300,plain,
% 22.00/22.18 (mult(c, mult(b, a)) = mult(mult(c, b), a)),
% 22.00/22.18 inference(symmetry,[status(thm)],[2299])).
% 22.00/22.18 tff(2301,plain,
% 22.00/22.18 (mult(c, mult(b, a)) = mult(c, mult(a, b))),
% 22.00/22.18 inference(transitivity,[status(thm)],[2300, 2298, 2297, 2294, 2282, 1443])).
% 22.00/22.18 tff(2302,assumption,(~(mult(c, mult(b, a)) = mult(c, mult(a, b)))), introduced(assumption)).
% 22.00/22.18 tff(2303,plain,
% 22.00/22.18 ($false),
% 22.00/22.18 inference(unit_resolution,[status(thm)],[2302, 2301])).
% 22.00/22.18 tff(2304,plain,((~(mult(c, mult(b, mult(c, a))) = mult(c, mult(mult(c, a), b)))) | (mult(c, mult(b, a)) = mult(c, mult(a, b))) | (~(mult(mult(c, b), a) = mult(c, mult(b, a)))) | (~(mult(mult(c, a), b) = mult(c, mult(a, b)))) | (~(mult(mult(b, c), a) = mult(b, mult(c, a))))), inference(lemma,lemma(discharge,[]))).
% 22.00/22.18 tff(2305,plain,
% 22.00/22.18 (~(mult(c, mult(b, mult(c, a))) = mult(c, mult(mult(c, a), b)))),
% 22.00/22.18 inference(unit_resolution,[status(thm)],[2304, 2280, 2278, 2243, 2252])).
% 22.00/22.18 tff(2306,plain,
% 22.00/22.18 (((~(mult(mult(c, b), mult(c, a)) = mult(mult(c, mult(c, a)), b))) | (~(mult(c, mult(b, mult(c, a))) = mult(c, mult(mult(c, a), b))))) | (mult(c, mult(b, mult(c, a))) = mult(c, mult(mult(c, a), b)))),
% 22.00/22.18 inference(tautology,[status(thm)],[])).
% 22.00/22.18 tff(2307,plain,
% 22.00/22.18 ((~(mult(mult(c, b), mult(c, a)) = mult(mult(c, mult(c, a)), b))) | (~(mult(c, mult(b, mult(c, a))) = mult(c, mult(mult(c, a), b))))),
% 22.00/22.18 inference(unit_resolution,[status(thm)],[2306, 2305])).
% 22.00/22.18 tff(2308,plain,
% 22.00/22.18 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(c, b), mult(c, a)) = mult(mult(c, mult(c, a)), b))) | (~(mult(c, mult(b, mult(c, a))) = mult(c, mult(mult(c, a), b)))))) | (~((~(mult(mult(c, b), mult(c, a)) = mult(c, mult(b, mult(c, a))))) | (~(mult(mult(c, mult(c, a)), b) = mult(c, mult(mult(c, a), b)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(c, b), mult(c, a)) = mult(mult(c, mult(c, a)), b))) | (~(mult(c, mult(b, mult(c, a))) = mult(c, mult(mult(c, a), b)))))) | (~((~(mult(mult(c, b), mult(c, a)) = mult(c, mult(b, mult(c, a))))) | (~(mult(mult(c, mult(c, a)), b) = mult(c, mult(mult(c, a), b)))))))),
% 22.00/22.18 inference(rewrite,[status(thm)],[])).
% 22.00/22.18 tff(2309,plain,
% 22.00/22.18 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(c, b), mult(c, a)) = mult(mult(c, mult(c, a)), b))) | (~(mult(c, mult(b, mult(c, a))) = mult(c, mult(mult(c, a), b)))))) | (~((~(mult(mult(c, b), mult(c, a)) = mult(c, mult(b, mult(c, a))))) | (~(mult(mult(c, mult(c, a)), b) = mult(c, mult(mult(c, a), b)))))))),
% 22.00/22.18 inference(quant_inst,[status(thm)],[])).
% 22.00/22.18 tff(2310,plain,
% 22.00/22.18 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(c, b), mult(c, a)) = mult(mult(c, mult(c, a)), b))) | (~(mult(c, mult(b, mult(c, a))) = mult(c, mult(mult(c, a), b)))))) | (~((~(mult(mult(c, b), mult(c, a)) = mult(c, mult(b, mult(c, a))))) | (~(mult(mult(c, mult(c, a)), b) = mult(c, mult(mult(c, a), b))))))),
% 22.00/22.18 inference(modus_ponens,[status(thm)],[2309, 2308])).
% 22.00/22.18 tff(2311,plain,
% 22.00/22.18 ((~((~(mult(mult(c, b), mult(c, a)) = mult(mult(c, mult(c, a)), b))) | (~(mult(c, mult(b, mult(c, a))) = mult(c, mult(mult(c, a), b)))))) | (~((~(mult(mult(c, b), mult(c, a)) = mult(c, mult(b, mult(c, a))))) | (~(mult(mult(c, mult(c, a)), b) = mult(c, mult(mult(c, a), b))))))),
% 22.00/22.18 inference(unit_resolution,[status(thm)],[2310, 27])).
% 22.00/22.18 tff(2312,plain,
% 22.00/22.18 (~((~(mult(mult(c, b), mult(c, a)) = mult(c, mult(b, mult(c, a))))) | (~(mult(mult(c, mult(c, a)), b) = mult(c, mult(mult(c, a), b)))))),
% 22.00/22.18 inference(unit_resolution,[status(thm)],[2311, 2307])).
% 22.00/22.18 tff(2313,plain,
% 22.00/22.18 (((~(mult(mult(c, b), mult(c, a)) = mult(c, mult(b, mult(c, a))))) | (~(mult(mult(c, mult(c, a)), b) = mult(c, mult(mult(c, a), b))))) | (mult(mult(c, b), mult(c, a)) = mult(c, mult(b, mult(c, a))))),
% 22.02/22.18 inference(tautology,[status(thm)],[])).
% 22.02/22.18 tff(2314,plain,
% 22.02/22.18 (mult(mult(c, b), mult(c, a)) = mult(c, mult(b, mult(c, a)))),
% 22.02/22.18 inference(unit_resolution,[status(thm)],[2313, 2312])).
% 22.02/22.18 tff(2315,plain,
% 22.02/22.18 (mult(c, mult(b, mult(c, a))) = mult(mult(c, b), mult(c, a))),
% 22.02/22.18 inference(symmetry,[status(thm)],[2314])).
% 22.02/22.18 tff(2316,plain,
% 22.02/22.18 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)) = mult(b, mult(c, a))),
% 22.02/22.18 inference(transitivity,[status(thm)],[1169, 1164, 2278])).
% 22.02/22.18 tff(2317,plain,
% 22.02/22.18 (mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) = mult(c, mult(b, mult(c, a)))),
% 22.02/22.18 inference(monotonicity,[status(thm)],[2316])).
% 22.02/22.18 tff(2318,plain,
% 22.02/22.18 (mult(c, mult(mult(a, c), b)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))),
% 22.02/22.18 inference(monotonicity,[status(thm)],[2160])).
% 22.02/22.18 tff(2319,assumption,(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))), introduced(assumption)).
% 22.02/22.18 tff(2320,plain,
% 22.02/22.18 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))),
% 22.02/22.18 inference(unit_resolution,[status(thm)],[340, 332])).
% 22.02/22.18 tff(2321,plain,
% 22.02/22.18 (mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)),
% 22.02/22.18 inference(symmetry,[status(thm)],[2320])).
% 22.02/22.18 tff(2322,plain,
% 22.02/22.18 (~((~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))))),
% 22.02/22.18 inference(unit_resolution,[status(thm)],[1805, 332])).
% 22.02/22.18 tff(2323,plain,
% 22.02/22.18 (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))),
% 22.02/22.18 inference(unit_resolution,[status(thm)],[1801, 2322])).
% 22.02/22.18 tff(2324,plain,
% 22.02/22.18 (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))),
% 22.02/22.18 inference(symmetry,[status(thm)],[2323])).
% 22.02/22.18 tff(2325,plain,
% 22.02/22.18 ((mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))) <=> (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))),
% 22.02/22.18 inference(monotonicity,[status(thm)],[2324, 2321])).
% 22.02/22.18 tff(2326,plain,
% 22.02/22.18 ((mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)) <=> (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))),
% 22.02/22.18 inference(symmetry,[status(thm)],[2325])).
% 22.02/22.18 tff(2327,plain,
% 22.02/22.18 (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))),
% 22.02/22.18 inference(modus_ponens,[status(thm)],[1683, 2326])).
% 22.02/22.18 tff(2328,plain,
% 22.02/22.18 ($false),
% 22.02/22.18 inference(unit_resolution,[status(thm)],[330, 2327])).
% 22.02/22.18 tff(2329,plain,((~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))) | (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))), inference(lemma,lemma(discharge,[]))).
% 22.02/22.18 tff(2330,plain,
% 22.02/22.18 (~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))),
% 22.02/22.18 inference(unit_resolution,[status(thm)],[2329, 330])).
% 22.02/22.18 tff(2331,assumption,(~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))), introduced(assumption)).
% 22.02/22.18 tff(2332,plain,
% 22.02/22.18 (mult(mult(a, rd(mult(b, c), mult(a, c))), c) = mult(b, c)),
% 22.02/22.18 inference(transitivity,[status(thm)],[2189, 2187, 2172, 2178, 2177, 2162, 296, 293, 291])).
% 22.02/22.18 tff(2333,plain,
% 22.02/22.18 (rd(mult(mult(a, rd(mult(b, c), mult(a, c))), c), c) = rd(mult(b, c), c)),
% 22.02/22.18 inference(monotonicity,[status(thm)],[2332])).
% 22.02/22.18 tff(2334,plain,
% 22.02/22.18 (mult(a, rd(mult(b, c), mult(a, c))) = b),
% 22.02/22.18 inference(transitivity,[status(thm)],[2194, 2333, 170])).
% 22.02/22.18 tff(2335,plain,
% 22.02/22.18 (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), b)),
% 22.02/22.18 inference(monotonicity,[status(thm)],[2334])).
% 22.02/22.18 tff(2336,plain,
% 22.02/22.18 (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)),
% 22.02/22.18 inference(transitivity,[status(thm)],[2319, 2335, 405, 1800])).
% 22.02/22.18 tff(2337,plain,
% 22.02/22.18 ($false),
% 22.02/22.18 inference(unit_resolution,[status(thm)],[2331, 2336])).
% 22.02/22.18 tff(2338,plain,((~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))) | (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit)))))), inference(lemma,lemma(discharge,[]))).
% 22.02/22.18 tff(2339,plain,
% 22.02/22.18 (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))),
% 22.02/22.18 inference(unit_resolution,[status(thm)],[2338, 286, 97, 2319, 1799, 2331])).
% 22.02/22.18 tff(2340,plain,
% 22.02/22.18 ((~(mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))),
% 22.02/22.18 inference(unit_resolution,[status(thm)],[2201, 2339])).
% 22.02/22.18 tff(2341,plain,
% 22.02/22.18 (~((~(mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)))))),
% 22.02/22.18 inference(unit_resolution,[status(thm)],[2213, 2340])).
% 22.02/22.18 tff(2342,plain,
% 22.02/22.18 (mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))),
% 22.02/22.18 inference(unit_resolution,[status(thm)],[2215, 2341])).
% 22.02/22.18 tff(2343,plain,
% 22.02/22.18 (mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))),
% 22.02/22.18 inference(symmetry,[status(thm)],[2342])).
% 22.02/22.18 tff(2344,plain,
% 22.02/22.18 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(c, a), mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c))))) = mult(c, rd(mult(b, c), mult(a, c))))),
% 22.02/22.18 inference(quant_inst,[status(thm)],[])).
% 22.02/22.18 tff(2345,plain,
% 22.02/22.18 (ld(mult(c, a), mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c))))) = mult(c, rd(mult(b, c), mult(a, c)))),
% 22.02/22.18 inference(unit_resolution,[status(thm)],[2344, 7])).
% 22.02/22.18 tff(2346,assumption,(mult(mult(c, a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c))))), introduced(assumption)).
% 22.02/22.18 tff(2347,plain,
% 22.02/22.18 (mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(c, a), mult(rd(mult(b, c), mult(a, c)), c))),
% 22.02/22.18 inference(symmetry,[status(thm)],[2346])).
% 22.02/22.18 tff(2348,plain,
% 22.02/22.18 (ld(mult(c, a), mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c))))) = ld(mult(c, a), mult(mult(c, a), mult(rd(mult(b, c), mult(a, c)), c)))),
% 22.02/22.18 inference(monotonicity,[status(thm)],[2347])).
% 22.02/22.18 tff(2349,plain,
% 22.02/22.18 (ld(mult(c, a), mult(mult(c, a), mult(rd(mult(b, c), mult(a, c)), c))) = ld(mult(c, a), mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c)))))),
% 22.02/22.18 inference(symmetry,[status(thm)],[2348])).
% 22.02/22.18 tff(2350,plain,
% 22.02/22.18 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(c, a), mult(mult(c, a), mult(rd(mult(b, c), mult(a, c)), c))) = mult(rd(mult(b, c), mult(a, c)), c))),
% 22.02/22.19 inference(quant_inst,[status(thm)],[])).
% 22.02/22.19 tff(2351,plain,
% 22.02/22.19 (ld(mult(c, a), mult(mult(c, a), mult(rd(mult(b, c), mult(a, c)), c))) = mult(rd(mult(b, c), mult(a, c)), c)),
% 22.02/22.19 inference(unit_resolution,[status(thm)],[2350, 7])).
% 22.02/22.19 tff(2352,plain,
% 22.02/22.19 (mult(rd(mult(b, c), mult(a, c)), c) = ld(mult(c, a), mult(mult(c, a), mult(rd(mult(b, c), mult(a, c)), c)))),
% 22.02/22.19 inference(symmetry,[status(thm)],[2351])).
% 22.02/22.19 tff(2353,plain,
% 22.02/22.19 (mult(rd(mult(b, c), mult(a, c)), c) = mult(c, rd(mult(b, c), mult(a, c)))),
% 22.02/22.19 inference(transitivity,[status(thm)],[2352, 2349, 2345])).
% 22.02/22.19 tff(2354,plain,
% 22.02/22.19 (mult(a, mult(rd(mult(b, c), mult(a, c)), c)) = mult(a, mult(c, rd(mult(b, c), mult(a, c))))),
% 22.02/22.19 inference(monotonicity,[status(thm)],[2353])).
% 22.02/22.19 tff(2355,plain,
% 22.02/22.19 (mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c) = mult(rd(mult(b, c), mult(a, c)), c)),
% 22.02/22.19 inference(monotonicity,[status(thm)],[1896])).
% 22.02/22.19 tff(2356,plain,
% 22.02/22.19 (mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), c))),
% 22.02/22.19 inference(monotonicity,[status(thm)],[2355])).
% 22.02/22.19 tff(2357,plain,
% 22.02/22.19 (((~(mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c))))) | (mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)))),
% 22.02/22.19 inference(tautology,[status(thm)],[])).
% 22.02/22.19 tff(2358,plain,
% 22.02/22.19 (mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c))),
% 22.02/22.19 inference(unit_resolution,[status(thm)],[2357, 2341])).
% 22.02/22.19 tff(2359,plain,
% 22.02/22.19 (mult(mult(a, rd(mult(b, c), mult(a, c))), c) = mult(b, c)),
% 22.02/22.19 inference(transitivity,[status(thm)],[2189, 2358, 2356, 2354, 2220, 2343, 2172, 2178, 2177, 2162, 296, 293, 291])).
% 22.02/22.19 tff(2360,plain,
% 22.02/22.19 (rd(mult(mult(a, rd(mult(b, c), mult(a, c))), c), c) = rd(mult(b, c), c)),
% 22.02/22.19 inference(monotonicity,[status(thm)],[2359])).
% 22.02/22.19 tff(2361,plain,
% 22.02/22.19 (mult(a, rd(mult(b, c), mult(a, c))) = b),
% 22.02/22.19 inference(transitivity,[status(thm)],[2194, 2360, 170])).
% 22.02/22.19 tff(2362,plain,
% 22.02/22.19 (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), b)),
% 22.02/22.19 inference(monotonicity,[status(thm)],[2361])).
% 22.02/22.19 tff(2363,plain,
% 22.02/22.19 (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)),
% 22.02/22.19 inference(transitivity,[status(thm)],[2319, 2362, 405, 1800])).
% 22.02/22.19 tff(2364,plain,
% 22.02/22.19 ($false),
% 22.02/22.19 inference(unit_resolution,[status(thm)],[2331, 2363])).
% 22.02/22.19 tff(2365,plain,((~(mult(mult(c, a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c)))))) | (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit)))))), inference(lemma,lemma(discharge,[]))).
% 22.02/22.19 tff(2366,plain,
% 22.02/22.19 (~(mult(mult(c, a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c)))))),
% 22.02/22.19 inference(unit_resolution,[status(thm)],[2365, 2330, 97, 2128, 2258, 2319])).
% 22.02/22.19 tff(2367,plain,
% 22.02/22.19 (((~(mult(mult(mult(c, a), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(c, a), c), rd(mult(b, c), mult(a, c))))) | (~(mult(mult(c, a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c))))))) | (mult(mult(c, a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c)))))),
% 22.02/22.19 inference(tautology,[status(thm)],[])).
% 22.02/22.19 tff(2368,plain,
% 22.02/22.19 ((~(mult(mult(mult(c, a), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(c, a), c), rd(mult(b, c), mult(a, c))))) | (~(mult(mult(c, a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c))))))),
% 22.02/22.19 inference(unit_resolution,[status(thm)],[2367, 2366])).
% 22.02/22.19 tff(2369,plain,
% 22.02/22.19 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(c, a), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(c, a), c), rd(mult(b, c), mult(a, c))))) | (~(mult(mult(c, a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(mult(c, a), rd(mult(b, c), mult(a, c))), c) = mult(mult(c, a), mult(rd(mult(b, c), mult(a, c)), c)))) | (~(mult(mult(mult(c, a), c), rd(mult(b, c), mult(a, c))) = mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c)))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(c, a), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(c, a), c), rd(mult(b, c), mult(a, c))))) | (~(mult(mult(c, a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(mult(c, a), rd(mult(b, c), mult(a, c))), c) = mult(mult(c, a), mult(rd(mult(b, c), mult(a, c)), c)))) | (~(mult(mult(mult(c, a), c), rd(mult(b, c), mult(a, c))) = mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c)))))))))),
% 22.02/22.19 inference(rewrite,[status(thm)],[])).
% 22.02/22.19 tff(2370,plain,
% 22.02/22.19 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(c, a), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(c, a), c), rd(mult(b, c), mult(a, c))))) | (~(mult(mult(c, a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(mult(c, a), rd(mult(b, c), mult(a, c))), c) = mult(mult(c, a), mult(rd(mult(b, c), mult(a, c)), c)))) | (~(mult(mult(mult(c, a), c), rd(mult(b, c), mult(a, c))) = mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c)))))))))),
% 22.02/22.19 inference(quant_inst,[status(thm)],[])).
% 22.02/22.19 tff(2371,plain,
% 22.02/22.19 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(c, a), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(c, a), c), rd(mult(b, c), mult(a, c))))) | (~(mult(mult(c, a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(mult(c, a), rd(mult(b, c), mult(a, c))), c) = mult(mult(c, a), mult(rd(mult(b, c), mult(a, c)), c)))) | (~(mult(mult(mult(c, a), c), rd(mult(b, c), mult(a, c))) = mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c))))))))),
% 22.02/22.19 inference(modus_ponens,[status(thm)],[2370, 2369])).
% 22.02/22.19 tff(2372,plain,
% 22.02/22.19 ((~((~(mult(mult(mult(c, a), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(c, a), c), rd(mult(b, c), mult(a, c))))) | (~(mult(mult(c, a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(mult(c, a), rd(mult(b, c), mult(a, c))), c) = mult(mult(c, a), mult(rd(mult(b, c), mult(a, c)), c)))) | (~(mult(mult(mult(c, a), c), rd(mult(b, c), mult(a, c))) = mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c))))))))),
% 22.02/22.19 inference(unit_resolution,[status(thm)],[2371, 27])).
% 22.02/22.19 tff(2373,plain,
% 22.02/22.19 (~((~(mult(mult(mult(c, a), rd(mult(b, c), mult(a, c))), c) = mult(mult(c, a), mult(rd(mult(b, c), mult(a, c)), c)))) | (~(mult(mult(mult(c, a), c), rd(mult(b, c), mult(a, c))) = mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c)))))))),
% 22.02/22.19 inference(unit_resolution,[status(thm)],[2372, 2368])).
% 22.02/22.19 tff(2374,plain,
% 22.02/22.19 (((~(mult(mult(mult(c, a), rd(mult(b, c), mult(a, c))), c) = mult(mult(c, a), mult(rd(mult(b, c), mult(a, c)), c)))) | (~(mult(mult(mult(c, a), c), rd(mult(b, c), mult(a, c))) = mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c))))))) | (mult(mult(mult(c, a), c), rd(mult(b, c), mult(a, c))) = mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c)))))),
% 22.02/22.19 inference(tautology,[status(thm)],[])).
% 22.02/22.19 tff(2375,plain,
% 22.02/22.19 (mult(mult(mult(c, a), c), rd(mult(b, c), mult(a, c))) = mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c))))),
% 22.02/22.19 inference(unit_resolution,[status(thm)],[2374, 2373])).
% 22.02/22.19 tff(2376,plain,
% 22.02/22.19 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(c, mult(a, c)), mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c))))) = mult(a, rd(mult(b, c), mult(a, c))))),
% 22.02/22.19 inference(quant_inst,[status(thm)],[])).
% 22.02/22.19 tff(2377,plain,
% 22.02/22.19 (ld(mult(c, mult(a, c)), mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c))))) = mult(a, rd(mult(b, c), mult(a, c)))),
% 22.02/22.19 inference(unit_resolution,[status(thm)],[2376, 7])).
% 22.02/22.19 tff(2378,assumption,(mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c))))), introduced(assumption)).
% 22.02/22.19 tff(2379,plain,
% 22.02/22.19 (mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a))),
% 22.02/22.19 inference(symmetry,[status(thm)],[2378])).
% 22.02/22.19 tff(2380,plain,
% 22.02/22.19 (ld(mult(c, mult(a, c)), mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c))))) = ld(mult(c, mult(a, c)), mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)))),
% 22.02/22.19 inference(monotonicity,[status(thm)],[2379])).
% 22.02/22.19 tff(2381,plain,
% 22.02/22.19 (ld(mult(c, mult(a, c)), mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a))) = ld(mult(c, mult(a, c)), mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))),
% 22.02/22.19 inference(symmetry,[status(thm)],[2380])).
% 22.02/22.19 tff(2382,plain,
% 22.02/22.19 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(c, mult(a, c)), mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a))) = mult(rd(mult(b, c), mult(a, c)), a))),
% 22.02/22.19 inference(quant_inst,[status(thm)],[])).
% 22.02/22.19 tff(2383,plain,
% 22.02/22.19 (ld(mult(c, mult(a, c)), mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a))) = mult(rd(mult(b, c), mult(a, c)), a)),
% 22.02/22.19 inference(unit_resolution,[status(thm)],[2382, 7])).
% 22.02/22.19 tff(2384,plain,
% 22.02/22.19 (mult(rd(mult(b, c), mult(a, c)), a) = ld(mult(c, mult(a, c)), mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)))),
% 22.02/22.19 inference(symmetry,[status(thm)],[2383])).
% 22.02/22.19 tff(2385,plain,
% 22.02/22.19 (mult(rd(mult(b, c), mult(a, c)), a) = mult(a, rd(mult(b, c), mult(a, c)))),
% 22.02/22.19 inference(transitivity,[status(thm)],[2384, 2381, 2377])).
% 22.02/22.19 tff(2386,plain,
% 22.02/22.19 (mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))),
% 22.02/22.19 inference(monotonicity,[status(thm)],[2385])).
% 22.02/22.19 tff(2387,plain,
% 22.02/22.19 (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))),
% 22.02/22.19 inference(symmetry,[status(thm)],[2386])).
% 22.02/22.19 tff(2388,plain,
% 22.02/22.19 (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)),
% 22.02/22.19 inference(transitivity,[status(thm)],[2319, 2387, 1800])).
% 22.02/22.19 tff(2389,plain,
% 22.02/22.19 ($false),
% 22.02/22.19 inference(unit_resolution,[status(thm)],[2331, 2388])).
% 22.02/22.19 tff(2390,plain,((~(mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))) | (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))))), inference(lemma,lemma(discharge,[]))).
% 22.02/22.19 tff(2391,plain,
% 22.02/22.19 (~(mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))),
% 22.02/22.19 inference(unit_resolution,[status(thm)],[2390, 2330, 2128, 2319])).
% 22.02/22.19 tff(2392,assumption,((~(mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a))))), introduced(assumption)).
% 22.02/22.19 tff(2393,assumption,(~(mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))), introduced(assumption)).
% 22.02/22.19 tff(2394,plain,
% 22.02/22.19 (((~(mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c)))))) | (mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))),
% 22.02/22.19 inference(tautology,[status(thm)],[])).
% 22.02/22.19 tff(2395,plain,
% 22.02/22.19 ((~(mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c)))))),
% 22.02/22.19 inference(unit_resolution,[status(thm)],[2394, 2393])).
% 22.02/22.19 tff(2396,assumption,((~(mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c)))))), introduced(assumption)).
% 22.02/22.19 tff(2397,plain,
% 22.02/22.19 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))))))) | (~((~(mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))))))) | (~((~(mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)))))))),
% 22.02/22.19 inference(rewrite,[status(thm)],[])).
% 22.02/22.19 tff(2398,plain,
% 22.02/22.19 (((~((~(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))))) | (~(mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c))))))))) <=> ((~((~(mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))))))) | (~((~(mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)))))))),
% 22.02/22.20 inference(rewrite,[status(thm)],[])).
% 22.02/22.20 tff(2399,plain,
% 22.02/22.20 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))))) | (~(mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))))))) | (~((~(mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a))))))))),
% 22.02/22.20 inference(monotonicity,[status(thm)],[2398])).
% 22.02/22.20 tff(2400,plain,
% 22.02/22.20 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))))) | (~(mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))))))) | (~((~(mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)))))))),
% 22.02/22.20 inference(transitivity,[status(thm)],[2399, 2397])).
% 22.02/22.20 tff(2401,plain,
% 22.02/22.20 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))))) | (~(mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))))))),
% 22.02/22.20 inference(quant_inst,[status(thm)],[])).
% 22.02/22.20 tff(2402,plain,
% 22.02/22.20 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))))))) | (~((~(mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a))))))),
% 22.02/22.20 inference(modus_ponens,[status(thm)],[2401, 2400])).
% 22.02/22.20 tff(2403,plain,
% 22.02/22.20 ($false),
% 22.02/22.20 inference(unit_resolution,[status(thm)],[2402, 27, 2392, 2396])).
% 22.02/22.20 tff(2404,plain,((~((~(mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))))))) | (~((~(mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a))))))), inference(lemma,lemma(discharge,[]))).
% 22.02/22.20 tff(2405,plain,
% 22.02/22.20 ($false),
% 22.02/22.20 inference(unit_resolution,[status(thm)],[2404, 2395, 2392])).
% 22.02/22.20 tff(2406,plain,((~((~(mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)))))) | (mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))), inference(lemma,lemma(discharge,[]))).
% 22.02/22.20 tff(2407,plain,
% 22.02/22.20 (~((~(mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)))))),
% 22.02/22.20 inference(unit_resolution,[status(thm)],[2406, 2391])).
% 22.02/22.20 tff(2408,plain,
% 22.02/22.20 (((~(mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a))))) | (mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)))),
% 22.02/22.20 inference(tautology,[status(thm)],[])).
% 22.02/22.20 tff(2409,plain,
% 22.02/22.20 (mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a))),
% 22.02/22.20 inference(unit_resolution,[status(thm)],[2408, 2407])).
% 22.02/22.20 tff(2410,plain,
% 22.02/22.20 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), b)),
% 22.02/22.20 inference(transitivity,[status(thm)],[1799, 177])).
% 22.02/22.20 tff(2411,plain,
% 22.02/22.20 (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(a, c), b), c)),
% 22.02/22.20 inference(monotonicity,[status(thm)],[2410])).
% 22.02/22.20 tff(2412,plain,
% 22.02/22.20 ((mult(a, mult(mult(b, c), c)) = mult(mult(a, mult(b, c)), c)) <=> (mult(mult(a, mult(b, c)), c) = mult(a, mult(mult(b, c), c)))),
% 22.02/22.20 inference(commutativity,[status(thm)],[])).
% 22.02/22.20 tff(2413,plain,
% 22.02/22.20 (mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c))) = mult(mult(a, mult(b, c)), c)),
% 22.02/22.20 inference(transitivity,[status(thm)],[138, 266])).
% 22.02/22.20 tff(2414,plain,
% 22.02/22.20 (mult(a, mult(mult(c, b), c)) = mult(a, mult(mult(b, c), c))),
% 22.02/22.20 inference(monotonicity,[status(thm)],[242])).
% 22.02/22.20 tff(2415,plain,
% 22.02/22.20 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(a, mult(mult(b, c), c))),
% 22.02/22.20 inference(transitivity,[status(thm)],[738, 2411, 233, 2414])).
% 22.02/22.20 tff(2416,plain,
% 22.02/22.20 ((mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))) <=> (mult(a, mult(mult(b, c), c)) = mult(mult(a, mult(b, c)), c))),
% 22.02/22.20 inference(monotonicity,[status(thm)],[2415, 2413])).
% 22.02/22.20 tff(2417,plain,
% 22.02/22.20 ((mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))) <=> (mult(mult(a, mult(b, c)), c) = mult(a, mult(mult(b, c), c)))),
% 22.02/22.20 inference(transitivity,[status(thm)],[2416, 2412])).
% 22.02/22.20 tff(2418,plain,
% 22.02/22.20 ((mult(mult(a, mult(b, c)), c) = mult(a, mult(mult(b, c), c))) <=> (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))),
% 22.02/22.20 inference(symmetry,[status(thm)],[2417])).
% 22.02/22.20 tff(2419,plain,
% 22.02/22.20 ((~(mult(mult(a, mult(b, c)), c) = mult(a, mult(mult(b, c), c)))) <=> (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))),
% 22.02/22.20 inference(monotonicity,[status(thm)],[2418])).
% 22.02/22.20 tff(2420,plain,
% 22.02/22.20 (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))),
% 22.02/22.20 inference(modus_ponens,[status(thm)],[258, 2419])).
% 22.02/22.20 tff(2421,plain,
% 22.02/22.20 ((~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))),
% 22.02/22.20 inference(unit_resolution,[status(thm)],[315, 2420])).
% 22.02/22.20 tff(2422,plain,
% 22.02/22.20 (~((~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))),
% 22.02/22.20 inference(unit_resolution,[status(thm)],[313, 2421])).
% 22.02/22.20 tff(2423,plain,
% 22.02/22.20 (mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))),
% 22.02/22.20 inference(unit_resolution,[status(thm)],[308, 2422])).
% 22.02/22.20 tff(2424,plain,
% 22.02/22.20 (mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(b, c))),
% 22.02/22.20 inference(transitivity,[status(thm)],[2423, 138])).
% 22.02/22.20 tff(2425,plain,
% 22.02/22.20 (ld(mult(a, c), mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c))))) = ld(mult(a, c), mult(mult(a, c), mult(b, c)))),
% 22.02/22.20 inference(monotonicity,[status(thm)],[2424])).
% 22.02/22.20 tff(2426,plain,
% 22.02/22.20 (ld(mult(a, c), mult(mult(a, c), mult(b, c))) = ld(mult(a, c), mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 22.02/22.20 inference(symmetry,[status(thm)],[2425])).
% 22.02/22.20 tff(2427,plain,
% 22.02/22.20 (mult(b, c) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))),
% 22.02/22.20 inference(transitivity,[status(thm)],[740, 2426, 295])).
% 22.02/22.20 tff(2428,plain,
% 22.02/22.20 (mult(mult(b, c), mult(a, c)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))),
% 22.02/22.20 inference(monotonicity,[status(thm)],[2427])).
% 22.02/22.20 tff(2429,plain,
% 22.02/22.20 (mult(mult(c, b), mult(a, c)) = mult(mult(b, c), mult(a, c))),
% 22.02/22.20 inference(monotonicity,[status(thm)],[241])).
% 22.02/22.20 tff(2430,assumption,(~(mult(mult(c, b), mult(a, c)) = mult(c, mult(b, mult(a, c))))), introduced(assumption)).
% 22.02/22.20 tff(2431,plain,
% 22.02/22.20 (((~(mult(mult(c, mult(a, c)), b) = mult(c, mult(mult(a, c), b)))) | (~(mult(mult(c, b), mult(a, c)) = mult(c, mult(b, mult(a, c)))))) | (mult(mult(c, b), mult(a, c)) = mult(c, mult(b, mult(a, c))))),
% 22.02/22.20 inference(tautology,[status(thm)],[])).
% 22.02/22.20 tff(2432,plain,
% 22.02/22.20 ((~(mult(mult(c, mult(a, c)), b) = mult(c, mult(mult(a, c), b)))) | (~(mult(mult(c, b), mult(a, c)) = mult(c, mult(b, mult(a, c)))))),
% 22.02/22.20 inference(unit_resolution,[status(thm)],[2431, 2430])).
% 22.02/22.20 tff(2433,plain,
% 22.02/22.20 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(c, mult(a, c)), b) = mult(mult(c, b), mult(a, c)))) | (~(mult(c, mult(mult(a, c), b)) = mult(c, mult(b, mult(a, c))))))) | (~((~(mult(mult(c, mult(a, c)), b) = mult(c, mult(mult(a, c), b)))) | (~(mult(mult(c, b), mult(a, c)) = mult(c, mult(b, mult(a, c))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(c, mult(a, c)), b) = mult(mult(c, b), mult(a, c)))) | (~(mult(c, mult(mult(a, c), b)) = mult(c, mult(b, mult(a, c))))))) | (~((~(mult(mult(c, mult(a, c)), b) = mult(c, mult(mult(a, c), b)))) | (~(mult(mult(c, b), mult(a, c)) = mult(c, mult(b, mult(a, c))))))))),
% 22.02/22.20 inference(rewrite,[status(thm)],[])).
% 22.02/22.20 tff(2434,plain,
% 22.02/22.20 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(c, mult(a, c)), b) = mult(mult(c, b), mult(a, c)))) | (~(mult(c, mult(mult(a, c), b)) = mult(c, mult(b, mult(a, c))))))) | (~((~(mult(mult(c, mult(a, c)), b) = mult(c, mult(mult(a, c), b)))) | (~(mult(mult(c, b), mult(a, c)) = mult(c, mult(b, mult(a, c))))))))),
% 22.02/22.20 inference(quant_inst,[status(thm)],[])).
% 22.02/22.20 tff(2435,plain,
% 22.02/22.20 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(c, mult(a, c)), b) = mult(mult(c, b), mult(a, c)))) | (~(mult(c, mult(mult(a, c), b)) = mult(c, mult(b, mult(a, c))))))) | (~((~(mult(mult(c, mult(a, c)), b) = mult(c, mult(mult(a, c), b)))) | (~(mult(mult(c, b), mult(a, c)) = mult(c, mult(b, mult(a, c)))))))),
% 22.02/22.20 inference(modus_ponens,[status(thm)],[2434, 2433])).
% 22.02/22.20 tff(2436,plain,
% 22.02/22.20 ((~((~(mult(mult(c, mult(a, c)), b) = mult(mult(c, b), mult(a, c)))) | (~(mult(c, mult(mult(a, c), b)) = mult(c, mult(b, mult(a, c))))))) | (~((~(mult(mult(c, mult(a, c)), b) = mult(c, mult(mult(a, c), b)))) | (~(mult(mult(c, b), mult(a, c)) = mult(c, mult(b, mult(a, c)))))))),
% 22.02/22.20 inference(unit_resolution,[status(thm)],[2435, 27])).
% 22.02/22.20 tff(2437,plain,
% 22.02/22.20 (~((~(mult(mult(c, mult(a, c)), b) = mult(mult(c, b), mult(a, c)))) | (~(mult(c, mult(mult(a, c), b)) = mult(c, mult(b, mult(a, c))))))),
% 22.02/22.20 inference(unit_resolution,[status(thm)],[2436, 2432])).
% 22.02/22.20 tff(2438,plain,
% 22.02/22.20 (((~(mult(mult(c, mult(a, c)), b) = mult(mult(c, b), mult(a, c)))) | (~(mult(c, mult(mult(a, c), b)) = mult(c, mult(b, mult(a, c)))))) | (mult(mult(c, mult(a, c)), b) = mult(mult(c, b), mult(a, c)))),
% 22.02/22.20 inference(tautology,[status(thm)],[])).
% 22.02/22.21 tff(2439,plain,
% 22.02/22.21 (mult(mult(c, mult(a, c)), b) = mult(mult(c, b), mult(a, c))),
% 22.02/22.21 inference(unit_resolution,[status(thm)],[2438, 2437])).
% 22.02/22.21 tff(2440,plain,
% 22.02/22.21 (mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(c, mult(a, c)), b)),
% 22.02/22.21 inference(monotonicity,[status(thm)],[176])).
% 22.02/22.21 tff(2441,plain,
% 22.02/22.21 (~((~(mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)))))),
% 22.02/22.21 inference(unit_resolution,[status(thm)],[2402, 27, 2395])).
% 22.02/22.21 tff(2442,plain,
% 22.02/22.21 (mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a))),
% 22.02/22.21 inference(unit_resolution,[status(thm)],[2408, 2441])).
% 22.02/22.21 tff(2443,assumption,(~(mult(mult(c, a), c) = mult(c, mult(a, c)))), introduced(assumption)).
% 22.02/22.21 tff(2444,plain,
% 22.02/22.21 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(b, mult(b, mult(c, mult(a, c)))) = mult(c, mult(a, c)))),
% 22.02/22.21 inference(quant_inst,[status(thm)],[])).
% 22.02/22.21 tff(2445,plain,
% 22.02/22.21 (ld(b, mult(b, mult(c, mult(a, c)))) = mult(c, mult(a, c))),
% 22.02/22.21 inference(unit_resolution,[status(thm)],[2444, 7])).
% 22.02/22.21 tff(2446,assumption,(mult(b, mult(mult(a, c), c)) = mult(b, mult(c, mult(a, c)))), introduced(assumption)).
% 22.02/22.21 tff(2447,plain,
% 22.02/22.21 (ld(b, mult(b, mult(mult(a, c), c))) = ld(b, mult(b, mult(c, mult(a, c))))),
% 22.02/22.21 inference(monotonicity,[status(thm)],[2446])).
% 22.02/22.21 tff(2448,plain,
% 22.02/22.21 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(b, mult(b, mult(mult(a, c), c))) = mult(mult(a, c), c))),
% 22.02/22.21 inference(quant_inst,[status(thm)],[])).
% 22.02/22.21 tff(2449,plain,
% 22.02/22.21 (ld(b, mult(b, mult(mult(a, c), c))) = mult(mult(a, c), c)),
% 22.02/22.21 inference(unit_resolution,[status(thm)],[2448, 7])).
% 22.02/22.21 tff(2450,plain,
% 22.02/22.21 (mult(mult(a, c), c) = ld(b, mult(b, mult(mult(a, c), c)))),
% 22.02/22.21 inference(symmetry,[status(thm)],[2449])).
% 22.02/22.21 tff(2451,plain,
% 22.02/22.21 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(c, mult(c, mult(a, c))) = mult(a, c))),
% 22.02/22.21 inference(quant_inst,[status(thm)],[])).
% 22.02/22.21 tff(2452,plain,
% 22.02/22.21 (ld(c, mult(c, mult(a, c))) = mult(a, c)),
% 22.02/22.21 inference(unit_resolution,[status(thm)],[2451, 7])).
% 22.02/22.21 tff(2453,plain,
% 22.02/22.21 (((~(mult(mult(c, c), a) = mult(c, mult(c, a)))) | (~(mult(mult(c, a), c) = mult(c, mult(a, c))))) | (mult(mult(c, a), c) = mult(c, mult(a, c)))),
% 22.02/22.21 inference(tautology,[status(thm)],[])).
% 22.02/22.21 tff(2454,plain,
% 22.02/22.21 ((~(mult(mult(c, c), a) = mult(c, mult(c, a)))) | (~(mult(mult(c, a), c) = mult(c, mult(a, c))))),
% 22.02/22.21 inference(unit_resolution,[status(thm)],[2453, 2443])).
% 22.02/22.21 tff(2455,plain,
% 22.02/22.21 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(c, mult(c, a)) = mult(c, mult(a, c)))) | (~(mult(mult(c, c), a) = mult(mult(c, a), c))))) | (~((~(mult(mult(c, c), a) = mult(c, mult(c, a)))) | (~(mult(mult(c, a), c) = mult(c, mult(a, c)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(c, mult(c, a)) = mult(c, mult(a, c)))) | (~(mult(mult(c, c), a) = mult(mult(c, a), c))))) | (~((~(mult(mult(c, c), a) = mult(c, mult(c, a)))) | (~(mult(mult(c, a), c) = mult(c, mult(a, c)))))))),
% 22.02/22.21 inference(rewrite,[status(thm)],[])).
% 22.02/22.21 tff(2456,plain,
% 22.02/22.21 (((~((~(mult(mult(c, c), a) = mult(mult(c, a), c))) | (~(mult(c, mult(c, a)) = mult(c, mult(a, c)))))) | (~((~(mult(mult(c, c), a) = mult(c, mult(c, a)))) | (~(mult(mult(c, a), c) = mult(c, mult(a, c))))))) <=> ((~((~(mult(c, mult(c, a)) = mult(c, mult(a, c)))) | (~(mult(mult(c, c), a) = mult(mult(c, a), c))))) | (~((~(mult(mult(c, c), a) = mult(c, mult(c, a)))) | (~(mult(mult(c, a), c) = mult(c, mult(a, c)))))))),
% 22.02/22.21 inference(rewrite,[status(thm)],[])).
% 22.02/22.21 tff(2457,plain,
% 22.02/22.21 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(c, c), a) = mult(mult(c, a), c))) | (~(mult(c, mult(c, a)) = mult(c, mult(a, c)))))) | (~((~(mult(mult(c, c), a) = mult(c, mult(c, a)))) | (~(mult(mult(c, a), c) = mult(c, mult(a, c)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(c, mult(c, a)) = mult(c, mult(a, c)))) | (~(mult(mult(c, c), a) = mult(mult(c, a), c))))) | (~((~(mult(mult(c, c), a) = mult(c, mult(c, a)))) | (~(mult(mult(c, a), c) = mult(c, mult(a, c))))))))),
% 22.02/22.21 inference(monotonicity,[status(thm)],[2456])).
% 22.02/22.21 tff(2458,plain,
% 22.02/22.21 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(c, c), a) = mult(mult(c, a), c))) | (~(mult(c, mult(c, a)) = mult(c, mult(a, c)))))) | (~((~(mult(mult(c, c), a) = mult(c, mult(c, a)))) | (~(mult(mult(c, a), c) = mult(c, mult(a, c)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(c, mult(c, a)) = mult(c, mult(a, c)))) | (~(mult(mult(c, c), a) = mult(mult(c, a), c))))) | (~((~(mult(mult(c, c), a) = mult(c, mult(c, a)))) | (~(mult(mult(c, a), c) = mult(c, mult(a, c)))))))),
% 22.02/22.21 inference(transitivity,[status(thm)],[2457, 2455])).
% 22.02/22.21 tff(2459,plain,
% 22.02/22.21 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(c, c), a) = mult(mult(c, a), c))) | (~(mult(c, mult(c, a)) = mult(c, mult(a, c)))))) | (~((~(mult(mult(c, c), a) = mult(c, mult(c, a)))) | (~(mult(mult(c, a), c) = mult(c, mult(a, c)))))))),
% 22.02/22.21 inference(quant_inst,[status(thm)],[])).
% 22.02/22.21 tff(2460,plain,
% 22.02/22.21 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(c, mult(c, a)) = mult(c, mult(a, c)))) | (~(mult(mult(c, c), a) = mult(mult(c, a), c))))) | (~((~(mult(mult(c, c), a) = mult(c, mult(c, a)))) | (~(mult(mult(c, a), c) = mult(c, mult(a, c))))))),
% 22.02/22.21 inference(modus_ponens,[status(thm)],[2459, 2458])).
% 22.02/22.21 tff(2461,plain,
% 22.02/22.21 ((~((~(mult(c, mult(c, a)) = mult(c, mult(a, c)))) | (~(mult(mult(c, c), a) = mult(mult(c, a), c))))) | (~((~(mult(mult(c, c), a) = mult(c, mult(c, a)))) | (~(mult(mult(c, a), c) = mult(c, mult(a, c))))))),
% 22.02/22.21 inference(unit_resolution,[status(thm)],[2460, 27])).
% 22.02/22.21 tff(2462,plain,
% 22.02/22.21 (~((~(mult(c, mult(c, a)) = mult(c, mult(a, c)))) | (~(mult(mult(c, c), a) = mult(mult(c, a), c))))),
% 22.02/22.21 inference(unit_resolution,[status(thm)],[2461, 2454])).
% 22.02/22.21 tff(2463,plain,
% 22.02/22.21 (((~(mult(c, mult(c, a)) = mult(c, mult(a, c)))) | (~(mult(mult(c, c), a) = mult(mult(c, a), c)))) | (mult(c, mult(c, a)) = mult(c, mult(a, c)))),
% 22.02/22.21 inference(tautology,[status(thm)],[])).
% 22.02/22.21 tff(2464,plain,
% 22.02/22.21 (mult(c, mult(c, a)) = mult(c, mult(a, c))),
% 22.02/22.21 inference(unit_resolution,[status(thm)],[2463, 2462])).
% 22.02/22.21 tff(2465,plain,
% 22.02/22.21 (ld(c, mult(c, mult(c, a))) = ld(c, mult(c, mult(a, c)))),
% 22.02/22.21 inference(monotonicity,[status(thm)],[2464])).
% 22.02/22.21 tff(2466,plain,
% 22.02/22.21 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(c, mult(c, mult(c, a))) = mult(c, a))),
% 22.02/22.21 inference(quant_inst,[status(thm)],[])).
% 22.02/22.21 tff(2467,plain,
% 22.02/22.21 (ld(c, mult(c, mult(c, a))) = mult(c, a)),
% 22.02/22.21 inference(unit_resolution,[status(thm)],[2466, 7])).
% 22.02/22.21 tff(2468,plain,
% 22.02/22.21 (mult(c, a) = ld(c, mult(c, mult(c, a)))),
% 22.02/22.21 inference(symmetry,[status(thm)],[2467])).
% 22.02/22.21 tff(2469,plain,
% 22.02/22.21 (mult(c, a) = mult(a, c)),
% 22.02/22.21 inference(transitivity,[status(thm)],[2468, 2465, 2452])).
% 22.02/22.21 tff(2470,plain,
% 22.02/22.21 (mult(mult(c, a), c) = mult(mult(a, c), c)),
% 22.02/22.21 inference(monotonicity,[status(thm)],[2469])).
% 22.02/22.21 tff(2471,plain,
% 22.02/22.21 (mult(mult(c, a), c) = mult(c, mult(a, c))),
% 22.02/22.21 inference(transitivity,[status(thm)],[2470, 2450, 2447, 2445])).
% 22.02/22.21 tff(2472,plain,
% 22.02/22.21 ($false),
% 22.02/22.21 inference(unit_resolution,[status(thm)],[2443, 2471])).
% 22.02/22.21 tff(2473,plain,((mult(mult(c, a), c) = mult(c, mult(a, c))) | (~(mult(b, mult(mult(a, c), c)) = mult(b, mult(c, mult(a, c)))))), inference(lemma,lemma(discharge,[]))).
% 22.02/22.21 tff(2474,plain,
% 22.02/22.21 (~(mult(b, mult(mult(a, c), c)) = mult(b, mult(c, mult(a, c))))),
% 22.02/22.21 inference(unit_resolution,[status(thm)],[2473, 2443])).
% 22.02/22.21 tff(2475,plain,
% 22.02/22.21 (((~(mult(mult(b, mult(a, c)), c) = mult(mult(b, c), mult(a, c)))) | (~(mult(b, mult(mult(a, c), c)) = mult(b, mult(c, mult(a, c)))))) | (mult(b, mult(mult(a, c), c)) = mult(b, mult(c, mult(a, c))))),
% 22.02/22.21 inference(tautology,[status(thm)],[])).
% 22.02/22.21 tff(2476,plain,
% 22.02/22.21 ((~(mult(mult(b, mult(a, c)), c) = mult(mult(b, c), mult(a, c)))) | (~(mult(b, mult(mult(a, c), c)) = mult(b, mult(c, mult(a, c)))))),
% 22.02/22.21 inference(unit_resolution,[status(thm)],[2475, 2474])).
% 22.02/22.21 tff(2477,plain,
% 22.02/22.21 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(b, mult(a, c)), c) = mult(mult(b, c), mult(a, c)))) | (~(mult(b, mult(mult(a, c), c)) = mult(b, mult(c, mult(a, c))))))) | (~((~(mult(mult(b, c), mult(a, c)) = mult(b, mult(c, mult(a, c))))) | (~(mult(mult(b, mult(a, c)), c) = mult(b, mult(mult(a, c), c)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(b, mult(a, c)), c) = mult(mult(b, c), mult(a, c)))) | (~(mult(b, mult(mult(a, c), c)) = mult(b, mult(c, mult(a, c))))))) | (~((~(mult(mult(b, c), mult(a, c)) = mult(b, mult(c, mult(a, c))))) | (~(mult(mult(b, mult(a, c)), c) = mult(b, mult(mult(a, c), c)))))))),
% 22.02/22.21 inference(rewrite,[status(thm)],[])).
% 22.02/22.21 tff(2478,plain,
% 22.02/22.21 (((~((~(mult(mult(b, mult(a, c)), c) = mult(mult(b, c), mult(a, c)))) | (~(mult(b, mult(mult(a, c), c)) = mult(b, mult(c, mult(a, c))))))) | (~((~(mult(mult(b, c), mult(a, c)) = mult(b, mult(c, mult(a, c))))) | (~(mult(mult(b, mult(a, c)), c) = mult(b, mult(mult(a, c), c))))))) <=> ((~((~(mult(mult(b, mult(a, c)), c) = mult(mult(b, c), mult(a, c)))) | (~(mult(b, mult(mult(a, c), c)) = mult(b, mult(c, mult(a, c))))))) | (~((~(mult(mult(b, c), mult(a, c)) = mult(b, mult(c, mult(a, c))))) | (~(mult(mult(b, mult(a, c)), c) = mult(b, mult(mult(a, c), c)))))))),
% 22.02/22.21 inference(rewrite,[status(thm)],[])).
% 22.02/22.21 tff(2479,plain,
% 22.02/22.21 ((~((~(mult(mult(b, mult(a, c)), c) = mult(b, mult(mult(a, c), c)))) | (~(mult(mult(b, c), mult(a, c)) = mult(b, mult(c, mult(a, c))))))) <=> (~((~(mult(mult(b, c), mult(a, c)) = mult(b, mult(c, mult(a, c))))) | (~(mult(mult(b, mult(a, c)), c) = mult(b, mult(mult(a, c), c))))))),
% 22.02/22.21 inference(rewrite,[status(thm)],[])).
% 22.02/22.21 tff(2480,plain,
% 22.02/22.21 ((~((~(mult(mult(b, mult(a, c)), c) = mult(mult(b, c), mult(a, c)))) | (~(mult(b, mult(mult(a, c), c)) = mult(b, mult(c, mult(a, c))))))) <=> (~((~(mult(mult(b, mult(a, c)), c) = mult(mult(b, c), mult(a, c)))) | (~(mult(b, mult(mult(a, c), c)) = mult(b, mult(c, mult(a, c)))))))),
% 22.02/22.21 inference(rewrite,[status(thm)],[])).
% 22.02/22.21 tff(2481,plain,
% 22.02/22.21 (((~((~(mult(mult(b, mult(a, c)), c) = mult(mult(b, c), mult(a, c)))) | (~(mult(b, mult(mult(a, c), c)) = mult(b, mult(c, mult(a, c))))))) | (~((~(mult(mult(b, mult(a, c)), c) = mult(b, mult(mult(a, c), c)))) | (~(mult(mult(b, c), mult(a, c)) = mult(b, mult(c, mult(a, c)))))))) <=> ((~((~(mult(mult(b, mult(a, c)), c) = mult(mult(b, c), mult(a, c)))) | (~(mult(b, mult(mult(a, c), c)) = mult(b, mult(c, mult(a, c))))))) | (~((~(mult(mult(b, c), mult(a, c)) = mult(b, mult(c, mult(a, c))))) | (~(mult(mult(b, mult(a, c)), c) = mult(b, mult(mult(a, c), c)))))))),
% 22.02/22.21 inference(monotonicity,[status(thm)],[2480, 2479])).
% 22.02/22.21 tff(2482,plain,
% 22.02/22.21 (((~((~(mult(mult(b, mult(a, c)), c) = mult(mult(b, c), mult(a, c)))) | (~(mult(b, mult(mult(a, c), c)) = mult(b, mult(c, mult(a, c))))))) | (~((~(mult(mult(b, mult(a, c)), c) = mult(b, mult(mult(a, c), c)))) | (~(mult(mult(b, c), mult(a, c)) = mult(b, mult(c, mult(a, c)))))))) <=> ((~((~(mult(mult(b, mult(a, c)), c) = mult(mult(b, c), mult(a, c)))) | (~(mult(b, mult(mult(a, c), c)) = mult(b, mult(c, mult(a, c))))))) | (~((~(mult(mult(b, c), mult(a, c)) = mult(b, mult(c, mult(a, c))))) | (~(mult(mult(b, mult(a, c)), c) = mult(b, mult(mult(a, c), c)))))))),
% 22.02/22.21 inference(transitivity,[status(thm)],[2481, 2478])).
% 22.02/22.21 tff(2483,plain,
% 22.02/22.21 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(b, mult(a, c)), c) = mult(mult(b, c), mult(a, c)))) | (~(mult(b, mult(mult(a, c), c)) = mult(b, mult(c, mult(a, c))))))) | (~((~(mult(mult(b, mult(a, c)), c) = mult(b, mult(mult(a, c), c)))) | (~(mult(mult(b, c), mult(a, c)) = mult(b, mult(c, mult(a, c))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(b, mult(a, c)), c) = mult(mult(b, c), mult(a, c)))) | (~(mult(b, mult(mult(a, c), c)) = mult(b, mult(c, mult(a, c))))))) | (~((~(mult(mult(b, c), mult(a, c)) = mult(b, mult(c, mult(a, c))))) | (~(mult(mult(b, mult(a, c)), c) = mult(b, mult(mult(a, c), c))))))))),
% 22.02/22.21 inference(monotonicity,[status(thm)],[2482])).
% 22.02/22.21 tff(2484,plain,
% 22.02/22.21 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(b, mult(a, c)), c) = mult(mult(b, c), mult(a, c)))) | (~(mult(b, mult(mult(a, c), c)) = mult(b, mult(c, mult(a, c))))))) | (~((~(mult(mult(b, mult(a, c)), c) = mult(b, mult(mult(a, c), c)))) | (~(mult(mult(b, c), mult(a, c)) = mult(b, mult(c, mult(a, c))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(b, mult(a, c)), c) = mult(mult(b, c), mult(a, c)))) | (~(mult(b, mult(mult(a, c), c)) = mult(b, mult(c, mult(a, c))))))) | (~((~(mult(mult(b, c), mult(a, c)) = mult(b, mult(c, mult(a, c))))) | (~(mult(mult(b, mult(a, c)), c) = mult(b, mult(mult(a, c), c)))))))),
% 22.02/22.21 inference(transitivity,[status(thm)],[2483, 2477])).
% 22.02/22.21 tff(2485,plain,
% 22.02/22.21 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(b, mult(a, c)), c) = mult(mult(b, c), mult(a, c)))) | (~(mult(b, mult(mult(a, c), c)) = mult(b, mult(c, mult(a, c))))))) | (~((~(mult(mult(b, mult(a, c)), c) = mult(b, mult(mult(a, c), c)))) | (~(mult(mult(b, c), mult(a, c)) = mult(b, mult(c, mult(a, c))))))))),
% 22.06/22.22 inference(quant_inst,[status(thm)],[])).
% 22.06/22.22 tff(2486,plain,
% 22.06/22.22 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(b, mult(a, c)), c) = mult(mult(b, c), mult(a, c)))) | (~(mult(b, mult(mult(a, c), c)) = mult(b, mult(c, mult(a, c))))))) | (~((~(mult(mult(b, c), mult(a, c)) = mult(b, mult(c, mult(a, c))))) | (~(mult(mult(b, mult(a, c)), c) = mult(b, mult(mult(a, c), c))))))),
% 22.06/22.22 inference(modus_ponens,[status(thm)],[2485, 2484])).
% 22.06/22.22 tff(2487,plain,
% 22.06/22.22 ((~((~(mult(mult(b, mult(a, c)), c) = mult(mult(b, c), mult(a, c)))) | (~(mult(b, mult(mult(a, c), c)) = mult(b, mult(c, mult(a, c))))))) | (~((~(mult(mult(b, c), mult(a, c)) = mult(b, mult(c, mult(a, c))))) | (~(mult(mult(b, mult(a, c)), c) = mult(b, mult(mult(a, c), c))))))),
% 22.06/22.22 inference(unit_resolution,[status(thm)],[2486, 27])).
% 22.06/22.22 tff(2488,plain,
% 22.06/22.22 (~((~(mult(mult(b, c), mult(a, c)) = mult(b, mult(c, mult(a, c))))) | (~(mult(mult(b, mult(a, c)), c) = mult(b, mult(mult(a, c), c)))))),
% 22.06/22.22 inference(unit_resolution,[status(thm)],[2487, 2476])).
% 22.06/22.22 tff(2489,plain,
% 22.06/22.22 (((~(mult(mult(b, c), mult(a, c)) = mult(b, mult(c, mult(a, c))))) | (~(mult(mult(b, mult(a, c)), c) = mult(b, mult(mult(a, c), c))))) | (mult(mult(b, c), mult(a, c)) = mult(b, mult(c, mult(a, c))))),
% 22.06/22.22 inference(tautology,[status(thm)],[])).
% 22.06/22.22 tff(2490,plain,
% 22.06/22.22 (mult(mult(b, c), mult(a, c)) = mult(b, mult(c, mult(a, c)))),
% 22.06/22.22 inference(unit_resolution,[status(thm)],[2489, 2488])).
% 22.06/22.22 tff(2491,plain,
% 22.06/22.22 (mult(b, mult(c, mult(a, c))) = mult(mult(b, c), mult(a, c))),
% 22.06/22.22 inference(symmetry,[status(thm)],[2490])).
% 22.06/22.22 tff(2492,plain,
% 22.06/22.22 (((~(mult(mult(b, c), mult(a, c)) = mult(b, mult(c, mult(a, c))))) | (~(mult(mult(b, mult(a, c)), c) = mult(b, mult(mult(a, c), c))))) | (mult(mult(b, mult(a, c)), c) = mult(b, mult(mult(a, c), c)))),
% 22.06/22.22 inference(tautology,[status(thm)],[])).
% 22.06/22.22 tff(2493,plain,
% 22.06/22.22 (mult(mult(b, mult(a, c)), c) = mult(b, mult(mult(a, c), c))),
% 22.06/22.22 inference(unit_resolution,[status(thm)],[2492, 2488])).
% 22.06/22.22 tff(2494,plain,
% 22.06/22.22 (mult(b, mult(mult(a, c), c)) = mult(mult(b, mult(a, c)), c)),
% 22.06/22.22 inference(symmetry,[status(thm)],[2493])).
% 22.06/22.22 tff(2495,plain,
% 22.06/22.22 ((mult(b, mult(mult(a, c), c)) = mult(b, mult(c, mult(a, c)))) <=> (mult(mult(b, mult(a, c)), c) = mult(mult(b, c), mult(a, c)))),
% 22.06/22.22 inference(monotonicity,[status(thm)],[2494, 2491])).
% 22.06/22.22 tff(2496,plain,
% 22.06/22.22 ((mult(mult(b, mult(a, c)), c) = mult(mult(b, c), mult(a, c))) <=> (mult(b, mult(mult(a, c), c)) = mult(b, mult(c, mult(a, c))))),
% 22.06/22.22 inference(symmetry,[status(thm)],[2495])).
% 22.06/22.22 tff(2497,plain,
% 22.06/22.22 (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), unit) = mult(mult(b, c), unit)),
% 22.06/22.22 inference(monotonicity,[status(thm)],[137])).
% 22.06/22.22 tff(2498,plain,
% 22.06/22.22 (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), unit) = mult(b, c)),
% 22.06/22.22 inference(transitivity,[status(thm)],[2497, 845, 837, 835, 240, 237, 141])).
% 22.06/22.22 tff(2499,plain,
% 22.06/22.22 (mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), unit), mult(a, c)) = mult(mult(b, c), mult(a, c))),
% 22.06/22.22 inference(monotonicity,[status(thm)],[2498])).
% 22.06/22.22 tff(2500,plain,
% 22.06/22.22 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), unit), mult(a, c)) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), unit), mult(a, c))))),
% 22.06/22.22 inference(quant_inst,[status(thm)],[])).
% 22.06/22.22 tff(2501,plain,
% 22.06/22.22 (mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), unit), mult(a, c)) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), unit), mult(a, c)))),
% 22.06/22.22 inference(unit_resolution,[status(thm)],[2500, 56])).
% 22.06/22.22 tff(2502,plain,
% 22.06/22.22 (mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), unit), mult(a, c))) = mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), unit), mult(a, c))),
% 22.06/22.22 inference(symmetry,[status(thm)],[2501])).
% 22.06/22.22 tff(2503,plain,
% 22.06/22.22 (mult(mult(mult(a, c), unit), mult(a, c)) = mult(mult(a, c), mult(a, c))),
% 22.06/22.22 inference(monotonicity,[status(thm)],[45])).
% 22.06/22.22 tff(2504,plain,
% 22.06/22.22 (mult(mult(a, c), mult(a, c)) = mult(mult(mult(a, c), unit), mult(a, c))),
% 22.06/22.22 inference(symmetry,[status(thm)],[2503])).
% 22.06/22.22 tff(2505,plain,
% 22.06/22.22 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(a, c), mult(a, c)), c), c) = mult(mult(a, c), mult(a, c)))),
% 22.06/22.22 inference(quant_inst,[status(thm)],[])).
% 22.06/22.22 tff(2506,plain,
% 22.06/22.22 (rd(mult(mult(mult(a, c), mult(a, c)), c), c) = mult(mult(a, c), mult(a, c))),
% 22.06/22.22 inference(unit_resolution,[status(thm)],[2505, 168])).
% 22.06/22.22 tff(2507,assumption,(~(mult(mult(b, mult(a, c)), c) = mult(mult(b, c), mult(a, c)))), introduced(assumption)).
% 22.06/22.22 tff(2508,plain,
% 22.06/22.22 (((~(mult(mult(b, mult(a, c)), c) = mult(mult(b, c), mult(a, c)))) | (~(mult(b, mult(mult(a, c), c)) = mult(b, mult(c, mult(a, c)))))) | (mult(mult(b, mult(a, c)), c) = mult(mult(b, c), mult(a, c)))),
% 22.06/22.22 inference(tautology,[status(thm)],[])).
% 22.06/22.22 tff(2509,plain,
% 22.06/22.22 ((~(mult(mult(b, mult(a, c)), c) = mult(mult(b, c), mult(a, c)))) | (~(mult(b, mult(mult(a, c), c)) = mult(b, mult(c, mult(a, c)))))),
% 22.06/22.22 inference(unit_resolution,[status(thm)],[2508, 2507])).
% 22.06/22.22 tff(2510,plain,
% 22.06/22.22 (~((~(mult(mult(b, c), mult(a, c)) = mult(b, mult(c, mult(a, c))))) | (~(mult(mult(b, mult(a, c)), c) = mult(b, mult(mult(a, c), c)))))),
% 22.06/22.22 inference(unit_resolution,[status(thm)],[2487, 2509])).
% 22.06/22.22 tff(2511,plain,
% 22.06/22.22 (mult(mult(b, c), mult(a, c)) = mult(b, mult(c, mult(a, c)))),
% 22.06/22.22 inference(unit_resolution,[status(thm)],[2489, 2510])).
% 22.06/22.22 tff(2512,plain,
% 22.06/22.22 (mult(b, mult(c, mult(a, c))) = mult(mult(b, c), mult(a, c))),
% 22.06/22.22 inference(symmetry,[status(thm)],[2511])).
% 22.06/22.22 tff(2513,plain,
% 22.06/22.22 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(a, c), mult(mult(a, c), mult(c, mult(a, c)))) = mult(c, mult(a, c)))),
% 22.06/22.22 inference(quant_inst,[status(thm)],[])).
% 22.06/22.22 tff(2514,plain,
% 22.06/22.22 (ld(mult(a, c), mult(mult(a, c), mult(c, mult(a, c)))) = mult(c, mult(a, c))),
% 22.06/22.22 inference(unit_resolution,[status(thm)],[2513, 7])).
% 22.06/22.22 tff(2515,assumption,(mult(mult(a, c), mult(c, mult(a, c))) = mult(mult(a, c), mult(mult(a, c), c))), introduced(assumption)).
% 22.06/22.22 tff(2516,plain,
% 22.06/22.22 (mult(mult(a, c), mult(mult(a, c), c)) = mult(mult(a, c), mult(c, mult(a, c)))),
% 22.06/22.22 inference(symmetry,[status(thm)],[2515])).
% 22.06/22.22 tff(2517,plain,
% 22.06/22.22 (ld(mult(a, c), mult(mult(a, c), mult(mult(a, c), c))) = ld(mult(a, c), mult(mult(a, c), mult(c, mult(a, c))))),
% 22.06/22.22 inference(monotonicity,[status(thm)],[2516])).
% 22.06/22.22 tff(2518,plain,
% 22.06/22.22 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(a, c), mult(mult(a, c), mult(mult(a, c), c))) = mult(mult(a, c), c))),
% 22.06/22.22 inference(quant_inst,[status(thm)],[])).
% 22.06/22.22 tff(2519,plain,
% 22.06/22.22 (ld(mult(a, c), mult(mult(a, c), mult(mult(a, c), c))) = mult(mult(a, c), c)),
% 22.06/22.22 inference(unit_resolution,[status(thm)],[2518, 7])).
% 22.06/22.22 tff(2520,plain,
% 22.06/22.22 (mult(mult(a, c), c) = ld(mult(a, c), mult(mult(a, c), mult(mult(a, c), c)))),
% 22.06/22.22 inference(symmetry,[status(thm)],[2519])).
% 22.06/22.22 tff(2521,plain,
% 22.06/22.22 (mult(mult(a, c), c) = mult(c, mult(a, c))),
% 22.06/22.22 inference(transitivity,[status(thm)],[2520, 2517, 2514])).
% 22.06/22.22 tff(2522,plain,
% 22.06/22.22 (mult(b, mult(mult(a, c), c)) = mult(b, mult(c, mult(a, c)))),
% 22.06/22.22 inference(monotonicity,[status(thm)],[2521])).
% 22.06/22.22 tff(2523,plain,
% 22.06/22.22 (mult(mult(b, mult(a, c)), c) = mult(b, mult(mult(a, c), c))),
% 22.06/22.22 inference(unit_resolution,[status(thm)],[2492, 2510])).
% 22.06/22.22 tff(2524,plain,
% 22.06/22.22 (mult(mult(b, mult(a, c)), c) = mult(mult(b, c), mult(a, c))),
% 22.06/22.22 inference(transitivity,[status(thm)],[2523, 2522, 2512])).
% 22.06/22.22 tff(2525,plain,
% 22.06/22.22 ($false),
% 22.06/22.22 inference(unit_resolution,[status(thm)],[2507, 2524])).
% 22.06/22.22 tff(2526,plain,((~(mult(mult(a, c), mult(c, mult(a, c))) = mult(mult(a, c), mult(mult(a, c), c)))) | (mult(mult(b, mult(a, c)), c) = mult(mult(b, c), mult(a, c)))), inference(lemma,lemma(discharge,[]))).
% 22.06/22.22 tff(2527,plain,
% 22.06/22.22 (~(mult(mult(a, c), mult(c, mult(a, c))) = mult(mult(a, c), mult(mult(a, c), c)))),
% 22.06/22.22 inference(unit_resolution,[status(thm)],[2526, 2507])).
% 22.06/22.22 tff(2528,plain,
% 22.06/22.22 (((~(mult(mult(a, c), mult(c, mult(a, c))) = mult(mult(a, c), mult(mult(a, c), c)))) | (~(mult(mult(mult(a, c), c), mult(a, c)) = mult(mult(mult(a, c), mult(a, c)), c)))) | (mult(mult(a, c), mult(c, mult(a, c))) = mult(mult(a, c), mult(mult(a, c), c)))),
% 22.06/22.22 inference(tautology,[status(thm)],[])).
% 22.06/22.22 tff(2529,plain,
% 22.06/22.22 ((~(mult(mult(a, c), mult(c, mult(a, c))) = mult(mult(a, c), mult(mult(a, c), c)))) | (~(mult(mult(mult(a, c), c), mult(a, c)) = mult(mult(mult(a, c), mult(a, c)), c)))),
% 22.06/22.22 inference(unit_resolution,[status(thm)],[2528, 2527])).
% 22.06/22.22 tff(2530,plain,
% 22.06/22.22 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, c), mult(c, mult(a, c))) = mult(mult(a, c), mult(mult(a, c), c)))) | (~(mult(mult(mult(a, c), c), mult(a, c)) = mult(mult(mult(a, c), mult(a, c)), c))))) | (~((~(mult(mult(mult(a, c), c), mult(a, c)) = mult(mult(a, c), mult(c, mult(a, c))))) | (~(mult(mult(mult(a, c), mult(a, c)), c) = mult(mult(a, c), mult(mult(a, c), c)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, c), mult(c, mult(a, c))) = mult(mult(a, c), mult(mult(a, c), c)))) | (~(mult(mult(mult(a, c), c), mult(a, c)) = mult(mult(mult(a, c), mult(a, c)), c))))) | (~((~(mult(mult(mult(a, c), c), mult(a, c)) = mult(mult(a, c), mult(c, mult(a, c))))) | (~(mult(mult(mult(a, c), mult(a, c)), c) = mult(mult(a, c), mult(mult(a, c), c)))))))),
% 22.06/22.22 inference(rewrite,[status(thm)],[])).
% 22.06/22.22 tff(2531,plain,
% 22.06/22.22 (((~((~(mult(mult(mult(a, c), c), mult(a, c)) = mult(mult(mult(a, c), mult(a, c)), c))) | (~(mult(mult(a, c), mult(c, mult(a, c))) = mult(mult(a, c), mult(mult(a, c), c)))))) | (~((~(mult(mult(mult(a, c), c), mult(a, c)) = mult(mult(a, c), mult(c, mult(a, c))))) | (~(mult(mult(mult(a, c), mult(a, c)), c) = mult(mult(a, c), mult(mult(a, c), c))))))) <=> ((~((~(mult(mult(a, c), mult(c, mult(a, c))) = mult(mult(a, c), mult(mult(a, c), c)))) | (~(mult(mult(mult(a, c), c), mult(a, c)) = mult(mult(mult(a, c), mult(a, c)), c))))) | (~((~(mult(mult(mult(a, c), c), mult(a, c)) = mult(mult(a, c), mult(c, mult(a, c))))) | (~(mult(mult(mult(a, c), mult(a, c)), c) = mult(mult(a, c), mult(mult(a, c), c)))))))),
% 22.06/22.22 inference(rewrite,[status(thm)],[])).
% 22.06/22.22 tff(2532,plain,
% 22.06/22.22 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, c), c), mult(a, c)) = mult(mult(mult(a, c), mult(a, c)), c))) | (~(mult(mult(a, c), mult(c, mult(a, c))) = mult(mult(a, c), mult(mult(a, c), c)))))) | (~((~(mult(mult(mult(a, c), c), mult(a, c)) = mult(mult(a, c), mult(c, mult(a, c))))) | (~(mult(mult(mult(a, c), mult(a, c)), c) = mult(mult(a, c), mult(mult(a, c), c)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, c), mult(c, mult(a, c))) = mult(mult(a, c), mult(mult(a, c), c)))) | (~(mult(mult(mult(a, c), c), mult(a, c)) = mult(mult(mult(a, c), mult(a, c)), c))))) | (~((~(mult(mult(mult(a, c), c), mult(a, c)) = mult(mult(a, c), mult(c, mult(a, c))))) | (~(mult(mult(mult(a, c), mult(a, c)), c) = mult(mult(a, c), mult(mult(a, c), c))))))))),
% 22.06/22.22 inference(monotonicity,[status(thm)],[2531])).
% 22.06/22.22 tff(2533,plain,
% 22.06/22.22 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, c), c), mult(a, c)) = mult(mult(mult(a, c), mult(a, c)), c))) | (~(mult(mult(a, c), mult(c, mult(a, c))) = mult(mult(a, c), mult(mult(a, c), c)))))) | (~((~(mult(mult(mult(a, c), c), mult(a, c)) = mult(mult(a, c), mult(c, mult(a, c))))) | (~(mult(mult(mult(a, c), mult(a, c)), c) = mult(mult(a, c), mult(mult(a, c), c)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, c), mult(c, mult(a, c))) = mult(mult(a, c), mult(mult(a, c), c)))) | (~(mult(mult(mult(a, c), c), mult(a, c)) = mult(mult(mult(a, c), mult(a, c)), c))))) | (~((~(mult(mult(mult(a, c), c), mult(a, c)) = mult(mult(a, c), mult(c, mult(a, c))))) | (~(mult(mult(mult(a, c), mult(a, c)), c) = mult(mult(a, c), mult(mult(a, c), c)))))))),
% 22.06/22.22 inference(transitivity,[status(thm)],[2532, 2530])).
% 22.06/22.22 tff(2534,plain,
% 22.06/22.22 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, c), c), mult(a, c)) = mult(mult(mult(a, c), mult(a, c)), c))) | (~(mult(mult(a, c), mult(c, mult(a, c))) = mult(mult(a, c), mult(mult(a, c), c)))))) | (~((~(mult(mult(mult(a, c), c), mult(a, c)) = mult(mult(a, c), mult(c, mult(a, c))))) | (~(mult(mult(mult(a, c), mult(a, c)), c) = mult(mult(a, c), mult(mult(a, c), c)))))))),
% 22.06/22.22 inference(quant_inst,[status(thm)],[])).
% 22.06/22.22 tff(2535,plain,
% 22.06/22.22 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, c), mult(c, mult(a, c))) = mult(mult(a, c), mult(mult(a, c), c)))) | (~(mult(mult(mult(a, c), c), mult(a, c)) = mult(mult(mult(a, c), mult(a, c)), c))))) | (~((~(mult(mult(mult(a, c), c), mult(a, c)) = mult(mult(a, c), mult(c, mult(a, c))))) | (~(mult(mult(mult(a, c), mult(a, c)), c) = mult(mult(a, c), mult(mult(a, c), c))))))),
% 22.06/22.22 inference(modus_ponens,[status(thm)],[2534, 2533])).
% 22.06/22.22 tff(2536,plain,
% 22.06/22.22 ((~((~(mult(mult(a, c), mult(c, mult(a, c))) = mult(mult(a, c), mult(mult(a, c), c)))) | (~(mult(mult(mult(a, c), c), mult(a, c)) = mult(mult(mult(a, c), mult(a, c)), c))))) | (~((~(mult(mult(mult(a, c), c), mult(a, c)) = mult(mult(a, c), mult(c, mult(a, c))))) | (~(mult(mult(mult(a, c), mult(a, c)), c) = mult(mult(a, c), mult(mult(a, c), c))))))),
% 22.06/22.22 inference(unit_resolution,[status(thm)],[2535, 27])).
% 22.06/22.22 tff(2537,plain,
% 22.06/22.22 (~((~(mult(mult(mult(a, c), c), mult(a, c)) = mult(mult(a, c), mult(c, mult(a, c))))) | (~(mult(mult(mult(a, c), mult(a, c)), c) = mult(mult(a, c), mult(mult(a, c), c)))))),
% 22.06/22.22 inference(unit_resolution,[status(thm)],[2536, 2529])).
% 22.06/22.22 tff(2538,plain,
% 22.06/22.22 (((~(mult(mult(mult(a, c), c), mult(a, c)) = mult(mult(a, c), mult(c, mult(a, c))))) | (~(mult(mult(mult(a, c), mult(a, c)), c) = mult(mult(a, c), mult(mult(a, c), c))))) | (mult(mult(mult(a, c), mult(a, c)), c) = mult(mult(a, c), mult(mult(a, c), c)))),
% 22.06/22.22 inference(tautology,[status(thm)],[])).
% 22.06/22.22 tff(2539,plain,
% 22.06/22.22 (mult(mult(mult(a, c), mult(a, c)), c) = mult(mult(a, c), mult(mult(a, c), c))),
% 22.06/22.22 inference(unit_resolution,[status(thm)],[2538, 2537])).
% 22.06/22.22 tff(2540,plain,
% 22.06/22.22 (mult(mult(a, c), mult(mult(a, c), c)) = mult(mult(mult(a, c), mult(a, c)), c)),
% 22.06/22.22 inference(symmetry,[status(thm)],[2539])).
% 22.06/22.22 tff(2541,assumption,(~((~(mult(c, mult(c, a)) = mult(c, mult(a, c)))) | (~(mult(mult(c, c), a) = mult(mult(c, a), c))))), introduced(assumption)).
% 22.06/22.22 tff(2542,plain,
% 22.06/22.22 (mult(c, mult(c, a)) = mult(c, mult(a, c))),
% 22.06/22.22 inference(unit_resolution,[status(thm)],[2463, 2541])).
% 22.06/22.22 tff(2543,plain,
% 22.06/22.22 (ld(c, mult(c, mult(c, a))) = ld(c, mult(c, mult(a, c)))),
% 22.06/22.23 inference(monotonicity,[status(thm)],[2542])).
% 22.06/22.23 tff(2544,plain,
% 22.06/22.23 (mult(c, a) = mult(a, c)),
% 22.06/22.23 inference(transitivity,[status(thm)],[2468, 2543, 2452])).
% 22.06/22.23 tff(2545,plain,
% 22.06/22.23 (mult(mult(c, a), c) = mult(mult(a, c), c)),
% 22.06/22.23 inference(monotonicity,[status(thm)],[2544])).
% 22.06/22.23 tff(2546,plain,
% 22.06/22.23 (((~(mult(c, mult(c, a)) = mult(c, mult(a, c)))) | (~(mult(mult(c, c), a) = mult(mult(c, a), c)))) | (mult(mult(c, c), a) = mult(mult(c, a), c))),
% 22.06/22.23 inference(tautology,[status(thm)],[])).
% 22.06/22.23 tff(2547,plain,
% 22.06/22.23 (mult(mult(c, c), a) = mult(mult(c, a), c)),
% 22.06/22.23 inference(unit_resolution,[status(thm)],[2546, 2541])).
% 22.06/22.23 tff(2548,plain,
% 22.06/22.23 (mult(mult(c, c), a) = mult(mult(a, c), c)),
% 22.06/22.23 inference(transitivity,[status(thm)],[2547, 2545])).
% 22.06/22.23 tff(2549,plain,
% 22.06/22.23 (mult(mult(a, c), mult(mult(c, c), a)) = mult(mult(a, c), mult(mult(a, c), c))),
% 22.06/22.23 inference(monotonicity,[status(thm)],[2548])).
% 22.06/22.23 tff(2550,plain,
% 22.06/22.23 (mult(mult(c, a), c) = mult(mult(c, c), a)),
% 22.06/22.23 inference(symmetry,[status(thm)],[2547])).
% 22.06/22.23 tff(2551,plain,
% 22.06/22.23 (mult(mult(a, c), mult(mult(c, a), c)) = mult(mult(a, c), mult(mult(c, c), a))),
% 22.06/22.23 inference(monotonicity,[status(thm)],[2550])).
% 22.06/22.23 tff(2552,plain,
% 22.06/22.23 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(a, c), c), a), c) = mult(mult(a, c), mult(mult(c, a), c)))),
% 22.06/22.23 inference(quant_inst,[status(thm)],[])).
% 22.06/22.23 tff(2553,plain,
% 22.06/22.23 (mult(mult(mult(mult(a, c), c), a), c) = mult(mult(a, c), mult(mult(c, a), c))),
% 22.06/22.23 inference(unit_resolution,[status(thm)],[2552, 56])).
% 22.06/22.23 tff(2554,plain,
% 22.06/22.23 (mult(mult(mult(mult(a, c), c), a), c) = mult(mult(mult(a, c), mult(a, c)), c)),
% 22.06/22.23 inference(transitivity,[status(thm)],[2553, 2551, 2549, 2540])).
% 22.06/22.23 tff(2555,plain,
% 22.06/22.23 (rd(mult(mult(mult(mult(a, c), c), a), c), c) = rd(mult(mult(mult(a, c), mult(a, c)), c), c)),
% 22.06/22.23 inference(monotonicity,[status(thm)],[2554])).
% 22.06/22.23 tff(2556,plain,
% 22.06/22.23 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(mult(a, c), c), a), c), c) = mult(mult(mult(a, c), c), a))),
% 22.06/22.23 inference(quant_inst,[status(thm)],[])).
% 22.06/22.23 tff(2557,plain,
% 22.06/22.23 (rd(mult(mult(mult(mult(a, c), c), a), c), c) = mult(mult(mult(a, c), c), a)),
% 22.06/22.23 inference(unit_resolution,[status(thm)],[2556, 168])).
% 22.06/22.23 tff(2558,plain,
% 22.06/22.23 (mult(mult(mult(a, c), c), a) = rd(mult(mult(mult(mult(a, c), c), a), c), c)),
% 22.06/22.23 inference(symmetry,[status(thm)],[2557])).
% 22.06/22.23 tff(2559,plain,
% 22.06/22.23 (mult(mult(mult(c, a), c), a) = mult(mult(mult(a, c), c), a)),
% 22.06/22.23 inference(monotonicity,[status(thm)],[2545])).
% 22.06/22.23 tff(2560,plain,
% 22.06/22.23 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(c, a), c), a) = mult(c, mult(mult(a, c), a)))),
% 22.06/22.23 inference(quant_inst,[status(thm)],[])).
% 22.06/22.23 tff(2561,plain,
% 22.06/22.23 (mult(mult(mult(c, a), c), a) = mult(c, mult(mult(a, c), a))),
% 22.06/22.23 inference(unit_resolution,[status(thm)],[2560, 56])).
% 22.06/22.23 tff(2562,plain,
% 22.06/22.23 (mult(c, mult(mult(a, c), a)) = mult(mult(mult(c, a), c), a)),
% 22.06/22.23 inference(symmetry,[status(thm)],[2561])).
% 22.06/22.23 tff(2563,plain,
% 22.06/22.23 (mult(c, mult(mult(a, c), a)) = mult(mult(mult(a, c), unit), mult(a, c))),
% 22.06/22.23 inference(transitivity,[status(thm)],[2562, 2559, 2558, 2555, 2506, 2504])).
% 22.06/22.23 tff(2564,plain,
% 22.06/22.23 (mult(rd(mult(b, c), mult(a, c)), mult(c, mult(mult(a, c), a))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), unit), mult(a, c)))),
% 22.06/22.23 inference(monotonicity,[status(thm)],[2563])).
% 22.06/22.23 tff(2565,plain,
% 22.06/22.23 (mult(rd(mult(b, c), mult(a, c)), mult(c, mult(mult(a, c), a))) = mult(mult(b, c), mult(a, c))),
% 22.06/22.23 inference(transitivity,[status(thm)],[2564, 2502, 2499])).
% 22.06/22.23 tff(2566,plain,
% 22.06/22.23 (mult(b, mult(mult(a, c), c)) = mult(mult(b, mult(a, c)), c)),
% 22.06/22.23 inference(symmetry,[status(thm)],[2523])).
% 22.06/22.23 tff(2567,plain,
% 22.06/22.23 (mult(b, mult(mult(c, c), a)) = mult(b, mult(mult(a, c), c))),
% 22.06/22.23 inference(monotonicity,[status(thm)],[2548])).
% 22.06/22.23 tff(2568,plain,
% 22.06/22.23 (mult(b, mult(mult(c, a), c)) = mult(b, mult(mult(c, c), a))),
% 22.06/22.23 inference(monotonicity,[status(thm)],[2550])).
% 22.06/22.23 tff(2569,plain,
% 22.06/22.23 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(b, c), a), c) = mult(b, mult(mult(c, a), c)))),
% 22.06/22.23 inference(quant_inst,[status(thm)],[])).
% 22.06/22.23 tff(2570,plain,
% 22.06/22.23 (mult(mult(mult(b, c), a), c) = mult(b, mult(mult(c, a), c))),
% 22.06/22.23 inference(unit_resolution,[status(thm)],[2569, 56])).
% 22.06/22.23 tff(2571,plain,
% 22.06/22.23 (mult(mult(mult(b, c), a), c) = mult(mult(b, mult(a, c)), c)),
% 22.06/22.23 inference(transitivity,[status(thm)],[2570, 2568, 2567, 2566])).
% 22.06/22.23 tff(2572,plain,
% 22.06/22.23 ((mult(mult(mult(b, c), a), c) = mult(mult(b, c), mult(a, c))) <=> (mult(mult(b, mult(a, c)), c) = mult(mult(b, c), mult(a, c)))),
% 22.06/22.23 inference(monotonicity,[status(thm)],[2571])).
% 22.06/22.23 tff(2573,plain,
% 22.06/22.23 ((mult(mult(b, mult(a, c)), c) = mult(mult(b, c), mult(a, c))) <=> (mult(mult(mult(b, c), a), c) = mult(mult(b, c), mult(a, c)))),
% 22.06/22.23 inference(symmetry,[status(thm)],[2572])).
% 22.06/22.23 tff(2574,plain,
% 22.06/22.23 ((~(mult(mult(b, mult(a, c)), c) = mult(mult(b, c), mult(a, c)))) <=> (~(mult(mult(mult(b, c), a), c) = mult(mult(b, c), mult(a, c))))),
% 22.06/22.23 inference(monotonicity,[status(thm)],[2573])).
% 22.06/22.23 tff(2575,plain,
% 22.06/22.23 (~(mult(mult(mult(b, c), a), c) = mult(mult(b, c), mult(a, c)))),
% 22.06/22.23 inference(modus_ponens,[status(thm)],[2507, 2574])).
% 22.06/22.23 tff(2576,plain,
% 22.06/22.23 (((~(mult(mult(mult(b, c), c), a) = mult(mult(b, c), mult(c, a)))) | (~(mult(mult(mult(b, c), a), c) = mult(mult(b, c), mult(a, c))))) | (mult(mult(mult(b, c), a), c) = mult(mult(b, c), mult(a, c)))),
% 22.06/22.23 inference(tautology,[status(thm)],[])).
% 22.06/22.23 tff(2577,plain,
% 22.06/22.23 ((~(mult(mult(mult(b, c), c), a) = mult(mult(b, c), mult(c, a)))) | (~(mult(mult(mult(b, c), a), c) = mult(mult(b, c), mult(a, c))))),
% 22.06/22.23 inference(unit_resolution,[status(thm)],[2576, 2575])).
% 22.06/22.23 tff(2578,plain,
% 22.06/22.23 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(b, c), mult(c, a)) = mult(mult(b, c), mult(a, c)))) | (~(mult(mult(mult(b, c), c), a) = mult(mult(mult(b, c), a), c))))) | (~((~(mult(mult(mult(b, c), c), a) = mult(mult(b, c), mult(c, a)))) | (~(mult(mult(mult(b, c), a), c) = mult(mult(b, c), mult(a, c)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(b, c), mult(c, a)) = mult(mult(b, c), mult(a, c)))) | (~(mult(mult(mult(b, c), c), a) = mult(mult(mult(b, c), a), c))))) | (~((~(mult(mult(mult(b, c), c), a) = mult(mult(b, c), mult(c, a)))) | (~(mult(mult(mult(b, c), a), c) = mult(mult(b, c), mult(a, c)))))))),
% 22.06/22.23 inference(rewrite,[status(thm)],[])).
% 22.06/22.23 tff(2579,plain,
% 22.06/22.23 (((~((~(mult(mult(mult(b, c), c), a) = mult(mult(mult(b, c), a), c))) | (~(mult(mult(b, c), mult(c, a)) = mult(mult(b, c), mult(a, c)))))) | (~((~(mult(mult(mult(b, c), c), a) = mult(mult(b, c), mult(c, a)))) | (~(mult(mult(mult(b, c), a), c) = mult(mult(b, c), mult(a, c))))))) <=> ((~((~(mult(mult(b, c), mult(c, a)) = mult(mult(b, c), mult(a, c)))) | (~(mult(mult(mult(b, c), c), a) = mult(mult(mult(b, c), a), c))))) | (~((~(mult(mult(mult(b, c), c), a) = mult(mult(b, c), mult(c, a)))) | (~(mult(mult(mult(b, c), a), c) = mult(mult(b, c), mult(a, c)))))))),
% 22.06/22.23 inference(rewrite,[status(thm)],[])).
% 22.06/22.23 tff(2580,plain,
% 22.06/22.23 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(b, c), c), a) = mult(mult(mult(b, c), a), c))) | (~(mult(mult(b, c), mult(c, a)) = mult(mult(b, c), mult(a, c)))))) | (~((~(mult(mult(mult(b, c), c), a) = mult(mult(b, c), mult(c, a)))) | (~(mult(mult(mult(b, c), a), c) = mult(mult(b, c), mult(a, c)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(b, c), mult(c, a)) = mult(mult(b, c), mult(a, c)))) | (~(mult(mult(mult(b, c), c), a) = mult(mult(mult(b, c), a), c))))) | (~((~(mult(mult(mult(b, c), c), a) = mult(mult(b, c), mult(c, a)))) | (~(mult(mult(mult(b, c), a), c) = mult(mult(b, c), mult(a, c))))))))),
% 22.06/22.23 inference(monotonicity,[status(thm)],[2579])).
% 22.06/22.23 tff(2581,plain,
% 22.06/22.23 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(b, c), c), a) = mult(mult(mult(b, c), a), c))) | (~(mult(mult(b, c), mult(c, a)) = mult(mult(b, c), mult(a, c)))))) | (~((~(mult(mult(mult(b, c), c), a) = mult(mult(b, c), mult(c, a)))) | (~(mult(mult(mult(b, c), a), c) = mult(mult(b, c), mult(a, c)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(b, c), mult(c, a)) = mult(mult(b, c), mult(a, c)))) | (~(mult(mult(mult(b, c), c), a) = mult(mult(mult(b, c), a), c))))) | (~((~(mult(mult(mult(b, c), c), a) = mult(mult(b, c), mult(c, a)))) | (~(mult(mult(mult(b, c), a), c) = mult(mult(b, c), mult(a, c)))))))),
% 22.06/22.23 inference(transitivity,[status(thm)],[2580, 2578])).
% 22.06/22.23 tff(2582,plain,
% 22.06/22.23 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(b, c), c), a) = mult(mult(mult(b, c), a), c))) | (~(mult(mult(b, c), mult(c, a)) = mult(mult(b, c), mult(a, c)))))) | (~((~(mult(mult(mult(b, c), c), a) = mult(mult(b, c), mult(c, a)))) | (~(mult(mult(mult(b, c), a), c) = mult(mult(b, c), mult(a, c)))))))),
% 22.06/22.23 inference(quant_inst,[status(thm)],[])).
% 22.06/22.23 tff(2583,plain,
% 22.06/22.23 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(b, c), mult(c, a)) = mult(mult(b, c), mult(a, c)))) | (~(mult(mult(mult(b, c), c), a) = mult(mult(mult(b, c), a), c))))) | (~((~(mult(mult(mult(b, c), c), a) = mult(mult(b, c), mult(c, a)))) | (~(mult(mult(mult(b, c), a), c) = mult(mult(b, c), mult(a, c))))))),
% 22.06/22.23 inference(modus_ponens,[status(thm)],[2582, 2581])).
% 22.06/22.23 tff(2584,plain,
% 22.06/22.23 ((~((~(mult(mult(b, c), mult(c, a)) = mult(mult(b, c), mult(a, c)))) | (~(mult(mult(mult(b, c), c), a) = mult(mult(mult(b, c), a), c))))) | (~((~(mult(mult(mult(b, c), c), a) = mult(mult(b, c), mult(c, a)))) | (~(mult(mult(mult(b, c), a), c) = mult(mult(b, c), mult(a, c))))))),
% 22.06/22.23 inference(unit_resolution,[status(thm)],[2583, 27])).
% 22.06/22.23 tff(2585,plain,
% 22.06/22.23 (~((~(mult(mult(b, c), mult(c, a)) = mult(mult(b, c), mult(a, c)))) | (~(mult(mult(mult(b, c), c), a) = mult(mult(mult(b, c), a), c))))),
% 22.06/22.23 inference(unit_resolution,[status(thm)],[2584, 2577])).
% 22.06/22.23 tff(2586,plain,
% 22.06/22.23 (((~(mult(mult(b, c), mult(c, a)) = mult(mult(b, c), mult(a, c)))) | (~(mult(mult(mult(b, c), c), a) = mult(mult(mult(b, c), a), c)))) | (mult(mult(mult(b, c), c), a) = mult(mult(mult(b, c), a), c))),
% 22.06/22.23 inference(tautology,[status(thm)],[])).
% 22.06/22.23 tff(2587,plain,
% 22.06/22.23 (mult(mult(mult(b, c), c), a) = mult(mult(mult(b, c), a), c)),
% 22.06/22.23 inference(unit_resolution,[status(thm)],[2586, 2585])).
% 22.06/22.23 tff(2588,plain,
% 22.06/22.23 (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), c) = mult(mult(b, c), c)),
% 22.06/22.23 inference(monotonicity,[status(thm)],[137])).
% 22.06/22.23 tff(2589,plain,
% 22.06/22.23 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))) = mult(c, mult(a, c)))),
% 22.07/22.23 inference(quant_inst,[status(thm)],[])).
% 22.07/22.23 tff(2590,plain,
% 22.07/22.23 (ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))) = mult(c, mult(a, c))),
% 22.07/22.23 inference(unit_resolution,[status(thm)],[2589, 7])).
% 22.07/22.23 tff(2591,assumption,(mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c))), introduced(assumption)).
% 22.07/22.23 tff(2592,plain,
% 22.07/22.23 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))),
% 22.07/22.23 inference(symmetry,[status(thm)],[2591])).
% 22.07/22.23 tff(2593,plain,
% 22.07/22.23 (ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c))) = ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))))),
% 22.07/22.23 inference(monotonicity,[status(thm)],[2592])).
% 22.07/22.23 tff(2594,plain,
% 22.07/22.23 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c))) = mult(mult(a, c), c))),
% 22.07/22.23 inference(quant_inst,[status(thm)],[])).
% 22.07/22.23 tff(2595,plain,
% 22.07/22.23 (ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c))) = mult(mult(a, c), c)),
% 22.07/22.23 inference(unit_resolution,[status(thm)],[2594, 7])).
% 22.07/22.23 tff(2596,plain,
% 22.07/22.23 (mult(mult(a, c), c) = ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c)))),
% 22.07/22.23 inference(symmetry,[status(thm)],[2595])).
% 22.07/22.23 tff(2597,plain,
% 22.07/22.23 (mult(mult(a, c), c) = mult(c, mult(a, c))),
% 22.07/22.23 inference(transitivity,[status(thm)],[2596, 2593, 2590])).
% 22.07/22.23 tff(2598,plain,
% 22.07/22.23 (mult(b, mult(mult(a, c), c)) = mult(b, mult(c, mult(a, c)))),
% 22.07/22.23 inference(monotonicity,[status(thm)],[2597])).
% 22.07/22.23 tff(2599,plain,
% 22.07/22.23 (mult(mult(b, mult(a, c)), c) = mult(mult(b, c), mult(a, c))),
% 22.07/22.23 inference(transitivity,[status(thm)],[2523, 2598, 2512])).
% 22.07/22.23 tff(2600,plain,
% 22.07/22.23 ($false),
% 22.07/22.23 inference(unit_resolution,[status(thm)],[2507, 2599])).
% 22.07/22.23 tff(2601,plain,((~(mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c)))) | (mult(mult(b, mult(a, c)), c) = mult(mult(b, c), mult(a, c)))), inference(lemma,lemma(discharge,[]))).
% 22.07/22.23 tff(2602,plain,
% 22.07/22.23 (~(mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c)))),
% 22.07/22.23 inference(unit_resolution,[status(thm)],[2601, 2507])).
% 22.07/22.23 tff(2603,plain,
% 22.07/22.23 (((~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), c))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c))))) | (mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c)))),
% 22.07/22.23 inference(tautology,[status(thm)],[])).
% 22.07/22.23 tff(2604,plain,
% 22.07/22.23 ((~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), c))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c))))),
% 22.07/22.23 inference(unit_resolution,[status(thm)],[2603, 2602])).
% 22.07/22.23 tff(2605,plain,
% 22.07/22.23 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), c))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c)))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), c))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c)))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c)))))))),
% 22.07/22.23 inference(rewrite,[status(thm)],[])).
% 22.07/22.23 tff(2606,plain,
% 22.07/22.23 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), c))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c)))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c)))))))),
% 22.07/22.23 inference(quant_inst,[status(thm)],[])).
% 22.07/22.23 tff(2607,plain,
% 22.07/22.23 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), c))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c)))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c))))))),
% 22.07/22.23 inference(modus_ponens,[status(thm)],[2606, 2605])).
% 22.07/22.23 tff(2608,plain,
% 22.07/22.23 (~((~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c)))))),
% 22.07/22.23 inference(unit_resolution,[status(thm)],[2607, 27, 2604])).
% 22.07/22.23 tff(2609,plain,
% 22.07/22.23 (((~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c))))) | (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c)))),
% 22.07/22.23 inference(tautology,[status(thm)],[])).
% 22.07/22.23 tff(2610,plain,
% 22.07/22.23 (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c))),
% 22.07/22.23 inference(unit_resolution,[status(thm)],[2609, 2608])).
% 22.07/22.23 tff(2611,plain,
% 22.07/22.23 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), c)),
% 22.07/22.23 inference(symmetry,[status(thm)],[2610])).
% 22.07/22.23 tff(2612,plain,
% 22.07/22.23 (mult(mult(mult(a, c), unit), c) = mult(mult(a, c), c)),
% 22.07/22.23 inference(monotonicity,[status(thm)],[45])).
% 22.07/22.23 tff(2613,plain,
% 22.07/22.23 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(a, c), unit), c) = mult(a, mult(mult(c, unit), c)))),
% 22.07/22.23 inference(quant_inst,[status(thm)],[])).
% 22.07/22.23 tff(2614,plain,
% 22.07/22.23 (mult(mult(mult(a, c), unit), c) = mult(a, mult(mult(c, unit), c))),
% 22.07/22.23 inference(unit_resolution,[status(thm)],[2613, 56])).
% 22.07/22.23 tff(2615,plain,
% 22.07/22.23 (mult(a, mult(mult(c, unit), c)) = mult(mult(mult(a, c), unit), c)),
% 22.07/22.23 inference(symmetry,[status(thm)],[2614])).
% 22.07/22.23 tff(2616,plain,
% 22.07/22.23 (mult(mult(c, unit), c) = mult(c, c)),
% 22.07/22.23 inference(monotonicity,[status(thm)],[206])).
% 22.07/22.24 tff(2617,plain,
% 22.07/22.24 (mult(c, c) = mult(mult(c, unit), c)),
% 22.07/22.24 inference(symmetry,[status(thm)],[2616])).
% 22.07/22.24 tff(2618,plain,
% 22.07/22.24 (mult(a, mult(c, c)) = mult(a, mult(mult(c, unit), c))),
% 22.07/22.24 inference(monotonicity,[status(thm)],[2617])).
% 22.07/22.24 tff(2619,plain,
% 22.07/22.24 (mult(a, mult(c, c)) = mult(mult(a, c), c)),
% 22.07/22.24 inference(transitivity,[status(thm)],[2618, 2615, 2612])).
% 22.07/22.24 tff(2620,plain,
% 22.07/22.24 (mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c))),
% 22.07/22.24 inference(monotonicity,[status(thm)],[2619])).
% 22.07/22.24 tff(2621,plain,
% 22.07/22.24 (mult(a, mult(mult(c, unit), c)) = mult(a, mult(c, c))),
% 22.07/22.24 inference(symmetry,[status(thm)],[2618])).
% 22.07/22.24 tff(2622,plain,
% 22.07/22.24 (mult(mult(a, c), c) = mult(mult(mult(a, c), unit), c)),
% 22.07/22.24 inference(symmetry,[status(thm)],[2612])).
% 22.07/22.24 tff(2623,plain,
% 22.07/22.24 (mult(mult(c, c), a) = mult(a, mult(c, c))),
% 22.07/22.24 inference(transitivity,[status(thm)],[2547, 2545, 2622, 2614, 2621])).
% 22.07/22.24 tff(2624,plain,
% 22.07/22.24 (mult(rd(mult(b, c), mult(a, c)), mult(mult(c, c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, c)))),
% 22.07/22.24 inference(monotonicity,[status(thm)],[2623])).
% 22.07/22.24 tff(2625,plain,
% 22.07/22.24 (mult(rd(mult(b, c), mult(a, c)), mult(mult(c, a), c)) = mult(rd(mult(b, c), mult(a, c)), mult(mult(c, c), a))),
% 22.07/22.24 inference(monotonicity,[status(thm)],[2550])).
% 22.07/22.24 tff(2626,plain,
% 22.07/22.24 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(c, a), c)))),
% 22.07/22.24 inference(quant_inst,[status(thm)],[])).
% 22.07/22.24 tff(2627,plain,
% 22.07/22.24 (mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(c, a), c))),
% 22.07/22.24 inference(unit_resolution,[status(thm)],[2626, 56])).
% 22.07/22.24 tff(2628,plain,
% 22.07/22.24 (mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c) = mult(mult(b, c), c)),
% 22.07/22.24 inference(transitivity,[status(thm)],[2627, 2625, 2624, 2620, 2611, 2588])).
% 22.07/22.24 tff(2629,plain,
% 22.07/22.24 (mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c), a) = mult(mult(mult(b, c), c), a)),
% 22.07/22.24 inference(monotonicity,[status(thm)],[2628])).
% 22.07/22.24 tff(2630,plain,
% 22.07/22.24 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c), a) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)))),
% 22.07/22.24 inference(quant_inst,[status(thm)],[])).
% 22.07/22.24 tff(2631,plain,
% 22.07/22.24 (mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c), a) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a))),
% 22.07/22.24 inference(unit_resolution,[status(thm)],[2630, 56])).
% 22.07/22.24 tff(2632,plain,
% 22.07/22.24 (mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)) = mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c), a)),
% 22.07/22.24 inference(symmetry,[status(thm)],[2631])).
% 22.07/22.24 tff(2633,plain,
% 22.07/22.24 (mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)) = mult(mult(b, mult(a, c)), c)),
% 22.07/22.24 inference(transitivity,[status(thm)],[2632, 2629, 2587, 2570, 2568, 2567, 2566])).
% 22.07/22.24 tff(2634,plain,
% 22.07/22.24 ((mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(mult(a, c), a)))) <=> (mult(mult(b, mult(a, c)), c) = mult(mult(b, c), mult(a, c)))),
% 22.07/22.24 inference(monotonicity,[status(thm)],[2633, 2565])).
% 22.07/22.24 tff(2635,plain,
% 22.07/22.24 ((mult(mult(b, mult(a, c)), c) = mult(mult(b, c), mult(a, c))) <=> (mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(mult(a, c), a))))),
% 22.07/22.24 inference(symmetry,[status(thm)],[2634])).
% 22.07/22.24 tff(2636,plain,
% 22.07/22.24 ((~(mult(mult(b, mult(a, c)), c) = mult(mult(b, c), mult(a, c)))) <=> (~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(mult(a, c), a)))))),
% 22.07/22.24 inference(monotonicity,[status(thm)],[2635])).
% 22.07/22.24 tff(2637,plain,
% 22.07/22.24 (~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(mult(a, c), a))))),
% 22.07/22.24 inference(modus_ponens,[status(thm)],[2507, 2636])).
% 22.07/22.24 tff(2638,plain,
% 22.07/22.24 (((~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(mult(a, c), a))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), c))))) | (mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(mult(a, c), a))))),
% 22.07/22.24 inference(tautology,[status(thm)],[])).
% 22.07/22.24 tff(2639,plain,
% 22.07/22.24 ((~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(mult(a, c), a))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), c))))),
% 22.07/22.24 inference(unit_resolution,[status(thm)],[2638, 2637])).
% 22.07/22.24 tff(2640,plain,
% 22.07/22.24 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), c)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(mult(a, c), a))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), c) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(mult(a, c), a))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), c)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), c)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(mult(a, c), a))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), c) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(mult(a, c), a))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), c)))))))),
% 22.07/22.24 inference(rewrite,[status(thm)],[])).
% 22.07/22.24 tff(2641,plain,
% 22.07/22.24 (((~((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), c) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), c)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(mult(a, c), a))))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), c)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(mult(a, c), a)))))))) <=> ((~((~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), c)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(mult(a, c), a))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), c) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(mult(a, c), a))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), c)))))))),
% 22.07/22.24 inference(rewrite,[status(thm)],[])).
% 22.07/22.24 tff(2642,plain,
% 22.07/22.24 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), c) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), c)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(mult(a, c), a))))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), c)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(mult(a, c), a))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), c)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(mult(a, c), a))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), c) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(mult(a, c), a))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), c))))))))),
% 22.07/22.24 inference(monotonicity,[status(thm)],[2641])).
% 22.07/22.24 tff(2643,plain,
% 22.07/22.24 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), c) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), c)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(mult(a, c), a))))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), c)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(mult(a, c), a))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), c)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(mult(a, c), a))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), c) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(mult(a, c), a))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), c)))))))),
% 22.07/22.24 inference(transitivity,[status(thm)],[2642, 2640])).
% 22.07/22.24 tff(2644,plain,
% 22.07/22.24 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), c) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), c)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(mult(a, c), a))))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), c)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(mult(a, c), a))))))))),
% 22.07/22.24 inference(quant_inst,[status(thm)],[])).
% 22.07/22.24 tff(2645,plain,
% 22.07/22.24 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), c)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(mult(a, c), a))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), c) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(mult(a, c), a))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), c))))))),
% 22.07/22.25 inference(modus_ponens,[status(thm)],[2644, 2643])).
% 22.07/22.25 tff(2646,plain,
% 22.07/22.25 ((~((~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), c)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(mult(a, c), a))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), c) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(mult(a, c), a))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), c))))))),
% 22.07/22.25 inference(unit_resolution,[status(thm)],[2645, 27])).
% 22.07/22.25 tff(2647,plain,
% 22.07/22.25 (~((~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), c)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(mult(a, c), a))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), c) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)))))),
% 22.07/22.25 inference(unit_resolution,[status(thm)],[2646, 2639])).
% 22.07/22.25 tff(2648,plain,
% 22.07/22.25 (((~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), c)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(mult(a, c), a))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), c) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a))))) | (mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), c)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(mult(a, c), a))))),
% 22.07/22.25 inference(tautology,[status(thm)],[])).
% 22.07/22.25 tff(2649,plain,
% 22.07/22.25 (mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), c)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(mult(a, c), a)))),
% 22.07/22.25 inference(unit_resolution,[status(thm)],[2648, 2647])).
% 22.07/22.25 tff(2650,plain,
% 22.07/22.25 (mult(mult(c, a), unit) = mult(mult(a, c), unit)),
% 22.07/22.25 inference(monotonicity,[status(thm)],[2544])).
% 22.07/22.25 tff(2651,plain,
% 22.07/22.25 (mult(mult(c, a), unit) = mult(a, c)),
% 22.07/22.25 inference(transitivity,[status(thm)],[2650, 45])).
% 22.07/22.25 tff(2652,plain,
% 22.07/22.25 (mult(mult(mult(c, a), unit), a) = mult(mult(a, c), a)),
% 22.07/22.25 inference(monotonicity,[status(thm)],[2651])).
% 22.07/22.25 tff(2653,plain,
% 22.07/22.25 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(c, a), unit), a) = mult(c, mult(mult(a, unit), a)))),
% 22.07/22.25 inference(quant_inst,[status(thm)],[])).
% 22.07/22.25 tff(2654,plain,
% 22.07/22.25 (mult(mult(mult(c, a), unit), a) = mult(c, mult(mult(a, unit), a))),
% 22.07/22.25 inference(unit_resolution,[status(thm)],[2653, 56])).
% 22.07/22.25 tff(2655,plain,
% 22.07/22.25 (mult(c, mult(mult(a, unit), a)) = mult(mult(mult(c, a), unit), a)),
% 22.07/22.25 inference(symmetry,[status(thm)],[2654])).
% 22.07/22.25 tff(2656,plain,
% 22.07/22.25 (mult(c, mult(a, a)) = mult(c, mult(mult(a, unit), a))),
% 22.07/22.25 inference(monotonicity,[status(thm)],[520])).
% 22.07/22.25 tff(2657,plain,
% 22.07/22.25 (mult(c, mult(a, a)) = mult(mult(a, c), a)),
% 22.07/22.25 inference(transitivity,[status(thm)],[2656, 2655, 2652])).
% 22.07/22.25 tff(2658,plain,
% 22.07/22.25 (mult(mult(c, mult(a, a)), c) = mult(mult(mult(a, c), a), c)),
% 22.07/22.25 inference(monotonicity,[status(thm)],[2657])).
% 22.07/22.25 tff(2659,plain,
% 22.07/22.25 (mult(rd(mult(b, c), mult(a, c)), mult(mult(c, mult(a, a)), c)) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), c))),
% 22.07/22.25 inference(monotonicity,[status(thm)],[2658])).
% 22.07/22.25 tff(2660,plain,
% 22.07/22.25 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, a)), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(c, mult(a, a)), c)))),
% 22.07/22.25 inference(quant_inst,[status(thm)],[])).
% 22.07/22.25 tff(2661,plain,
% 22.07/22.25 (mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, a)), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(c, mult(a, a)), c))),
% 22.07/22.25 inference(unit_resolution,[status(thm)],[2660, 56])).
% 22.07/22.25 tff(2662,plain,
% 22.07/22.25 (mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, a)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, unit), a))),
% 22.07/22.25 inference(monotonicity,[status(thm)],[520])).
% 22.07/22.25 tff(2663,plain,
% 22.07/22.25 (mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, unit), a)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, a))),
% 22.07/22.25 inference(symmetry,[status(thm)],[2662])).
% 22.07/22.25 tff(2664,plain,
% 22.07/22.25 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), unit), a) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, unit), a)))),
% 22.07/22.25 inference(quant_inst,[status(thm)],[])).
% 22.07/22.25 tff(2665,plain,
% 22.07/22.25 (mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), unit), a) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, unit), a))),
% 22.07/22.25 inference(unit_resolution,[status(thm)],[2664, 56])).
% 22.07/22.25 tff(2666,plain,
% 22.07/22.25 (rd(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c), c) = rd(mult(mult(b, c), c), c)),
% 22.07/22.25 inference(monotonicity,[status(thm)],[2628])).
% 22.07/22.25 tff(2667,plain,
% 22.07/22.25 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c), c) = mult(mult(rd(mult(b, c), mult(a, c)), c), a))),
% 22.07/22.25 inference(quant_inst,[status(thm)],[])).
% 22.07/22.25 tff(2668,plain,
% 22.07/22.25 (rd(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c), c) = mult(mult(rd(mult(b, c), mult(a, c)), c), a)),
% 22.07/22.25 inference(unit_resolution,[status(thm)],[2667, 168])).
% 22.07/22.25 tff(2669,plain,
% 22.07/22.25 (mult(mult(rd(mult(b, c), mult(a, c)), c), a) = rd(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c), c)),
% 22.07/22.25 inference(symmetry,[status(thm)],[2668])).
% 22.07/22.25 tff(2670,plain,
% 22.07/22.25 (mult(mult(rd(mult(b, c), mult(a, c)), c), a) = mult(b, c)),
% 22.07/22.25 inference(transitivity,[status(thm)],[2669, 2666, 2224])).
% 22.07/22.25 tff(2671,plain,
% 22.07/22.25 (mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), unit) = mult(mult(b, c), unit)),
% 22.07/22.25 inference(monotonicity,[status(thm)],[2670])).
% 22.07/22.25 tff(2672,plain,
% 22.07/22.25 (mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), unit) = mult(b, c)),
% 22.07/22.25 inference(transitivity,[status(thm)],[2671, 845, 837, 835, 240, 237, 141])).
% 22.07/22.25 tff(2673,plain,
% 22.07/22.25 (mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), unit), a) = mult(mult(b, c), a)),
% 22.07/22.25 inference(monotonicity,[status(thm)],[2672])).
% 22.07/22.25 tff(2674,plain,
% 22.07/22.25 (mult(mult(b, c), a) = mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), unit), a)),
% 22.07/22.25 inference(symmetry,[status(thm)],[2673])).
% 22.07/22.25 tff(2675,plain,
% 22.07/22.25 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(b, c), a), c), c) = mult(mult(b, c), a))),
% 22.07/22.25 inference(quant_inst,[status(thm)],[])).
% 22.07/22.25 tff(2676,plain,
% 22.07/22.25 (rd(mult(mult(mult(b, c), a), c), c) = mult(mult(b, c), a)),
% 22.07/22.25 inference(unit_resolution,[status(thm)],[2675, 168])).
% 22.07/22.25 tff(2677,plain,
% 22.07/22.25 (rd(mult(mult(mult(b, c), a), c), c) = rd(mult(mult(b, mult(a, c)), c), c)),
% 22.07/22.25 inference(monotonicity,[status(thm)],[2571])).
% 22.07/22.25 tff(2678,plain,
% 22.07/22.25 (rd(mult(mult(b, mult(a, c)), c), c) = rd(mult(mult(mult(b, c), a), c), c)),
% 22.07/22.25 inference(symmetry,[status(thm)],[2677])).
% 22.07/22.25 tff(2679,plain,
% 22.07/22.25 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(b, mult(a, c)), c), c) = mult(b, mult(a, c)))),
% 22.07/22.25 inference(quant_inst,[status(thm)],[])).
% 22.07/22.25 tff(2680,plain,
% 22.07/22.25 (rd(mult(mult(b, mult(a, c)), c), c) = mult(b, mult(a, c))),
% 22.07/22.25 inference(unit_resolution,[status(thm)],[2679, 168])).
% 22.07/22.25 tff(2681,plain,
% 22.07/22.25 (mult(b, mult(a, c)) = rd(mult(mult(b, mult(a, c)), c), c)),
% 22.07/22.25 inference(symmetry,[status(thm)],[2680])).
% 22.07/22.25 tff(2682,plain,
% 22.07/22.25 (mult(b, mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, a))),
% 22.07/22.25 inference(transitivity,[status(thm)],[2681, 2678, 2676, 2674, 2665, 2663])).
% 22.07/22.25 tff(2683,plain,
% 22.07/22.25 (mult(mult(b, mult(a, c)), c) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, a)), c)),
% 22.07/22.25 inference(monotonicity,[status(thm)],[2682])).
% 22.07/22.25 tff(2684,plain,
% 22.07/22.25 (mult(mult(b, mult(a, c)), c) = mult(mult(b, c), mult(a, c))),
% 22.07/22.25 inference(transitivity,[status(thm)],[2683, 2661, 2659, 2649, 2564, 2502, 2499])).
% 22.07/22.25 tff(2685,plain,
% 22.07/22.25 ($false),
% 22.07/22.25 inference(unit_resolution,[status(thm)],[2507, 2684])).
% 22.07/22.25 tff(2686,plain,(((~(mult(c, mult(c, a)) = mult(c, mult(a, c)))) | (~(mult(mult(c, c), a) = mult(mult(c, a), c)))) | (mult(mult(b, mult(a, c)), c) = mult(mult(b, c), mult(a, c)))), inference(lemma,lemma(discharge,[]))).
% 22.07/22.25 tff(2687,plain,
% 22.07/22.25 (mult(mult(b, mult(a, c)), c) = mult(mult(b, c), mult(a, c))),
% 22.07/22.25 inference(unit_resolution,[status(thm)],[2686, 2462])).
% 22.07/22.25 tff(2688,plain,
% 22.07/22.25 (mult(b, mult(mult(a, c), c)) = mult(b, mult(c, mult(a, c)))),
% 22.07/22.25 inference(modus_ponens,[status(thm)],[2687, 2496])).
% 22.07/22.25 tff(2689,plain,
% 22.07/22.25 ($false),
% 22.07/22.25 inference(unit_resolution,[status(thm)],[2474, 2688])).
% 22.07/22.25 tff(2690,plain,(mult(mult(c, a), c) = mult(c, mult(a, c))), inference(lemma,lemma(discharge,[]))).
% 22.07/22.25 tff(2691,plain,
% 22.07/22.25 (mult(mult(mult(c, a), c), rd(mult(b, c), mult(a, c))) = mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 22.07/22.25 inference(monotonicity,[status(thm)],[2690])).
% 22.07/22.25 tff(2692,assumption,(mult(mult(mult(c, a), c), rd(mult(b, c), mult(a, c))) = mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c))))), introduced(assumption)).
% 22.07/22.25 tff(2693,plain,
% 22.07/22.25 (mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(c, a), c), rd(mult(b, c), mult(a, c)))),
% 22.07/22.25 inference(symmetry,[status(thm)],[2692])).
% 22.07/22.25 tff(2694,plain,
% 22.07/22.25 (mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 22.07/22.25 inference(transitivity,[status(thm)],[2693, 2691])).
% 22.07/22.25 tff(2695,plain,
% 22.07/22.25 (mult(mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a)),
% 22.07/22.25 inference(monotonicity,[status(thm)],[2694])).
% 22.07/22.25 tff(2696,plain,
% 22.07/22.25 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(c, mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a)))),
% 22.07/22.25 inference(quant_inst,[status(thm)],[])).
% 22.07/22.25 tff(2697,plain,
% 22.07/22.25 (mult(mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(c, mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a))),
% 22.07/22.25 inference(unit_resolution,[status(thm)],[2696, 56])).
% 22.07/22.25 tff(2698,plain,
% 22.07/22.25 (mult(c, mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a)) = mult(mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c)))), a)),
% 22.07/22.25 inference(symmetry,[status(thm)],[2697])).
% 22.07/22.25 tff(2699,assumption,(mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))), introduced(assumption)).
% 22.07/22.25 tff(2700,plain,
% 22.07/22.25 (mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))),
% 22.07/22.25 inference(symmetry,[status(thm)],[2699])).
% 22.07/22.25 tff(2701,plain,
% 22.07/22.25 (mult(a, mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))),
% 22.07/22.25 inference(transitivity,[status(thm)],[2220, 2700, 2172, 2178, 2177, 2162])).
% 22.07/22.25 tff(2702,plain,
% 22.07/22.25 (mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)),
% 22.07/22.25 inference(monotonicity,[status(thm)],[2701])).
% 22.07/22.25 tff(2703,plain,
% 22.07/22.25 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a)),
% 22.07/22.25 inference(symmetry,[status(thm)],[2702])).
% 22.07/22.25 tff(2704,plain,
% 22.07/22.25 (mult(mult(a, c), b) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a)),
% 22.07/22.25 inference(transitivity,[status(thm)],[405, 1800, 2703])).
% 22.07/22.25 tff(2705,plain,
% 22.07/22.25 (mult(c, mult(mult(a, c), b)) = mult(c, mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a))),
% 22.07/22.25 inference(monotonicity,[status(thm)],[2704])).
% 22.07/22.25 tff(2706,plain,
% 22.07/22.25 (mult(mult(unit, c), mult(mult(a, b), c)) = mult(c, mult(mult(a, c), b))),
% 22.07/22.25 inference(monotonicity,[status(thm)],[73, 227])).
% 22.07/22.25 tff(2707,plain,
% 22.07/22.25 (mult(mult(unit, c), mult(mult(a, b), c)) = mult(mult(unit, mult(mult(a, b), c)), c)),
% 22.07/22.25 inference(transitivity,[status(thm)],[2706, 2705, 2698, 2695, 2442, 2440, 2439, 2429, 2428, 738, 2411, 231])).
% 22.07/22.25 tff(2708,plain,
% 22.07/22.25 ((mult(mult(unit, mult(mult(a, b), c)), c) = mult(mult(unit, c), mult(mult(a, b), c))) <=> (mult(mult(unit, c), mult(mult(a, b), c)) = mult(mult(unit, mult(mult(a, b), c)), c))),
% 22.07/22.25 inference(commutativity,[status(thm)],[])).
% 22.07/22.25 tff(2709,plain,
% 22.07/22.25 (mult(c, mult(mult(a, c), b)) = mult(mult(unit, c), mult(mult(a, b), c))),
% 22.07/22.25 inference(symmetry,[status(thm)],[2706])).
% 22.07/22.25 tff(2710,plain,
% 22.07/22.25 (((~(mult(mult(c, mult(a, c)), b) = mult(mult(c, b), mult(a, c)))) | (~(mult(c, mult(mult(a, c), b)) = mult(c, mult(b, mult(a, c)))))) | (mult(c, mult(mult(a, c), b)) = mult(c, mult(b, mult(a, c))))),
% 22.07/22.25 inference(tautology,[status(thm)],[])).
% 22.07/22.25 tff(2711,plain,
% 22.07/22.25 (mult(c, mult(mult(a, c), b)) = mult(c, mult(b, mult(a, c)))),
% 22.07/22.25 inference(unit_resolution,[status(thm)],[2710, 2437])).
% 22.07/22.25 tff(2712,plain,
% 22.07/22.25 (mult(c, mult(b, mult(a, c))) = mult(c, mult(mult(a, c), b))),
% 22.07/22.25 inference(symmetry,[status(thm)],[2711])).
% 22.07/22.25 tff(2713,plain,
% 22.07/22.25 (mult(c, mult(b, mult(a, c))) = mult(mult(unit, c), mult(mult(a, b), c))),
% 22.07/22.25 inference(transitivity,[status(thm)],[2712, 2709])).
% 22.07/22.25 tff(2714,plain,
% 22.07/22.25 (mult(mult(c, b), mult(a, c)) = mult(mult(unit, mult(mult(a, b), c)), c)),
% 22.07/22.25 inference(transitivity,[status(thm)],[2429, 2428, 738, 2411, 231])).
% 22.07/22.25 tff(2715,plain,
% 22.07/22.25 ((mult(mult(c, b), mult(a, c)) = mult(c, mult(b, mult(a, c)))) <=> (mult(mult(unit, mult(mult(a, b), c)), c) = mult(mult(unit, c), mult(mult(a, b), c)))),
% 22.07/22.25 inference(monotonicity,[status(thm)],[2714, 2713])).
% 22.07/22.25 tff(2716,plain,
% 22.07/22.25 ((mult(mult(c, b), mult(a, c)) = mult(c, mult(b, mult(a, c)))) <=> (mult(mult(unit, c), mult(mult(a, b), c)) = mult(mult(unit, mult(mult(a, b), c)), c))),
% 22.07/22.25 inference(transitivity,[status(thm)],[2715, 2708])).
% 22.07/22.25 tff(2717,plain,
% 22.07/22.25 ((~(mult(mult(c, b), mult(a, c)) = mult(c, mult(b, mult(a, c))))) <=> (~(mult(mult(unit, c), mult(mult(a, b), c)) = mult(mult(unit, mult(mult(a, b), c)), c)))),
% 22.07/22.25 inference(monotonicity,[status(thm)],[2716])).
% 22.07/22.25 tff(2718,plain,
% 22.07/22.25 (~(mult(mult(unit, c), mult(mult(a, b), c)) = mult(mult(unit, mult(mult(a, b), c)), c))),
% 22.07/22.25 inference(modus_ponens,[status(thm)],[2430, 2717])).
% 22.07/22.25 tff(2719,plain,
% 22.07/22.25 ($false),
% 22.07/22.25 inference(unit_resolution,[status(thm)],[2718, 2707])).
% 22.07/22.25 tff(2720,plain,((mult(mult(c, b), mult(a, c)) = mult(c, mult(b, mult(a, c)))) | (~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit))))) | (~(mult(mult(mult(c, a), c), rd(mult(b, c), mult(a, c))) = mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))), inference(lemma,lemma(discharge,[]))).
% 22.07/22.25 tff(2721,plain,
% 22.07/22.25 (mult(mult(c, b), mult(a, c)) = mult(c, mult(b, mult(a, c)))),
% 22.07/22.25 inference(unit_resolution,[status(thm)],[2720, 2375, 97, 2128, 1032, 2216, 2391])).
% 22.07/22.25 tff(2722,plain,
% 22.07/22.25 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(a, c), c), c) = mult(a, c))),
% 22.07/22.25 inference(quant_inst,[status(thm)],[])).
% 22.07/22.25 tff(2723,plain,
% 22.07/22.25 (rd(mult(mult(a, c), c), c) = mult(a, c)),
% 22.07/22.25 inference(unit_resolution,[status(thm)],[2722, 168])).
% 22.07/22.25 tff(2724,plain,
% 22.07/22.25 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(a, c), c), b), b) = mult(mult(a, c), c))),
% 22.07/22.25 inference(quant_inst,[status(thm)],[])).
% 22.07/22.25 tff(2725,plain,
% 22.07/22.25 (rd(mult(mult(mult(a, c), c), b), b) = mult(mult(a, c), c)),
% 22.07/22.25 inference(unit_resolution,[status(thm)],[2724, 168])).
% 22.07/22.25 tff(2726,plain,
% 22.07/22.25 (rd(mult(b, c), c) = rd(mult(mult(rd(mult(b, c), mult(a, c)), a), c), c)),
% 22.07/22.25 inference(symmetry,[status(thm)],[172])).
% 22.07/22.25 tff(2727,plain,
% 22.07/22.25 (b = rd(mult(b, c), c)),
% 22.07/22.25 inference(symmetry,[status(thm)],[170])).
% 22.07/22.25 tff(2728,plain,
% 22.07/22.25 (b = mult(rd(mult(b, c), mult(a, c)), a)),
% 22.07/22.25 inference(transitivity,[status(thm)],[2727, 2726, 174])).
% 22.07/22.25 tff(2729,plain,
% 22.07/22.25 (mult(mult(c, mult(a, c)), b) = mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a))),
% 22.07/22.25 inference(monotonicity,[status(thm)],[2728])).
% 22.07/22.25 tff(2730,plain,
% 22.07/22.25 (mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(c, mult(a, c)), b)),
% 22.07/22.25 inference(symmetry,[status(thm)],[2729])).
% 22.07/22.25 tff(2731,assumption,(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a))), introduced(assumption)).
% 22.07/22.25 tff(2732,plain,
% 22.07/22.25 (mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(c, a), c), rd(mult(b, c), mult(a, c)))),
% 22.07/22.25 inference(symmetry,[status(thm)],[2691])).
% 22.07/22.25 tff(2733,plain,
% 22.07/22.25 (mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c))))),
% 22.07/22.25 inference(transitivity,[status(thm)],[2732, 2692])).
% 22.07/22.25 tff(2734,plain,
% 22.07/22.25 (mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c)))), a)),
% 22.07/22.25 inference(monotonicity,[status(thm)],[2733])).
% 22.07/22.25 tff(2735,plain,
% 22.07/22.25 (mult(mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a)),
% 22.07/22.25 inference(symmetry,[status(thm)],[2734])).
% 22.07/22.25 tff(2736,plain,
% 22.07/22.25 (mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, c), b)),
% 22.07/22.25 inference(transitivity,[status(thm)],[2702, 1799, 177])).
% 22.07/22.25 tff(2737,plain,
% 22.07/22.25 (mult(c, mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a)) = mult(c, mult(mult(a, c), b))),
% 22.07/22.25 inference(monotonicity,[status(thm)],[2736])).
% 22.07/22.25 tff(2738,plain,
% 22.07/22.25 (mult(c, mult(mult(a, c), b)) = mult(c, mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a))),
% 22.07/22.25 inference(symmetry,[status(thm)],[2737])).
% 22.07/22.25 tff(2739,assumption,(mult(c, mult(mult(a, c), b)) = mult(c, mult(b, mult(a, c)))), introduced(assumption)).
% 22.07/22.25 tff(2740,plain,
% 22.07/22.25 (mult(c, mult(b, mult(a, c))) = mult(c, mult(mult(a, c), b))),
% 22.07/22.25 inference(symmetry,[status(thm)],[2739])).
% 22.07/22.25 tff(2741,assumption,(mult(mult(c, b), mult(a, c)) = mult(c, mult(b, mult(a, c)))), introduced(assumption)).
% 22.07/22.25 tff(2742,plain,
% 22.07/22.25 (mult(mult(b, c), mult(a, c)) = mult(mult(c, b), mult(a, c))),
% 22.07/22.25 inference(symmetry,[status(thm)],[2429])).
% 22.07/22.25 tff(2743,plain,
% 22.07/22.25 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(b, c), mult(a, c))),
% 22.07/22.25 inference(symmetry,[status(thm)],[2428])).
% 22.07/22.25 tff(2744,plain,
% 22.07/22.25 (mult(mult(mult(a, c), b), c) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c)),
% 22.07/22.25 inference(symmetry,[status(thm)],[2411])).
% 22.07/22.25 tff(2745,plain,
% 22.07/22.25 (mult(mult(mult(a, c), b), c) = mult(a, mult(mult(b, c), c))),
% 22.07/22.25 inference(transitivity,[status(thm)],[233, 2414])).
% 22.07/22.25 tff(2746,plain,
% 22.07/22.25 ((mult(mult(mult(a, c), b), c) = mult(mult(a, c), mult(b, c))) <=> (mult(a, mult(mult(b, c), c)) = mult(mult(a, mult(b, c)), c))),
% 22.07/22.25 inference(monotonicity,[status(thm)],[2745, 266])).
% 22.07/22.25 tff(2747,plain,
% 22.07/22.25 ((mult(mult(mult(a, c), b), c) = mult(mult(a, c), mult(b, c))) <=> (mult(mult(a, mult(b, c)), c) = mult(a, mult(mult(b, c), c)))),
% 22.07/22.25 inference(transitivity,[status(thm)],[2746, 2412])).
% 22.07/22.25 tff(2748,plain,
% 22.07/22.25 ((mult(mult(a, mult(b, c)), c) = mult(a, mult(mult(b, c), c))) <=> (mult(mult(mult(a, c), b), c) = mult(mult(a, c), mult(b, c)))),
% 22.07/22.25 inference(symmetry,[status(thm)],[2747])).
% 22.07/22.25 tff(2749,plain,
% 22.07/22.25 ((~(mult(mult(a, mult(b, c)), c) = mult(a, mult(mult(b, c), c)))) <=> (~(mult(mult(mult(a, c), b), c) = mult(mult(a, c), mult(b, c))))),
% 22.07/22.25 inference(monotonicity,[status(thm)],[2748])).
% 22.07/22.25 tff(2750,plain,
% 22.07/22.25 (~(mult(mult(mult(a, c), b), c) = mult(mult(a, c), mult(b, c)))),
% 22.07/22.25 inference(modus_ponens,[status(thm)],[258, 2749])).
% 22.07/22.25 tff(2751,plain,
% 22.07/22.25 (((~(mult(mult(mult(a, c), c), b) = mult(mult(a, c), mult(c, b)))) | (~(mult(mult(mult(a, c), b), c) = mult(mult(a, c), mult(b, c))))) | (mult(mult(mult(a, c), b), c) = mult(mult(a, c), mult(b, c)))),
% 22.07/22.26 inference(tautology,[status(thm)],[])).
% 22.07/22.26 tff(2752,plain,
% 22.07/22.26 ((~(mult(mult(mult(a, c), c), b) = mult(mult(a, c), mult(c, b)))) | (~(mult(mult(mult(a, c), b), c) = mult(mult(a, c), mult(b, c))))),
% 22.07/22.26 inference(unit_resolution,[status(thm)],[2751, 2750])).
% 22.07/22.26 tff(2753,plain,
% 22.07/22.26 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, c), c), b) = mult(mult(mult(a, c), b), c))) | (~(mult(mult(a, c), mult(c, b)) = mult(mult(a, c), mult(b, c)))))) | (~((~(mult(mult(mult(a, c), c), b) = mult(mult(a, c), mult(c, b)))) | (~(mult(mult(mult(a, c), b), c) = mult(mult(a, c), mult(b, c)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(a, c), c), b) = mult(mult(mult(a, c), b), c))) | (~(mult(mult(a, c), mult(c, b)) = mult(mult(a, c), mult(b, c)))))) | (~((~(mult(mult(mult(a, c), c), b) = mult(mult(a, c), mult(c, b)))) | (~(mult(mult(mult(a, c), b), c) = mult(mult(a, c), mult(b, c)))))))),
% 22.07/22.26 inference(rewrite,[status(thm)],[])).
% 22.07/22.26 tff(2754,plain,
% 22.07/22.26 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, c), c), b) = mult(mult(mult(a, c), b), c))) | (~(mult(mult(a, c), mult(c, b)) = mult(mult(a, c), mult(b, c)))))) | (~((~(mult(mult(mult(a, c), c), b) = mult(mult(a, c), mult(c, b)))) | (~(mult(mult(mult(a, c), b), c) = mult(mult(a, c), mult(b, c)))))))),
% 22.07/22.26 inference(quant_inst,[status(thm)],[])).
% 22.07/22.26 tff(2755,plain,
% 22.07/22.26 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(a, c), c), b) = mult(mult(mult(a, c), b), c))) | (~(mult(mult(a, c), mult(c, b)) = mult(mult(a, c), mult(b, c)))))) | (~((~(mult(mult(mult(a, c), c), b) = mult(mult(a, c), mult(c, b)))) | (~(mult(mult(mult(a, c), b), c) = mult(mult(a, c), mult(b, c))))))),
% 22.07/22.26 inference(modus_ponens,[status(thm)],[2754, 2753])).
% 22.07/22.26 tff(2756,plain,
% 22.07/22.26 ((~((~(mult(mult(mult(a, c), c), b) = mult(mult(mult(a, c), b), c))) | (~(mult(mult(a, c), mult(c, b)) = mult(mult(a, c), mult(b, c)))))) | (~((~(mult(mult(mult(a, c), c), b) = mult(mult(a, c), mult(c, b)))) | (~(mult(mult(mult(a, c), b), c) = mult(mult(a, c), mult(b, c))))))),
% 22.07/22.26 inference(unit_resolution,[status(thm)],[2755, 27])).
% 22.07/22.26 tff(2757,plain,
% 22.07/22.26 (~((~(mult(mult(mult(a, c), c), b) = mult(mult(mult(a, c), b), c))) | (~(mult(mult(a, c), mult(c, b)) = mult(mult(a, c), mult(b, c)))))),
% 22.07/22.26 inference(unit_resolution,[status(thm)],[2756, 2752])).
% 22.07/22.26 tff(2758,plain,
% 22.07/22.26 (((~(mult(mult(mult(a, c), c), b) = mult(mult(mult(a, c), b), c))) | (~(mult(mult(a, c), mult(c, b)) = mult(mult(a, c), mult(b, c))))) | (mult(mult(mult(a, c), c), b) = mult(mult(mult(a, c), b), c))),
% 22.07/22.26 inference(tautology,[status(thm)],[])).
% 22.07/22.26 tff(2759,plain,
% 22.07/22.26 (mult(mult(mult(a, c), c), b) = mult(mult(mult(a, c), b), c)),
% 22.07/22.26 inference(unit_resolution,[status(thm)],[2758, 2757])).
% 22.07/22.26 tff(2760,plain,
% 22.07/22.26 (mult(mult(mult(a, c), c), b) = mult(mult(c, mult(a, c)), b)),
% 22.07/22.26 inference(transitivity,[status(thm)],[2759, 2744, 317, 2743, 2742, 2741, 2740, 2738, 2698, 2735, 2731, 2730])).
% 22.07/22.26 tff(2761,plain,
% 22.07/22.26 (rd(mult(mult(mult(a, c), c), b), b) = rd(mult(mult(c, mult(a, c)), b), b)),
% 22.07/22.26 inference(monotonicity,[status(thm)],[2760])).
% 22.07/22.26 tff(2762,plain,
% 22.07/22.26 (rd(mult(mult(c, mult(a, c)), b), b) = rd(mult(mult(mult(a, c), c), b), b)),
% 22.07/22.26 inference(symmetry,[status(thm)],[2761])).
% 22.07/22.26 tff(2763,plain,
% 22.07/22.26 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(c, mult(a, c)), b), b) = mult(c, mult(a, c)))),
% 22.07/22.26 inference(quant_inst,[status(thm)],[])).
% 22.07/22.26 tff(2764,plain,
% 22.07/22.26 (rd(mult(mult(c, mult(a, c)), b), b) = mult(c, mult(a, c))),
% 22.07/22.26 inference(unit_resolution,[status(thm)],[2763, 168])).
% 22.07/22.26 tff(2765,plain,
% 22.07/22.26 (mult(c, mult(a, c)) = rd(mult(mult(c, mult(a, c)), b), b)),
% 22.07/22.26 inference(symmetry,[status(thm)],[2764])).
% 22.07/22.26 tff(2766,plain,
% 22.07/22.26 (mult(mult(c, a), c) = mult(mult(a, c), c)),
% 22.07/22.26 inference(transitivity,[status(thm)],[2690, 2765, 2762, 2725])).
% 22.07/22.26 tff(2767,plain,
% 22.07/22.26 (rd(mult(mult(c, a), c), c) = rd(mult(mult(a, c), c), c)),
% 22.07/22.26 inference(monotonicity,[status(thm)],[2766])).
% 22.07/22.26 tff(2768,plain,
% 22.07/22.26 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(c, a), c), c) = mult(c, a))),
% 22.07/22.26 inference(quant_inst,[status(thm)],[])).
% 22.07/22.26 tff(2769,plain,
% 22.07/22.26 (rd(mult(mult(c, a), c), c) = mult(c, a)),
% 22.07/22.26 inference(unit_resolution,[status(thm)],[2768, 168])).
% 22.07/22.26 tff(2770,plain,
% 22.07/22.26 (mult(c, a) = rd(mult(mult(c, a), c), c)),
% 22.07/22.26 inference(symmetry,[status(thm)],[2769])).
% 22.07/22.26 tff(2771,plain,
% 22.07/22.26 (mult(c, a) = mult(a, c)),
% 22.07/22.26 inference(transitivity,[status(thm)],[2770, 2767, 2723])).
% 22.07/22.26 tff(2772,plain,
% 22.07/22.26 (mult(mult(b, c), mult(c, a)) = mult(mult(b, c), mult(a, c))),
% 22.07/22.26 inference(monotonicity,[status(thm)],[2771])).
% 22.07/22.26 tff(2773,plain,
% 22.07/22.26 (mult(mult(a, c), rd(mult(b, c), mult(a, c))) = mult(b, c)),
% 22.07/22.26 inference(transitivity,[status(thm)],[296, 2425, 291])).
% 22.07/22.26 tff(2774,plain,
% 22.07/22.26 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(b, c), mult(c, a))),
% 22.07/22.26 inference(monotonicity,[status(thm)],[2773])).
% 22.07/22.26 tff(2775,plain,
% 22.07/22.26 (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c)),
% 22.07/22.26 inference(transitivity,[status(thm)],[751, 2774, 2772, 2428, 738])).
% 22.07/22.26 tff(2776,plain,
% 22.07/22.26 ($false),
% 22.07/22.26 inference(unit_resolution,[status(thm)],[753, 2775])).
% 22.07/22.26 tff(2777,plain,((~(mult(c, mult(mult(a, c), b)) = mult(c, mult(b, mult(a, c))))) | (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c)) | (~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)))) | (~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(c, b), mult(a, c)) = mult(c, mult(b, mult(a, c))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(mult(mult(c, a), c), rd(mult(b, c), mult(a, c))) = mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit)))))), inference(lemma,lemma(discharge,[]))).
% 22.07/22.26 tff(2778,plain,
% 22.07/22.26 (~(mult(c, mult(mult(a, c), b)) = mult(c, mult(b, mult(a, c))))),
% 22.07/22.26 inference(unit_resolution,[status(thm)],[2777, 2721, 1032, 2256, 2409, 2228, 2128, 2216, 2375, 97])).
% 22.07/22.26 tff(2779,plain,
% 22.07/22.26 ((~(mult(mult(c, mult(a, c)), b) = mult(mult(c, b), mult(a, c)))) | (~(mult(c, mult(mult(a, c), b)) = mult(c, mult(b, mult(a, c)))))),
% 22.07/22.26 inference(unit_resolution,[status(thm)],[2710, 2778])).
% 22.07/22.26 tff(2780,plain,
% 22.07/22.26 (~((~(mult(mult(c, mult(a, c)), b) = mult(c, mult(mult(a, c), b)))) | (~(mult(mult(c, b), mult(a, c)) = mult(c, mult(b, mult(a, c))))))),
% 22.07/22.26 inference(unit_resolution,[status(thm)],[2436, 2779])).
% 22.07/22.26 tff(2781,plain,
% 22.07/22.26 (((~(mult(mult(c, mult(a, c)), b) = mult(c, mult(mult(a, c), b)))) | (~(mult(mult(c, b), mult(a, c)) = mult(c, mult(b, mult(a, c)))))) | (mult(mult(c, mult(a, c)), b) = mult(c, mult(mult(a, c), b)))),
% 22.07/22.26 inference(tautology,[status(thm)],[])).
% 22.07/22.26 tff(2782,plain,
% 22.07/22.26 (mult(mult(c, mult(a, c)), b) = mult(c, mult(mult(a, c), b))),
% 22.07/22.26 inference(unit_resolution,[status(thm)],[2781, 2780])).
% 22.07/22.26 tff(2783,plain,
% 22.07/22.26 (mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a)),
% 22.07/22.26 inference(transitivity,[status(thm)],[2409, 2440, 2782, 2318, 2317, 2315, 2231, 2230, 2229])).
% 22.07/22.26 tff(2784,plain,
% 22.07/22.26 (rd(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a), a) = rd(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a), a)),
% 22.07/22.26 inference(monotonicity,[status(thm)],[2783])).
% 22.07/22.26 tff(2785,plain,
% 22.07/22.26 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a), a) = mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))))),
% 22.07/22.26 inference(quant_inst,[status(thm)],[])).
% 22.07/22.26 tff(2786,plain,
% 22.07/22.26 (rd(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a), a) = mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 22.07/22.26 inference(unit_resolution,[status(thm)],[2785, 168])).
% 22.07/22.26 tff(2787,plain,
% 22.07/22.26 (mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = rd(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a), a)),
% 22.07/22.26 inference(symmetry,[status(thm)],[2786])).
% 22.07/22.26 tff(2788,assumption,(~(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))), introduced(assumption)).
% 22.07/22.26 tff(2789,plain,
% 22.07/22.26 (((~(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))) | (mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 22.07/22.26 inference(tautology,[status(thm)],[])).
% 22.07/22.26 tff(2790,plain,
% 22.07/22.26 ((~(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))),
% 22.07/22.26 inference(unit_resolution,[status(thm)],[2789, 2788])).
% 22.07/22.26 tff(2791,plain,
% 22.07/22.26 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))) | (~((~(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))) | (~((~(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))))),
% 22.07/22.26 inference(rewrite,[status(thm)],[])).
% 22.07/22.26 tff(2792,plain,
% 22.07/22.26 (((~((~(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))) | (~((~(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))))) <=> ((~((~(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))) | (~((~(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))))),
% 22.07/22.26 inference(rewrite,[status(thm)],[])).
% 22.07/22.26 tff(2793,plain,
% 22.07/22.26 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))) | (~((~(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))) | (~((~(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))))))),
% 22.07/22.26 inference(monotonicity,[status(thm)],[2792])).
% 22.07/22.26 tff(2794,plain,
% 22.07/22.26 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))) | (~((~(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))) | (~((~(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))))),
% 22.07/22.26 inference(transitivity,[status(thm)],[2793, 2791])).
% 22.07/22.26 tff(2795,plain,
% 22.07/22.26 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))) | (~((~(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))))),
% 22.07/22.27 inference(quant_inst,[status(thm)],[])).
% 22.07/22.27 tff(2796,plain,
% 22.07/22.27 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))) | (~((~(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))))),
% 22.07/22.27 inference(modus_ponens,[status(thm)],[2795, 2794])).
% 22.07/22.27 tff(2797,plain,
% 22.07/22.27 ((~((~(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))) | (~((~(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))))),
% 22.07/22.27 inference(unit_resolution,[status(thm)],[2796, 27])).
% 22.07/22.27 tff(2798,plain,
% 22.07/22.27 (~((~(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))),
% 22.07/22.27 inference(unit_resolution,[status(thm)],[2797, 2790])).
% 22.07/22.27 tff(2799,plain,
% 22.07/22.27 (((~(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))) | (mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))),
% 22.07/22.27 inference(tautology,[status(thm)],[])).
% 22.07/22.27 tff(2800,plain,
% 22.07/22.27 (mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))),
% 22.07/22.27 inference(unit_resolution,[status(thm)],[2799, 2798])).
% 22.07/22.27 tff(2801,plain,
% 22.07/22.27 (mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))),
% 22.07/22.27 inference(symmetry,[status(thm)],[2800])).
% 22.07/22.27 tff(2802,plain,
% 22.07/22.27 (mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c))) = mult(c, mult(b, c))),
% 22.07/22.27 inference(monotonicity,[status(thm)],[137])).
% 22.07/22.27 tff(2803,plain,
% 22.07/22.27 (mult(c, mult(b, c)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))),
% 22.07/22.27 inference(symmetry,[status(thm)],[2802])).
% 22.07/22.27 tff(2804,plain,
% 22.07/22.27 (mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(b, c))),
% 22.07/22.27 inference(monotonicity,[status(thm)],[1491])).
% 22.07/22.27 tff(2805,plain,
% 22.07/22.27 (mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))),
% 22.07/22.27 inference(transitivity,[status(thm)],[2804, 2803, 2801])).
% 22.07/22.27 tff(2806,plain,
% 22.07/22.27 ((mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c))))) <=> (mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 22.07/22.27 inference(monotonicity,[status(thm)],[2805])).
% 22.07/22.27 tff(2807,plain,
% 22.07/22.27 ((mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))) <=> (mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 22.07/22.27 inference(symmetry,[status(thm)],[2806])).
% 22.07/22.27 tff(2808,plain,
% 22.07/22.27 ((~(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))) <=> (~(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))),
% 22.07/22.27 inference(monotonicity,[status(thm)],[2807])).
% 22.07/22.27 tff(2809,plain,
% 22.07/22.27 (~(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 22.07/22.27 inference(modus_ponens,[status(thm)],[2788, 2808])).
% 22.07/22.27 tff(2810,plain,
% 22.07/22.27 (((~(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))) | (mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 22.07/22.27 inference(tautology,[status(thm)],[])).
% 22.07/22.27 tff(2811,plain,
% 22.07/22.27 (mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 22.07/22.27 inference(unit_resolution,[status(thm)],[2810, 2798])).
% 22.07/22.27 tff(2812,plain,
% 22.07/22.27 ($false),
% 22.07/22.27 inference(unit_resolution,[status(thm)],[2811, 2809])).
% 22.07/22.27 tff(2813,plain,((mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))) | (~(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))), inference(lemma,lemma(discharge,[]))).
% 22.07/22.27 tff(2814,plain,
% 22.07/22.27 (mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))),
% 22.07/22.27 inference(unit_resolution,[status(thm)],[2813, 1488])).
% 22.07/22.27 tff(2815,plain,
% 22.07/22.27 (mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 22.07/22.27 inference(symmetry,[status(thm)],[2814])).
% 22.07/22.27 tff(2816,assumption,(~(mult(c, mult(mult(a, c), b)) = mult(c, mult(b, mult(a, c))))), introduced(assumption)).
% 22.07/22.27 tff(2817,plain,
% 22.07/22.27 ((~(mult(mult(c, mult(a, c)), b) = mult(mult(c, b), mult(a, c)))) | (~(mult(c, mult(mult(a, c), b)) = mult(c, mult(b, mult(a, c)))))),
% 22.07/22.27 inference(unit_resolution,[status(thm)],[2710, 2816])).
% 22.07/22.27 tff(2818,plain,
% 22.07/22.27 (~((~(mult(mult(c, mult(a, c)), b) = mult(c, mult(mult(a, c), b)))) | (~(mult(mult(c, b), mult(a, c)) = mult(c, mult(b, mult(a, c))))))),
% 22.07/22.27 inference(unit_resolution,[status(thm)],[2436, 2817])).
% 22.07/22.27 tff(2819,plain,
% 22.07/22.27 (mult(mult(c, b), mult(a, c)) = mult(c, mult(b, mult(a, c)))),
% 22.07/22.27 inference(unit_resolution,[status(thm)],[2431, 2818])).
% 22.07/22.27 tff(2820,plain,
% 22.07/22.27 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))) = mult(a, c))),
% 22.07/22.27 inference(quant_inst,[status(thm)],[])).
% 22.07/22.27 tff(2821,plain,
% 22.07/22.27 (ld(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))) = mult(a, c)),
% 22.07/22.27 inference(unit_resolution,[status(thm)],[2820, 7])).
% 22.07/22.27 tff(2822,assumption,(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))), introduced(assumption)).
% 22.07/22.27 tff(2823,plain,
% 22.07/22.27 (ld(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(c, rd(mult(b, c), mult(a, c))), mult(c, a))) = ld(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 22.07/22.27 inference(monotonicity,[status(thm)],[2822])).
% 22.07/22.27 tff(2824,plain,
% 22.07/22.27 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(c, rd(mult(b, c), mult(a, c))), mult(c, a))) = mult(c, a))),
% 22.07/22.27 inference(quant_inst,[status(thm)],[])).
% 22.07/22.27 tff(2825,plain,
% 22.07/22.27 (ld(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(c, rd(mult(b, c), mult(a, c))), mult(c, a))) = mult(c, a)),
% 22.07/22.27 inference(unit_resolution,[status(thm)],[2824, 7])).
% 22.07/22.27 tff(2826,plain,
% 22.07/22.27 (mult(c, a) = ld(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(c, rd(mult(b, c), mult(a, c))), mult(c, a)))),
% 22.07/22.27 inference(symmetry,[status(thm)],[2825])).
% 22.07/22.27 tff(2827,plain,
% 22.07/22.27 (mult(c, a) = mult(a, c)),
% 22.07/22.27 inference(transitivity,[status(thm)],[2826, 2823, 2821])).
% 22.07/22.27 tff(2828,plain,
% 22.07/22.27 (mult(mult(b, c), mult(c, a)) = mult(mult(b, c), mult(a, c))),
% 22.07/22.27 inference(monotonicity,[status(thm)],[2827])).
% 22.07/22.27 tff(2829,assumption,(mult(mult(c, b), mult(c, a)) = mult(c, mult(b, mult(c, a)))), introduced(assumption)).
% 22.07/22.27 tff(2830,plain,
% 22.07/22.27 (mult(c, mult(b, mult(c, a))) = mult(mult(c, b), mult(c, a))),
% 22.07/22.27 inference(symmetry,[status(thm)],[2829])).
% 22.07/22.27 tff(2831,plain,
% 22.07/22.27 (mult(mult(b, c), a) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)),
% 22.07/22.27 inference(monotonicity,[status(thm)],[741])).
% 22.07/22.27 tff(2832,plain,
% 22.07/22.27 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(b, c), a)),
% 22.07/22.27 inference(symmetry,[status(thm)],[2831])).
% 22.07/22.27 tff(2833,plain,
% 22.07/22.27 (mult(mult(a, c), b) = mult(b, mult(c, a))),
% 22.07/22.27 inference(transitivity,[status(thm)],[405, 1800, 2832, 2283])).
% 22.07/22.27 tff(2834,plain,
% 22.07/22.27 (mult(c, mult(mult(a, c), b)) = mult(c, mult(b, mult(c, a)))),
% 22.07/22.27 inference(monotonicity,[status(thm)],[2833])).
% 22.07/22.27 tff(2835,plain,
% 22.07/22.27 (mult(c, mult(mult(a, c), b)) = mult(c, mult(b, mult(a, c)))),
% 22.07/22.27 inference(transitivity,[status(thm)],[2834, 2830, 2231, 2828, 2742, 2819])).
% 22.07/22.27 tff(2836,plain,
% 22.07/22.27 ($false),
% 22.07/22.27 inference(unit_resolution,[status(thm)],[2816, 2835])).
% 22.07/22.27 tff(2837,plain,((~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))) | (mult(c, mult(mult(a, c), b)) = mult(c, mult(b, mult(a, c)))) | (~(mult(mult(c, b), mult(c, a)) = mult(c, mult(b, mult(c, a))))) | (~(mult(mult(b, c), a) = mult(b, mult(c, a)))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit))))) | (~(mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))), inference(lemma,lemma(discharge,[]))).
% 22.07/22.27 tff(2838,plain,
% 22.07/22.27 (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 22.07/22.27 inference(unit_resolution,[status(thm)],[2837, 2314, 2278, 2258, 2128, 97, 2778])).
% 22.07/22.27 tff(2839,plain,
% 22.07/22.27 (((~(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(c, rd(mult(b, c), mult(a, c))), a), c))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))) | (mult(mult(c, rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 22.07/22.27 inference(tautology,[status(thm)],[])).
% 22.07/22.27 tff(2840,plain,
% 22.07/22.27 ((~(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(c, rd(mult(b, c), mult(a, c))), a), c))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))),
% 22.07/22.27 inference(unit_resolution,[status(thm)],[2839, 2838])).
% 22.07/22.27 tff(2841,plain,
% 22.07/22.27 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(c, rd(mult(b, c), mult(a, c))), a), c))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))))) | (~((~(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(c, a)))) | (~(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), a), c) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(c, rd(mult(b, c), mult(a, c))), a), c))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))))) | (~((~(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(c, a)))) | (~(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), a), c) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))))))),
% 22.07/22.27 inference(rewrite,[status(thm)],[])).
% 22.07/22.27 tff(2842,plain,
% 22.07/22.27 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(c, rd(mult(b, c), mult(a, c))), a), c))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))))) | (~((~(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(c, a)))) | (~(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), a), c) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))))))),
% 22.07/22.27 inference(quant_inst,[status(thm)],[])).
% 22.07/22.27 tff(2843,plain,
% 22.07/22.27 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(c, rd(mult(b, c), mult(a, c))), a), c))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))))) | (~((~(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(c, a)))) | (~(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), a), c) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))))),
% 22.07/22.27 inference(modus_ponens,[status(thm)],[2842, 2841])).
% 22.07/22.27 tff(2844,plain,
% 22.07/22.27 ((~((~(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(c, rd(mult(b, c), mult(a, c))), a), c))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))))) | (~((~(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(c, a)))) | (~(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), a), c) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))))),
% 22.07/22.27 inference(unit_resolution,[status(thm)],[2843, 27])).
% 22.07/22.27 tff(2845,plain,
% 22.07/22.27 (~((~(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(c, a)))) | (~(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), a), c) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))))),
% 22.07/22.27 inference(unit_resolution,[status(thm)],[2844, 2840])).
% 22.07/22.27 tff(2846,plain,
% 22.07/22.27 (((~(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(c, a)))) | (~(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), a), c) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))) | (mult(mult(mult(c, rd(mult(b, c), mult(a, c))), a), c) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 22.07/22.27 inference(tautology,[status(thm)],[])).
% 22.07/22.27 tff(2847,plain,
% 22.07/22.27 (mult(mult(mult(c, rd(mult(b, c), mult(a, c))), a), c) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))),
% 22.07/22.27 inference(unit_resolution,[status(thm)],[2846, 2845])).
% 22.07/22.27 tff(2848,plain,
% 22.07/22.27 (mult(mult(mult(c, rd(mult(b, c), mult(a, c))), a), c) = mult(mult(b, c), c)),
% 22.07/22.27 inference(transitivity,[status(thm)],[2847, 2815, 2787, 2784, 2227, 2225])).
% 22.07/22.27 tff(2849,plain,
% 22.07/22.27 (rd(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), a), c), c) = rd(mult(mult(b, c), c), c)),
% 22.07/22.27 inference(monotonicity,[status(thm)],[2848])).
% 22.07/22.27 tff(2850,plain,
% 22.07/22.27 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), a), c), c) = mult(mult(c, rd(mult(b, c), mult(a, c))), a))),
% 22.07/22.28 inference(quant_inst,[status(thm)],[])).
% 22.07/22.28 tff(2851,plain,
% 22.07/22.28 (rd(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), a), c), c) = mult(mult(c, rd(mult(b, c), mult(a, c))), a)),
% 22.07/22.28 inference(unit_resolution,[status(thm)],[2850, 168])).
% 22.07/22.28 tff(2852,plain,
% 22.07/22.28 (mult(mult(c, rd(mult(b, c), mult(a, c))), a) = rd(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), a), c), c)),
% 22.07/22.28 inference(symmetry,[status(thm)],[2851])).
% 22.07/22.28 tff(2853,plain,
% 22.07/22.28 (mult(mult(c, rd(mult(b, c), mult(a, c))), a) = mult(b, c)),
% 22.07/22.28 inference(transitivity,[status(thm)],[2852, 2849, 2224])).
% 22.07/22.28 tff(2854,plain,
% 22.07/22.28 (mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), a)) = mult(a, mult(b, c))),
% 22.07/22.28 inference(monotonicity,[status(thm)],[2853])).
% 22.07/22.28 tff(2855,plain,
% 22.07/22.28 (mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, b), c)),
% 22.07/22.28 inference(transitivity,[status(thm)],[2222, 2126, 2128, 177, 161])).
% 22.07/22.28 tff(2856,plain,
% 22.07/22.28 ((mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), a))) <=> (mult(mult(a, b), c) = mult(a, mult(b, c)))),
% 22.07/22.28 inference(monotonicity,[status(thm)],[2855, 2854])).
% 22.07/22.28 tff(2857,plain,
% 22.07/22.28 ((mult(mult(a, b), c) = mult(a, mult(b, c))) <=> (mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), a)))),
% 22.07/22.28 inference(symmetry,[status(thm)],[2856])).
% 22.07/22.28 tff(2858,plain,
% 22.07/22.28 ((~(mult(mult(a, b), c) = mult(a, mult(b, c)))) <=> (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), a))))),
% 22.07/22.28 inference(monotonicity,[status(thm)],[2857])).
% 22.07/22.28 tff(2859,plain,
% 22.07/22.28 (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), a)))),
% 22.07/22.28 inference(modus_ponens,[status(thm)],[146, 2858])).
% 22.07/22.28 tff(2860,plain,
% 22.07/22.28 (((~(mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(a, mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), a))))) | (mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), a)))),
% 22.07/22.28 inference(tautology,[status(thm)],[])).
% 22.07/22.28 tff(2861,plain,
% 22.07/22.28 ((~(mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(a, mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), a))))),
% 22.07/22.28 inference(unit_resolution,[status(thm)],[2860, 2859])).
% 22.07/22.28 tff(2862,plain,
% 22.07/22.28 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(a, mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), a)))))) | (~((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), a)) = mult(a, mult(a, mult(c, rd(mult(b, c), mult(a, c))))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(a, mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), a)))))) | (~((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), a)) = mult(a, mult(a, mult(c, rd(mult(b, c), mult(a, c))))))))))),
% 22.07/22.28 inference(rewrite,[status(thm)],[])).
% 22.07/22.28 tff(2863,plain,
% 22.07/22.28 (((~((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), a)) = mult(a, mult(a, mult(c, rd(mult(b, c), mult(a, c))))))))) | (~((~(mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(a, mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), a))))))) <=> ((~((~(mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(a, mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), a)))))) | (~((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), a)) = mult(a, mult(a, mult(c, rd(mult(b, c), mult(a, c))))))))))),
% 22.07/22.28 inference(rewrite,[status(thm)],[])).
% 22.07/22.28 tff(2864,plain,
% 22.07/22.28 ((~((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), a)))) | (~(mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(a, mult(c, rd(mult(b, c), mult(a, c))))))))) <=> (~((~(mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(a, mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), a))))))),
% 22.07/22.28 inference(rewrite,[status(thm)],[])).
% 22.07/22.28 tff(2865,plain,
% 22.07/22.28 ((~((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), a)) = mult(a, mult(a, mult(c, rd(mult(b, c), mult(a, c))))))))) <=> (~((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), a)) = mult(a, mult(a, mult(c, rd(mult(b, c), mult(a, c)))))))))),
% 22.07/22.28 inference(rewrite,[status(thm)],[])).
% 22.07/22.28 tff(2866,plain,
% 22.07/22.28 (((~((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), a)) = mult(a, mult(a, mult(c, rd(mult(b, c), mult(a, c))))))))) | (~((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), a)))) | (~(mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(a, mult(c, rd(mult(b, c), mult(a, c)))))))))) <=> ((~((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), a)) = mult(a, mult(a, mult(c, rd(mult(b, c), mult(a, c))))))))) | (~((~(mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(a, mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), a)))))))),
% 22.07/22.28 inference(monotonicity,[status(thm)],[2865, 2864])).
% 22.07/22.28 tff(2867,plain,
% 22.07/22.28 (((~((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), a)) = mult(a, mult(a, mult(c, rd(mult(b, c), mult(a, c))))))))) | (~((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), a)))) | (~(mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(a, mult(c, rd(mult(b, c), mult(a, c)))))))))) <=> ((~((~(mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(a, mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), a)))))) | (~((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), a)) = mult(a, mult(a, mult(c, rd(mult(b, c), mult(a, c))))))))))),
% 22.07/22.28 inference(transitivity,[status(thm)],[2866, 2863])).
% 22.07/22.28 tff(2868,plain,
% 22.07/22.28 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), a)) = mult(a, mult(a, mult(c, rd(mult(b, c), mult(a, c))))))))) | (~((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), a)))) | (~(mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(a, mult(c, rd(mult(b, c), mult(a, c))))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(a, mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), a)))))) | (~((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), a)) = mult(a, mult(a, mult(c, rd(mult(b, c), mult(a, c)))))))))))),
% 22.07/22.28 inference(monotonicity,[status(thm)],[2867])).
% 22.07/22.28 tff(2869,plain,
% 22.07/22.28 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), a)) = mult(a, mult(a, mult(c, rd(mult(b, c), mult(a, c))))))))) | (~((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), a)))) | (~(mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(a, mult(c, rd(mult(b, c), mult(a, c))))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(a, mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), a)))))) | (~((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), a)) = mult(a, mult(a, mult(c, rd(mult(b, c), mult(a, c))))))))))),
% 22.07/22.28 inference(transitivity,[status(thm)],[2868, 2862])).
% 22.07/22.28 tff(2870,plain,
% 22.07/22.28 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), a)) = mult(a, mult(a, mult(c, rd(mult(b, c), mult(a, c))))))))) | (~((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), a)))) | (~(mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(a, mult(c, rd(mult(b, c), mult(a, c))))))))))),
% 22.07/22.28 inference(quant_inst,[status(thm)],[])).
% 22.07/22.28 tff(2871,plain,
% 22.07/22.28 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(a, mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), a)))))) | (~((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), a)) = mult(a, mult(a, mult(c, rd(mult(b, c), mult(a, c)))))))))),
% 22.07/22.29 inference(modus_ponens,[status(thm)],[2870, 2869])).
% 22.07/22.29 tff(2872,plain,
% 22.07/22.29 ((~((~(mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(a, mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), a)))))) | (~((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), a)) = mult(a, mult(a, mult(c, rd(mult(b, c), mult(a, c)))))))))),
% 22.07/22.29 inference(unit_resolution,[status(thm)],[2871, 27])).
% 22.07/22.29 tff(2873,plain,
% 22.07/22.29 (~((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), a)) = mult(a, mult(a, mult(c, rd(mult(b, c), mult(a, c))))))))),
% 22.07/22.29 inference(unit_resolution,[status(thm)],[2872, 2861])).
% 22.07/22.29 tff(2874,plain,
% 22.07/22.29 (((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), a)) = mult(a, mult(a, mult(c, rd(mult(b, c), mult(a, c)))))))) | (mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))))),
% 22.07/22.29 inference(tautology,[status(thm)],[])).
% 22.07/22.29 tff(2875,plain,
% 22.07/22.29 (mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c))))),
% 22.07/22.29 inference(unit_resolution,[status(thm)],[2874, 2873])).
% 22.07/22.29 tff(2876,plain,
% 22.07/22.29 (mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a)),
% 22.07/22.29 inference(symmetry,[status(thm)],[2875])).
% 22.07/22.29 tff(2877,plain,
% 22.07/22.29 (mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), b)),
% 22.07/22.29 inference(transitivity,[status(thm)],[2876, 2222, 2126, 2128, 177])).
% 22.07/22.29 tff(2878,plain,
% 22.07/22.29 (mult(mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))), mult(a, b)) = mult(mult(mult(a, c), b), mult(a, b))),
% 22.07/22.29 inference(monotonicity,[status(thm)],[2877])).
% 22.07/22.29 tff(2879,plain,
% 22.07/22.29 (mult(mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))), mult(a, b)) = mult(mult(a, mult(mult(mult(b, c), a), rd(mult(b, c), mult(a, c)))), a)),
% 22.07/22.29 inference(transitivity,[status(thm)],[2878, 2161, 2159, 2074, 2153])).
% 22.07/22.29 tff(2880,plain,
% 22.07/22.29 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a), a) = mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))))),
% 22.07/22.29 inference(quant_inst,[status(thm)],[])).
% 22.07/22.29 tff(2881,plain,
% 22.07/22.29 (rd(mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a), a) = mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))),
% 22.07/22.29 inference(unit_resolution,[status(thm)],[2880, 168])).
% 22.07/22.29 tff(2882,plain,
% 22.07/22.29 (mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(mult(b, c), a), rd(mult(b, c), mult(a, c))), a)),
% 22.07/22.29 inference(monotonicity,[status(thm)],[2145])).
% 22.07/22.29 tff(2883,plain,
% 22.07/22.29 (mult(mult(mult(mult(b, c), a), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a)),
% 22.07/22.29 inference(symmetry,[status(thm)],[2882])).
% 22.07/22.29 tff(2884,plain,
% 22.07/22.29 (mult(mult(b, c), mult(mult(a, rd(mult(b, c), mult(a, c))), a)) = mult(mult(b, c), mult(a, b))),
% 22.07/22.29 inference(monotonicity,[status(thm)],[2122])).
% 22.07/22.29 tff(2885,plain,
% 22.07/22.29 (mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(mult(a, rd(mult(b, c), mult(a, c))), a))),
% 22.07/22.29 inference(symmetry,[status(thm)],[2884])).
% 22.07/22.29 tff(2886,plain,
% 22.07/22.29 ((mult(mult(unit, mult(a, b)), c) = mult(mult(unit, c), mult(a, b))) <=> (mult(mult(unit, c), mult(a, b)) = mult(mult(unit, mult(a, b)), c))),
% 22.07/22.29 inference(commutativity,[status(thm)],[])).
% 22.07/22.29 tff(2887,plain,
% 22.07/22.29 (mult(mult(unit, c), mult(a, b)) = mult(c, mult(c, ld(c, mult(a, b))))),
% 22.07/22.29 inference(monotonicity,[status(thm)],[73, 1441])).
% 22.07/22.29 tff(2888,plain,
% 22.07/22.29 (mult(c, mult(c, ld(c, mult(a, b)))) = mult(mult(unit, c), mult(a, b))),
% 22.07/22.29 inference(symmetry,[status(thm)],[2887])).
% 22.07/22.29 tff(2889,plain,
% 22.07/22.29 (mult(c, mult(a, b)) = mult(mult(unit, c), mult(a, b))),
% 22.07/22.29 inference(transitivity,[status(thm)],[1442, 2888])).
% 22.07/22.29 tff(2890,plain,
% 22.07/22.29 (mult(mult(unit, a), rd(mult(b, c), mult(a, c))) = mult(a, rd(mult(b, c), mult(a, c)))),
% 22.07/22.29 inference(monotonicity,[status(thm)],[244])).
% 22.07/22.29 tff(2891,plain,
% 22.07/22.29 (mult(mult(mult(unit, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, rd(mult(b, c), mult(a, c))), a)),
% 22.07/22.29 inference(monotonicity,[status(thm)],[2890])).
% 22.07/22.29 tff(2892,plain,
% 22.07/22.29 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(unit, a), rd(mult(b, c), mult(a, c))), a) = mult(unit, mult(mult(a, rd(mult(b, c), mult(a, c))), a)))),
% 22.07/22.29 inference(quant_inst,[status(thm)],[])).
% 22.07/22.29 tff(2893,plain,
% 22.07/22.29 (mult(mult(mult(unit, a), rd(mult(b, c), mult(a, c))), a) = mult(unit, mult(mult(a, rd(mult(b, c), mult(a, c))), a))),
% 22.07/22.29 inference(unit_resolution,[status(thm)],[2892, 56])).
% 22.07/22.29 tff(2894,plain,
% 22.07/22.29 (mult(unit, mult(mult(a, rd(mult(b, c), mult(a, c))), a)) = mult(mult(mult(unit, a), rd(mult(b, c), mult(a, c))), a)),
% 22.07/22.29 inference(symmetry,[status(thm)],[2893])).
% 22.07/22.29 tff(2895,plain,
% 22.07/22.29 (mult(a, mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, rd(mult(b, c), mult(a, c))), a)),
% 22.07/22.29 inference(symmetry,[status(thm)],[2121])).
% 22.07/22.29 tff(2896,plain,
% 22.07/22.29 (mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(a, rd(mult(b, c), mult(a, c))), a)),
% 22.07/22.29 inference(transitivity,[status(thm)],[212, 209, 195, 189, 187, 1574, 2895])).
% 22.07/22.29 tff(2897,plain,
% 22.07/22.29 (mult(unit, mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(unit, mult(mult(a, rd(mult(b, c), mult(a, c))), a))),
% 22.07/22.29 inference(monotonicity,[status(thm)],[2896])).
% 22.07/22.29 tff(2898,plain,
% 22.07/22.29 (mult(mult(a, b), unit) = mult(mult(mult(c, unit), ld(c, mult(a, b))), unit)),
% 22.07/22.29 inference(symmetry,[status(thm)],[209])).
% 22.07/22.29 tff(2899,plain,
% 22.07/22.29 (mult(a, b) = mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))),
% 22.07/22.29 inference(transitivity,[status(thm)],[193, 192, 557, 2898, 211])).
% 22.07/22.29 tff(2900,plain,
% 22.07/22.29 (mult(unit, mult(a, b)) = mult(unit, mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)))),
% 22.07/22.29 inference(monotonicity,[status(thm)],[2899])).
% 22.07/22.29 tff(2901,plain,
% 22.07/22.29 (mult(unit, mult(a, b)) = mult(a, b)),
% 22.07/22.29 inference(transitivity,[status(thm)],[2900, 2897, 2894, 2891, 2121, 913])).
% 22.07/22.29 tff(2902,plain,
% 22.07/22.29 (mult(mult(unit, mult(a, b)), c) = mult(mult(a, b), c)),
% 22.07/22.29 inference(monotonicity,[status(thm)],[2901])).
% 22.07/22.29 tff(2903,plain,
% 22.07/22.29 (mult(mult(a, b), c) = mult(mult(unit, mult(a, b)), c)),
% 22.07/22.29 inference(symmetry,[status(thm)],[2902])).
% 22.07/22.29 tff(2904,plain,
% 22.07/22.29 (mult(c, mult(b, a)) = mult(mult(c, b), a)),
% 22.07/22.29 inference(symmetry,[status(thm)],[2252])).
% 22.07/22.29 tff(2905,plain,
% 22.07/22.29 (mult(c, mult(b, a)) = mult(mult(unit, mult(a, b)), c)),
% 22.07/22.29 inference(transitivity,[status(thm)],[2904, 2298, 2126, 2128, 177, 161, 2903])).
% 22.07/22.29 tff(2906,plain,
% 22.07/22.29 ((mult(c, mult(b, a)) = mult(c, mult(a, b))) <=> (mult(mult(unit, mult(a, b)), c) = mult(mult(unit, c), mult(a, b)))),
% 22.07/22.29 inference(monotonicity,[status(thm)],[2905, 2889])).
% 22.07/22.29 tff(2907,plain,
% 22.07/22.29 ((mult(c, mult(b, a)) = mult(c, mult(a, b))) <=> (mult(mult(unit, c), mult(a, b)) = mult(mult(unit, mult(a, b)), c))),
% 22.07/22.29 inference(transitivity,[status(thm)],[2906, 2886])).
% 22.07/22.29 tff(2908,plain,
% 22.07/22.29 ((~(mult(c, mult(b, a)) = mult(c, mult(a, b)))) <=> (~(mult(mult(unit, c), mult(a, b)) = mult(mult(unit, mult(a, b)), c)))),
% 22.07/22.29 inference(monotonicity,[status(thm)],[2907])).
% 22.07/22.29 tff(2909,plain,
% 22.07/22.29 (~(mult(mult(unit, c), mult(a, b)) = mult(mult(unit, mult(a, b)), c))),
% 22.07/22.29 inference(modus_ponens,[status(thm)],[2243, 2908])).
% 22.07/22.29 tff(2910,plain,
% 22.07/22.29 (mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(a, rd(mult(b, c), mult(a, c))), a)),
% 22.07/22.29 inference(transitivity,[status(thm)],[212, 209, 195, 189, 187, 1574, 1334])).
% 22.07/22.29 tff(2911,plain,
% 22.07/22.29 (mult(unit, mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(unit, mult(mult(a, rd(mult(b, c), mult(a, c))), a))),
% 22.07/22.29 inference(monotonicity,[status(thm)],[2910])).
% 22.07/22.29 tff(2912,plain,
% 22.07/22.29 (mult(unit, mult(a, b)) = mult(a, b)),
% 22.07/22.29 inference(transitivity,[status(thm)],[2900, 2911, 2894, 2891, 1287, 913])).
% 22.07/22.29 tff(2913,plain,
% 22.07/22.29 (mult(mult(unit, mult(a, b)), c) = mult(mult(a, b), c)),
% 22.07/22.29 inference(monotonicity,[status(thm)],[2912])).
% 22.07/22.29 tff(2914,plain,
% 22.07/22.29 (mult(mult(a, b), c) = mult(mult(unit, mult(a, b)), c)),
% 22.07/22.29 inference(symmetry,[status(thm)],[2913])).
% 22.07/22.29 tff(2915,plain,
% 22.07/22.29 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(mult(a, b), c), mult(mult(mult(a, b), c), mult(b, a))) = mult(b, a))),
% 22.07/22.29 inference(quant_inst,[status(thm)],[])).
% 22.07/22.29 tff(2916,plain,
% 22.07/22.29 (ld(mult(mult(a, b), c), mult(mult(mult(a, b), c), mult(b, a))) = mult(b, a)),
% 22.07/22.29 inference(unit_resolution,[status(thm)],[2915, 7])).
% 22.07/22.29 tff(2917,plain,
% 22.07/22.29 (ld(mult(mult(a, b), c), mult(mult(mult(a, b), c), mult(b, a))) = ld(mult(mult(a, b), c), mult(mult(mult(a, b), c), mult(a, b)))),
% 22.07/22.29 inference(monotonicity,[status(thm)],[633])).
% 22.07/22.29 tff(2918,plain,
% 22.07/22.29 (ld(mult(mult(a, b), c), mult(mult(mult(a, b), c), mult(a, b))) = ld(mult(mult(a, b), c), mult(mult(mult(a, b), c), mult(b, a)))),
% 22.07/22.29 inference(symmetry,[status(thm)],[2917])).
% 22.07/22.29 tff(2919,plain,
% 22.07/22.29 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(mult(a, b), c), mult(mult(mult(a, b), c), mult(a, b))) = mult(a, b))),
% 22.07/22.29 inference(quant_inst,[status(thm)],[])).
% 22.07/22.29 tff(2920,plain,
% 22.07/22.29 (ld(mult(mult(a, b), c), mult(mult(mult(a, b), c), mult(a, b))) = mult(a, b)),
% 22.07/22.29 inference(unit_resolution,[status(thm)],[2919, 7])).
% 22.07/22.29 tff(2921,plain,
% 22.07/22.29 (mult(a, b) = ld(mult(mult(a, b), c), mult(mult(mult(a, b), c), mult(a, b)))),
% 22.07/22.29 inference(symmetry,[status(thm)],[2920])).
% 22.07/22.29 tff(2922,plain,
% 22.07/22.29 (mult(c, ld(c, mult(a, b))) = mult(b, a)),
% 22.07/22.29 inference(transitivity,[status(thm)],[204, 2921, 2918, 2916])).
% 22.07/22.29 tff(2923,plain,
% 22.07/22.29 (mult(c, mult(c, ld(c, mult(a, b)))) = mult(c, mult(b, a))),
% 22.07/22.29 inference(monotonicity,[status(thm)],[2922])).
% 22.07/22.29 tff(2924,plain,
% 22.07/22.29 (mult(mult(unit, c), mult(a, b)) = mult(mult(unit, mult(a, b)), c)),
% 22.07/22.29 inference(transitivity,[status(thm)],[2887, 2923, 2300, 2298, 2831, 1799, 177, 161, 2914])).
% 22.07/22.29 tff(2925,assumption,(~(mult(mult(unit, c), mult(a, b)) = mult(mult(unit, mult(a, b)), c))), introduced(assumption)).
% 22.07/22.29 tff(2926,plain,
% 22.07/22.29 ($false),
% 22.07/22.29 inference(unit_resolution,[status(thm)],[2925, 2924])).
% 22.07/22.29 tff(2927,plain,((~(mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(a, b)))) | (mult(mult(unit, c), mult(a, b)) = mult(mult(unit, mult(a, b)), c)) | (~(mult(mult(c, b), a) = mult(c, mult(b, a)))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit))))) | (~(mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))), inference(lemma,lemma(discharge,[]))).
% 22.07/22.29 tff(2928,plain,
% 22.07/22.29 (~(mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(a, b)))),
% 22.07/22.29 inference(unit_resolution,[status(thm)],[2927, 2909, 2128, 2252, 2121, 97, 2258])).
% 22.07/22.29 tff(2929,plain,
% 22.07/22.29 (~(mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a)))),
% 22.07/22.29 inference(unit_resolution,[status(thm)],[1192, 2928])).
% 22.07/22.29 tff(2930,plain,
% 22.07/22.29 ((~(mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a))) | (~(mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a))))),
% 22.07/22.29 inference(unit_resolution,[status(thm)],[1194, 2929])).
% 22.07/22.29 tff(2931,plain,
% 22.07/22.29 (~((~(mult(mult(mult(b, c), a), b) = mult(mult(b, c), mult(a, b)))) | (~(mult(mult(mult(b, c), b), a) = mult(mult(b, c), mult(b, a)))))),
% 22.07/22.29 inference(unit_resolution,[status(thm)],[1205, 2930])).
% 22.07/22.29 tff(2932,plain,
% 22.07/22.29 (mult(mult(mult(b, c), a), b) = mult(mult(b, c), mult(a, b))),
% 22.07/22.29 inference(unit_resolution,[status(thm)],[1229, 2931])).
% 22.07/22.29 tff(2933,plain,
% 22.07/22.29 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)) = mult(mult(a, b), c)),
% 22.07/22.29 inference(transitivity,[status(thm)],[1169, 1164, 2126, 2128, 177, 161])).
% 22.07/22.29 tff(2934,plain,
% 22.07/22.29 (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), b) = mult(mult(mult(a, b), c), b)),
% 22.07/22.29 inference(monotonicity,[status(thm)],[2933])).
% 22.07/22.29 tff(2935,plain,
% 22.07/22.29 (mult(mult(mult(a, b), c), b) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), b)),
% 22.07/22.29 inference(symmetry,[status(thm)],[2934])).
% 22.07/22.29 tff(2936,plain,
% 22.07/22.29 (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 22.07/22.29 inference(unit_resolution,[status(thm)],[755, 2258, 2228, 1032, 2256])).
% 22.07/22.29 tff(2937,plain,
% 22.07/22.29 ((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), c))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))))),
% 22.07/22.29 inference(unit_resolution,[status(thm)],[757, 2936])).
% 22.07/22.29 tff(2938,plain,
% 22.07/22.29 (~((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), a) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, a)))) | (~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), c) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))))),
% 22.07/22.29 inference(unit_resolution,[status(thm)],[762, 2937])).
% 22.07/22.29 tff(2939,plain,
% 22.07/22.29 (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), c) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))),
% 22.07/22.29 inference(unit_resolution,[status(thm)],[764, 2938])).
% 22.07/22.29 tff(2940,plain,
% 22.07/22.29 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), c)),
% 22.07/22.29 inference(symmetry,[status(thm)],[2939])).
% 22.07/22.29 tff(2941,plain,
% 22.07/22.29 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, b), c)),
% 22.07/22.29 inference(transitivity,[status(thm)],[2940, 2132])).
% 22.07/22.29 tff(2942,plain,
% 22.07/22.29 (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)), b) = mult(mult(mult(a, b), c), b)),
% 22.07/22.29 inference(monotonicity,[status(thm)],[2941])).
% 22.07/22.29 tff(2943,plain,
% 22.07/22.29 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), c)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), b))),
% 22.07/22.29 inference(monotonicity,[status(thm)],[227])).
% 22.07/22.29 tff(2944,plain,
% 22.07/22.29 (mult(c, mult(b, a)) = mult(mult(a, b), c)),
% 22.07/22.29 inference(transitivity,[status(thm)],[2904, 2298, 2126, 2128, 177, 161])).
% 22.07/22.29 tff(2945,plain,
% 22.07/22.29 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(b, a))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), c))),
% 22.07/22.29 inference(monotonicity,[status(thm)],[2944])).
% 22.07/22.29 tff(2946,plain,
% 22.07/22.29 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(b, a))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), b))),
% 22.07/22.29 inference(transitivity,[status(thm)],[2945, 2943])).
% 22.07/22.29 tff(2947,plain,
% 22.07/22.29 (((~(mult(mult(b, a), c) = mult(b, mult(a, c)))) | (~(mult(mult(b, c), a) = mult(b, mult(c, a))))) | (mult(mult(b, a), c) = mult(b, mult(a, c)))),
% 22.07/22.29 inference(tautology,[status(thm)],[])).
% 22.07/22.29 tff(2948,plain,
% 22.07/22.29 (mult(mult(b, a), c) = mult(b, mult(a, c))),
% 22.07/22.29 inference(unit_resolution,[status(thm)],[2947, 2276])).
% 22.07/22.29 tff(2949,plain,
% 22.07/22.29 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(b, a), c)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(b, mult(a, c)))),
% 22.07/22.29 inference(monotonicity,[status(thm)],[2948])).
% 22.07/22.29 tff(2950,plain,
% 22.07/22.29 ((mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(b, a), c)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(b, a)))) <=> (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(b, mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), b)))),
% 22.07/22.29 inference(monotonicity,[status(thm)],[2949, 2946])).
% 22.07/22.29 tff(2951,plain,
% 22.07/22.29 ((~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(b, a), c)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(b, a))))) <=> (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(b, mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), b))))),
% 22.07/22.30 inference(monotonicity,[status(thm)],[2950])).
% 22.07/22.30 tff(2952,plain,
% 22.07/22.30 (mult(mult(rd(mult(b, c), mult(a, c)), a), a) = mult(b, a)),
% 22.07/22.30 inference(monotonicity,[status(thm)],[176])).
% 22.07/22.30 tff(2953,plain,
% 22.07/22.30 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c) = mult(mult(b, a), c)),
% 22.07/22.30 inference(monotonicity,[status(thm)],[2952])).
% 22.07/22.30 tff(2954,plain,
% 22.07/22.30 ((mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c))) <=> (mult(mult(b, a), c) = mult(b, mult(a, c)))),
% 22.07/22.30 inference(monotonicity,[status(thm)],[2953, 1425])).
% 22.07/22.30 tff(2955,plain,
% 22.07/22.30 ((mult(mult(b, a), c) = mult(b, mult(a, c))) <=> (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)))),
% 22.07/22.30 inference(symmetry,[status(thm)],[2954])).
% 22.07/22.30 tff(2956,plain,
% 22.07/22.30 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c))),
% 22.07/22.30 inference(modus_ponens,[status(thm)],[2948, 2955])).
% 22.07/22.30 tff(2957,plain,
% 22.07/22.30 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, a)) = mult(b, mult(c, a))),
% 22.07/22.30 inference(monotonicity,[status(thm)],[176])).
% 22.07/22.30 tff(2958,plain,
% 22.07/22.30 ((mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, a))) <=> (mult(mult(b, c), a) = mult(b, mult(c, a)))),
% 22.07/22.30 inference(monotonicity,[status(thm)],[1164, 2957])).
% 22.07/22.30 tff(2959,plain,
% 22.07/22.30 ((mult(mult(b, c), a) = mult(b, mult(c, a))) <=> (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, a)))),
% 22.07/22.30 inference(symmetry,[status(thm)],[2958])).
% 22.07/22.30 tff(2960,plain,
% 22.07/22.30 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, a))),
% 22.07/22.30 inference(modus_ponens,[status(thm)],[2278, 2959])).
% 22.07/22.30 tff(2961,plain,
% 22.07/22.30 (mult(b, c) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))),
% 22.07/22.30 inference(transitivity,[status(thm)],[740, 2426, 1028])).
% 22.07/22.30 tff(2962,plain,
% 22.07/22.30 (mult(mult(b, c), mult(a, c)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))),
% 22.07/22.30 inference(monotonicity,[status(thm)],[2961])).
% 22.07/22.30 tff(2963,plain,
% 22.07/22.30 (mult(c, mult(b, mult(a, c))) = mult(mult(c, b), mult(a, c))),
% 22.07/22.30 inference(symmetry,[status(thm)],[2741])).
% 22.07/22.30 tff(2964,plain,
% 22.07/22.30 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, rd(mult(b, c), mult(a, c))), mult(b, mult(a, c)))) = mult(b, mult(a, c)))),
% 22.07/22.30 inference(quant_inst,[status(thm)],[])).
% 22.07/22.30 tff(2965,plain,
% 22.07/22.30 (ld(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, rd(mult(b, c), mult(a, c))), mult(b, mult(a, c)))) = mult(b, mult(a, c))),
% 22.07/22.30 inference(unit_resolution,[status(thm)],[2964, 7])).
% 22.07/22.30 tff(2966,plain,
% 22.07/22.30 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), b)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), c))),
% 22.07/22.30 inference(monotonicity,[status(thm)],[161])).
% 22.07/22.30 tff(2967,plain,
% 22.07/22.30 (mult(mult(b, c), a) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)),
% 22.07/22.30 inference(monotonicity,[status(thm)],[2961])).
% 22.07/22.30 tff(2968,plain,
% 22.07/22.30 (mult(c, mult(b, a)) = mult(mult(a, c), b)),
% 22.07/22.30 inference(transitivity,[status(thm)],[2300, 2298, 2967, 1799, 177])).
% 22.07/22.30 tff(2969,plain,
% 22.07/22.30 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(b, a))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), b))),
% 22.07/22.30 inference(monotonicity,[status(thm)],[2968])).
% 22.07/22.30 tff(2970,assumption,(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(b, a), c)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(b, a)))), introduced(assumption)).
% 22.07/22.30 tff(2971,plain,
% 22.07/22.30 (mult(b, a) = mult(mult(rd(mult(b, c), mult(a, c)), a), a)),
% 22.07/22.30 inference(symmetry,[status(thm)],[2952])).
% 22.07/22.30 tff(2972,plain,
% 22.07/22.30 (mult(mult(b, a), c) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c)),
% 22.07/22.30 inference(monotonicity,[status(thm)],[2971])).
% 22.07/22.30 tff(2973,plain,
% 22.07/22.30 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c) = mult(mult(b, a), c)),
% 22.07/22.30 inference(symmetry,[status(thm)],[2972])).
% 22.07/22.30 tff(2974,assumption,(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c))), introduced(assumption)).
% 22.07/22.30 tff(2975,plain,
% 22.07/22.30 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c)),
% 22.07/22.30 inference(symmetry,[status(thm)],[2974])).
% 22.07/22.30 tff(2976,plain,
% 22.07/22.30 (mult(b, mult(a, c)) = mult(mult(b, a), c)),
% 22.07/22.30 inference(transitivity,[status(thm)],[1430, 2975, 2973])).
% 22.07/22.30 tff(2977,plain,
% 22.07/22.30 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(b, mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(b, a), c))),
% 22.07/22.30 inference(monotonicity,[status(thm)],[2976])).
% 22.07/22.30 tff(2978,plain,
% 22.07/22.30 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(b, mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), c))),
% 22.07/22.30 inference(transitivity,[status(thm)],[2977, 2970, 2969, 2966])).
% 22.07/22.30 tff(2979,plain,
% 22.07/22.30 (ld(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, rd(mult(b, c), mult(a, c))), mult(b, mult(a, c)))) = ld(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), c)))),
% 22.07/22.30 inference(monotonicity,[status(thm)],[2978])).
% 22.07/22.30 tff(2980,plain,
% 22.07/22.30 (ld(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), c))) = ld(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, rd(mult(b, c), mult(a, c))), mult(b, mult(a, c))))),
% 22.07/22.30 inference(symmetry,[status(thm)],[2979])).
% 22.07/22.30 tff(2981,plain,
% 22.07/22.30 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), c))) = mult(mult(a, b), c))),
% 22.07/22.30 inference(quant_inst,[status(thm)],[])).
% 22.07/22.30 tff(2982,plain,
% 22.07/22.30 (ld(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), c))) = mult(mult(a, b), c)),
% 22.07/22.30 inference(unit_resolution,[status(thm)],[2981, 7])).
% 22.07/22.30 tff(2983,plain,
% 22.07/22.30 (mult(mult(a, b), c) = ld(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), c)))),
% 22.07/22.30 inference(symmetry,[status(thm)],[2982])).
% 22.07/22.30 tff(2984,plain,
% 22.07/22.30 (mult(mult(a, c), b) = mult(b, mult(a, c))),
% 22.07/22.30 inference(transitivity,[status(thm)],[161, 2983, 2980, 2965])).
% 22.07/22.30 tff(2985,plain,
% 22.07/22.30 (mult(c, mult(mult(a, c), b)) = mult(c, mult(b, mult(a, c)))),
% 22.07/22.30 inference(monotonicity,[status(thm)],[2984])).
% 22.07/22.30 tff(2986,plain,
% 22.07/22.30 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)) = mult(mult(a, c), b)),
% 22.07/22.30 inference(transitivity,[status(thm)],[1169, 1164, 2967, 1799, 177])).
% 22.07/22.30 tff(2987,plain,
% 22.07/22.30 (mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) = mult(c, mult(mult(a, c), b))),
% 22.07/22.30 inference(monotonicity,[status(thm)],[2986])).
% 22.07/22.30 tff(2988,assumption,(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, a))), introduced(assumption)).
% 22.07/22.30 tff(2989,plain,
% 22.07/22.30 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, a)) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a)),
% 22.07/22.30 inference(symmetry,[status(thm)],[2988])).
% 22.07/22.30 tff(2990,plain,
% 22.07/22.30 (mult(b, mult(c, a)) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, a))),
% 22.07/22.30 inference(monotonicity,[status(thm)],[2728])).
% 22.07/22.30 tff(2991,plain,
% 22.07/22.30 (mult(b, mult(c, a)) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))),
% 22.07/22.30 inference(transitivity,[status(thm)],[2990, 2989, 1168])).
% 22.07/22.30 tff(2992,plain,
% 22.07/22.30 (mult(c, mult(b, mult(c, a))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))),
% 22.07/22.30 inference(monotonicity,[status(thm)],[2991])).
% 22.07/22.30 tff(2993,plain,
% 22.07/22.30 (mult(mult(b, c), mult(c, a)) = mult(mult(c, b), mult(c, a))),
% 22.07/22.30 inference(monotonicity,[status(thm)],[1399])).
% 22.07/22.30 tff(2994,plain,
% 22.07/22.30 (mult(mult(a, c), rd(mult(b, c), mult(a, c))) = mult(b, c)),
% 22.07/22.30 inference(transitivity,[status(thm)],[1642, 2425, 291])).
% 22.07/22.30 tff(2995,plain,
% 22.07/22.30 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(b, c), mult(c, a))),
% 22.07/22.30 inference(monotonicity,[status(thm)],[2994])).
% 22.07/22.30 tff(2996,plain,
% 22.07/22.30 (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c)),
% 22.07/22.30 inference(transitivity,[status(thm)],[751, 2995, 2993, 2829, 2992, 2987, 2985, 2963, 2429, 2962, 738])).
% 22.07/22.30 tff(2997,plain,
% 22.07/22.30 ($false),
% 22.07/22.30 inference(unit_resolution,[status(thm)],[753, 2996])).
% 22.07/22.30 tff(2998,plain,((~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(b, a), c)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(b, a))))) | (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c)) | (~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)))) | (~(mult(mult(c, b), mult(c, a)) = mult(c, mult(b, mult(c, a))))) | (~(mult(mult(c, b), mult(a, c)) = mult(c, mult(b, mult(a, c))))) | (~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(mult(c, b), a) = mult(c, mult(b, a)))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit))))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, a))))), inference(lemma,lemma(discharge,[]))).
% 22.07/22.30 tff(2999,plain,
% 22.07/22.30 (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(b, a), c)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(b, a))))),
% 22.07/22.30 inference(unit_resolution,[status(thm)],[2998, 2314, 2960, 2228, 2721, 1032, 2252, 2128, 97, 2956, 2256])).
% 22.07/22.30 tff(3000,plain,
% 22.07/22.30 (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(b, mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), b)))),
% 22.07/22.30 inference(modus_ponens,[status(thm)],[2999, 2951])).
% 22.07/22.30 tff(3001,plain,
% 22.07/22.30 (((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), b), mult(a, c)) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)), b))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(b, mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), b))))) | (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(b, mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), b)))),
% 22.07/22.30 inference(tautology,[status(thm)],[])).
% 22.07/22.30 tff(3002,plain,
% 22.07/22.30 ((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), b), mult(a, c)) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)), b))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(b, mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), b))))),
% 22.07/22.30 inference(unit_resolution,[status(thm)],[3001, 3000])).
% 22.07/22.30 tff(3003,plain,
% 22.07/22.30 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), b), mult(a, c)) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)), b))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(b, mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), b)))))) | (~((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), b), mult(a, c)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(b, mult(a, c))))) | (~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)), b) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), b)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), b), mult(a, c)) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)), b))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(b, mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), b)))))) | (~((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), b), mult(a, c)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(b, mult(a, c))))) | (~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)), b) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), b)))))))),
% 22.07/22.30 inference(rewrite,[status(thm)],[])).
% 22.07/22.30 tff(3004,plain,
% 22.07/22.30 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), b), mult(a, c)) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)), b))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(b, mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), b)))))) | (~((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), b), mult(a, c)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(b, mult(a, c))))) | (~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)), b) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), b)))))))),
% 22.07/22.30 inference(quant_inst,[status(thm)],[])).
% 22.07/22.30 tff(3005,plain,
% 22.07/22.30 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), b), mult(a, c)) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)), b))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(b, mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), b)))))) | (~((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), b), mult(a, c)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(b, mult(a, c))))) | (~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)), b) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), b))))))),
% 22.07/22.30 inference(modus_ponens,[status(thm)],[3004, 3003])).
% 22.07/22.30 tff(3006,plain,
% 22.07/22.30 ((~((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), b), mult(a, c)) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)), b))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(b, mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), b)))))) | (~((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), b), mult(a, c)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(b, mult(a, c))))) | (~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)), b) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), b))))))),
% 22.07/22.30 inference(unit_resolution,[status(thm)],[3005, 27])).
% 22.07/22.30 tff(3007,plain,
% 22.07/22.30 (~((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), b), mult(a, c)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(b, mult(a, c))))) | (~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)), b) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), b)))))),
% 22.07/22.30 inference(unit_resolution,[status(thm)],[3006, 3002])).
% 22.07/22.30 tff(3008,plain,
% 22.07/22.30 (((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), b), mult(a, c)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(b, mult(a, c))))) | (~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)), b) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), b))))) | (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)), b) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), b)))),
% 22.07/22.30 inference(tautology,[status(thm)],[])).
% 22.07/22.30 tff(3009,plain,
% 22.07/22.30 (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)), b) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), b))),
% 22.07/22.30 inference(unit_resolution,[status(thm)],[3008, 3007])).
% 22.07/22.30 tff(3010,plain,
% 22.07/22.30 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), b)) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)), b)),
% 22.07/22.30 inference(symmetry,[status(thm)],[3009])).
% 22.07/22.31 tff(3011,plain,
% 22.07/22.31 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), c))),
% 22.07/22.31 inference(monotonicity,[status(thm)],[2855])).
% 22.07/22.31 tff(3012,plain,
% 22.07/22.31 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a)))),
% 22.07/22.31 inference(quant_inst,[status(thm)],[])).
% 22.07/22.31 tff(3013,plain,
% 22.07/22.31 (mult(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a))),
% 22.07/22.31 inference(unit_resolution,[status(thm)],[3012, 56])).
% 22.07/22.31 tff(3014,plain,
% 22.07/22.31 (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, b), mult(c, rd(mult(b, c), mult(a, c))))),
% 22.07/22.31 inference(monotonicity,[status(thm)],[2122])).
% 22.07/22.31 tff(3015,plain,
% 22.07/22.31 (mult(mult(a, b), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(c, rd(mult(b, c), mult(a, c))))),
% 22.07/22.31 inference(symmetry,[status(thm)],[3014])).
% 22.07/22.31 tff(3016,plain,
% 22.07/22.31 (mult(mult(mult(a, b), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(c, rd(mult(b, c), mult(a, c)))), a)),
% 22.07/22.31 inference(monotonicity,[status(thm)],[3015])).
% 22.07/22.31 tff(3017,plain,
% 22.07/22.31 (mult(mult(mult(a, b), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a)),
% 22.07/22.31 inference(transitivity,[status(thm)],[3016, 3013, 3011, 2943, 3010, 2942, 2935, 1221, 2932, 2885, 1597, 2883])).
% 22.07/22.31 tff(3018,plain,
% 22.07/22.31 (rd(mult(mult(mult(a, b), mult(c, rd(mult(b, c), mult(a, c)))), a), a) = rd(mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a), a)),
% 22.07/22.31 inference(monotonicity,[status(thm)],[3017])).
% 22.07/22.31 tff(3019,plain,
% 22.07/22.31 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(a, b), mult(c, rd(mult(b, c), mult(a, c)))), a), a) = mult(mult(a, b), mult(c, rd(mult(b, c), mult(a, c)))))),
% 22.07/22.31 inference(quant_inst,[status(thm)],[])).
% 22.07/22.31 tff(3020,plain,
% 22.07/22.31 (rd(mult(mult(mult(a, b), mult(c, rd(mult(b, c), mult(a, c)))), a), a) = mult(mult(a, b), mult(c, rd(mult(b, c), mult(a, c))))),
% 22.07/22.31 inference(unit_resolution,[status(thm)],[3019, 168])).
% 22.07/22.31 tff(3021,plain,
% 22.07/22.31 (mult(mult(a, b), mult(c, rd(mult(b, c), mult(a, c)))) = rd(mult(mult(mult(a, b), mult(c, rd(mult(b, c), mult(a, c)))), a), a)),
% 22.07/22.31 inference(symmetry,[status(thm)],[3020])).
% 22.07/22.31 tff(3022,plain,
% 22.07/22.31 (mult(mult(a, b), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(b, c), a), rd(mult(b, c), mult(a, c)))),
% 22.07/22.31 inference(transitivity,[status(thm)],[3021, 3018, 2881, 2145])).
% 22.07/22.31 tff(3023,plain,
% 22.07/22.31 (mult(mult(a, a), mult(mult(a, b), mult(c, rd(mult(b, c), mult(a, c))))) = mult(mult(a, a), mult(mult(mult(b, c), a), rd(mult(b, c), mult(a, c))))),
% 22.07/22.31 inference(monotonicity,[status(thm)],[3022])).
% 22.07/22.31 tff(3024,assumption,(~(mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a)))), introduced(assumption)).
% 22.07/22.31 tff(3025,plain,
% 22.07/22.31 ((~(mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a))) | (~(mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a))))),
% 22.07/22.31 inference(unit_resolution,[status(thm)],[1194, 3024])).
% 22.07/22.31 tff(3026,plain,
% 22.07/22.31 (~((~(mult(mult(mult(b, c), a), b) = mult(mult(b, c), mult(a, b)))) | (~(mult(mult(mult(b, c), b), a) = mult(mult(b, c), mult(b, a)))))),
% 22.07/22.31 inference(unit_resolution,[status(thm)],[1205, 3025])).
% 22.07/22.31 tff(3027,plain,
% 22.07/22.31 (mult(mult(mult(b, c), b), a) = mult(mult(b, c), mult(b, a))),
% 22.07/22.31 inference(unit_resolution,[status(thm)],[1207, 3026])).
% 22.07/22.31 tff(3028,plain,
% 22.07/22.31 ((~![A: $i] : (mult(A, unit) = A)) | (mult(mult(mult(mult(b, c), b), a), unit) = mult(mult(mult(b, c), b), a))),
% 22.07/22.31 inference(quant_inst,[status(thm)],[])).
% 22.07/22.31 tff(3029,plain,
% 22.07/22.31 (mult(mult(mult(mult(b, c), b), a), unit) = mult(mult(mult(b, c), b), a)),
% 22.07/22.31 inference(unit_resolution,[status(thm)],[3028, 43])).
% 22.07/22.31 tff(3030,plain,
% 22.07/22.31 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(mult(mult(b, c), b), a), unit), a), a) = mult(mult(mult(mult(b, c), b), a), unit))),
% 22.07/22.31 inference(quant_inst,[status(thm)],[])).
% 22.07/22.31 tff(3031,plain,
% 22.07/22.31 (rd(mult(mult(mult(mult(mult(b, c), b), a), unit), a), a) = mult(mult(mult(mult(b, c), b), a), unit)),
% 22.07/22.31 inference(unit_resolution,[status(thm)],[3030, 168])).
% 22.07/22.31 tff(3032,assumption,(~(mult(mult(mult(mult(mult(b, c), b), a), unit), a) = mult(mult(mult(b, c), b), mult(mult(a, unit), a)))), introduced(assumption)).
% 22.07/22.31 tff(3033,plain,
% 22.07/22.31 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(mult(b, c), b), a), unit), a) = mult(mult(mult(b, c), b), mult(mult(a, unit), a)))),
% 22.07/22.31 inference(quant_inst,[status(thm)],[])).
% 22.07/22.31 tff(3034,plain,
% 22.07/22.31 ($false),
% 22.07/22.31 inference(unit_resolution,[status(thm)],[3033, 56, 3032])).
% 22.07/22.31 tff(3035,plain,(mult(mult(mult(mult(mult(b, c), b), a), unit), a) = mult(mult(mult(b, c), b), mult(mult(a, unit), a))), inference(lemma,lemma(discharge,[]))).
% 22.07/22.31 tff(3036,plain,
% 22.07/22.31 (mult(mult(mult(b, c), b), mult(mult(a, unit), a)) = mult(mult(mult(mult(mult(b, c), b), a), unit), a)),
% 22.07/22.31 inference(symmetry,[status(thm)],[3035])).
% 22.07/22.31 tff(3037,plain,
% 22.07/22.31 (mult(mult(mult(b, c), b), mult(a, a)) = mult(mult(mult(b, c), b), mult(mult(a, unit), a))),
% 22.07/22.31 inference(monotonicity,[status(thm)],[520])).
% 22.07/22.31 tff(3038,assumption,(~(mult(mult(mult(b, c), mult(a, a)), b) = mult(mult(b, c), mult(mult(a, a), b)))), introduced(assumption)).
% 22.07/22.31 tff(3039,plain,
% 22.07/22.31 (((~(mult(mult(mult(b, c), b), mult(a, a)) = mult(mult(b, c), mult(b, mult(a, a))))) | (~(mult(mult(mult(b, c), mult(a, a)), b) = mult(mult(b, c), mult(mult(a, a), b))))) | (mult(mult(mult(b, c), mult(a, a)), b) = mult(mult(b, c), mult(mult(a, a), b)))),
% 22.07/22.31 inference(tautology,[status(thm)],[])).
% 22.07/22.31 tff(3040,plain,
% 22.07/22.31 ((~(mult(mult(mult(b, c), b), mult(a, a)) = mult(mult(b, c), mult(b, mult(a, a))))) | (~(mult(mult(mult(b, c), mult(a, a)), b) = mult(mult(b, c), mult(mult(a, a), b))))),
% 22.07/22.31 inference(unit_resolution,[status(thm)],[3039, 3038])).
% 22.07/22.31 tff(3041,plain,
% 22.07/22.31 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(b, c), b), mult(a, a)) = mult(mult(b, c), mult(b, mult(a, a))))) | (~(mult(mult(mult(b, c), mult(a, a)), b) = mult(mult(b, c), mult(mult(a, a), b)))))) | (~((~(mult(mult(mult(b, c), mult(a, a)), b) = mult(mult(mult(b, c), b), mult(a, a)))) | (~(mult(mult(b, c), mult(mult(a, a), b)) = mult(mult(b, c), mult(b, mult(a, a))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(b, c), b), mult(a, a)) = mult(mult(b, c), mult(b, mult(a, a))))) | (~(mult(mult(mult(b, c), mult(a, a)), b) = mult(mult(b, c), mult(mult(a, a), b)))))) | (~((~(mult(mult(mult(b, c), mult(a, a)), b) = mult(mult(mult(b, c), b), mult(a, a)))) | (~(mult(mult(b, c), mult(mult(a, a), b)) = mult(mult(b, c), mult(b, mult(a, a))))))))),
% 22.07/22.31 inference(rewrite,[status(thm)],[])).
% 22.07/22.31 tff(3042,plain,
% 22.07/22.31 (((~((~(mult(mult(mult(b, c), mult(a, a)), b) = mult(mult(mult(b, c), b), mult(a, a)))) | (~(mult(mult(b, c), mult(mult(a, a), b)) = mult(mult(b, c), mult(b, mult(a, a))))))) | (~((~(mult(mult(mult(b, c), b), mult(a, a)) = mult(mult(b, c), mult(b, mult(a, a))))) | (~(mult(mult(mult(b, c), mult(a, a)), b) = mult(mult(b, c), mult(mult(a, a), b))))))) <=> ((~((~(mult(mult(mult(b, c), b), mult(a, a)) = mult(mult(b, c), mult(b, mult(a, a))))) | (~(mult(mult(mult(b, c), mult(a, a)), b) = mult(mult(b, c), mult(mult(a, a), b)))))) | (~((~(mult(mult(mult(b, c), mult(a, a)), b) = mult(mult(mult(b, c), b), mult(a, a)))) | (~(mult(mult(b, c), mult(mult(a, a), b)) = mult(mult(b, c), mult(b, mult(a, a))))))))),
% 22.07/22.31 inference(rewrite,[status(thm)],[])).
% 22.07/22.31 tff(3043,plain,
% 22.07/22.31 ((~((~(mult(mult(mult(b, c), mult(a, a)), b) = mult(mult(b, c), mult(mult(a, a), b)))) | (~(mult(mult(mult(b, c), b), mult(a, a)) = mult(mult(b, c), mult(b, mult(a, a))))))) <=> (~((~(mult(mult(mult(b, c), b), mult(a, a)) = mult(mult(b, c), mult(b, mult(a, a))))) | (~(mult(mult(mult(b, c), mult(a, a)), b) = mult(mult(b, c), mult(mult(a, a), b))))))),
% 22.07/22.31 inference(rewrite,[status(thm)],[])).
% 22.07/22.31 tff(3044,plain,
% 22.07/22.31 ((~((~(mult(mult(mult(b, c), mult(a, a)), b) = mult(mult(mult(b, c), b), mult(a, a)))) | (~(mult(mult(b, c), mult(mult(a, a), b)) = mult(mult(b, c), mult(b, mult(a, a))))))) <=> (~((~(mult(mult(mult(b, c), mult(a, a)), b) = mult(mult(mult(b, c), b), mult(a, a)))) | (~(mult(mult(b, c), mult(mult(a, a), b)) = mult(mult(b, c), mult(b, mult(a, a)))))))),
% 22.07/22.31 inference(rewrite,[status(thm)],[])).
% 22.07/22.31 tff(3045,plain,
% 22.07/22.31 (((~((~(mult(mult(mult(b, c), mult(a, a)), b) = mult(mult(mult(b, c), b), mult(a, a)))) | (~(mult(mult(b, c), mult(mult(a, a), b)) = mult(mult(b, c), mult(b, mult(a, a))))))) | (~((~(mult(mult(mult(b, c), mult(a, a)), b) = mult(mult(b, c), mult(mult(a, a), b)))) | (~(mult(mult(mult(b, c), b), mult(a, a)) = mult(mult(b, c), mult(b, mult(a, a)))))))) <=> ((~((~(mult(mult(mult(b, c), mult(a, a)), b) = mult(mult(mult(b, c), b), mult(a, a)))) | (~(mult(mult(b, c), mult(mult(a, a), b)) = mult(mult(b, c), mult(b, mult(a, a))))))) | (~((~(mult(mult(mult(b, c), b), mult(a, a)) = mult(mult(b, c), mult(b, mult(a, a))))) | (~(mult(mult(mult(b, c), mult(a, a)), b) = mult(mult(b, c), mult(mult(a, a), b)))))))),
% 22.07/22.31 inference(monotonicity,[status(thm)],[3044, 3043])).
% 22.07/22.31 tff(3046,plain,
% 22.07/22.31 (((~((~(mult(mult(mult(b, c), mult(a, a)), b) = mult(mult(mult(b, c), b), mult(a, a)))) | (~(mult(mult(b, c), mult(mult(a, a), b)) = mult(mult(b, c), mult(b, mult(a, a))))))) | (~((~(mult(mult(mult(b, c), mult(a, a)), b) = mult(mult(b, c), mult(mult(a, a), b)))) | (~(mult(mult(mult(b, c), b), mult(a, a)) = mult(mult(b, c), mult(b, mult(a, a)))))))) <=> ((~((~(mult(mult(mult(b, c), b), mult(a, a)) = mult(mult(b, c), mult(b, mult(a, a))))) | (~(mult(mult(mult(b, c), mult(a, a)), b) = mult(mult(b, c), mult(mult(a, a), b)))))) | (~((~(mult(mult(mult(b, c), mult(a, a)), b) = mult(mult(mult(b, c), b), mult(a, a)))) | (~(mult(mult(b, c), mult(mult(a, a), b)) = mult(mult(b, c), mult(b, mult(a, a))))))))),
% 22.07/22.31 inference(transitivity,[status(thm)],[3045, 3042])).
% 22.07/22.31 tff(3047,plain,
% 22.07/22.31 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(b, c), mult(a, a)), b) = mult(mult(mult(b, c), b), mult(a, a)))) | (~(mult(mult(b, c), mult(mult(a, a), b)) = mult(mult(b, c), mult(b, mult(a, a))))))) | (~((~(mult(mult(mult(b, c), mult(a, a)), b) = mult(mult(b, c), mult(mult(a, a), b)))) | (~(mult(mult(mult(b, c), b), mult(a, a)) = mult(mult(b, c), mult(b, mult(a, a))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(b, c), b), mult(a, a)) = mult(mult(b, c), mult(b, mult(a, a))))) | (~(mult(mult(mult(b, c), mult(a, a)), b) = mult(mult(b, c), mult(mult(a, a), b)))))) | (~((~(mult(mult(mult(b, c), mult(a, a)), b) = mult(mult(mult(b, c), b), mult(a, a)))) | (~(mult(mult(b, c), mult(mult(a, a), b)) = mult(mult(b, c), mult(b, mult(a, a)))))))))),
% 22.07/22.31 inference(monotonicity,[status(thm)],[3046])).
% 22.07/22.31 tff(3048,plain,
% 22.07/22.31 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(b, c), mult(a, a)), b) = mult(mult(mult(b, c), b), mult(a, a)))) | (~(mult(mult(b, c), mult(mult(a, a), b)) = mult(mult(b, c), mult(b, mult(a, a))))))) | (~((~(mult(mult(mult(b, c), mult(a, a)), b) = mult(mult(b, c), mult(mult(a, a), b)))) | (~(mult(mult(mult(b, c), b), mult(a, a)) = mult(mult(b, c), mult(b, mult(a, a))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(b, c), b), mult(a, a)) = mult(mult(b, c), mult(b, mult(a, a))))) | (~(mult(mult(mult(b, c), mult(a, a)), b) = mult(mult(b, c), mult(mult(a, a), b)))))) | (~((~(mult(mult(mult(b, c), mult(a, a)), b) = mult(mult(mult(b, c), b), mult(a, a)))) | (~(mult(mult(b, c), mult(mult(a, a), b)) = mult(mult(b, c), mult(b, mult(a, a))))))))),
% 22.07/22.31 inference(transitivity,[status(thm)],[3047, 3041])).
% 22.07/22.31 tff(3049,plain,
% 22.07/22.31 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(b, c), mult(a, a)), b) = mult(mult(mult(b, c), b), mult(a, a)))) | (~(mult(mult(b, c), mult(mult(a, a), b)) = mult(mult(b, c), mult(b, mult(a, a))))))) | (~((~(mult(mult(mult(b, c), mult(a, a)), b) = mult(mult(b, c), mult(mult(a, a), b)))) | (~(mult(mult(mult(b, c), b), mult(a, a)) = mult(mult(b, c), mult(b, mult(a, a))))))))),
% 22.07/22.31 inference(quant_inst,[status(thm)],[])).
% 22.07/22.31 tff(3050,plain,
% 22.07/22.31 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(b, c), b), mult(a, a)) = mult(mult(b, c), mult(b, mult(a, a))))) | (~(mult(mult(mult(b, c), mult(a, a)), b) = mult(mult(b, c), mult(mult(a, a), b)))))) | (~((~(mult(mult(mult(b, c), mult(a, a)), b) = mult(mult(mult(b, c), b), mult(a, a)))) | (~(mult(mult(b, c), mult(mult(a, a), b)) = mult(mult(b, c), mult(b, mult(a, a)))))))),
% 22.07/22.31 inference(modus_ponens,[status(thm)],[3049, 3048])).
% 22.07/22.31 tff(3051,plain,
% 22.07/22.31 ((~((~(mult(mult(mult(b, c), b), mult(a, a)) = mult(mult(b, c), mult(b, mult(a, a))))) | (~(mult(mult(mult(b, c), mult(a, a)), b) = mult(mult(b, c), mult(mult(a, a), b)))))) | (~((~(mult(mult(mult(b, c), mult(a, a)), b) = mult(mult(mult(b, c), b), mult(a, a)))) | (~(mult(mult(b, c), mult(mult(a, a), b)) = mult(mult(b, c), mult(b, mult(a, a)))))))),
% 22.07/22.31 inference(unit_resolution,[status(thm)],[3050, 27])).
% 22.07/22.31 tff(3052,plain,
% 22.07/22.31 (~((~(mult(mult(mult(b, c), mult(a, a)), b) = mult(mult(mult(b, c), b), mult(a, a)))) | (~(mult(mult(b, c), mult(mult(a, a), b)) = mult(mult(b, c), mult(b, mult(a, a))))))),
% 22.07/22.31 inference(unit_resolution,[status(thm)],[3051, 3040])).
% 22.07/22.31 tff(3053,plain,
% 22.07/22.31 (((~(mult(mult(mult(b, c), mult(a, a)), b) = mult(mult(mult(b, c), b), mult(a, a)))) | (~(mult(mult(b, c), mult(mult(a, a), b)) = mult(mult(b, c), mult(b, mult(a, a)))))) | (mult(mult(mult(b, c), mult(a, a)), b) = mult(mult(mult(b, c), b), mult(a, a)))),
% 22.07/22.31 inference(tautology,[status(thm)],[])).
% 22.07/22.31 tff(3054,plain,
% 22.07/22.31 (mult(mult(mult(b, c), mult(a, a)), b) = mult(mult(mult(b, c), b), mult(a, a))),
% 22.07/22.31 inference(unit_resolution,[status(thm)],[3053, 3052])).
% 22.07/22.31 tff(3055,plain,
% 22.07/22.31 (mult(c, mult(b, a)) = mult(mult(mult(b, c), unit), a)),
% 22.07/22.31 inference(transitivity,[status(thm)],[2300, 2298, 1257])).
% 22.07/22.31 tff(3056,plain,
% 22.07/22.31 (mult(mult(c, mult(b, a)), unit) = mult(mult(mult(mult(b, c), unit), a), unit)),
% 22.07/22.31 inference(monotonicity,[status(thm)],[3055])).
% 22.07/22.31 tff(3057,plain,
% 22.07/22.31 (mult(mult(b, c), a) = mult(mult(c, b), a)),
% 22.07/22.31 inference(symmetry,[status(thm)],[2298])).
% 22.07/22.31 tff(3058,plain,
% 22.07/22.31 (mult(mult(b, c), a) = mult(c, mult(b, a))),
% 22.07/22.31 inference(transitivity,[status(thm)],[3057, 2299])).
% 22.07/22.31 tff(3059,plain,
% 22.15/22.32 (mult(mult(mult(b, c), a), unit) = mult(mult(c, mult(b, a)), unit)),
% 22.15/22.32 inference(monotonicity,[status(thm)],[3058])).
% 22.15/22.32 tff(3060,plain,
% 22.15/22.32 (mult(mult(mult(b, c), a), unit) = mult(mult(b, c), a)),
% 22.15/22.32 inference(transitivity,[status(thm)],[3059, 3056, 1261, 1263])).
% 22.15/22.32 tff(3061,plain,
% 22.15/22.32 (mult(mult(mult(mult(b, c), a), unit), a) = mult(mult(mult(b, c), a), a)),
% 22.15/22.32 inference(monotonicity,[status(thm)],[3060])).
% 22.15/22.32 tff(3062,plain,
% 22.15/22.32 (mult(mult(mult(b, c), a), a) = mult(mult(mult(mult(b, c), a), unit), a)),
% 22.15/22.32 inference(symmetry,[status(thm)],[3061])).
% 22.15/22.32 tff(3063,plain,
% 22.15/22.32 (mult(mult(mult(b, c), a), a) = mult(mult(b, c), mult(a, a))),
% 22.15/22.32 inference(transitivity,[status(thm)],[3062, 1254, 1559])).
% 22.15/22.32 tff(3064,plain,
% 22.15/22.32 (mult(mult(mult(mult(b, c), a), a), b) = mult(mult(mult(b, c), mult(a, a)), b)),
% 22.15/22.32 inference(monotonicity,[status(thm)],[3063])).
% 22.15/22.32 tff(3065,plain,
% 22.15/22.32 (mult(b, mult(mult(a, unit), a)) = mult(b, mult(a, a))),
% 22.15/22.32 inference(monotonicity,[status(thm)],[519])).
% 22.15/22.32 tff(3066,plain,
% 22.15/22.32 (mult(mult(mult(b, unit), a), unit) = mult(mult(b, a), unit)),
% 22.15/22.32 inference(symmetry,[status(thm)],[513])).
% 22.15/22.32 tff(3067,plain,
% 22.15/22.32 (mult(b, mult(mult(unit, a), unit)) = mult(mult(mult(b, unit), a), unit)),
% 22.15/22.32 inference(symmetry,[status(thm)],[510])).
% 22.15/22.32 tff(3068,plain,
% 22.15/22.32 (mult(b, a) = mult(b, mult(mult(unit, a), unit))),
% 22.15/22.32 inference(symmetry,[status(thm)],[508])).
% 22.15/22.32 tff(3069,plain,
% 22.15/22.32 (mult(b, a) = mult(mult(b, a), unit)),
% 22.15/22.32 inference(transitivity,[status(thm)],[3068, 3067, 3066])).
% 22.15/22.32 tff(3070,plain,
% 22.15/22.32 (mult(mult(b, a), a) = mult(mult(mult(b, a), unit), a)),
% 22.15/22.32 inference(monotonicity,[status(thm)],[3069])).
% 22.15/22.32 tff(3071,plain,
% 22.15/22.32 (mult(mult(b, a), a) = mult(b, mult(a, a))),
% 22.15/22.32 inference(transitivity,[status(thm)],[3070, 517, 3065])).
% 22.15/22.32 tff(3072,plain,
% 22.15/22.32 (mult(mult(b, c), mult(mult(b, a), a)) = mult(mult(b, c), mult(b, mult(a, a)))),
% 22.15/22.32 inference(monotonicity,[status(thm)],[3071])).
% 22.15/22.32 tff(3073,plain,
% 22.15/22.32 (mult(mult(mult(b, c), b), mult(mult(a, unit), a)) = mult(mult(mult(b, c), b), mult(a, a))),
% 22.15/22.32 inference(symmetry,[status(thm)],[3037])).
% 22.15/22.32 tff(3074,plain,
% 22.15/22.32 (mult(mult(mult(b, c), b), a) = mult(mult(mult(mult(b, c), b), a), unit)),
% 22.15/22.32 inference(symmetry,[status(thm)],[3029])).
% 22.15/22.32 tff(3075,plain,
% 22.15/22.32 (mult(mult(b, c), mult(b, a)) = mult(mult(mult(b, c), b), a)),
% 22.15/22.32 inference(symmetry,[status(thm)],[3027])).
% 22.15/22.32 tff(3076,plain,
% 22.15/22.32 (mult(mult(b, c), mult(b, a)) = mult(mult(mult(mult(b, c), b), a), unit)),
% 22.15/22.32 inference(transitivity,[status(thm)],[3075, 3074])).
% 22.15/22.32 tff(3077,plain,
% 22.15/22.32 (mult(mult(mult(b, c), mult(b, a)), a) = mult(mult(mult(mult(mult(b, c), b), a), unit), a)),
% 22.15/22.32 inference(monotonicity,[status(thm)],[3076])).
% 22.15/22.32 tff(3078,plain,
% 22.15/22.32 (mult(mult(mult(b, c), mult(b, a)), a) = mult(mult(mult(b, c), b), mult(a, a))),
% 22.15/22.32 inference(transitivity,[status(thm)],[3077, 3035, 3073])).
% 22.15/22.32 tff(3079,plain,
% 22.15/22.32 ((mult(mult(mult(b, c), mult(b, a)), a) = mult(mult(b, c), mult(mult(b, a), a))) <=> (mult(mult(mult(b, c), b), mult(a, a)) = mult(mult(b, c), mult(b, mult(a, a))))),
% 22.15/22.32 inference(monotonicity,[status(thm)],[3078, 3072])).
% 22.15/22.32 tff(3080,plain,
% 22.15/22.32 ((mult(mult(mult(b, c), b), mult(a, a)) = mult(mult(b, c), mult(b, mult(a, a)))) <=> (mult(mult(mult(b, c), mult(b, a)), a) = mult(mult(b, c), mult(mult(b, a), a)))),
% 22.15/22.32 inference(symmetry,[status(thm)],[3079])).
% 22.15/22.32 tff(3081,plain,
% 22.15/22.32 ((~(mult(mult(mult(b, c), b), mult(a, a)) = mult(mult(b, c), mult(b, mult(a, a))))) <=> (~(mult(mult(mult(b, c), mult(b, a)), a) = mult(mult(b, c), mult(mult(b, a), a))))),
% 22.15/22.32 inference(monotonicity,[status(thm)],[3080])).
% 22.15/22.32 tff(3082,plain,
% 22.15/22.32 (((~(mult(mult(mult(b, c), mult(a, a)), b) = mult(mult(mult(b, c), b), mult(a, a)))) | (~(mult(mult(b, c), mult(mult(a, a), b)) = mult(mult(b, c), mult(b, mult(a, a)))))) | (mult(mult(b, c), mult(mult(a, a), b)) = mult(mult(b, c), mult(b, mult(a, a))))),
% 22.15/22.32 inference(tautology,[status(thm)],[])).
% 22.15/22.32 tff(3083,plain,
% 22.15/22.32 (mult(mult(b, c), mult(mult(a, a), b)) = mult(mult(b, c), mult(b, mult(a, a)))),
% 22.15/22.32 inference(unit_resolution,[status(thm)],[3082, 3052])).
% 22.15/22.32 tff(3084,plain,
% 22.15/22.32 ((mult(mult(mult(b, c), mult(a, a)), b) = mult(mult(b, c), mult(mult(a, a), b))) <=> (mult(mult(mult(b, c), b), mult(a, a)) = mult(mult(b, c), mult(b, mult(a, a))))),
% 22.15/22.32 inference(monotonicity,[status(thm)],[3054, 3083])).
% 22.15/22.32 tff(3085,plain,
% 22.15/22.32 ((~(mult(mult(mult(b, c), mult(a, a)), b) = mult(mult(b, c), mult(mult(a, a), b)))) <=> (~(mult(mult(mult(b, c), b), mult(a, a)) = mult(mult(b, c), mult(b, mult(a, a)))))),
% 22.15/22.32 inference(monotonicity,[status(thm)],[3084])).
% 22.15/22.32 tff(3086,plain,
% 22.15/22.32 (~(mult(mult(mult(b, c), b), mult(a, a)) = mult(mult(b, c), mult(b, mult(a, a))))),
% 22.15/22.32 inference(modus_ponens,[status(thm)],[3038, 3085])).
% 22.15/22.32 tff(3087,plain,
% 22.15/22.32 (~(mult(mult(mult(b, c), mult(b, a)), a) = mult(mult(b, c), mult(mult(b, a), a)))),
% 22.15/22.32 inference(modus_ponens,[status(thm)],[3086, 3081])).
% 22.15/22.32 tff(3088,plain,
% 22.15/22.32 (((~(mult(mult(mult(b, c), a), mult(b, a)) = mult(mult(b, c), mult(a, mult(b, a))))) | (~(mult(mult(mult(b, c), mult(b, a)), a) = mult(mult(b, c), mult(mult(b, a), a))))) | (mult(mult(mult(b, c), mult(b, a)), a) = mult(mult(b, c), mult(mult(b, a), a)))),
% 22.15/22.32 inference(tautology,[status(thm)],[])).
% 22.15/22.32 tff(3089,plain,
% 22.15/22.32 ((~(mult(mult(mult(b, c), a), mult(b, a)) = mult(mult(b, c), mult(a, mult(b, a))))) | (~(mult(mult(mult(b, c), mult(b, a)), a) = mult(mult(b, c), mult(mult(b, a), a))))),
% 22.15/22.32 inference(unit_resolution,[status(thm)],[3088, 3087])).
% 22.15/22.32 tff(3090,plain,
% 22.15/22.32 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(b, c), a), mult(b, a)) = mult(mult(b, c), mult(a, mult(b, a))))) | (~(mult(mult(mult(b, c), mult(b, a)), a) = mult(mult(b, c), mult(mult(b, a), a)))))) | (~((~(mult(mult(mult(b, c), a), mult(b, a)) = mult(mult(mult(b, c), mult(b, a)), a))) | (~(mult(mult(b, c), mult(a, mult(b, a))) = mult(mult(b, c), mult(mult(b, a), a)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(b, c), a), mult(b, a)) = mult(mult(b, c), mult(a, mult(b, a))))) | (~(mult(mult(mult(b, c), mult(b, a)), a) = mult(mult(b, c), mult(mult(b, a), a)))))) | (~((~(mult(mult(mult(b, c), a), mult(b, a)) = mult(mult(mult(b, c), mult(b, a)), a))) | (~(mult(mult(b, c), mult(a, mult(b, a))) = mult(mult(b, c), mult(mult(b, a), a)))))))),
% 22.15/22.32 inference(rewrite,[status(thm)],[])).
% 22.15/22.32 tff(3091,plain,
% 22.15/22.32 (((~((~(mult(mult(mult(b, c), a), mult(b, a)) = mult(mult(mult(b, c), mult(b, a)), a))) | (~(mult(mult(b, c), mult(a, mult(b, a))) = mult(mult(b, c), mult(mult(b, a), a)))))) | (~((~(mult(mult(mult(b, c), a), mult(b, a)) = mult(mult(b, c), mult(a, mult(b, a))))) | (~(mult(mult(mult(b, c), mult(b, a)), a) = mult(mult(b, c), mult(mult(b, a), a))))))) <=> ((~((~(mult(mult(mult(b, c), a), mult(b, a)) = mult(mult(b, c), mult(a, mult(b, a))))) | (~(mult(mult(mult(b, c), mult(b, a)), a) = mult(mult(b, c), mult(mult(b, a), a)))))) | (~((~(mult(mult(mult(b, c), a), mult(b, a)) = mult(mult(mult(b, c), mult(b, a)), a))) | (~(mult(mult(b, c), mult(a, mult(b, a))) = mult(mult(b, c), mult(mult(b, a), a)))))))),
% 22.15/22.32 inference(rewrite,[status(thm)],[])).
% 22.15/22.32 tff(3092,plain,
% 22.15/22.32 ((~((~(mult(mult(mult(b, c), a), mult(b, a)) = mult(mult(mult(b, c), mult(b, a)), a))) | (~(mult(mult(b, c), mult(a, mult(b, a))) = mult(mult(b, c), mult(mult(b, a), a)))))) <=> (~((~(mult(mult(mult(b, c), a), mult(b, a)) = mult(mult(mult(b, c), mult(b, a)), a))) | (~(mult(mult(b, c), mult(a, mult(b, a))) = mult(mult(b, c), mult(mult(b, a), a))))))),
% 22.15/22.32 inference(rewrite,[status(thm)],[])).
% 22.15/22.32 tff(3093,plain,
% 22.15/22.32 (((~((~(mult(mult(mult(b, c), a), mult(b, a)) = mult(mult(mult(b, c), mult(b, a)), a))) | (~(mult(mult(b, c), mult(a, mult(b, a))) = mult(mult(b, c), mult(mult(b, a), a)))))) | (~((~(mult(mult(mult(b, c), a), mult(b, a)) = mult(mult(b, c), mult(a, mult(b, a))))) | (~(mult(mult(mult(b, c), mult(b, a)), a) = mult(mult(b, c), mult(mult(b, a), a))))))) <=> ((~((~(mult(mult(mult(b, c), a), mult(b, a)) = mult(mult(mult(b, c), mult(b, a)), a))) | (~(mult(mult(b, c), mult(a, mult(b, a))) = mult(mult(b, c), mult(mult(b, a), a)))))) | (~((~(mult(mult(mult(b, c), a), mult(b, a)) = mult(mult(b, c), mult(a, mult(b, a))))) | (~(mult(mult(mult(b, c), mult(b, a)), a) = mult(mult(b, c), mult(mult(b, a), a)))))))),
% 22.15/22.32 inference(monotonicity,[status(thm)],[3092])).
% 22.15/22.32 tff(3094,plain,
% 22.15/22.32 (((~((~(mult(mult(mult(b, c), a), mult(b, a)) = mult(mult(mult(b, c), mult(b, a)), a))) | (~(mult(mult(b, c), mult(a, mult(b, a))) = mult(mult(b, c), mult(mult(b, a), a)))))) | (~((~(mult(mult(mult(b, c), a), mult(b, a)) = mult(mult(b, c), mult(a, mult(b, a))))) | (~(mult(mult(mult(b, c), mult(b, a)), a) = mult(mult(b, c), mult(mult(b, a), a))))))) <=> ((~((~(mult(mult(mult(b, c), a), mult(b, a)) = mult(mult(b, c), mult(a, mult(b, a))))) | (~(mult(mult(mult(b, c), mult(b, a)), a) = mult(mult(b, c), mult(mult(b, a), a)))))) | (~((~(mult(mult(mult(b, c), a), mult(b, a)) = mult(mult(mult(b, c), mult(b, a)), a))) | (~(mult(mult(b, c), mult(a, mult(b, a))) = mult(mult(b, c), mult(mult(b, a), a)))))))),
% 22.15/22.32 inference(transitivity,[status(thm)],[3093, 3091])).
% 22.15/22.32 tff(3095,plain,
% 22.15/22.32 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(b, c), a), mult(b, a)) = mult(mult(mult(b, c), mult(b, a)), a))) | (~(mult(mult(b, c), mult(a, mult(b, a))) = mult(mult(b, c), mult(mult(b, a), a)))))) | (~((~(mult(mult(mult(b, c), a), mult(b, a)) = mult(mult(b, c), mult(a, mult(b, a))))) | (~(mult(mult(mult(b, c), mult(b, a)), a) = mult(mult(b, c), mult(mult(b, a), a)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(b, c), a), mult(b, a)) = mult(mult(b, c), mult(a, mult(b, a))))) | (~(mult(mult(mult(b, c), mult(b, a)), a) = mult(mult(b, c), mult(mult(b, a), a)))))) | (~((~(mult(mult(mult(b, c), a), mult(b, a)) = mult(mult(mult(b, c), mult(b, a)), a))) | (~(mult(mult(b, c), mult(a, mult(b, a))) = mult(mult(b, c), mult(mult(b, a), a))))))))),
% 22.15/22.32 inference(monotonicity,[status(thm)],[3094])).
% 22.15/22.32 tff(3096,plain,
% 22.15/22.32 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(b, c), a), mult(b, a)) = mult(mult(mult(b, c), mult(b, a)), a))) | (~(mult(mult(b, c), mult(a, mult(b, a))) = mult(mult(b, c), mult(mult(b, a), a)))))) | (~((~(mult(mult(mult(b, c), a), mult(b, a)) = mult(mult(b, c), mult(a, mult(b, a))))) | (~(mult(mult(mult(b, c), mult(b, a)), a) = mult(mult(b, c), mult(mult(b, a), a)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(b, c), a), mult(b, a)) = mult(mult(b, c), mult(a, mult(b, a))))) | (~(mult(mult(mult(b, c), mult(b, a)), a) = mult(mult(b, c), mult(mult(b, a), a)))))) | (~((~(mult(mult(mult(b, c), a), mult(b, a)) = mult(mult(mult(b, c), mult(b, a)), a))) | (~(mult(mult(b, c), mult(a, mult(b, a))) = mult(mult(b, c), mult(mult(b, a), a)))))))),
% 22.15/22.32 inference(transitivity,[status(thm)],[3095, 3090])).
% 22.15/22.32 tff(3097,plain,
% 22.15/22.32 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(b, c), a), mult(b, a)) = mult(mult(mult(b, c), mult(b, a)), a))) | (~(mult(mult(b, c), mult(a, mult(b, a))) = mult(mult(b, c), mult(mult(b, a), a)))))) | (~((~(mult(mult(mult(b, c), a), mult(b, a)) = mult(mult(b, c), mult(a, mult(b, a))))) | (~(mult(mult(mult(b, c), mult(b, a)), a) = mult(mult(b, c), mult(mult(b, a), a)))))))),
% 22.15/22.32 inference(quant_inst,[status(thm)],[])).
% 22.15/22.32 tff(3098,plain,
% 22.15/22.32 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(b, c), a), mult(b, a)) = mult(mult(b, c), mult(a, mult(b, a))))) | (~(mult(mult(mult(b, c), mult(b, a)), a) = mult(mult(b, c), mult(mult(b, a), a)))))) | (~((~(mult(mult(mult(b, c), a), mult(b, a)) = mult(mult(mult(b, c), mult(b, a)), a))) | (~(mult(mult(b, c), mult(a, mult(b, a))) = mult(mult(b, c), mult(mult(b, a), a))))))),
% 22.15/22.32 inference(modus_ponens,[status(thm)],[3097, 3096])).
% 22.15/22.32 tff(3099,plain,
% 22.15/22.32 ((~((~(mult(mult(mult(b, c), a), mult(b, a)) = mult(mult(b, c), mult(a, mult(b, a))))) | (~(mult(mult(mult(b, c), mult(b, a)), a) = mult(mult(b, c), mult(mult(b, a), a)))))) | (~((~(mult(mult(mult(b, c), a), mult(b, a)) = mult(mult(mult(b, c), mult(b, a)), a))) | (~(mult(mult(b, c), mult(a, mult(b, a))) = mult(mult(b, c), mult(mult(b, a), a))))))),
% 22.15/22.32 inference(unit_resolution,[status(thm)],[3098, 27])).
% 22.15/22.32 tff(3100,plain,
% 22.15/22.32 (~((~(mult(mult(mult(b, c), a), mult(b, a)) = mult(mult(mult(b, c), mult(b, a)), a))) | (~(mult(mult(b, c), mult(a, mult(b, a))) = mult(mult(b, c), mult(mult(b, a), a)))))),
% 22.15/22.32 inference(unit_resolution,[status(thm)],[3099, 3089])).
% 22.15/22.32 tff(3101,plain,
% 22.15/22.32 (((~(mult(mult(mult(b, c), a), mult(b, a)) = mult(mult(mult(b, c), mult(b, a)), a))) | (~(mult(mult(b, c), mult(a, mult(b, a))) = mult(mult(b, c), mult(mult(b, a), a))))) | (mult(mult(mult(b, c), a), mult(b, a)) = mult(mult(mult(b, c), mult(b, a)), a))),
% 22.15/22.32 inference(tautology,[status(thm)],[])).
% 22.15/22.32 tff(3102,plain,
% 22.15/22.32 (mult(mult(mult(b, c), a), mult(b, a)) = mult(mult(mult(b, c), mult(b, a)), a)),
% 22.15/22.32 inference(unit_resolution,[status(thm)],[3101, 3100])).
% 22.15/22.32 tff(3103,plain,
% 22.15/22.32 (mult(mult(mult(b, c), mult(a, a)), b) = mult(mult(mult(mult(b, c), a), a), b)),
% 22.15/22.32 inference(symmetry,[status(thm)],[3064])).
% 22.15/22.32 tff(3104,assumption,(mult(mult(mult(b, c), mult(a, a)), b) = mult(mult(mult(b, c), b), mult(a, a))), introduced(assumption)).
% 22.15/22.32 tff(3105,plain,
% 22.15/22.32 (mult(mult(mult(b, c), b), mult(a, a)) = mult(mult(mult(b, c), mult(a, a)), b)),
% 22.15/22.32 inference(symmetry,[status(thm)],[3104])).
% 22.15/22.32 tff(3106,assumption,(mult(mult(mult(b, c), b), a) = mult(mult(b, c), mult(b, a))), introduced(assumption)).
% 22.15/22.32 tff(3107,plain,
% 22.15/22.32 (mult(mult(b, c), mult(b, a)) = mult(mult(mult(b, c), b), a)),
% 22.15/22.32 inference(symmetry,[status(thm)],[3106])).
% 22.15/22.32 tff(3108,plain,
% 22.15/22.32 (mult(mult(b, c), mult(b, a)) = mult(mult(mult(mult(b, c), b), a), unit)),
% 22.15/22.32 inference(transitivity,[status(thm)],[3107, 3074])).
% 22.15/22.32 tff(3109,plain,
% 22.15/22.32 (mult(mult(mult(b, c), mult(b, a)), a) = mult(mult(mult(mult(mult(b, c), b), a), unit), a)),
% 22.15/22.32 inference(monotonicity,[status(thm)],[3108])).
% 22.15/22.32 tff(3110,assumption,(mult(mult(mult(b, c), a), mult(b, a)) = mult(mult(mult(b, c), mult(b, a)), a)), introduced(assumption)).
% 22.15/22.32 tff(3111,plain,
% 22.15/22.32 (mult(mult(mult(b, c), a), mult(b, a)) = mult(mult(mult(mult(b, c), a), a), b)),
% 22.15/22.32 inference(transitivity,[status(thm)],[3110, 3109, 3035, 3073, 3105, 3103])).
% 22.15/22.32 tff(3112,plain,
% 22.15/22.32 ((mult(mult(mult(mult(b, c), a), b), a) = mult(mult(mult(b, c), a), mult(b, a))) <=> (mult(mult(mult(mult(b, c), a), b), a) = mult(mult(mult(mult(b, c), a), a), b))),
% 22.15/22.32 inference(monotonicity,[status(thm)],[3111])).
% 22.15/22.32 tff(3113,assumption,(~(mult(mult(mult(mult(b, c), a), b), a) = mult(mult(mult(mult(b, c), a), a), b))), introduced(assumption)).
% 22.15/22.32 tff(3114,plain,
% 22.15/22.32 ((~(mult(mult(mult(mult(b, c), a), b), a) = mult(mult(mult(mult(b, c), a), a), b))) | (~(mult(mult(mult(b, c), a), mult(b, a)) = mult(mult(mult(b, c), a), mult(a, b))))),
% 22.15/22.33 inference(unit_resolution,[status(thm)],[2112, 3113])).
% 22.15/22.33 tff(3115,plain,
% 22.15/22.33 ((~((~(mult(mult(mult(mult(b, c), a), b), a) = mult(mult(mult(mult(b, c), a), a), b))) | (~(mult(mult(mult(b, c), a), mult(b, a)) = mult(mult(mult(b, c), a), mult(a, b)))))) | (~((~(mult(mult(mult(mult(b, c), a), b), a) = mult(mult(mult(b, c), a), mult(b, a)))) | (~(mult(mult(mult(mult(b, c), a), a), b) = mult(mult(mult(b, c), a), mult(a, b))))))),
% 22.15/22.33 inference(unit_resolution,[status(thm)],[2108, 27])).
% 22.15/22.33 tff(3116,plain,
% 22.15/22.33 (~((~(mult(mult(mult(mult(b, c), a), b), a) = mult(mult(mult(b, c), a), mult(b, a)))) | (~(mult(mult(mult(mult(b, c), a), a), b) = mult(mult(mult(b, c), a), mult(a, b)))))),
% 22.15/22.33 inference(unit_resolution,[status(thm)],[3115, 3114])).
% 22.15/22.33 tff(3117,plain,
% 22.15/22.33 (((~(mult(mult(mult(mult(b, c), a), b), a) = mult(mult(mult(b, c), a), mult(b, a)))) | (~(mult(mult(mult(mult(b, c), a), a), b) = mult(mult(mult(b, c), a), mult(a, b))))) | (mult(mult(mult(mult(b, c), a), b), a) = mult(mult(mult(b, c), a), mult(b, a)))),
% 22.15/22.33 inference(tautology,[status(thm)],[])).
% 22.15/22.33 tff(3118,plain,
% 22.15/22.33 (mult(mult(mult(mult(b, c), a), b), a) = mult(mult(mult(b, c), a), mult(b, a))),
% 22.15/22.33 inference(unit_resolution,[status(thm)],[3117, 3116])).
% 22.15/22.33 tff(3119,plain,
% 22.15/22.33 (mult(mult(mult(mult(b, c), a), b), a) = mult(mult(mult(mult(b, c), a), a), b)),
% 22.15/22.33 inference(modus_ponens,[status(thm)],[3118, 3112])).
% 22.15/22.33 tff(3120,plain,
% 22.15/22.33 ($false),
% 22.15/22.33 inference(unit_resolution,[status(thm)],[3113, 3119])).
% 22.15/22.33 tff(3121,plain,((mult(mult(mult(mult(b, c), a), b), a) = mult(mult(mult(mult(b, c), a), a), b)) | (~(mult(mult(mult(b, c), mult(a, a)), b) = mult(mult(mult(b, c), b), mult(a, a)))) | (~(mult(mult(mult(b, c), a), mult(b, a)) = mult(mult(mult(b, c), mult(b, a)), a))) | (~(mult(mult(mult(b, c), b), a) = mult(mult(b, c), mult(b, a)))) | (~(mult(mult(c, b), a) = mult(c, mult(b, a))))), inference(lemma,lemma(discharge,[]))).
% 22.15/22.33 tff(3122,plain,
% 22.15/22.33 (mult(mult(mult(mult(b, c), a), b), a) = mult(mult(mult(mult(b, c), a), a), b)),
% 22.15/22.33 inference(unit_resolution,[status(thm)],[3121, 3054, 3102, 3027, 2299])).
% 22.15/22.33 tff(3123,plain,
% 22.15/22.33 (mult(mult(mult(b, c), a), b) = mult(mult(b, c), mult(a, b))),
% 22.15/22.33 inference(unit_resolution,[status(thm)],[1229, 3026])).
% 22.15/22.33 tff(3124,plain,
% 22.15/22.33 (mult(mult(b, c), mult(a, b)) = mult(mult(mult(b, c), a), b)),
% 22.15/22.33 inference(symmetry,[status(thm)],[3123])).
% 22.15/22.33 tff(3125,plain,
% 22.15/22.33 (mult(mult(mult(b, c), mult(a, b)), a) = mult(mult(mult(mult(b, c), a), b), a)),
% 22.15/22.33 inference(monotonicity,[status(thm)],[3124])).
% 22.15/22.33 tff(3126,plain,
% 22.15/22.33 (mult(mult(mult(b, c), mult(a, b)), a) = mult(mult(mult(mult(mult(b, c), b), a), unit), a)),
% 22.15/22.33 inference(transitivity,[status(thm)],[3125, 3122, 3064, 3054, 3037, 3036])).
% 22.15/22.33 tff(3127,plain,
% 22.15/22.33 (rd(mult(mult(mult(b, c), mult(a, b)), a), a) = rd(mult(mult(mult(mult(mult(b, c), b), a), unit), a), a)),
% 22.15/22.33 inference(monotonicity,[status(thm)],[3126])).
% 22.15/22.33 tff(3128,plain,
% 22.15/22.33 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(b, c), mult(a, b)), a), a) = mult(mult(b, c), mult(a, b)))),
% 22.15/22.33 inference(quant_inst,[status(thm)],[])).
% 22.15/22.33 tff(3129,plain,
% 22.15/22.33 (rd(mult(mult(mult(b, c), mult(a, b)), a), a) = mult(mult(b, c), mult(a, b))),
% 22.15/22.33 inference(unit_resolution,[status(thm)],[3128, 168])).
% 22.15/22.33 tff(3130,plain,
% 22.15/22.33 (mult(mult(b, c), mult(a, b)) = rd(mult(mult(mult(b, c), mult(a, b)), a), a)),
% 22.15/22.33 inference(symmetry,[status(thm)],[3129])).
% 22.15/22.33 tff(3131,plain,
% 22.15/22.33 (mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a))),
% 22.15/22.33 inference(transitivity,[status(thm)],[3130, 3127, 3031, 3029, 3027])).
% 22.15/22.33 tff(3132,plain,
% 22.15/22.33 ($false),
% 22.15/22.33 inference(unit_resolution,[status(thm)],[3024, 3131])).
% 22.15/22.33 tff(3133,plain,((mult(mult(mult(b, c), mult(a, a)), b) = mult(mult(b, c), mult(mult(a, a), b))) | (mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a))) | (~(mult(mult(c, b), a) = mult(c, mult(b, a))))), inference(lemma,lemma(discharge,[]))).
% 22.15/22.33 tff(3134,plain,
% 22.15/22.33 (mult(mult(mult(b, c), mult(a, a)), b) = mult(mult(b, c), mult(mult(a, a), b))),
% 22.15/22.33 inference(unit_resolution,[status(thm)],[3133, 2929, 2252])).
% 22.15/22.33 tff(3135,plain,
% 22.15/22.33 (mult(mult(unit, a), mult(mult(b, c), c)) = mult(a, mult(mult(b, c), c))),
% 22.15/22.33 inference(monotonicity,[status(thm)],[244])).
% 22.15/22.33 tff(3136,plain,
% 22.15/22.33 (mult(a, mult(mult(b, c), c)) = mult(mult(unit, a), mult(mult(b, c), c))),
% 22.15/22.33 inference(symmetry,[status(thm)],[3135])).
% 22.15/22.33 tff(3137,plain,
% 22.15/22.33 (mult(mult(b, c), c) = mult(mult(c, b), c)),
% 22.15/22.33 inference(symmetry,[status(thm)],[242])).
% 22.15/22.33 tff(3138,plain,
% 22.15/22.33 (mult(a, mult(mult(b, c), c)) = mult(a, mult(mult(c, b), c))),
% 22.15/22.33 inference(monotonicity,[status(thm)],[3137])).
% 22.15/22.33 tff(3139,plain,
% 22.15/22.33 (mult(a, mult(mult(c, b), c)) = mult(a, mult(mult(b, c), c))),
% 22.15/22.33 inference(symmetry,[status(thm)],[3138])).
% 22.15/22.33 tff(3140,plain,
% 22.15/22.33 (mult(mult(unit, mult(mult(a, b), c)), c) = mult(mult(unit, a), mult(mult(b, c), c))),
% 22.15/22.33 inference(transitivity,[status(thm)],[230, 233, 3139, 3136])).
% 22.15/22.33 tff(3141,plain,
% 22.15/22.33 (mult(mult(unit, c), b) = mult(c, b)),
% 22.15/22.33 inference(monotonicity,[status(thm)],[73])).
% 22.15/22.33 tff(3142,plain,
% 22.15/22.33 (mult(mult(unit, c), b) = mult(b, c)),
% 22.15/22.33 inference(transitivity,[status(thm)],[3141, 240, 237, 141])).
% 22.15/22.33 tff(3143,plain,
% 22.15/22.33 (mult(mult(mult(unit, c), b), c) = mult(mult(b, c), c)),
% 22.15/22.33 inference(monotonicity,[status(thm)],[3142])).
% 22.15/22.33 tff(3144,plain,
% 22.15/22.33 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(unit, c), b), c) = mult(unit, mult(mult(c, b), c)))),
% 22.15/22.33 inference(quant_inst,[status(thm)],[])).
% 22.15/22.33 tff(3145,plain,
% 22.15/22.33 (mult(mult(mult(unit, c), b), c) = mult(unit, mult(mult(c, b), c))),
% 22.15/22.33 inference(unit_resolution,[status(thm)],[3144, 56])).
% 22.15/22.33 tff(3146,plain,
% 22.15/22.33 (mult(unit, mult(mult(c, b), c)) = mult(mult(mult(unit, c), b), c)),
% 22.15/22.33 inference(symmetry,[status(thm)],[3145])).
% 22.15/22.33 tff(3147,plain,
% 22.15/22.33 (mult(unit, mult(mult(b, c), c)) = mult(unit, mult(mult(c, b), c))),
% 22.15/22.33 inference(monotonicity,[status(thm)],[3137])).
% 22.15/22.33 tff(3148,plain,
% 22.15/22.33 (mult(unit, mult(mult(b, c), c)) = mult(mult(b, c), c)),
% 22.15/22.33 inference(transitivity,[status(thm)],[3147, 3146, 3143])).
% 22.15/22.33 tff(3149,plain,
% 22.15/22.33 (mult(mult(unit, mult(mult(b, c), c)), a) = mult(mult(mult(b, c), c), a)),
% 22.15/22.33 inference(monotonicity,[status(thm)],[3148])).
% 22.15/22.33 tff(3150,plain,
% 22.15/22.33 (mult(mult(mult(b, c), c), a) = mult(mult(unit, mult(mult(b, c), c)), a)),
% 22.15/22.33 inference(symmetry,[status(thm)],[3149])).
% 22.15/22.33 tff(3151,plain,
% 22.15/22.33 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)))),
% 22.15/22.33 inference(quant_inst,[status(thm)],[])).
% 22.15/22.33 tff(3152,plain,
% 22.15/22.33 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c))),
% 22.15/22.33 inference(unit_resolution,[status(thm)],[3151, 56])).
% 22.15/22.33 tff(3153,plain,
% 22.15/22.33 (mult(mult(b, c), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)),
% 22.15/22.33 inference(symmetry,[status(thm)],[2225])).
% 22.15/22.33 tff(3154,plain,
% 22.15/22.33 (mult(mult(b, c), c) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c))),
% 22.15/22.33 inference(transitivity,[status(thm)],[3153, 3152])).
% 22.15/22.33 tff(3155,plain,
% 22.15/22.33 (mult(mult(mult(b, c), c), a) = mult(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)), a)),
% 22.15/22.33 inference(monotonicity,[status(thm)],[3154])).
% 22.15/22.33 tff(3156,plain,
% 22.15/22.33 (mult(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)), a) = mult(mult(mult(b, c), c), a)),
% 22.15/22.33 inference(symmetry,[status(thm)],[3155])).
% 22.15/22.33 tff(3157,plain,
% 22.15/22.33 (mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)),
% 22.15/22.33 inference(symmetry,[status(thm)],[3152])).
% 22.15/22.33 tff(3158,plain,
% 22.15/22.33 (mult(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)), a) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a)),
% 22.15/22.33 inference(monotonicity,[status(thm)],[3157])).
% 22.15/22.33 tff(3159,plain,
% 22.15/22.33 (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)), a)),
% 22.15/22.33 inference(symmetry,[status(thm)],[3158])).
% 22.15/22.33 tff(3160,plain,
% 22.15/22.33 (mult(mult(unit, c), mult(mult(a, b), c)) = mult(mult(unit, mult(mult(b, c), c)), a)),
% 22.15/22.33 inference(transitivity,[status(thm)],[2706, 2318, 2317, 2315, 2231, 2230, 2229, 3159, 3156, 3150])).
% 22.15/22.33 tff(3161,plain,
% 22.15/22.33 ((mult(mult(unit, c), mult(mult(a, b), c)) = mult(mult(unit, mult(mult(a, b), c)), c)) <=> (mult(mult(unit, mult(mult(b, c), c)), a) = mult(mult(unit, a), mult(mult(b, c), c)))),
% 22.15/22.33 inference(monotonicity,[status(thm)],[3160, 3140])).
% 22.15/22.33 tff(3162,plain,
% 22.15/22.33 ((mult(mult(unit, mult(mult(b, c), c)), a) = mult(mult(unit, a), mult(mult(b, c), c))) <=> (mult(mult(unit, c), mult(mult(a, b), c)) = mult(mult(unit, mult(mult(a, b), c)), c))),
% 22.15/22.33 inference(symmetry,[status(thm)],[3161])).
% 22.15/22.33 tff(3163,plain,
% 22.15/22.33 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)),
% 22.15/22.33 inference(transitivity,[status(thm)],[1169, 1164, 2126])).
% 22.15/22.33 tff(3164,plain,
% 22.15/22.33 (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), c) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c)),
% 22.15/22.33 inference(monotonicity,[status(thm)],[3163])).
% 22.15/22.33 tff(3165,plain,
% 22.15/22.33 (mult(mult(mult(a, c), b), c) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), c)),
% 22.15/22.33 inference(monotonicity,[status(thm)],[2160])).
% 22.15/22.33 tff(3166,plain,
% 22.15/22.33 (mult(mult(unit, a), mult(mult(b, c), c)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))),
% 22.15/22.33 inference(transitivity,[status(thm)],[3135, 3138, 234, 3165, 3164, 1032])).
% 22.15/22.33 tff(3167,plain,
% 22.15/22.33 (mult(mult(unit, mult(mult(b, c), c)), a) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a))),
% 22.15/22.33 inference(transitivity,[status(thm)],[3149, 3155, 3158, 2228])).
% 22.15/22.33 tff(3168,plain,
% 22.15/22.33 ((mult(mult(unit, mult(mult(b, c), c)), a) = mult(mult(unit, a), mult(mult(b, c), c))) <=> (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 22.15/22.33 inference(monotonicity,[status(thm)],[3167, 3166])).
% 22.15/22.33 tff(3169,plain,
% 22.15/22.33 ((mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))) <=> (mult(mult(unit, mult(mult(b, c), c)), a) = mult(mult(unit, a), mult(mult(b, c), c)))),
% 22.15/22.33 inference(symmetry,[status(thm)],[3168])).
% 22.15/22.33 tff(3170,plain,
% 22.15/22.33 ((mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))) <=> (mult(mult(unit, c), mult(mult(a, b), c)) = mult(mult(unit, mult(mult(a, b), c)), c))),
% 22.15/22.33 inference(transitivity,[status(thm)],[3169, 3162])).
% 22.15/22.33 tff(3171,plain,
% 22.15/22.33 ((~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))) <=> (~(mult(mult(unit, c), mult(mult(a, b), c)) = mult(mult(unit, mult(mult(a, b), c)), c)))),
% 22.15/22.33 inference(monotonicity,[status(thm)],[3170])).
% 22.15/22.33 tff(3172,plain,
% 22.15/22.33 (~(mult(mult(unit, c), mult(mult(a, b), c)) = mult(mult(unit, mult(mult(a, b), c)), c))),
% 22.15/22.33 inference(modus_ponens,[status(thm)],[1029, 3171])).
% 22.15/22.33 tff(3173,plain,
% 22.15/22.33 (mult(mult(mult(a, b), unit), c) = mult(mult(a, b), c)),
% 22.15/22.33 inference(monotonicity,[status(thm)],[440])).
% 22.15/22.33 tff(3174,plain,
% 22.15/22.33 (mult(mult(mult(a, b), unit), c) = mult(mult(a, c), b)),
% 22.15/22.33 inference(transitivity,[status(thm)],[3173, 227])).
% 22.15/22.33 tff(3175,plain,
% 22.15/22.33 (mult(mult(mult(mult(a, b), unit), c), unit) = mult(mult(mult(a, c), b), unit)),
% 22.15/22.33 inference(monotonicity,[status(thm)],[3174])).
% 22.15/22.33 tff(3176,plain,
% 22.15/22.33 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(a, b), unit), c), unit) = mult(mult(a, b), mult(mult(unit, c), unit)))),
% 22.15/22.33 inference(quant_inst,[status(thm)],[])).
% 22.15/22.33 tff(3177,plain,
% 22.15/22.33 (mult(mult(mult(mult(a, b), unit), c), unit) = mult(mult(a, b), mult(mult(unit, c), unit))),
% 22.15/22.33 inference(unit_resolution,[status(thm)],[3176, 56])).
% 22.15/22.33 tff(3178,plain,
% 22.15/22.33 (mult(mult(a, b), mult(mult(unit, c), unit)) = mult(mult(mult(mult(a, b), unit), c), unit)),
% 22.15/22.33 inference(symmetry,[status(thm)],[3177])).
% 22.15/22.33 tff(3179,plain,
% 22.15/22.33 (mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(mult(unit, c), unit)) = mult(mult(a, b), mult(mult(unit, c), unit))),
% 22.15/22.33 inference(monotonicity,[status(thm)],[213])).
% 22.15/22.33 tff(3180,assumption,(mult(mult(c, mult(mult(unit, c), unit)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(mult(unit, c), unit))), introduced(assumption)).
% 22.15/22.33 tff(3181,plain,
% 22.15/22.33 (mult(c, mult(mult(unit, c), unit)) = mult(c, c)),
% 22.15/22.33 inference(monotonicity,[status(thm)],[78])).
% 22.15/22.33 tff(3182,plain,
% 22.15/22.33 (mult(c, c) = mult(c, mult(mult(unit, c), unit))),
% 22.15/22.33 inference(symmetry,[status(thm)],[3181])).
% 22.15/22.33 tff(3183,plain,
% 22.15/22.33 (mult(mult(c, c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(c, mult(mult(unit, c), unit)), mult(mult(unit, ld(c, mult(a, b))), unit))),
% 22.15/22.33 inference(monotonicity,[status(thm)],[3182])).
% 22.15/22.33 tff(3184,plain,
% 22.15/22.33 (mult(mult(c, c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(a, c), b)),
% 22.15/22.33 inference(transitivity,[status(thm)],[3183, 3180, 3179, 3178, 3175, 864, 858, 856])).
% 22.15/22.33 tff(3185,plain,
% 22.15/22.33 (mult(mult(mult(c, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(mult(a, c), b), c)),
% 22.15/22.33 inference(monotonicity,[status(thm)],[3184])).
% 22.15/22.33 tff(3186,plain,
% 22.15/22.33 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(c, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(c, mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), c)))),
% 22.15/22.33 inference(quant_inst,[status(thm)],[])).
% 22.15/22.33 tff(3187,plain,
% 22.15/22.33 (mult(mult(mult(c, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(c, mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), c))),
% 22.15/22.33 inference(unit_resolution,[status(thm)],[3186, 56])).
% 22.15/22.33 tff(3188,plain,
% 22.15/22.33 (mult(c, mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), c)) = mult(mult(mult(c, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c)),
% 22.15/22.33 inference(symmetry,[status(thm)],[3187])).
% 22.15/22.33 tff(3189,plain,
% 22.15/22.33 (mult(mult(a, c), b) = mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), c)),
% 22.15/22.33 inference(transitivity,[status(thm)],[161, 215])).
% 22.15/22.33 tff(3190,plain,
% 22.15/22.33 (mult(c, mult(mult(a, c), b)) = mult(c, mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), c))),
% 22.15/22.33 inference(monotonicity,[status(thm)],[3189])).
% 22.15/22.33 tff(3191,plain,
% 22.15/22.33 (mult(mult(unit, c), mult(mult(a, b), c)) = mult(mult(unit, mult(mult(a, b), c)), c)),
% 22.15/22.33 inference(transitivity,[status(thm)],[2706, 3190, 3188, 3185, 231])).
% 22.15/22.33 tff(3192,assumption,(~(mult(mult(unit, c), mult(mult(a, b), c)) = mult(mult(unit, mult(mult(a, b), c)), c))), introduced(assumption)).
% 22.15/22.33 tff(3193,plain,
% 22.15/22.33 ($false),
% 22.15/22.33 inference(unit_resolution,[status(thm)],[3192, 3191])).
% 22.15/22.33 tff(3194,plain,((~(mult(mult(c, mult(mult(unit, c), unit)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(mult(unit, c), unit)))) | (mult(mult(unit, c), mult(mult(a, b), c)) = mult(mult(unit, mult(mult(a, b), c)), c))), inference(lemma,lemma(discharge,[]))).
% 22.15/22.33 tff(3195,plain,
% 22.15/22.33 (~(mult(mult(c, mult(mult(unit, c), unit)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(mult(unit, c), unit)))),
% 22.15/22.33 inference(unit_resolution,[status(thm)],[3194, 3172])).
% 22.15/22.33 tff(3196,plain,
% 22.15/22.33 (((~(mult(mult(c, mult(mult(unit, c), unit)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(mult(unit, c), unit)))) | (~(mult(c, mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(unit, c), unit)))))) | (mult(mult(c, mult(mult(unit, c), unit)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(mult(unit, c), unit)))),
% 22.15/22.33 inference(tautology,[status(thm)],[])).
% 22.15/22.33 tff(3197,plain,
% 22.15/22.33 ((~(mult(mult(c, mult(mult(unit, c), unit)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(mult(unit, c), unit)))) | (~(mult(c, mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(unit, c), unit)))))),
% 22.15/22.33 inference(unit_resolution,[status(thm)],[3196, 3195])).
% 22.15/22.33 tff(3198,plain,
% 22.15/22.33 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(c, mult(mult(unit, c), unit)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(mult(unit, c), unit)))) | (~(mult(c, mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(unit, c), unit))))))) | (~((~(mult(mult(c, mult(mult(unit, c), unit)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(c, mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit))))) | (~(mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(mult(unit, c), unit)) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(unit, c), unit))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(c, mult(mult(unit, c), unit)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(mult(unit, c), unit)))) | (~(mult(c, mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(unit, c), unit))))))) | (~((~(mult(mult(c, mult(mult(unit, c), unit)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(c, mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit))))) | (~(mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(mult(unit, c), unit)) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(unit, c), unit))))))))),
% 22.15/22.33 inference(rewrite,[status(thm)],[])).
% 22.15/22.33 tff(3199,plain,
% 22.15/22.33 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(c, mult(mult(unit, c), unit)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(mult(unit, c), unit)))) | (~(mult(c, mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(unit, c), unit))))))) | (~((~(mult(mult(c, mult(mult(unit, c), unit)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(c, mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit))))) | (~(mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(mult(unit, c), unit)) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(unit, c), unit))))))))),
% 22.15/22.33 inference(quant_inst,[status(thm)],[])).
% 22.15/22.33 tff(3200,plain,
% 22.15/22.33 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(c, mult(mult(unit, c), unit)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(mult(unit, c), unit)))) | (~(mult(c, mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(unit, c), unit))))))) | (~((~(mult(mult(c, mult(mult(unit, c), unit)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(c, mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit))))) | (~(mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(mult(unit, c), unit)) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(unit, c), unit)))))))),
% 22.15/22.34 inference(modus_ponens,[status(thm)],[3199, 3198])).
% 22.15/22.34 tff(3201,plain,
% 22.15/22.34 ((~((~(mult(mult(c, mult(mult(unit, c), unit)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(mult(unit, c), unit)))) | (~(mult(c, mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(unit, c), unit))))))) | (~((~(mult(mult(c, mult(mult(unit, c), unit)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(c, mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit))))) | (~(mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(mult(unit, c), unit)) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(unit, c), unit)))))))),
% 22.15/22.34 inference(unit_resolution,[status(thm)],[3200, 27])).
% 22.15/22.34 tff(3202,plain,
% 22.15/22.34 (~((~(mult(mult(c, mult(mult(unit, c), unit)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(c, mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit))))) | (~(mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(mult(unit, c), unit)) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(unit, c), unit))))))),
% 22.15/22.34 inference(unit_resolution,[status(thm)],[3201, 3197])).
% 22.15/22.34 tff(3203,plain,
% 22.15/22.34 (((~(mult(mult(c, mult(mult(unit, c), unit)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(c, mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit))))) | (~(mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(mult(unit, c), unit)) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(unit, c), unit)))))) | (mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(mult(unit, c), unit)) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(unit, c), unit))))),
% 22.15/22.34 inference(tautology,[status(thm)],[])).
% 22.15/22.34 tff(3204,plain,
% 22.15/22.34 (mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(mult(unit, c), unit)) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(unit, c), unit)))),
% 22.15/22.34 inference(unit_resolution,[status(thm)],[3203, 3202])).
% 22.15/22.34 tff(3205,plain,
% 22.15/22.34 (mult(mult(b, c), a) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)),
% 22.15/22.34 inference(monotonicity,[status(thm)],[1631])).
% 22.15/22.34 tff(3206,plain,
% 22.15/22.34 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(b, c), a)),
% 22.15/22.34 inference(symmetry,[status(thm)],[3205])).
% 22.15/22.34 tff(3207,plain,
% 22.15/22.34 (mult(mult(a, b), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))),
% 22.15/22.34 inference(transitivity,[status(thm)],[227, 405, 1800, 3206, 1172, 1168])).
% 22.15/22.34 tff(3208,plain,
% 22.15/22.34 (mult(mult(mult(a, b), c), a) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a)),
% 22.15/22.34 inference(monotonicity,[status(thm)],[3207])).
% 22.15/22.34 tff(3209,plain,
% 22.15/22.34 (mult(mult(mult(mult(a, b), c), a), b) = mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), b)),
% 22.15/22.34 inference(monotonicity,[status(thm)],[3208])).
% 22.15/22.34 tff(3210,plain,
% 22.15/22.34 (mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), b) = mult(mult(mult(mult(a, b), c), a), b)),
% 22.15/22.34 inference(symmetry,[status(thm)],[3209])).
% 22.15/22.34 tff(3211,plain,
% 22.15/22.34 (mult(a, mult(c, rd(mult(b, c), mult(a, c)))) = mult(b, c)),
% 22.15/22.34 inference(transitivity,[status(thm)],[2220, 2700, 2172, 2178, 2177, 2162, 1642, 293, 291])).
% 22.15/22.34 tff(3212,plain,
% 22.15/22.34 (mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(b, c), a)),
% 22.15/22.34 inference(monotonicity,[status(thm)],[3211])).
% 22.15/22.34 tff(3213,plain,
% 22.15/22.34 (mult(mult(b, c), a) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a)),
% 22.15/22.34 inference(symmetry,[status(thm)],[3212])).
% 22.15/22.34 tff(3214,plain,
% 22.15/22.34 (mult(mult(a, b), c) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a)),
% 22.15/22.34 inference(transitivity,[status(thm)],[227, 405, 1800, 3206, 3213])).
% 22.15/22.34 tff(3215,plain,
% 22.15/22.34 (mult(a, mult(mult(a, b), c)) = mult(a, mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a))),
% 22.15/22.34 inference(monotonicity,[status(thm)],[3214])).
% 22.15/22.34 tff(3216,plain,
% 22.15/22.34 (mult(a, mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a)) = mult(a, mult(mult(a, b), c))),
% 22.15/22.34 inference(symmetry,[status(thm)],[3215])).
% 22.15/22.34 tff(3217,plain,
% 22.15/22.34 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(a, mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a)))),
% 22.15/22.34 inference(quant_inst,[status(thm)],[])).
% 22.15/22.34 tff(3218,plain,
% 22.15/22.34 (mult(mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(a, mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a))),
% 22.15/22.34 inference(unit_resolution,[status(thm)],[3217, 56])).
% 22.15/22.34 tff(3219,plain,
% 22.15/22.34 (mult(mult(a, unit), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(c, rd(mult(b, c), mult(a, c))))),
% 22.15/22.34 inference(monotonicity,[status(thm)],[47])).
% 22.15/22.34 tff(3220,plain,
% 22.15/22.34 (mult(mult(a, unit), mult(c, rd(mult(b, c), mult(a, c)))) = mult(b, c)),
% 22.15/22.34 inference(transitivity,[status(thm)],[3219, 2220, 2700, 2172, 2178, 2177, 2162, 1642, 293, 291])).
% 22.15/22.34 tff(3221,plain,
% 22.15/22.34 (mult(mult(mult(a, unit), mult(c, rd(mult(b, c), mult(a, c)))), unit) = mult(mult(b, c), unit)),
% 22.15/22.34 inference(monotonicity,[status(thm)],[3220])).
% 22.15/22.34 tff(3222,plain,
% 22.15/22.34 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(a, unit), mult(c, rd(mult(b, c), mult(a, c)))), unit) = mult(a, mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit)))),
% 22.15/22.34 inference(quant_inst,[status(thm)],[])).
% 22.15/22.34 tff(3223,plain,
% 22.15/22.34 (mult(mult(mult(a, unit), mult(c, rd(mult(b, c), mult(a, c)))), unit) = mult(a, mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit))),
% 22.15/22.34 inference(unit_resolution,[status(thm)],[3222, 56])).
% 22.15/22.34 tff(3224,plain,
% 22.15/22.34 (mult(a, mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit)) = mult(mult(mult(a, unit), mult(c, rd(mult(b, c), mult(a, c)))), unit)),
% 22.15/22.34 inference(symmetry,[status(thm)],[3223])).
% 22.15/22.34 tff(3225,plain,
% 22.15/22.34 (mult(a, mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit)) = mult(b, c)),
% 22.15/22.34 inference(transitivity,[status(thm)],[3224, 3221, 845, 837, 835, 240, 237, 141])).
% 22.15/22.34 tff(3226,plain,
% 22.15/22.34 (mult(mult(a, mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit)), a) = mult(mult(b, c), a)),
% 22.15/22.34 inference(monotonicity,[status(thm)],[3225])).
% 22.15/22.34 tff(3227,plain,
% 22.15/22.34 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(b, c), c)),
% 22.15/22.34 inference(monotonicity,[status(thm)],[1643])).
% 22.15/22.34 tff(3228,plain,
% 22.15/22.34 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a)),
% 22.15/22.34 inference(symmetry,[status(thm)],[751])).
% 22.15/22.34 tff(3229,plain,
% 22.15/22.34 (mult(mult(b, c), mult(c, a)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a))),
% 22.15/22.34 inference(monotonicity,[status(thm)],[1631])).
% 22.15/22.34 tff(3230,plain,
% 22.15/22.34 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, a)) = mult(b, mult(c, a))),
% 22.15/22.34 inference(symmetry,[status(thm)],[2990])).
% 22.15/22.34 tff(3231,plain,
% 22.15/22.34 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)) = mult(b, mult(c, a))),
% 22.15/22.34 inference(transitivity,[status(thm)],[1169, 2988, 3230])).
% 22.15/22.34 tff(3232,plain,
% 22.15/22.34 (mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) = mult(c, mult(b, mult(c, a)))),
% 22.15/22.34 inference(monotonicity,[status(thm)],[3231])).
% 22.15/22.34 tff(3233,plain,
% 22.15/22.34 (mult(mult(a, c), b) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))),
% 22.15/22.34 inference(transitivity,[status(thm)],[405, 1800, 3206, 1172, 1168])).
% 22.15/22.34 tff(3234,plain,
% 22.15/22.34 (mult(c, mult(mult(a, c), b)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))),
% 22.15/22.34 inference(monotonicity,[status(thm)],[3233])).
% 22.15/22.34 tff(3235,plain,
% 22.15/22.34 (mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, c), b)),
% 22.15/22.34 inference(transitivity,[status(thm)],[3212, 3205, 1799, 177])).
% 22.15/22.34 tff(3236,plain,
% 22.15/22.34 (mult(c, mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a)) = mult(c, mult(mult(a, c), b))),
% 22.15/22.34 inference(monotonicity,[status(thm)],[3235])).
% 22.15/22.34 tff(3237,plain,
% 22.15/22.34 (mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a)),
% 22.15/22.34 inference(transitivity,[status(thm)],[2734, 2697, 3236, 3234, 3232, 2830, 2231, 3229, 3228])).
% 22.15/22.34 tff(3238,plain,
% 22.15/22.34 (rd(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a), a) = rd(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a), a)),
% 22.15/22.34 inference(monotonicity,[status(thm)],[3237])).
% 22.15/22.34 tff(3239,plain,
% 22.15/22.34 (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(b, c))),
% 22.15/22.34 inference(monotonicity,[status(thm)],[1643])).
% 22.15/22.34 tff(3240,plain,
% 22.15/22.34 (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))),
% 22.15/22.34 inference(transitivity,[status(thm)],[3239, 289])).
% 22.15/22.34 tff(3241,plain,
% 22.15/22.34 (mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))),
% 22.15/22.34 inference(unit_resolution,[status(thm)],[2813, 3240])).
% 22.15/22.34 tff(3242,plain,
% 22.15/22.34 (mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 22.15/22.34 inference(symmetry,[status(thm)],[3241])).
% 22.15/22.34 tff(3243,assumption,(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), a), c) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))), introduced(assumption)).
% 22.15/22.34 tff(3244,plain,
% 22.15/22.34 ((~![A: $i] : (mult(A, unit) = A)) | (mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit) = mult(unit, mult(c, rd(mult(b, c), mult(a, c)))))),
% 22.15/22.34 inference(quant_inst,[status(thm)],[])).
% 22.15/22.34 tff(3245,plain,
% 22.15/22.34 (mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit) = mult(unit, mult(c, rd(mult(b, c), mult(a, c))))),
% 22.15/22.34 inference(unit_resolution,[status(thm)],[3244, 43])).
% 22.15/22.34 tff(3246,plain,
% 22.15/22.34 (mult(unit, mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit)),
% 22.15/22.34 inference(symmetry,[status(thm)],[3245])).
% 22.15/22.34 tff(3247,plain,
% 22.15/22.34 ((~![A: $i] : (mult(unit, A) = A)) | (mult(unit, mult(c, rd(mult(b, c), mult(a, c)))) = mult(c, rd(mult(b, c), mult(a, c))))),
% 22.15/22.34 inference(quant_inst,[status(thm)],[])).
% 22.15/22.34 tff(3248,plain,
% 22.15/22.34 (mult(unit, mult(c, rd(mult(b, c), mult(a, c)))) = mult(c, rd(mult(b, c), mult(a, c)))),
% 22.15/22.34 inference(unit_resolution,[status(thm)],[3247, 71])).
% 22.15/22.34 tff(3249,plain,
% 22.15/22.34 (mult(c, rd(mult(b, c), mult(a, c))) = mult(unit, mult(c, rd(mult(b, c), mult(a, c))))),
% 22.15/22.34 inference(symmetry,[status(thm)],[3248])).
% 22.15/22.34 tff(3250,plain,
% 22.15/22.34 (mult(c, rd(mult(b, c), mult(a, c))) = mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit)),
% 22.15/22.34 inference(transitivity,[status(thm)],[3249, 3246])).
% 22.15/22.34 tff(3251,plain,
% 22.15/22.34 (mult(mult(c, rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit), a)),
% 22.15/22.34 inference(monotonicity,[status(thm)],[3250])).
% 22.15/22.34 tff(3252,plain,
% 22.15/22.34 (mult(mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit), a) = mult(mult(c, rd(mult(b, c), mult(a, c))), a)),
% 22.15/22.34 inference(symmetry,[status(thm)],[3251])).
% 22.15/22.34 tff(3253,plain,
% 22.15/22.34 (mult(mult(mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit), a), c) = mult(mult(mult(c, rd(mult(b, c), mult(a, c))), a), c)),
% 22.15/22.34 inference(monotonicity,[status(thm)],[3252])).
% 22.15/22.34 tff(3254,plain,
% 22.15/22.34 (mult(mult(mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit), a), c) = mult(mult(b, c), c)),
% 22.15/22.34 inference(transitivity,[status(thm)],[3253, 3243, 3242, 2787, 3238, 2227, 3227])).
% 22.15/22.34 tff(3255,plain,
% 22.15/22.34 (rd(mult(mult(mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit), a), c), c) = rd(mult(mult(b, c), c), c)),
% 22.15/22.34 inference(monotonicity,[status(thm)],[3254])).
% 22.15/22.34 tff(3256,plain,
% 22.15/22.34 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit), a), c), c) = mult(mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit), a))),
% 22.15/22.34 inference(quant_inst,[status(thm)],[])).
% 22.15/22.34 tff(3257,plain,
% 22.15/22.34 (rd(mult(mult(mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit), a), c), c) = mult(mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit), a)),
% 22.15/22.34 inference(unit_resolution,[status(thm)],[3256, 168])).
% 22.15/22.34 tff(3258,plain,
% 22.15/22.34 (mult(mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit), a) = rd(mult(mult(mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit), a), c), c)),
% 22.15/22.34 inference(symmetry,[status(thm)],[3257])).
% 22.15/22.34 tff(3259,plain,
% 22.15/22.34 (mult(mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit), a) = mult(b, c)),
% 22.15/22.34 inference(transitivity,[status(thm)],[3258, 3255, 2224])).
% 22.15/22.34 tff(3260,plain,
% 22.15/22.34 (mult(a, mult(mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit), a)) = mult(a, mult(b, c))),
% 22.15/22.34 inference(monotonicity,[status(thm)],[3259])).
% 22.15/22.34 tff(3261,plain,
% 22.15/22.34 (mult(mult(a, mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit)), a) = mult(mult(a, b), c)),
% 22.15/22.34 inference(transitivity,[status(thm)],[3226, 3205, 1799, 177, 161])).
% 22.15/22.34 tff(3262,plain,
% 22.15/22.34 ((mult(mult(a, mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit)), a) = mult(a, mult(mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit), a))) <=> (mult(mult(a, b), c) = mult(a, mult(b, c)))),
% 22.15/22.34 inference(monotonicity,[status(thm)],[3261, 3260])).
% 22.15/22.34 tff(3263,plain,
% 22.15/22.34 ((mult(mult(a, b), c) = mult(a, mult(b, c))) <=> (mult(mult(a, mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit)), a) = mult(a, mult(mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit), a)))),
% 22.15/22.34 inference(symmetry,[status(thm)],[3262])).
% 22.15/22.34 tff(3264,plain,
% 22.15/22.34 ((~(mult(mult(a, b), c) = mult(a, mult(b, c)))) <=> (~(mult(mult(a, mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit)), a) = mult(a, mult(mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit), a))))),
% 22.15/22.34 inference(monotonicity,[status(thm)],[3263])).
% 22.15/22.34 tff(3265,plain,
% 22.15/22.34 (~(mult(mult(a, mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit)), a) = mult(a, mult(mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit), a)))),
% 22.15/22.34 inference(modus_ponens,[status(thm)],[146, 3264])).
% 22.15/22.34 tff(3266,plain,
% 22.15/22.34 (((~(mult(mult(a, a), mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit)) = mult(a, mult(a, mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit))))) | (~(mult(mult(a, mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit)), a) = mult(a, mult(mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit), a))))) | (mult(mult(a, mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit)), a) = mult(a, mult(mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit), a)))),
% 22.15/22.34 inference(tautology,[status(thm)],[])).
% 22.15/22.34 tff(3267,plain,
% 22.15/22.34 ((~(mult(mult(a, a), mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit)) = mult(a, mult(a, mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit))))) | (~(mult(mult(a, mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit)), a) = mult(a, mult(mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit), a))))),
% 22.15/22.34 inference(unit_resolution,[status(thm)],[3266, 3265])).
% 22.15/22.34 tff(3268,plain,
% 22.15/22.34 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, a), mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit)) = mult(a, mult(a, mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit))))) | (~(mult(mult(a, mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit)), a) = mult(a, mult(mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit), a)))))) | (~((~(mult(mult(a, a), mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit)) = mult(mult(a, mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit)), a))) | (~(mult(a, mult(a, mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit))) = mult(a, mult(mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit), a)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, a), mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit)) = mult(a, mult(a, mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit))))) | (~(mult(mult(a, mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit)), a) = mult(a, mult(mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit), a)))))) | (~((~(mult(mult(a, a), mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit)) = mult(mult(a, mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit)), a))) | (~(mult(a, mult(a, mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit))) = mult(a, mult(mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit), a)))))))),
% 22.15/22.35 inference(rewrite,[status(thm)],[])).
% 22.15/22.35 tff(3269,plain,
% 22.15/22.35 (((~((~(mult(mult(a, a), mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit)) = mult(mult(a, mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit)), a))) | (~(mult(a, mult(a, mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit))) = mult(a, mult(mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit), a)))))) | (~((~(mult(mult(a, a), mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit)) = mult(a, mult(a, mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit))))) | (~(mult(mult(a, mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit)), a) = mult(a, mult(mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit), a))))))) <=> ((~((~(mult(mult(a, a), mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit)) = mult(a, mult(a, mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit))))) | (~(mult(mult(a, mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit)), a) = mult(a, mult(mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit), a)))))) | (~((~(mult(mult(a, a), mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit)) = mult(mult(a, mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit)), a))) | (~(mult(a, mult(a, mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit))) = mult(a, mult(mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit), a)))))))),
% 22.15/22.35 inference(rewrite,[status(thm)],[])).
% 22.15/22.35 tff(3270,plain,
% 22.15/22.35 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, a), mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit)) = mult(mult(a, mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit)), a))) | (~(mult(a, mult(a, mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit))) = mult(a, mult(mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit), a)))))) | (~((~(mult(mult(a, a), mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit)) = mult(a, mult(a, mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit))))) | (~(mult(mult(a, mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit)), a) = mult(a, mult(mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit), a)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, a), mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit)) = mult(a, mult(a, mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit))))) | (~(mult(mult(a, mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit)), a) = mult(a, mult(mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit), a)))))) | (~((~(mult(mult(a, a), mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit)) = mult(mult(a, mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit)), a))) | (~(mult(a, mult(a, mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit))) = mult(a, mult(mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit), a))))))))),
% 22.15/22.35 inference(monotonicity,[status(thm)],[3269])).
% 22.15/22.35 tff(3271,plain,
% 22.15/22.35 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, a), mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit)) = mult(mult(a, mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit)), a))) | (~(mult(a, mult(a, mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit))) = mult(a, mult(mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit), a)))))) | (~((~(mult(mult(a, a), mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit)) = mult(a, mult(a, mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit))))) | (~(mult(mult(a, mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit)), a) = mult(a, mult(mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit), a)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, a), mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit)) = mult(a, mult(a, mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit))))) | (~(mult(mult(a, mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit)), a) = mult(a, mult(mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit), a)))))) | (~((~(mult(mult(a, a), mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit)) = mult(mult(a, mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit)), a))) | (~(mult(a, mult(a, mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit))) = mult(a, mult(mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit), a)))))))),
% 22.15/22.35 inference(transitivity,[status(thm)],[3270, 3268])).
% 22.15/22.35 tff(3272,plain,
% 22.15/22.35 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, a), mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit)) = mult(mult(a, mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit)), a))) | (~(mult(a, mult(a, mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit))) = mult(a, mult(mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit), a)))))) | (~((~(mult(mult(a, a), mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit)) = mult(a, mult(a, mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit))))) | (~(mult(mult(a, mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit)), a) = mult(a, mult(mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit), a)))))))),
% 22.15/22.35 inference(quant_inst,[status(thm)],[])).
% 22.15/22.35 tff(3273,plain,
% 22.15/22.35 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, a), mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit)) = mult(a, mult(a, mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit))))) | (~(mult(mult(a, mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit)), a) = mult(a, mult(mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit), a)))))) | (~((~(mult(mult(a, a), mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit)) = mult(mult(a, mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit)), a))) | (~(mult(a, mult(a, mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit))) = mult(a, mult(mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit), a))))))),
% 22.15/22.35 inference(modus_ponens,[status(thm)],[3272, 3271])).
% 22.15/22.35 tff(3274,plain,
% 22.15/22.35 ((~((~(mult(mult(a, a), mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit)) = mult(a, mult(a, mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit))))) | (~(mult(mult(a, mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit)), a) = mult(a, mult(mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit), a)))))) | (~((~(mult(mult(a, a), mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit)) = mult(mult(a, mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit)), a))) | (~(mult(a, mult(a, mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit))) = mult(a, mult(mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit), a))))))),
% 22.15/22.35 inference(unit_resolution,[status(thm)],[3273, 27])).
% 22.15/22.35 tff(3275,plain,
% 22.15/22.35 (~((~(mult(mult(a, a), mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit)) = mult(mult(a, mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit)), a))) | (~(mult(a, mult(a, mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit))) = mult(a, mult(mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit), a)))))),
% 22.15/22.35 inference(unit_resolution,[status(thm)],[3274, 3267])).
% 22.15/22.35 tff(3276,plain,
% 22.15/22.35 (((~(mult(mult(a, a), mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit)) = mult(mult(a, mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit)), a))) | (~(mult(a, mult(a, mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit))) = mult(a, mult(mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit), a))))) | (mult(mult(a, a), mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit)) = mult(mult(a, mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit)), a))),
% 22.15/22.35 inference(tautology,[status(thm)],[])).
% 22.15/22.35 tff(3277,plain,
% 22.15/22.35 (mult(mult(a, a), mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit)) = mult(mult(a, mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit)), a)),
% 22.15/22.35 inference(unit_resolution,[status(thm)],[3276, 3275])).
% 22.15/22.35 tff(3278,plain,
% 22.15/22.35 (mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, a), mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit))),
% 22.15/22.35 inference(monotonicity,[status(thm)],[3250])).
% 22.15/22.35 tff(3279,plain,
% 22.15/22.35 (mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, b), c)),
% 22.15/22.35 inference(transitivity,[status(thm)],[3278, 3277, 3226, 3205, 1799, 177, 161])).
% 22.15/22.35 tff(3280,plain,
% 22.15/22.35 (mult(mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(a, b), c), a)),
% 22.15/22.35 inference(monotonicity,[status(thm)],[3279])).
% 22.15/22.35 tff(3281,plain,
% 22.15/22.35 (mult(mult(mult(a, b), c), a) = mult(mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))), a)),
% 22.15/22.35 inference(symmetry,[status(thm)],[3280])).
% 22.15/22.35 tff(3282,plain,
% 22.15/22.35 (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a) = mult(mult(mult(a, b), c), a)),
% 22.15/22.35 inference(symmetry,[status(thm)],[3208])).
% 22.15/22.35 tff(3283,plain,
% 22.15/22.35 (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a) = mult(a, mult(mult(a, b), c))),
% 22.15/22.35 inference(transitivity,[status(thm)],[3282, 3281, 3218, 3216])).
% 22.15/22.35 tff(3284,plain,
% 22.15/22.35 (mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), b) = mult(mult(a, mult(mult(a, b), c)), b)),
% 22.15/22.35 inference(monotonicity,[status(thm)],[3283])).
% 22.15/22.35 tff(3285,plain,
% 22.15/22.35 (mult(mult(a, mult(mult(a, b), c)), b) = mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), b)),
% 22.15/22.35 inference(symmetry,[status(thm)],[3284])).
% 22.15/22.35 tff(3286,assumption,(mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(mult(unit, c), unit)) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(unit, c), unit)))), introduced(assumption)).
% 22.15/22.35 tff(3287,plain,
% 22.15/22.35 (mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(unit, c), unit))) = mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(mult(unit, c), unit))),
% 22.15/22.35 inference(symmetry,[status(thm)],[3286])).
% 22.15/22.35 tff(3288,plain,
% 22.15/22.35 (mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(unit, c), unit)) = mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)),
% 22.15/22.35 inference(monotonicity,[status(thm)],[78])).
% 22.15/22.35 tff(3289,plain,
% 22.15/22.35 (mult(mult(mult(unit, ld(c, mult(a, b))), unit), c) = mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(unit, c), unit))),
% 22.15/22.35 inference(symmetry,[status(thm)],[3288])).
% 22.15/22.35 tff(3290,plain,
% 22.15/22.35 (mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(unit, c), unit)))),
% 22.15/22.35 inference(monotonicity,[status(thm)],[3289])).
% 22.15/22.35 tff(3291,plain,
% 22.15/22.35 (mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)) = mult(c, mult(b, a))),
% 22.15/22.35 inference(transitivity,[status(thm)],[3290, 3287, 3179, 3178, 3175, 864, 858, 856, 405, 1800, 3206, 3057, 2299])).
% 22.15/22.35 tff(3292,plain,
% 22.15/22.35 (ld(c, mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), c))) = ld(c, mult(c, mult(b, a)))),
% 22.15/22.35 inference(monotonicity,[status(thm)],[3291])).
% 22.15/22.35 tff(3293,plain,
% 22.15/22.35 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(c, mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), c))) = mult(mult(mult(unit, ld(c, mult(a, b))), unit), c))),
% 22.15/22.35 inference(quant_inst,[status(thm)],[])).
% 22.15/22.35 tff(3294,plain,
% 22.15/22.35 (ld(c, mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), c))) = mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)),
% 22.15/22.35 inference(unit_resolution,[status(thm)],[3293, 7])).
% 22.15/22.35 tff(3295,plain,
% 22.15/22.35 (mult(mult(mult(unit, ld(c, mult(a, b))), unit), c) = ld(c, mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)))),
% 22.15/22.35 inference(symmetry,[status(thm)],[3294])).
% 22.15/22.35 tff(3296,plain,
% 22.15/22.35 (mult(mult(mult(unit, ld(c, mult(a, b))), unit), c) = mult(b, a)),
% 22.15/22.35 inference(transitivity,[status(thm)],[3295, 3292, 1472])).
% 22.15/22.35 tff(3297,plain,
% 22.15/22.35 (mult(mult(mult(a, b), c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)) = mult(mult(mult(a, b), c), mult(b, a))),
% 22.15/22.35 inference(monotonicity,[status(thm)],[3296])).
% 22.15/22.35 tff(3298,plain,
% 22.15/22.35 (mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(mult(a, b), c), mult(a, b))),
% 22.15/22.35 inference(monotonicity,[status(thm)],[161])).
% 22.15/22.35 tff(3299,plain,
% 22.15/22.35 (mult(mult(mult(a, b), c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(mult(mult(a, c), b), mult(a, b))),
% 22.15/22.35 inference(monotonicity,[status(thm)],[227, 213])).
% 22.15/22.35 tff(3300,plain,
% 22.15/22.35 (mult(mult(mult(a, b), c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(mult(mult(a, b), c), mult(a, b))),
% 22.15/22.35 inference(transitivity,[status(thm)],[3299, 3298])).
% 22.15/22.35 tff(3301,plain,
% 22.15/22.35 ((mult(mult(mult(a, b), c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)) = mult(mult(mult(a, b), c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)))) <=> (mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(a, b)))),
% 22.15/22.35 inference(monotonicity,[status(thm)],[3297, 3300])).
% 22.15/22.35 tff(3302,plain,
% 22.15/22.35 ((mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(a, b))) <=> (mult(mult(mult(a, b), c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)) = mult(mult(mult(a, b), c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))),
% 22.15/22.35 inference(symmetry,[status(thm)],[3301])).
% 22.15/22.35 tff(3303,plain,
% 22.15/22.35 ((~(mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(a, b)))) <=> (~(mult(mult(mult(a, b), c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)) = mult(mult(mult(a, b), c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)))))),
% 22.15/22.35 inference(monotonicity,[status(thm)],[3302])).
% 22.15/22.35 tff(3304,plain,
% 22.15/22.35 (~(mult(mult(mult(a, b), c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)) = mult(mult(mult(a, b), c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))),
% 22.15/22.35 inference(modus_ponens,[status(thm)],[1064, 3303])).
% 22.15/22.35 tff(3305,plain,
% 22.15/22.35 (((~(mult(mult(mult(mult(a, b), c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(mult(mult(a, b), c), c), mult(mult(unit, ld(c, mult(a, b))), unit)))) | (~(mult(mult(mult(a, b), c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)) = mult(mult(mult(a, b), c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)))))) | (mult(mult(mult(a, b), c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)) = mult(mult(mult(a, b), c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))),
% 22.15/22.35 inference(tautology,[status(thm)],[])).
% 22.15/22.35 tff(3306,plain,
% 22.15/22.35 ((~(mult(mult(mult(mult(a, b), c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(mult(mult(a, b), c), c), mult(mult(unit, ld(c, mult(a, b))), unit)))) | (~(mult(mult(mult(a, b), c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)) = mult(mult(mult(a, b), c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)))))),
% 22.15/22.35 inference(unit_resolution,[status(thm)],[3305, 3304])).
% 22.15/22.35 tff(3307,plain,
% 22.15/22.35 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(mult(a, b), c), c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(mult(a, b), c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))) | (~(mult(mult(mult(mult(a, b), c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(mult(a, b), c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)))))) | (~((~(mult(mult(mult(mult(a, b), c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(mult(mult(a, b), c), c), mult(mult(unit, ld(c, mult(a, b))), unit)))) | (~(mult(mult(mult(a, b), c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)) = mult(mult(mult(a, b), c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(mult(a, b), c), c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(mult(a, b), c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))) | (~(mult(mult(mult(mult(a, b), c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(mult(a, b), c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)))))) | (~((~(mult(mult(mult(mult(a, b), c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(mult(mult(a, b), c), c), mult(mult(unit, ld(c, mult(a, b))), unit)))) | (~(mult(mult(mult(a, b), c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)) = mult(mult(mult(a, b), c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))))))),
% 22.15/22.36 inference(rewrite,[status(thm)],[])).
% 22.15/22.36 tff(3308,plain,
% 22.15/22.36 (((~((~(mult(mult(mult(mult(a, b), c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(mult(mult(a, b), c), c), mult(mult(unit, ld(c, mult(a, b))), unit)))) | (~(mult(mult(mult(a, b), c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)) = mult(mult(mult(a, b), c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))))) | (~((~(mult(mult(mult(mult(a, b), c), c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(mult(a, b), c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))) | (~(mult(mult(mult(mult(a, b), c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(mult(a, b), c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c))))))) <=> ((~((~(mult(mult(mult(mult(a, b), c), c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(mult(a, b), c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))) | (~(mult(mult(mult(mult(a, b), c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(mult(a, b), c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)))))) | (~((~(mult(mult(mult(mult(a, b), c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(mult(mult(a, b), c), c), mult(mult(unit, ld(c, mult(a, b))), unit)))) | (~(mult(mult(mult(a, b), c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)) = mult(mult(mult(a, b), c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))))))),
% 22.15/22.36 inference(rewrite,[status(thm)],[])).
% 22.15/22.36 tff(3309,plain,
% 22.15/22.36 ((~((~(mult(mult(mult(mult(a, b), c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(mult(a, b), c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)))) | (~(mult(mult(mult(mult(a, b), c), c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(mult(a, b), c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))))) <=> (~((~(mult(mult(mult(mult(a, b), c), c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(mult(a, b), c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))) | (~(mult(mult(mult(mult(a, b), c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(mult(a, b), c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c))))))),
% 22.15/22.36 inference(rewrite,[status(thm)],[])).
% 22.15/22.36 tff(3310,plain,
% 22.15/22.36 ((~((~(mult(mult(mult(mult(a, b), c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(mult(mult(a, b), c), c), mult(mult(unit, ld(c, mult(a, b))), unit)))) | (~(mult(mult(mult(a, b), c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)) = mult(mult(mult(a, b), c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))))) <=> (~((~(mult(mult(mult(mult(a, b), c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(mult(mult(a, b), c), c), mult(mult(unit, ld(c, mult(a, b))), unit)))) | (~(mult(mult(mult(a, b), c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)) = mult(mult(mult(a, b), c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)))))))),
% 22.15/22.36 inference(rewrite,[status(thm)],[])).
% 22.15/22.36 tff(3311,plain,
% 22.15/22.36 (((~((~(mult(mult(mult(mult(a, b), c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(mult(mult(a, b), c), c), mult(mult(unit, ld(c, mult(a, b))), unit)))) | (~(mult(mult(mult(a, b), c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)) = mult(mult(mult(a, b), c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))))) | (~((~(mult(mult(mult(mult(a, b), c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(mult(a, b), c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)))) | (~(mult(mult(mult(mult(a, b), c), c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(mult(a, b), c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)))))))) <=> ((~((~(mult(mult(mult(mult(a, b), c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(mult(mult(a, b), c), c), mult(mult(unit, ld(c, mult(a, b))), unit)))) | (~(mult(mult(mult(a, b), c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)) = mult(mult(mult(a, b), c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))))) | (~((~(mult(mult(mult(mult(a, b), c), c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(mult(a, b), c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))) | (~(mult(mult(mult(mult(a, b), c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(mult(a, b), c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)))))))),
% 22.15/22.36 inference(monotonicity,[status(thm)],[3310, 3309])).
% 22.15/22.36 tff(3312,plain,
% 22.15/22.36 (((~((~(mult(mult(mult(mult(a, b), c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(mult(mult(a, b), c), c), mult(mult(unit, ld(c, mult(a, b))), unit)))) | (~(mult(mult(mult(a, b), c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)) = mult(mult(mult(a, b), c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))))) | (~((~(mult(mult(mult(mult(a, b), c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(mult(a, b), c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)))) | (~(mult(mult(mult(mult(a, b), c), c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(mult(a, b), c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)))))))) <=> ((~((~(mult(mult(mult(mult(a, b), c), c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(mult(a, b), c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))) | (~(mult(mult(mult(mult(a, b), c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(mult(a, b), c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)))))) | (~((~(mult(mult(mult(mult(a, b), c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(mult(mult(a, b), c), c), mult(mult(unit, ld(c, mult(a, b))), unit)))) | (~(mult(mult(mult(a, b), c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)) = mult(mult(mult(a, b), c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))))))),
% 22.15/22.36 inference(transitivity,[status(thm)],[3311, 3308])).
% 22.15/22.36 tff(3313,plain,
% 22.15/22.36 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(mult(a, b), c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(mult(mult(a, b), c), c), mult(mult(unit, ld(c, mult(a, b))), unit)))) | (~(mult(mult(mult(a, b), c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)) = mult(mult(mult(a, b), c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))))) | (~((~(mult(mult(mult(mult(a, b), c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(mult(a, b), c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)))) | (~(mult(mult(mult(mult(a, b), c), c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(mult(a, b), c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(mult(a, b), c), c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(mult(a, b), c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))) | (~(mult(mult(mult(mult(a, b), c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(mult(a, b), c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)))))) | (~((~(mult(mult(mult(mult(a, b), c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(mult(mult(a, b), c), c), mult(mult(unit, ld(c, mult(a, b))), unit)))) | (~(mult(mult(mult(a, b), c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)) = mult(mult(mult(a, b), c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)))))))))),
% 22.15/22.36 inference(monotonicity,[status(thm)],[3312])).
% 22.15/22.36 tff(3314,plain,
% 22.15/22.36 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(mult(a, b), c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(mult(mult(a, b), c), c), mult(mult(unit, ld(c, mult(a, b))), unit)))) | (~(mult(mult(mult(a, b), c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)) = mult(mult(mult(a, b), c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))))) | (~((~(mult(mult(mult(mult(a, b), c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(mult(a, b), c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)))) | (~(mult(mult(mult(mult(a, b), c), c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(mult(a, b), c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(mult(a, b), c), c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(mult(a, b), c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))) | (~(mult(mult(mult(mult(a, b), c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(mult(a, b), c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)))))) | (~((~(mult(mult(mult(mult(a, b), c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(mult(mult(a, b), c), c), mult(mult(unit, ld(c, mult(a, b))), unit)))) | (~(mult(mult(mult(a, b), c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)) = mult(mult(mult(a, b), c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))))))),
% 22.15/22.36 inference(transitivity,[status(thm)],[3313, 3307])).
% 22.15/22.36 tff(3315,plain,
% 22.15/22.36 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(mult(a, b), c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(mult(mult(a, b), c), c), mult(mult(unit, ld(c, mult(a, b))), unit)))) | (~(mult(mult(mult(a, b), c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)) = mult(mult(mult(a, b), c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))))) | (~((~(mult(mult(mult(mult(a, b), c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(mult(a, b), c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)))) | (~(mult(mult(mult(mult(a, b), c), c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(mult(a, b), c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))))))),
% 22.15/22.37 inference(quant_inst,[status(thm)],[])).
% 22.15/22.37 tff(3316,plain,
% 22.15/22.37 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(mult(a, b), c), c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(mult(a, b), c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))) | (~(mult(mult(mult(mult(a, b), c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(mult(a, b), c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)))))) | (~((~(mult(mult(mult(mult(a, b), c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(mult(mult(a, b), c), c), mult(mult(unit, ld(c, mult(a, b))), unit)))) | (~(mult(mult(mult(a, b), c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)) = mult(mult(mult(a, b), c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)))))))),
% 22.15/22.37 inference(modus_ponens,[status(thm)],[3315, 3314])).
% 22.15/22.37 tff(3317,plain,
% 22.15/22.37 ((~((~(mult(mult(mult(mult(a, b), c), c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(mult(a, b), c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))) | (~(mult(mult(mult(mult(a, b), c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(mult(a, b), c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)))))) | (~((~(mult(mult(mult(mult(a, b), c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(mult(mult(a, b), c), c), mult(mult(unit, ld(c, mult(a, b))), unit)))) | (~(mult(mult(mult(a, b), c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)) = mult(mult(mult(a, b), c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)))))))),
% 22.15/22.37 inference(unit_resolution,[status(thm)],[3316, 27])).
% 22.15/22.37 tff(3318,plain,
% 22.15/22.37 (~((~(mult(mult(mult(mult(a, b), c), c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(mult(a, b), c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))) | (~(mult(mult(mult(mult(a, b), c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(mult(a, b), c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)))))),
% 22.15/22.37 inference(unit_resolution,[status(thm)],[3317, 3306])).
% 22.15/22.37 tff(3319,plain,
% 22.15/22.37 (((~(mult(mult(mult(mult(a, b), c), c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(mult(a, b), c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))) | (~(mult(mult(mult(mult(a, b), c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(mult(a, b), c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c))))) | (mult(mult(mult(mult(a, b), c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(mult(a, b), c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)))),
% 22.15/22.37 inference(tautology,[status(thm)],[])).
% 22.15/22.37 tff(3320,plain,
% 22.15/22.37 (mult(mult(mult(mult(a, b), c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(mult(a, b), c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c))),
% 22.15/22.37 inference(unit_resolution,[status(thm)],[3319, 3318])).
% 22.15/22.37 tff(3321,plain,
% 22.15/22.37 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(a, b), c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(a, b), mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), c)))),
% 22.15/22.37 inference(quant_inst,[status(thm)],[])).
% 22.15/22.37 tff(3322,plain,
% 22.15/22.37 (mult(mult(mult(mult(a, b), c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(a, b), mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), c))),
% 22.15/22.37 inference(unit_resolution,[status(thm)],[3321, 56])).
% 22.15/22.37 tff(3323,plain,
% 22.15/22.37 (mult(mult(a, b), mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), c)) = mult(mult(mult(mult(a, b), c), mult(mult(unit, ld(c, mult(a, b))), unit)), c)),
% 22.15/22.37 inference(symmetry,[status(thm)],[3322])).
% 22.15/22.37 tff(3324,plain,
% 22.15/22.37 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)) = mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), c)),
% 22.15/22.37 inference(transitivity,[status(thm)],[1169, 1164, 3205, 1799, 177, 161, 215])).
% 22.15/22.37 tff(3325,plain,
% 22.15/22.37 (mult(mult(a, b), mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) = mult(mult(a, b), mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), c))),
% 22.15/22.37 inference(monotonicity,[status(thm)],[3324])).
% 22.15/22.37 tff(3326,plain,
% 22.15/22.37 (mult(mult(a, b), mult(mult(a, b), c)) = mult(mult(a, b), mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))),
% 22.15/22.37 inference(monotonicity,[status(thm)],[3207])).
% 22.15/22.37 tff(3327,plain,
% 22.15/22.37 (mult(mult(a, b), mult(mult(a, b), c)) = mult(mult(mult(a, b), c), mult(b, a))),
% 22.15/22.37 inference(transitivity,[status(thm)],[3326, 3325, 3323, 3320, 3297])).
% 22.15/22.37 tff(3328,plain,
% 22.15/22.37 (mult(mult(a, mult(mult(a, b), c)), b) = mult(mult(mult(a, b), c), mult(a, b))),
% 22.15/22.37 inference(transitivity,[status(thm)],[3285, 3210, 1097])).
% 22.15/22.37 tff(3329,plain,
% 22.15/22.37 ((mult(mult(a, mult(mult(a, b), c)), b) = mult(mult(a, b), mult(mult(a, b), c))) <=> (mult(mult(mult(a, b), c), mult(a, b)) = mult(mult(mult(a, b), c), mult(b, a)))),
% 22.15/22.37 inference(monotonicity,[status(thm)],[3328, 3327])).
% 22.15/22.37 tff(3330,plain,
% 22.15/22.37 ((mult(mult(a, mult(mult(a, b), c)), b) = mult(mult(a, b), mult(mult(a, b), c))) <=> (mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(a, b)))),
% 22.15/22.37 inference(transitivity,[status(thm)],[3329, 897])).
% 22.15/22.37 tff(3331,plain,
% 22.15/22.37 ((mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(a, b))) <=> (mult(mult(a, mult(mult(a, b), c)), b) = mult(mult(a, b), mult(mult(a, b), c)))),
% 22.15/22.37 inference(symmetry,[status(thm)],[3330])).
% 22.15/22.37 tff(3332,plain,
% 22.15/22.37 ((~(mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(a, b)))) <=> (~(mult(mult(a, mult(mult(a, b), c)), b) = mult(mult(a, b), mult(mult(a, b), c))))),
% 22.15/22.37 inference(monotonicity,[status(thm)],[3331])).
% 22.15/22.37 tff(3333,plain,
% 22.15/22.37 (~(mult(mult(a, mult(mult(a, b), c)), b) = mult(mult(a, b), mult(mult(a, b), c)))),
% 22.15/22.37 inference(modus_ponens,[status(thm)],[1064, 3332])).
% 22.15/22.37 tff(3334,plain,
% 22.15/22.37 (((~(mult(mult(a, mult(mult(a, b), c)), b) = mult(mult(a, b), mult(mult(a, b), c)))) | (~(mult(a, mult(mult(mult(a, b), c), b)) = mult(a, mult(b, mult(mult(a, b), c)))))) | (mult(mult(a, mult(mult(a, b), c)), b) = mult(mult(a, b), mult(mult(a, b), c)))),
% 22.15/22.37 inference(tautology,[status(thm)],[])).
% 22.15/22.37 tff(3335,plain,
% 22.15/22.37 ((~(mult(mult(a, mult(mult(a, b), c)), b) = mult(mult(a, b), mult(mult(a, b), c)))) | (~(mult(a, mult(mult(mult(a, b), c), b)) = mult(a, mult(b, mult(mult(a, b), c)))))),
% 22.15/22.37 inference(unit_resolution,[status(thm)],[3334, 3333])).
% 22.15/22.37 tff(3336,plain,
% 22.15/22.37 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, b), mult(mult(a, b), c)) = mult(a, mult(b, mult(mult(a, b), c))))) | (~(mult(mult(a, mult(mult(a, b), c)), b) = mult(a, mult(mult(mult(a, b), c), b)))))) | (~((~(mult(mult(a, mult(mult(a, b), c)), b) = mult(mult(a, b), mult(mult(a, b), c)))) | (~(mult(a, mult(mult(mult(a, b), c), b)) = mult(a, mult(b, mult(mult(a, b), c))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, b), mult(mult(a, b), c)) = mult(a, mult(b, mult(mult(a, b), c))))) | (~(mult(mult(a, mult(mult(a, b), c)), b) = mult(a, mult(mult(mult(a, b), c), b)))))) | (~((~(mult(mult(a, mult(mult(a, b), c)), b) = mult(mult(a, b), mult(mult(a, b), c)))) | (~(mult(a, mult(mult(mult(a, b), c), b)) = mult(a, mult(b, mult(mult(a, b), c))))))))),
% 22.15/22.37 inference(rewrite,[status(thm)],[])).
% 22.15/22.37 tff(3337,plain,
% 22.15/22.37 (((~((~(mult(mult(a, mult(mult(a, b), c)), b) = mult(mult(a, b), mult(mult(a, b), c)))) | (~(mult(a, mult(mult(mult(a, b), c), b)) = mult(a, mult(b, mult(mult(a, b), c))))))) | (~((~(mult(mult(a, b), mult(mult(a, b), c)) = mult(a, mult(b, mult(mult(a, b), c))))) | (~(mult(mult(a, mult(mult(a, b), c)), b) = mult(a, mult(mult(mult(a, b), c), b))))))) <=> ((~((~(mult(mult(a, b), mult(mult(a, b), c)) = mult(a, mult(b, mult(mult(a, b), c))))) | (~(mult(mult(a, mult(mult(a, b), c)), b) = mult(a, mult(mult(mult(a, b), c), b)))))) | (~((~(mult(mult(a, mult(mult(a, b), c)), b) = mult(mult(a, b), mult(mult(a, b), c)))) | (~(mult(a, mult(mult(mult(a, b), c), b)) = mult(a, mult(b, mult(mult(a, b), c))))))))),
% 22.15/22.37 inference(rewrite,[status(thm)],[])).
% 22.15/22.37 tff(3338,plain,
% 22.15/22.37 ((~((~(mult(mult(a, mult(mult(a, b), c)), b) = mult(a, mult(mult(mult(a, b), c), b)))) | (~(mult(mult(a, b), mult(mult(a, b), c)) = mult(a, mult(b, mult(mult(a, b), c))))))) <=> (~((~(mult(mult(a, b), mult(mult(a, b), c)) = mult(a, mult(b, mult(mult(a, b), c))))) | (~(mult(mult(a, mult(mult(a, b), c)), b) = mult(a, mult(mult(mult(a, b), c), b))))))),
% 22.15/22.37 inference(rewrite,[status(thm)],[])).
% 22.15/22.37 tff(3339,plain,
% 22.15/22.37 ((~((~(mult(mult(a, mult(mult(a, b), c)), b) = mult(mult(a, b), mult(mult(a, b), c)))) | (~(mult(a, mult(mult(mult(a, b), c), b)) = mult(a, mult(b, mult(mult(a, b), c))))))) <=> (~((~(mult(mult(a, mult(mult(a, b), c)), b) = mult(mult(a, b), mult(mult(a, b), c)))) | (~(mult(a, mult(mult(mult(a, b), c), b)) = mult(a, mult(b, mult(mult(a, b), c)))))))),
% 22.15/22.37 inference(rewrite,[status(thm)],[])).
% 22.15/22.37 tff(3340,plain,
% 22.15/22.37 (((~((~(mult(mult(a, mult(mult(a, b), c)), b) = mult(mult(a, b), mult(mult(a, b), c)))) | (~(mult(a, mult(mult(mult(a, b), c), b)) = mult(a, mult(b, mult(mult(a, b), c))))))) | (~((~(mult(mult(a, mult(mult(a, b), c)), b) = mult(a, mult(mult(mult(a, b), c), b)))) | (~(mult(mult(a, b), mult(mult(a, b), c)) = mult(a, mult(b, mult(mult(a, b), c)))))))) <=> ((~((~(mult(mult(a, mult(mult(a, b), c)), b) = mult(mult(a, b), mult(mult(a, b), c)))) | (~(mult(a, mult(mult(mult(a, b), c), b)) = mult(a, mult(b, mult(mult(a, b), c))))))) | (~((~(mult(mult(a, b), mult(mult(a, b), c)) = mult(a, mult(b, mult(mult(a, b), c))))) | (~(mult(mult(a, mult(mult(a, b), c)), b) = mult(a, mult(mult(mult(a, b), c), b)))))))),
% 22.15/22.37 inference(monotonicity,[status(thm)],[3339, 3338])).
% 22.15/22.37 tff(3341,plain,
% 22.15/22.37 (((~((~(mult(mult(a, mult(mult(a, b), c)), b) = mult(mult(a, b), mult(mult(a, b), c)))) | (~(mult(a, mult(mult(mult(a, b), c), b)) = mult(a, mult(b, mult(mult(a, b), c))))))) | (~((~(mult(mult(a, mult(mult(a, b), c)), b) = mult(a, mult(mult(mult(a, b), c), b)))) | (~(mult(mult(a, b), mult(mult(a, b), c)) = mult(a, mult(b, mult(mult(a, b), c)))))))) <=> ((~((~(mult(mult(a, b), mult(mult(a, b), c)) = mult(a, mult(b, mult(mult(a, b), c))))) | (~(mult(mult(a, mult(mult(a, b), c)), b) = mult(a, mult(mult(mult(a, b), c), b)))))) | (~((~(mult(mult(a, mult(mult(a, b), c)), b) = mult(mult(a, b), mult(mult(a, b), c)))) | (~(mult(a, mult(mult(mult(a, b), c), b)) = mult(a, mult(b, mult(mult(a, b), c))))))))),
% 22.15/22.37 inference(transitivity,[status(thm)],[3340, 3337])).
% 22.15/22.37 tff(3342,plain,
% 22.15/22.37 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, mult(mult(a, b), c)), b) = mult(mult(a, b), mult(mult(a, b), c)))) | (~(mult(a, mult(mult(mult(a, b), c), b)) = mult(a, mult(b, mult(mult(a, b), c))))))) | (~((~(mult(mult(a, mult(mult(a, b), c)), b) = mult(a, mult(mult(mult(a, b), c), b)))) | (~(mult(mult(a, b), mult(mult(a, b), c)) = mult(a, mult(b, mult(mult(a, b), c))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, b), mult(mult(a, b), c)) = mult(a, mult(b, mult(mult(a, b), c))))) | (~(mult(mult(a, mult(mult(a, b), c)), b) = mult(a, mult(mult(mult(a, b), c), b)))))) | (~((~(mult(mult(a, mult(mult(a, b), c)), b) = mult(mult(a, b), mult(mult(a, b), c)))) | (~(mult(a, mult(mult(mult(a, b), c), b)) = mult(a, mult(b, mult(mult(a, b), c)))))))))),
% 22.15/22.37 inference(monotonicity,[status(thm)],[3341])).
% 22.15/22.37 tff(3343,plain,
% 22.15/22.37 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, mult(mult(a, b), c)), b) = mult(mult(a, b), mult(mult(a, b), c)))) | (~(mult(a, mult(mult(mult(a, b), c), b)) = mult(a, mult(b, mult(mult(a, b), c))))))) | (~((~(mult(mult(a, mult(mult(a, b), c)), b) = mult(a, mult(mult(mult(a, b), c), b)))) | (~(mult(mult(a, b), mult(mult(a, b), c)) = mult(a, mult(b, mult(mult(a, b), c))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, b), mult(mult(a, b), c)) = mult(a, mult(b, mult(mult(a, b), c))))) | (~(mult(mult(a, mult(mult(a, b), c)), b) = mult(a, mult(mult(mult(a, b), c), b)))))) | (~((~(mult(mult(a, mult(mult(a, b), c)), b) = mult(mult(a, b), mult(mult(a, b), c)))) | (~(mult(a, mult(mult(mult(a, b), c), b)) = mult(a, mult(b, mult(mult(a, b), c))))))))),
% 22.15/22.37 inference(transitivity,[status(thm)],[3342, 3336])).
% 22.15/22.37 tff(3344,plain,
% 22.15/22.37 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, mult(mult(a, b), c)), b) = mult(mult(a, b), mult(mult(a, b), c)))) | (~(mult(a, mult(mult(mult(a, b), c), b)) = mult(a, mult(b, mult(mult(a, b), c))))))) | (~((~(mult(mult(a, mult(mult(a, b), c)), b) = mult(a, mult(mult(mult(a, b), c), b)))) | (~(mult(mult(a, b), mult(mult(a, b), c)) = mult(a, mult(b, mult(mult(a, b), c))))))))),
% 22.15/22.37 inference(quant_inst,[status(thm)],[])).
% 22.15/22.37 tff(3345,plain,
% 22.15/22.37 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, b), mult(mult(a, b), c)) = mult(a, mult(b, mult(mult(a, b), c))))) | (~(mult(mult(a, mult(mult(a, b), c)), b) = mult(a, mult(mult(mult(a, b), c), b)))))) | (~((~(mult(mult(a, mult(mult(a, b), c)), b) = mult(mult(a, b), mult(mult(a, b), c)))) | (~(mult(a, mult(mult(mult(a, b), c), b)) = mult(a, mult(b, mult(mult(a, b), c)))))))),
% 22.15/22.37 inference(modus_ponens,[status(thm)],[3344, 3343])).
% 22.15/22.37 tff(3346,plain,
% 22.15/22.37 ((~((~(mult(mult(a, b), mult(mult(a, b), c)) = mult(a, mult(b, mult(mult(a, b), c))))) | (~(mult(mult(a, mult(mult(a, b), c)), b) = mult(a, mult(mult(mult(a, b), c), b)))))) | (~((~(mult(mult(a, mult(mult(a, b), c)), b) = mult(mult(a, b), mult(mult(a, b), c)))) | (~(mult(a, mult(mult(mult(a, b), c), b)) = mult(a, mult(b, mult(mult(a, b), c)))))))),
% 22.15/22.37 inference(unit_resolution,[status(thm)],[3345, 27])).
% 22.15/22.37 tff(3347,plain,
% 22.15/22.37 (~((~(mult(mult(a, b), mult(mult(a, b), c)) = mult(a, mult(b, mult(mult(a, b), c))))) | (~(mult(mult(a, mult(mult(a, b), c)), b) = mult(a, mult(mult(mult(a, b), c), b)))))),
% 22.15/22.37 inference(unit_resolution,[status(thm)],[3346, 3335])).
% 22.15/22.37 tff(3348,plain,
% 22.15/22.37 (((~(mult(mult(a, b), mult(mult(a, b), c)) = mult(a, mult(b, mult(mult(a, b), c))))) | (~(mult(mult(a, mult(mult(a, b), c)), b) = mult(a, mult(mult(mult(a, b), c), b))))) | (mult(mult(a, mult(mult(a, b), c)), b) = mult(a, mult(mult(mult(a, b), c), b)))),
% 22.15/22.37 inference(tautology,[status(thm)],[])).
% 22.15/22.37 tff(3349,plain,
% 22.15/22.37 (mult(mult(a, mult(mult(a, b), c)), b) = mult(a, mult(mult(mult(a, b), c), b))),
% 22.15/22.37 inference(unit_resolution,[status(thm)],[3348, 3347])).
% 22.15/22.37 tff(3350,plain,
% 22.15/22.37 (mult(a, mult(mult(mult(a, b), c), b)) = mult(mult(a, mult(mult(a, b), c)), b)),
% 22.15/22.37 inference(symmetry,[status(thm)],[3349])).
% 22.15/22.38 tff(3351,plain,
% 22.15/22.38 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))), a), a) = mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))))),
% 22.15/22.38 inference(quant_inst,[status(thm)],[])).
% 22.15/22.38 tff(3352,plain,
% 22.15/22.38 (rd(mult(mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))), a), a) = mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c))))),
% 22.15/22.38 inference(unit_resolution,[status(thm)],[3351, 168])).
% 22.15/22.38 tff(3353,plain,
% 22.15/22.38 (mult(mult(mult(a, b), c), b) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), b)),
% 22.15/22.38 inference(monotonicity,[status(thm)],[3207])).
% 22.15/22.38 tff(3354,plain,
% 22.15/22.38 (mult(mult(mult(mult(a, b), c), b), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), b), a)),
% 22.15/22.38 inference(monotonicity,[status(thm)],[3353])).
% 22.15/22.38 tff(3355,plain,
% 22.15/22.38 (mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))),
% 22.15/22.38 inference(transitivity,[status(thm)],[3212, 1172, 1168])).
% 22.15/22.38 tff(3356,plain,
% 22.15/22.38 (mult(mult(a, b), mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a)) = mult(mult(a, b), mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))),
% 22.15/22.38 inference(monotonicity,[status(thm)],[3355])).
% 22.15/22.38 tff(3357,plain,
% 22.15/22.38 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, b), mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a)))),
% 22.15/22.38 inference(quant_inst,[status(thm)],[])).
% 22.15/22.38 tff(3358,plain,
% 22.15/22.38 (mult(mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, b), mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a))),
% 22.15/22.38 inference(unit_resolution,[status(thm)],[3357, 56])).
% 22.15/22.38 tff(3359,plain,
% 22.15/22.38 (mult(mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), b), a)),
% 22.15/22.38 inference(transitivity,[status(thm)],[3358, 3356, 3325, 3323, 3320, 3297, 1068, 3354])).
% 22.15/22.38 tff(3360,plain,
% 22.15/22.38 (rd(mult(mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))), a), a) = rd(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), b), a), a)),
% 22.15/22.38 inference(monotonicity,[status(thm)],[3359])).
% 22.15/22.38 tff(3361,plain,
% 22.15/22.38 (rd(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), b), a), a) = rd(mult(mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))), a), a)),
% 22.15/22.38 inference(symmetry,[status(thm)],[3360])).
% 22.15/22.38 tff(3362,plain,
% 22.15/22.38 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), b), a), a) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), b))),
% 22.15/22.38 inference(quant_inst,[status(thm)],[])).
% 22.15/22.38 tff(3363,plain,
% 22.15/22.38 (rd(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), b), a), a) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), b)),
% 22.15/22.38 inference(unit_resolution,[status(thm)],[3362, 168])).
% 22.15/22.38 tff(3364,plain,
% 22.15/22.38 (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), b) = rd(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), b), a), a)),
% 22.15/22.38 inference(symmetry,[status(thm)],[3363])).
% 22.15/22.38 tff(3365,plain,
% 22.15/22.38 (mult(mult(mult(a, b), c), b) = mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c))))),
% 22.15/22.38 inference(transitivity,[status(thm)],[3353, 3364, 3361, 3352])).
% 22.15/22.38 tff(3366,plain,
% 22.15/22.38 (mult(a, mult(mult(mult(a, b), c), b)) = mult(a, mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))))),
% 22.15/22.38 inference(monotonicity,[status(thm)],[3365])).
% 22.15/22.38 tff(3367,plain,
% 22.15/22.38 (mult(a, mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(mult(a, b), c), b))),
% 22.15/22.38 inference(symmetry,[status(thm)],[3366])).
% 22.15/22.38 tff(3368,plain,
% 22.15/22.38 ((mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a))) = mult(a, mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))))) <=> (mult(a, mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a))))),
% 22.22/22.38 inference(commutativity,[status(thm)],[])).
% 22.22/22.38 tff(3369,plain,
% 22.22/22.38 ((mult(a, mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a)))) <=> (mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a))) = mult(a, mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c))))))),
% 22.22/22.38 inference(symmetry,[status(thm)],[3368])).
% 22.22/22.38 tff(3370,plain,
% 22.22/22.38 (mult(mult(c, rd(mult(b, c), mult(a, c))), a) = mult(b, c)),
% 22.22/22.38 inference(transitivity,[status(thm)],[3251, 3258, 3255, 2224])).
% 22.22/22.38 tff(3371,plain,
% 22.22/22.38 (mult(mult(mult(c, rd(mult(b, c), mult(a, c))), a), b) = mult(mult(b, c), b)),
% 22.22/22.38 inference(monotonicity,[status(thm)],[3370])).
% 22.22/22.38 tff(3372,plain,
% 22.22/22.38 (mult(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), a), b), a) = mult(mult(mult(b, c), b), a)),
% 22.22/22.38 inference(monotonicity,[status(thm)],[3371])).
% 22.22/22.38 tff(3373,plain,
% 22.22/22.38 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), a), b), a) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a)))),
% 22.22/22.38 inference(quant_inst,[status(thm)],[])).
% 22.22/22.38 tff(3374,plain,
% 22.22/22.38 (mult(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), a), b), a) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a))),
% 22.22/22.38 inference(unit_resolution,[status(thm)],[3373, 56])).
% 22.22/22.38 tff(3375,plain,
% 22.22/22.38 (mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a)) = mult(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), a), b), a)),
% 22.22/22.38 inference(symmetry,[status(thm)],[3374])).
% 22.22/22.38 tff(3376,plain,
% 22.22/22.38 (mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a)) = mult(mult(mult(b, c), b), a)),
% 22.22/22.38 inference(transitivity,[status(thm)],[3375, 3372])).
% 22.22/22.38 tff(3377,plain,
% 22.22/22.38 (mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a))) = mult(a, mult(mult(mult(b, c), b), a))),
% 22.22/22.38 inference(monotonicity,[status(thm)],[3376])).
% 22.22/22.38 tff(3378,plain,
% 22.22/22.38 (mult(a, mult(a, mult(mult(b, c), b))) = mult(a, mult(mult(mult(a, b), c), b))),
% 22.22/22.38 inference(monotonicity,[status(thm)],[783])).
% 22.22/22.38 tff(3379,plain,
% 22.22/22.38 (mult(a, mult(mult(mult(a, b), c), b)) = mult(a, mult(a, mult(mult(b, c), b)))),
% 22.22/22.38 inference(symmetry,[status(thm)],[3378])).
% 22.22/22.38 tff(3380,plain,
% 22.22/22.38 (mult(a, mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c))))) = mult(a, mult(a, mult(mult(b, c), b)))),
% 22.22/22.38 inference(transitivity,[status(thm)],[3367, 3379])).
% 22.22/22.38 tff(3381,plain,
% 22.22/22.38 ((mult(a, mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a)))) <=> (mult(a, mult(a, mult(mult(b, c), b))) = mult(a, mult(mult(mult(b, c), b), a)))),
% 22.22/22.38 inference(monotonicity,[status(thm)],[3380, 3377])).
% 22.22/22.38 tff(3382,plain,
% 22.22/22.38 ((mult(a, mult(a, mult(mult(b, c), b))) = mult(a, mult(mult(mult(b, c), b), a))) <=> (mult(a, mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a))))),
% 22.22/22.38 inference(symmetry,[status(thm)],[3381])).
% 22.22/22.38 tff(3383,plain,
% 22.22/22.38 (((~(mult(mult(a, b), mult(mult(a, b), c)) = mult(a, mult(b, mult(mult(a, b), c))))) | (~(mult(mult(a, mult(mult(a, b), c)), b) = mult(a, mult(mult(mult(a, b), c), b))))) | (mult(mult(a, b), mult(mult(a, b), c)) = mult(a, mult(b, mult(mult(a, b), c))))),
% 22.22/22.38 inference(tautology,[status(thm)],[])).
% 22.22/22.38 tff(3384,plain,
% 22.22/22.38 (mult(mult(a, b), mult(mult(a, b), c)) = mult(a, mult(b, mult(mult(a, b), c)))),
% 22.22/22.38 inference(unit_resolution,[status(thm)],[3383, 3347])).
% 22.22/22.38 tff(3385,plain,
% 22.22/22.38 (mult(a, mult(b, mult(mult(a, b), c))) = mult(mult(a, b), mult(mult(a, b), c))),
% 22.22/22.38 inference(symmetry,[status(thm)],[3384])).
% 22.22/22.38 tff(3386,plain,
% 22.22/22.38 (b = mult(unit, b)),
% 22.22/22.38 inference(symmetry,[status(thm)],[184])).
% 22.22/22.38 tff(3387,plain,
% 22.22/22.38 (mult(b, mult(mult(a, b), c)) = mult(mult(unit, b), mult(mult(a, b), c))),
% 22.22/22.38 inference(monotonicity,[status(thm)],[3386])).
% 22.22/22.38 tff(3388,plain,
% 22.22/22.38 (mult(mult(unit, b), mult(mult(a, b), c)) = mult(b, mult(mult(a, b), c))),
% 22.22/22.38 inference(symmetry,[status(thm)],[3387])).
% 22.22/22.38 tff(3389,plain,
% 22.22/22.38 (mult(b, mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), c)) = mult(mult(unit, b), mult(mult(a, b), c))),
% 22.22/22.38 inference(monotonicity,[status(thm)],[3386, 214])).
% 22.22/22.38 tff(3390,plain,
% 22.22/22.38 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(b, mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), c)))),
% 22.22/22.38 inference(quant_inst,[status(thm)],[])).
% 22.22/22.38 tff(3391,plain,
% 22.22/22.38 (mult(mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(b, mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), c))),
% 22.22/22.38 inference(unit_resolution,[status(thm)],[3390, 56])).
% 22.22/22.38 tff(3392,plain,
% 22.22/22.38 ((mult(mult(b, c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)) = mult(mult(b, c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)))) <=> (mult(mult(b, c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(mult(b, c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)))),
% 22.22/22.38 inference(commutativity,[status(thm)],[])).
% 22.22/22.38 tff(3393,plain,
% 22.22/22.38 ((mult(mult(b, c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(mult(b, c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c))) <=> (mult(mult(b, c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)) = mult(mult(b, c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))),
% 22.22/22.38 inference(symmetry,[status(thm)],[3392])).
% 22.22/22.38 tff(3394,plain,
% 22.22/22.38 (ld(c, mult(c, mult(b, a))) = ld(c, mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)))),
% 22.22/22.38 inference(symmetry,[status(thm)],[3292])).
% 22.22/22.38 tff(3395,plain,
% 22.22/22.38 (mult(b, a) = mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)),
% 22.22/22.38 inference(transitivity,[status(thm)],[1473, 3394, 3294])).
% 22.22/22.38 tff(3396,plain,
% 22.22/22.38 (mult(mult(b, c), mult(b, a)) = mult(mult(b, c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c))),
% 22.22/22.38 inference(monotonicity,[status(thm)],[3395])).
% 22.22/22.38 tff(3397,plain,
% 22.22/22.38 (mult(mult(b, c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)) = mult(mult(b, c), mult(b, a))),
% 22.22/22.38 inference(symmetry,[status(thm)],[3396])).
% 22.22/22.38 tff(3398,plain,
% 22.22/22.38 (mult(mult(b, c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(mult(b, c), mult(a, b))),
% 22.22/22.38 inference(monotonicity,[status(thm)],[213])).
% 22.22/22.38 tff(3399,plain,
% 22.22/22.38 ((mult(mult(b, c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(mult(b, c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c))) <=> (mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a)))),
% 22.22/22.38 inference(monotonicity,[status(thm)],[3398, 3397])).
% 22.22/22.38 tff(3400,plain,
% 22.22/22.38 ((mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a))) <=> (mult(mult(b, c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(mult(b, c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)))),
% 22.22/22.38 inference(symmetry,[status(thm)],[3399])).
% 22.22/22.38 tff(3401,plain,
% 22.22/22.38 ((mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a))) <=> (mult(mult(b, c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)) = mult(mult(b, c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))),
% 22.22/22.38 inference(transitivity,[status(thm)],[3400, 3393])).
% 22.22/22.38 tff(3402,plain,
% 22.22/22.38 ((~(mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a)))) <=> (~(mult(mult(b, c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)) = mult(mult(b, c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)))))),
% 22.22/22.38 inference(monotonicity,[status(thm)],[3401])).
% 22.22/22.38 tff(3403,plain,
% 22.22/22.38 (~(mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a)))),
% 22.22/22.38 inference(unit_resolution,[status(thm)],[1192, 1064])).
% 22.22/22.38 tff(3404,plain,
% 22.22/22.38 (~(mult(mult(b, c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)) = mult(mult(b, c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))),
% 22.22/22.38 inference(modus_ponens,[status(thm)],[3403, 3402])).
% 22.22/22.38 tff(3405,plain,
% 22.22/22.38 (((~(mult(mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(mult(b, c), c), mult(mult(unit, ld(c, mult(a, b))), unit)))) | (~(mult(mult(b, c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)) = mult(mult(b, c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)))))) | (mult(mult(b, c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)) = mult(mult(b, c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))),
% 22.22/22.38 inference(tautology,[status(thm)],[])).
% 22.22/22.38 tff(3406,plain,
% 22.22/22.38 ((~(mult(mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(mult(b, c), c), mult(mult(unit, ld(c, mult(a, b))), unit)))) | (~(mult(mult(b, c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)) = mult(mult(b, c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)))))),
% 22.22/22.38 inference(unit_resolution,[status(thm)],[3405, 3404])).
% 22.22/22.38 tff(3407,plain,
% 22.22/22.38 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(b, c), c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(b, c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))) | (~(mult(mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(b, c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)))))) | (~((~(mult(mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(mult(b, c), c), mult(mult(unit, ld(c, mult(a, b))), unit)))) | (~(mult(mult(b, c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)) = mult(mult(b, c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(b, c), c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(b, c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))) | (~(mult(mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(b, c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)))))) | (~((~(mult(mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(mult(b, c), c), mult(mult(unit, ld(c, mult(a, b))), unit)))) | (~(mult(mult(b, c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)) = mult(mult(b, c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))))))),
% 22.22/22.38 inference(rewrite,[status(thm)],[])).
% 22.22/22.38 tff(3408,plain,
% 22.22/22.38 (((~((~(mult(mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(mult(b, c), c), mult(mult(unit, ld(c, mult(a, b))), unit)))) | (~(mult(mult(b, c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)) = mult(mult(b, c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))))) | (~((~(mult(mult(mult(b, c), c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(b, c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))) | (~(mult(mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(b, c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c))))))) <=> ((~((~(mult(mult(mult(b, c), c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(b, c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))) | (~(mult(mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(b, c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)))))) | (~((~(mult(mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(mult(b, c), c), mult(mult(unit, ld(c, mult(a, b))), unit)))) | (~(mult(mult(b, c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)) = mult(mult(b, c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))))))),
% 22.22/22.38 inference(rewrite,[status(thm)],[])).
% 22.22/22.38 tff(3409,plain,
% 22.22/22.38 ((~((~(mult(mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(b, c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)))) | (~(mult(mult(mult(b, c), c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(b, c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))))) <=> (~((~(mult(mult(mult(b, c), c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(b, c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))) | (~(mult(mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(b, c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c))))))),
% 22.22/22.39 inference(rewrite,[status(thm)],[])).
% 22.22/22.39 tff(3410,plain,
% 22.22/22.39 ((~((~(mult(mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(mult(b, c), c), mult(mult(unit, ld(c, mult(a, b))), unit)))) | (~(mult(mult(b, c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)) = mult(mult(b, c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))))) <=> (~((~(mult(mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(mult(b, c), c), mult(mult(unit, ld(c, mult(a, b))), unit)))) | (~(mult(mult(b, c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)) = mult(mult(b, c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)))))))),
% 22.22/22.39 inference(rewrite,[status(thm)],[])).
% 22.22/22.39 tff(3411,plain,
% 22.22/22.39 (((~((~(mult(mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(mult(b, c), c), mult(mult(unit, ld(c, mult(a, b))), unit)))) | (~(mult(mult(b, c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)) = mult(mult(b, c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))))) | (~((~(mult(mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(b, c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)))) | (~(mult(mult(mult(b, c), c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(b, c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)))))))) <=> ((~((~(mult(mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(mult(b, c), c), mult(mult(unit, ld(c, mult(a, b))), unit)))) | (~(mult(mult(b, c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)) = mult(mult(b, c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))))) | (~((~(mult(mult(mult(b, c), c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(b, c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))) | (~(mult(mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(b, c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)))))))),
% 22.22/22.39 inference(monotonicity,[status(thm)],[3410, 3409])).
% 22.22/22.39 tff(3412,plain,
% 22.22/22.39 (((~((~(mult(mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(mult(b, c), c), mult(mult(unit, ld(c, mult(a, b))), unit)))) | (~(mult(mult(b, c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)) = mult(mult(b, c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))))) | (~((~(mult(mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(b, c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)))) | (~(mult(mult(mult(b, c), c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(b, c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)))))))) <=> ((~((~(mult(mult(mult(b, c), c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(b, c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))) | (~(mult(mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(b, c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)))))) | (~((~(mult(mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(mult(b, c), c), mult(mult(unit, ld(c, mult(a, b))), unit)))) | (~(mult(mult(b, c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)) = mult(mult(b, c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))))))),
% 22.22/22.39 inference(transitivity,[status(thm)],[3411, 3408])).
% 22.22/22.39 tff(3413,plain,
% 22.22/22.39 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(mult(b, c), c), mult(mult(unit, ld(c, mult(a, b))), unit)))) | (~(mult(mult(b, c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)) = mult(mult(b, c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))))) | (~((~(mult(mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(b, c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)))) | (~(mult(mult(mult(b, c), c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(b, c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(b, c), c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(b, c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))) | (~(mult(mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(b, c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)))))) | (~((~(mult(mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(mult(b, c), c), mult(mult(unit, ld(c, mult(a, b))), unit)))) | (~(mult(mult(b, c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)) = mult(mult(b, c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)))))))))),
% 22.22/22.39 inference(monotonicity,[status(thm)],[3412])).
% 22.22/22.39 tff(3414,plain,
% 22.22/22.39 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(mult(b, c), c), mult(mult(unit, ld(c, mult(a, b))), unit)))) | (~(mult(mult(b, c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)) = mult(mult(b, c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))))) | (~((~(mult(mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(b, c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)))) | (~(mult(mult(mult(b, c), c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(b, c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(b, c), c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(b, c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))) | (~(mult(mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(b, c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)))))) | (~((~(mult(mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(mult(b, c), c), mult(mult(unit, ld(c, mult(a, b))), unit)))) | (~(mult(mult(b, c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)) = mult(mult(b, c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))))))),
% 22.22/22.39 inference(transitivity,[status(thm)],[3413, 3407])).
% 22.22/22.39 tff(3415,plain,
% 22.22/22.39 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(mult(b, c), c), mult(mult(unit, ld(c, mult(a, b))), unit)))) | (~(mult(mult(b, c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)) = mult(mult(b, c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))))) | (~((~(mult(mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(b, c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)))) | (~(mult(mult(mult(b, c), c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(b, c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))))))),
% 22.22/22.39 inference(quant_inst,[status(thm)],[])).
% 22.22/22.39 tff(3416,plain,
% 22.22/22.39 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(b, c), c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(b, c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))) | (~(mult(mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(b, c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)))))) | (~((~(mult(mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(mult(b, c), c), mult(mult(unit, ld(c, mult(a, b))), unit)))) | (~(mult(mult(b, c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)) = mult(mult(b, c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)))))))),
% 22.22/22.39 inference(modus_ponens,[status(thm)],[3415, 3414])).
% 22.22/22.39 tff(3417,plain,
% 22.22/22.39 ((~((~(mult(mult(mult(b, c), c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(b, c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))) | (~(mult(mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(b, c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)))))) | (~((~(mult(mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(mult(b, c), c), mult(mult(unit, ld(c, mult(a, b))), unit)))) | (~(mult(mult(b, c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)) = mult(mult(b, c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)))))))),
% 22.22/22.39 inference(unit_resolution,[status(thm)],[3416, 27])).
% 22.22/22.39 tff(3418,plain,
% 22.22/22.39 (~((~(mult(mult(mult(b, c), c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(b, c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))) | (~(mult(mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(b, c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)))))),
% 22.22/22.39 inference(unit_resolution,[status(thm)],[3417, 3406])).
% 22.22/22.39 tff(3419,plain,
% 22.22/22.39 (((~(mult(mult(mult(b, c), c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(b, c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))) | (~(mult(mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(b, c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c))))) | (mult(mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(b, c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)))),
% 22.22/22.39 inference(tautology,[status(thm)],[])).
% 22.22/22.39 tff(3420,plain,
% 22.22/22.39 (mult(mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(b, c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c))),
% 22.22/22.39 inference(unit_resolution,[status(thm)],[3419, 3418])).
% 22.22/22.39 tff(3421,plain,
% 22.22/22.39 (mult(mult(b, c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)) = mult(mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c)),
% 22.22/22.39 inference(symmetry,[status(thm)],[3420])).
% 22.22/22.39 tff(3422,plain,
% 22.22/22.39 (mult(mult(c, b), mult(b, a)) = mult(mult(b, c), mult(b, a))),
% 22.22/22.39 inference(monotonicity,[status(thm)],[241])).
% 22.22/22.39 tff(3423,plain,
% 22.22/22.39 (mult(c, mult(b, a)) = mult(mult(a, b), c)),
% 22.22/22.39 inference(transitivity,[status(thm)],[2300, 2298, 2831, 1799, 177, 161])).
% 22.22/22.39 tff(3424,plain,
% 22.22/22.39 (mult(mult(c, mult(b, a)), b) = mult(mult(mult(a, b), c), b)),
% 22.22/22.39 inference(monotonicity,[status(thm)],[3423])).
% 22.22/22.39 tff(3425,plain,
% 22.22/22.39 (mult(mult(mult(a, b), c), b) = mult(mult(c, mult(b, a)), b)),
% 22.22/22.39 inference(symmetry,[status(thm)],[3424])).
% 22.22/22.39 tff(3426,plain,
% 22.22/22.39 (mult(mult(c, b), a) = mult(mult(a, b), c)),
% 22.22/22.39 inference(transitivity,[status(thm)],[2298, 2831, 1799, 177, 161])).
% 22.22/22.39 tff(3427,plain,
% 22.22/22.39 (mult(mult(mult(c, b), a), b) = mult(mult(mult(a, b), c), b)),
% 22.22/22.39 inference(monotonicity,[status(thm)],[3426])).
% 22.22/22.39 tff(3428,plain,
% 22.22/22.39 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(c, b), a), b) = mult(c, mult(mult(b, a), b)))),
% 22.22/22.39 inference(quant_inst,[status(thm)],[])).
% 22.22/22.39 tff(3429,plain,
% 22.22/22.39 (mult(mult(mult(c, b), a), b) = mult(c, mult(mult(b, a), b))),
% 22.22/22.39 inference(unit_resolution,[status(thm)],[3428, 56])).
% 22.22/22.39 tff(3430,plain,
% 22.22/22.39 (mult(c, mult(mult(b, a), b)) = mult(mult(mult(c, b), a), b)),
% 22.22/22.39 inference(symmetry,[status(thm)],[3429])).
% 22.22/22.39 tff(3431,assumption,(~(mult(mult(c, b), mult(b, a)) = mult(c, mult(b, mult(b, a))))), introduced(assumption)).
% 22.22/22.39 tff(3432,plain,
% 22.22/22.39 (((~(mult(mult(c, b), mult(b, a)) = mult(c, mult(b, mult(b, a))))) | (~(mult(mult(c, mult(b, a)), b) = mult(c, mult(mult(b, a), b))))) | (mult(mult(c, b), mult(b, a)) = mult(c, mult(b, mult(b, a))))),
% 22.22/22.39 inference(tautology,[status(thm)],[])).
% 22.22/22.39 tff(3433,plain,
% 22.22/22.39 ((~(mult(mult(c, b), mult(b, a)) = mult(c, mult(b, mult(b, a))))) | (~(mult(mult(c, mult(b, a)), b) = mult(c, mult(mult(b, a), b))))),
% 22.22/22.39 inference(unit_resolution,[status(thm)],[3432, 3431])).
% 22.22/22.39 tff(3434,plain,
% 22.22/22.39 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(c, b), mult(b, a)) = mult(c, mult(b, mult(b, a))))) | (~(mult(mult(c, mult(b, a)), b) = mult(c, mult(mult(b, a), b)))))) | (~((~(mult(mult(c, b), mult(b, a)) = mult(mult(c, mult(b, a)), b))) | (~(mult(c, mult(b, mult(b, a))) = mult(c, mult(mult(b, a), b)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(c, b), mult(b, a)) = mult(c, mult(b, mult(b, a))))) | (~(mult(mult(c, mult(b, a)), b) = mult(c, mult(mult(b, a), b)))))) | (~((~(mult(mult(c, b), mult(b, a)) = mult(mult(c, mult(b, a)), b))) | (~(mult(c, mult(b, mult(b, a))) = mult(c, mult(mult(b, a), b)))))))),
% 22.22/22.39 inference(rewrite,[status(thm)],[])).
% 22.22/22.39 tff(3435,plain,
% 22.22/22.39 (((~((~(mult(mult(c, b), mult(b, a)) = mult(mult(c, mult(b, a)), b))) | (~(mult(c, mult(b, mult(b, a))) = mult(c, mult(mult(b, a), b)))))) | (~((~(mult(mult(c, b), mult(b, a)) = mult(c, mult(b, mult(b, a))))) | (~(mult(mult(c, mult(b, a)), b) = mult(c, mult(mult(b, a), b))))))) <=> ((~((~(mult(mult(c, b), mult(b, a)) = mult(c, mult(b, mult(b, a))))) | (~(mult(mult(c, mult(b, a)), b) = mult(c, mult(mult(b, a), b)))))) | (~((~(mult(mult(c, b), mult(b, a)) = mult(mult(c, mult(b, a)), b))) | (~(mult(c, mult(b, mult(b, a))) = mult(c, mult(mult(b, a), b)))))))),
% 22.22/22.39 inference(rewrite,[status(thm)],[])).
% 22.22/22.39 tff(3436,plain,
% 22.22/22.39 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(c, b), mult(b, a)) = mult(mult(c, mult(b, a)), b))) | (~(mult(c, mult(b, mult(b, a))) = mult(c, mult(mult(b, a), b)))))) | (~((~(mult(mult(c, b), mult(b, a)) = mult(c, mult(b, mult(b, a))))) | (~(mult(mult(c, mult(b, a)), b) = mult(c, mult(mult(b, a), b)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(c, b), mult(b, a)) = mult(c, mult(b, mult(b, a))))) | (~(mult(mult(c, mult(b, a)), b) = mult(c, mult(mult(b, a), b)))))) | (~((~(mult(mult(c, b), mult(b, a)) = mult(mult(c, mult(b, a)), b))) | (~(mult(c, mult(b, mult(b, a))) = mult(c, mult(mult(b, a), b))))))))),
% 22.22/22.39 inference(monotonicity,[status(thm)],[3435])).
% 22.22/22.39 tff(3437,plain,
% 22.22/22.39 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(c, b), mult(b, a)) = mult(mult(c, mult(b, a)), b))) | (~(mult(c, mult(b, mult(b, a))) = mult(c, mult(mult(b, a), b)))))) | (~((~(mult(mult(c, b), mult(b, a)) = mult(c, mult(b, mult(b, a))))) | (~(mult(mult(c, mult(b, a)), b) = mult(c, mult(mult(b, a), b)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(c, b), mult(b, a)) = mult(c, mult(b, mult(b, a))))) | (~(mult(mult(c, mult(b, a)), b) = mult(c, mult(mult(b, a), b)))))) | (~((~(mult(mult(c, b), mult(b, a)) = mult(mult(c, mult(b, a)), b))) | (~(mult(c, mult(b, mult(b, a))) = mult(c, mult(mult(b, a), b)))))))),
% 22.22/22.40 inference(transitivity,[status(thm)],[3436, 3434])).
% 22.22/22.40 tff(3438,plain,
% 22.22/22.40 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(c, b), mult(b, a)) = mult(mult(c, mult(b, a)), b))) | (~(mult(c, mult(b, mult(b, a))) = mult(c, mult(mult(b, a), b)))))) | (~((~(mult(mult(c, b), mult(b, a)) = mult(c, mult(b, mult(b, a))))) | (~(mult(mult(c, mult(b, a)), b) = mult(c, mult(mult(b, a), b)))))))),
% 22.22/22.40 inference(quant_inst,[status(thm)],[])).
% 22.22/22.40 tff(3439,plain,
% 22.22/22.40 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(c, b), mult(b, a)) = mult(c, mult(b, mult(b, a))))) | (~(mult(mult(c, mult(b, a)), b) = mult(c, mult(mult(b, a), b)))))) | (~((~(mult(mult(c, b), mult(b, a)) = mult(mult(c, mult(b, a)), b))) | (~(mult(c, mult(b, mult(b, a))) = mult(c, mult(mult(b, a), b))))))),
% 22.22/22.40 inference(modus_ponens,[status(thm)],[3438, 3437])).
% 22.22/22.40 tff(3440,plain,
% 22.22/22.40 ((~((~(mult(mult(c, b), mult(b, a)) = mult(c, mult(b, mult(b, a))))) | (~(mult(mult(c, mult(b, a)), b) = mult(c, mult(mult(b, a), b)))))) | (~((~(mult(mult(c, b), mult(b, a)) = mult(mult(c, mult(b, a)), b))) | (~(mult(c, mult(b, mult(b, a))) = mult(c, mult(mult(b, a), b))))))),
% 22.22/22.40 inference(unit_resolution,[status(thm)],[3439, 27])).
% 22.22/22.40 tff(3441,plain,
% 22.22/22.40 (~((~(mult(mult(c, b), mult(b, a)) = mult(mult(c, mult(b, a)), b))) | (~(mult(c, mult(b, mult(b, a))) = mult(c, mult(mult(b, a), b)))))),
% 22.22/22.40 inference(unit_resolution,[status(thm)],[3440, 3433])).
% 22.22/22.40 tff(3442,plain,
% 22.22/22.40 (((~(mult(mult(c, b), mult(b, a)) = mult(mult(c, mult(b, a)), b))) | (~(mult(c, mult(b, mult(b, a))) = mult(c, mult(mult(b, a), b))))) | (mult(c, mult(b, mult(b, a))) = mult(c, mult(mult(b, a), b)))),
% 22.22/22.40 inference(tautology,[status(thm)],[])).
% 22.22/22.40 tff(3443,plain,
% 22.22/22.40 (mult(c, mult(b, mult(b, a))) = mult(c, mult(mult(b, a), b))),
% 22.22/22.40 inference(unit_resolution,[status(thm)],[3442, 3441])).
% 22.22/22.40 tff(3444,plain,
% 22.22/22.40 (mult(c, mult(b, mult(b, a))) = mult(mult(c, mult(b, a)), b)),
% 22.22/22.40 inference(transitivity,[status(thm)],[3443, 3430, 3427, 3425])).
% 22.22/22.40 tff(3445,plain,
% 22.22/22.40 ((mult(mult(c, b), mult(b, a)) = mult(c, mult(b, mult(b, a)))) <=> (mult(mult(c, b), mult(b, a)) = mult(mult(c, mult(b, a)), b))),
% 22.22/22.40 inference(monotonicity,[status(thm)],[3444])).
% 22.22/22.40 tff(3446,plain,
% 22.22/22.40 ((mult(mult(c, b), mult(b, a)) = mult(mult(c, mult(b, a)), b)) <=> (mult(mult(c, b), mult(b, a)) = mult(c, mult(b, mult(b, a))))),
% 22.22/22.40 inference(symmetry,[status(thm)],[3445])).
% 22.22/22.40 tff(3447,plain,
% 22.22/22.40 (((~(mult(mult(c, b), mult(b, a)) = mult(mult(c, mult(b, a)), b))) | (~(mult(c, mult(b, mult(b, a))) = mult(c, mult(mult(b, a), b))))) | (mult(mult(c, b), mult(b, a)) = mult(mult(c, mult(b, a)), b))),
% 22.22/22.40 inference(tautology,[status(thm)],[])).
% 22.22/22.40 tff(3448,plain,
% 22.22/22.40 (mult(mult(c, b), mult(b, a)) = mult(mult(c, mult(b, a)), b)),
% 22.22/22.40 inference(unit_resolution,[status(thm)],[3447, 3441])).
% 22.22/22.40 tff(3449,plain,
% 22.22/22.40 (mult(mult(c, b), mult(b, a)) = mult(c, mult(b, mult(b, a)))),
% 22.22/22.40 inference(modus_ponens,[status(thm)],[3448, 3446])).
% 22.22/22.40 tff(3450,plain,
% 22.22/22.40 ($false),
% 22.22/22.40 inference(unit_resolution,[status(thm)],[3431, 3449])).
% 22.22/22.40 tff(3451,plain,((mult(mult(c, b), mult(b, a)) = mult(c, mult(b, mult(b, a)))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit))))) | (~(mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (~(mult(mult(c, b), a) = mult(c, mult(b, a))))), inference(lemma,lemma(discharge,[]))).
% 22.22/22.40 tff(3452,plain,
% 22.22/22.40 (mult(mult(c, b), mult(b, a)) = mult(c, mult(b, mult(b, a)))),
% 22.22/22.40 inference(unit_resolution,[status(thm)],[3451, 286, 97, 2299, 1799])).
% 22.22/22.40 tff(3453,plain,
% 22.22/22.40 (mult(c, mult(b, mult(b, a))) = mult(mult(c, b), mult(b, a))),
% 22.22/22.40 inference(symmetry,[status(thm)],[3452])).
% 22.22/22.40 tff(3454,plain,
% 22.22/22.40 (mult(b, a) = mult(a, b)),
% 22.22/22.40 inference(transitivity,[status(thm)],[939, 393, 396])).
% 22.22/22.40 tff(3455,plain,
% 22.22/22.40 (mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, c), b), mult(a, b))),
% 22.22/22.40 inference(monotonicity,[status(thm)],[227, 3454])).
% 22.22/22.40 tff(3456,plain,
% 22.22/22.40 (mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(a, b))),
% 22.22/22.40 inference(transitivity,[status(thm)],[3455, 949])).
% 22.22/22.40 tff(3457,plain,
% 22.22/22.40 ($false),
% 22.22/22.40 inference(unit_resolution,[status(thm)],[1064, 3456])).
% 22.22/22.40 tff(3458,plain,((~(mult(b, mult(a, b)) = mult(b, mult(b, a)))) | (mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(a, b)))), inference(lemma,lemma(discharge,[]))).
% 22.22/22.40 tff(3459,plain,
% 22.22/22.40 (~(mult(b, mult(a, b)) = mult(b, mult(b, a)))),
% 22.22/22.40 inference(unit_resolution,[status(thm)],[3458, 1064])).
% 22.22/22.40 tff(3460,plain,
% 22.22/22.40 ((~(mult(mult(b, a), b) = mult(mult(b, b), a))) | (~(mult(b, mult(a, b)) = mult(b, mult(b, a))))),
% 22.22/22.40 inference(unit_resolution,[status(thm)],[413, 3459])).
% 22.22/22.40 tff(3461,plain,
% 22.22/22.40 (~((~(mult(mult(b, a), b) = mult(b, mult(a, b)))) | (~(mult(mult(b, b), a) = mult(b, mult(b, a)))))),
% 22.22/22.40 inference(unit_resolution,[status(thm)],[418, 3460])).
% 22.22/22.40 tff(3462,plain,
% 22.22/22.40 (mult(mult(b, b), a) = mult(b, mult(b, a))),
% 22.22/22.40 inference(unit_resolution,[status(thm)],[422, 3461])).
% 22.22/22.40 tff(3463,plain,
% 22.22/22.40 (mult(unit, mult(mult(mult(b, unit), b), a)) = mult(b, mult(b, a))),
% 22.22/22.40 inference(transitivity,[status(thm)],[466, 435, 3462])).
% 22.22/22.40 tff(3464,plain,
% 22.22/22.40 (mult(c, mult(unit, mult(mult(mult(b, unit), b), a))) = mult(c, mult(b, mult(b, a)))),
% 22.22/22.40 inference(monotonicity,[status(thm)],[3463])).
% 22.22/22.40 tff(3465,plain,
% 22.22/22.40 (mult(c, mult(unit, mult(mult(mult(b, unit), b), a))) = mult(b, mult(mult(a, b), c))),
% 22.22/22.40 inference(transitivity,[status(thm)],[3464, 3453, 3422, 3396, 3421, 3391, 3389, 3388])).
% 22.22/22.40 tff(3466,plain,
% 22.22/22.40 (mult(a, mult(c, mult(unit, mult(mult(mult(b, unit), b), a)))) = mult(a, mult(b, mult(mult(a, b), c)))),
% 22.22/22.40 inference(monotonicity,[status(thm)],[3465])).
% 22.22/22.40 tff(3467,plain,
% 22.22/22.40 (mult(c, mult(b, mult(b, a))) = mult(c, mult(unit, mult(mult(mult(b, unit), b), a)))),
% 22.22/22.40 inference(symmetry,[status(thm)],[3464])).
% 22.22/22.40 tff(3468,plain,
% 22.22/22.40 (mult(mult(b, c), mult(b, a)) = mult(mult(c, b), mult(b, a))),
% 22.22/22.40 inference(symmetry,[status(thm)],[3422])).
% 22.22/22.40 tff(3469,plain,
% 22.22/22.40 ((~(mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a))) | (~(mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a))))),
% 22.22/22.40 inference(unit_resolution,[status(thm)],[1194, 3403])).
% 22.22/22.40 tff(3470,plain,
% 22.22/22.40 (~((~(mult(mult(mult(b, c), a), b) = mult(mult(b, c), mult(a, b)))) | (~(mult(mult(mult(b, c), b), a) = mult(mult(b, c), mult(b, a)))))),
% 22.22/22.40 inference(unit_resolution,[status(thm)],[1205, 3469])).
% 22.22/22.40 tff(3471,plain,
% 22.22/22.40 (mult(mult(mult(b, c), b), a) = mult(mult(b, c), mult(b, a))),
% 22.22/22.40 inference(unit_resolution,[status(thm)],[1207, 3470])).
% 22.22/22.40 tff(3472,plain,
% 22.22/22.40 (mult(mult(mult(b, c), b), a) = mult(c, mult(unit, mult(mult(mult(b, unit), b), a)))),
% 22.22/22.40 inference(transitivity,[status(thm)],[3471, 3468, 3452, 3467])).
% 22.22/22.40 tff(3473,plain,
% 22.22/22.40 (mult(a, mult(mult(mult(b, c), b), a)) = mult(a, mult(c, mult(unit, mult(mult(mult(b, unit), b), a))))),
% 22.22/22.40 inference(monotonicity,[status(thm)],[3472])).
% 22.22/22.40 tff(3474,plain,
% 22.22/22.40 (mult(a, mult(mult(mult(b, c), b), a)) = mult(mult(mult(a, b), c), mult(b, a))),
% 22.22/22.40 inference(transitivity,[status(thm)],[3473, 3466, 3385, 3326, 3325, 3323, 3320, 3297])).
% 22.22/22.40 tff(3475,plain,
% 22.22/22.40 (mult(a, mult(a, mult(mult(b, c), b))) = mult(mult(mult(a, b), c), mult(a, b))),
% 22.22/22.40 inference(transitivity,[status(thm)],[3378, 3350, 3285, 3210, 1097])).
% 22.22/22.40 tff(3476,plain,
% 22.22/22.40 ((mult(a, mult(a, mult(mult(b, c), b))) = mult(a, mult(mult(mult(b, c), b), a))) <=> (mult(mult(mult(a, b), c), mult(a, b)) = mult(mult(mult(a, b), c), mult(b, a)))),
% 22.22/22.40 inference(monotonicity,[status(thm)],[3475, 3474])).
% 22.22/22.40 tff(3477,plain,
% 22.22/22.40 ((mult(a, mult(a, mult(mult(b, c), b))) = mult(a, mult(mult(mult(b, c), b), a))) <=> (mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(a, b)))),
% 22.22/22.40 inference(transitivity,[status(thm)],[3476, 897])).
% 22.22/22.40 tff(3478,plain,
% 22.22/22.40 ((mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(a, b))) <=> (mult(a, mult(a, mult(mult(b, c), b))) = mult(a, mult(mult(mult(b, c), b), a)))),
% 22.22/22.40 inference(symmetry,[status(thm)],[3477])).
% 22.22/22.40 tff(3479,plain,
% 22.22/22.40 ((mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(a, b))) <=> (mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a))) = mult(a, mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c))))))),
% 22.22/22.40 inference(transitivity,[status(thm)],[3478, 3382, 3369])).
% 22.22/22.40 tff(3480,plain,
% 22.22/22.40 ((~(mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(a, b)))) <=> (~(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a))) = mult(a, mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))))))),
% 22.22/22.40 inference(monotonicity,[status(thm)],[3479])).
% 22.22/22.40 tff(3481,plain,
% 22.22/22.40 (~(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a))) = mult(a, mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c))))))),
% 22.22/22.40 inference(modus_ponens,[status(thm)],[1064, 3480])).
% 22.22/22.40 tff(3482,plain,
% 22.22/22.40 (((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(mult(a, b), a)) = mult(mult(a, mult(mult(a, b), a)), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a))) = mult(a, mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))))))) | (mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a))) = mult(a, mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c))))))),
% 22.22/22.40 inference(tautology,[status(thm)],[])).
% 22.22/22.40 tff(3483,plain,
% 22.22/22.40 ((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(mult(a, b), a)) = mult(mult(a, mult(mult(a, b), a)), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a))) = mult(a, mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))))))),
% 22.22/22.40 inference(unit_resolution,[status(thm)],[3482, 3481])).
% 22.22/22.40 tff(3484,plain,
% 22.22/22.40 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, mult(mult(a, b), a)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(mult(a, b), a)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a))))))) | (~((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(mult(a, b), a)) = mult(mult(a, mult(mult(a, b), a)), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a))) = mult(a, mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c))))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, mult(mult(a, b), a)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(mult(a, b), a)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a))))))) | (~((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(mult(a, b), a)) = mult(mult(a, mult(mult(a, b), a)), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a))) = mult(a, mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c))))))))))),
% 22.22/22.40 inference(rewrite,[status(thm)],[])).
% 22.22/22.40 tff(3485,plain,
% 22.22/22.40 (((~((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(mult(a, b), a)) = mult(mult(a, mult(mult(a, b), a)), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a))) = mult(a, mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c))))))))) | (~((~(mult(mult(a, mult(mult(a, b), a)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(mult(a, b), a)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a)))))))) <=> ((~((~(mult(mult(a, mult(mult(a, b), a)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(mult(a, b), a)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a))))))) | (~((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(mult(a, b), a)) = mult(mult(a, mult(mult(a, b), a)), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a))) = mult(a, mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c))))))))))),
% 22.22/22.40 inference(rewrite,[status(thm)],[])).
% 22.22/22.40 tff(3486,plain,
% 22.22/22.40 ((~((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(mult(a, b), a)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a))))) | (~(mult(mult(a, mult(mult(a, b), a)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c))))))))) <=> (~((~(mult(mult(a, mult(mult(a, b), a)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(mult(a, b), a)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a)))))))),
% 22.22/22.40 inference(rewrite,[status(thm)],[])).
% 22.22/22.40 tff(3487,plain,
% 22.22/22.40 ((~((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(mult(a, b), a)) = mult(mult(a, mult(mult(a, b), a)), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a))) = mult(a, mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c))))))))) <=> (~((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(mult(a, b), a)) = mult(mult(a, mult(mult(a, b), a)), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a))) = mult(a, mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))))))))),
% 22.22/22.40 inference(rewrite,[status(thm)],[])).
% 22.22/22.40 tff(3488,plain,
% 22.22/22.40 (((~((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(mult(a, b), a)) = mult(mult(a, mult(mult(a, b), a)), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a))) = mult(a, mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c))))))))) | (~((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(mult(a, b), a)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a))))) | (~(mult(mult(a, mult(mult(a, b), a)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))))))))) <=> ((~((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(mult(a, b), a)) = mult(mult(a, mult(mult(a, b), a)), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a))) = mult(a, mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c))))))))) | (~((~(mult(mult(a, mult(mult(a, b), a)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(mult(a, b), a)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a))))))))),
% 22.22/22.41 inference(monotonicity,[status(thm)],[3487, 3486])).
% 22.22/22.41 tff(3489,plain,
% 22.22/22.41 (((~((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(mult(a, b), a)) = mult(mult(a, mult(mult(a, b), a)), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a))) = mult(a, mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c))))))))) | (~((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(mult(a, b), a)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a))))) | (~(mult(mult(a, mult(mult(a, b), a)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))))))))) <=> ((~((~(mult(mult(a, mult(mult(a, b), a)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(mult(a, b), a)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a))))))) | (~((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(mult(a, b), a)) = mult(mult(a, mult(mult(a, b), a)), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a))) = mult(a, mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c))))))))))),
% 22.22/22.41 inference(transitivity,[status(thm)],[3488, 3485])).
% 22.22/22.41 tff(3490,plain,
% 22.22/22.41 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(mult(a, b), a)) = mult(mult(a, mult(mult(a, b), a)), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a))) = mult(a, mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c))))))))) | (~((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(mult(a, b), a)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a))))) | (~(mult(mult(a, mult(mult(a, b), a)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c))))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, mult(mult(a, b), a)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(mult(a, b), a)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a))))))) | (~((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(mult(a, b), a)) = mult(mult(a, mult(mult(a, b), a)), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a))) = mult(a, mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))))))))))),
% 22.22/22.41 inference(monotonicity,[status(thm)],[3489])).
% 22.22/22.41 tff(3491,plain,
% 22.22/22.41 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(mult(a, b), a)) = mult(mult(a, mult(mult(a, b), a)), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a))) = mult(a, mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c))))))))) | (~((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(mult(a, b), a)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a))))) | (~(mult(mult(a, mult(mult(a, b), a)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c))))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, mult(mult(a, b), a)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(mult(a, b), a)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a))))))) | (~((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(mult(a, b), a)) = mult(mult(a, mult(mult(a, b), a)), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a))) = mult(a, mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c))))))))))),
% 22.22/22.41 inference(transitivity,[status(thm)],[3490, 3484])).
% 22.22/22.41 tff(3492,plain,
% 22.22/22.41 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(mult(a, b), a)) = mult(mult(a, mult(mult(a, b), a)), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a))) = mult(a, mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c))))))))) | (~((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(mult(a, b), a)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a))))) | (~(mult(mult(a, mult(mult(a, b), a)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c))))))))))),
% 22.22/22.41 inference(quant_inst,[status(thm)],[])).
% 22.22/22.41 tff(3493,plain,
% 22.22/22.41 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, mult(mult(a, b), a)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(mult(a, b), a)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a))))))) | (~((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(mult(a, b), a)) = mult(mult(a, mult(mult(a, b), a)), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a))) = mult(a, mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))))))))),
% 22.22/22.41 inference(modus_ponens,[status(thm)],[3492, 3491])).
% 22.22/22.41 tff(3494,plain,
% 22.22/22.41 ((~((~(mult(mult(a, mult(mult(a, b), a)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(mult(a, b), a)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a))))))) | (~((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(mult(a, b), a)) = mult(mult(a, mult(mult(a, b), a)), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a))) = mult(a, mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))))))))),
% 22.22/22.41 inference(unit_resolution,[status(thm)],[3493, 27])).
% 22.22/22.41 tff(3495,plain,
% 22.22/22.41 (~((~(mult(mult(a, mult(mult(a, b), a)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(mult(a, b), a)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a))))))),
% 22.22/22.41 inference(unit_resolution,[status(thm)],[3494, 3483])).
% 22.22/22.41 tff(3496,plain,
% 22.22/22.41 (((~(mult(mult(a, mult(mult(a, b), a)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(mult(a, b), a)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a)))))) | (mult(mult(a, mult(mult(a, b), a)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c))))))),
% 22.22/22.41 inference(tautology,[status(thm)],[])).
% 22.22/22.41 tff(3497,plain,
% 22.22/22.41 (mult(mult(a, mult(mult(a, b), a)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))))),
% 22.22/22.41 inference(unit_resolution,[status(thm)],[3496, 3495])).
% 22.22/22.41 tff(3498,plain,
% 22.22/22.41 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(b, c), mult(mult(b, c), mult(a, mult(a, b)))) = mult(a, mult(a, b)))),
% 22.22/22.41 inference(quant_inst,[status(thm)],[])).
% 22.22/22.41 tff(3499,plain,
% 22.22/22.41 (ld(mult(b, c), mult(mult(b, c), mult(a, mult(a, b)))) = mult(a, mult(a, b))),
% 22.22/22.41 inference(unit_resolution,[status(thm)],[3498, 7])).
% 22.22/22.41 tff(3500,plain,
% 22.22/22.41 (mult(mult(b, c), a) = mult(mult(a, c), b)),
% 22.22/22.41 inference(transitivity,[status(thm)],[3205, 1799, 177])).
% 22.22/22.41 tff(3501,plain,
% 22.22/22.41 (mult(mult(mult(b, c), a), mult(a, b)) = mult(mult(mult(a, c), b), mult(a, b))),
% 22.22/22.41 inference(monotonicity,[status(thm)],[3500])).
% 22.22/22.41 tff(3502,plain,
% 22.22/22.41 (mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(mult(b, c), a), mult(a, b))),
% 22.22/22.41 inference(symmetry,[status(thm)],[3501])).
% 22.22/22.41 tff(3503,plain,
% 22.22/22.41 (mult(mult(mult(a, b), c), mult(a, b)) = mult(mult(mult(a, c), b), mult(a, b))),
% 22.22/22.41 inference(symmetry,[status(thm)],[3298])).
% 22.22/22.41 tff(3504,plain,
% 22.22/22.41 (mult(mult(mult(b, c), a), unit) = mult(mult(mult(a, c), b), unit)),
% 22.22/22.41 inference(monotonicity,[status(thm)],[3500])).
% 22.22/22.41 tff(3505,plain,
% 22.22/22.41 (mult(mult(mult(b, c), a), unit) = mult(mult(a, b), c)),
% 22.22/22.41 inference(transitivity,[status(thm)],[3504, 864, 858, 856, 161])).
% 22.22/22.41 tff(3506,plain,
% 22.22/22.41 (mult(mult(mult(mult(b, c), a), unit), a) = mult(mult(mult(a, b), c), a)),
% 22.22/22.41 inference(monotonicity,[status(thm)],[3505])).
% 22.22/22.41 tff(3507,plain,
% 22.22/22.41 (mult(mult(b, c), mult(mult(a, unit), a)) = mult(mult(mult(mult(b, c), a), unit), a)),
% 22.22/22.41 inference(symmetry,[status(thm)],[1254])).
% 22.22/22.41 tff(3508,plain,
% 22.22/22.41 (mult(mult(b, c), mult(a, a)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a)),
% 22.22/22.41 inference(transitivity,[status(thm)],[1558, 3507, 3506, 3208])).
% 22.22/22.41 tff(3509,plain,
% 22.22/22.41 (mult(mult(mult(b, c), mult(a, a)), b) = mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), b)),
% 22.22/22.41 inference(monotonicity,[status(thm)],[3508])).
% 22.22/22.41 tff(3510,assumption,(mult(mult(mult(b, c), mult(a, a)), b) = mult(mult(b, c), mult(mult(a, a), b))), introduced(assumption)).
% 22.22/22.41 tff(3511,plain,
% 22.22/22.41 (mult(mult(b, c), mult(mult(a, a), b)) = mult(mult(mult(b, c), mult(a, a)), b)),
% 22.22/22.41 inference(symmetry,[status(thm)],[3510])).
% 22.22/22.41 tff(3512,plain,
% 22.22/22.41 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(a, a), b), c), c) = mult(mult(a, a), b))),
% 22.22/22.41 inference(quant_inst,[status(thm)],[])).
% 22.22/22.41 tff(3513,plain,
% 22.22/22.41 (rd(mult(mult(mult(a, a), b), c), c) = mult(mult(a, a), b)),
% 22.22/22.41 inference(unit_resolution,[status(thm)],[3512, 168])).
% 22.22/22.41 tff(3514,plain,
% 22.22/22.41 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(a, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(a, mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), c)))),
% 22.22/22.41 inference(quant_inst,[status(thm)],[])).
% 22.22/22.41 tff(3515,plain,
% 22.22/22.41 (mult(mult(mult(a, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(a, mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), c))),
% 22.22/22.41 inference(unit_resolution,[status(thm)],[3514, 56])).
% 22.22/22.41 tff(3516,plain,
% 22.22/22.41 (mult(a, mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), c)) = mult(mult(mult(a, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c)),
% 22.22/22.41 inference(symmetry,[status(thm)],[3515])).
% 22.22/22.41 tff(3517,plain,
% 22.22/22.41 (mult(a, mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), c)) = mult(a, mult(mult(a, b), c))),
% 22.22/22.41 inference(monotonicity,[status(thm)],[214])).
% 22.22/22.41 tff(3518,plain,
% 22.22/22.41 (mult(a, mult(mult(a, b), c)) = mult(a, mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), c))),
% 22.22/22.41 inference(symmetry,[status(thm)],[3517])).
% 22.22/22.41 tff(3519,plain,
% 22.22/22.41 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), b), b) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a))),
% 22.22/22.41 inference(quant_inst,[status(thm)],[])).
% 22.22/22.41 tff(3520,plain,
% 22.22/22.41 (rd(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), b), b) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a)),
% 22.22/22.41 inference(unit_resolution,[status(thm)],[3519, 168])).
% 22.22/22.41 tff(3521,plain,
% 22.22/22.41 ((~(mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(a, b)))) <=> (~(mult(a, mult(a, mult(mult(b, c), b))) = mult(a, mult(mult(mult(b, c), b), a))))),
% 22.22/22.41 inference(monotonicity,[status(thm)],[3478])).
% 22.22/22.41 tff(3522,plain,
% 22.22/22.41 (~(mult(a, mult(a, mult(mult(b, c), b))) = mult(a, mult(mult(mult(b, c), b), a)))),
% 22.22/22.41 inference(modus_ponens,[status(thm)],[1064, 3521])).
% 22.22/22.41 tff(3523,plain,
% 22.22/22.41 (((~(mult(mult(a, a), mult(mult(b, c), b)) = mult(mult(a, mult(mult(b, c), b)), a))) | (~(mult(a, mult(a, mult(mult(b, c), b))) = mult(a, mult(mult(mult(b, c), b), a))))) | (mult(a, mult(a, mult(mult(b, c), b))) = mult(a, mult(mult(mult(b, c), b), a)))),
% 22.22/22.41 inference(tautology,[status(thm)],[])).
% 22.22/22.41 tff(3524,plain,
% 22.22/22.41 ((~(mult(mult(a, a), mult(mult(b, c), b)) = mult(mult(a, mult(mult(b, c), b)), a))) | (~(mult(a, mult(a, mult(mult(b, c), b))) = mult(a, mult(mult(mult(b, c), b), a))))),
% 22.22/22.41 inference(unit_resolution,[status(thm)],[3523, 3522])).
% 22.22/22.41 tff(3525,plain,
% 22.22/22.41 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, a), mult(mult(b, c), b)) = mult(mult(a, mult(mult(b, c), b)), a))) | (~(mult(a, mult(a, mult(mult(b, c), b))) = mult(a, mult(mult(mult(b, c), b), a)))))) | (~((~(mult(mult(a, a), mult(mult(b, c), b)) = mult(a, mult(a, mult(mult(b, c), b))))) | (~(mult(mult(a, mult(mult(b, c), b)), a) = mult(a, mult(mult(mult(b, c), b), a)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, a), mult(mult(b, c), b)) = mult(mult(a, mult(mult(b, c), b)), a))) | (~(mult(a, mult(a, mult(mult(b, c), b))) = mult(a, mult(mult(mult(b, c), b), a)))))) | (~((~(mult(mult(a, a), mult(mult(b, c), b)) = mult(a, mult(a, mult(mult(b, c), b))))) | (~(mult(mult(a, mult(mult(b, c), b)), a) = mult(a, mult(mult(mult(b, c), b), a)))))))),
% 22.22/22.41 inference(rewrite,[status(thm)],[])).
% 22.22/22.41 tff(3526,plain,
% 22.22/22.41 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, a), mult(mult(b, c), b)) = mult(mult(a, mult(mult(b, c), b)), a))) | (~(mult(a, mult(a, mult(mult(b, c), b))) = mult(a, mult(mult(mult(b, c), b), a)))))) | (~((~(mult(mult(a, a), mult(mult(b, c), b)) = mult(a, mult(a, mult(mult(b, c), b))))) | (~(mult(mult(a, mult(mult(b, c), b)), a) = mult(a, mult(mult(mult(b, c), b), a)))))))),
% 22.22/22.41 inference(quant_inst,[status(thm)],[])).
% 22.22/22.41 tff(3527,plain,
% 22.22/22.41 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, a), mult(mult(b, c), b)) = mult(mult(a, mult(mult(b, c), b)), a))) | (~(mult(a, mult(a, mult(mult(b, c), b))) = mult(a, mult(mult(mult(b, c), b), a)))))) | (~((~(mult(mult(a, a), mult(mult(b, c), b)) = mult(a, mult(a, mult(mult(b, c), b))))) | (~(mult(mult(a, mult(mult(b, c), b)), a) = mult(a, mult(mult(mult(b, c), b), a))))))),
% 22.22/22.42 inference(modus_ponens,[status(thm)],[3526, 3525])).
% 22.22/22.42 tff(3528,plain,
% 22.22/22.42 ((~((~(mult(mult(a, a), mult(mult(b, c), b)) = mult(mult(a, mult(mult(b, c), b)), a))) | (~(mult(a, mult(a, mult(mult(b, c), b))) = mult(a, mult(mult(mult(b, c), b), a)))))) | (~((~(mult(mult(a, a), mult(mult(b, c), b)) = mult(a, mult(a, mult(mult(b, c), b))))) | (~(mult(mult(a, mult(mult(b, c), b)), a) = mult(a, mult(mult(mult(b, c), b), a))))))),
% 22.22/22.42 inference(unit_resolution,[status(thm)],[3527, 27])).
% 22.22/22.42 tff(3529,plain,
% 22.22/22.42 (~((~(mult(mult(a, a), mult(mult(b, c), b)) = mult(a, mult(a, mult(mult(b, c), b))))) | (~(mult(mult(a, mult(mult(b, c), b)), a) = mult(a, mult(mult(mult(b, c), b), a)))))),
% 22.22/22.42 inference(unit_resolution,[status(thm)],[3528, 3524])).
% 22.22/22.42 tff(3530,plain,
% 22.22/22.42 (((~(mult(mult(a, a), mult(mult(b, c), b)) = mult(a, mult(a, mult(mult(b, c), b))))) | (~(mult(mult(a, mult(mult(b, c), b)), a) = mult(a, mult(mult(mult(b, c), b), a))))) | (mult(mult(a, a), mult(mult(b, c), b)) = mult(a, mult(a, mult(mult(b, c), b))))),
% 22.22/22.42 inference(tautology,[status(thm)],[])).
% 22.22/22.42 tff(3531,plain,
% 22.22/22.42 (mult(mult(a, a), mult(mult(b, c), b)) = mult(a, mult(a, mult(mult(b, c), b)))),
% 22.22/22.42 inference(unit_resolution,[status(thm)],[3530, 3529])).
% 22.22/22.42 tff(3532,plain,
% 22.22/22.42 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(a, a), b), c), b) = mult(mult(a, a), mult(mult(b, c), b)))),
% 22.22/22.42 inference(quant_inst,[status(thm)],[])).
% 22.22/22.42 tff(3533,plain,
% 22.22/22.42 (mult(mult(mult(mult(a, a), b), c), b) = mult(mult(a, a), mult(mult(b, c), b))),
% 22.22/22.42 inference(unit_resolution,[status(thm)],[3532, 56])).
% 22.22/22.42 tff(3534,plain,
% 22.22/22.42 (mult(mult(mult(mult(a, a), b), c), b) = mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), b)),
% 22.22/22.42 inference(transitivity,[status(thm)],[3533, 3531, 3378, 3350, 3285])).
% 22.22/22.42 tff(3535,plain,
% 22.22/22.42 (rd(mult(mult(mult(mult(a, a), b), c), b), b) = rd(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), b), b)),
% 22.22/22.42 inference(monotonicity,[status(thm)],[3534])).
% 22.22/22.42 tff(3536,plain,
% 22.22/22.42 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(mult(a, a), b), c), b), b) = mult(mult(mult(a, a), b), c))),
% 22.22/22.42 inference(quant_inst,[status(thm)],[])).
% 22.22/22.42 tff(3537,plain,
% 22.22/22.42 (rd(mult(mult(mult(mult(a, a), b), c), b), b) = mult(mult(mult(a, a), b), c)),
% 22.22/22.42 inference(unit_resolution,[status(thm)],[3536, 168])).
% 22.22/22.42 tff(3538,plain,
% 22.22/22.42 (mult(mult(mult(a, a), b), c) = rd(mult(mult(mult(mult(a, a), b), c), b), b)),
% 22.22/22.42 inference(symmetry,[status(thm)],[3537])).
% 22.22/22.42 tff(3539,plain,
% 22.22/22.42 (mult(mult(mult(a, a), b), c) = mult(mult(mult(a, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c)),
% 22.22/22.42 inference(transitivity,[status(thm)],[3538, 3535, 3520, 3282, 3281, 3218, 3216, 3518, 3516])).
% 22.22/22.42 tff(3540,plain,
% 22.22/22.42 (rd(mult(mult(mult(a, a), b), c), c) = rd(mult(mult(mult(a, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c), c)),
% 22.22/22.42 inference(monotonicity,[status(thm)],[3539])).
% 22.22/22.42 tff(3541,plain,
% 22.22/22.42 (rd(mult(mult(mult(a, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c), c) = rd(mult(mult(mult(a, a), b), c), c)),
% 22.22/22.42 inference(symmetry,[status(thm)],[3540])).
% 22.22/22.42 tff(3542,plain,
% 22.22/22.42 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(a, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c), c) = mult(mult(a, c), mult(mult(unit, ld(c, mult(a, b))), unit)))),
% 22.22/22.42 inference(quant_inst,[status(thm)],[])).
% 22.22/22.42 tff(3543,plain,
% 22.22/22.42 (rd(mult(mult(mult(a, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c), c) = mult(mult(a, c), mult(mult(unit, ld(c, mult(a, b))), unit))),
% 22.22/22.42 inference(unit_resolution,[status(thm)],[3542, 168])).
% 22.22/22.42 tff(3544,plain,
% 22.22/22.42 (mult(mult(a, c), mult(mult(unit, ld(c, mult(a, b))), unit)) = rd(mult(mult(mult(a, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c), c)),
% 22.22/22.42 inference(symmetry,[status(thm)],[3543])).
% 22.22/22.42 tff(3545,plain,
% 22.22/22.42 (mult(mult(a, c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(a, a), b)),
% 22.22/22.42 inference(transitivity,[status(thm)],[3544, 3541, 3513])).
% 22.22/22.42 tff(3546,plain,
% 22.22/22.42 (mult(mult(b, c), mult(mult(a, c), mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(mult(b, c), mult(mult(a, a), b))),
% 22.22/22.42 inference(monotonicity,[status(thm)],[3545])).
% 22.22/22.42 tff(3547,plain,
% 22.22/22.42 (mult(mult(b, c), mult(mult(a, c), mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(mult(b, c), mult(a, mult(a, b)))),
% 22.22/22.42 inference(transitivity,[status(thm)],[3546, 3511, 3509, 3210, 1097, 3503, 3502, 2070])).
% 22.22/22.42 tff(3548,plain,
% 22.22/22.42 (ld(mult(b, c), mult(mult(b, c), mult(mult(a, c), mult(mult(unit, ld(c, mult(a, b))), unit)))) = ld(mult(b, c), mult(mult(b, c), mult(a, mult(a, b))))),
% 22.22/22.42 inference(monotonicity,[status(thm)],[3547])).
% 22.22/22.42 tff(3549,plain,
% 22.22/22.42 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(b, c), mult(mult(b, c), mult(mult(a, c), mult(mult(unit, ld(c, mult(a, b))), unit)))) = mult(mult(a, c), mult(mult(unit, ld(c, mult(a, b))), unit)))),
% 22.22/22.42 inference(quant_inst,[status(thm)],[])).
% 22.22/22.42 tff(3550,plain,
% 22.22/22.42 (ld(mult(b, c), mult(mult(b, c), mult(mult(a, c), mult(mult(unit, ld(c, mult(a, b))), unit)))) = mult(mult(a, c), mult(mult(unit, ld(c, mult(a, b))), unit))),
% 22.22/22.42 inference(unit_resolution,[status(thm)],[3549, 7])).
% 22.22/22.42 tff(3551,plain,
% 22.22/22.42 (mult(mult(a, c), mult(mult(unit, ld(c, mult(a, b))), unit)) = ld(mult(b, c), mult(mult(b, c), mult(mult(a, c), mult(mult(unit, ld(c, mult(a, b))), unit))))),
% 22.22/22.42 inference(symmetry,[status(thm)],[3550])).
% 22.22/22.42 tff(3552,plain,
% 22.22/22.42 (mult(mult(a, c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(a, mult(a, b))),
% 22.22/22.42 inference(transitivity,[status(thm)],[3551, 3548, 3499])).
% 22.22/22.42 tff(3553,plain,
% 22.22/22.42 (mult(mult(mult(a, c), mult(mult(unit, ld(c, mult(a, b))), unit)), a) = mult(mult(a, mult(a, b)), a)),
% 22.22/22.42 inference(monotonicity,[status(thm)],[3552])).
% 22.22/22.42 tff(3554,plain,
% 22.22/22.42 (mult(mult(a, a), b) = rd(mult(mult(mult(a, a), b), c), c)),
% 22.22/22.42 inference(symmetry,[status(thm)],[3513])).
% 22.22/22.42 tff(3555,plain,
% 22.22/22.42 (mult(mult(a, a), b) = mult(mult(a, c), mult(mult(unit, ld(c, mult(a, b))), unit))),
% 22.22/22.42 inference(transitivity,[status(thm)],[3554, 3540, 3543])).
% 22.22/22.42 tff(3556,plain,
% 22.22/22.42 (mult(mult(mult(a, a), b), a) = mult(mult(mult(a, c), mult(mult(unit, ld(c, mult(a, b))), unit)), a)),
% 22.22/22.42 inference(monotonicity,[status(thm)],[3555])).
% 22.22/22.42 tff(3557,plain,
% 22.22/22.42 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(a, a), b), a) = mult(a, mult(mult(a, b), a)))),
% 22.22/22.42 inference(quant_inst,[status(thm)],[])).
% 22.22/22.42 tff(3558,plain,
% 22.22/22.42 (mult(mult(mult(a, a), b), a) = mult(a, mult(mult(a, b), a))),
% 22.22/22.42 inference(unit_resolution,[status(thm)],[3557, 56])).
% 22.22/22.42 tff(3559,plain,
% 22.22/22.42 (mult(a, mult(mult(a, b), a)) = mult(mult(mult(a, a), b), a)),
% 22.22/22.42 inference(symmetry,[status(thm)],[3558])).
% 22.22/22.42 tff(3560,plain,
% 22.22/22.42 (mult(a, mult(mult(a, b), a)) = mult(mult(a, mult(a, b)), a)),
% 22.22/22.42 inference(transitivity,[status(thm)],[3559, 3556, 3553])).
% 22.22/22.42 tff(3561,plain,
% 22.22/22.42 (mult(mult(a, mult(mult(a, b), a)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, mult(a, b)), a), mult(c, rd(mult(b, c), mult(a, c))))),
% 22.22/22.42 inference(monotonicity,[status(thm)],[3560])).
% 22.22/22.42 tff(3562,plain,
% 22.22/22.42 (mult(mult(mult(a, mult(a, b)), a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(mult(a, b), a)), mult(c, rd(mult(b, c), mult(a, c))))),
% 22.22/22.42 inference(symmetry,[status(thm)],[3561])).
% 22.22/22.42 tff(3563,plain,
% 22.22/22.42 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(mult(a, b), a), a))) = mult(mult(mult(a, b), a), a))),
% 22.22/22.42 inference(quant_inst,[status(thm)],[])).
% 22.22/22.42 tff(3564,plain,
% 22.22/22.42 (ld(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(mult(a, b), a), a))) = mult(mult(mult(a, b), a), a)),
% 22.22/22.42 inference(unit_resolution,[status(thm)],[3563, 7])).
% 22.22/22.42 tff(3565,assumption,(mult(mult(mult(a, a), mult(a, b)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))), mult(a, b))), introduced(assumption)).
% 22.22/22.42 tff(3566,plain,
% 22.22/22.42 (mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, unit), a))),
% 22.22/22.42 inference(monotonicity,[status(thm)],[520])).
% 22.22/22.42 tff(3567,plain,
% 22.22/22.42 (mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, unit), a)) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, a))),
% 22.22/22.42 inference(symmetry,[status(thm)],[3566])).
% 22.22/22.42 tff(3568,plain,
% 22.22/22.42 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), a), unit), a) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, unit), a)))),
% 22.22/22.42 inference(quant_inst,[status(thm)],[])).
% 22.22/22.42 tff(3569,plain,
% 22.22/22.42 (mult(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), a), unit), a) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, unit), a))),
% 22.22/22.42 inference(unit_resolution,[status(thm)],[3568, 56])).
% 22.22/22.42 tff(3570,plain,
% 22.22/22.42 (mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(unit, a), unit)) = mult(mult(c, rd(mult(b, c), mult(a, c))), a)),
% 22.22/22.42 inference(monotonicity,[status(thm)],[507])).
% 22.22/22.42 tff(3571,plain,
% 22.22/22.42 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), unit), a), unit) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(unit, a), unit)))),
% 22.22/22.42 inference(quant_inst,[status(thm)],[])).
% 22.22/22.42 tff(3572,plain,
% 22.22/22.42 (mult(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), unit), a), unit) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(unit, a), unit))),
% 22.22/22.42 inference(unit_resolution,[status(thm)],[3571, 56])).
% 22.22/22.42 tff(3573,plain,
% 22.22/22.42 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(c, unit), rd(mult(b, c), mult(a, c))), unit) = mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))),
% 22.22/22.42 inference(quant_inst,[status(thm)],[])).
% 22.22/22.42 tff(3574,plain,
% 22.22/22.42 (mult(mult(mult(c, unit), rd(mult(b, c), mult(a, c))), unit) = mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))),
% 22.22/22.42 inference(unit_resolution,[status(thm)],[3573, 56])).
% 22.22/22.42 tff(3575,plain,
% 22.22/22.42 (mult(mult(c, unit), rd(mult(b, c), mult(a, c))) = mult(c, rd(mult(b, c), mult(a, c)))),
% 22.22/22.42 inference(monotonicity,[status(thm)],[206])).
% 22.22/22.42 tff(3576,plain,
% 22.22/22.42 (mult(c, rd(mult(b, c), mult(a, c))) = mult(mult(c, unit), rd(mult(b, c), mult(a, c)))),
% 22.22/22.42 inference(symmetry,[status(thm)],[3575])).
% 22.22/22.42 tff(3577,plain,
% 22.22/22.42 (mult(mult(c, rd(mult(b, c), mult(a, c))), unit) = mult(mult(mult(c, unit), rd(mult(b, c), mult(a, c))), unit)),
% 22.22/22.42 inference(monotonicity,[status(thm)],[3576])).
% 22.22/22.42 tff(3578,plain,
% 22.22/22.42 (mult(mult(c, rd(mult(b, c), mult(a, c))), unit) = mult(c, rd(mult(b, c), mult(a, c)))),
% 22.22/22.42 inference(transitivity,[status(thm)],[3577, 3574, 2218])).
% 22.22/22.42 tff(3579,plain,
% 22.22/22.42 (mult(mult(mult(c, rd(mult(b, c), mult(a, c))), unit), a) = mult(mult(c, rd(mult(b, c), mult(a, c))), a)),
% 22.22/22.42 inference(monotonicity,[status(thm)],[3578])).
% 22.22/22.42 tff(3580,plain,
% 22.22/22.42 (mult(mult(c, rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(c, rd(mult(b, c), mult(a, c))), unit), a)),
% 22.22/22.42 inference(symmetry,[status(thm)],[3579])).
% 22.22/22.42 tff(3581,plain,
% 22.22/22.42 (mult(mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit), a) = mult(mult(mult(c, rd(mult(b, c), mult(a, c))), unit), a)),
% 22.22/22.42 inference(transitivity,[status(thm)],[3252, 3580])).
% 22.22/22.42 tff(3582,plain,
% 22.22/22.42 (mult(mult(mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit), a), unit) = mult(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), unit), a), unit)),
% 22.22/22.42 inference(monotonicity,[status(thm)],[3581])).
% 22.22/22.42 tff(3583,plain,
% 22.22/22.42 (mult(mult(mult(c, rd(mult(b, c), mult(a, c))), a), unit) = mult(mult(mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit), a), unit)),
% 22.22/22.42 inference(monotonicity,[status(thm)],[3251])).
% 22.22/22.42 tff(3584,plain,
% 22.22/22.42 (mult(mult(mult(c, rd(mult(b, c), mult(a, c))), a), unit) = mult(b, c)),
% 22.22/22.42 inference(transitivity,[status(thm)],[3583, 3582, 3572, 3570, 3251, 3258, 3255, 2224])).
% 22.22/22.42 tff(3585,plain,
% 22.22/22.42 (mult(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), a), unit), a) = mult(mult(b, c), a)),
% 22.22/22.42 inference(monotonicity,[status(thm)],[3584])).
% 22.22/22.42 tff(3586,plain,
% 22.22/22.42 (mult(mult(b, c), a) = mult(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), a), unit), a)),
% 22.22/22.42 inference(symmetry,[status(thm)],[3585])).
% 22.22/22.42 tff(3587,plain,
% 22.22/22.42 (mult(mult(a, c), b) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, a))),
% 22.22/22.42 inference(transitivity,[status(thm)],[405, 1800, 3206, 3586, 3569, 3567])).
% 22.22/22.42 tff(3588,plain,
% 22.22/22.42 (mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, a)), mult(a, b))),
% 22.22/22.42 inference(monotonicity,[status(thm)],[3587])).
% 22.22/22.42 tff(3589,plain,
% 22.22/22.42 (mult(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, a)), mult(a, b)) = mult(mult(mult(a, c), b), mult(a, b))),
% 22.22/22.42 inference(symmetry,[status(thm)],[3588])).
% 22.22/22.42 tff(3590,assumption,(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, a)), mult(a, b)) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, a), mult(a, b)))), introduced(assumption)).
% 22.22/22.42 tff(3591,plain,
% 22.22/22.42 (mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, a), mult(a, b))) = mult(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, a)), mult(a, b))),
% 22.22/22.42 inference(symmetry,[status(thm)],[3590])).
% 22.22/22.42 tff(3592,plain,
% 22.22/22.42 (mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), b) = mult(mult(mult(mult(a, b), c), a), b)),
% 22.22/22.42 inference(monotonicity,[status(thm)],[3282])).
% 22.22/22.42 tff(3593,plain,
% 22.22/22.42 (mult(a, mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a)) = mult(mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))), a)),
% 22.22/22.42 inference(symmetry,[status(thm)],[3218])).
% 22.22/22.42 tff(3594,plain,
% 22.22/22.42 (mult(a, mult(mult(a, b), c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a)),
% 22.22/22.42 inference(transitivity,[status(thm)],[3215, 3593, 3280, 3208])).
% 22.22/22.42 tff(3595,plain,
% 22.22/22.42 (mult(mult(a, mult(mult(a, b), c)), b) = mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), b)),
% 22.22/22.42 inference(monotonicity,[status(thm)],[3594])).
% 22.22/22.42 tff(3596,plain,
% 22.22/22.42 (mult(mult(mult(a, b), c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(mult(mult(a, b), c), mult(a, b))),
% 22.22/22.42 inference(transitivity,[status(thm)],[3299, 949])).
% 22.22/22.42 tff(3597,plain,
% 22.22/22.42 ((mult(mult(mult(a, b), c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)) = mult(mult(mult(a, b), c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)))) <=> (mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(a, b)))),
% 22.22/22.42 inference(monotonicity,[status(thm)],[3297, 3596])).
% 22.22/22.42 tff(3598,plain,
% 22.22/22.42 ((mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(a, b))) <=> (mult(mult(mult(a, b), c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)) = mult(mult(mult(a, b), c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))),
% 22.22/22.42 inference(symmetry,[status(thm)],[3597])).
% 22.22/22.42 tff(3599,plain,
% 22.22/22.42 ((~(mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(a, b)))) <=> (~(mult(mult(mult(a, b), c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)) = mult(mult(mult(a, b), c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)))))),
% 22.22/22.42 inference(monotonicity,[status(thm)],[3598])).
% 22.22/22.42 tff(3600,plain,
% 22.22/22.42 (~(mult(mult(mult(a, b), c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)) = mult(mult(mult(a, b), c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))),
% 22.22/22.42 inference(modus_ponens,[status(thm)],[1064, 3599])).
% 22.22/22.42 tff(3601,plain,
% 22.22/22.42 ((~(mult(mult(mult(mult(a, b), c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(mult(mult(a, b), c), c), mult(mult(unit, ld(c, mult(a, b))), unit)))) | (~(mult(mult(mult(a, b), c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)) = mult(mult(mult(a, b), c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)))))),
% 22.22/22.42 inference(unit_resolution,[status(thm)],[3305, 3600])).
% 22.22/22.42 tff(3602,plain,
% 22.22/22.42 (~((~(mult(mult(mult(mult(a, b), c), c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(mult(a, b), c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))) | (~(mult(mult(mult(mult(a, b), c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(mult(a, b), c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)))))),
% 22.22/22.43 inference(unit_resolution,[status(thm)],[3317, 3601])).
% 22.22/22.43 tff(3603,plain,
% 22.22/22.43 (mult(mult(mult(mult(a, b), c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(mult(a, b), c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c))),
% 22.22/22.43 inference(unit_resolution,[status(thm)],[3319, 3602])).
% 22.22/22.43 tff(3604,plain,
% 22.22/22.43 (mult(mult(a, b), mult(mult(a, b), c)) = mult(mult(mult(a, b), c), mult(b, a))),
% 22.22/22.43 inference(transitivity,[status(thm)],[3326, 3325, 3323, 3603, 3297])).
% 22.22/22.43 tff(3605,plain,
% 22.22/22.43 (mult(mult(a, mult(mult(a, b), c)), b) = mult(mult(mult(a, b), c), mult(a, b))),
% 22.22/22.43 inference(transitivity,[status(thm)],[3595, 3592, 1097])).
% 22.22/22.43 tff(3606,plain,
% 22.22/22.43 ((mult(mult(a, mult(mult(a, b), c)), b) = mult(mult(a, b), mult(mult(a, b), c))) <=> (mult(mult(mult(a, b), c), mult(a, b)) = mult(mult(mult(a, b), c), mult(b, a)))),
% 22.22/22.43 inference(monotonicity,[status(thm)],[3605, 3604])).
% 22.22/22.43 tff(3607,plain,
% 22.22/22.43 ((mult(mult(a, mult(mult(a, b), c)), b) = mult(mult(a, b), mult(mult(a, b), c))) <=> (mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(a, b)))),
% 22.22/22.43 inference(transitivity,[status(thm)],[3606, 897])).
% 22.22/22.43 tff(3608,plain,
% 22.22/22.43 ((mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(a, b))) <=> (mult(mult(a, mult(mult(a, b), c)), b) = mult(mult(a, b), mult(mult(a, b), c)))),
% 22.22/22.43 inference(symmetry,[status(thm)],[3607])).
% 22.22/22.43 tff(3609,plain,
% 22.22/22.43 ((~(mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(a, b)))) <=> (~(mult(mult(a, mult(mult(a, b), c)), b) = mult(mult(a, b), mult(mult(a, b), c))))),
% 22.22/22.43 inference(monotonicity,[status(thm)],[3608])).
% 22.22/22.43 tff(3610,plain,
% 22.22/22.43 (~(mult(mult(a, mult(mult(a, b), c)), b) = mult(mult(a, b), mult(mult(a, b), c)))),
% 22.22/22.43 inference(modus_ponens,[status(thm)],[1064, 3609])).
% 22.22/22.43 tff(3611,plain,
% 22.22/22.43 ((~(mult(mult(a, mult(mult(a, b), c)), b) = mult(mult(a, b), mult(mult(a, b), c)))) | (~(mult(a, mult(mult(mult(a, b), c), b)) = mult(a, mult(b, mult(mult(a, b), c)))))),
% 22.22/22.43 inference(unit_resolution,[status(thm)],[3334, 3610])).
% 22.22/22.43 tff(3612,plain,
% 22.22/22.43 (~((~(mult(mult(a, b), mult(mult(a, b), c)) = mult(a, mult(b, mult(mult(a, b), c))))) | (~(mult(mult(a, mult(mult(a, b), c)), b) = mult(a, mult(mult(mult(a, b), c), b)))))),
% 22.22/22.43 inference(unit_resolution,[status(thm)],[3346, 3611])).
% 22.22/22.43 tff(3613,plain,
% 22.22/22.43 (mult(mult(a, mult(mult(a, b), c)), b) = mult(a, mult(mult(mult(a, b), c), b))),
% 22.22/22.43 inference(unit_resolution,[status(thm)],[3348, 3612])).
% 22.22/22.43 tff(3614,plain,
% 22.22/22.43 (mult(a, mult(mult(mult(a, b), c), b)) = mult(mult(a, mult(mult(a, b), c)), b)),
% 22.22/22.43 inference(symmetry,[status(thm)],[3613])).
% 22.22/22.43 tff(3615,plain,
% 22.22/22.43 (mult(mult(a, b), mult(mult(a, b), c)) = mult(a, mult(b, mult(mult(a, b), c)))),
% 22.22/22.43 inference(unit_resolution,[status(thm)],[3383, 3612])).
% 22.22/22.43 tff(3616,plain,
% 22.22/22.43 (mult(a, mult(b, mult(mult(a, b), c))) = mult(mult(a, b), mult(mult(a, b), c))),
% 22.22/22.43 inference(symmetry,[status(thm)],[3615])).
% 22.22/22.43 tff(3617,plain,
% 22.22/22.43 (mult(a, mult(mult(mult(b, c), b), a)) = mult(mult(mult(a, b), c), mult(b, a))),
% 22.22/22.43 inference(transitivity,[status(thm)],[3473, 3466, 3616, 3326, 3325, 3323, 3603, 3297])).
% 22.22/22.43 tff(3618,plain,
% 22.22/22.43 (mult(a, mult(a, mult(mult(b, c), b))) = mult(mult(mult(a, b), c), mult(a, b))),
% 22.22/22.43 inference(transitivity,[status(thm)],[3378, 3614, 3595, 3592, 1097])).
% 22.22/22.43 tff(3619,plain,
% 22.22/22.43 ((mult(a, mult(a, mult(mult(b, c), b))) = mult(a, mult(mult(mult(b, c), b), a))) <=> (mult(mult(mult(a, b), c), mult(a, b)) = mult(mult(mult(a, b), c), mult(b, a)))),
% 22.22/22.43 inference(monotonicity,[status(thm)],[3618, 3617])).
% 22.22/22.43 tff(3620,plain,
% 22.22/22.43 ((mult(a, mult(a, mult(mult(b, c), b))) = mult(a, mult(mult(mult(b, c), b), a))) <=> (mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(a, b)))),
% 22.22/22.43 inference(transitivity,[status(thm)],[3619, 897])).
% 22.22/22.43 tff(3621,plain,
% 22.22/22.43 ((mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(a, b))) <=> (mult(a, mult(a, mult(mult(b, c), b))) = mult(a, mult(mult(mult(b, c), b), a)))),
% 22.22/22.43 inference(symmetry,[status(thm)],[3620])).
% 22.22/22.43 tff(3622,plain,
% 22.22/22.43 ((~(mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(a, b)))) <=> (~(mult(a, mult(a, mult(mult(b, c), b))) = mult(a, mult(mult(mult(b, c), b), a))))),
% 22.22/22.43 inference(monotonicity,[status(thm)],[3621])).
% 22.22/22.43 tff(3623,plain,
% 22.22/22.43 (~(mult(a, mult(a, mult(mult(b, c), b))) = mult(a, mult(mult(mult(b, c), b), a)))),
% 22.22/22.43 inference(modus_ponens,[status(thm)],[1064, 3622])).
% 22.22/22.43 tff(3624,plain,
% 22.22/22.43 ((~(mult(mult(a, a), mult(mult(b, c), b)) = mult(mult(a, mult(mult(b, c), b)), a))) | (~(mult(a, mult(a, mult(mult(b, c), b))) = mult(a, mult(mult(mult(b, c), b), a))))),
% 22.22/22.43 inference(unit_resolution,[status(thm)],[3523, 3623])).
% 22.22/22.43 tff(3625,plain,
% 22.22/22.43 (~((~(mult(mult(a, a), mult(mult(b, c), b)) = mult(a, mult(a, mult(mult(b, c), b))))) | (~(mult(mult(a, mult(mult(b, c), b)), a) = mult(a, mult(mult(mult(b, c), b), a)))))),
% 22.22/22.43 inference(unit_resolution,[status(thm)],[3528, 3624])).
% 22.22/22.43 tff(3626,plain,
% 22.22/22.43 (mult(mult(a, a), mult(mult(b, c), b)) = mult(a, mult(a, mult(mult(b, c), b)))),
% 22.22/22.43 inference(unit_resolution,[status(thm)],[3530, 3625])).
% 22.22/22.43 tff(3627,plain,
% 22.22/22.43 (mult(mult(mult(mult(a, a), b), c), b) = mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), b)),
% 22.22/22.43 inference(transitivity,[status(thm)],[3533, 3626, 3378, 3614, 3595])).
% 22.22/22.43 tff(3628,plain,
% 22.22/22.43 (rd(mult(mult(mult(mult(a, a), b), c), b), b) = rd(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), b), b)),
% 22.22/22.43 inference(monotonicity,[status(thm)],[3627])).
% 22.22/22.43 tff(3629,plain,
% 22.22/22.43 (mult(mult(mult(a, a), b), c) = mult(mult(mult(a, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c)),
% 22.22/22.43 inference(transitivity,[status(thm)],[3538, 3628, 3520, 3282, 3281, 3218, 3216, 3518, 3516])).
% 22.22/22.43 tff(3630,plain,
% 22.22/22.43 (rd(mult(mult(mult(a, a), b), c), c) = rd(mult(mult(mult(a, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c), c)),
% 22.22/22.43 inference(monotonicity,[status(thm)],[3629])).
% 22.22/22.43 tff(3631,plain,
% 22.22/22.43 (rd(mult(mult(mult(a, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c), c) = rd(mult(mult(mult(a, a), b), c), c)),
% 22.22/22.43 inference(symmetry,[status(thm)],[3630])).
% 22.22/22.43 tff(3632,plain,
% 22.22/22.43 (mult(mult(a, c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(a, a), b)),
% 22.22/22.43 inference(transitivity,[status(thm)],[3544, 3631, 3513])).
% 22.22/22.43 tff(3633,plain,
% 22.22/22.43 (mult(mult(b, c), mult(mult(a, c), mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(mult(b, c), mult(mult(a, a), b))),
% 22.22/22.43 inference(monotonicity,[status(thm)],[3632])).
% 22.22/22.43 tff(3634,plain,
% 22.22/22.43 (mult(mult(b, c), mult(mult(a, c), mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(mult(b, c), mult(a, mult(a, b)))),
% 22.22/22.43 inference(transitivity,[status(thm)],[3633, 3511, 3509, 3592, 1097, 574, 3502, 2070])).
% 22.22/22.43 tff(3635,plain,
% 22.22/22.43 (ld(mult(b, c), mult(mult(b, c), mult(mult(a, c), mult(mult(unit, ld(c, mult(a, b))), unit)))) = ld(mult(b, c), mult(mult(b, c), mult(a, mult(a, b))))),
% 22.22/22.43 inference(monotonicity,[status(thm)],[3634])).
% 22.22/22.43 tff(3636,plain,
% 22.22/22.43 (mult(mult(a, c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(a, mult(a, b))),
% 22.22/22.43 inference(transitivity,[status(thm)],[3551, 3635, 3499])).
% 22.22/22.43 tff(3637,plain,
% 22.22/22.43 (mult(mult(mult(a, c), mult(mult(unit, ld(c, mult(a, b))), unit)), a) = mult(mult(a, mult(a, b)), a)),
% 22.22/22.43 inference(monotonicity,[status(thm)],[3636])).
% 22.22/22.43 tff(3638,plain,
% 22.22/22.43 (mult(mult(a, a), b) = mult(mult(a, c), mult(mult(unit, ld(c, mult(a, b))), unit))),
% 22.22/22.43 inference(transitivity,[status(thm)],[3554, 3630, 3543])).
% 22.22/22.43 tff(3639,plain,
% 22.22/22.43 (mult(mult(mult(a, a), b), a) = mult(mult(mult(a, c), mult(mult(unit, ld(c, mult(a, b))), unit)), a)),
% 22.22/22.43 inference(monotonicity,[status(thm)],[3638])).
% 22.22/22.43 tff(3640,plain,
% 22.22/22.43 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(a, mult(mult(a, b), a)), mult(c, rd(mult(b, c), mult(a, c)))), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(a, b), a)))),
% 22.22/22.43 inference(quant_inst,[status(thm)],[])).
% 22.22/22.43 tff(3641,plain,
% 22.22/22.43 (rd(mult(mult(a, mult(mult(a, b), a)), mult(c, rd(mult(b, c), mult(a, c)))), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(a, b), a))),
% 22.22/22.43 inference(unit_resolution,[status(thm)],[3640, 168])).
% 22.22/22.43 tff(3642,plain,
% 22.22/22.43 (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), b) = mult(mult(mult(a, b), c), b)),
% 22.22/22.43 inference(symmetry,[status(thm)],[3353])).
% 22.22/22.43 tff(3643,plain,
% 22.22/22.43 (mult(mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), b), a)),
% 22.22/22.43 inference(transitivity,[status(thm)],[3358, 3356, 3325, 3323, 3603, 3297, 1068, 3354])).
% 22.22/22.43 tff(3644,plain,
% 22.22/22.43 (rd(mult(mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))), a), a) = rd(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), b), a), a)),
% 22.22/22.43 inference(monotonicity,[status(thm)],[3643])).
% 22.22/22.43 tff(3645,plain,
% 22.22/22.43 (mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))) = rd(mult(mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))), a), a)),
% 22.22/22.43 inference(symmetry,[status(thm)],[3352])).
% 22.22/22.43 tff(3646,plain,
% 22.22/22.43 (mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, b), c), b)),
% 22.22/22.43 inference(transitivity,[status(thm)],[3645, 3644, 3363, 3642])).
% 22.22/22.43 tff(3647,plain,
% 22.22/22.43 (mult(a, mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(mult(a, b), c), b))),
% 22.22/22.43 inference(monotonicity,[status(thm)],[3646])).
% 22.22/22.43 tff(3648,plain,
% 22.22/22.43 (mult(a, mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c))))) = mult(a, mult(a, mult(mult(b, c), b)))),
% 22.22/22.43 inference(transitivity,[status(thm)],[3647, 3379])).
% 22.22/22.43 tff(3649,plain,
% 22.22/22.43 ((mult(a, mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a)))) <=> (mult(a, mult(a, mult(mult(b, c), b))) = mult(a, mult(mult(mult(b, c), b), a)))),
% 22.22/22.43 inference(monotonicity,[status(thm)],[3648, 3377])).
% 22.22/22.43 tff(3650,plain,
% 22.22/22.43 ((mult(a, mult(a, mult(mult(b, c), b))) = mult(a, mult(mult(mult(b, c), b), a))) <=> (mult(a, mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a))))),
% 22.22/22.43 inference(symmetry,[status(thm)],[3649])).
% 22.22/22.43 tff(3651,plain,
% 22.22/22.43 ((mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(a, b))) <=> (mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a))) = mult(a, mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c))))))),
% 22.22/22.43 inference(transitivity,[status(thm)],[3621, 3650, 3369])).
% 22.22/22.43 tff(3652,plain,
% 22.22/22.43 ((~(mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(a, b)))) <=> (~(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a))) = mult(a, mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))))))),
% 22.22/22.43 inference(monotonicity,[status(thm)],[3651])).
% 22.22/22.43 tff(3653,plain,
% 22.22/22.43 (~(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a))) = mult(a, mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c))))))),
% 22.22/22.43 inference(modus_ponens,[status(thm)],[1064, 3652])).
% 22.22/22.43 tff(3654,plain,
% 22.22/22.43 ((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(mult(a, b), a)) = mult(mult(a, mult(mult(a, b), a)), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a))) = mult(a, mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))))))),
% 22.22/22.43 inference(unit_resolution,[status(thm)],[3482, 3653])).
% 22.22/22.43 tff(3655,plain,
% 22.22/22.43 (~((~(mult(mult(a, mult(mult(a, b), a)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(mult(a, b), a)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a))))))),
% 22.22/22.43 inference(unit_resolution,[status(thm)],[3494, 3654])).
% 22.22/22.43 tff(3656,plain,
% 22.22/22.43 (mult(mult(a, mult(mult(a, b), a)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))))),
% 22.22/22.43 inference(unit_resolution,[status(thm)],[3496, 3655])).
% 22.22/22.43 tff(3657,plain,
% 22.22/22.43 (mult(a, mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c))))) = mult(mult(a, mult(mult(a, b), a)), mult(c, rd(mult(b, c), mult(a, c))))),
% 22.22/22.43 inference(symmetry,[status(thm)],[3656])).
% 22.22/22.43 tff(3658,plain,
% 22.22/22.43 (mult(a, mult(mult(mult(a, b), c), b)) = mult(a, mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))))),
% 22.22/22.43 inference(symmetry,[status(thm)],[3647])).
% 22.22/22.43 tff(3659,plain,
% 22.22/22.43 (mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), b) = mult(mult(a, mult(mult(a, b), c)), b)),
% 22.22/22.43 inference(symmetry,[status(thm)],[3595])).
% 22.22/22.43 tff(3660,plain,
% 22.22/22.43 (mult(mult(mult(mult(a, b), c), a), b) = mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), b)),
% 22.22/22.43 inference(symmetry,[status(thm)],[3592])).
% 22.22/22.43 tff(3661,plain,
% 22.22/22.43 (mult(mult(mult(a, b), c), mult(a, b)) = mult(mult(mult(mult(a, b), c), a), b)),
% 22.22/22.43 inference(symmetry,[status(thm)],[1097])).
% 22.22/22.43 tff(3662,plain,
% 22.22/22.43 (mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), b)),
% 22.22/22.43 inference(transitivity,[status(thm)],[3278, 3277, 3226, 3205, 1799, 177])).
% 22.22/22.43 tff(3663,plain,
% 22.22/22.43 (mult(mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))), mult(a, b)) = mult(mult(mult(a, c), b), mult(a, b))),
% 22.22/22.43 inference(monotonicity,[status(thm)],[3662])).
% 22.22/22.43 tff(3664,plain,
% 22.22/22.43 (mult(mult(mult(a, a), mult(a, b)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(mult(a, b), a)), mult(c, rd(mult(b, c), mult(a, c))))),
% 22.22/22.43 inference(transitivity,[status(thm)],[3565, 3663, 949, 3661, 3660, 3659, 3613, 3658, 3657])).
% 22.22/22.43 tff(3665,plain,
% 22.22/22.43 (rd(mult(mult(mult(a, a), mult(a, b)), mult(c, rd(mult(b, c), mult(a, c)))), mult(c, rd(mult(b, c), mult(a, c)))) = rd(mult(mult(a, mult(mult(a, b), a)), mult(c, rd(mult(b, c), mult(a, c)))), mult(c, rd(mult(b, c), mult(a, c))))),
% 22.22/22.43 inference(monotonicity,[status(thm)],[3664])).
% 22.22/22.43 tff(3666,plain,
% 22.22/22.43 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(a, a), mult(a, b)), mult(c, rd(mult(b, c), mult(a, c)))), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, a), mult(a, b)))),
% 22.22/22.43 inference(quant_inst,[status(thm)],[])).
% 22.22/22.43 tff(3667,plain,
% 22.22/22.43 (rd(mult(mult(mult(a, a), mult(a, b)), mult(c, rd(mult(b, c), mult(a, c)))), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, a), mult(a, b))),
% 22.22/22.43 inference(unit_resolution,[status(thm)],[3666, 168])).
% 22.22/22.43 tff(3668,plain,
% 22.22/22.43 (mult(mult(a, a), mult(a, b)) = rd(mult(mult(mult(a, a), mult(a, b)), mult(c, rd(mult(b, c), mult(a, c)))), mult(c, rd(mult(b, c), mult(a, c))))),
% 22.22/22.43 inference(symmetry,[status(thm)],[3667])).
% 22.22/22.43 tff(3669,plain,
% 22.22/22.43 (mult(mult(a, a), mult(a, b)) = mult(mult(a, mult(a, b)), a)),
% 22.22/22.43 inference(transitivity,[status(thm)],[3668, 3665, 3641, 3559, 3639, 3637])).
% 22.22/22.43 tff(3670,plain,
% 22.22/22.43 (mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, a), mult(a, b))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, mult(a, b)), a))),
% 22.22/22.43 inference(monotonicity,[status(thm)],[3669])).
% 22.22/22.43 tff(3671,plain,
% 22.22/22.43 (mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, mult(a, b)), a)) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, a), mult(a, b)))),
% 22.22/22.43 inference(symmetry,[status(thm)],[3670])).
% 22.22/22.43 tff(3672,plain,
% 22.22/22.43 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), a), mult(a, b)), a) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, mult(a, b)), a)))),
% 22.22/22.43 inference(quant_inst,[status(thm)],[])).
% 22.22/22.43 tff(3673,plain,
% 22.22/22.43 (mult(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), a), mult(a, b)), a) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, mult(a, b)), a))),
% 22.22/22.43 inference(unit_resolution,[status(thm)],[3672, 56])).
% 22.22/22.43 tff(3674,plain,
% 22.22/22.43 (mult(mult(mult(b, c), a), b) = mult(mult(b, c), mult(a, b))),
% 22.22/22.43 inference(unit_resolution,[status(thm)],[1229, 3470])).
% 22.22/22.43 tff(3675,plain,
% 22.22/22.43 (mult(mult(b, c), mult(a, b)) = mult(mult(mult(b, c), a), b)),
% 22.22/22.43 inference(symmetry,[status(thm)],[3674])).
% 22.22/22.43 tff(3676,plain,
% 22.22/22.43 (mult(mult(mult(c, rd(mult(b, c), mult(a, c))), a), mult(a, b)) = mult(mult(b, c), mult(a, b))),
% 22.22/22.43 inference(monotonicity,[status(thm)],[3370])).
% 22.22/22.43 tff(3677,plain,
% 22.22/22.43 (mult(mult(mult(c, rd(mult(b, c), mult(a, c))), a), mult(a, b)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), b)),
% 22.22/22.43 inference(transitivity,[status(thm)],[3676, 3675, 1174])).
% 22.22/22.43 tff(3678,plain,
% 22.22/22.43 (mult(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), a), mult(a, b)), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), b), a)),
% 22.22/22.44 inference(monotonicity,[status(thm)],[3677])).
% 22.22/22.44 tff(3679,plain,
% 22.22/22.44 (mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), b), a) = mult(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), a), mult(a, b)), a)),
% 22.22/22.44 inference(symmetry,[status(thm)],[3678])).
% 22.22/22.44 tff(3680,plain,
% 22.22/22.44 (mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(a, b))),
% 22.22/22.44 inference(transitivity,[status(thm)],[1068, 3354, 3679, 3673, 3671, 3591, 3589, 949])).
% 22.22/22.44 tff(3681,plain,
% 22.22/22.44 ($false),
% 22.22/22.44 inference(unit_resolution,[status(thm)],[1064, 3680])).
% 22.22/22.44 tff(3682,plain,((~(mult(mult(mult(a, a), mult(a, b)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))), mult(a, b)))) | (mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(a, b))) | (~(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, a)), mult(a, b)) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, a), mult(a, b))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit))))) | (~(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), a), c) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (~(mult(mult(c, b), mult(c, a)) = mult(c, mult(b, mult(c, a))))) | (~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, a)))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(mult(mult(c, a), c), rd(mult(b, c), mult(a, c))) = mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(b, c), a), mult(a, b)) = mult(mult(b, c), mult(a, mult(a, b))))) | (~(mult(mult(mult(b, c), mult(a, a)), b) = mult(mult(b, c), mult(mult(a, a), b)))) | (~(mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(mult(unit, c), unit)) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(unit, c), unit))))) | (~(mult(mult(c, b), a) = mult(c, mult(b, a))))), inference(lemma,lemma(discharge,[]))).
% 22.22/22.44 tff(3683,plain,
% 22.22/22.44 (~(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, a)), mult(a, b)) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, a), mult(a, b))))),
% 22.22/22.44 inference(unit_resolution,[status(thm)],[3682, 3565, 1064, 97, 3243, 286, 2829, 751, 2988, 1799, 2699, 2692, 2070, 3510, 3286, 2299])).
% 22.22/22.44 tff(3684,plain,
% 22.22/22.44 (((~(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, a)), mult(a, b)) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, a), mult(a, b))))) | (~(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, b)), mult(a, a)) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), mult(a, a)))))) | (mult(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, a)), mult(a, b)) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, a), mult(a, b))))),
% 22.22/22.44 inference(tautology,[status(thm)],[])).
% 22.22/22.44 tff(3685,plain,
% 22.22/22.44 ((~(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, a)), mult(a, b)) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, a), mult(a, b))))) | (~(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, b)), mult(a, a)) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), mult(a, a)))))),
% 22.22/22.44 inference(unit_resolution,[status(thm)],[3684, 3683])).
% 22.22/22.44 tff(3686,plain,
% 22.22/22.44 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), mult(a, a))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, a), mult(a, b))))) | (~(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, b)), mult(a, a)) = mult(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, a)), mult(a, b)))))) | (~((~(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, a)), mult(a, b)) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, a), mult(a, b))))) | (~(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, b)), mult(a, a)) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), mult(a, a))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), mult(a, a))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, a), mult(a, b))))) | (~(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, b)), mult(a, a)) = mult(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, a)), mult(a, b)))))) | (~((~(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, a)), mult(a, b)) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, a), mult(a, b))))) | (~(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, b)), mult(a, a)) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), mult(a, a))))))))),
% 22.22/22.44 inference(rewrite,[status(thm)],[])).
% 22.22/22.44 tff(3687,plain,
% 22.22/22.44 (((~((~(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, b)), mult(a, a)) = mult(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, a)), mult(a, b)))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), mult(a, a))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, a), mult(a, b))))))) | (~((~(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, b)), mult(a, a)) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), mult(a, a))))) | (~(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, a)), mult(a, b)) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, a), mult(a, b)))))))) <=> ((~((~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), mult(a, a))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, a), mult(a, b))))) | (~(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, b)), mult(a, a)) = mult(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, a)), mult(a, b)))))) | (~((~(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, a)), mult(a, b)) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, a), mult(a, b))))) | (~(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, b)), mult(a, a)) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), mult(a, a))))))))),
% 22.22/22.44 inference(rewrite,[status(thm)],[])).
% 22.22/22.44 tff(3688,plain,
% 22.22/22.44 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, b)), mult(a, a)) = mult(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, a)), mult(a, b)))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), mult(a, a))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, a), mult(a, b))))))) | (~((~(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, b)), mult(a, a)) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), mult(a, a))))) | (~(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, a)), mult(a, b)) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, a), mult(a, b))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), mult(a, a))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, a), mult(a, b))))) | (~(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, b)), mult(a, a)) = mult(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, a)), mult(a, b)))))) | (~((~(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, a)), mult(a, b)) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, a), mult(a, b))))) | (~(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, b)), mult(a, a)) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), mult(a, a)))))))))),
% 22.22/22.44 inference(monotonicity,[status(thm)],[3687])).
% 22.22/22.44 tff(3689,plain,
% 22.22/22.44 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, b)), mult(a, a)) = mult(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, a)), mult(a, b)))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), mult(a, a))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, a), mult(a, b))))))) | (~((~(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, b)), mult(a, a)) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), mult(a, a))))) | (~(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, a)), mult(a, b)) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, a), mult(a, b))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), mult(a, a))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, a), mult(a, b))))) | (~(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, b)), mult(a, a)) = mult(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, a)), mult(a, b)))))) | (~((~(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, a)), mult(a, b)) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, a), mult(a, b))))) | (~(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, b)), mult(a, a)) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), mult(a, a))))))))),
% 22.22/22.44 inference(transitivity,[status(thm)],[3688, 3686])).
% 22.22/22.44 tff(3690,plain,
% 22.22/22.44 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, b)), mult(a, a)) = mult(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, a)), mult(a, b)))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), mult(a, a))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, a), mult(a, b))))))) | (~((~(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, b)), mult(a, a)) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), mult(a, a))))) | (~(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, a)), mult(a, b)) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, a), mult(a, b))))))))),
% 22.22/22.44 inference(quant_inst,[status(thm)],[])).
% 22.22/22.44 tff(3691,plain,
% 22.22/22.44 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), mult(a, a))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, a), mult(a, b))))) | (~(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, b)), mult(a, a)) = mult(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, a)), mult(a, b)))))) | (~((~(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, a)), mult(a, b)) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, a), mult(a, b))))) | (~(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, b)), mult(a, a)) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), mult(a, a)))))))),
% 22.22/22.44 inference(modus_ponens,[status(thm)],[3690, 3689])).
% 22.22/22.44 tff(3692,plain,
% 22.22/22.44 ((~((~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), mult(a, a))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, a), mult(a, b))))) | (~(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, b)), mult(a, a)) = mult(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, a)), mult(a, b)))))) | (~((~(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, a)), mult(a, b)) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, a), mult(a, b))))) | (~(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, b)), mult(a, a)) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), mult(a, a)))))))),
% 22.22/22.44 inference(unit_resolution,[status(thm)],[3691, 27])).
% 22.22/22.44 tff(3693,plain,
% 22.22/22.44 (~((~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), mult(a, a))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, a), mult(a, b))))) | (~(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, b)), mult(a, a)) = mult(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, a)), mult(a, b)))))),
% 22.22/22.44 inference(unit_resolution,[status(thm)],[3692, 3685])).
% 22.22/22.44 tff(3694,plain,
% 22.22/22.44 (((~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), mult(a, a))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, a), mult(a, b))))) | (~(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, b)), mult(a, a)) = mult(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, a)), mult(a, b))))) | (mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), mult(a, a))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, a), mult(a, b))))),
% 22.22/22.44 inference(tautology,[status(thm)],[])).
% 22.22/22.44 tff(3695,plain,
% 22.22/22.44 (mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), mult(a, a))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, a), mult(a, b)))),
% 22.22/22.44 inference(unit_resolution,[status(thm)],[3694, 3693])).
% 22.22/22.44 tff(3696,plain,
% 22.22/22.44 (mult(mult(a, b), mult(a, a)) = mult(mult(a, b), mult(mult(a, unit), a))),
% 22.22/22.44 inference(monotonicity,[status(thm)],[520])).
% 22.22/22.44 tff(3697,plain,
% 22.22/22.44 (mult(mult(a, b), mult(mult(a, unit), a)) = mult(mult(a, b), mult(a, a))),
% 22.22/22.44 inference(symmetry,[status(thm)],[3696])).
% 22.22/22.44 tff(3698,plain,
% 22.22/22.44 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(a, b), a), unit), a) = mult(mult(a, b), mult(mult(a, unit), a)))),
% 22.22/22.44 inference(quant_inst,[status(thm)],[])).
% 22.22/22.44 tff(3699,plain,
% 22.22/22.44 (mult(mult(mult(mult(a, b), a), unit), a) = mult(mult(a, b), mult(mult(a, unit), a))),
% 22.22/22.44 inference(unit_resolution,[status(thm)],[3698, 56])).
% 22.22/22.44 tff(3700,plain,
% 22.22/22.44 (mult(mult(a, b), mult(mult(unit, a), unit)) = mult(mult(a, b), a)),
% 22.22/22.44 inference(monotonicity,[status(thm)],[507])).
% 22.22/22.44 tff(3701,plain,
% 22.22/22.44 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(a, b), unit), a), unit) = mult(mult(a, b), mult(mult(unit, a), unit)))),
% 22.22/22.44 inference(quant_inst,[status(thm)],[])).
% 22.22/22.44 tff(3702,plain,
% 22.22/22.44 (mult(mult(mult(mult(a, b), unit), a), unit) = mult(mult(a, b), mult(mult(unit, a), unit))),
% 22.22/22.44 inference(unit_resolution,[status(thm)],[3701, 56])).
% 22.22/22.44 tff(3703,plain,
% 22.22/22.44 (mult(mult(mult(a, b), unit), a) = mult(mult(a, b), a)),
% 22.22/22.44 inference(monotonicity,[status(thm)],[440])).
% 22.22/22.44 tff(3704,plain,
% 22.22/22.44 (mult(mult(a, b), a) = mult(mult(mult(a, b), unit), a)),
% 22.22/22.44 inference(symmetry,[status(thm)],[3703])).
% 22.22/22.44 tff(3705,plain,
% 22.22/22.44 (mult(mult(mult(a, b), a), unit) = mult(mult(mult(mult(a, b), unit), a), unit)),
% 22.22/22.44 inference(monotonicity,[status(thm)],[3704])).
% 22.22/22.44 tff(3706,plain,
% 22.22/22.44 (mult(mult(mult(a, b), a), unit) = mult(mult(a, b), a)),
% 22.22/22.44 inference(transitivity,[status(thm)],[3705, 3702, 3700])).
% 22.22/22.44 tff(3707,plain,
% 22.22/22.44 (mult(mult(mult(mult(a, b), a), unit), a) = mult(mult(mult(a, b), a), a)),
% 22.22/22.44 inference(monotonicity,[status(thm)],[3706])).
% 22.22/22.44 tff(3708,plain,
% 22.22/22.44 (mult(mult(mult(a, b), a), a) = mult(mult(mult(mult(a, b), a), unit), a)),
% 22.22/22.45 inference(symmetry,[status(thm)],[3707])).
% 22.22/22.45 tff(3709,plain,
% 22.22/22.45 (mult(mult(mult(a, b), a), a) = mult(mult(a, b), mult(a, a))),
% 22.22/22.45 inference(transitivity,[status(thm)],[3708, 3699, 3697])).
% 22.22/22.45 tff(3710,plain,
% 22.22/22.45 (mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(mult(a, b), a), a)) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, b), mult(a, a)))),
% 22.22/22.45 inference(monotonicity,[status(thm)],[3709])).
% 22.22/22.45 tff(3711,plain,
% 22.22/22.45 (mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(mult(a, b), a), a)) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, a), mult(a, b)))),
% 22.22/22.45 inference(transitivity,[status(thm)],[3710, 3695])).
% 22.22/22.45 tff(3712,plain,
% 22.22/22.45 (ld(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(mult(a, b), a), a))) = ld(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, a), mult(a, b))))),
% 22.22/22.45 inference(monotonicity,[status(thm)],[3711])).
% 22.22/22.45 tff(3713,plain,
% 22.22/22.45 (ld(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, a), mult(a, b)))) = ld(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(mult(a, b), a), a)))),
% 22.22/22.45 inference(symmetry,[status(thm)],[3712])).
% 22.22/22.45 tff(3714,plain,
% 22.22/22.45 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, a), mult(a, b)))) = mult(mult(a, a), mult(a, b)))),
% 22.22/22.45 inference(quant_inst,[status(thm)],[])).
% 22.22/22.45 tff(3715,plain,
% 22.22/22.45 (ld(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, a), mult(a, b)))) = mult(mult(a, a), mult(a, b))),
% 22.22/22.45 inference(unit_resolution,[status(thm)],[3714, 7])).
% 22.22/22.45 tff(3716,plain,
% 22.22/22.45 (mult(mult(a, a), mult(a, b)) = ld(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, a), mult(a, b))))),
% 22.22/22.45 inference(symmetry,[status(thm)],[3715])).
% 22.22/22.45 tff(3717,plain,
% 22.22/22.45 (mult(a, mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c))))) = mult(mult(a, mult(mult(a, b), a)), mult(c, rd(mult(b, c), mult(a, c))))),
% 22.22/22.45 inference(symmetry,[status(thm)],[3497])).
% 22.22/22.45 tff(3718,plain,
% 22.22/22.45 (mult(mult(mult(a, a), mult(a, b)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(mult(a, b), a)), mult(c, rd(mult(b, c), mult(a, c))))),
% 22.22/22.45 inference(transitivity,[status(thm)],[3565, 3663, 3298, 3661, 3209, 3284, 3349, 3366, 3717])).
% 22.22/22.45 tff(3719,plain,
% 22.22/22.45 (rd(mult(mult(mult(a, a), mult(a, b)), mult(c, rd(mult(b, c), mult(a, c)))), mult(c, rd(mult(b, c), mult(a, c)))) = rd(mult(mult(a, mult(mult(a, b), a)), mult(c, rd(mult(b, c), mult(a, c)))), mult(c, rd(mult(b, c), mult(a, c))))),
% 22.22/22.45 inference(monotonicity,[status(thm)],[3718])).
% 22.22/22.45 tff(3720,plain,
% 22.22/22.45 (rd(mult(mult(a, mult(mult(a, b), a)), mult(c, rd(mult(b, c), mult(a, c)))), mult(c, rd(mult(b, c), mult(a, c)))) = rd(mult(mult(mult(a, a), mult(a, b)), mult(c, rd(mult(b, c), mult(a, c)))), mult(c, rd(mult(b, c), mult(a, c))))),
% 22.22/22.45 inference(symmetry,[status(thm)],[3719])).
% 22.22/22.45 tff(3721,plain,
% 22.22/22.45 (mult(a, mult(mult(a, b), a)) = rd(mult(mult(a, mult(mult(a, b), a)), mult(c, rd(mult(b, c), mult(a, c)))), mult(c, rd(mult(b, c), mult(a, c))))),
% 22.22/22.45 inference(symmetry,[status(thm)],[3641])).
% 22.22/22.45 tff(3722,plain,
% 22.22/22.45 (mult(mult(mult(a, c), mult(mult(unit, ld(c, mult(a, b))), unit)), a) = mult(mult(mult(a, a), b), a)),
% 22.22/22.45 inference(symmetry,[status(thm)],[3556])).
% 22.22/22.45 tff(3723,plain,
% 22.22/22.45 (mult(mult(a, mult(a, b)), a) = mult(mult(mult(a, c), mult(mult(unit, ld(c, mult(a, b))), unit)), a)),
% 22.22/22.45 inference(symmetry,[status(thm)],[3553])).
% 22.22/22.45 tff(3724,plain,
% 22.22/22.45 (mult(mult(a, mult(a, b)), a) = mult(mult(mult(a, b), a), a)),
% 22.22/22.45 inference(transitivity,[status(thm)],[3723, 3722, 3558, 3721, 3720, 3667, 3716, 3713, 3564])).
% 22.22/22.45 tff(3725,plain,
% 22.22/22.45 (mult(mult(mult(a, mult(a, b)), a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(mult(a, b), a), a), mult(c, rd(mult(b, c), mult(a, c))))),
% 22.22/22.45 inference(monotonicity,[status(thm)],[3724])).
% 22.22/22.45 tff(3726,plain,
% 22.22/22.45 (mult(mult(mult(mult(a, b), a), a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, mult(a, b)), a), mult(c, rd(mult(b, c), mult(a, c))))),
% 22.22/22.45 inference(symmetry,[status(thm)],[3725])).
% 22.22/22.45 tff(3727,plain,
% 22.22/22.45 ((mult(mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(mult(a, b), a), a), mult(c, rd(mult(b, c), mult(a, c))))) <=> (mult(mult(mult(mult(a, b), a), a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))), a))),
% 22.22/22.45 inference(commutativity,[status(thm)],[])).
% 22.22/22.45 tff(3728,plain,
% 22.22/22.45 ((mult(mult(mult(mult(a, b), a), a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))), a)) <=> (mult(mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(mult(a, b), a), a), mult(c, rd(mult(b, c), mult(a, c)))))),
% 22.22/22.45 inference(symmetry,[status(thm)],[3727])).
% 22.22/22.45 tff(3729,assumption,(~(mult(mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(mult(a, b), a), a), mult(c, rd(mult(b, c), mult(a, c)))))), introduced(assumption)).
% 22.22/22.45 tff(3730,plain,
% 22.22/22.45 (((~(mult(mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(mult(a, b), a), a), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, b), a), mult(mult(c, rd(mult(b, c), mult(a, c))), a)) = mult(mult(mult(a, b), a), mult(a, mult(c, rd(mult(b, c), mult(a, c)))))))) | (mult(mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(mult(a, b), a), a), mult(c, rd(mult(b, c), mult(a, c)))))),
% 22.22/22.45 inference(tautology,[status(thm)],[])).
% 22.22/22.45 tff(3731,plain,
% 22.22/22.45 ((~(mult(mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(mult(a, b), a), a), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, b), a), mult(mult(c, rd(mult(b, c), mult(a, c))), a)) = mult(mult(mult(a, b), a), mult(a, mult(c, rd(mult(b, c), mult(a, c)))))))),
% 22.22/22.45 inference(unit_resolution,[status(thm)],[3730, 3729])).
% 22.22/22.45 tff(3732,plain,
% 22.22/22.45 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(mult(a, b), a), a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, b), a), mult(a, mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(a, b), a), mult(mult(c, rd(mult(b, c), mult(a, c))), a)))))) | (~((~(mult(mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(mult(a, b), a), a), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, b), a), mult(mult(c, rd(mult(b, c), mult(a, c))), a)) = mult(mult(mult(a, b), a), mult(a, mult(c, rd(mult(b, c), mult(a, c))))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(mult(a, b), a), a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, b), a), mult(a, mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(a, b), a), mult(mult(c, rd(mult(b, c), mult(a, c))), a)))))) | (~((~(mult(mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(mult(a, b), a), a), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, b), a), mult(mult(c, rd(mult(b, c), mult(a, c))), a)) = mult(mult(mult(a, b), a), mult(a, mult(c, rd(mult(b, c), mult(a, c))))))))))),
% 22.22/22.45 inference(rewrite,[status(thm)],[])).
% 22.22/22.45 tff(3733,plain,
% 22.22/22.45 (((~((~(mult(mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(mult(a, b), a), a), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, b), a), mult(mult(c, rd(mult(b, c), mult(a, c))), a)) = mult(mult(mult(a, b), a), mult(a, mult(c, rd(mult(b, c), mult(a, c))))))))) | (~((~(mult(mult(mult(mult(a, b), a), a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, b), a), mult(a, mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(a, b), a), mult(mult(c, rd(mult(b, c), mult(a, c))), a))))))) <=> ((~((~(mult(mult(mult(mult(a, b), a), a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, b), a), mult(a, mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(a, b), a), mult(mult(c, rd(mult(b, c), mult(a, c))), a)))))) | (~((~(mult(mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(mult(a, b), a), a), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, b), a), mult(mult(c, rd(mult(b, c), mult(a, c))), a)) = mult(mult(mult(a, b), a), mult(a, mult(c, rd(mult(b, c), mult(a, c))))))))))),
% 22.22/22.45 inference(rewrite,[status(thm)],[])).
% 22.22/22.45 tff(3734,plain,
% 22.22/22.45 ((~((~(mult(mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(a, b), a), mult(mult(c, rd(mult(b, c), mult(a, c))), a)))) | (~(mult(mult(mult(mult(a, b), a), a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, b), a), mult(a, mult(c, rd(mult(b, c), mult(a, c))))))))) <=> (~((~(mult(mult(mult(mult(a, b), a), a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, b), a), mult(a, mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(a, b), a), mult(mult(c, rd(mult(b, c), mult(a, c))), a))))))),
% 22.22/22.45 inference(rewrite,[status(thm)],[])).
% 22.22/22.45 tff(3735,plain,
% 22.22/22.45 ((~((~(mult(mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(mult(a, b), a), a), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, b), a), mult(mult(c, rd(mult(b, c), mult(a, c))), a)) = mult(mult(mult(a, b), a), mult(a, mult(c, rd(mult(b, c), mult(a, c))))))))) <=> (~((~(mult(mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(mult(a, b), a), a), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, b), a), mult(mult(c, rd(mult(b, c), mult(a, c))), a)) = mult(mult(mult(a, b), a), mult(a, mult(c, rd(mult(b, c), mult(a, c)))))))))),
% 22.22/22.45 inference(rewrite,[status(thm)],[])).
% 22.22/22.45 tff(3736,plain,
% 22.22/22.45 (((~((~(mult(mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(mult(a, b), a), a), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, b), a), mult(mult(c, rd(mult(b, c), mult(a, c))), a)) = mult(mult(mult(a, b), a), mult(a, mult(c, rd(mult(b, c), mult(a, c))))))))) | (~((~(mult(mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(a, b), a), mult(mult(c, rd(mult(b, c), mult(a, c))), a)))) | (~(mult(mult(mult(mult(a, b), a), a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, b), a), mult(a, mult(c, rd(mult(b, c), mult(a, c)))))))))) <=> ((~((~(mult(mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(mult(a, b), a), a), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, b), a), mult(mult(c, rd(mult(b, c), mult(a, c))), a)) = mult(mult(mult(a, b), a), mult(a, mult(c, rd(mult(b, c), mult(a, c))))))))) | (~((~(mult(mult(mult(mult(a, b), a), a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, b), a), mult(a, mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(a, b), a), mult(mult(c, rd(mult(b, c), mult(a, c))), a)))))))),
% 22.22/22.45 inference(monotonicity,[status(thm)],[3735, 3734])).
% 22.22/22.45 tff(3737,plain,
% 22.22/22.45 (((~((~(mult(mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(mult(a, b), a), a), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, b), a), mult(mult(c, rd(mult(b, c), mult(a, c))), a)) = mult(mult(mult(a, b), a), mult(a, mult(c, rd(mult(b, c), mult(a, c))))))))) | (~((~(mult(mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(a, b), a), mult(mult(c, rd(mult(b, c), mult(a, c))), a)))) | (~(mult(mult(mult(mult(a, b), a), a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, b), a), mult(a, mult(c, rd(mult(b, c), mult(a, c)))))))))) <=> ((~((~(mult(mult(mult(mult(a, b), a), a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, b), a), mult(a, mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(a, b), a), mult(mult(c, rd(mult(b, c), mult(a, c))), a)))))) | (~((~(mult(mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(mult(a, b), a), a), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, b), a), mult(mult(c, rd(mult(b, c), mult(a, c))), a)) = mult(mult(mult(a, b), a), mult(a, mult(c, rd(mult(b, c), mult(a, c))))))))))),
% 22.22/22.46 inference(transitivity,[status(thm)],[3736, 3733])).
% 22.22/22.46 tff(3738,plain,
% 22.22/22.46 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(mult(a, b), a), a), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, b), a), mult(mult(c, rd(mult(b, c), mult(a, c))), a)) = mult(mult(mult(a, b), a), mult(a, mult(c, rd(mult(b, c), mult(a, c))))))))) | (~((~(mult(mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(a, b), a), mult(mult(c, rd(mult(b, c), mult(a, c))), a)))) | (~(mult(mult(mult(mult(a, b), a), a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, b), a), mult(a, mult(c, rd(mult(b, c), mult(a, c))))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(mult(a, b), a), a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, b), a), mult(a, mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(a, b), a), mult(mult(c, rd(mult(b, c), mult(a, c))), a)))))) | (~((~(mult(mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(mult(a, b), a), a), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, b), a), mult(mult(c, rd(mult(b, c), mult(a, c))), a)) = mult(mult(mult(a, b), a), mult(a, mult(c, rd(mult(b, c), mult(a, c)))))))))))),
% 22.22/22.46 inference(monotonicity,[status(thm)],[3737])).
% 22.22/22.46 tff(3739,plain,
% 22.22/22.46 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(mult(a, b), a), a), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, b), a), mult(mult(c, rd(mult(b, c), mult(a, c))), a)) = mult(mult(mult(a, b), a), mult(a, mult(c, rd(mult(b, c), mult(a, c))))))))) | (~((~(mult(mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(a, b), a), mult(mult(c, rd(mult(b, c), mult(a, c))), a)))) | (~(mult(mult(mult(mult(a, b), a), a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, b), a), mult(a, mult(c, rd(mult(b, c), mult(a, c))))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(mult(a, b), a), a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, b), a), mult(a, mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(a, b), a), mult(mult(c, rd(mult(b, c), mult(a, c))), a)))))) | (~((~(mult(mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(mult(a, b), a), a), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, b), a), mult(mult(c, rd(mult(b, c), mult(a, c))), a)) = mult(mult(mult(a, b), a), mult(a, mult(c, rd(mult(b, c), mult(a, c))))))))))),
% 22.22/22.46 inference(transitivity,[status(thm)],[3738, 3732])).
% 22.22/22.46 tff(3740,plain,
% 22.22/22.46 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(mult(a, b), a), a), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, b), a), mult(mult(c, rd(mult(b, c), mult(a, c))), a)) = mult(mult(mult(a, b), a), mult(a, mult(c, rd(mult(b, c), mult(a, c))))))))) | (~((~(mult(mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(a, b), a), mult(mult(c, rd(mult(b, c), mult(a, c))), a)))) | (~(mult(mult(mult(mult(a, b), a), a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, b), a), mult(a, mult(c, rd(mult(b, c), mult(a, c))))))))))),
% 22.22/22.46 inference(quant_inst,[status(thm)],[])).
% 22.22/22.46 tff(3741,plain,
% 22.22/22.46 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(mult(a, b), a), a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, b), a), mult(a, mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(a, b), a), mult(mult(c, rd(mult(b, c), mult(a, c))), a)))))) | (~((~(mult(mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(mult(a, b), a), a), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, b), a), mult(mult(c, rd(mult(b, c), mult(a, c))), a)) = mult(mult(mult(a, b), a), mult(a, mult(c, rd(mult(b, c), mult(a, c)))))))))),
% 22.22/22.46 inference(modus_ponens,[status(thm)],[3740, 3739])).
% 22.22/22.46 tff(3742,plain,
% 22.22/22.46 ((~((~(mult(mult(mult(mult(a, b), a), a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, b), a), mult(a, mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(a, b), a), mult(mult(c, rd(mult(b, c), mult(a, c))), a)))))) | (~((~(mult(mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(mult(a, b), a), a), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, b), a), mult(mult(c, rd(mult(b, c), mult(a, c))), a)) = mult(mult(mult(a, b), a), mult(a, mult(c, rd(mult(b, c), mult(a, c)))))))))),
% 22.22/22.46 inference(unit_resolution,[status(thm)],[3741, 27])).
% 22.22/22.46 tff(3743,plain,
% 22.22/22.46 (~((~(mult(mult(mult(mult(a, b), a), a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, b), a), mult(a, mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(a, b), a), mult(mult(c, rd(mult(b, c), mult(a, c))), a)))))),
% 22.22/22.46 inference(unit_resolution,[status(thm)],[3742, 3731])).
% 22.22/22.46 tff(3744,plain,
% 22.22/22.46 (((~(mult(mult(mult(mult(a, b), a), a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, b), a), mult(a, mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(a, b), a), mult(mult(c, rd(mult(b, c), mult(a, c))), a))))) | (mult(mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(a, b), a), mult(mult(c, rd(mult(b, c), mult(a, c))), a)))),
% 22.30/22.46 inference(tautology,[status(thm)],[])).
% 22.30/22.46 tff(3745,plain,
% 22.30/22.46 (mult(mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(a, b), a), mult(mult(c, rd(mult(b, c), mult(a, c))), a))),
% 22.30/22.46 inference(unit_resolution,[status(thm)],[3744, 3743])).
% 22.30/22.46 tff(3746,plain,
% 22.30/22.46 (mult(mult(mult(a, b), a), mult(mult(c, rd(mult(b, c), mult(a, c))), a)) = mult(mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))), a)),
% 22.30/22.46 inference(symmetry,[status(thm)],[3745])).
% 22.30/22.46 tff(3747,plain,
% 22.30/22.46 (rd(mult(mult(b, c), c), c) = rd(mult(mult(mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit), a), c), c)),
% 22.30/22.46 inference(symmetry,[status(thm)],[3255])).
% 22.30/22.46 tff(3748,plain,
% 22.30/22.46 (mult(b, c) = rd(mult(mult(b, c), c), c)),
% 22.30/22.46 inference(symmetry,[status(thm)],[2224])).
% 22.30/22.46 tff(3749,plain,
% 22.30/22.46 (mult(b, c) = mult(mult(c, rd(mult(b, c), mult(a, c))), a)),
% 22.30/22.46 inference(transitivity,[status(thm)],[3748, 3747, 3257, 3252])).
% 22.30/22.46 tff(3750,plain,
% 22.30/22.46 (mult(mult(mult(unit, a), b), a) = mult(mult(a, b), a)),
% 22.30/22.46 inference(monotonicity,[status(thm)],[926])).
% 22.30/22.46 tff(3751,plain,
% 22.30/22.46 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(unit, a), b), a) = mult(unit, mult(mult(a, b), a)))),
% 22.30/22.46 inference(quant_inst,[status(thm)],[])).
% 22.30/22.46 tff(3752,plain,
% 22.30/22.46 (mult(mult(mult(unit, a), b), a) = mult(unit, mult(mult(a, b), a))),
% 22.30/22.46 inference(unit_resolution,[status(thm)],[3751, 56])).
% 22.30/22.46 tff(3753,plain,
% 22.30/22.46 (mult(unit, mult(mult(a, b), a)) = mult(mult(mult(unit, a), b), a)),
% 22.30/22.46 inference(symmetry,[status(thm)],[3752])).
% 22.30/22.46 tff(3754,plain,
% 22.30/22.46 (mult(unit, mult(mult(a, b), a)) = mult(mult(a, b), a)),
% 22.30/22.46 inference(transitivity,[status(thm)],[3753, 3750])).
% 22.30/22.46 tff(3755,plain,
% 22.30/22.46 (mult(mult(unit, mult(mult(a, b), a)), mult(b, c)) = mult(mult(mult(a, b), a), mult(mult(c, rd(mult(b, c), mult(a, c))), a))),
% 22.30/22.46 inference(monotonicity,[status(thm)],[3754, 3749])).
% 22.30/22.46 tff(3756,plain,
% 22.30/22.46 (mult(mult(a, b), a) = mult(mult(mult(unit, a), b), a)),
% 22.30/22.46 inference(symmetry,[status(thm)],[3750])).
% 22.30/22.46 tff(3757,plain,
% 22.30/22.46 (mult(mult(a, b), a) = mult(unit, mult(mult(a, b), a))),
% 22.30/22.46 inference(transitivity,[status(thm)],[3756, 3752])).
% 22.30/22.46 tff(3758,plain,
% 22.30/22.46 (mult(mult(mult(a, b), a), mult(a, mult(c, rd(mult(b, c), mult(a, c))))) = mult(mult(unit, mult(mult(a, b), a)), mult(b, c))),
% 22.30/22.46 inference(monotonicity,[status(thm)],[3757, 3211])).
% 22.30/22.46 tff(3759,plain,
% 22.30/22.46 (((~(mult(mult(mult(mult(a, b), a), a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, b), a), mult(a, mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(a, b), a), mult(mult(c, rd(mult(b, c), mult(a, c))), a))))) | (mult(mult(mult(mult(a, b), a), a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, b), a), mult(a, mult(c, rd(mult(b, c), mult(a, c))))))),
% 22.30/22.46 inference(tautology,[status(thm)],[])).
% 22.30/22.46 tff(3760,plain,
% 22.30/22.46 (mult(mult(mult(mult(a, b), a), a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, b), a), mult(a, mult(c, rd(mult(b, c), mult(a, c)))))),
% 22.30/22.46 inference(unit_resolution,[status(thm)],[3759, 3743])).
% 22.30/22.46 tff(3761,plain,
% 22.30/22.46 (mult(mult(mult(mult(a, b), a), a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))), a)),
% 22.30/22.46 inference(transitivity,[status(thm)],[3760, 3758, 3755, 3746])).
% 22.30/22.46 tff(3762,plain,
% 22.30/22.46 (mult(mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(mult(a, b), a), a), mult(c, rd(mult(b, c), mult(a, c))))),
% 22.30/22.46 inference(modus_ponens,[status(thm)],[3761, 3728])).
% 22.30/22.46 tff(3763,plain,
% 22.30/22.46 ($false),
% 22.30/22.46 inference(unit_resolution,[status(thm)],[3729, 3762])).
% 22.30/22.46 tff(3764,plain,((mult(mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(mult(a, b), a), a), mult(c, rd(mult(b, c), mult(a, c))))) | (~(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), a), c) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (~(mult(mult(c, b), mult(c, a)) = mult(c, mult(b, mult(c, a))))) | (~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(mult(c, a), c), rd(mult(b, c), mult(a, c))) = mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))))), inference(lemma,lemma(discharge,[]))).
% 22.30/22.46 tff(3765,plain,
% 22.30/22.46 (mult(mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(mult(a, b), a), a), mult(c, rd(mult(b, c), mult(a, c))))),
% 22.30/22.46 inference(unit_resolution,[status(thm)],[3764, 3243, 286, 2829, 751, 2988, 97, 1799, 2692, 2699])).
% 22.30/22.46 tff(3766,plain,
% 22.30/22.46 (mult(mult(a, b), mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a)) = mult(mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))), a)),
% 22.30/22.46 inference(symmetry,[status(thm)],[3358])).
% 22.30/22.46 tff(3767,plain,
% 22.30/22.46 (mult(mult(a, b), mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) = mult(mult(a, b), mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a))),
% 22.30/22.46 inference(symmetry,[status(thm)],[3356])).
% 22.30/22.46 tff(3768,plain,
% 22.30/22.46 (mult(mult(a, b), mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), c)) = mult(mult(a, b), mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))),
% 22.30/22.46 inference(symmetry,[status(thm)],[3325])).
% 22.30/22.46 tff(3769,plain,
% 22.30/22.46 (mult(mult(mult(a, b), c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)) = mult(mult(mult(mult(a, b), c), mult(mult(unit, ld(c, mult(a, b))), unit)), c)),
% 22.30/22.46 inference(symmetry,[status(thm)],[3320])).
% 22.30/22.46 tff(3770,plain,
% 22.30/22.46 (mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c))),
% 22.30/22.46 inference(symmetry,[status(thm)],[3297])).
% 22.30/22.46 tff(3771,plain,
% 22.30/22.46 (mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(a, b))),
% 22.30/22.46 inference(transitivity,[status(thm)],[3770, 3769, 3322, 3768, 3767, 3766, 3765, 3726, 3562, 3497, 3367, 3350, 3285, 3210, 1097])).
% 22.30/22.46 tff(3772,plain,
% 22.30/22.46 ($false),
% 22.30/22.46 inference(unit_resolution,[status(thm)],[1064, 3771])).
% 22.30/22.46 tff(3773,plain,((~(mult(mult(mult(a, a), mult(a, b)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))), mult(a, b)))) | (mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(a, b))) | (~(mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(mult(unit, c), unit)) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(unit, c), unit))))) | (~(mult(mult(c, b), a) = mult(c, mult(b, a)))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit))))) | (~(mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (~(mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(mult(mult(b, c), a), mult(a, b)) = mult(mult(b, c), mult(a, mult(a, b))))) | (~(mult(mult(mult(b, c), mult(a, a)), b) = mult(mult(b, c), mult(mult(a, a), b)))) | (~(mult(mult(mult(c, rd(mult(b, c), mult(a, c))), a), c) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(mult(c, b), mult(c, a)) = mult(c, mult(b, mult(c, a))))) | (~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, a)))) | (~(mult(mult(mult(c, a), c), rd(mult(b, c), mult(a, c))) = mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c))))))), inference(lemma,lemma(discharge,[]))).
% 22.30/22.47 tff(3774,plain,
% 22.30/22.47 (~(mult(mult(mult(a, a), mult(a, b)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))), mult(a, b)))),
% 22.30/22.47 inference(unit_resolution,[status(thm)],[3773, 3204, 2375, 2252, 2128, 97, 2258, 2216, 2070, 3134, 2847, 2314, 2228, 2960, 2928])).
% 22.30/22.47 tff(3775,plain,
% 22.30/22.47 (((~(mult(mult(mult(a, a), mult(a, b)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))), mult(a, b)))) | (~(mult(mult(a, a), mult(mult(a, b), mult(c, rd(mult(b, c), mult(a, c))))) = mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, b)))))) | (mult(mult(mult(a, a), mult(a, b)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))), mult(a, b)))),
% 22.30/22.47 inference(tautology,[status(thm)],[])).
% 22.30/22.47 tff(3776,plain,
% 22.30/22.47 ((~(mult(mult(mult(a, a), mult(a, b)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))), mult(a, b)))) | (~(mult(mult(a, a), mult(mult(a, b), mult(c, rd(mult(b, c), mult(a, c))))) = mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, b)))))),
% 22.30/22.47 inference(unit_resolution,[status(thm)],[3775, 3774])).
% 22.30/22.47 tff(3777,plain,
% 22.30/22.47 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, a), mult(a, b)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, a), mult(mult(a, b), mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))), mult(a, b)) = mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, b))))))) | (~((~(mult(mult(mult(a, a), mult(a, b)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))), mult(a, b)))) | (~(mult(mult(a, a), mult(mult(a, b), mult(c, rd(mult(b, c), mult(a, c))))) = mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, b))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(a, a), mult(a, b)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, a), mult(mult(a, b), mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))), mult(a, b)) = mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, b))))))) | (~((~(mult(mult(mult(a, a), mult(a, b)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))), mult(a, b)))) | (~(mult(mult(a, a), mult(mult(a, b), mult(c, rd(mult(b, c), mult(a, c))))) = mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, b))))))))),
% 22.30/22.47 inference(rewrite,[status(thm)],[])).
% 22.30/22.47 tff(3778,plain,
% 22.30/22.47 (((~((~(mult(mult(mult(a, a), mult(a, b)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))), mult(a, b)))) | (~(mult(mult(a, a), mult(mult(a, b), mult(c, rd(mult(b, c), mult(a, c))))) = mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, b))))))) | (~((~(mult(mult(mult(a, a), mult(a, b)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, a), mult(mult(a, b), mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))), mult(a, b)) = mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, b)))))))) <=> ((~((~(mult(mult(mult(a, a), mult(a, b)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, a), mult(mult(a, b), mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))), mult(a, b)) = mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, b))))))) | (~((~(mult(mult(mult(a, a), mult(a, b)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))), mult(a, b)))) | (~(mult(mult(a, a), mult(mult(a, b), mult(c, rd(mult(b, c), mult(a, c))))) = mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, b))))))))),
% 22.30/22.47 inference(rewrite,[status(thm)],[])).
% 22.30/22.47 tff(3779,plain,
% 22.30/22.47 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, a), mult(a, b)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))), mult(a, b)))) | (~(mult(mult(a, a), mult(mult(a, b), mult(c, rd(mult(b, c), mult(a, c))))) = mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, b))))))) | (~((~(mult(mult(mult(a, a), mult(a, b)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, a), mult(mult(a, b), mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))), mult(a, b)) = mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, b))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, a), mult(a, b)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, a), mult(mult(a, b), mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))), mult(a, b)) = mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, b))))))) | (~((~(mult(mult(mult(a, a), mult(a, b)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))), mult(a, b)))) | (~(mult(mult(a, a), mult(mult(a, b), mult(c, rd(mult(b, c), mult(a, c))))) = mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, b)))))))))),
% 22.30/22.47 inference(monotonicity,[status(thm)],[3778])).
% 22.30/22.47 tff(3780,plain,
% 22.30/22.47 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, a), mult(a, b)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))), mult(a, b)))) | (~(mult(mult(a, a), mult(mult(a, b), mult(c, rd(mult(b, c), mult(a, c))))) = mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, b))))))) | (~((~(mult(mult(mult(a, a), mult(a, b)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, a), mult(mult(a, b), mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))), mult(a, b)) = mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, b))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(a, a), mult(a, b)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, a), mult(mult(a, b), mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))), mult(a, b)) = mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, b))))))) | (~((~(mult(mult(mult(a, a), mult(a, b)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))), mult(a, b)))) | (~(mult(mult(a, a), mult(mult(a, b), mult(c, rd(mult(b, c), mult(a, c))))) = mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, b))))))))),
% 22.30/22.47 inference(transitivity,[status(thm)],[3779, 3777])).
% 22.30/22.47 tff(3781,plain,
% 22.30/22.47 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, a), mult(a, b)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))), mult(a, b)))) | (~(mult(mult(a, a), mult(mult(a, b), mult(c, rd(mult(b, c), mult(a, c))))) = mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, b))))))) | (~((~(mult(mult(mult(a, a), mult(a, b)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, a), mult(mult(a, b), mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))), mult(a, b)) = mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, b))))))))),
% 22.30/22.47 inference(quant_inst,[status(thm)],[])).
% 22.30/22.47 tff(3782,plain,
% 22.30/22.47 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(a, a), mult(a, b)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, a), mult(mult(a, b), mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))), mult(a, b)) = mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, b))))))) | (~((~(mult(mult(mult(a, a), mult(a, b)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))), mult(a, b)))) | (~(mult(mult(a, a), mult(mult(a, b), mult(c, rd(mult(b, c), mult(a, c))))) = mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, b)))))))),
% 22.30/22.47 inference(modus_ponens,[status(thm)],[3781, 3780])).
% 22.30/22.47 tff(3783,plain,
% 22.30/22.47 (~((~(mult(mult(mult(a, a), mult(a, b)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, a), mult(mult(a, b), mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))), mult(a, b)) = mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, b))))))),
% 22.30/22.47 inference(unit_resolution,[status(thm)],[3782, 27, 3776])).
% 22.30/22.47 tff(3784,plain,
% 22.30/22.47 (((~(mult(mult(mult(a, a), mult(a, b)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, a), mult(mult(a, b), mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))), mult(a, b)) = mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, b)))))) | (mult(mult(mult(a, a), mult(a, b)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, a), mult(mult(a, b), mult(c, rd(mult(b, c), mult(a, c))))))),
% 22.30/22.47 inference(tautology,[status(thm)],[])).
% 22.30/22.47 tff(3785,plain,
% 22.30/22.47 (mult(mult(mult(a, a), mult(a, b)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, a), mult(mult(a, b), mult(c, rd(mult(b, c), mult(a, c)))))),
% 22.30/22.47 inference(unit_resolution,[status(thm)],[3784, 3783])).
% 22.30/22.47 tff(3786,plain,
% 22.30/22.47 (mult(mult(mult(a, a), mult(a, b)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, a), mult(mult(mult(b, c), a), rd(mult(b, c), mult(a, c))))),
% 22.30/22.47 inference(transitivity,[status(thm)],[3785, 3023])).
% 22.30/22.47 tff(3787,plain,
% 22.30/22.47 ((mult(mult(mult(a, a), mult(a, b)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))), mult(a, b))) <=> (mult(mult(a, a), mult(mult(mult(b, c), a), rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(mult(mult(b, c), a), rd(mult(b, c), mult(a, c)))), a))),
% 22.30/22.47 inference(monotonicity,[status(thm)],[3786, 2879])).
% 22.30/22.47 tff(3788,plain,
% 22.30/22.47 ((mult(mult(mult(a, a), mult(a, b)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))), mult(a, b))) <=> (mult(mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, a), mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))))),
% 22.30/22.48 inference(transitivity,[status(thm)],[3787, 2158, 2150])).
% 22.30/22.48 tff(3789,plain,
% 22.30/22.48 ((~(mult(mult(mult(a, a), mult(a, b)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, a), mult(c, rd(mult(b, c), mult(a, c)))), mult(a, b)))) <=> (~(mult(mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, a), mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))))))),
% 22.30/22.48 inference(monotonicity,[status(thm)],[3788])).
% 22.30/22.48 tff(3790,plain,
% 22.30/22.48 (~(mult(mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, a), mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))))),
% 22.30/22.48 inference(modus_ponens,[status(thm)],[3774, 3789])).
% 22.30/22.48 tff(3791,plain,
% 22.30/22.48 (((~(mult(mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, a), mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a)) = mult(a, mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))))))) | (mult(mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, a), mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))))),
% 22.30/22.48 inference(tautology,[status(thm)],[])).
% 22.30/22.48 tff(3792,plain,
% 22.30/22.48 ((~(mult(mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, a), mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a)) = mult(a, mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))))))),
% 22.30/22.48 inference(unit_resolution,[status(thm)],[3791, 3790])).
% 22.30/22.48 tff(3793,plain,
% 22.30/22.48 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, a), mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))), a) = mult(a, mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a)))))) | (~((~(mult(mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, a), mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a)) = mult(a, mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, a), mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))), a) = mult(a, mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a)))))) | (~((~(mult(mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, a), mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a)) = mult(a, mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))))))))))),
% 22.30/22.48 inference(rewrite,[status(thm)],[])).
% 22.30/22.48 tff(3794,plain,
% 22.30/22.48 (((~((~(mult(mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, a), mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a)) = mult(a, mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))))))))) | (~((~(mult(mult(a, a), mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))), a) = mult(a, mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a))))))) <=> ((~((~(mult(mult(a, a), mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))), a) = mult(a, mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a)))))) | (~((~(mult(mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, a), mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a)) = mult(a, mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))))))))))),
% 22.32/22.48 inference(rewrite,[status(thm)],[])).
% 22.32/22.48 tff(3795,plain,
% 22.32/22.48 ((~((~(mult(mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))), a) = mult(a, mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a)))) | (~(mult(mult(a, a), mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))))))))) <=> (~((~(mult(mult(a, a), mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))), a) = mult(a, mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a))))))),
% 22.32/22.48 inference(rewrite,[status(thm)],[])).
% 22.32/22.48 tff(3796,plain,
% 22.32/22.48 ((~((~(mult(mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, a), mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a)) = mult(a, mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))))))))) <=> (~((~(mult(mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, a), mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a)) = mult(a, mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))))))))),
% 22.32/22.48 inference(rewrite,[status(thm)],[])).
% 22.32/22.48 tff(3797,plain,
% 22.32/22.48 (((~((~(mult(mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, a), mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a)) = mult(a, mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))))))))) | (~((~(mult(mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))), a) = mult(a, mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a)))) | (~(mult(mult(a, a), mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))))))))) <=> ((~((~(mult(mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, a), mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a)) = mult(a, mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))))))))) | (~((~(mult(mult(a, a), mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))), a) = mult(a, mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a)))))))),
% 22.32/22.48 inference(monotonicity,[status(thm)],[3796, 3795])).
% 22.32/22.48 tff(3798,plain,
% 22.32/22.48 (((~((~(mult(mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, a), mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a)) = mult(a, mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))))))))) | (~((~(mult(mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))), a) = mult(a, mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a)))) | (~(mult(mult(a, a), mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))))))))) <=> ((~((~(mult(mult(a, a), mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))), a) = mult(a, mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a)))))) | (~((~(mult(mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, a), mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a)) = mult(a, mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))))))))))),
% 22.32/22.48 inference(transitivity,[status(thm)],[3797, 3794])).
% 22.32/22.48 tff(3799,plain,
% 22.32/22.48 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, a), mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a)) = mult(a, mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))))))))) | (~((~(mult(mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))), a) = mult(a, mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a)))) | (~(mult(mult(a, a), mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, a), mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))), a) = mult(a, mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a)))))) | (~((~(mult(mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, a), mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a)) = mult(a, mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))))))))))),
% 22.32/22.48 inference(monotonicity,[status(thm)],[3798])).
% 22.32/22.48 tff(3800,plain,
% 22.32/22.48 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, a), mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a)) = mult(a, mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))))))))) | (~((~(mult(mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))), a) = mult(a, mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a)))) | (~(mult(mult(a, a), mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, a), mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))), a) = mult(a, mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a)))))) | (~((~(mult(mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, a), mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a)) = mult(a, mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))))))))))),
% 22.32/22.48 inference(transitivity,[status(thm)],[3799, 3793])).
% 22.32/22.48 tff(3801,plain,
% 22.32/22.48 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, a), mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a)) = mult(a, mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))))))))) | (~((~(mult(mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))), a) = mult(a, mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a)))) | (~(mult(mult(a, a), mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))))))))))),
% 22.32/22.48 inference(quant_inst,[status(thm)],[])).
% 22.32/22.48 tff(3802,plain,
% 22.32/22.48 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, a), mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))), a) = mult(a, mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a)))))) | (~((~(mult(mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, a), mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a)) = mult(a, mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))))))))),
% 22.32/22.49 inference(modus_ponens,[status(thm)],[3801, 3800])).
% 22.32/22.49 tff(3803,plain,
% 22.32/22.49 ((~((~(mult(mult(a, a), mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))), a) = mult(a, mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a)))))) | (~((~(mult(mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, a), mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a)) = mult(a, mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))))))))),
% 22.32/22.49 inference(unit_resolution,[status(thm)],[3802, 27])).
% 22.32/22.49 tff(3804,plain,
% 22.32/22.49 (~((~(mult(mult(a, a), mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))), a) = mult(a, mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a)))))),
% 22.32/22.49 inference(unit_resolution,[status(thm)],[3803, 3792])).
% 22.32/22.49 tff(3805,plain,
% 22.32/22.49 (((~(mult(mult(a, a), mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))), a) = mult(a, mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a))))) | (mult(mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))), a) = mult(a, mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a)))),
% 22.32/22.49 inference(tautology,[status(thm)],[])).
% 22.32/22.49 tff(3806,plain,
% 22.32/22.49 (mult(mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))), a) = mult(a, mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a))),
% 22.32/22.49 inference(unit_resolution,[status(thm)],[3805, 3804])).
% 22.32/22.49 tff(3807,plain,
% 22.32/22.49 (mult(a, mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a)) = mult(mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))), a)),
% 22.32/22.49 inference(symmetry,[status(thm)],[3806])).
% 22.32/22.49 tff(3808,plain,
% 22.32/22.49 (mult(mult(mult(a, b), b), c) = mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a)),
% 22.32/22.49 inference(transitivity,[status(thm)],[828, 2935, 1221, 2932, 2885, 1597, 2883])).
% 22.32/22.49 tff(3809,plain,
% 22.32/22.49 (mult(a, mult(mult(mult(a, b), b), c)) = mult(a, mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a))),
% 22.32/22.49 inference(monotonicity,[status(thm)],[3808])).
% 22.32/22.49 tff(3810,plain,
% 22.32/22.49 (mult(mult(b, c), mult(a, b)) = mult(mult(mult(b, c), a), b)),
% 22.32/22.49 inference(symmetry,[status(thm)],[2932])).
% 22.32/22.49 tff(3811,plain,
% 22.32/22.49 (mult(mult(b, c), mult(a, b)) = mult(mult(mult(a, b), b), c)),
% 22.32/22.49 inference(transitivity,[status(thm)],[3810, 1174, 2934, 827])).
% 22.32/22.49 tff(3812,plain,
% 22.32/22.49 (mult(a, mult(mult(b, c), mult(a, b))) = mult(a, mult(mult(mult(a, b), b), c))),
% 22.32/22.49 inference(monotonicity,[status(thm)],[3811])).
% 22.32/22.49 tff(3813,plain,
% 22.32/22.49 (mult(a, mult(mult(unit, mult(mult(b, unit), b)), c)) = mult(mult(mult(a, b), b), c)),
% 22.32/22.49 inference(transitivity,[status(thm)],[893, 833])).
% 22.32/22.49 tff(3814,plain,
% 22.32/22.49 (mult(a, mult(a, mult(mult(unit, mult(mult(b, unit), b)), c))) = mult(a, mult(mult(mult(a, b), b), c))),
% 22.32/22.49 inference(monotonicity,[status(thm)],[3813])).
% 22.32/22.49 tff(3815,plain,
% 22.32/22.49 (mult(a, mult(mult(mult(a, b), b), c)) = mult(a, mult(a, mult(mult(unit, mult(mult(b, unit), b)), c)))),
% 22.32/22.49 inference(symmetry,[status(thm)],[3814])).
% 22.32/22.49 tff(3816,plain,
% 22.32/22.49 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)) = mult(mult(a, b), c)),
% 22.32/22.49 inference(transitivity,[status(thm)],[1169, 1164, 2126, 1799, 177, 161])).
% 22.32/22.49 tff(3817,plain,
% 22.32/22.49 (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), b) = mult(mult(mult(a, b), c), b)),
% 22.32/22.49 inference(monotonicity,[status(thm)],[3816])).
% 22.32/22.49 tff(3818,plain,
% 22.32/22.49 (mult(mult(b, c), mult(a, b)) = mult(mult(mult(a, b), b), c)),
% 22.32/22.49 inference(transitivity,[status(thm)],[1312, 1174, 3817, 827])).
% 22.32/22.49 tff(3819,plain,
% 22.32/22.49 (mult(a, mult(mult(b, c), mult(a, b))) = mult(a, mult(mult(mult(a, b), b), c))),
% 22.32/22.49 inference(monotonicity,[status(thm)],[3818])).
% 22.32/22.49 tff(3820,assumption,(mult(a, mult(mult(a, b), mult(b, c))) = mult(a, mult(mult(b, c), mult(a, b)))), introduced(assumption)).
% 22.32/22.49 tff(3821,plain,
% 22.32/22.49 (mult(a, mult(mult(a, b), mult(b, c))) = mult(a, mult(a, mult(mult(unit, mult(mult(b, unit), b)), c)))),
% 22.32/22.49 inference(transitivity,[status(thm)],[3820, 3819, 3815])).
% 22.32/22.49 tff(3822,plain,
% 22.32/22.49 (ld(a, mult(a, mult(mult(a, b), mult(b, c)))) = ld(a, mult(a, mult(a, mult(mult(unit, mult(mult(b, unit), b)), c))))),
% 22.32/22.49 inference(monotonicity,[status(thm)],[3821])).
% 22.32/22.49 tff(3823,plain,
% 22.32/22.49 (ld(a, mult(a, mult(a, mult(mult(unit, mult(mult(b, unit), b)), c)))) = ld(a, mult(a, mult(mult(a, b), mult(b, c))))),
% 22.32/22.49 inference(symmetry,[status(thm)],[3822])).
% 22.32/22.49 tff(3824,plain,
% 22.32/22.49 (mult(mult(mult(a, b), b), c) = mult(mult(a, b), mult(b, c))),
% 22.32/22.49 inference(transitivity,[status(thm)],[832, 892, 1793, 3823, 1280])).
% 22.32/22.49 tff(3825,plain,
% 22.32/22.49 ($false),
% 22.32/22.49 inference(unit_resolution,[status(thm)],[1729, 3824])).
% 22.32/22.49 tff(3826,plain,((~(mult(a, mult(mult(a, b), mult(b, c))) = mult(a, mult(mult(b, c), mult(a, b))))) | (~(mult(mult(mult(b, c), a), b) = mult(mult(b, c), mult(a, b)))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit)))))), inference(lemma,lemma(discharge,[]))).
% 22.32/22.49 tff(3827,plain,
% 22.32/22.49 (~(mult(a, mult(mult(a, b), mult(b, c))) = mult(a, mult(mult(b, c), mult(a, b))))),
% 22.32/22.49 inference(unit_resolution,[status(thm)],[3826, 2932, 2128, 1488, 97])).
% 22.32/22.49 tff(3828,plain,
% 22.32/22.49 ((~(mult(mult(a, mult(a, b)), mult(b, c)) = mult(mult(a, mult(b, c)), mult(a, b)))) | (~(mult(a, mult(mult(a, b), mult(b, c))) = mult(a, mult(mult(b, c), mult(a, b)))))),
% 22.32/22.49 inference(unit_resolution,[status(thm)],[1786, 3827])).
% 22.32/22.49 tff(3829,plain,
% 22.32/22.49 (~((~(mult(mult(a, mult(a, b)), mult(b, c)) = mult(a, mult(mult(a, b), mult(b, c))))) | (~(mult(mult(a, mult(b, c)), mult(a, b)) = mult(a, mult(mult(b, c), mult(a, b))))))),
% 22.32/22.49 inference(unit_resolution,[status(thm)],[1784, 3828])).
% 22.32/22.49 tff(3830,plain,
% 22.32/22.49 (mult(mult(a, mult(b, c)), mult(a, b)) = mult(a, mult(mult(b, c), mult(a, b)))),
% 22.32/22.49 inference(unit_resolution,[status(thm)],[1773, 3829])).
% 22.32/22.49 tff(3831,plain,
% 22.32/22.49 (mult(mult(a, mult(b, c)), mult(a, b)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(a, b))),
% 22.32/22.49 inference(transitivity,[status(thm)],[3830, 3812, 3809, 3807, 2148, 2036, 2123])).
% 22.32/22.49 tff(3832,plain,
% 22.32/22.49 (rd(mult(mult(a, mult(b, c)), mult(a, b)), mult(a, b)) = rd(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(a, b)), mult(a, b))),
% 22.32/22.49 inference(monotonicity,[status(thm)],[3831])).
% 22.32/22.49 tff(3833,plain,
% 22.32/22.49 (rd(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(a, b)), mult(a, b)) = rd(mult(mult(a, mult(b, c)), mult(a, b)), mult(a, b))),
% 22.32/22.49 inference(symmetry,[status(thm)],[3832])).
% 22.32/22.49 tff(3834,plain,
% 22.32/22.49 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(a, b)), mult(a, b)) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))),
% 22.32/22.49 inference(quant_inst,[status(thm)],[])).
% 22.32/22.49 tff(3835,plain,
% 22.32/22.49 (rd(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(a, b)), mult(a, b)) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))),
% 22.32/22.49 inference(unit_resolution,[status(thm)],[3834, 168])).
% 22.32/22.49 tff(3836,plain,
% 22.32/22.49 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)) = rd(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), mult(a, b)), mult(a, b))),
% 22.32/22.49 inference(symmetry,[status(thm)],[3835])).
% 22.32/22.49 tff(3837,plain,
% 22.32/22.49 (mult(mult(a, b), c) = mult(a, mult(b, c))),
% 22.32/22.49 inference(transitivity,[status(thm)],[227, 405, 2129, 2127, 1172, 1168, 3836, 3833, 1661])).
% 22.32/22.49 tff(3838,plain,
% 22.32/22.49 ($false),
% 22.32/22.49 inference(unit_resolution,[status(thm)],[146, 3837])).
% 22.32/22.49 tff(3839,plain,((mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))) | (~(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit))))) | (~(mult(mult(mult(b, c), a), mult(a, b)) = mult(mult(b, c), mult(a, mult(a, b))))) | (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))) | (~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))))), inference(lemma,lemma(discharge,[]))).
% 22.32/22.49 tff(3840,plain,
% 22.32/22.49 (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))),
% 22.32/22.49 inference(unit_resolution,[status(thm)],[3839, 729, 34, 1797, 114, 2120])).
% 22.32/22.49 tff(3841,plain,
% 22.32/22.49 (~((~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))) | (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))))),
% 22.32/22.49 inference(unit_resolution,[status(thm)],[340, 329])).
% 22.32/22.49 tff(3842,plain,
% 22.32/22.49 (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)),
% 22.32/22.49 inference(unit_resolution,[status(thm)],[346, 3841])).
% 22.32/22.49 tff(3843,plain,
% 22.32/22.49 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))),
% 22.32/22.49 inference(symmetry,[status(thm)],[3842])).
% 22.32/22.49 tff(3844,plain,
% 22.32/22.49 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))),
% 22.32/22.49 inference(transitivity,[status(thm)],[3843, 2319, 359])).
% 22.32/22.49 tff(3845,plain,
% 22.32/22.49 ($false),
% 22.32/22.49 inference(unit_resolution,[status(thm)],[329, 3844])).
% 22.32/22.49 tff(3846,plain,((mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))) | (~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))))), inference(lemma,lemma(discharge,[]))).
% 22.32/22.49 tff(3847,plain,
% 22.32/22.49 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))),
% 22.32/22.49 inference(unit_resolution,[status(thm)],[3846, 2120, 3840])).
% 22.32/22.49 tff(3848,plain,
% 22.32/22.49 (ld(a, mult(a, mult(b, c))) = ld(a, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 22.32/22.49 inference(symmetry,[status(thm)],[731])).
% 22.32/22.49 tff(3849,plain,
% 22.32/22.49 (mult(b, c) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))),
% 22.32/22.49 inference(transitivity,[status(thm)],[843, 3848, 733])).
% 22.32/22.49 tff(3850,plain,
% 22.32/22.49 (mult(mult(b, c), a) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)),
% 22.32/22.49 inference(monotonicity,[status(thm)],[3849])).
% 22.32/22.49 tff(3851,plain,
% 22.32/22.49 (~(mult(b, mult(a, c)) = mult(b, mult(c, a)))),
% 22.32/22.49 inference(unit_resolution,[status(thm)],[2268, 737, 124, 122, 128])).
% 22.32/22.49 tff(3852,plain,
% 22.32/22.49 ((~(mult(mult(b, a), c) = mult(mult(b, c), a))) | (~(mult(b, mult(a, c)) = mult(b, mult(c, a))))),
% 22.32/22.49 inference(unit_resolution,[status(thm)],[2270, 3851])).
% 22.32/22.49 tff(3853,plain,
% 22.32/22.49 (~((~(mult(mult(b, a), c) = mult(b, mult(a, c)))) | (~(mult(mult(b, c), a) = mult(b, mult(c, a)))))),
% 22.32/22.49 inference(unit_resolution,[status(thm)],[2275, 3852])).
% 22.32/22.49 tff(3854,plain,
% 22.32/22.49 (mult(mult(b, c), a) = mult(b, mult(c, a))),
% 22.32/22.49 inference(unit_resolution,[status(thm)],[2277, 3853])).
% 22.32/22.49 tff(3855,plain,
% 22.32/22.49 (mult(b, mult(c, a)) = mult(mult(b, c), a)),
% 22.32/22.49 inference(symmetry,[status(thm)],[3854])).
% 22.32/22.49 tff(3856,plain,
% 22.32/22.49 (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), b)),
% 22.32/22.49 inference(transitivity,[status(thm)],[3840, 1278])).
% 22.32/22.49 tff(3857,plain,
% 22.32/22.49 (ld(mult(a, c), mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = ld(mult(a, c), mult(mult(a, c), b))),
% 22.32/22.49 inference(monotonicity,[status(thm)],[3856])).
% 22.32/22.49 tff(3858,plain,
% 22.32/22.49 (mult(a, rd(mult(b, c), mult(a, c))) = b),
% 22.32/22.49 inference(transitivity,[status(thm)],[471, 3857, 364])).
% 22.32/22.49 tff(3859,plain,
% 22.32/22.49 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(b, mult(c, a))),
% 22.32/22.49 inference(monotonicity,[status(thm)],[3858])).
% 22.32/22.49 tff(3860,plain,
% 22.32/22.49 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))),
% 22.32/22.49 inference(transitivity,[status(thm)],[3859, 3855, 3850, 3847, 1278, 161, 1277, 765])).
% 22.32/22.49 tff(3861,plain,
% 22.32/22.49 ($false),
% 22.32/22.49 inference(unit_resolution,[status(thm)],[756, 3860])).
% 22.32/22.49 tff(3862,plain,(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit)))), inference(lemma,lemma(discharge,[]))).
% 22.32/22.49 tff(3863,plain,
% 22.32/22.49 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(c, a))) = mult(c, a))),
% 22.32/22.49 inference(quant_inst,[status(thm)],[])).
% 22.32/22.49 tff(3864,plain,
% 22.32/22.49 (ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(c, a))) = mult(c, a)),
% 22.32/22.49 inference(unit_resolution,[status(thm)],[3863, 7])).
% 22.32/22.49 tff(3865,assumption,(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit)))), introduced(assumption)).
% 22.32/22.49 tff(3866,plain,
% 22.32/22.49 (mult(c, a) = mult(mult(mult(unit, c), unit), a)),
% 22.32/22.49 inference(symmetry,[status(thm)],[79])).
% 22.32/22.49 tff(3867,plain,
% 22.32/22.49 (mult(rd(mult(b, c), mult(a, c)), mult(c, a)) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a))),
% 22.32/22.49 inference(monotonicity,[status(thm)],[3866])).
% 22.32/22.49 tff(3868,plain,
% 22.32/22.49 (mult(rd(mult(b, c), mult(a, c)), mult(c, a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, c))),
% 22.32/22.49 inference(transitivity,[status(thm)],[3867, 3865, 61])).
% 22.32/22.49 tff(3869,plain,
% 22.32/22.49 (ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(c, a))) = ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))),
% 22.32/22.49 inference(monotonicity,[status(thm)],[3868])).
% 22.32/22.49 tff(3870,plain,
% 22.32/22.49 (ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(a, c))) = ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(c, a)))),
% 22.32/22.49 inference(symmetry,[status(thm)],[3869])).
% 22.32/22.49 tff(3871,plain,
% 22.32/22.49 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(a, c))) = mult(a, c))),
% 22.32/22.49 inference(quant_inst,[status(thm)],[])).
% 22.32/22.49 tff(3872,plain,
% 22.32/22.49 (ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(a, c))) = mult(a, c)),
% 22.32/22.49 inference(unit_resolution,[status(thm)],[3871, 7])).
% 22.32/22.49 tff(3873,plain,
% 22.32/22.49 (mult(a, c) = ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))),
% 22.32/22.49 inference(symmetry,[status(thm)],[3872])).
% 22.32/22.49 tff(3874,plain,
% 22.32/22.49 (mult(a, c) = mult(c, a)),
% 22.32/22.49 inference(transitivity,[status(thm)],[3873, 3870, 3864])).
% 22.32/22.49 tff(3875,plain,
% 22.32/22.49 (mult(mult(a, c), c) = mult(mult(c, a), c)),
% 22.32/22.49 inference(monotonicity,[status(thm)],[3874])).
% 22.32/22.49 tff(3876,plain,
% 22.32/22.49 (mult(mult(c, a), c) = mult(mult(a, c), c)),
% 22.32/22.49 inference(symmetry,[status(thm)],[3875])).
% 22.32/22.49 tff(3877,plain,
% 22.32/22.49 (mult(c, mult(a, c)) = mult(mult(c, a), c)),
% 22.32/22.49 inference(symmetry,[status(thm)],[2690])).
% 22.32/22.49 tff(3878,plain,
% 22.32/22.49 (mult(c, mult(a, c)) = mult(mult(a, c), c)),
% 22.32/22.49 inference(transitivity,[status(thm)],[3877, 3876])).
% 22.32/22.49 tff(3879,plain,
% 22.32/22.49 (mult(mult(c, mult(a, c)), b) = mult(mult(mult(a, c), c), b)),
% 22.32/22.49 inference(monotonicity,[status(thm)],[3878])).
% 22.32/22.49 tff(3880,plain,
% 22.32/22.49 (mult(mult(c, mult(a, c)), b) = mult(mult(unit, mult(mult(a, b), c)), c)),
% 22.32/22.49 inference(transitivity,[status(thm)],[3879, 2759, 231])).
% 22.32/22.49 tff(3881,plain,
% 22.32/22.49 ((mult(mult(c, mult(a, c)), b) = mult(c, mult(mult(a, c), b))) <=> (mult(mult(unit, mult(mult(a, b), c)), c) = mult(mult(unit, c), mult(mult(a, b), c)))),
% 22.32/22.49 inference(monotonicity,[status(thm)],[3880, 2709])).
% 22.32/22.49 tff(3882,plain,
% 22.32/22.49 ((mult(mult(c, mult(a, c)), b) = mult(c, mult(mult(a, c), b))) <=> (mult(mult(unit, c), mult(mult(a, b), c)) = mult(mult(unit, mult(mult(a, b), c)), c))),
% 22.32/22.49 inference(transitivity,[status(thm)],[3881, 2708])).
% 22.32/22.49 tff(3883,plain,
% 22.32/22.49 ((mult(mult(unit, c), mult(mult(a, b), c)) = mult(mult(unit, mult(mult(a, b), c)), c)) <=> (mult(mult(c, mult(a, c)), b) = mult(c, mult(mult(a, c), b)))),
% 22.32/22.49 inference(symmetry,[status(thm)],[3882])).
% 22.32/22.49 tff(3884,plain,
% 22.32/22.49 (mult(c, a) = ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(c, a)))),
% 22.32/22.49 inference(symmetry,[status(thm)],[3864])).
% 22.32/22.49 tff(3885,plain,
% 22.32/22.49 (mult(c, a) = mult(a, c)),
% 22.32/22.49 inference(transitivity,[status(thm)],[3884, 3869, 3872])).
% 22.32/22.49 tff(3886,plain,
% 22.32/22.49 (mult(mult(c, a), b) = mult(mult(a, c), b)),
% 22.32/22.49 inference(monotonicity,[status(thm)],[3885])).
% 22.32/22.49 tff(3887,assumption,(~(mult(mult(c, b), a) = mult(c, mult(b, a)))), introduced(assumption)).
% 22.32/22.49 tff(3888,plain,
% 22.32/22.49 ((~(mult(mult(c, b), a) = mult(c, mult(b, a)))) | (~(mult(mult(c, a), b) = mult(c, mult(a, b))))),
% 22.32/22.49 inference(unit_resolution,[status(thm)],[2251, 3887])).
% 22.32/22.49 tff(3889,plain,
% 22.32/22.49 (~((~(mult(mult(c, b), a) = mult(mult(c, a), b))) | (~(mult(c, mult(b, a)) = mult(c, mult(a, b)))))),
% 22.32/22.49 inference(unit_resolution,[status(thm)],[2249, 3888])).
% 22.32/22.49 tff(3890,plain,
% 22.32/22.49 (((~(mult(mult(c, b), a) = mult(mult(c, a), b))) | (~(mult(c, mult(b, a)) = mult(c, mult(a, b))))) | (mult(mult(c, b), a) = mult(mult(c, a), b))),
% 22.32/22.49 inference(tautology,[status(thm)],[])).
% 22.32/22.49 tff(3891,plain,
% 22.32/22.49 (mult(mult(c, b), a) = mult(mult(c, a), b)),
% 22.32/22.49 inference(unit_resolution,[status(thm)],[3890, 3889])).
% 22.32/22.49 tff(3892,plain,
% 22.32/22.49 (mult(mult(b, c), a) = mult(mult(c, b), a)),
% 22.32/22.49 inference(monotonicity,[status(thm)],[1399])).
% 22.32/22.49 tff(3893,plain,
% 22.32/22.49 (mult(mult(b, c), a) = mult(mult(a, c), b)),
% 22.32/22.49 inference(transitivity,[status(thm)],[3892, 3891, 3886])).
% 22.32/22.49 tff(3894,plain,
% 22.32/22.49 (mult(c, mult(mult(b, c), a)) = mult(c, mult(mult(a, c), b))),
% 22.32/22.49 inference(monotonicity,[status(thm)],[3893])).
% 22.32/22.49 tff(3895,plain,
% 22.32/22.49 (mult(c, mult(mult(b, c), a)) = mult(mult(unit, c), mult(mult(a, b), c))),
% 22.32/22.49 inference(transitivity,[status(thm)],[3894, 2709])).
% 22.32/22.49 tff(3896,plain,
% 22.32/22.49 (mult(mult(mult(b, c), a), c) = mult(mult(mult(a, c), b), c)),
% 22.32/22.49 inference(monotonicity,[status(thm)],[3893])).
% 22.32/22.49 tff(3897,plain,
% 22.32/22.49 (mult(mult(mult(a, c), c), mult(c, a)) = mult(mult(mult(a, c), c), mult(a, c))),
% 22.32/22.50 inference(monotonicity,[status(thm)],[3885])).
% 22.32/22.50 tff(3898,assumption,(~(mult(mult(c, c), a) = mult(c, mult(c, a)))), introduced(assumption)).
% 22.32/22.50 tff(3899,plain,
% 22.32/22.50 (((~(mult(mult(c, c), a) = mult(c, mult(c, a)))) | (~(mult(mult(c, a), c) = mult(c, mult(a, c))))) | (mult(mult(c, c), a) = mult(c, mult(c, a)))),
% 22.32/22.50 inference(tautology,[status(thm)],[])).
% 22.32/22.50 tff(3900,plain,
% 22.32/22.50 ((~(mult(mult(c, c), a) = mult(c, mult(c, a)))) | (~(mult(mult(c, a), c) = mult(c, mult(a, c))))),
% 22.32/22.50 inference(unit_resolution,[status(thm)],[3899, 3898])).
% 22.32/22.50 tff(3901,plain,
% 22.32/22.50 (~((~(mult(c, mult(c, a)) = mult(c, mult(a, c)))) | (~(mult(mult(c, c), a) = mult(mult(c, a), c))))),
% 22.32/22.50 inference(unit_resolution,[status(thm)],[2461, 3900])).
% 22.32/22.50 tff(3902,plain,
% 22.32/22.50 (mult(c, mult(c, a)) = mult(c, mult(a, c))),
% 22.32/22.50 inference(unit_resolution,[status(thm)],[2463, 3901])).
% 22.32/22.50 tff(3903,plain,
% 22.32/22.50 (mult(c, mult(a, c)) = mult(c, mult(c, a))),
% 22.32/22.50 inference(symmetry,[status(thm)],[3902])).
% 22.32/22.50 tff(3904,plain,
% 22.32/22.50 (mult(mult(c, c), a) = mult(mult(c, a), c)),
% 22.32/22.50 inference(unit_resolution,[status(thm)],[2546, 3901])).
% 22.32/22.50 tff(3905,plain,
% 22.32/22.50 (mult(mult(c, a), c) = mult(mult(c, c), a)),
% 22.32/22.50 inference(symmetry,[status(thm)],[3904])).
% 22.32/22.50 tff(3906,plain,
% 22.32/22.50 ((mult(mult(c, a), c) = mult(c, mult(a, c))) <=> (mult(mult(c, c), a) = mult(c, mult(c, a)))),
% 22.32/22.50 inference(monotonicity,[status(thm)],[3905, 3903])).
% 22.32/22.50 tff(3907,plain,
% 22.32/22.50 ((mult(mult(c, c), a) = mult(c, mult(c, a))) <=> (mult(mult(c, a), c) = mult(c, mult(a, c)))),
% 22.32/22.50 inference(symmetry,[status(thm)],[3906])).
% 22.32/22.50 tff(3908,plain,
% 22.32/22.50 ((~(mult(mult(c, c), a) = mult(c, mult(c, a)))) <=> (~(mult(mult(c, a), c) = mult(c, mult(a, c))))),
% 22.32/22.50 inference(monotonicity,[status(thm)],[3907])).
% 22.32/22.50 tff(3909,plain,
% 22.32/22.50 (~(mult(mult(c, a), c) = mult(c, mult(a, c)))),
% 22.32/22.50 inference(modus_ponens,[status(thm)],[3898, 3908])).
% 22.32/22.50 tff(3910,plain,
% 22.32/22.50 ($false),
% 22.32/22.50 inference(unit_resolution,[status(thm)],[2690, 3909])).
% 22.32/22.50 tff(3911,plain,(mult(mult(c, c), a) = mult(c, mult(c, a))), inference(lemma,lemma(discharge,[]))).
% 22.32/22.50 tff(3912,assumption,(mult(mult(c, a), c) = mult(c, mult(a, c))), introduced(assumption)).
% 22.32/22.50 tff(3913,plain,
% 22.32/22.50 (mult(rd(mult(b, c), mult(a, c)), mult(mult(c, a), c)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))),
% 22.32/22.50 inference(monotonicity,[status(thm)],[3912])).
% 22.32/22.50 tff(3914,plain,
% 22.32/22.50 ((mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))) <=> (mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c)))),
% 22.32/22.50 inference(commutativity,[status(thm)],[])).
% 22.32/22.50 tff(3915,assumption,(~(mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c)))), introduced(assumption)).
% 22.32/22.50 tff(3916,plain,
% 22.32/22.50 ((~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), c))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c))))),
% 22.32/22.50 inference(unit_resolution,[status(thm)],[2603, 3915])).
% 22.32/22.50 tff(3917,plain,
% 22.32/22.50 ((~((~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), c))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c)))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c))))))),
% 22.32/22.50 inference(unit_resolution,[status(thm)],[2607, 27])).
% 22.32/22.50 tff(3918,plain,
% 22.32/22.50 (~((~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c)))))),
% 22.32/22.50 inference(unit_resolution,[status(thm)],[3917, 3916])).
% 22.32/22.50 tff(3919,plain,
% 22.32/22.50 (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c))),
% 22.32/22.50 inference(unit_resolution,[status(thm)],[2609, 3918])).
% 22.32/22.50 tff(3920,plain,
% 22.32/22.50 (mult(mult(b, c), c) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), c)),
% 22.32/22.50 inference(symmetry,[status(thm)],[2588])).
% 22.32/22.50 tff(3921,plain,
% 22.32/22.50 (mult(rd(mult(b, c), mult(a, c)), mult(c, a)) = mult(b, c)),
% 22.32/22.50 inference(transitivity,[status(thm)],[3867, 3865, 61, 137])).
% 22.32/22.50 tff(3922,plain,
% 22.32/22.50 (mult(mult(rd(mult(b, c), mult(a, c)), mult(c, a)), c) = mult(mult(b, c), c)),
% 22.32/22.50 inference(monotonicity,[status(thm)],[3921])).
% 22.32/22.50 tff(3923,plain,
% 22.32/22.50 (mult(mult(rd(mult(b, c), mult(a, c)), mult(c, a)), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c))),
% 22.32/22.50 inference(transitivity,[status(thm)],[3922, 3920, 3919])).
% 22.32/22.50 tff(3924,plain,
% 22.32/22.50 ((mult(mult(rd(mult(b, c), mult(a, c)), mult(c, a)), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(c, a), c))) <=> (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))))),
% 22.32/22.50 inference(monotonicity,[status(thm)],[3923, 3913])).
% 22.32/22.50 tff(3925,plain,
% 22.32/22.50 ((mult(mult(rd(mult(b, c), mult(a, c)), mult(c, a)), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(c, a), c))) <=> (mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c)))),
% 22.32/22.50 inference(transitivity,[status(thm)],[3924, 3914])).
% 22.32/22.50 tff(3926,plain,
% 22.32/22.50 ((mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c))) <=> (mult(mult(rd(mult(b, c), mult(a, c)), mult(c, a)), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(c, a), c)))),
% 22.32/22.50 inference(symmetry,[status(thm)],[3925])).
% 22.32/22.50 tff(3927,plain,
% 22.32/22.50 ((~(mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c)))) <=> (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(c, a)), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(c, a), c))))),
% 22.32/22.50 inference(monotonicity,[status(thm)],[3926])).
% 22.32/22.50 tff(3928,plain,
% 22.32/22.50 (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(c, a)), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(c, a), c)))),
% 22.32/22.50 inference(modus_ponens,[status(thm)],[3915, 3927])).
% 22.32/22.50 tff(3929,plain,
% 22.32/22.50 (((~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(c, a)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(c, a))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(c, a)), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(c, a), c))))) | (mult(mult(rd(mult(b, c), mult(a, c)), mult(c, a)), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(c, a), c)))),
% 22.32/22.50 inference(tautology,[status(thm)],[])).
% 22.32/22.50 tff(3930,plain,
% 22.32/22.50 ((~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(c, a)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(c, a))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(c, a)), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(c, a), c))))),
% 22.32/22.50 inference(unit_resolution,[status(thm)],[3929, 3928])).
% 22.32/22.50 tff(3931,plain,
% 22.32/22.50 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(c, a)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(c, a)), c))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(c, mult(c, a))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(c, a), c)))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(c, a)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(c, a))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(c, a)), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(c, a), c)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(c, a)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(c, a)), c))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(c, mult(c, a))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(c, a), c)))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(c, a)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(c, a))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(c, a)), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(c, a), c)))))))),
% 22.32/22.50 inference(rewrite,[status(thm)],[])).
% 22.32/22.50 tff(3932,plain,
% 22.32/22.50 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(c, a)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(c, a)), c))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(c, mult(c, a))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(c, a), c)))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(c, a)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(c, a))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(c, a)), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(c, a), c)))))))),
% 22.32/22.50 inference(quant_inst,[status(thm)],[])).
% 22.32/22.50 tff(3933,plain,
% 22.32/22.50 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(c, a)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(c, a)), c))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(c, mult(c, a))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(c, a), c)))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(c, a)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(c, a))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(c, a)), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(c, a), c))))))),
% 22.32/22.50 inference(modus_ponens,[status(thm)],[3932, 3931])).
% 22.32/22.50 tff(3934,plain,
% 22.32/22.50 ((~((~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(c, a)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(c, a)), c))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(c, mult(c, a))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(c, a), c)))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(c, a)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(c, a))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(c, a)), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(c, a), c))))))),
% 22.32/22.50 inference(unit_resolution,[status(thm)],[3933, 27])).
% 22.32/22.50 tff(3935,plain,
% 22.32/22.50 (~((~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(c, a)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(c, a)), c))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(c, mult(c, a))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(c, a), c)))))),
% 22.32/22.50 inference(unit_resolution,[status(thm)],[3934, 3930])).
% 22.32/22.50 tff(3936,plain,
% 22.32/22.50 (((~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(c, a)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(c, a)), c))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(c, mult(c, a))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(c, a), c))))) | (mult(rd(mult(b, c), mult(a, c)), mult(c, mult(c, a))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(c, a), c)))),
% 22.32/22.50 inference(tautology,[status(thm)],[])).
% 22.32/22.50 tff(3937,plain,
% 22.32/22.50 (mult(rd(mult(b, c), mult(a, c)), mult(c, mult(c, a))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(c, a), c))),
% 22.32/22.50 inference(unit_resolution,[status(thm)],[3936, 3935])).
% 22.32/22.50 tff(3938,assumption,(mult(mult(c, c), a) = mult(c, mult(c, a))), introduced(assumption)).
% 22.32/22.50 tff(3939,plain,
% 22.32/22.50 (mult(rd(mult(b, c), mult(a, c)), mult(mult(c, c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(c, a)))),
% 22.32/22.50 inference(monotonicity,[status(thm)],[3938])).
% 22.32/22.50 tff(3940,plain,
% 22.32/22.50 (mult(rd(mult(b, c), mult(a, c)), mult(mult(c, c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))),
% 22.32/22.50 inference(transitivity,[status(thm)],[3939, 3937, 3913])).
% 22.32/22.50 tff(3941,plain,
% 22.32/22.50 ((mult(rd(mult(b, c), mult(a, c)), mult(mult(c, c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, c)))) <=> (mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c)))),
% 22.32/22.50 inference(monotonicity,[status(thm)],[3940, 2620])).
% 22.32/22.50 tff(3942,plain,
% 22.32/22.50 ((mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c))) <=> (mult(rd(mult(b, c), mult(a, c)), mult(mult(c, c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, c))))),
% 22.32/22.50 inference(symmetry,[status(thm)],[3941])).
% 22.32/22.50 tff(3943,plain,
% 22.32/22.50 ((~(mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c)))) <=> (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(c, c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, c)))))),
% 22.32/22.50 inference(monotonicity,[status(thm)],[3942])).
% 22.32/22.50 tff(3944,plain,
% 22.32/22.50 (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(c, c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, c))))),
% 22.32/22.50 inference(modus_ponens,[status(thm)],[3915, 3943])).
% 22.32/22.50 tff(3945,plain,
% 22.32/22.50 (mult(a, mult(c, c)) = mult(mult(c, a), c)),
% 22.32/22.50 inference(transitivity,[status(thm)],[2618, 2615, 2612, 3875])).
% 22.32/22.51 tff(3946,plain,
% 22.32/22.51 (mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(c, a), c))),
% 22.32/22.51 inference(monotonicity,[status(thm)],[3945])).
% 22.32/22.51 tff(3947,plain,
% 22.32/22.51 (mult(rd(mult(b, c), mult(a, c)), mult(mult(c, a), c)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, c)))),
% 22.32/22.51 inference(symmetry,[status(thm)],[3946])).
% 22.32/22.51 tff(3948,plain,
% 22.32/22.51 (mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, c)))),
% 22.32/22.51 inference(transitivity,[status(thm)],[2627, 3947])).
% 22.32/22.51 tff(3949,assumption,(~(mult(rd(mult(b, c), mult(a, c)), mult(mult(c, c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, c))))), introduced(assumption)).
% 22.32/22.51 tff(3950,plain,
% 22.32/22.51 (((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(c, c)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(c, c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, c)))))) | (mult(rd(mult(b, c), mult(a, c)), mult(mult(c, c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, c))))),
% 22.32/22.51 inference(tautology,[status(thm)],[])).
% 22.32/22.51 tff(3951,plain,
% 22.32/22.51 ((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(c, c)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(c, c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, c)))))),
% 22.32/22.51 inference(unit_resolution,[status(thm)],[3950, 3949])).
% 22.32/22.51 tff(3952,plain,
% 22.32/22.51 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(c, c)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(c, c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, c))))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(c, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(c, c), a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, c))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(c, c)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(c, c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, c))))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(c, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(c, c), a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, c))))))))),
% 22.32/22.51 inference(rewrite,[status(thm)],[])).
% 22.32/22.51 tff(3953,plain,
% 22.32/22.51 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(c, c)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(c, c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, c))))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(c, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(c, c), a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, c))))))))),
% 22.32/22.51 inference(quant_inst,[status(thm)],[])).
% 22.32/22.51 tff(3954,plain,
% 22.32/22.51 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(c, c)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(c, c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, c))))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(c, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(c, c), a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, c)))))))),
% 22.32/22.51 inference(modus_ponens,[status(thm)],[3953, 3952])).
% 22.32/22.51 tff(3955,plain,
% 22.32/22.51 ((~((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(c, c)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(c, c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, c))))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(c, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(c, c), a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, c)))))))),
% 22.32/22.51 inference(unit_resolution,[status(thm)],[3954, 27])).
% 22.32/22.51 tff(3956,plain,
% 22.32/22.51 (~((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(c, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(c, c), a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, c))))))),
% 22.32/22.51 inference(unit_resolution,[status(thm)],[3955, 3951])).
% 22.32/22.51 tff(3957,plain,
% 22.32/22.51 (((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(c, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(c, c), a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, c)))))) | (mult(mult(rd(mult(b, c), mult(a, c)), mult(c, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(c, c), a)))),
% 22.32/22.51 inference(tautology,[status(thm)],[])).
% 22.32/22.51 tff(3958,plain,
% 22.32/22.51 (mult(mult(rd(mult(b, c), mult(a, c)), mult(c, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(c, c), a))),
% 22.32/22.51 inference(unit_resolution,[status(thm)],[3957, 3956])).
% 22.32/22.51 tff(3959,plain,
% 22.32/22.51 (mult(mult(rd(mult(b, c), mult(a, c)), unit), c) = mult(rd(mult(b, c), mult(a, c)), c)),
% 22.32/22.51 inference(monotonicity,[status(thm)],[532])).
% 22.32/22.51 tff(3960,plain,
% 22.32/22.51 (mult(rd(mult(b, c), mult(a, c)), c) = mult(mult(rd(mult(b, c), mult(a, c)), unit), c)),
% 22.32/22.51 inference(symmetry,[status(thm)],[3959])).
% 22.32/22.51 tff(3961,plain,
% 22.32/22.51 (mult(mult(rd(mult(b, c), mult(a, c)), c), unit) = mult(mult(mult(rd(mult(b, c), mult(a, c)), unit), c), unit)),
% 22.32/22.51 inference(monotonicity,[status(thm)],[3960])).
% 22.32/22.51 tff(3962,plain,
% 22.32/22.51 (mult(mult(mult(rd(mult(b, c), mult(a, c)), unit), c), unit) = mult(mult(rd(mult(b, c), mult(a, c)), c), unit)),
% 22.32/22.51 inference(symmetry,[status(thm)],[3961])).
% 22.32/22.51 tff(3963,plain,
% 22.32/22.51 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(rd(mult(b, c), mult(a, c)), unit), c), unit) = mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)))),
% 22.32/22.51 inference(quant_inst,[status(thm)],[])).
% 22.32/22.51 tff(3964,plain,
% 22.32/22.51 (mult(mult(mult(rd(mult(b, c), mult(a, c)), unit), c), unit) = mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit))),
% 22.32/22.51 inference(unit_resolution,[status(thm)],[3963, 56])).
% 22.32/22.51 tff(3965,plain,
% 22.32/22.51 (mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)) = mult(mult(mult(rd(mult(b, c), mult(a, c)), unit), c), unit)),
% 22.32/22.51 inference(symmetry,[status(thm)],[3964])).
% 22.32/22.51 tff(3966,plain,
% 22.32/22.51 (mult(rd(mult(b, c), mult(a, c)), c) = mult(mult(rd(mult(b, c), mult(a, c)), c), unit)),
% 22.32/22.51 inference(transitivity,[status(thm)],[82, 3965, 3962])).
% 22.32/22.51 tff(3967,plain,
% 22.32/22.51 (mult(mult(rd(mult(b, c), mult(a, c)), c), c) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), unit), c)),
% 22.32/22.51 inference(monotonicity,[status(thm)],[3966])).
% 22.32/22.51 tff(3968,plain,
% 22.32/22.51 (mult(mult(mult(rd(mult(b, c), mult(a, c)), c), unit), c) = mult(mult(rd(mult(b, c), mult(a, c)), c), c)),
% 22.32/22.51 inference(symmetry,[status(thm)],[3967])).
% 22.32/22.51 tff(3969,plain,
% 22.32/22.51 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(rd(mult(b, c), mult(a, c)), c), unit), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(c, unit), c)))),
% 22.32/22.51 inference(quant_inst,[status(thm)],[])).
% 22.32/22.51 tff(3970,plain,
% 22.32/22.51 (mult(mult(mult(rd(mult(b, c), mult(a, c)), c), unit), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(c, unit), c))),
% 22.32/22.51 inference(unit_resolution,[status(thm)],[3969, 56])).
% 22.32/22.51 tff(3971,plain,
% 22.32/22.51 (mult(rd(mult(b, c), mult(a, c)), mult(mult(c, unit), c)) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), unit), c)),
% 22.32/22.51 inference(symmetry,[status(thm)],[3970])).
% 22.32/22.51 tff(3972,plain,
% 22.32/22.51 (mult(rd(mult(b, c), mult(a, c)), mult(c, c)) = mult(rd(mult(b, c), mult(a, c)), mult(mult(c, unit), c))),
% 22.32/22.51 inference(monotonicity,[status(thm)],[2617])).
% 22.32/22.51 tff(3973,plain,
% 22.32/22.51 (mult(rd(mult(b, c), mult(a, c)), mult(c, c)) = mult(mult(rd(mult(b, c), mult(a, c)), c), c)),
% 22.32/22.51 inference(transitivity,[status(thm)],[3972, 3971, 3968])).
% 22.32/22.51 tff(3974,plain,
% 22.32/22.51 (mult(mult(rd(mult(b, c), mult(a, c)), mult(c, c)), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), c), a)),
% 22.32/22.51 inference(monotonicity,[status(thm)],[3973])).
% 22.32/22.51 tff(3975,plain,
% 22.32/22.51 (mult(mult(mult(rd(mult(b, c), mult(a, c)), c), c), a) = mult(mult(rd(mult(b, c), mult(a, c)), mult(c, c)), a)),
% 22.32/22.51 inference(symmetry,[status(thm)],[3974])).
% 22.32/22.51 tff(3976,plain,
% 22.32/22.51 (mult(mult(mult(rd(mult(b, c), mult(a, c)), c), c), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(c, c), a))),
% 22.32/22.51 inference(transitivity,[status(thm)],[3975, 3958])).
% 22.32/22.51 tff(3977,plain,
% 22.32/22.51 ((mult(mult(mult(rd(mult(b, c), mult(a, c)), c), c), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c)) <=> (mult(rd(mult(b, c), mult(a, c)), mult(mult(c, c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, c))))),
% 22.32/22.51 inference(monotonicity,[status(thm)],[3976, 3948])).
% 22.32/22.51 tff(3978,plain,
% 22.32/22.51 ((mult(rd(mult(b, c), mult(a, c)), mult(mult(c, c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, c)))) <=> (mult(mult(mult(rd(mult(b, c), mult(a, c)), c), c), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c))),
% 22.32/22.51 inference(symmetry,[status(thm)],[3977])).
% 22.32/22.51 tff(3979,plain,
% 22.32/22.51 ((~(mult(rd(mult(b, c), mult(a, c)), mult(mult(c, c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, c))))) <=> (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), c), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c)))),
% 22.32/22.51 inference(monotonicity,[status(thm)],[3978])).
% 22.32/22.51 tff(3980,plain,
% 22.32/22.51 (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), c), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c))),
% 22.32/22.51 inference(modus_ponens,[status(thm)],[3949, 3979])).
% 22.32/22.51 tff(3981,plain,
% 22.32/22.51 (((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), c), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(c, a)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c))))) | (mult(mult(mult(rd(mult(b, c), mult(a, c)), c), c), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c))),
% 22.32/22.51 inference(tautology,[status(thm)],[])).
% 22.32/22.51 tff(3982,plain,
% 22.32/22.51 ((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), c), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(c, a)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c))))),
% 22.32/22.51 inference(unit_resolution,[status(thm)],[3981, 3980])).
% 22.32/22.51 tff(3983,plain,
% 22.32/22.51 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), c), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(c, a)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)))))) | (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), c), a) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(c, a)))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), c), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(c, a)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)))))) | (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), c), a) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(c, a)))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)))))))),
% 22.32/22.51 inference(rewrite,[status(thm)],[])).
% 22.32/22.51 tff(3984,plain,
% 22.32/22.51 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), c), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(c, a)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)))))) | (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), c), a) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(c, a)))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)))))))),
% 22.32/22.51 inference(quant_inst,[status(thm)],[])).
% 22.32/22.51 tff(3985,plain,
% 22.32/22.51 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), c), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(c, a)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)))))) | (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), c), a) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(c, a)))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c))))))),
% 22.32/22.51 inference(modus_ponens,[status(thm)],[3984, 3983])).
% 22.32/22.51 tff(3986,plain,
% 22.32/22.51 ((~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), c), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(c, a)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)))))) | (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), c), a) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(c, a)))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c))))))),
% 22.32/22.51 inference(unit_resolution,[status(thm)],[3985, 27])).
% 22.32/22.51 tff(3987,plain,
% 22.32/22.51 (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), c), a) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(c, a)))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)))))),
% 22.36/22.52 inference(unit_resolution,[status(thm)],[3986, 3982])).
% 22.36/22.52 tff(3988,plain,
% 22.36/22.52 (((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), c), a) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(c, a)))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c))))) | (mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)))),
% 22.36/22.52 inference(tautology,[status(thm)],[])).
% 22.36/22.52 tff(3989,plain,
% 22.36/22.52 (mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c))),
% 22.36/22.52 inference(unit_resolution,[status(thm)],[3988, 3987])).
% 22.36/22.52 tff(3990,plain,
% 22.36/22.52 (mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c)),
% 22.36/22.52 inference(symmetry,[status(thm)],[3989])).
% 22.36/22.52 tff(3991,plain,
% 22.36/22.52 (mult(mult(rd(mult(b, c), mult(a, c)), c), mult(c, a)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c))),
% 22.36/22.52 inference(monotonicity,[status(thm)],[3885])).
% 22.36/22.52 tff(3992,plain,
% 22.36/22.52 (((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), c), a) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(c, a)))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c))))) | (mult(mult(mult(rd(mult(b, c), mult(a, c)), c), c), a) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(c, a)))),
% 22.36/22.52 inference(tautology,[status(thm)],[])).
% 22.36/22.52 tff(3993,plain,
% 22.36/22.52 (mult(mult(mult(rd(mult(b, c), mult(a, c)), c), c), a) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(c, a))),
% 22.36/22.52 inference(unit_resolution,[status(thm)],[3992, 3987])).
% 22.36/22.52 tff(3994,plain,
% 22.36/22.52 (mult(rd(mult(b, c), mult(a, c)), mult(mult(c, c), a)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(c, c)), a)),
% 22.36/22.52 inference(symmetry,[status(thm)],[3958])).
% 22.36/22.52 tff(3995,plain,
% 22.36/22.52 (mult(rd(mult(b, c), mult(a, c)), mult(mult(c, c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, c)))),
% 22.36/22.52 inference(transitivity,[status(thm)],[3994, 3974, 3993, 3991, 3990, 2627, 3947])).
% 22.36/22.52 tff(3996,plain,
% 22.36/22.52 ($false),
% 22.36/22.52 inference(unit_resolution,[status(thm)],[3949, 3995])).
% 22.36/22.52 tff(3997,plain,((mult(rd(mult(b, c), mult(a, c)), mult(mult(c, c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, c)))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit)))))), inference(lemma,lemma(discharge,[]))).
% 22.36/22.52 tff(3998,plain,
% 22.36/22.52 (mult(rd(mult(b, c), mult(a, c)), mult(mult(c, c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, c)))),
% 22.36/22.52 inference(unit_resolution,[status(thm)],[3997, 3865])).
% 22.36/22.52 tff(3999,plain,
% 22.36/22.52 ($false),
% 22.36/22.52 inference(unit_resolution,[status(thm)],[3998, 3944])).
% 22.36/22.52 tff(4000,plain,((~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit))))) | (mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c))) | (~(mult(mult(c, a), c) = mult(c, mult(a, c)))) | (~(mult(mult(c, c), a) = mult(c, mult(c, a))))), inference(lemma,lemma(discharge,[]))).
% 22.36/22.52 tff(4001,plain,
% 22.36/22.52 ((~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit))))) | (mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c))) | (~(mult(mult(c, c), a) = mult(c, mult(c, a))))),
% 22.36/22.52 inference(unit_resolution,[status(thm)],[4000, 2690])).
% 22.36/22.52 tff(4002,plain,
% 22.36/22.52 ((~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit))))) | (mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c)))),
% 22.36/22.52 inference(unit_resolution,[status(thm)],[4001, 3911])).
% 22.36/22.52 tff(4003,plain,
% 22.36/22.52 (mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c))),
% 22.36/22.52 inference(unit_resolution,[status(thm)],[4002, 3865])).
% 22.36/22.52 tff(4004,plain,
% 22.36/22.52 (mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(unit, c), unit))) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), c))),
% 22.36/22.52 inference(symmetry,[status(thm)],[3290])).
% 22.36/22.52 tff(4005,plain,
% 22.36/22.52 (mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(c, ld(c, mult(a, b)))),
% 22.36/22.52 inference(transitivity,[status(thm)],[212, 209, 195, 189, 187, 1441])).
% 22.36/22.52 tff(4006,plain,
% 22.36/22.52 (mult(c, mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(c, mult(c, ld(c, mult(a, b))))),
% 22.36/22.52 inference(monotonicity,[status(thm)],[4005])).
% 22.36/22.52 tff(4007,plain,
% 22.36/22.52 (mult(c, mult(c, ld(c, mult(a, b)))) = mult(c, mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)))),
% 22.36/22.52 inference(symmetry,[status(thm)],[4006])).
% 22.36/22.52 tff(4008,plain,
% 22.36/22.52 (mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))),
% 22.36/22.52 inference(monotonicity,[status(thm)],[78])).
% 22.36/22.52 tff(4009,plain,
% 22.36/22.52 (mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(c, ld(c, mult(a, b)))),
% 22.36/22.52 inference(transitivity,[status(thm)],[4008, 212, 209, 195, 189, 187, 1441])).
% 22.36/22.52 tff(4010,plain,
% 22.36/22.52 (mult(c, mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(c, mult(c, ld(c, mult(a, b))))),
% 22.36/22.52 inference(monotonicity,[status(thm)],[4009])).
% 22.36/22.52 tff(4011,plain,
% 22.36/22.52 (mult(c, mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(c, mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)))),
% 22.36/22.52 inference(transitivity,[status(thm)],[4010, 4007])).
% 22.36/22.52 tff(4012,plain,
% 22.36/22.52 ((mult(c, mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(unit, c), unit)))) <=> (mult(c, mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)))),
% 22.36/22.52 inference(monotonicity,[status(thm)],[4011, 4004])).
% 22.36/22.52 tff(4013,plain,
% 22.36/22.52 ((mult(c, mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), c))) <=> (mult(c, mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(unit, c), unit))))),
% 22.36/22.52 inference(symmetry,[status(thm)],[4012])).
% 22.36/22.52 tff(4014,plain,
% 22.36/22.52 ((mult(c, mult(a, b)) = mult(mult(c, a), b)) <=> (mult(mult(c, a), b) = mult(c, mult(a, b)))),
% 22.36/22.52 inference(commutativity,[status(thm)],[])).
% 22.36/22.52 tff(4015,plain,
% 22.36/22.52 (mult(mult(a, c), b) = mult(mult(c, a), b)),
% 22.36/22.52 inference(symmetry,[status(thm)],[3886])).
% 22.36/22.52 tff(4016,plain,
% 22.36/22.52 (mult(c, mult(b, a)) = mult(c, mult(a, b))),
% 22.36/22.52 inference(unit_resolution,[status(thm)],[2244, 3889])).
% 22.36/22.52 tff(4017,plain,
% 22.36/22.52 ((mult(mult(c, b), a) = mult(c, mult(b, a))) <=> (mult(mult(c, a), b) = mult(c, mult(a, b)))),
% 22.36/22.52 inference(monotonicity,[status(thm)],[3891, 4016])).
% 22.36/22.52 tff(4018,plain,
% 22.36/22.52 ((~(mult(mult(c, b), a) = mult(c, mult(b, a)))) <=> (~(mult(mult(c, a), b) = mult(c, mult(a, b))))),
% 22.36/22.52 inference(monotonicity,[status(thm)],[4017])).
% 22.36/22.52 tff(4019,plain,
% 22.36/22.52 (~(mult(mult(c, a), b) = mult(c, mult(a, b)))),
% 22.36/22.52 inference(modus_ponens,[status(thm)],[3887, 4018])).
% 22.36/22.52 tff(4020,plain,
% 22.36/22.52 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(c, mult(c, ld(c, mult(a, b)))), c), c) = mult(c, mult(c, ld(c, mult(a, b)))))),
% 22.36/22.52 inference(quant_inst,[status(thm)],[])).
% 22.36/22.52 tff(4021,plain,
% 22.36/22.52 (rd(mult(mult(c, mult(c, ld(c, mult(a, b)))), c), c) = mult(c, mult(c, ld(c, mult(a, b))))),
% 22.36/22.52 inference(unit_resolution,[status(thm)],[4020, 168])).
% 22.36/22.52 tff(4022,plain,
% 22.36/22.52 (mult(mult(mult(a, b), c), c) = mult(mult(mult(a, c), b), c)),
% 22.36/22.52 inference(monotonicity,[status(thm)],[227])).
% 22.36/22.52 tff(4023,plain,
% 22.36/22.52 (mult(mult(mult(a, c), b), c) = mult(mult(mult(a, b), c), c)),
% 22.36/22.52 inference(symmetry,[status(thm)],[4022])).
% 22.36/22.52 tff(4024,plain,
% 22.36/22.52 (mult(c, mult(mult(a, b), c)) = mult(c, mult(mult(a, c), b))),
% 22.36/22.52 inference(monotonicity,[status(thm)],[227])).
% 22.36/22.52 tff(4025,assumption,(~(mult(mult(c, a), b) = mult(c, mult(a, b)))), introduced(assumption)).
% 22.36/22.52 tff(4026,assumption,(mult(c, mult(c, mult(a, b))) = mult(c, mult(mult(a, b), c))), introduced(assumption)).
% 22.36/22.52 tff(4027,plain,
% 22.36/22.52 (mult(c, mult(c, mult(c, ld(c, mult(a, b))))) = mult(c, mult(mult(a, b), c))),
% 22.36/22.52 inference(transitivity,[status(thm)],[2291, 4026])).
% 22.36/22.52 tff(4028,plain,
% 22.36/22.52 (ld(c, mult(c, mult(c, mult(c, ld(c, mult(a, b)))))) = ld(c, mult(c, mult(mult(a, b), c)))),
% 22.36/22.52 inference(monotonicity,[status(thm)],[4027])).
% 22.36/22.52 tff(4029,plain,
% 22.36/22.52 (ld(c, mult(c, mult(mult(a, b), c))) = ld(c, mult(c, mult(c, mult(c, ld(c, mult(a, b))))))),
% 22.36/22.52 inference(symmetry,[status(thm)],[4028])).
% 22.36/22.52 tff(4030,plain,
% 22.36/22.52 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(c, mult(c, mult(mult(a, b), c))) = mult(mult(a, b), c))),
% 22.36/22.52 inference(quant_inst,[status(thm)],[])).
% 22.36/22.52 tff(4031,plain,
% 22.36/22.52 (ld(c, mult(c, mult(mult(a, b), c))) = mult(mult(a, b), c)),
% 22.36/22.52 inference(unit_resolution,[status(thm)],[4030, 7])).
% 22.36/22.52 tff(4032,plain,
% 22.36/22.52 (mult(mult(a, b), c) = ld(c, mult(c, mult(mult(a, b), c)))),
% 22.36/22.52 inference(symmetry,[status(thm)],[4031])).
% 22.36/22.52 tff(4033,plain,
% 22.36/22.52 (mult(mult(c, a), b) = mult(c, mult(a, b))),
% 22.36/22.52 inference(transitivity,[status(thm)],[3886, 161, 4032, 4029, 2282, 1443])).
% 22.36/22.52 tff(4034,plain,
% 22.36/22.52 ($false),
% 22.36/22.52 inference(unit_resolution,[status(thm)],[4025, 4033])).
% 22.36/22.52 tff(4035,plain,((~(mult(c, mult(c, mult(a, b))) = mult(c, mult(mult(a, b), c)))) | (mult(mult(c, a), b) = mult(c, mult(a, b))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit)))))), inference(lemma,lemma(discharge,[]))).
% 22.36/22.52 tff(4036,plain,
% 22.36/22.52 (~(mult(c, mult(c, mult(a, b))) = mult(c, mult(mult(a, b), c)))),
% 22.36/22.52 inference(unit_resolution,[status(thm)],[4035, 4025, 3865])).
% 22.36/22.52 tff(4037,plain,
% 22.36/22.52 (((~(mult(mult(c, c), mult(a, b)) = mult(mult(c, mult(a, b)), c))) | (~(mult(c, mult(c, mult(a, b))) = mult(c, mult(mult(a, b), c))))) | (mult(c, mult(c, mult(a, b))) = mult(c, mult(mult(a, b), c)))),
% 22.36/22.52 inference(tautology,[status(thm)],[])).
% 22.36/22.52 tff(4038,plain,
% 22.36/22.52 ((~(mult(mult(c, c), mult(a, b)) = mult(mult(c, mult(a, b)), c))) | (~(mult(c, mult(c, mult(a, b))) = mult(c, mult(mult(a, b), c))))),
% 22.36/22.52 inference(unit_resolution,[status(thm)],[4037, 4036])).
% 22.36/22.52 tff(4039,plain,
% 22.36/22.52 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(c, c), mult(a, b)) = mult(mult(c, mult(a, b)), c))) | (~(mult(c, mult(c, mult(a, b))) = mult(c, mult(mult(a, b), c)))))) | (~((~(mult(mult(c, c), mult(a, b)) = mult(c, mult(c, mult(a, b))))) | (~(mult(mult(c, mult(a, b)), c) = mult(c, mult(mult(a, b), c)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(c, c), mult(a, b)) = mult(mult(c, mult(a, b)), c))) | (~(mult(c, mult(c, mult(a, b))) = mult(c, mult(mult(a, b), c)))))) | (~((~(mult(mult(c, c), mult(a, b)) = mult(c, mult(c, mult(a, b))))) | (~(mult(mult(c, mult(a, b)), c) = mult(c, mult(mult(a, b), c)))))))),
% 22.36/22.52 inference(rewrite,[status(thm)],[])).
% 22.36/22.52 tff(4040,plain,
% 22.36/22.52 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(c, c), mult(a, b)) = mult(mult(c, mult(a, b)), c))) | (~(mult(c, mult(c, mult(a, b))) = mult(c, mult(mult(a, b), c)))))) | (~((~(mult(mult(c, c), mult(a, b)) = mult(c, mult(c, mult(a, b))))) | (~(mult(mult(c, mult(a, b)), c) = mult(c, mult(mult(a, b), c)))))))),
% 22.36/22.52 inference(quant_inst,[status(thm)],[])).
% 22.36/22.52 tff(4041,plain,
% 22.36/22.52 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(c, c), mult(a, b)) = mult(mult(c, mult(a, b)), c))) | (~(mult(c, mult(c, mult(a, b))) = mult(c, mult(mult(a, b), c)))))) | (~((~(mult(mult(c, c), mult(a, b)) = mult(c, mult(c, mult(a, b))))) | (~(mult(mult(c, mult(a, b)), c) = mult(c, mult(mult(a, b), c))))))),
% 22.36/22.52 inference(modus_ponens,[status(thm)],[4040, 4039])).
% 22.36/22.52 tff(4042,plain,
% 22.36/22.52 (~((~(mult(mult(c, c), mult(a, b)) = mult(c, mult(c, mult(a, b))))) | (~(mult(mult(c, mult(a, b)), c) = mult(c, mult(mult(a, b), c)))))),
% 22.36/22.52 inference(unit_resolution,[status(thm)],[4041, 27, 4038])).
% 22.36/22.52 tff(4043,plain,
% 22.36/22.52 (((~(mult(mult(c, c), mult(a, b)) = mult(c, mult(c, mult(a, b))))) | (~(mult(mult(c, mult(a, b)), c) = mult(c, mult(mult(a, b), c))))) | (mult(mult(c, mult(a, b)), c) = mult(c, mult(mult(a, b), c)))),
% 22.36/22.52 inference(tautology,[status(thm)],[])).
% 22.36/22.52 tff(4044,plain,
% 22.36/22.52 (mult(mult(c, mult(a, b)), c) = mult(c, mult(mult(a, b), c))),
% 22.36/22.52 inference(unit_resolution,[status(thm)],[4043, 4042])).
% 22.36/22.52 tff(4045,plain,
% 22.36/22.52 (mult(mult(c, mult(c, ld(c, mult(a, b)))), c) = mult(mult(c, mult(a, b)), c)),
% 22.36/22.52 inference(monotonicity,[status(thm)],[1443])).
% 22.36/22.52 tff(4046,plain,
% 22.36/22.52 (mult(mult(c, mult(c, ld(c, mult(a, b)))), c) = mult(mult(mult(a, b), c), c)),
% 22.36/22.52 inference(transitivity,[status(thm)],[4045, 4044, 4024, 3190, 3188, 3185, 4023])).
% 22.36/22.52 tff(4047,plain,
% 22.36/22.52 (rd(mult(mult(c, mult(c, ld(c, mult(a, b)))), c), c) = rd(mult(mult(mult(a, b), c), c), c)),
% 22.36/22.52 inference(monotonicity,[status(thm)],[4046])).
% 22.36/22.52 tff(4048,plain,
% 22.36/22.52 (rd(mult(mult(mult(a, b), c), c), c) = rd(mult(mult(c, mult(c, ld(c, mult(a, b)))), c), c)),
% 22.36/22.52 inference(symmetry,[status(thm)],[4047])).
% 22.36/22.52 tff(4049,plain,
% 22.36/22.52 (mult(mult(c, a), b) = mult(c, mult(a, b))),
% 22.36/22.52 inference(transitivity,[status(thm)],[3886, 161, 255, 4048, 4021, 1443])).
% 22.36/22.52 tff(4050,plain,
% 22.36/22.52 ($false),
% 22.36/22.52 inference(unit_resolution,[status(thm)],[4025, 4049])).
% 22.36/22.52 tff(4051,plain,((~(mult(mult(c, mult(mult(unit, c), unit)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(mult(unit, c), unit)))) | (mult(mult(c, a), b) = mult(c, mult(a, b))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit)))))), inference(lemma,lemma(discharge,[]))).
% 22.36/22.52 tff(4052,plain,
% 22.36/22.52 (~(mult(mult(c, mult(mult(unit, c), unit)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(mult(unit, c), unit)))),
% 22.36/22.52 inference(unit_resolution,[status(thm)],[4051, 4019, 3865])).
% 22.36/22.52 tff(4053,plain,
% 22.36/22.52 ((~(mult(mult(c, mult(mult(unit, c), unit)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(mult(unit, c), unit)))) | (~(mult(c, mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(unit, c), unit)))))),
% 22.36/22.52 inference(unit_resolution,[status(thm)],[3196, 4052])).
% 22.36/22.52 tff(4054,plain,
% 22.36/22.52 (~((~(mult(mult(c, mult(mult(unit, c), unit)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(c, mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit))))) | (~(mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(mult(unit, c), unit)) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(unit, c), unit))))))),
% 22.36/22.52 inference(unit_resolution,[status(thm)],[3201, 4053])).
% 22.36/22.52 tff(4055,plain,
% 22.36/22.52 (mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(mult(unit, c), unit)) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(unit, c), unit)))),
% 22.36/22.52 inference(unit_resolution,[status(thm)],[3203, 4054])).
% 22.36/22.52 tff(4056,plain,
% 22.36/22.52 (mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(unit, c), unit))) = mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(mult(unit, c), unit))),
% 22.36/22.52 inference(symmetry,[status(thm)],[4055])).
% 22.36/22.52 tff(4057,plain,
% 22.36/22.53 (mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)) = mult(mult(c, a), b)),
% 22.36/22.53 inference(transitivity,[status(thm)],[3290, 4056, 3179, 3178, 3175, 864, 858, 856, 4015])).
% 22.36/22.53 tff(4058,plain,
% 22.36/22.53 (mult(c, mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(c, mult(a, b))),
% 22.36/22.53 inference(transitivity,[status(thm)],[4006, 1443])).
% 22.36/22.53 tff(4059,plain,
% 22.36/22.53 ((mult(c, mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), c))) <=> (mult(c, mult(a, b)) = mult(mult(c, a), b))),
% 22.36/22.53 inference(monotonicity,[status(thm)],[4058, 4057])).
% 22.36/22.53 tff(4060,plain,
% 22.36/22.53 ((mult(c, mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), c))) <=> (mult(mult(c, a), b) = mult(c, mult(a, b)))),
% 22.36/22.53 inference(transitivity,[status(thm)],[4059, 4014])).
% 22.36/22.53 tff(4061,plain,
% 22.36/22.53 ((mult(mult(c, a), b) = mult(c, mult(a, b))) <=> (mult(c, mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)))),
% 22.36/22.53 inference(symmetry,[status(thm)],[4060])).
% 22.36/22.53 tff(4062,plain,
% 22.36/22.53 ((mult(mult(c, a), b) = mult(c, mult(a, b))) <=> (mult(c, mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(unit, c), unit))))),
% 22.36/22.53 inference(transitivity,[status(thm)],[4061, 4013])).
% 22.36/22.53 tff(4063,plain,
% 22.36/22.53 ((~(mult(mult(c, a), b) = mult(c, mult(a, b)))) <=> (~(mult(c, mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(unit, c), unit)))))),
% 22.36/22.53 inference(monotonicity,[status(thm)],[4062])).
% 22.36/22.53 tff(4064,plain,
% 22.36/22.53 (~(mult(c, mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(unit, c), unit))))),
% 22.36/22.53 inference(modus_ponens,[status(thm)],[4019, 4063])).
% 22.36/22.53 tff(4065,plain,
% 22.36/22.53 (mult(mult(c, a), c) = mult(mult(a, c), c)),
% 22.36/22.53 inference(monotonicity,[status(thm)],[3885])).
% 22.36/22.53 tff(4066,plain,
% 22.36/22.53 (mult(mult(a, c), c) = mult(mult(c, a), c)),
% 22.36/22.53 inference(symmetry,[status(thm)],[4065])).
% 22.36/22.53 tff(4067,plain,
% 22.36/22.53 (ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))) = ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c)))),
% 22.36/22.53 inference(symmetry,[status(thm)],[2593])).
% 22.36/22.53 tff(4068,plain,
% 22.36/22.53 (mult(c, mult(a, c)) = ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))))),
% 22.36/22.53 inference(symmetry,[status(thm)],[2590])).
% 22.36/22.53 tff(4069,plain,
% 22.36/22.53 (mult(c, mult(a, c)) = mult(mult(c, a), c)),
% 22.36/22.53 inference(transitivity,[status(thm)],[4068, 4067, 2595, 4066])).
% 22.36/22.53 tff(4070,plain,
% 22.36/22.53 (mult(b, mult(c, mult(a, c))) = mult(b, mult(mult(c, a), c))),
% 22.36/22.53 inference(monotonicity,[status(thm)],[4069])).
% 22.36/22.53 tff(4071,plain,
% 22.36/22.53 (mult(b, mult(mult(c, a), c)) = mult(b, mult(c, mult(a, c)))),
% 22.36/22.53 inference(symmetry,[status(thm)],[4070])).
% 22.36/22.53 tff(4072,assumption,(~(mult(c, mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(unit, c), unit))))), introduced(assumption)).
% 22.36/22.53 tff(4073,plain,
% 22.36/22.53 ((mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)) = mult(c, mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)))) <=> (mult(c, mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)))),
% 22.36/22.53 inference(commutativity,[status(thm)],[])).
% 22.36/22.53 tff(4074,plain,
% 22.36/22.53 (mult(c, mult(a, b)) = mult(c, mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)))),
% 22.36/22.53 inference(transitivity,[status(thm)],[1442, 4007])).
% 22.36/22.53 tff(4075,plain,
% 22.36/22.53 (((~(mult(mult(c, mult(mult(unit, c), unit)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(mult(unit, c), unit)))) | (~(mult(c, mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(unit, c), unit)))))) | (mult(c, mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(unit, c), unit))))),
% 22.36/22.53 inference(tautology,[status(thm)],[])).
% 22.36/22.53 tff(4076,plain,
% 22.36/22.53 ((~(mult(mult(c, mult(mult(unit, c), unit)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(mult(unit, c), unit)))) | (~(mult(c, mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(unit, c), unit)))))),
% 22.36/22.53 inference(unit_resolution,[status(thm)],[4075, 4072])).
% 22.36/22.53 tff(4077,plain,
% 22.36/22.53 (~((~(mult(mult(c, mult(mult(unit, c), unit)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(c, mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit))))) | (~(mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(mult(unit, c), unit)) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(unit, c), unit))))))),
% 22.36/22.53 inference(unit_resolution,[status(thm)],[3201, 4076])).
% 22.36/22.53 tff(4078,plain,
% 22.36/22.53 (mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(mult(unit, c), unit)) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(unit, c), unit)))),
% 22.36/22.53 inference(unit_resolution,[status(thm)],[3203, 4077])).
% 22.36/22.53 tff(4079,plain,
% 22.36/22.53 (mult(mult(a, b), mult(mult(unit, c), unit)) = mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(mult(unit, c), unit))),
% 22.36/22.53 inference(symmetry,[status(thm)],[3179])).
% 22.36/22.53 tff(4080,plain,
% 22.36/22.53 (mult(mult(mult(a, c), b), unit) = mult(mult(mult(mult(a, b), unit), c), unit)),
% 22.36/22.53 inference(symmetry,[status(thm)],[3175])).
% 22.36/22.53 tff(4081,plain,
% 22.36/22.53 (mult(mult(mult(mult(a, c), unit), b), unit) = mult(mult(mult(a, c), b), unit)),
% 22.36/22.53 inference(symmetry,[status(thm)],[864])).
% 22.36/22.53 tff(4082,plain,
% 22.36/22.53 (mult(mult(c, a), b) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), c))),
% 22.36/22.53 inference(transitivity,[status(thm)],[3886, 862, 861, 4081, 4080, 3177, 4079, 4078, 4004])).
% 22.36/22.53 tff(4083,plain,
% 22.36/22.53 ((mult(mult(c, a), b) = mult(c, mult(a, b))) <=> (mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)) = mult(c, mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))),
% 22.36/22.53 inference(monotonicity,[status(thm)],[4082, 4074])).
% 22.36/22.53 tff(4084,plain,
% 22.36/22.53 ((mult(mult(c, a), b) = mult(c, mult(a, b))) <=> (mult(c, mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)))),
% 22.36/22.53 inference(transitivity,[status(thm)],[4083, 4073])).
% 22.36/22.53 tff(4085,plain,
% 22.36/22.53 ((mult(mult(c, a), b) = mult(c, mult(a, b))) <=> (mult(c, mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(unit, c), unit))))),
% 22.36/22.53 inference(transitivity,[status(thm)],[4084, 4013])).
% 22.36/22.53 tff(4086,plain,
% 22.36/22.53 (mult(c, mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(unit, c), unit)))),
% 22.36/22.53 inference(modus_ponens,[status(thm)],[2288, 4085])).
% 22.36/22.53 tff(4087,plain,
% 22.36/22.53 ($false),
% 22.36/22.53 inference(unit_resolution,[status(thm)],[4072, 4086])).
% 22.36/22.53 tff(4088,plain,((~(mult(mult(c, a), b) = mult(c, mult(a, b)))) | (mult(c, mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(unit, c), unit)))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit)))))), inference(lemma,lemma(discharge,[]))).
% 22.36/22.53 tff(4089,plain,
% 22.36/22.53 (~(mult(mult(c, a), b) = mult(c, mult(a, b)))),
% 22.36/22.53 inference(unit_resolution,[status(thm)],[4088, 4072, 3865])).
% 22.36/22.53 tff(4090,plain,
% 22.36/22.53 ((~(mult(mult(c, b), a) = mult(c, mult(b, a)))) | (~(mult(mult(c, a), b) = mult(c, mult(a, b))))),
% 22.36/22.53 inference(unit_resolution,[status(thm)],[2279, 4089])).
% 22.36/22.53 tff(4091,plain,
% 22.36/22.53 (~((~(mult(mult(c, b), a) = mult(mult(c, a), b))) | (~(mult(c, mult(b, a)) = mult(c, mult(a, b)))))),
% 22.36/22.53 inference(unit_resolution,[status(thm)],[2249, 4090])).
% 22.36/22.53 tff(4092,plain,
% 22.36/22.53 (mult(mult(c, b), a) = mult(mult(c, a), b)),
% 22.36/22.53 inference(unit_resolution,[status(thm)],[3890, 4091])).
% 22.36/22.53 tff(4093,plain,
% 22.36/22.53 (mult(mult(b, c), a) = mult(mult(a, c), b)),
% 22.36/22.53 inference(transitivity,[status(thm)],[3892, 4092, 3886])).
% 22.36/22.53 tff(4094,plain,
% 22.36/22.53 (mult(mult(mult(b, c), a), c) = mult(mult(mult(a, c), b), c)),
% 22.36/22.53 inference(monotonicity,[status(thm)],[4093])).
% 22.36/22.53 tff(4095,plain,
% 22.36/22.53 (mult(mult(mult(a, c), b), c) = mult(mult(mult(b, c), a), c)),
% 22.36/22.53 inference(symmetry,[status(thm)],[4094])).
% 22.36/22.53 tff(4096,plain,
% 22.36/22.53 (mult(mult(mult(a, c), b), c) = mult(a, mult(mult(b, c), c))),
% 22.36/22.53 inference(transitivity,[status(thm)],[233, 3139])).
% 22.36/22.53 tff(4097,plain,
% 22.36/22.53 ((mult(mult(mult(a, c), b), c) = mult(mult(a, c), mult(b, c))) <=> (mult(a, mult(mult(b, c), c)) = mult(mult(a, mult(b, c)), c))),
% 22.36/22.53 inference(monotonicity,[status(thm)],[4096, 266])).
% 22.36/22.53 tff(4098,plain,
% 22.36/22.53 ((mult(mult(mult(a, c), b), c) = mult(mult(a, c), mult(b, c))) <=> (mult(mult(a, mult(b, c)), c) = mult(a, mult(mult(b, c), c)))),
% 22.36/22.53 inference(transitivity,[status(thm)],[4097, 2412])).
% 22.36/22.53 tff(4099,plain,
% 22.36/22.53 ((mult(mult(a, mult(b, c)), c) = mult(a, mult(mult(b, c), c))) <=> (mult(mult(mult(a, c), b), c) = mult(mult(a, c), mult(b, c)))),
% 22.36/22.53 inference(symmetry,[status(thm)],[4098])).
% 22.36/22.53 tff(4100,plain,
% 22.36/22.53 ((~(mult(mult(a, mult(b, c)), c) = mult(a, mult(mult(b, c), c)))) <=> (~(mult(mult(mult(a, c), b), c) = mult(mult(a, c), mult(b, c))))),
% 22.36/22.53 inference(monotonicity,[status(thm)],[4099])).
% 22.36/22.53 tff(4101,plain,
% 22.36/22.53 (~(mult(mult(mult(a, c), b), c) = mult(mult(a, c), mult(b, c)))),
% 22.36/22.53 inference(modus_ponens,[status(thm)],[258, 4100])).
% 22.36/22.53 tff(4102,plain,
% 22.36/22.53 ((~(mult(mult(mult(a, c), c), b) = mult(mult(a, c), mult(c, b)))) | (~(mult(mult(mult(a, c), b), c) = mult(mult(a, c), mult(b, c))))),
% 22.36/22.53 inference(unit_resolution,[status(thm)],[2751, 4101])).
% 22.36/22.53 tff(4103,plain,
% 22.36/22.53 (~((~(mult(mult(mult(a, c), c), b) = mult(mult(mult(a, c), b), c))) | (~(mult(mult(a, c), mult(c, b)) = mult(mult(a, c), mult(b, c)))))),
% 22.36/22.53 inference(unit_resolution,[status(thm)],[2756, 4102])).
% 22.36/22.53 tff(4104,plain,
% 22.36/22.53 (mult(mult(mult(a, c), c), b) = mult(mult(mult(a, c), b), c)),
% 22.36/22.53 inference(unit_resolution,[status(thm)],[2758, 4103])).
% 22.36/22.53 tff(4105,plain,
% 22.36/22.53 (mult(mult(mult(a, c), c), b) = mult(mult(c, mult(a, c)), b)),
% 22.36/22.53 inference(monotonicity,[status(thm)],[2597])).
% 22.36/22.53 tff(4106,plain,
% 22.36/22.53 (mult(mult(c, mult(a, c)), b) = mult(mult(mult(a, c), c), b)),
% 22.36/22.53 inference(symmetry,[status(thm)],[4105])).
% 22.36/22.53 tff(4107,plain,
% 22.36/22.53 (((~(mult(mult(c, mult(mult(unit, c), unit)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(c, mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit))))) | (~(mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(mult(unit, c), unit)) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(unit, c), unit)))))) | (mult(mult(c, mult(mult(unit, c), unit)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(c, mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit))))),
% 22.36/22.53 inference(tautology,[status(thm)],[])).
% 22.36/22.53 tff(4108,plain,
% 22.36/22.53 (mult(mult(c, mult(mult(unit, c), unit)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(c, mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit)))),
% 22.36/22.53 inference(unit_resolution,[status(thm)],[4107, 4077])).
% 22.36/22.53 tff(4109,plain,
% 22.36/22.53 (mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(unit, c), unit))) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), c))),
% 22.36/22.53 inference(monotonicity,[status(thm)],[3288])).
% 22.36/22.53 tff(4110,plain,
% 22.36/22.53 (mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit))),
% 22.36/22.53 inference(symmetry,[status(thm)],[4008])).
% 22.36/22.53 tff(4111,plain,
% 22.36/22.53 (mult(c, ld(c, mult(a, b))) = mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit))),
% 22.36/22.53 inference(transitivity,[status(thm)],[204, 193, 192, 557, 2898, 211, 4110])).
% 22.36/22.53 tff(4112,plain,
% 22.36/22.53 (mult(c, mult(c, ld(c, mult(a, b)))) = mult(c, mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit)))),
% 22.36/22.53 inference(monotonicity,[status(thm)],[4111])).
% 22.36/22.53 tff(4113,plain,
% 22.36/22.53 (mult(c, mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(c, mult(c, ld(c, mult(a, b))))),
% 22.36/22.53 inference(symmetry,[status(thm)],[4112])).
% 22.36/22.53 tff(4114,plain,
% 22.36/22.53 (mult(c, mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(c, mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)))),
% 22.36/22.53 inference(transitivity,[status(thm)],[4113, 4007])).
% 22.36/22.53 tff(4115,plain,
% 22.36/22.53 ((mult(c, mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(unit, c), unit)))) <=> (mult(c, mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)))),
% 22.36/22.53 inference(monotonicity,[status(thm)],[4114, 4109])).
% 22.36/22.53 tff(4116,plain,
% 22.36/22.53 ((mult(c, mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), c))) <=> (mult(c, mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(unit, c), unit))))),
% 22.36/22.53 inference(symmetry,[status(thm)],[4115])).
% 22.36/22.53 tff(4117,assumption,(mult(mult(c, mult(mult(unit, c), unit)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(c, mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit)))), introduced(assumption)).
% 22.36/22.53 tff(4118,plain,
% 22.36/22.53 (mult(mult(c, mult(mult(unit, c), unit)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(c, c), mult(mult(unit, ld(c, mult(a, b))), unit))),
% 22.36/22.53 inference(monotonicity,[status(thm)],[3181])).
% 22.36/22.53 tff(4119,plain,
% 22.36/22.53 (mult(mult(c, c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(c, mult(mult(unit, c), unit)), mult(mult(unit, ld(c, mult(a, b))), unit))),
% 22.36/22.53 inference(symmetry,[status(thm)],[4118])).
% 22.36/22.53 tff(4120,plain,
% 22.36/22.53 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(c, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c), c) = mult(mult(c, c), mult(mult(unit, ld(c, mult(a, b))), unit)))),
% 22.36/22.53 inference(quant_inst,[status(thm)],[])).
% 22.36/22.53 tff(4121,plain,
% 22.36/22.53 (rd(mult(mult(mult(c, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c), c) = mult(mult(c, c), mult(mult(unit, ld(c, mult(a, b))), unit))),
% 22.36/22.53 inference(unit_resolution,[status(thm)],[4120, 168])).
% 22.36/22.53 tff(4122,plain,
% 22.36/22.53 (mult(c, mult(a, c)) = mult(mult(a, c), c)),
% 22.36/22.53 inference(transitivity,[status(thm)],[4068, 4067, 2595])).
% 22.36/22.53 tff(4123,plain,
% 22.36/22.53 (mult(mult(c, mult(a, c)), b) = mult(mult(mult(a, c), c), b)),
% 22.36/22.53 inference(monotonicity,[status(thm)],[4122])).
% 22.36/22.53 tff(4124,assumption,(mult(mult(c, mult(a, c)), b) = mult(c, mult(mult(a, c), b))), introduced(assumption)).
% 22.36/22.53 tff(4125,plain,
% 22.36/22.53 (mult(c, mult(mult(a, c), b)) = mult(mult(c, mult(a, c)), b)),
% 22.36/22.53 inference(symmetry,[status(thm)],[4124])).
% 22.36/22.53 tff(4126,plain,
% 22.36/22.53 (mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(a, c), b)),
% 22.36/22.53 inference(transitivity,[status(thm)],[214, 227])).
% 22.36/22.53 tff(4127,plain,
% 22.36/22.53 (mult(c, mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), c)) = mult(c, mult(mult(a, c), b))),
% 22.36/22.53 inference(monotonicity,[status(thm)],[4126])).
% 22.36/22.53 tff(4128,plain,
% 22.36/22.53 (mult(mult(mult(c, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(mult(a, b), c), c)),
% 22.36/22.53 inference(transitivity,[status(thm)],[3187, 4127, 4125, 4123, 2759, 4023])).
% 22.36/22.53 tff(4129,plain,
% 22.36/22.53 (rd(mult(mult(mult(c, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c), c) = rd(mult(mult(mult(a, b), c), c), c)),
% 22.36/22.53 inference(monotonicity,[status(thm)],[4128])).
% 22.36/22.53 tff(4130,plain,
% 22.36/22.53 (rd(mult(mult(mult(a, b), c), c), c) = rd(mult(mult(mult(c, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c), c)),
% 22.36/22.53 inference(symmetry,[status(thm)],[4129])).
% 22.36/22.53 tff(4131,plain,
% 22.36/22.53 (mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(c, mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)))),
% 22.36/22.53 inference(transitivity,[status(thm)],[214, 255, 4130, 4121, 4119, 4117, 4113, 4007])).
% 22.36/22.53 tff(4132,plain,
% 22.36/22.53 ((mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), c))) <=> (mult(c, mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)))),
% 22.36/22.53 inference(monotonicity,[status(thm)],[4131])).
% 22.36/22.53 tff(4133,plain,
% 22.36/22.53 (mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(mult(unit, c), unit)) = mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), c)),
% 22.36/22.53 inference(transitivity,[status(thm)],[3179, 3178, 3175, 864, 858, 856, 161, 215])).
% 22.36/22.53 tff(4134,plain,
% 22.36/22.53 ((mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(mult(unit, c), unit)) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(unit, c), unit)))) <=> (mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)))),
% 22.36/22.53 inference(monotonicity,[status(thm)],[4133, 4109])).
% 22.36/22.53 tff(4135,plain,
% 22.36/22.53 ((mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(mult(unit, c), unit)) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(unit, c), unit)))) <=> (mult(c, mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(unit, c), unit))))),
% 22.36/22.53 inference(transitivity,[status(thm)],[4134, 4132, 4116])).
% 22.36/22.53 tff(4136,plain,
% 22.36/22.53 (mult(c, mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(unit, c), unit)))),
% 22.36/22.53 inference(modus_ponens,[status(thm)],[4078, 4135])).
% 22.36/22.53 tff(4137,plain,
% 22.36/22.53 ($false),
% 22.36/22.53 inference(unit_resolution,[status(thm)],[4072, 4136])).
% 22.36/22.53 tff(4138,plain,((mult(c, mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(unit, c), unit)))) | (~(mult(mult(c, mult(mult(unit, c), unit)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(c, mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit))))) | (~(mult(mult(c, mult(a, c)), b) = mult(c, mult(mult(a, c), b)))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c))))), inference(lemma,lemma(discharge,[]))).
% 22.36/22.53 tff(4139,plain,
% 22.36/22.53 (~(mult(mult(c, mult(a, c)), b) = mult(c, mult(mult(a, c), b)))),
% 22.36/22.53 inference(unit_resolution,[status(thm)],[4138, 4108, 4072, 2591])).
% 22.36/22.53 tff(4140,plain,
% 22.36/22.53 ((~(mult(mult(c, mult(a, c)), b) = mult(c, mult(mult(a, c), b)))) | (~(mult(mult(c, b), mult(a, c)) = mult(c, mult(b, mult(a, c)))))),
% 22.36/22.53 inference(unit_resolution,[status(thm)],[2781, 4139])).
% 22.36/22.53 tff(4141,plain,
% 22.36/22.53 (~((~(mult(mult(c, mult(a, c)), b) = mult(mult(c, b), mult(a, c)))) | (~(mult(c, mult(mult(a, c), b)) = mult(c, mult(b, mult(a, c))))))),
% 22.36/22.53 inference(unit_resolution,[status(thm)],[2436, 4140])).
% 22.36/22.53 tff(4142,plain,
% 22.36/22.53 (mult(mult(c, mult(a, c)), b) = mult(mult(c, b), mult(a, c))),
% 22.36/22.53 inference(unit_resolution,[status(thm)],[2438, 4141])).
% 22.36/22.53 tff(4143,plain,
% 22.36/22.53 (mult(mult(c, b), mult(a, c)) = mult(mult(c, mult(a, c)), b)),
% 22.36/22.53 inference(symmetry,[status(thm)],[4142])).
% 22.36/22.53 tff(4144,plain,
% 22.36/22.53 (mult(mult(b, c), mult(a, c)) = mult(b, mult(c, mult(a, c)))),
% 22.36/22.53 inference(transitivity,[status(thm)],[2742, 4143, 4106, 4104, 4095, 2570, 4071])).
% 22.36/22.53 tff(4145,assumption,(~(mult(mult(b, c), mult(a, c)) = mult(b, mult(c, mult(a, c))))), introduced(assumption)).
% 22.36/22.53 tff(4146,plain,
% 22.36/22.53 ($false),
% 22.36/22.53 inference(unit_resolution,[status(thm)],[4145, 4144])).
% 22.36/22.53 tff(4147,plain,((mult(c, mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(unit, c), unit)))) | (mult(mult(b, c), mult(a, c)) = mult(b, mult(c, mult(a, c)))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c)))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit)))))), inference(lemma,lemma(discharge,[]))).
% 22.36/22.53 tff(4148,plain,
% 22.36/22.53 (mult(mult(b, c), mult(a, c)) = mult(b, mult(c, mult(a, c)))),
% 22.36/22.53 inference(unit_resolution,[status(thm)],[4147, 4064, 4003, 3865])).
% 22.36/22.54 tff(4149,plain,
% 22.36/22.54 (mult(b, mult(mult(c, a), c)) = mult(mult(mult(b, c), a), c)),
% 22.36/22.54 inference(symmetry,[status(thm)],[2570])).
% 22.36/22.54 tff(4150,plain,
% 22.36/22.54 (mult(b, mult(mult(c, a), c)) = mult(b, mult(c, mult(a, c)))),
% 22.36/22.54 inference(monotonicity,[status(thm)],[3912])).
% 22.36/22.54 tff(4151,plain,
% 22.36/22.54 (mult(b, mult(c, mult(a, c))) = mult(b, mult(mult(c, a), c))),
% 22.36/22.54 inference(symmetry,[status(thm)],[4150])).
% 22.36/22.54 tff(4152,assumption,(mult(mult(b, c), mult(a, c)) = mult(b, mult(c, mult(a, c)))), introduced(assumption)).
% 22.36/22.54 tff(4153,plain,
% 22.36/22.54 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(mult(a, c), c), mult(mult(mult(a, c), c), mult(a, c))) = mult(a, c))),
% 22.36/22.54 inference(quant_inst,[status(thm)],[])).
% 22.36/22.54 tff(4154,plain,
% 22.36/22.54 (ld(mult(mult(a, c), c), mult(mult(mult(a, c), c), mult(a, c))) = mult(a, c)),
% 22.36/22.54 inference(unit_resolution,[status(thm)],[4153, 7])).
% 22.36/22.54 tff(4155,assumption,(mult(mult(mult(a, c), c), mult(c, a)) = mult(mult(mult(a, c), c), mult(a, c))), introduced(assumption)).
% 22.36/22.54 tff(4156,plain,
% 22.36/22.54 (ld(mult(mult(a, c), c), mult(mult(mult(a, c), c), mult(c, a))) = ld(mult(mult(a, c), c), mult(mult(mult(a, c), c), mult(a, c)))),
% 22.36/22.54 inference(monotonicity,[status(thm)],[4155])).
% 22.36/22.54 tff(4157,plain,
% 22.36/22.54 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(mult(a, c), c), mult(mult(mult(a, c), c), mult(c, a))) = mult(c, a))),
% 22.36/22.54 inference(quant_inst,[status(thm)],[])).
% 22.36/22.54 tff(4158,plain,
% 22.36/22.54 (ld(mult(mult(a, c), c), mult(mult(mult(a, c), c), mult(c, a))) = mult(c, a)),
% 22.36/22.54 inference(unit_resolution,[status(thm)],[4157, 7])).
% 22.36/22.54 tff(4159,plain,
% 22.36/22.54 (mult(c, a) = ld(mult(mult(a, c), c), mult(mult(mult(a, c), c), mult(c, a)))),
% 22.36/22.54 inference(symmetry,[status(thm)],[4158])).
% 22.36/22.54 tff(4160,plain,
% 22.36/22.54 (mult(c, a) = mult(a, c)),
% 22.36/22.54 inference(transitivity,[status(thm)],[4159, 4156, 4154])).
% 22.36/22.54 tff(4161,plain,
% 22.36/22.54 (mult(mult(b, c), mult(c, a)) = mult(mult(b, c), mult(a, c))),
% 22.36/22.54 inference(monotonicity,[status(thm)],[4160])).
% 22.36/22.54 tff(4162,assumption,(~(mult(mult(mult(b, c), c), a) = mult(mult(mult(b, c), a), c))), introduced(assumption)).
% 22.36/22.54 tff(4163,plain,
% 22.36/22.54 ((~(mult(mult(b, c), mult(c, a)) = mult(mult(b, c), mult(a, c)))) | (~(mult(mult(mult(b, c), c), a) = mult(mult(mult(b, c), a), c)))),
% 22.36/22.54 inference(unit_resolution,[status(thm)],[2586, 4162])).
% 22.36/22.54 tff(4164,plain,
% 22.36/22.54 (~((~(mult(mult(mult(b, c), c), a) = mult(mult(b, c), mult(c, a)))) | (~(mult(mult(mult(b, c), a), c) = mult(mult(b, c), mult(a, c)))))),
% 22.36/22.54 inference(unit_resolution,[status(thm)],[2584, 4163])).
% 22.36/22.54 tff(4165,plain,
% 22.36/22.54 (((~(mult(mult(mult(b, c), c), a) = mult(mult(b, c), mult(c, a)))) | (~(mult(mult(mult(b, c), a), c) = mult(mult(b, c), mult(a, c))))) | (mult(mult(mult(b, c), c), a) = mult(mult(b, c), mult(c, a)))),
% 22.36/22.54 inference(tautology,[status(thm)],[])).
% 22.36/22.54 tff(4166,plain,
% 22.36/22.54 (mult(mult(mult(b, c), c), a) = mult(mult(b, c), mult(c, a))),
% 22.36/22.54 inference(unit_resolution,[status(thm)],[4165, 4164])).
% 22.36/22.54 tff(4167,plain,
% 22.36/22.54 (mult(mult(mult(b, c), c), a) = mult(mult(mult(b, c), a), c)),
% 22.36/22.54 inference(transitivity,[status(thm)],[4166, 4161, 4152, 4151, 4149])).
% 22.36/22.54 tff(4168,plain,
% 22.36/22.54 ($false),
% 22.36/22.54 inference(unit_resolution,[status(thm)],[4162, 4167])).
% 22.36/22.54 tff(4169,plain,((~(mult(mult(mult(a, c), c), mult(c, a)) = mult(mult(mult(a, c), c), mult(a, c)))) | (mult(mult(mult(b, c), c), a) = mult(mult(mult(b, c), a), c)) | (~(mult(mult(b, c), mult(a, c)) = mult(b, mult(c, mult(a, c))))) | (~(mult(mult(c, a), c) = mult(c, mult(a, c))))), inference(lemma,lemma(discharge,[]))).
% 22.36/22.54 tff(4170,plain,
% 22.36/22.54 ((~(mult(mult(mult(a, c), c), mult(c, a)) = mult(mult(mult(a, c), c), mult(a, c)))) | (mult(mult(mult(b, c), c), a) = mult(mult(mult(b, c), a), c)) | (~(mult(mult(b, c), mult(a, c)) = mult(b, mult(c, mult(a, c)))))),
% 22.36/22.54 inference(unit_resolution,[status(thm)],[4169, 2690])).
% 22.36/22.54 tff(4171,plain,
% 22.36/22.54 (mult(mult(mult(b, c), c), a) = mult(mult(mult(b, c), a), c)),
% 22.36/22.54 inference(unit_resolution,[status(thm)],[4170, 4148, 3897])).
% 22.36/22.54 tff(4172,plain,
% 22.36/22.54 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(a, mult(a, mult(mult(b, c), c))) = mult(mult(b, c), c))),
% 22.36/22.54 inference(quant_inst,[status(thm)],[])).
% 22.36/22.54 tff(4173,plain,
% 22.36/22.54 (ld(a, mult(a, mult(mult(b, c), c))) = mult(mult(b, c), c)),
% 22.36/22.54 inference(unit_resolution,[status(thm)],[4172, 7])).
% 22.36/22.54 tff(4174,plain,
% 22.36/22.54 (((~(mult(mult(a, c), mult(b, c)) = mult(mult(a, mult(b, c)), c))) | (~(mult(a, mult(c, mult(b, c))) = mult(a, mult(mult(b, c), c))))) | (mult(a, mult(c, mult(b, c))) = mult(a, mult(mult(b, c), c)))),
% 22.36/22.54 inference(tautology,[status(thm)],[])).
% 22.36/22.54 tff(4175,plain,
% 22.36/22.54 (mult(a, mult(c, mult(b, c))) = mult(a, mult(mult(b, c), c))),
% 22.36/22.54 inference(unit_resolution,[status(thm)],[4174, 264])).
% 22.36/22.54 tff(4176,plain,
% 22.36/22.54 (ld(a, mult(a, mult(c, mult(b, c)))) = ld(a, mult(a, mult(mult(b, c), c)))),
% 22.36/22.54 inference(monotonicity,[status(thm)],[4175])).
% 22.36/22.54 tff(4177,plain,
% 22.36/22.54 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(a, mult(a, mult(c, mult(b, c)))) = mult(c, mult(b, c)))),
% 22.36/22.54 inference(quant_inst,[status(thm)],[])).
% 22.36/22.54 tff(4178,plain,
% 22.36/22.54 (ld(a, mult(a, mult(c, mult(b, c)))) = mult(c, mult(b, c))),
% 22.36/22.54 inference(unit_resolution,[status(thm)],[4177, 7])).
% 22.36/22.54 tff(4179,plain,
% 22.36/22.54 (mult(c, mult(b, c)) = ld(a, mult(a, mult(c, mult(b, c))))),
% 22.36/22.54 inference(symmetry,[status(thm)],[4178])).
% 22.36/22.54 tff(4180,plain,
% 22.36/22.54 (mult(c, mult(b, c)) = mult(mult(b, c), c)),
% 22.36/22.54 inference(transitivity,[status(thm)],[4179, 4176, 4173])).
% 22.36/22.54 tff(4181,plain,
% 22.36/22.54 (mult(mult(c, mult(b, c)), a) = mult(mult(mult(b, c), c), a)),
% 22.36/22.54 inference(monotonicity,[status(thm)],[4180])).
% 22.36/22.54 tff(4182,plain,
% 22.36/22.54 (mult(mult(c, mult(b, c)), a) = mult(mult(unit, mult(mult(a, b), c)), c)),
% 22.36/22.54 inference(transitivity,[status(thm)],[4181, 4171, 3896, 231])).
% 22.36/22.54 tff(4183,plain,
% 22.36/22.54 ((mult(mult(c, mult(b, c)), a) = mult(c, mult(mult(b, c), a))) <=> (mult(mult(unit, mult(mult(a, b), c)), c) = mult(mult(unit, c), mult(mult(a, b), c)))),
% 22.36/22.54 inference(monotonicity,[status(thm)],[4182, 3895])).
% 22.36/22.54 tff(4184,plain,
% 22.36/22.54 ((mult(mult(c, mult(b, c)), a) = mult(c, mult(mult(b, c), a))) <=> (mult(mult(unit, c), mult(mult(a, b), c)) = mult(mult(unit, mult(mult(a, b), c)), c))),
% 22.36/22.54 inference(transitivity,[status(thm)],[4183, 2708])).
% 22.36/22.54 tff(4185,plain,
% 22.36/22.54 ((mult(mult(c, mult(b, c)), a) = mult(c, mult(mult(b, c), a))) <=> (mult(mult(c, mult(a, c)), b) = mult(c, mult(mult(a, c), b)))),
% 22.36/22.54 inference(transitivity,[status(thm)],[4184, 3883])).
% 22.36/22.54 tff(4186,plain,
% 22.36/22.54 (mult(mult(c, a), mult(b, c)) = mult(mult(a, c), mult(b, c))),
% 22.36/22.54 inference(monotonicity,[status(thm)],[3885])).
% 22.36/22.54 tff(4187,plain,
% 22.36/22.54 (mult(mult(c, a), mult(b, c)) = mult(mult(a, mult(b, c)), c)),
% 22.36/22.54 inference(transitivity,[status(thm)],[4186, 266])).
% 22.36/22.54 tff(4188,plain,
% 22.36/22.54 (mult(mult(c, mult(b, c)), a) = mult(a, mult(mult(b, c), c))),
% 22.36/22.54 inference(transitivity,[status(thm)],[4181, 4171, 3896, 233, 2414])).
% 22.36/22.54 tff(4189,plain,
% 22.36/22.54 ((mult(mult(c, mult(b, c)), a) = mult(mult(c, a), mult(b, c))) <=> (mult(a, mult(mult(b, c), c)) = mult(mult(a, mult(b, c)), c))),
% 22.36/22.54 inference(monotonicity,[status(thm)],[4188, 4187])).
% 22.36/22.54 tff(4190,plain,
% 22.36/22.54 ((mult(mult(c, mult(b, c)), a) = mult(mult(c, a), mult(b, c))) <=> (mult(mult(a, mult(b, c)), c) = mult(a, mult(mult(b, c), c)))),
% 22.36/22.54 inference(transitivity,[status(thm)],[4189, 2412])).
% 22.36/22.54 tff(4191,plain,
% 22.36/22.54 ((mult(mult(a, mult(b, c)), c) = mult(a, mult(mult(b, c), c))) <=> (mult(mult(c, mult(b, c)), a) = mult(mult(c, a), mult(b, c)))),
% 22.36/22.54 inference(symmetry,[status(thm)],[4190])).
% 22.36/22.54 tff(4192,plain,
% 22.36/22.54 ((~(mult(mult(a, mult(b, c)), c) = mult(a, mult(mult(b, c), c)))) <=> (~(mult(mult(c, mult(b, c)), a) = mult(mult(c, a), mult(b, c))))),
% 22.36/22.54 inference(monotonicity,[status(thm)],[4191])).
% 22.36/22.54 tff(4193,plain,
% 22.36/22.54 (~(mult(mult(c, mult(b, c)), a) = mult(mult(c, a), mult(b, c)))),
% 22.36/22.54 inference(modus_ponens,[status(thm)],[258, 4192])).
% 22.36/22.54 tff(4194,plain,
% 22.36/22.54 (((~(mult(mult(c, mult(b, c)), a) = mult(mult(c, a), mult(b, c)))) | (~(mult(c, mult(mult(b, c), a)) = mult(c, mult(a, mult(b, c)))))) | (mult(mult(c, mult(b, c)), a) = mult(mult(c, a), mult(b, c)))),
% 22.36/22.54 inference(tautology,[status(thm)],[])).
% 22.36/22.54 tff(4195,plain,
% 22.36/22.54 ((~(mult(mult(c, mult(b, c)), a) = mult(mult(c, a), mult(b, c)))) | (~(mult(c, mult(mult(b, c), a)) = mult(c, mult(a, mult(b, c)))))),
% 22.36/22.54 inference(unit_resolution,[status(thm)],[4194, 4193])).
% 22.36/22.54 tff(4196,plain,
% 22.36/22.54 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(c, mult(b, c)), a) = mult(mult(c, a), mult(b, c)))) | (~(mult(c, mult(mult(b, c), a)) = mult(c, mult(a, mult(b, c))))))) | (~((~(mult(mult(c, mult(b, c)), a) = mult(c, mult(mult(b, c), a)))) | (~(mult(mult(c, a), mult(b, c)) = mult(c, mult(a, mult(b, c))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(c, mult(b, c)), a) = mult(mult(c, a), mult(b, c)))) | (~(mult(c, mult(mult(b, c), a)) = mult(c, mult(a, mult(b, c))))))) | (~((~(mult(mult(c, mult(b, c)), a) = mult(c, mult(mult(b, c), a)))) | (~(mult(mult(c, a), mult(b, c)) = mult(c, mult(a, mult(b, c))))))))),
% 22.36/22.54 inference(rewrite,[status(thm)],[])).
% 22.36/22.54 tff(4197,plain,
% 22.36/22.54 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(c, mult(b, c)), a) = mult(mult(c, a), mult(b, c)))) | (~(mult(c, mult(mult(b, c), a)) = mult(c, mult(a, mult(b, c))))))) | (~((~(mult(mult(c, mult(b, c)), a) = mult(c, mult(mult(b, c), a)))) | (~(mult(mult(c, a), mult(b, c)) = mult(c, mult(a, mult(b, c))))))))),
% 22.36/22.54 inference(quant_inst,[status(thm)],[])).
% 22.36/22.54 tff(4198,plain,
% 22.36/22.54 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(c, mult(b, c)), a) = mult(mult(c, a), mult(b, c)))) | (~(mult(c, mult(mult(b, c), a)) = mult(c, mult(a, mult(b, c))))))) | (~((~(mult(mult(c, mult(b, c)), a) = mult(c, mult(mult(b, c), a)))) | (~(mult(mult(c, a), mult(b, c)) = mult(c, mult(a, mult(b, c)))))))),
% 22.36/22.54 inference(modus_ponens,[status(thm)],[4197, 4196])).
% 22.36/22.54 tff(4199,plain,
% 22.36/22.54 ((~((~(mult(mult(c, mult(b, c)), a) = mult(mult(c, a), mult(b, c)))) | (~(mult(c, mult(mult(b, c), a)) = mult(c, mult(a, mult(b, c))))))) | (~((~(mult(mult(c, mult(b, c)), a) = mult(c, mult(mult(b, c), a)))) | (~(mult(mult(c, a), mult(b, c)) = mult(c, mult(a, mult(b, c)))))))),
% 22.36/22.54 inference(unit_resolution,[status(thm)],[4198, 27])).
% 22.36/22.54 tff(4200,plain,
% 22.36/22.54 (~((~(mult(mult(c, mult(b, c)), a) = mult(c, mult(mult(b, c), a)))) | (~(mult(mult(c, a), mult(b, c)) = mult(c, mult(a, mult(b, c))))))),
% 22.36/22.54 inference(unit_resolution,[status(thm)],[4199, 4195])).
% 22.36/22.54 tff(4201,plain,
% 22.36/22.54 (((~(mult(mult(c, mult(b, c)), a) = mult(c, mult(mult(b, c), a)))) | (~(mult(mult(c, a), mult(b, c)) = mult(c, mult(a, mult(b, c)))))) | (mult(mult(c, mult(b, c)), a) = mult(c, mult(mult(b, c), a)))),
% 22.36/22.54 inference(tautology,[status(thm)],[])).
% 22.36/22.54 tff(4202,plain,
% 22.36/22.54 (mult(mult(c, mult(b, c)), a) = mult(c, mult(mult(b, c), a))),
% 22.36/22.54 inference(unit_resolution,[status(thm)],[4201, 4200])).
% 22.36/22.54 tff(4203,plain,
% 22.36/22.54 (mult(mult(c, mult(a, c)), b) = mult(c, mult(mult(a, c), b))),
% 22.36/22.54 inference(modus_ponens,[status(thm)],[4202, 4185])).
% 22.36/22.54 tff(4204,plain,
% 22.36/22.54 (mult(mult(c, mult(mult(unit, c), unit)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(c, mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit)))),
% 22.36/22.54 inference(unit_resolution,[status(thm)],[4107, 4054])).
% 22.36/22.54 tff(4205,plain,
% 22.36/22.54 (~(mult(mult(c, mult(a, c)), b) = mult(c, mult(mult(a, c), b)))),
% 22.36/22.54 inference(unit_resolution,[status(thm)],[4138, 4064, 4003, 4204])).
% 22.36/22.54 tff(4206,plain,
% 22.36/22.54 ($false),
% 22.36/22.54 inference(unit_resolution,[status(thm)],[4205, 4203])).
% 22.36/22.54 tff(4207,plain,((mult(mult(c, b), a) = mult(c, mult(b, a))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit)))))), inference(lemma,lemma(discharge,[]))).
% 22.36/22.54 tff(4208,plain,
% 22.36/22.54 (mult(mult(c, b), a) = mult(c, mult(b, a))),
% 22.36/22.54 inference(unit_resolution,[status(thm)],[4207, 3862])).
% 22.36/22.54 tff(4209,plain,
% 22.36/22.54 ((~(mult(mult(c, b), a) = mult(c, mult(b, a)))) | (~(mult(mult(c, a), b) = mult(c, mult(a, b))))),
% 22.36/22.54 inference(unit_resolution,[status(thm)],[2279, 4025])).
% 22.36/22.54 tff(4210,plain,
% 22.36/22.54 (~((~(mult(mult(c, b), a) = mult(mult(c, a), b))) | (~(mult(c, mult(b, a)) = mult(c, mult(a, b)))))),
% 22.36/22.54 inference(unit_resolution,[status(thm)],[2249, 4209])).
% 22.36/22.54 tff(4211,plain,
% 22.36/22.54 (mult(c, mult(b, a)) = mult(c, mult(a, b))),
% 22.36/22.54 inference(unit_resolution,[status(thm)],[2244, 4210])).
% 22.36/22.54 tff(4212,plain,
% 22.36/22.54 (mult(mult(c, b), a) = mult(c, mult(a, b))),
% 22.36/22.54 inference(transitivity,[status(thm)],[2299, 4211])).
% 22.36/22.54 tff(4213,plain,
% 22.36/22.54 ((mult(mult(c, b), a) = mult(mult(c, a), b)) <=> (mult(c, mult(a, b)) = mult(mult(c, a), b))),
% 22.36/22.54 inference(monotonicity,[status(thm)],[4212])).
% 22.36/22.54 tff(4214,plain,
% 22.36/22.54 ((mult(mult(c, b), a) = mult(mult(c, a), b)) <=> (mult(mult(c, a), b) = mult(c, mult(a, b)))),
% 22.36/22.54 inference(transitivity,[status(thm)],[4213, 4014])).
% 22.36/22.54 tff(4215,plain,
% 22.36/22.54 ((mult(mult(c, a), b) = mult(c, mult(a, b))) <=> (mult(mult(c, b), a) = mult(mult(c, a), b))),
% 22.36/22.54 inference(symmetry,[status(thm)],[4214])).
% 22.36/22.54 tff(4216,plain,
% 22.36/22.54 ((~(mult(mult(c, a), b) = mult(c, mult(a, b)))) <=> (~(mult(mult(c, b), a) = mult(mult(c, a), b)))),
% 22.36/22.54 inference(monotonicity,[status(thm)],[4215])).
% 22.36/22.54 tff(4217,plain,
% 22.36/22.54 (~(mult(mult(c, b), a) = mult(mult(c, a), b))),
% 22.36/22.54 inference(modus_ponens,[status(thm)],[4025, 4216])).
% 22.36/22.54 tff(4218,plain,
% 22.36/22.54 (mult(mult(c, b), a) = mult(mult(c, a), b)),
% 22.36/22.54 inference(unit_resolution,[status(thm)],[3890, 4210])).
% 22.36/22.54 tff(4219,plain,
% 22.36/22.54 ($false),
% 22.36/22.54 inference(unit_resolution,[status(thm)],[4218, 4217])).
% 22.36/22.54 tff(4220,plain,((mult(mult(c, a), b) = mult(c, mult(a, b))) | (~(mult(mult(c, b), a) = mult(c, mult(b, a))))), inference(lemma,lemma(discharge,[]))).
% 22.36/22.54 tff(4221,plain,
% 22.36/22.54 (mult(mult(c, a), b) = mult(c, mult(a, b))),
% 22.36/22.54 inference(unit_resolution,[status(thm)],[4220, 4208])).
% 22.36/22.54 tff(4222,plain,
% 22.36/22.54 ((mult(mult(c, mult(mult(unit, c), unit)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(c, mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit)))) <=> (mult(mult(c, c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(c, mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))),
% 22.36/22.54 inference(monotonicity,[status(thm)],[4118, 4011])).
% 22.36/22.54 tff(4223,plain,
% 22.36/22.54 ((mult(mult(c, c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(c, mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)))) <=> (mult(mult(c, mult(mult(unit, c), unit)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(c, mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit))))),
% 22.36/22.54 inference(symmetry,[status(thm)],[4222])).
% 22.36/22.54 tff(4224,plain,
% 22.36/22.54 (mult(c, mult(a, b)) = mult(mult(c, a), b)),
% 22.36/22.54 inference(symmetry,[status(thm)],[2288])).
% 22.36/22.54 tff(4225,plain,
% 22.36/22.54 (mult(c, mult(c, ld(c, mult(a, b)))) = mult(c, mult(a, b))),
% 22.36/22.54 inference(monotonicity,[status(thm)],[204])).
% 22.36/22.54 tff(4226,plain,
% 22.36/22.54 (mult(c, mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), c)),
% 22.36/22.54 inference(transitivity,[status(thm)],[4006, 4225, 4224, 3886, 161, 215])).
% 22.36/22.54 tff(4227,plain,
% 22.36/22.54 ((mult(mult(c, c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(c, mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)))) <=> (mult(mult(c, c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), c))),
% 22.36/22.54 inference(monotonicity,[status(thm)],[4226])).
% 22.36/22.54 tff(4228,plain,
% 22.36/22.54 ((mult(mult(c, c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), c)) <=> (mult(mult(c, c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(c, mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))),
% 22.36/22.54 inference(symmetry,[status(thm)],[4227])).
% 22.36/22.54 tff(4229,plain,
% 22.36/22.54 ((mult(mult(c, mult(mult(unit, c), unit)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(mult(unit, c), unit))) <=> (mult(mult(c, c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), c))),
% 22.36/22.55 inference(monotonicity,[status(thm)],[4118, 4133])).
% 22.36/22.55 tff(4230,plain,
% 22.36/22.55 ((mult(mult(c, mult(mult(unit, c), unit)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(mult(unit, c), unit))) <=> (mult(mult(c, mult(mult(unit, c), unit)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(c, mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit))))),
% 22.36/22.55 inference(transitivity,[status(thm)],[4229, 4228, 4223])).
% 22.36/22.55 tff(4231,assumption,(~(mult(mult(c, mult(mult(unit, c), unit)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(c, mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit))))), introduced(assumption)).
% 22.36/22.55 tff(4232,plain,
% 22.36/22.55 ((~(mult(mult(c, mult(mult(unit, c), unit)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(c, mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit))))) | (~(mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(mult(unit, c), unit)) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(unit, c), unit)))))),
% 22.36/22.55 inference(unit_resolution,[status(thm)],[4107, 4231])).
% 22.36/22.55 tff(4233,plain,
% 22.36/22.55 (~((~(mult(mult(c, mult(mult(unit, c), unit)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(mult(unit, c), unit)))) | (~(mult(c, mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(unit, c), unit))))))),
% 22.36/22.55 inference(unit_resolution,[status(thm)],[3201, 4232])).
% 22.36/22.55 tff(4234,plain,
% 22.36/22.55 (mult(mult(c, mult(mult(unit, c), unit)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(mult(unit, c), unit))),
% 22.36/22.55 inference(unit_resolution,[status(thm)],[3196, 4233])).
% 22.36/22.55 tff(4235,plain,
% 22.36/22.55 (mult(mult(c, mult(mult(unit, c), unit)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(c, mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit)))),
% 22.36/22.55 inference(modus_ponens,[status(thm)],[4234, 4230])).
% 22.36/22.55 tff(4236,plain,
% 22.36/22.55 ($false),
% 22.36/22.55 inference(unit_resolution,[status(thm)],[4231, 4235])).
% 22.36/22.55 tff(4237,plain,((mult(mult(c, mult(mult(unit, c), unit)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(c, mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit)))) | (~(mult(mult(c, a), b) = mult(c, mult(a, b)))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit)))))), inference(lemma,lemma(discharge,[]))).
% 22.36/22.55 tff(4238,plain,
% 22.36/22.55 (mult(mult(c, mult(mult(unit, c), unit)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(c, mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit)))),
% 22.36/22.55 inference(unit_resolution,[status(thm)],[4237, 4221, 3862])).
% 22.36/22.55 tff(4239,plain,
% 22.36/22.55 (mult(mult(c, mult(mult(unit, c), unit)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(c, c), mult(mult(unit, ld(c, mult(a, b))), unit))),
% 22.36/22.55 inference(symmetry,[status(thm)],[3183])).
% 22.36/22.55 tff(4240,plain,
% 22.36/22.55 (mult(c, mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(mult(c, mult(mult(unit, c), unit)), mult(mult(unit, ld(c, mult(a, b))), unit))),
% 22.36/22.55 inference(symmetry,[status(thm)],[4117])).
% 22.36/22.55 tff(4241,plain,
% 22.36/22.55 (mult(c, mult(c, ld(c, mult(a, b)))) = mult(c, mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit)))),
% 22.36/22.55 inference(symmetry,[status(thm)],[4010])).
% 22.36/22.55 tff(4242,plain,
% 22.36/22.55 (mult(c, mult(a, b)) = mult(mult(c, c), mult(mult(unit, ld(c, mult(a, b))), unit))),
% 22.36/22.55 inference(transitivity,[status(thm)],[1442, 4241, 4240, 4239])).
% 22.36/22.55 tff(4243,plain,
% 22.36/22.55 (mult(mult(c, mult(a, b)), c) = mult(mult(mult(c, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c)),
% 22.36/22.55 inference(monotonicity,[status(thm)],[4242])).
% 22.36/22.55 tff(4244,plain,
% 22.36/22.55 (mult(mult(mult(c, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(c, mult(a, b)), c)),
% 22.36/22.55 inference(symmetry,[status(thm)],[4243])).
% 22.36/22.55 tff(4245,plain,
% 22.36/22.55 (mult(c, mult(mult(a, c), b)) = mult(c, mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), c))),
% 22.36/22.55 inference(symmetry,[status(thm)],[4127])).
% 22.36/22.55 tff(4246,assumption,(~(mult(mult(c, c), mult(a, b)) = mult(c, mult(c, mult(a, b))))), introduced(assumption)).
% 22.36/22.55 tff(4247,plain,
% 22.36/22.55 (((~(mult(mult(c, c), mult(a, b)) = mult(c, mult(c, mult(a, b))))) | (~(mult(mult(c, mult(a, b)), c) = mult(c, mult(mult(a, b), c))))) | (mult(mult(c, c), mult(a, b)) = mult(c, mult(c, mult(a, b))))),
% 22.36/22.55 inference(tautology,[status(thm)],[])).
% 22.36/22.55 tff(4248,plain,
% 22.36/22.55 ((~(mult(mult(c, c), mult(a, b)) = mult(c, mult(c, mult(a, b))))) | (~(mult(mult(c, mult(a, b)), c) = mult(c, mult(mult(a, b), c))))),
% 22.36/22.55 inference(unit_resolution,[status(thm)],[4247, 4246])).
% 22.36/22.55 tff(4249,plain,
% 22.36/22.55 ((~((~(mult(mult(c, c), mult(a, b)) = mult(mult(c, mult(a, b)), c))) | (~(mult(c, mult(c, mult(a, b))) = mult(c, mult(mult(a, b), c)))))) | (~((~(mult(mult(c, c), mult(a, b)) = mult(c, mult(c, mult(a, b))))) | (~(mult(mult(c, mult(a, b)), c) = mult(c, mult(mult(a, b), c))))))),
% 22.36/22.55 inference(unit_resolution,[status(thm)],[4041, 27])).
% 22.36/22.55 tff(4250,plain,
% 22.36/22.55 (~((~(mult(mult(c, c), mult(a, b)) = mult(mult(c, mult(a, b)), c))) | (~(mult(c, mult(c, mult(a, b))) = mult(c, mult(mult(a, b), c)))))),
% 22.36/22.55 inference(unit_resolution,[status(thm)],[4249, 4248])).
% 22.36/22.55 tff(4251,plain,
% 22.36/22.55 (mult(c, mult(c, mult(a, b))) = mult(c, mult(mult(a, b), c))),
% 22.36/22.55 inference(unit_resolution,[status(thm)],[4037, 4250])).
% 22.36/22.55 tff(4252,plain,
% 22.36/22.55 (mult(c, mult(c, mult(a, b))) = mult(mult(c, mult(a, b)), c)),
% 22.36/22.55 inference(transitivity,[status(thm)],[4251, 4024, 4245, 3188, 4244])).
% 22.36/22.55 tff(4253,plain,
% 22.36/22.55 ((mult(mult(c, c), mult(a, b)) = mult(c, mult(c, mult(a, b)))) <=> (mult(mult(c, c), mult(a, b)) = mult(mult(c, mult(a, b)), c))),
% 22.36/22.55 inference(monotonicity,[status(thm)],[4252])).
% 22.36/22.55 tff(4254,plain,
% 22.36/22.55 ((mult(mult(c, c), mult(a, b)) = mult(mult(c, mult(a, b)), c)) <=> (mult(mult(c, c), mult(a, b)) = mult(c, mult(c, mult(a, b))))),
% 22.36/22.55 inference(symmetry,[status(thm)],[4253])).
% 22.36/22.55 tff(4255,plain,
% 22.36/22.55 (((~(mult(mult(c, c), mult(a, b)) = mult(mult(c, mult(a, b)), c))) | (~(mult(c, mult(c, mult(a, b))) = mult(c, mult(mult(a, b), c))))) | (mult(mult(c, c), mult(a, b)) = mult(mult(c, mult(a, b)), c))),
% 22.36/22.55 inference(tautology,[status(thm)],[])).
% 22.36/22.55 tff(4256,plain,
% 22.36/22.55 (mult(mult(c, c), mult(a, b)) = mult(mult(c, mult(a, b)), c)),
% 22.36/22.55 inference(unit_resolution,[status(thm)],[4255, 4250])).
% 22.36/22.55 tff(4257,plain,
% 22.36/22.55 (mult(mult(c, c), mult(a, b)) = mult(c, mult(c, mult(a, b)))),
% 22.36/22.55 inference(modus_ponens,[status(thm)],[4256, 4254])).
% 22.36/22.55 tff(4258,plain,
% 22.36/22.55 ($false),
% 22.36/22.55 inference(unit_resolution,[status(thm)],[4246, 4257])).
% 22.36/22.55 tff(4259,plain,((mult(mult(c, c), mult(a, b)) = mult(c, mult(c, mult(a, b)))) | (~(mult(mult(c, mult(mult(unit, c), unit)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(c, mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit)))))), inference(lemma,lemma(discharge,[]))).
% 22.36/22.55 tff(4260,plain,
% 22.36/22.55 (mult(mult(c, c), mult(a, b)) = mult(c, mult(c, mult(a, b)))),
% 22.36/22.55 inference(unit_resolution,[status(thm)],[4259, 4238])).
% 22.36/22.55 tff(4261,plain,
% 22.36/22.55 (mult(c, mult(c, mult(a, b))) = mult(mult(c, c), mult(a, b))),
% 22.36/22.55 inference(symmetry,[status(thm)],[4260])).
% 22.36/22.55 tff(4262,plain,
% 22.36/22.55 (mult(rd(mult(b, c), mult(a, c)), mult(c, a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, c))),
% 22.36/22.55 inference(transitivity,[status(thm)],[3867, 3862, 61])).
% 22.36/22.55 tff(4263,plain,
% 22.36/22.55 (ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(c, a))) = ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))),
% 22.36/22.55 inference(monotonicity,[status(thm)],[4262])).
% 22.36/22.55 tff(4264,assumption,(~(ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(c, a))) = mult(c, a))), introduced(assumption)).
% 22.36/22.55 tff(4265,plain,
% 22.36/22.55 ($false),
% 22.36/22.55 inference(unit_resolution,[status(thm)],[3863, 7, 4264])).
% 22.39/22.55 tff(4266,plain,(ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(c, a))) = mult(c, a)), inference(lemma,lemma(discharge,[]))).
% 22.39/22.55 tff(4267,plain,
% 22.39/22.55 (mult(c, a) = ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(c, a)))),
% 22.39/22.55 inference(symmetry,[status(thm)],[4266])).
% 22.39/22.55 tff(4268,plain,
% 22.39/22.55 (mult(c, a) = mult(a, c)),
% 22.39/22.55 inference(transitivity,[status(thm)],[4267, 4263, 3872])).
% 22.39/22.55 tff(4269,plain,
% 22.39/22.55 (mult(mult(c, a), b) = mult(mult(a, c), b)),
% 22.39/22.55 inference(monotonicity,[status(thm)],[4268])).
% 22.39/22.55 tff(4270,plain,
% 22.39/22.55 (mult(c, mult(a, b)) = mult(mult(c, a), b)),
% 22.39/22.55 inference(symmetry,[status(thm)],[4221])).
% 22.39/22.55 tff(4271,plain,
% 22.39/22.55 (mult(c, mult(a, b)) = mult(mult(a, c), b)),
% 22.39/22.55 inference(transitivity,[status(thm)],[4270, 4269])).
% 22.39/22.55 tff(4272,plain,
% 22.39/22.55 (mult(c, mult(c, mult(a, b))) = mult(c, mult(mult(a, c), b))),
% 22.39/22.55 inference(monotonicity,[status(thm)],[4271])).
% 22.39/22.55 tff(4273,plain,
% 22.39/22.55 (mult(c, mult(mult(a, c), b)) = mult(c, mult(c, mult(a, b)))),
% 22.39/22.55 inference(symmetry,[status(thm)],[4272])).
% 22.39/22.55 tff(4274,plain,
% 22.39/22.55 (mult(c, mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), c)) = mult(c, mult(mult(a, c), b))),
% 22.39/22.55 inference(symmetry,[status(thm)],[3190])).
% 22.39/22.55 tff(4275,plain,
% 22.39/22.55 ((mult(mult(c, c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), c)) <=> (mult(mult(c, mult(mult(unit, c), unit)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(mult(unit, c), unit)))),
% 22.39/22.55 inference(symmetry,[status(thm)],[4229])).
% 22.39/22.55 tff(4276,plain,
% 22.39/22.55 ((mult(mult(c, mult(mult(unit, c), unit)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(c, mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit)))) <=> (mult(mult(c, mult(mult(unit, c), unit)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(mult(unit, c), unit)))),
% 22.39/22.55 inference(transitivity,[status(thm)],[4222, 4227, 4275])).
% 22.39/22.55 tff(4277,plain,
% 22.39/22.55 (mult(mult(c, mult(mult(unit, c), unit)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(c, mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit)))),
% 22.39/22.55 inference(unit_resolution,[status(thm)],[4237, 2288, 3865])).
% 22.39/22.55 tff(4278,plain,
% 22.39/22.55 (mult(mult(c, mult(mult(unit, c), unit)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(mult(unit, c), unit))),
% 22.39/22.55 inference(modus_ponens,[status(thm)],[4277, 4276])).
% 22.39/22.55 tff(4279,assumption,(~(mult(mult(c, mult(mult(unit, c), unit)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(mult(unit, c), unit)))), introduced(assumption)).
% 22.39/22.55 tff(4280,plain,
% 22.39/22.55 ($false),
% 22.39/22.55 inference(unit_resolution,[status(thm)],[4279, 4278])).
% 22.39/22.55 tff(4281,plain,((mult(mult(c, mult(mult(unit, c), unit)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(mult(unit, c), unit))) | (~(mult(mult(c, a), b) = mult(c, mult(a, b)))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit)))))), inference(lemma,lemma(discharge,[]))).
% 22.39/22.55 tff(4282,plain,
% 22.39/22.55 (mult(mult(c, mult(mult(unit, c), unit)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(mult(unit, c), unit))),
% 22.39/22.55 inference(unit_resolution,[status(thm)],[4281, 4221, 3862])).
% 22.39/22.55 tff(4283,plain,
% 22.39/22.55 (mult(mult(c, c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(a, c), b)),
% 22.39/22.55 inference(transitivity,[status(thm)],[3183, 4282, 3179, 3178, 3175, 864, 858, 856])).
% 22.39/22.55 tff(4284,plain,
% 22.39/22.55 (mult(mult(mult(c, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(mult(a, c), b), c)),
% 22.39/22.55 inference(monotonicity,[status(thm)],[4283])).
% 22.39/22.55 tff(4285,plain,
% 22.39/22.55 (mult(mult(mult(a, c), b), c) = mult(mult(mult(c, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c)),
% 22.39/22.55 inference(symmetry,[status(thm)],[4284])).
% 22.39/22.55 tff(4286,plain,
% 22.39/22.55 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(a, mult(b, c))),
% 22.39/22.55 inference(transitivity,[status(thm)],[279, 142])).
% 22.39/22.55 tff(4287,plain,
% 22.39/22.55 (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)), b) = mult(mult(a, mult(b, c)), b)),
% 22.39/22.55 inference(monotonicity,[status(thm)],[4286])).
% 22.39/22.55 tff(4288,assumption,(~((~(mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)))))), introduced(assumption)).
% 22.39/22.55 tff(4289,plain,
% 22.39/22.55 (mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c))),
% 22.39/22.55 inference(unit_resolution,[status(thm)],[2357, 4288])).
% 22.39/22.55 tff(4290,plain,
% 22.39/22.55 (((~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))) | (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))),
% 22.39/22.55 inference(tautology,[status(thm)],[])).
% 22.39/22.55 tff(4291,plain,
% 22.39/22.55 ((~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))),
% 22.39/22.55 inference(unit_resolution,[status(thm)],[4290, 1364])).
% 22.39/22.55 tff(4292,plain,
% 22.39/22.55 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))))))),
% 22.39/22.55 inference(rewrite,[status(thm)],[])).
% 22.39/22.55 tff(4293,plain,
% 22.39/22.55 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))))))),
% 22.39/22.55 inference(quant_inst,[status(thm)],[])).
% 22.39/22.55 tff(4294,plain,
% 22.39/22.55 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))))),
% 22.39/22.56 inference(modus_ponens,[status(thm)],[4293, 4292])).
% 22.39/22.56 tff(4295,plain,
% 22.39/22.56 ((~((~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))))),
% 22.39/22.56 inference(unit_resolution,[status(thm)],[4294, 27])).
% 22.39/22.56 tff(4296,plain,
% 22.39/22.56 (~((~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))))),
% 22.39/22.56 inference(unit_resolution,[status(thm)],[4295, 4291])).
% 22.39/22.56 tff(4297,plain,
% 22.39/22.56 (((~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))) | (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a))),
% 22.39/22.56 inference(tautology,[status(thm)],[])).
% 22.39/22.56 tff(4298,plain,
% 22.39/22.56 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a)),
% 22.39/22.56 inference(unit_resolution,[status(thm)],[4297, 4296])).
% 22.39/22.56 tff(4299,plain,
% 22.39/22.56 (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit))))),
% 22.39/22.56 inference(unit_resolution,[status(thm)],[1367, 1364])).
% 22.39/22.56 tff(4300,plain,
% 22.39/22.56 ((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit)))))),
% 22.39/22.56 inference(unit_resolution,[status(thm)],[33, 4299])).
% 22.39/22.56 tff(4301,plain,
% 22.39/22.56 (~((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit))))))),
% 22.39/22.56 inference(unit_resolution,[status(thm)],[31, 4300])).
% 22.39/22.56 tff(4302,plain,
% 22.39/22.56 (((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit)))))) | (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)))),
% 22.39/22.56 inference(tautology,[status(thm)],[])).
% 22.39/22.56 tff(4303,plain,
% 22.39/22.56 (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit))),
% 22.39/22.56 inference(unit_resolution,[status(thm)],[4302, 4301])).
% 22.39/22.56 tff(4304,plain,
% 22.39/22.56 (mult(c, mult(b, a)) = mult(mult(c, b), a)),
% 22.39/22.56 inference(symmetry,[status(thm)],[4208])).
% 22.39/22.56 tff(4305,plain,
% 22.39/22.56 (mult(c, mult(b, a)) = mult(mult(b, c), a)),
% 22.39/22.56 inference(transitivity,[status(thm)],[4304, 2298])).
% 22.39/22.56 tff(4306,plain,
% 22.39/22.56 (mult(mult(c, mult(b, a)), b) = mult(mult(mult(b, c), a), b)),
% 22.39/22.56 inference(monotonicity,[status(thm)],[4305])).
% 22.39/22.56 tff(4307,plain,
% 22.39/22.56 (mult(mult(mult(b, c), a), b) = mult(mult(c, mult(b, a)), b)),
% 22.39/22.56 inference(symmetry,[status(thm)],[4306])).
% 22.39/22.56 tff(4308,plain,
% 22.39/22.56 (mult(mult(c, unit), mult(b, a)) = mult(c, mult(b, a))),
% 22.39/22.56 inference(monotonicity,[status(thm)],[206])).
% 22.39/22.56 tff(4309,plain,
% 22.39/22.56 (mult(mult(c, unit), mult(b, a)) = mult(mult(b, c), a)),
% 22.39/22.56 inference(transitivity,[status(thm)],[4308, 4304, 2298])).
% 22.39/22.56 tff(4310,plain,
% 22.39/22.56 (mult(mult(mult(c, unit), mult(b, a)), unit) = mult(mult(mult(b, c), a), unit)),
% 22.39/22.56 inference(monotonicity,[status(thm)],[4309])).
% 22.39/22.56 tff(4311,plain,
% 22.39/22.56 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(c, unit), mult(b, a)), unit) = mult(c, mult(mult(unit, mult(b, a)), unit)))),
% 22.39/22.56 inference(quant_inst,[status(thm)],[])).
% 22.39/22.56 tff(4312,plain,
% 22.39/22.56 (mult(mult(mult(c, unit), mult(b, a)), unit) = mult(c, mult(mult(unit, mult(b, a)), unit))),
% 22.39/22.56 inference(unit_resolution,[status(thm)],[4311, 56])).
% 22.39/22.56 tff(4313,plain,
% 22.39/22.56 (mult(c, mult(mult(unit, mult(b, a)), unit)) = mult(mult(mult(c, unit), mult(b, a)), unit)),
% 22.39/22.56 inference(symmetry,[status(thm)],[4312])).
% 22.39/22.56 tff(4314,plain,
% 22.39/22.56 (mult(c, mult(mult(unit, mult(b, a)), unit)) = mult(mult(b, c), a)),
% 22.39/22.56 inference(transitivity,[status(thm)],[4313, 4310, 1258, 1261, 1263])).
% 22.39/22.56 tff(4315,plain,
% 22.39/22.56 (mult(mult(c, mult(mult(unit, mult(b, a)), unit)), b) = mult(mult(mult(b, c), a), b)),
% 22.39/22.56 inference(monotonicity,[status(thm)],[4314])).
% 22.39/22.56 tff(4316,plain,
% 22.39/22.56 (mult(mult(c, mult(mult(unit, mult(b, a)), unit)), b) = mult(mult(c, mult(b, a)), b)),
% 22.39/22.56 inference(transitivity,[status(thm)],[4315, 4307])).
% 22.39/22.56 tff(4317,plain,
% 22.39/22.56 ((~![A: $i] : (mult(unit, A) = A)) | (mult(unit, mult(b, a)) = mult(b, a))),
% 22.39/22.56 inference(quant_inst,[status(thm)],[])).
% 22.39/22.56 tff(4318,plain,
% 22.39/22.56 (mult(unit, mult(b, a)) = mult(b, a)),
% 22.39/22.56 inference(unit_resolution,[status(thm)],[4317, 71])).
% 22.39/22.56 tff(4319,plain,
% 22.39/22.56 ((~![A: $i] : (mult(A, unit) = A)) | (mult(mult(unit, mult(b, a)), unit) = mult(unit, mult(b, a)))),
% 22.39/22.56 inference(quant_inst,[status(thm)],[])).
% 22.39/22.56 tff(4320,plain,
% 22.39/22.56 (mult(mult(unit, mult(b, a)), unit) = mult(unit, mult(b, a))),
% 22.39/22.56 inference(unit_resolution,[status(thm)],[4319, 43])).
% 22.39/22.56 tff(4321,plain,
% 22.39/22.56 (mult(mult(unit, mult(b, a)), unit) = mult(b, a)),
% 22.39/22.56 inference(transitivity,[status(thm)],[4320, 4318])).
% 22.39/22.56 tff(4322,plain,
% 22.39/22.56 (mult(mult(c, b), mult(mult(unit, mult(b, a)), unit)) = mult(mult(b, c), mult(b, a))),
% 22.39/22.56 inference(monotonicity,[status(thm)],[241, 4321])).
% 22.39/22.56 tff(4323,plain,
% 22.39/22.56 (mult(mult(c, b), mult(mult(unit, mult(b, a)), unit)) = mult(mult(c, b), mult(b, a))),
% 22.39/22.56 inference(transitivity,[status(thm)],[4322, 3468])).
% 22.39/22.56 tff(4324,plain,
% 22.39/22.56 ((mult(mult(c, b), mult(mult(unit, mult(b, a)), unit)) = mult(mult(c, mult(mult(unit, mult(b, a)), unit)), b)) <=> (mult(mult(c, b), mult(b, a)) = mult(mult(c, mult(b, a)), b))),
% 22.39/22.56 inference(monotonicity,[status(thm)],[4323, 4316])).
% 22.39/22.56 tff(4325,plain,
% 22.39/22.56 ((mult(mult(c, b), mult(b, a)) = mult(mult(c, mult(b, a)), b)) <=> (mult(mult(c, b), mult(mult(unit, mult(b, a)), unit)) = mult(mult(c, mult(mult(unit, mult(b, a)), unit)), b))),
% 22.39/22.56 inference(symmetry,[status(thm)],[4324])).
% 22.39/22.56 tff(4326,plain,
% 22.39/22.56 ((mult(mult(c, mult(b, a)), b) = mult(mult(c, b), mult(b, a))) <=> (mult(mult(c, b), mult(b, a)) = mult(mult(c, mult(b, a)), b))),
% 22.39/22.56 inference(commutativity,[status(thm)],[])).
% 22.39/22.56 tff(4327,assumption,(~(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))), introduced(assumption)).
% 22.39/22.56 tff(4328,plain,
% 22.39/22.56 (((~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))) | (mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))),
% 22.39/22.56 inference(tautology,[status(thm)],[])).
% 22.39/22.56 tff(4329,plain,
% 22.39/22.56 ((~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))),
% 22.39/22.56 inference(unit_resolution,[status(thm)],[4328, 4327])).
% 22.39/22.56 tff(4330,plain,
% 22.39/22.56 (~((~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))))),
% 22.39/22.56 inference(unit_resolution,[status(thm)],[4295, 4329])).
% 22.39/22.56 tff(4331,plain,
% 22.39/22.56 (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))),
% 22.39/22.56 inference(unit_resolution,[status(thm)],[4290, 4330])).
% 22.39/22.56 tff(4332,plain,
% 22.39/22.56 (((~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))) | (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))))),
% 22.39/22.56 inference(tautology,[status(thm)],[])).
% 22.39/22.56 tff(4333,plain,
% 22.39/22.56 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c)))),
% 22.39/22.56 inference(unit_resolution,[status(thm)],[4332, 4330])).
% 22.39/22.56 tff(4334,assumption,(~(ld(a, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))) = mult(mult(a, c), rd(mult(b, c), mult(a, c))))), introduced(assumption)).
% 22.39/22.56 tff(4335,plain,
% 22.39/22.56 ($false),
% 22.39/22.56 inference(unit_resolution,[status(thm)],[732, 7, 4334])).
% 22.39/22.56 tff(4336,plain,(ld(a, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))), inference(lemma,lemma(discharge,[]))).
% 22.39/22.56 tff(4337,plain,
% 22.39/22.56 (mult(b, c) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))),
% 22.39/22.56 inference(transitivity,[status(thm)],[843, 2124, 4336])).
% 22.39/22.56 tff(4338,plain,
% 22.39/22.56 (mult(mult(b, c), a) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)),
% 22.39/22.56 inference(monotonicity,[status(thm)],[4337])).
% 22.39/22.56 tff(4339,plain,
% 22.39/22.56 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(b, c), a)),
% 22.39/22.56 inference(symmetry,[status(thm)],[4338])).
% 22.39/22.56 tff(4340,plain,
% 22.39/22.56 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)) = mult(mult(rd(mult(b, c), mult(a, c)), a), c)),
% 22.39/22.56 inference(monotonicity,[status(thm)],[78])).
% 22.39/22.56 tff(4341,plain,
% 22.39/22.56 ((mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit)))) <=> (mult(mult(rd(mult(b, c), mult(a, c)), a), c) = mult(rd(mult(b, c), mult(a, c)), mult(a, c)))),
% 22.39/22.56 inference(monotonicity,[status(thm)],[4340, 61])).
% 22.39/22.56 tff(4342,plain,
% 22.39/22.56 ((~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit))))) <=> (~(mult(mult(rd(mult(b, c), mult(a, c)), a), c) = mult(rd(mult(b, c), mult(a, c)), mult(a, c))))),
% 22.39/22.56 inference(monotonicity,[status(thm)],[4341])).
% 22.39/22.56 tff(4343,assumption,(~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit))))), introduced(assumption)).
% 22.39/22.56 tff(4344,plain,
% 22.39/22.56 (~(mult(mult(rd(mult(b, c), mult(a, c)), a), c) = mult(rd(mult(b, c), mult(a, c)), mult(a, c)))),
% 22.39/22.56 inference(modus_ponens,[status(thm)],[4343, 4342])).
% 22.39/22.56 tff(4345,plain,
% 22.39/22.56 ((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit)))))),
% 22.39/22.56 inference(unit_resolution,[status(thm)],[33, 4343])).
% 22.39/22.56 tff(4346,plain,
% 22.39/22.56 (~((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit))))))),
% 22.39/22.56 inference(unit_resolution,[status(thm)],[31, 4345])).
% 22.39/22.56 tff(4347,plain,
% 22.39/22.56 (mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit)))),
% 22.39/22.56 inference(unit_resolution,[status(thm)],[13, 4346])).
% 22.39/22.56 tff(4348,plain,
% 22.39/22.56 (mult(mult(c, b), a) = mult(c, mult(b, a))),
% 22.39/22.56 inference(unit_resolution,[status(thm)],[4207, 4347])).
% 22.39/22.56 tff(4349,plain,
% 22.39/22.56 (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit))),
% 22.39/22.56 inference(unit_resolution,[status(thm)],[4302, 4346])).
% 22.39/22.56 tff(4350,assumption,(~(mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))), introduced(assumption)).
% 22.39/22.56 tff(4351,plain,
% 22.39/22.56 ((~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))),
% 22.39/22.57 inference(unit_resolution,[status(thm)],[308, 4350])).
% 22.39/22.57 tff(4352,plain,
% 22.39/22.57 (~((~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))),
% 22.39/22.57 inference(unit_resolution,[status(thm)],[313, 4351])).
% 22.39/22.57 tff(4353,plain,
% 22.39/22.57 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))),
% 22.39/22.57 inference(unit_resolution,[status(thm)],[315, 4352])).
% 22.39/22.57 tff(4354,plain,
% 22.39/22.57 (((~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))) | (mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 22.39/22.57 inference(tautology,[status(thm)],[])).
% 22.39/22.57 tff(4355,plain,
% 22.39/22.57 (mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 22.39/22.57 inference(unit_resolution,[status(thm)],[4354, 4352])).
% 22.39/22.57 tff(4356,plain,
% 22.39/22.57 ((mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))) <=> (mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))),
% 22.39/22.57 inference(monotonicity,[status(thm)],[4355, 4353])).
% 22.39/22.57 tff(4357,plain,
% 22.39/22.57 ((mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))) <=> (mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 22.39/22.57 inference(symmetry,[status(thm)],[4356])).
% 22.39/22.57 tff(4358,plain,
% 22.39/22.57 ((~(mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) <=> (~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))))),
% 22.39/22.57 inference(monotonicity,[status(thm)],[4357])).
% 22.39/22.57 tff(4359,plain,
% 22.39/22.57 (~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 22.39/22.57 inference(modus_ponens,[status(thm)],[4350, 4358])).
% 22.39/22.57 tff(4360,assumption,(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit))), introduced(assumption)).
% 22.39/22.57 tff(4361,plain,
% 22.39/22.57 (mult(mult(unit, c), a) = mult(c, a)),
% 22.39/22.57 inference(monotonicity,[status(thm)],[73])).
% 22.39/22.57 tff(4362,plain,
% 22.39/22.57 (mult(mult(mult(unit, c), a), c) = mult(mult(c, a), c)),
% 22.39/22.57 inference(monotonicity,[status(thm)],[4361])).
% 22.39/22.57 tff(4363,plain,
% 22.39/22.57 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(unit, c), a), c) = mult(unit, mult(mult(c, a), c)))),
% 22.39/22.57 inference(quant_inst,[status(thm)],[])).
% 22.39/22.57 tff(4364,plain,
% 22.39/22.57 (mult(mult(mult(unit, c), a), c) = mult(unit, mult(mult(c, a), c))),
% 22.39/22.57 inference(unit_resolution,[status(thm)],[4363, 56])).
% 22.39/22.57 tff(4365,plain,
% 22.39/22.57 (mult(unit, mult(mult(c, a), c)) = mult(mult(mult(unit, c), a), c)),
% 22.39/22.57 inference(symmetry,[status(thm)],[4364])).
% 22.39/22.57 tff(4366,plain,
% 22.39/22.57 (mult(unit, mult(c, mult(a, c))) = mult(unit, mult(mult(c, a), c))),
% 22.39/22.57 inference(monotonicity,[status(thm)],[3877])).
% 22.39/22.57 tff(4367,plain,
% 22.39/22.57 (mult(unit, mult(c, mult(a, c))) = mult(c, mult(a, c))),
% 22.39/22.57 inference(transitivity,[status(thm)],[4366, 4365, 4362, 2690])).
% 22.39/22.57 tff(4368,plain,
% 22.39/22.57 (mult(mult(unit, mult(c, mult(a, c))), b) = mult(mult(c, mult(a, c)), b)),
% 22.39/22.57 inference(monotonicity,[status(thm)],[4367])).
% 22.39/22.57 tff(4369,plain,
% 22.39/22.57 (mult(mult(c, mult(a, c)), b) = mult(mult(unit, mult(c, mult(a, c))), b)),
% 22.39/22.57 inference(symmetry,[status(thm)],[4368])).
% 22.39/22.57 tff(4370,plain,
% 22.39/22.57 (mult(mult(mult(a, c), c), b) = mult(mult(c, mult(a, c)), b)),
% 22.39/22.57 inference(symmetry,[status(thm)],[3879])).
% 22.39/22.57 tff(4371,plain,
% 22.39/22.57 (mult(mult(mult(a, c), b), c) = mult(mult(mult(a, c), c), b)),
% 22.39/22.57 inference(symmetry,[status(thm)],[2759])).
% 22.39/22.57 tff(4372,plain,
% 22.39/22.57 (mult(a, mult(mult(b, c), c)) = mult(a, mult(mult(c, b), c))),
% 22.39/22.57 inference(symmetry,[status(thm)],[2414])).
% 22.39/22.57 tff(4373,plain,
% 22.39/22.57 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(c, mult(c, mult(b, c))) = mult(b, c))),
% 22.39/22.57 inference(quant_inst,[status(thm)],[])).
% 22.39/22.57 tff(4374,plain,
% 22.39/22.57 (ld(c, mult(c, mult(b, c))) = mult(b, c)),
% 22.39/22.57 inference(unit_resolution,[status(thm)],[4373, 7])).
% 22.39/22.57 tff(4375,assumption,(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))), introduced(assumption)).
% 22.39/22.57 tff(4376,plain,
% 22.39/22.57 (mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(b, c))),
% 22.39/22.57 inference(transitivity,[status(thm)],[4375, 2802])).
% 22.39/22.57 tff(4377,plain,
% 22.39/22.57 (ld(c, mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c))))) = ld(c, mult(c, mult(b, c)))),
% 22.39/22.57 inference(monotonicity,[status(thm)],[4376])).
% 22.39/22.57 tff(4378,plain,
% 22.39/22.57 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(c, mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c))))) = mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 22.39/22.57 inference(quant_inst,[status(thm)],[])).
% 22.39/22.57 tff(4379,plain,
% 22.39/22.57 (ld(c, mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c))))) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))),
% 22.39/22.57 inference(unit_resolution,[status(thm)],[4378, 7])).
% 22.39/22.57 tff(4380,plain,
% 22.39/22.57 (mult(mult(a, c), rd(mult(b, c), mult(a, c))) = ld(c, mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 22.39/22.57 inference(symmetry,[status(thm)],[4379])).
% 22.39/22.57 tff(4381,plain,
% 22.39/22.57 (mult(mult(a, c), rd(mult(b, c), mult(a, c))) = mult(b, c)),
% 22.39/22.57 inference(transitivity,[status(thm)],[4380, 4377, 4374])).
% 22.39/22.57 tff(4382,plain,
% 22.39/22.57 (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(b, c))),
% 22.39/22.57 inference(monotonicity,[status(thm)],[4381])).
% 22.39/22.57 tff(4383,plain,
% 22.39/22.57 (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))),
% 22.39/22.57 inference(transitivity,[status(thm)],[4382, 289])).
% 22.39/22.57 tff(4384,plain,
% 22.39/22.57 ($false),
% 22.39/22.57 inference(unit_resolution,[status(thm)],[270, 4383])).
% 22.39/22.57 tff(4385,plain,((~(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))), inference(lemma,lemma(discharge,[]))).
% 22.39/22.57 tff(4386,plain,
% 22.39/22.57 (~(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))),
% 22.39/22.57 inference(unit_resolution,[status(thm)],[4385, 270])).
% 22.39/22.57 tff(4387,plain,
% 22.39/22.57 (((~(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))) | (mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))),
% 22.39/22.57 inference(tautology,[status(thm)],[])).
% 22.39/22.57 tff(4388,plain,
% 22.39/22.57 ((~(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))),
% 22.39/22.57 inference(unit_resolution,[status(thm)],[4387, 4386])).
% 22.39/22.57 tff(4389,plain,
% 22.39/22.57 (~((~(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))),
% 22.39/22.57 inference(unit_resolution,[status(thm)],[2797, 4388])).
% 22.39/22.57 tff(4390,plain,
% 22.39/22.57 (mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))),
% 22.39/22.57 inference(unit_resolution,[status(thm)],[2799, 4389])).
% 22.39/22.57 tff(4391,plain,
% 22.39/22.57 (mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(b, c), c)),
% 22.39/22.57 inference(transitivity,[status(thm)],[4390, 2802, 4179, 4176, 4173])).
% 22.39/22.57 tff(4392,plain,
% 22.39/22.57 (mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))) = mult(a, mult(mult(b, c), c))),
% 22.39/22.57 inference(monotonicity,[status(thm)],[4391])).
% 22.39/22.57 tff(4393,plain,
% 22.39/22.57 (mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))) = mult(mult(unit, mult(c, mult(a, c))), b)),
% 22.39/22.57 inference(transitivity,[status(thm)],[4392, 4372, 234, 4371, 4370, 4369])).
% 22.39/22.57 tff(4394,plain,
% 22.39/22.57 (mult(mult(unit, b), mult(c, mult(a, c))) = mult(b, mult(c, mult(a, c)))),
% 22.39/22.57 inference(monotonicity,[status(thm)],[184])).
% 22.39/22.57 tff(4395,plain,
% 22.39/22.57 (mult(b, mult(c, mult(a, c))) = mult(mult(unit, b), mult(c, mult(a, c)))),
% 22.39/22.57 inference(symmetry,[status(thm)],[4394])).
% 22.39/22.57 tff(4396,plain,
% 22.39/22.57 (mult(b, mult(mult(c, a), c)) = mult(b, mult(c, mult(a, c)))),
% 22.39/22.57 inference(monotonicity,[status(thm)],[2690])).
% 22.39/22.57 tff(4397,plain,
% 22.39/22.57 (mult(mult(b, c), a) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a)),
% 22.39/22.57 inference(monotonicity,[status(thm)],[267])).
% 22.39/22.57 tff(4398,plain,
% 22.39/22.57 (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(mult(b, c), a)),
% 22.39/22.57 inference(symmetry,[status(thm)],[4397])).
% 22.39/22.57 tff(4399,plain,
% 22.39/22.57 (mult(mult(b, mult(a, c)), c) = mult(mult(b, c), mult(a, c))),
% 22.39/22.57 inference(unit_resolution,[status(thm)],[2601, 4003])).
% 22.39/22.57 tff(4400,plain,
% 22.39/22.57 (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))),
% 22.39/22.57 inference(unit_resolution,[status(thm)],[342, 329])).
% 22.39/22.57 tff(4401,plain,
% 22.39/22.57 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(b, c), mult(a, c)), mult(a, c)) = mult(b, c))),
% 22.39/22.57 inference(quant_inst,[status(thm)],[])).
% 22.39/22.57 tff(4402,plain,
% 22.39/22.57 (rd(mult(mult(b, c), mult(a, c)), mult(a, c)) = mult(b, c)),
% 22.39/22.57 inference(unit_resolution,[status(thm)],[4401, 168])).
% 22.39/22.57 tff(4403,assumption,(mult(mult(b, mult(a, c)), c) = mult(mult(b, c), mult(a, c))), introduced(assumption)).
% 22.39/22.57 tff(4404,plain,
% 22.39/22.57 (rd(mult(b, c), c) = rd(mult(mult(rd(mult(b, c), mult(a, c)), a), c), c)),
% 22.39/22.57 inference(symmetry,[status(thm)],[1379])).
% 22.39/22.57 tff(4405,plain,
% 22.39/22.57 (b = mult(rd(mult(b, c), mult(a, c)), a)),
% 22.39/22.57 inference(transitivity,[status(thm)],[2727, 4404, 174])).
% 22.39/22.57 tff(4406,plain,
% 22.39/22.57 (mult(b, mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c))),
% 22.39/22.57 inference(monotonicity,[status(thm)],[4405])).
% 22.39/22.57 tff(4407,plain,
% 22.39/22.57 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(b, mult(a, c))),
% 22.39/22.57 inference(symmetry,[status(thm)],[4406])).
% 22.39/22.57 tff(4408,plain,
% 22.39/22.57 (ld(mult(a, c), mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = ld(mult(a, c), mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))),
% 22.39/22.57 inference(monotonicity,[status(thm)],[359])).
% 22.39/22.57 tff(4409,plain,
% 22.39/22.57 (ld(mult(a, c), mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))) = ld(mult(a, c), mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))),
% 22.39/22.57 inference(symmetry,[status(thm)],[4408])).
% 22.39/22.57 tff(4410,plain,
% 22.39/22.57 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(a, c), mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))) = mult(rd(mult(b, c), mult(a, c)), a))),
% 22.39/22.57 inference(quant_inst,[status(thm)],[])).
% 22.39/22.57 tff(4411,plain,
% 22.39/22.57 (ld(mult(a, c), mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))) = mult(rd(mult(b, c), mult(a, c)), a)),
% 22.39/22.57 inference(unit_resolution,[status(thm)],[4410, 7])).
% 22.39/22.57 tff(4412,plain,
% 22.39/22.57 (mult(rd(mult(b, c), mult(a, c)), a) = ld(mult(a, c), mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))),
% 22.39/22.57 inference(symmetry,[status(thm)],[4411])).
% 22.39/22.57 tff(4413,plain,
% 22.39/22.57 (mult(rd(mult(b, c), mult(a, c)), a) = mult(a, rd(mult(b, c), mult(a, c)))),
% 22.39/22.57 inference(transitivity,[status(thm)],[4412, 4409, 358])).
% 22.39/22.57 tff(4414,plain,
% 22.39/22.57 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))),
% 22.39/22.57 inference(monotonicity,[status(thm)],[4413])).
% 22.39/22.57 tff(4415,plain,
% 22.39/22.57 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c))),
% 22.39/22.57 inference(symmetry,[status(thm)],[4414])).
% 22.39/22.57 tff(4416,plain,
% 22.39/22.57 (mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))),
% 22.39/22.57 inference(symmetry,[status(thm)],[279])).
% 22.39/22.57 tff(4417,plain,
% 22.39/22.57 (mult(a, mult(b, c)) = mult(b, mult(a, c))),
% 22.39/22.57 inference(transitivity,[status(thm)],[289, 4416, 4415, 4407])).
% 22.39/22.57 tff(4418,plain,
% 22.39/22.57 (mult(mult(a, mult(b, c)), c) = mult(mult(b, mult(a, c)), c)),
% 22.39/22.57 inference(monotonicity,[status(thm)],[4417])).
% 22.39/22.57 tff(4419,plain,
% 22.39/22.57 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(b, c), mult(a, c))),
% 22.39/22.57 inference(transitivity,[status(thm)],[1039, 138, 266, 4418, 4403])).
% 22.39/22.57 tff(4420,plain,
% 22.39/22.57 (rd(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)), mult(a, c)) = rd(mult(mult(b, c), mult(a, c)), mult(a, c))),
% 22.39/22.57 inference(monotonicity,[status(thm)],[4419])).
% 22.39/22.57 tff(4421,plain,
% 22.39/22.57 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)), mult(a, c)) = mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 22.39/22.57 inference(quant_inst,[status(thm)],[])).
% 22.39/22.57 tff(4422,plain,
% 22.39/22.57 (rd(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)), mult(a, c)) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))),
% 22.39/22.57 inference(unit_resolution,[status(thm)],[4421, 168])).
% 22.39/22.57 tff(4423,plain,
% 22.39/22.57 (mult(mult(a, c), rd(mult(b, c), mult(a, c))) = rd(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)), mult(a, c))),
% 22.39/22.57 inference(symmetry,[status(thm)],[4422])).
% 22.39/22.57 tff(4424,plain,
% 22.39/22.57 (mult(mult(a, c), rd(mult(b, c), mult(a, c))) = mult(b, c)),
% 22.39/22.57 inference(transitivity,[status(thm)],[4423, 4420, 4402])).
% 22.39/22.57 tff(4425,plain,
% 22.39/22.57 (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(b, c))),
% 22.39/22.57 inference(monotonicity,[status(thm)],[4424])).
% 22.39/22.57 tff(4426,plain,
% 22.39/22.57 (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))),
% 22.39/22.57 inference(transitivity,[status(thm)],[4425, 289])).
% 22.39/22.57 tff(4427,plain,
% 22.39/22.57 ($false),
% 22.39/22.57 inference(unit_resolution,[status(thm)],[270, 4426])).
% 22.39/22.57 tff(4428,plain,((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) | (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (~(mult(mult(b, mult(a, c)), c) = mult(mult(b, c), mult(a, c)))) | (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))))), inference(lemma,lemma(discharge,[]))).
% 22.39/22.57 tff(4429,plain,
% 22.39/22.57 (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))),
% 22.39/22.57 inference(unit_resolution,[status(thm)],[4428, 4400, 1039, 4399, 270])).
% 22.39/22.57 tff(4430,plain,
% 22.39/22.57 ((~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))),
% 22.39/22.57 inference(unit_resolution,[status(thm)],[4290, 4429])).
% 22.39/22.57 tff(4431,plain,
% 22.39/22.57 (~((~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))))),
% 22.39/22.57 inference(unit_resolution,[status(thm)],[4295, 4430])).
% 22.39/22.57 tff(4432,plain,
% 22.39/22.57 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a)),
% 22.39/22.57 inference(unit_resolution,[status(thm)],[4297, 4431])).
% 22.39/22.57 tff(4433,plain,
% 22.39/22.57 (ld(mult(a, c), mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = ld(mult(a, c), mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))),
% 22.39/22.57 inference(monotonicity,[status(thm)],[4400])).
% 22.39/22.57 tff(4434,plain,
% 22.39/22.57 (ld(mult(a, c), mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))) = ld(mult(a, c), mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))),
% 22.39/22.57 inference(symmetry,[status(thm)],[4433])).
% 22.39/22.57 tff(4435,plain,
% 22.39/22.57 (mult(rd(mult(b, c), mult(a, c)), a) = mult(a, rd(mult(b, c), mult(a, c)))),
% 22.39/22.57 inference(transitivity,[status(thm)],[4412, 4434, 358])).
% 22.39/22.57 tff(4436,plain,
% 22.39/22.57 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))),
% 22.39/22.57 inference(monotonicity,[status(thm)],[4435])).
% 22.39/22.57 tff(4437,plain,
% 22.39/22.57 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c))),
% 22.39/22.57 inference(symmetry,[status(thm)],[4436])).
% 22.39/22.57 tff(4438,plain,
% 22.39/22.57 (mult(a, mult(b, c)) = mult(mult(b, c), a)),
% 22.39/22.57 inference(transitivity,[status(thm)],[289, 4416, 4437, 4432, 4398])).
% 22.39/22.57 tff(4439,plain,
% 22.39/22.57 (mult(mult(a, mult(b, c)), c) = mult(mult(mult(b, c), a), c)),
% 22.39/22.57 inference(monotonicity,[status(thm)],[4438])).
% 22.39/22.57 tff(4440,plain,
% 22.39/22.57 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), a) = mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 22.39/22.57 inference(quant_inst,[status(thm)],[])).
% 22.39/22.57 tff(4441,plain,
% 22.39/22.57 (rd(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), a) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))),
% 22.39/22.57 inference(unit_resolution,[status(thm)],[4440, 168])).
% 22.39/22.57 tff(4442,plain,
% 22.39/22.57 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(c, mult(c, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))),
% 22.39/22.57 inference(quant_inst,[status(thm)],[])).
% 22.39/22.57 tff(4443,plain,
% 22.39/22.57 (ld(c, mult(c, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)),
% 22.39/22.57 inference(unit_resolution,[status(thm)],[4442, 7])).
% 22.39/22.57 tff(4444,plain,
% 22.39/22.57 (mult(c, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)) = mult(mult(unit, c), mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))),
% 22.39/22.57 inference(monotonicity,[status(thm)],[74])).
% 22.39/22.57 tff(4445,plain,
% 22.39/22.57 (mult(mult(unit, c), mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)) = mult(c, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))),
% 22.39/22.57 inference(symmetry,[status(thm)],[4444])).
% 22.39/22.57 tff(4446,plain,
% 22.39/22.57 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) = mult(mult(a, c), a))),
% 22.39/22.57 inference(quant_inst,[status(thm)],[])).
% 22.39/22.57 tff(4447,plain,
% 22.39/22.57 (ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) = mult(mult(a, c), a)),
% 22.39/22.57 inference(unit_resolution,[status(thm)],[4446, 7])).
% 22.39/22.57 tff(4448,plain,
% 22.39/22.57 (mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))),
% 22.39/22.57 inference(unit_resolution,[status(thm)],[4328, 4431])).
% 22.39/22.57 tff(4449,plain,
% 22.39/22.57 (ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c)))) = ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))),
% 22.39/22.57 inference(monotonicity,[status(thm)],[4448])).
% 22.39/22.57 tff(4450,plain,
% 22.39/22.57 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c)))) = mult(a, mult(a, c)))),
% 22.39/22.58 inference(quant_inst,[status(thm)],[])).
% 22.39/22.58 tff(4451,plain,
% 22.39/22.58 (ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c)))) = mult(a, mult(a, c))),
% 22.39/22.58 inference(unit_resolution,[status(thm)],[4450, 7])).
% 22.39/22.58 tff(4452,plain,
% 22.39/22.58 (mult(a, mult(a, c)) = ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))))),
% 22.39/22.58 inference(symmetry,[status(thm)],[4451])).
% 22.39/22.58 tff(4453,plain,
% 22.39/22.58 (mult(a, mult(a, c)) = mult(mult(a, c), a)),
% 22.39/22.58 inference(transitivity,[status(thm)],[4452, 4449, 4447])).
% 22.39/22.58 tff(4454,plain,
% 22.39/22.58 (mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))),
% 22.39/22.58 inference(monotonicity,[status(thm)],[4453])).
% 22.39/22.58 tff(4455,plain,
% 22.39/22.58 (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 22.39/22.58 inference(symmetry,[status(thm)],[281])).
% 22.39/22.58 tff(4456,plain,
% 22.39/22.58 (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)),
% 22.39/22.58 inference(transitivity,[status(thm)],[4455, 4454, 3842])).
% 22.39/22.58 tff(4457,plain,
% 22.39/22.58 (mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))) = mult(mult(unit, c), mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))),
% 22.39/22.58 inference(monotonicity,[status(thm)],[74, 4456])).
% 22.39/22.58 tff(4458,plain,
% 22.39/22.58 (mult(mult(unit, c), mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 22.39/22.58 inference(symmetry,[status(thm)],[4457])).
% 22.39/22.58 tff(4459,plain,
% 22.39/22.58 (mult(c, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 22.39/22.58 inference(transitivity,[status(thm)],[4444, 4458])).
% 22.39/22.58 tff(4460,plain,
% 22.39/22.58 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(c, mult(c, mult(a, mult(b, c)))) = mult(a, mult(b, c)))),
% 22.39/22.58 inference(quant_inst,[status(thm)],[])).
% 22.39/22.58 tff(4461,plain,
% 22.39/22.58 (ld(c, mult(c, mult(a, mult(b, c)))) = mult(a, mult(b, c))),
% 22.39/22.58 inference(unit_resolution,[status(thm)],[4460, 7])).
% 22.39/22.58 tff(4462,plain,
% 22.39/22.58 (mult(c, mult(a, mult(b, c))) = mult(mult(unit, c), mult(a, mult(b, c)))),
% 22.39/22.58 inference(monotonicity,[status(thm)],[74])).
% 22.39/22.58 tff(4463,plain,
% 22.39/22.58 (mult(mult(unit, c), mult(a, mult(b, c))) = mult(c, mult(a, mult(b, c)))),
% 22.39/22.58 inference(symmetry,[status(thm)],[4462])).
% 22.39/22.58 tff(4464,plain,
% 22.39/22.58 (~(mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))),
% 22.39/22.58 inference(unit_resolution,[status(thm)],[303, 285, 281, 279])).
% 22.39/22.58 tff(4465,plain,
% 22.39/22.58 ((~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))),
% 22.39/22.58 inference(unit_resolution,[status(thm)],[308, 4464])).
% 22.39/22.58 tff(4466,plain,
% 22.39/22.58 (~((~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))),
% 22.39/22.58 inference(unit_resolution,[status(thm)],[313, 4465])).
% 22.39/22.58 tff(4467,plain,
% 22.39/22.58 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))),
% 22.39/22.58 inference(unit_resolution,[status(thm)],[315, 4466])).
% 22.39/22.58 tff(4468,plain,
% 22.39/22.58 (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(a, mult(b, c)), c)),
% 22.39/22.58 inference(transitivity,[status(thm)],[317, 4467, 138, 266])).
% 22.39/22.58 tff(4469,plain,
% 22.39/22.58 (rd(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c), c) = rd(mult(mult(a, mult(b, c)), c), c)),
% 22.39/22.58 inference(monotonicity,[status(thm)],[4468])).
% 22.39/22.58 tff(4470,plain,
% 22.39/22.58 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(a, mult(b, c))),
% 22.39/22.58 inference(transitivity,[status(thm)],[322, 4469, 180])).
% 22.39/22.58 tff(4471,plain,
% 22.39/22.58 (mult(mult(unit, c), mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)) = mult(mult(unit, c), mult(a, mult(b, c)))),
% 22.39/22.58 inference(monotonicity,[status(thm)],[4470])).
% 22.39/22.58 tff(4472,assumption,(mult(c, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))), introduced(assumption)).
% 22.39/22.58 tff(4473,plain,
% 22.39/22.58 (mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))) = mult(c, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))),
% 22.39/22.58 inference(symmetry,[status(thm)],[4472])).
% 22.39/22.58 tff(4474,plain,
% 22.39/22.58 (mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))) = mult(c, mult(a, mult(b, c)))),
% 22.39/22.58 inference(transitivity,[status(thm)],[4473, 4444, 4471, 4463])).
% 22.39/22.58 tff(4475,plain,
% 22.39/22.58 (ld(c, mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) = ld(c, mult(c, mult(a, mult(b, c))))),
% 22.39/22.58 inference(monotonicity,[status(thm)],[4474])).
% 22.39/22.58 tff(4476,plain,
% 22.39/22.58 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(c, mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 22.39/22.58 inference(quant_inst,[status(thm)],[])).
% 22.39/22.58 tff(4477,plain,
% 22.39/22.58 (ld(c, mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 22.39/22.58 inference(unit_resolution,[status(thm)],[4476, 7])).
% 22.39/22.58 tff(4478,plain,
% 22.39/22.58 (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = ld(c, mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))),
% 22.39/22.58 inference(symmetry,[status(thm)],[4477])).
% 22.39/22.58 tff(4479,plain,
% 22.39/22.58 (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))),
% 22.39/22.58 inference(transitivity,[status(thm)],[4478, 4475, 4461, 289])).
% 22.39/22.58 tff(4480,plain,
% 22.39/22.58 ($false),
% 22.39/22.58 inference(unit_resolution,[status(thm)],[270, 4479])).
% 22.39/22.58 tff(4481,plain,((~(mult(c, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))) | (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))) | (~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))))), inference(lemma,lemma(discharge,[]))).
% 22.39/22.58 tff(4482,plain,
% 22.39/22.58 (~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 22.39/22.58 inference(unit_resolution,[status(thm)],[4481, 4459, 270])).
% 22.39/22.58 tff(4483,plain,
% 22.39/22.58 ((~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)))) | (~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))))),
% 22.39/22.58 inference(unit_resolution,[status(thm)],[121, 4482])).
% 22.39/22.58 tff(4484,plain,
% 22.39/22.58 ((~((~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))))) | (~((~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)))) | (~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))))))),
% 22.39/22.58 inference(unit_resolution,[status(thm)],[119, 27])).
% 22.39/22.58 tff(4485,plain,
% 22.39/22.58 (~((~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))))),
% 22.39/22.58 inference(unit_resolution,[status(thm)],[4484, 4483])).
% 22.39/22.58 tff(4486,plain,
% 22.39/22.58 (((~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))))) | (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c))),
% 22.39/22.58 inference(tautology,[status(thm)],[])).
% 22.39/22.58 tff(4487,plain,
% 22.39/22.58 (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c)),
% 22.39/22.58 inference(unit_resolution,[status(thm)],[4486, 4485])).
% 22.39/22.58 tff(4488,plain,
% 22.39/22.58 (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), c), a)),
% 22.39/22.58 inference(symmetry,[status(thm)],[83])).
% 22.39/22.58 tff(4489,plain,
% 22.39/22.58 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a)),
% 22.39/22.58 inference(symmetry,[status(thm)],[4360])).
% 22.39/22.58 tff(4490,plain,
% 22.39/22.58 (mult(mult(rd(mult(b, c), mult(a, c)), a), c) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit))),
% 22.39/22.58 inference(symmetry,[status(thm)],[4340])).
% 22.39/22.58 tff(4491,plain,
% 22.39/22.58 (mult(mult(rd(mult(b, c), mult(a, c)), a), c) = mult(mult(a, rd(mult(b, c), mult(a, c))), c)),
% 22.39/22.58 inference(monotonicity,[status(thm)],[4435])).
% 22.39/22.58 tff(4492,plain,
% 22.39/22.58 (mult(mult(a, rd(mult(b, c), mult(a, c))), c) = mult(mult(rd(mult(b, c), mult(a, c)), a), c)),
% 22.39/22.58 inference(symmetry,[status(thm)],[4491])).
% 22.39/22.58 tff(4493,plain,
% 22.39/22.58 (mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, rd(mult(b, c), mult(a, c))), c)),
% 22.39/22.58 inference(symmetry,[status(thm)],[2189])).
% 22.39/22.58 tff(4494,plain,
% 22.39/22.58 (mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))),
% 22.39/22.58 inference(symmetry,[status(thm)],[4390])).
% 22.39/22.58 tff(4495,plain,
% 22.39/22.58 (mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 22.39/22.58 inference(unit_resolution,[status(thm)],[2810, 4389])).
% 22.39/22.58 tff(4496,plain,
% 22.39/22.58 (mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 22.39/22.58 inference(symmetry,[status(thm)],[4495])).
% 22.39/22.58 tff(4497,plain,
% 22.39/22.58 ((mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))) <=> (mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 22.39/22.58 inference(monotonicity,[status(thm)],[4496, 4494])).
% 22.39/22.58 tff(4498,plain,
% 22.39/22.58 ((~(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) <=> (~(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))),
% 22.39/22.58 inference(monotonicity,[status(thm)],[4497])).
% 22.39/22.58 tff(4499,plain,
% 22.39/22.58 (~(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 22.39/22.58 inference(modus_ponens,[status(thm)],[4386, 4498])).
% 22.39/22.58 tff(4500,plain,
% 22.39/22.58 (mult(mult(c, a), b) = mult(mult(a, b), c)),
% 22.39/22.58 inference(transitivity,[status(thm)],[3886, 161])).
% 22.39/22.58 tff(4501,assumption,(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a)), introduced(assumption)).
% 22.39/22.58 tff(4502,plain,
% 22.39/22.58 (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c))),
% 22.39/22.58 inference(symmetry,[status(thm)],[4501])).
% 22.39/22.58 tff(4503,plain,
% 22.39/22.58 (mult(mult(c, b), a) = mult(a, mult(b, c))),
% 22.39/22.58 inference(transitivity,[status(thm)],[2298, 4397, 4502, 4414, 287, 142])).
% 22.39/22.58 tff(4504,plain,
% 22.39/22.58 ((mult(mult(c, b), a) = mult(mult(c, a), b)) <=> (mult(a, mult(b, c)) = mult(mult(a, b), c))),
% 22.39/22.58 inference(monotonicity,[status(thm)],[4503, 4500])).
% 22.39/22.58 tff(4505,plain,
% 22.39/22.58 ((mult(mult(c, b), a) = mult(mult(c, a), b)) <=> (mult(mult(a, b), c) = mult(a, mult(b, c)))),
% 22.39/22.58 inference(transitivity,[status(thm)],[4504, 143])).
% 22.39/22.58 tff(4506,plain,
% 22.39/22.58 ((mult(mult(a, b), c) = mult(a, mult(b, c))) <=> (mult(mult(c, b), a) = mult(mult(c, a), b))),
% 22.39/22.58 inference(symmetry,[status(thm)],[4505])).
% 22.39/22.58 tff(4507,plain,
% 22.39/22.58 ((~(mult(mult(a, b), c) = mult(a, mult(b, c)))) <=> (~(mult(mult(c, b), a) = mult(mult(c, a), b)))),
% 22.39/22.58 inference(monotonicity,[status(thm)],[4506])).
% 22.39/22.58 tff(4508,plain,
% 22.39/22.58 (~(mult(mult(c, b), a) = mult(mult(c, a), b))),
% 22.39/22.58 inference(modus_ponens,[status(thm)],[146, 4507])).
% 22.39/22.58 tff(4509,plain,
% 22.39/22.58 ((~(mult(mult(c, b), a) = mult(mult(c, a), b))) | (~(mult(c, mult(b, a)) = mult(c, mult(a, b))))),
% 22.39/22.58 inference(unit_resolution,[status(thm)],[3890, 4508])).
% 22.39/22.58 tff(4510,plain,
% 22.39/22.58 (~((~(mult(mult(c, b), a) = mult(c, mult(b, a)))) | (~(mult(mult(c, a), b) = mult(c, mult(a, b)))))),
% 22.39/22.58 inference(unit_resolution,[status(thm)],[2249, 4509])).
% 22.39/22.58 tff(4511,plain,
% 22.39/22.58 (mult(mult(c, a), b) = mult(c, mult(a, b))),
% 22.39/22.58 inference(unit_resolution,[status(thm)],[2279, 4510])).
% 22.39/22.58 tff(4512,plain,
% 22.39/22.58 (mult(c, mult(a, b)) = mult(mult(c, a), b)),
% 22.39/22.58 inference(symmetry,[status(thm)],[4511])).
% 22.39/22.58 tff(4513,plain,
% 22.39/22.58 (mult(c, mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), c)),
% 22.39/22.58 inference(transitivity,[status(thm)],[4006, 4225, 4512, 3886, 161, 215])).
% 22.39/22.58 tff(4514,plain,
% 22.39/22.59 ((mult(mult(c, c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(c, mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)))) <=> (mult(mult(c, c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), c))),
% 22.39/22.59 inference(monotonicity,[status(thm)],[4513])).
% 22.39/22.59 tff(4515,plain,
% 22.39/22.59 ((mult(mult(c, c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), c)) <=> (mult(mult(c, c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(c, mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))),
% 22.39/22.59 inference(symmetry,[status(thm)],[4514])).
% 22.39/22.59 tff(4516,plain,
% 22.39/22.59 ((mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c)))) <=> (mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 22.39/22.59 inference(commutativity,[status(thm)],[])).
% 22.39/22.59 tff(4517,assumption,(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))), introduced(assumption)).
% 22.39/22.59 tff(4518,plain,
% 22.39/22.59 (ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c)))) = ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))),
% 22.39/22.59 inference(monotonicity,[status(thm)],[4517])).
% 22.39/22.59 tff(4519,plain,
% 22.39/22.59 (mult(a, mult(a, c)) = mult(mult(a, c), a)),
% 22.39/22.59 inference(transitivity,[status(thm)],[4452, 4518, 4447])).
% 22.39/22.59 tff(4520,plain,
% 22.39/22.59 (mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))),
% 22.39/22.59 inference(monotonicity,[status(thm)],[4519])).
% 22.39/22.59 tff(4521,plain,
% 22.39/22.59 (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 22.39/22.59 inference(symmetry,[status(thm)],[4520])).
% 22.39/22.59 tff(4522,plain,
% 22.39/22.59 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(c, mult(c, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))))) = mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))))),
% 22.39/22.59 inference(quant_inst,[status(thm)],[])).
% 22.39/22.59 tff(4523,plain,
% 22.39/22.59 (ld(c, mult(c, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))))) = mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))),
% 22.39/22.59 inference(unit_resolution,[status(thm)],[4522, 7])).
% 22.39/22.59 tff(4524,plain,
% 22.39/22.59 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), c), c) = mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))))),
% 22.39/22.59 inference(quant_inst,[status(thm)],[])).
% 22.39/22.59 tff(4525,plain,
% 22.39/22.59 (rd(mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), c), c) = mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))),
% 22.39/22.59 inference(unit_resolution,[status(thm)],[4524, 168])).
% 22.39/22.59 tff(4526,plain,
% 22.39/22.59 (mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c)),
% 22.39/22.59 inference(monotonicity,[status(thm)],[1683])).
% 22.39/22.59 tff(4527,plain,
% 22.39/22.59 (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), c)),
% 22.39/22.59 inference(symmetry,[status(thm)],[4526])).
% 22.39/22.59 tff(4528,assumption,(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c)), introduced(assumption)).
% 22.39/22.59 tff(4529,plain,
% 22.39/22.59 (mult(mult(a, c), c) = mult(c, mult(a, c))),
% 22.39/22.59 inference(transitivity,[status(thm)],[3875, 2690])).
% 22.39/22.59 tff(4530,plain,
% 22.39/22.59 (mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))) = mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 22.39/22.59 inference(monotonicity,[status(thm)],[4529])).
% 22.39/22.59 tff(4531,plain,
% 22.39/22.59 (mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c))))),
% 22.39/22.59 inference(monotonicity,[status(thm)],[3874])).
% 22.39/22.59 tff(4532,plain,
% 22.39/22.59 (mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))) = mult(mult(mult(c, a), c), rd(mult(b, c), mult(a, c)))),
% 22.39/22.59 inference(transitivity,[status(thm)],[4530, 2732])).
% 22.39/22.59 tff(4533,plain,
% 22.39/22.59 ((mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) <=> (mult(mult(mult(c, a), c), rd(mult(b, c), mult(a, c))) = mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c)))))),
% 22.39/22.59 inference(monotonicity,[status(thm)],[4532, 4531])).
% 22.39/22.59 tff(4534,plain,
% 22.39/22.59 ((mult(mult(mult(c, a), c), rd(mult(b, c), mult(a, c))) = mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c))))) <=> (mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))),
% 22.39/22.59 inference(symmetry,[status(thm)],[4533])).
% 22.39/22.59 tff(4535,assumption,(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))), introduced(assumption)).
% 22.39/22.59 tff(4536,plain,
% 22.39/22.59 (mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))),
% 22.39/22.59 inference(symmetry,[status(thm)],[4535])).
% 22.39/22.59 tff(4537,plain,
% 22.39/22.59 (ld(a, mult(a, mult(mult(b, c), c))) = ld(a, mult(a, mult(c, mult(b, c))))),
% 22.39/22.59 inference(symmetry,[status(thm)],[4176])).
% 22.39/22.59 tff(4538,plain,
% 22.39/22.59 (mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(b, c), c)),
% 22.39/22.59 inference(transitivity,[status(thm)],[4535, 2802, 4179, 4176, 4173])).
% 22.39/22.59 tff(4539,plain,
% 22.39/22.59 (mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))) = mult(a, mult(mult(b, c), c))),
% 22.39/22.59 inference(monotonicity,[status(thm)],[4538])).
% 22.39/22.59 tff(4540,plain,
% 22.39/22.59 (mult(mult(mult(a, c), c), b) = mult(mult(c, mult(a, c)), b)),
% 22.39/22.59 inference(monotonicity,[status(thm)],[4529])).
% 22.39/22.59 tff(4541,plain,
% 22.39/22.59 (mult(mult(mult(a, c), b), c) = mult(mult(mult(a, c), c), b)),
% 22.39/22.59 inference(symmetry,[status(thm)],[4104])).
% 22.39/22.59 tff(4542,plain,
% 22.39/22.59 (mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))) = mult(mult(unit, mult(c, mult(a, c))), b)),
% 22.39/22.59 inference(transitivity,[status(thm)],[4539, 3138, 234, 4541, 4540, 4369])).
% 22.39/22.59 tff(4543,plain,
% 22.39/22.59 (mult(a, mult(b, c)) = mult(mult(b, c), a)),
% 22.39/22.59 inference(transitivity,[status(thm)],[289, 288, 4415, 4501, 4398])).
% 22.39/22.59 tff(4544,plain,
% 22.39/22.59 (mult(mult(a, mult(b, c)), c) = mult(mult(mult(b, c), a), c)),
% 22.39/22.59 inference(monotonicity,[status(thm)],[4543])).
% 22.39/22.59 tff(4545,plain,
% 22.39/22.59 (~(mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))),
% 22.39/22.59 inference(unit_resolution,[status(thm)],[303, 301, 299, 287])).
% 22.39/22.59 tff(4546,plain,
% 22.39/22.59 ((~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))),
% 22.39/22.59 inference(unit_resolution,[status(thm)],[308, 4545])).
% 22.39/22.59 tff(4547,plain,
% 22.39/22.59 (~((~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))),
% 22.39/22.59 inference(unit_resolution,[status(thm)],[313, 4546])).
% 22.39/22.59 tff(4548,plain,
% 22.39/22.59 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))),
% 22.39/22.59 inference(unit_resolution,[status(thm)],[315, 4547])).
% 22.39/22.59 tff(4549,plain,
% 22.39/22.59 (mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))),
% 22.39/22.59 inference(monotonicity,[status(thm)],[2701])).
% 22.39/22.59 tff(4550,plain,
% 22.39/22.59 (mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(mult(unit, b), mult(c, mult(a, c)))),
% 22.39/22.59 inference(transitivity,[status(thm)],[4549, 4548, 138, 266, 4544, 2570, 4396, 4395])).
% 22.39/22.59 tff(4551,plain,
% 22.39/22.59 ((mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))) <=> (mult(mult(unit, b), mult(c, mult(a, c))) = mult(mult(unit, mult(c, mult(a, c))), b))),
% 22.39/22.59 inference(monotonicity,[status(thm)],[4550, 4542])).
% 22.39/22.59 tff(4552,plain,
% 22.39/22.59 ((mult(mult(unit, b), mult(c, mult(a, c))) = mult(mult(unit, mult(c, mult(a, c))), b)) <=> (mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))),
% 22.39/22.59 inference(symmetry,[status(thm)],[4551])).
% 22.39/22.59 tff(4553,plain,
% 22.39/22.59 ((~(mult(mult(unit, b), mult(c, mult(a, c))) = mult(mult(unit, mult(c, mult(a, c))), b))) <=> (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))))),
% 22.39/22.59 inference(monotonicity,[status(thm)],[4552])).
% 22.39/22.59 tff(4554,plain,
% 22.39/22.59 (mult(a, mult(mult(b, c), c)) = mult(mult(unit, mult(c, mult(a, c))), b)),
% 22.39/22.59 inference(transitivity,[status(thm)],[3138, 234, 4541, 4540, 4369])).
% 22.39/22.59 tff(4555,plain,
% 22.39/22.59 (mult(mult(a, mult(b, c)), c) = mult(mult(unit, b), mult(c, mult(a, c)))),
% 22.39/22.59 inference(transitivity,[status(thm)],[4544, 2570, 4396, 4395])).
% 22.39/22.59 tff(4556,plain,
% 22.39/22.59 ((mult(mult(a, mult(b, c)), c) = mult(a, mult(mult(b, c), c))) <=> (mult(mult(unit, b), mult(c, mult(a, c))) = mult(mult(unit, mult(c, mult(a, c))), b))),
% 22.39/22.59 inference(monotonicity,[status(thm)],[4555, 4554])).
% 22.39/22.59 tff(4557,plain,
% 22.39/22.59 ((~(mult(mult(a, mult(b, c)), c) = mult(a, mult(mult(b, c), c)))) <=> (~(mult(mult(unit, b), mult(c, mult(a, c))) = mult(mult(unit, mult(c, mult(a, c))), b)))),
% 22.39/22.59 inference(monotonicity,[status(thm)],[4556])).
% 22.39/22.59 tff(4558,plain,
% 22.39/22.59 (~(mult(mult(unit, b), mult(c, mult(a, c))) = mult(mult(unit, mult(c, mult(a, c))), b))),
% 22.39/22.59 inference(modus_ponens,[status(thm)],[258, 4557])).
% 22.39/22.59 tff(4559,plain,
% 22.39/22.59 (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))),
% 22.39/22.59 inference(modus_ponens,[status(thm)],[4558, 4553])).
% 22.39/22.59 tff(4560,plain,
% 22.39/22.59 (((~(mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))))) | (mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))),
% 22.39/22.59 inference(tautology,[status(thm)],[])).
% 22.39/22.59 tff(4561,plain,
% 22.39/22.59 ((~(mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))))),
% 22.39/22.59 inference(unit_resolution,[status(thm)],[4560, 4559])).
% 22.39/22.59 tff(4562,plain,
% 22.39/22.59 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)))) | (~(mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))))) | (~((~(mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)))) | (~(mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))))) | (~((~(mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))))))),
% 22.39/22.59 inference(rewrite,[status(thm)],[])).
% 22.39/22.59 tff(4563,plain,
% 22.39/22.59 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)))) | (~(mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))))) | (~((~(mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))))))),
% 22.39/22.59 inference(quant_inst,[status(thm)],[])).
% 22.39/22.59 tff(4564,plain,
% 22.39/22.59 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)))) | (~(mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))))) | (~((~(mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))))))),
% 22.39/22.59 inference(modus_ponens,[status(thm)],[4563, 4562])).
% 22.39/22.59 tff(4565,plain,
% 22.39/22.59 ((~((~(mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)))) | (~(mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))))) | (~((~(mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))))))),
% 22.39/22.59 inference(unit_resolution,[status(thm)],[4564, 27])).
% 22.39/22.59 tff(4566,plain,
% 22.39/22.59 (~((~(mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)))) | (~(mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))))),
% 22.39/22.59 inference(unit_resolution,[status(thm)],[4565, 4561])).
% 22.39/22.59 tff(4567,plain,
% 22.39/22.59 (((~(mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)))) | (~(mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))))) | (mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))),
% 22.39/22.60 inference(tautology,[status(thm)],[])).
% 22.39/22.60 tff(4568,plain,
% 22.39/22.60 (mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 22.39/22.60 inference(unit_resolution,[status(thm)],[4567, 4566])).
% 22.39/22.60 tff(4569,plain,
% 22.39/22.60 (mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))),
% 22.39/22.60 inference(symmetry,[status(thm)],[4531])).
% 22.39/22.60 tff(4570,plain,
% 22.39/22.60 (mult(a, mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))),
% 22.39/22.60 inference(monotonicity,[status(thm)],[4569])).
% 22.39/22.60 tff(4571,plain,
% 22.39/22.60 (mult(a, mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(b, c), c))),
% 22.39/22.60 inference(transitivity,[status(thm)],[4570, 4568, 4539])).
% 22.39/22.60 tff(4572,plain,
% 22.39/22.60 (ld(a, mult(a, mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c)))))) = ld(a, mult(a, mult(mult(b, c), c)))),
% 22.39/22.60 inference(monotonicity,[status(thm)],[4571])).
% 22.39/22.60 tff(4573,plain,
% 22.39/22.60 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(a, mult(a, mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c)))))) = mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c)))))),
% 22.39/22.60 inference(quant_inst,[status(thm)],[])).
% 22.39/22.60 tff(4574,plain,
% 22.39/22.60 (ld(a, mult(a, mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c)))))) = mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c))))),
% 22.39/22.60 inference(unit_resolution,[status(thm)],[4573, 7])).
% 22.39/22.60 tff(4575,plain,
% 22.39/22.60 (mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c)))) = ld(a, mult(a, mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c))))))),
% 22.39/22.60 inference(symmetry,[status(thm)],[4574])).
% 22.39/22.60 tff(4576,plain,
% 22.39/22.60 (mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))),
% 22.39/22.60 inference(transitivity,[status(thm)],[4575, 4572, 4537, 4178, 2803, 4536])).
% 22.39/22.60 tff(4577,plain,
% 22.39/22.60 ((mult(mult(mult(c, a), c), rd(mult(b, c), mult(a, c))) = mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c))))) <=> (mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 22.39/22.60 inference(monotonicity,[status(thm)],[2691, 4576])).
% 22.39/22.60 tff(4578,plain,
% 22.39/22.60 ((mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))) <=> (mult(mult(mult(c, a), c), rd(mult(b, c), mult(a, c))) = mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c)))))),
% 22.39/22.60 inference(symmetry,[status(thm)],[4577])).
% 22.39/22.60 tff(4579,plain,
% 22.39/22.60 ((mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))) <=> (mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))),
% 22.39/22.60 inference(transitivity,[status(thm)],[4578, 4534])).
% 22.39/22.60 tff(4580,plain,
% 22.39/22.60 ((~(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))) <=> (~(mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))))),
% 22.39/22.60 inference(monotonicity,[status(thm)],[4579])).
% 22.39/22.60 tff(4581,plain,
% 22.39/22.60 (~(mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))),
% 22.39/22.60 inference(modus_ponens,[status(thm)],[2788, 4580])).
% 22.39/22.60 tff(4582,plain,
% 22.39/22.60 (((~(mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c))))) | (mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))),
% 22.39/22.60 inference(tautology,[status(thm)],[])).
% 22.39/22.60 tff(4583,plain,
% 22.39/22.60 ((~(mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c))))),
% 22.39/22.60 inference(unit_resolution,[status(thm)],[4582, 4581])).
% 22.39/22.60 tff(4584,plain,
% 22.39/22.60 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)))))) | (~((~(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)))))) | (~((~(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))))))))),
% 22.39/22.60 inference(rewrite,[status(thm)],[])).
% 22.39/22.60 tff(4585,plain,
% 22.39/22.60 (((~((~(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))))))) | (~((~(mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c))))))) <=> ((~((~(mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)))))) | (~((~(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))))))))),
% 22.39/22.60 inference(rewrite,[status(thm)],[])).
% 22.39/22.60 tff(4586,plain,
% 22.39/22.60 ((~((~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)))) | (~(mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))))) <=> (~((~(mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c))))))),
% 22.39/22.60 inference(rewrite,[status(thm)],[])).
% 22.39/22.60 tff(4587,plain,
% 22.39/22.60 ((~((~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))))) | (~(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))))) <=> (~((~(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c)))))))),
% 22.39/22.60 inference(rewrite,[status(thm)],[])).
% 22.39/22.60 tff(4588,plain,
% 22.39/22.60 (((~((~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))))) | (~(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)))) | (~(mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))))))) <=> ((~((~(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))))))) | (~((~(mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)))))))),
% 22.39/22.60 inference(monotonicity,[status(thm)],[4587, 4586])).
% 22.39/22.60 tff(4589,plain,
% 22.39/22.60 (((~((~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))))) | (~(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)))) | (~(mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))))))) <=> ((~((~(mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)))))) | (~((~(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))))))))),
% 22.39/22.60 inference(transitivity,[status(thm)],[4588, 4585])).
% 22.39/22.60 tff(4590,plain,
% 22.39/22.60 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))))) | (~(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)))) | (~(mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)))))) | (~((~(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c)))))))))),
% 22.39/22.60 inference(monotonicity,[status(thm)],[4589])).
% 22.39/22.60 tff(4591,plain,
% 22.39/22.60 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))))) | (~(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)))) | (~(mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)))))) | (~((~(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))))))))),
% 22.39/22.60 inference(transitivity,[status(thm)],[4590, 4584])).
% 22.39/22.60 tff(4592,plain,
% 22.39/22.60 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))))) | (~(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)))) | (~(mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))))))),
% 22.39/22.60 inference(quant_inst,[status(thm)],[])).
% 22.39/22.60 tff(4593,plain,
% 22.39/22.60 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)))))) | (~((~(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c)))))))),
% 22.39/22.60 inference(modus_ponens,[status(thm)],[4592, 4591])).
% 22.39/22.60 tff(4594,plain,
% 22.39/22.60 ((~((~(mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)))))) | (~((~(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c)))))))),
% 22.39/22.60 inference(unit_resolution,[status(thm)],[4593, 27])).
% 22.39/22.60 tff(4595,plain,
% 22.39/22.60 (~((~(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))))))),
% 22.39/22.60 inference(unit_resolution,[status(thm)],[4594, 4583])).
% 22.39/22.60 tff(4596,plain,
% 22.39/22.60 (((~(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c)))))) | (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))))),
% 22.39/22.60 inference(tautology,[status(thm)],[])).
% 22.39/22.60 tff(4597,plain,
% 22.39/22.60 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c)))),
% 22.39/22.60 inference(unit_resolution,[status(thm)],[4596, 4595])).
% 22.39/22.60 tff(4598,plain,
% 22.39/22.60 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 22.39/22.60 inference(transitivity,[status(thm)],[4597, 4530])).
% 22.39/22.60 tff(4599,plain,
% 22.39/22.60 (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a)),
% 22.39/22.61 inference(monotonicity,[status(thm)],[4598])).
% 22.39/22.61 tff(4600,plain,
% 22.39/22.61 (mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a)),
% 22.39/22.61 inference(symmetry,[status(thm)],[4599])).
% 22.39/22.61 tff(4601,plain,
% 22.39/22.61 (mult(mult(a, c), mult(a, mult(c, rd(mult(b, c), mult(a, c))))) = mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 22.39/22.61 inference(monotonicity,[status(thm)],[2701])).
% 22.39/22.61 tff(4602,plain,
% 22.39/22.61 ((mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c)))) <=> (mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 22.39/22.61 inference(commutativity,[status(thm)],[])).
% 22.39/22.61 tff(4603,plain,
% 22.39/22.61 (mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 22.39/22.61 inference(unit_resolution,[status(thm)],[4354, 4547])).
% 22.39/22.61 tff(4604,plain,
% 22.39/22.61 (mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 22.39/22.61 inference(symmetry,[status(thm)],[4603])).
% 22.39/22.61 tff(4605,plain,
% 22.39/22.61 (mult(mult(a, c), mult(a, mult(c, rd(mult(b, c), mult(a, c))))) = mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 22.39/22.61 inference(transitivity,[status(thm)],[4601, 4604])).
% 22.39/22.61 tff(4606,plain,
% 22.39/22.61 (((~(mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)))) | (~(mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))))) | (mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)))),
% 22.39/22.61 inference(tautology,[status(thm)],[])).
% 22.39/22.61 tff(4607,plain,
% 22.39/22.61 (mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c))),
% 22.39/22.61 inference(unit_resolution,[status(thm)],[4606, 4566])).
% 22.39/22.61 tff(4608,plain,
% 22.39/22.61 (ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) = ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))))),
% 22.39/22.61 inference(symmetry,[status(thm)],[4518])).
% 22.39/22.61 tff(4609,plain,
% 22.39/22.61 (mult(mult(a, c), a) = ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))),
% 22.39/22.61 inference(symmetry,[status(thm)],[4447])).
% 22.39/22.61 tff(4610,plain,
% 22.39/22.61 (mult(mult(a, c), a) = mult(a, mult(a, c))),
% 22.39/22.61 inference(transitivity,[status(thm)],[4609, 4608, 4451])).
% 22.39/22.61 tff(4611,plain,
% 22.39/22.61 (mult(mult(mult(a, c), a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c))))),
% 22.39/22.61 inference(monotonicity,[status(thm)],[4610])).
% 22.39/22.61 tff(4612,plain,
% 22.39/22.61 (mult(mult(mult(a, c), a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))),
% 22.39/22.61 inference(transitivity,[status(thm)],[4611, 4607, 4549])).
% 22.39/22.61 tff(4613,plain,
% 22.39/22.61 ((mult(mult(mult(a, c), a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(a, mult(c, rd(mult(b, c), mult(a, c)))))) <=> (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))))),
% 22.39/22.61 inference(monotonicity,[status(thm)],[4612, 4605])).
% 22.39/22.61 tff(4614,plain,
% 22.39/22.61 ((mult(mult(mult(a, c), a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(a, mult(c, rd(mult(b, c), mult(a, c)))))) <=> (mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 22.39/22.61 inference(transitivity,[status(thm)],[4613, 4602])).
% 22.39/22.61 tff(4615,plain,
% 22.39/22.61 ((mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))) <=> (mult(mult(mult(a, c), a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(a, mult(c, rd(mult(b, c), mult(a, c))))))),
% 22.39/22.61 inference(symmetry,[status(thm)],[4614])).
% 22.39/22.61 tff(4616,plain,
% 22.39/22.61 ((~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))) <=> (~(mult(mult(mult(a, c), a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(a, mult(c, rd(mult(b, c), mult(a, c)))))))),
% 22.39/22.61 inference(monotonicity,[status(thm)],[4615])).
% 22.39/22.61 tff(4617,plain,
% 22.39/22.61 ((mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))) <=> (mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))),
% 22.39/22.61 inference(monotonicity,[status(thm)],[4603, 4548])).
% 22.39/22.61 tff(4618,plain,
% 22.39/22.61 ((mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))) <=> (mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 22.39/22.61 inference(symmetry,[status(thm)],[4617])).
% 22.39/22.61 tff(4619,plain,
% 22.39/22.61 ((~(mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) <=> (~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))))),
% 22.39/22.61 inference(monotonicity,[status(thm)],[4618])).
% 22.39/22.61 tff(4620,plain,
% 22.39/22.61 (~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 22.39/22.61 inference(modus_ponens,[status(thm)],[4545, 4619])).
% 22.39/22.61 tff(4621,plain,
% 22.39/22.61 (~(mult(mult(mult(a, c), a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(a, mult(c, rd(mult(b, c), mult(a, c))))))),
% 22.39/22.61 inference(modus_ponens,[status(thm)],[4620, 4616])).
% 22.39/22.61 tff(4622,plain,
% 22.39/22.61 (((~(mult(mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, c), mult(mult(c, rd(mult(b, c), mult(a, c))), a)))) | (~(mult(mult(mult(a, c), a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(a, mult(c, rd(mult(b, c), mult(a, c)))))))) | (mult(mult(mult(a, c), a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(a, mult(c, rd(mult(b, c), mult(a, c))))))),
% 22.39/22.61 inference(tautology,[status(thm)],[])).
% 22.39/22.61 tff(4623,plain,
% 22.39/22.61 ((~(mult(mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, c), mult(mult(c, rd(mult(b, c), mult(a, c))), a)))) | (~(mult(mult(mult(a, c), a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(a, mult(c, rd(mult(b, c), mult(a, c)))))))),
% 22.39/22.61 inference(unit_resolution,[status(thm)],[4622, 4621])).
% 22.39/22.61 tff(4624,plain,
% 22.39/22.61 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, c), mult(mult(c, rd(mult(b, c), mult(a, c))), a)) = mult(mult(a, c), mult(a, mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(a, c), a), mult(c, rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, c), mult(mult(c, rd(mult(b, c), mult(a, c))), a)))) | (~(mult(mult(mult(a, c), a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(a, mult(c, rd(mult(b, c), mult(a, c))))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, c), mult(mult(c, rd(mult(b, c), mult(a, c))), a)) = mult(mult(a, c), mult(a, mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(a, c), a), mult(c, rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, c), mult(mult(c, rd(mult(b, c), mult(a, c))), a)))) | (~(mult(mult(mult(a, c), a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(a, mult(c, rd(mult(b, c), mult(a, c))))))))))),
% 22.39/22.61 inference(rewrite,[status(thm)],[])).
% 22.39/22.61 tff(4625,plain,
% 22.39/22.61 (((~((~(mult(mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(a, c), a), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, c), mult(mult(c, rd(mult(b, c), mult(a, c))), a)) = mult(mult(a, c), mult(a, mult(c, rd(mult(b, c), mult(a, c))))))))) | (~((~(mult(mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, c), mult(mult(c, rd(mult(b, c), mult(a, c))), a)))) | (~(mult(mult(mult(a, c), a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(a, mult(c, rd(mult(b, c), mult(a, c)))))))))) <=> ((~((~(mult(mult(a, c), mult(mult(c, rd(mult(b, c), mult(a, c))), a)) = mult(mult(a, c), mult(a, mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(a, c), a), mult(c, rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, c), mult(mult(c, rd(mult(b, c), mult(a, c))), a)))) | (~(mult(mult(mult(a, c), a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(a, mult(c, rd(mult(b, c), mult(a, c))))))))))),
% 22.39/22.61 inference(rewrite,[status(thm)],[])).
% 22.39/22.61 tff(4626,plain,
% 22.39/22.61 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(a, c), a), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, c), mult(mult(c, rd(mult(b, c), mult(a, c))), a)) = mult(mult(a, c), mult(a, mult(c, rd(mult(b, c), mult(a, c))))))))) | (~((~(mult(mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, c), mult(mult(c, rd(mult(b, c), mult(a, c))), a)))) | (~(mult(mult(mult(a, c), a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(a, mult(c, rd(mult(b, c), mult(a, c))))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, c), mult(mult(c, rd(mult(b, c), mult(a, c))), a)) = mult(mult(a, c), mult(a, mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(a, c), a), mult(c, rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, c), mult(mult(c, rd(mult(b, c), mult(a, c))), a)))) | (~(mult(mult(mult(a, c), a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(a, mult(c, rd(mult(b, c), mult(a, c)))))))))))),
% 22.39/22.61 inference(monotonicity,[status(thm)],[4625])).
% 22.39/22.61 tff(4627,plain,
% 22.39/22.61 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(a, c), a), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, c), mult(mult(c, rd(mult(b, c), mult(a, c))), a)) = mult(mult(a, c), mult(a, mult(c, rd(mult(b, c), mult(a, c))))))))) | (~((~(mult(mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, c), mult(mult(c, rd(mult(b, c), mult(a, c))), a)))) | (~(mult(mult(mult(a, c), a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(a, mult(c, rd(mult(b, c), mult(a, c))))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, c), mult(mult(c, rd(mult(b, c), mult(a, c))), a)) = mult(mult(a, c), mult(a, mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(a, c), a), mult(c, rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, c), mult(mult(c, rd(mult(b, c), mult(a, c))), a)))) | (~(mult(mult(mult(a, c), a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(a, mult(c, rd(mult(b, c), mult(a, c))))))))))),
% 22.39/22.61 inference(transitivity,[status(thm)],[4626, 4624])).
% 22.39/22.61 tff(4628,plain,
% 22.39/22.61 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(a, c), a), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, c), mult(mult(c, rd(mult(b, c), mult(a, c))), a)) = mult(mult(a, c), mult(a, mult(c, rd(mult(b, c), mult(a, c))))))))) | (~((~(mult(mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, c), mult(mult(c, rd(mult(b, c), mult(a, c))), a)))) | (~(mult(mult(mult(a, c), a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(a, mult(c, rd(mult(b, c), mult(a, c))))))))))),
% 22.39/22.61 inference(quant_inst,[status(thm)],[])).
% 22.39/22.61 tff(4629,plain,
% 22.39/22.61 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, c), mult(mult(c, rd(mult(b, c), mult(a, c))), a)) = mult(mult(a, c), mult(a, mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(a, c), a), mult(c, rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, c), mult(mult(c, rd(mult(b, c), mult(a, c))), a)))) | (~(mult(mult(mult(a, c), a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(a, mult(c, rd(mult(b, c), mult(a, c)))))))))),
% 22.39/22.61 inference(modus_ponens,[status(thm)],[4628, 4627])).
% 22.39/22.61 tff(4630,plain,
% 22.39/22.61 ((~((~(mult(mult(a, c), mult(mult(c, rd(mult(b, c), mult(a, c))), a)) = mult(mult(a, c), mult(a, mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(a, c), a), mult(c, rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, c), mult(mult(c, rd(mult(b, c), mult(a, c))), a)))) | (~(mult(mult(mult(a, c), a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(a, mult(c, rd(mult(b, c), mult(a, c)))))))))),
% 22.39/22.61 inference(unit_resolution,[status(thm)],[4629, 27])).
% 22.39/22.61 tff(4631,plain,
% 22.39/22.61 (~((~(mult(mult(a, c), mult(mult(c, rd(mult(b, c), mult(a, c))), a)) = mult(mult(a, c), mult(a, mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(a, c), a), mult(c, rd(mult(b, c), mult(a, c)))))))),
% 22.39/22.61 inference(unit_resolution,[status(thm)],[4630, 4623])).
% 22.39/22.61 tff(4632,plain,
% 22.39/22.61 (((~(mult(mult(a, c), mult(mult(c, rd(mult(b, c), mult(a, c))), a)) = mult(mult(a, c), mult(a, mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(a, c), a), mult(c, rd(mult(b, c), mult(a, c))))))) | (mult(mult(a, c), mult(mult(c, rd(mult(b, c), mult(a, c))), a)) = mult(mult(a, c), mult(a, mult(c, rd(mult(b, c), mult(a, c))))))),
% 22.39/22.61 inference(tautology,[status(thm)],[])).
% 22.39/22.61 tff(4633,plain,
% 22.39/22.61 (mult(mult(a, c), mult(mult(c, rd(mult(b, c), mult(a, c))), a)) = mult(mult(a, c), mult(a, mult(c, rd(mult(b, c), mult(a, c)))))),
% 22.39/22.62 inference(unit_resolution,[status(thm)],[4632, 4631])).
% 22.39/22.62 tff(4634,plain,
% 22.39/22.62 (mult(mult(a, c), mult(mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit), a)) = mult(mult(a, c), mult(mult(c, rd(mult(b, c), mult(a, c))), a))),
% 22.39/22.62 inference(monotonicity,[status(thm)],[3252])).
% 22.39/22.62 tff(4635,plain,
% 22.39/22.62 (mult(mult(a, c), mult(mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit), a)) = mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 22.39/22.62 inference(transitivity,[status(thm)],[4634, 4633, 4601])).
% 22.39/22.62 tff(4636,plain,
% 22.39/22.62 (ld(mult(a, c), mult(mult(a, c), mult(mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit), a))) = ld(mult(a, c), mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 22.39/22.62 inference(monotonicity,[status(thm)],[4635])).
% 22.39/22.62 tff(4637,plain,
% 22.39/22.62 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(a, c), mult(mult(a, c), mult(mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit), a))) = mult(mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit), a))),
% 22.39/22.62 inference(quant_inst,[status(thm)],[])).
% 22.39/22.62 tff(4638,plain,
% 22.39/22.62 (ld(mult(a, c), mult(mult(a, c), mult(mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit), a))) = mult(mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit), a)),
% 22.39/22.62 inference(unit_resolution,[status(thm)],[4637, 7])).
% 22.39/22.62 tff(4639,plain,
% 22.39/22.62 (mult(mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit), a) = ld(mult(a, c), mult(mult(a, c), mult(mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), unit), a)))),
% 22.39/22.62 inference(symmetry,[status(thm)],[4638])).
% 22.39/22.62 tff(4640,plain,
% 22.39/22.62 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(a, c), mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(c, rd(mult(b, c), mult(a, c))))),
% 22.39/22.62 inference(quant_inst,[status(thm)],[])).
% 22.39/22.62 tff(4641,plain,
% 22.39/22.62 (ld(mult(a, c), mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(c, rd(mult(b, c), mult(a, c)))),
% 22.39/22.62 inference(unit_resolution,[status(thm)],[4640, 7])).
% 22.39/22.62 tff(4642,plain,
% 22.39/22.62 (((~(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c)))))) | (mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))),
% 22.39/22.62 inference(tautology,[status(thm)],[])).
% 22.39/22.62 tff(4643,plain,
% 22.39/22.62 (mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))),
% 22.39/22.62 inference(unit_resolution,[status(thm)],[4642, 4595])).
% 22.39/22.62 tff(4644,plain,
% 22.39/22.62 (ld(mult(a, c), mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c))) = ld(mult(a, c), mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))),
% 22.39/22.62 inference(monotonicity,[status(thm)],[4643])).
% 22.39/22.62 tff(4645,plain,
% 22.39/22.62 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(a, c), mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c))) = mult(rd(mult(b, c), mult(a, c)), c))),
% 22.39/22.62 inference(quant_inst,[status(thm)],[])).
% 22.39/22.62 tff(4646,plain,
% 22.39/22.62 (ld(mult(a, c), mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c))) = mult(rd(mult(b, c), mult(a, c)), c)),
% 22.39/22.62 inference(unit_resolution,[status(thm)],[4645, 7])).
% 22.39/22.62 tff(4647,plain,
% 22.39/22.62 (mult(rd(mult(b, c), mult(a, c)), c) = ld(mult(a, c), mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)))),
% 22.39/22.62 inference(symmetry,[status(thm)],[4646])).
% 22.39/22.62 tff(4648,plain,
% 22.39/22.62 (mult(rd(mult(b, c), mult(a, c)), c) = mult(c, rd(mult(b, c), mult(a, c)))),
% 22.39/22.62 inference(transitivity,[status(thm)],[4647, 4644, 4641])).
% 22.39/22.62 tff(4649,plain,
% 22.39/22.62 (mult(mult(rd(mult(b, c), mult(a, c)), c), a) = mult(mult(c, rd(mult(b, c), mult(a, c))), a)),
% 22.39/22.62 inference(monotonicity,[status(thm)],[4648])).
% 22.39/22.62 tff(4650,plain,
% 22.39/22.62 (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), c), a)),
% 22.39/22.62 inference(monotonicity,[status(thm)],[81])).
% 22.39/22.62 tff(4651,plain,
% 22.39/22.62 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), unit) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))),
% 22.39/22.62 inference(transitivity,[status(thm)],[1875, 1871, 4489, 4650, 4649, 3251, 4639, 4636, 295])).
% 22.39/22.62 tff(4652,plain,
% 22.39/22.62 (mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), unit), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)),
% 22.39/22.62 inference(monotonicity,[status(thm)],[4651])).
% 22.39/22.62 tff(4653,plain,
% 22.39/22.62 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), unit), c) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(c, unit), c)))),
% 22.39/22.62 inference(quant_inst,[status(thm)],[])).
% 22.39/22.62 tff(4654,plain,
% 22.39/22.62 (mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), unit), c) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(c, unit), c))),
% 22.39/22.62 inference(unit_resolution,[status(thm)],[4653, 56])).
% 22.39/22.62 tff(4655,plain,
% 22.39/22.62 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(c, unit), c)) = mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), unit), c)),
% 22.39/22.62 inference(symmetry,[status(thm)],[4654])).
% 22.39/22.62 tff(4656,plain,
% 22.39/22.62 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(c, unit), c))),
% 22.39/22.62 inference(monotonicity,[status(thm)],[2617])).
% 22.39/22.62 tff(4657,plain,
% 22.39/22.62 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)) = mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 22.39/22.62 inference(transitivity,[status(thm)],[4656, 4655, 4652, 4597, 4530])).
% 22.39/22.62 tff(4658,plain,
% 22.39/22.62 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)), a) = mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a)),
% 22.39/22.62 inference(monotonicity,[status(thm)],[4657])).
% 22.39/22.62 tff(4659,plain,
% 22.39/22.62 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(c, c)), a)))),
% 22.39/22.62 inference(quant_inst,[status(thm)],[])).
% 22.39/22.62 tff(4660,plain,
% 22.39/22.62 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(c, c)), a))),
% 22.39/22.62 inference(unit_resolution,[status(thm)],[4659, 56])).
% 22.39/22.62 tff(4661,plain,
% 22.39/22.62 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(c, c)), a)) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)), a)),
% 22.39/22.62 inference(symmetry,[status(thm)],[4660])).
% 22.39/22.62 tff(4662,plain,
% 22.39/22.62 (mult(mult(a, mult(c, c)), a) = mult(mult(mult(a, c), c), a)),
% 22.39/22.62 inference(monotonicity,[status(thm)],[2619])).
% 22.39/22.62 tff(4663,plain,
% 22.39/22.62 (mult(mult(mult(a, c), c), a) = mult(mult(a, mult(c, c)), a)),
% 22.39/22.62 inference(symmetry,[status(thm)],[4662])).
% 22.39/22.62 tff(4664,plain,
% 22.39/22.62 (mult(mult(c, mult(a, c)), a) = mult(mult(mult(a, c), c), a)),
% 22.39/22.62 inference(monotonicity,[status(thm)],[3878])).
% 22.39/22.62 tff(4665,plain,
% 22.39/22.62 (mult(mult(c, mult(a, c)), a) = mult(mult(a, mult(c, c)), a)),
% 22.39/22.62 inference(transitivity,[status(thm)],[4664, 4663])).
% 22.39/22.62 tff(4666,plain,
% 22.39/22.62 (mult(rd(mult(b, c), mult(a, c)), mult(mult(c, mult(a, c)), a)) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(c, c)), a))),
% 22.39/22.62 inference(monotonicity,[status(thm)],[4665])).
% 22.39/22.62 tff(4667,plain,
% 22.39/22.62 (mult(mult(mult(a, c), c), a) = mult(mult(c, mult(a, c)), a)),
% 22.39/22.62 inference(symmetry,[status(thm)],[4664])).
% 22.39/22.62 tff(4668,plain,
% 22.39/22.62 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(mult(a, c), c), a), rd(mult(b, c), mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), c), a))),
% 22.39/22.62 inference(quant_inst,[status(thm)],[])).
% 22.39/22.62 tff(4669,plain,
% 22.39/22.62 (rd(mult(mult(mult(mult(a, c), c), a), rd(mult(b, c), mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), c), a)),
% 22.39/22.62 inference(unit_resolution,[status(thm)],[4668, 168])).
% 22.39/22.62 tff(4670,plain,
% 22.39/22.62 (mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 22.39/22.62 inference(monotonicity,[status(thm)],[3885])).
% 22.39/22.62 tff(4671,plain,
% 22.39/22.62 (((~(mult(mult(a, c), mult(mult(c, rd(mult(b, c), mult(a, c))), a)) = mult(mult(a, c), mult(a, mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(a, c), a), mult(c, rd(mult(b, c), mult(a, c))))))) | (mult(mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(a, c), a), mult(c, rd(mult(b, c), mult(a, c)))))),
% 22.39/22.62 inference(tautology,[status(thm)],[])).
% 22.39/22.62 tff(4672,plain,
% 22.39/22.62 (mult(mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(a, c), a), mult(c, rd(mult(b, c), mult(a, c))))),
% 22.39/22.62 inference(unit_resolution,[status(thm)],[4671, 4631])).
% 22.39/22.62 tff(4673,plain,
% 22.39/22.62 (mult(mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))), a)),
% 22.39/22.62 inference(monotonicity,[status(thm)],[4569])).
% 22.39/22.62 tff(4674,plain,
% 22.39/22.62 (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a)),
% 22.39/22.62 inference(transitivity,[status(thm)],[1683, 2703])).
% 22.39/22.62 tff(4675,plain,
% 22.39/22.62 (mult(c, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))) = mult(c, mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a))),
% 22.39/22.62 inference(monotonicity,[status(thm)],[4674])).
% 22.39/22.62 tff(4676,plain,
% 22.39/22.62 (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 22.39/22.62 inference(symmetry,[status(thm)],[299])).
% 22.39/22.62 tff(4677,plain,
% 22.39/22.62 (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))),
% 22.39/22.62 inference(transitivity,[status(thm)],[4676, 4520])).
% 22.39/22.62 tff(4678,plain,
% 22.39/22.62 (mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))) = mult(c, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))))),
% 22.39/22.62 inference(monotonicity,[status(thm)],[4677])).
% 22.39/22.62 tff(4679,plain,
% 22.39/22.62 (mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))),
% 22.39/22.62 inference(transitivity,[status(thm)],[4678, 4675, 2698, 4673, 4672, 4611, 4607, 4549])).
% 22.39/22.62 tff(4680,plain,
% 22.39/22.62 (mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 22.39/22.62 inference(transitivity,[status(thm)],[4670, 4604])).
% 22.39/22.62 tff(4681,plain,
% 22.39/22.62 ((mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) <=> (mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 22.39/22.62 inference(monotonicity,[status(thm)],[4680, 4679])).
% 22.39/22.62 tff(4682,plain,
% 22.39/22.62 ((mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))) <=> (mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))),
% 22.39/22.62 inference(symmetry,[status(thm)],[4681])).
% 22.39/22.62 tff(4683,plain,
% 22.39/22.62 ((~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))) <=> (~(mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))))),
% 22.39/22.62 inference(monotonicity,[status(thm)],[4682])).
% 22.39/22.62 tff(4684,plain,
% 22.39/22.62 (~(mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))),
% 22.39/22.62 inference(modus_ponens,[status(thm)],[4620, 4683])).
% 22.39/22.62 tff(4685,plain,
% 22.39/22.62 (((~(mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(c, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))))) | (mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))),
% 22.39/22.62 inference(tautology,[status(thm)],[])).
% 22.39/22.62 tff(4686,plain,
% 22.39/22.62 ((~(mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(c, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))))),
% 22.39/22.62 inference(unit_resolution,[status(thm)],[4685, 4684])).
% 22.39/22.62 tff(4687,plain,
% 22.39/22.62 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(c, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)))))) | (~((~(mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(c, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(c, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)))))) | (~((~(mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(c, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))))))),
% 22.39/22.63 inference(rewrite,[status(thm)],[])).
% 22.39/22.63 tff(4688,plain,
% 22.39/22.63 (((~((~(mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(c, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))))) | (~((~(mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(c, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))))))) <=> ((~((~(mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(c, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)))))) | (~((~(mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(c, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))))))),
% 22.39/22.63 inference(rewrite,[status(thm)],[])).
% 22.39/22.63 tff(4689,plain,
% 22.39/22.63 ((~((~(mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(c, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)))) | (~(mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))))) <=> (~((~(mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(c, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))))))),
% 22.39/22.63 inference(rewrite,[status(thm)],[])).
% 22.39/22.63 tff(4690,plain,
% 22.39/22.63 ((~((~(mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(c, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))))) <=> (~((~(mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(c, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))))))),
% 22.39/22.63 inference(rewrite,[status(thm)],[])).
% 22.39/22.63 tff(4691,plain,
% 22.39/22.63 (((~((~(mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(c, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))))) | (~((~(mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(c, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)))) | (~(mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))))))) <=> ((~((~(mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(c, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))))) | (~((~(mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(c, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)))))))),
% 22.39/22.63 inference(monotonicity,[status(thm)],[4690, 4689])).
% 22.39/22.63 tff(4692,plain,
% 22.39/22.63 (((~((~(mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(c, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))))) | (~((~(mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(c, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)))) | (~(mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))))))) <=> ((~((~(mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(c, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)))))) | (~((~(mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(c, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))))))),
% 22.39/22.63 inference(transitivity,[status(thm)],[4691, 4688])).
% 22.39/22.63 tff(4693,plain,
% 22.39/22.63 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(c, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))))) | (~((~(mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(c, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)))) | (~(mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(c, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)))))) | (~((~(mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(c, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))))))))),
% 22.39/22.63 inference(monotonicity,[status(thm)],[4692])).
% 22.39/22.63 tff(4694,plain,
% 22.39/22.63 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(c, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))))) | (~((~(mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(c, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)))) | (~(mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(c, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)))))) | (~((~(mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(c, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))))))),
% 22.39/22.63 inference(transitivity,[status(thm)],[4693, 4687])).
% 22.39/22.63 tff(4695,plain,
% 22.39/22.63 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(c, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))))) | (~((~(mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(c, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)))) | (~(mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))))))),
% 22.39/22.63 inference(quant_inst,[status(thm)],[])).
% 22.39/22.63 tff(4696,plain,
% 22.39/22.63 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(c, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)))))) | (~((~(mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(c, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))))))),
% 22.39/22.63 inference(modus_ponens,[status(thm)],[4695, 4694])).
% 22.39/22.63 tff(4697,plain,
% 22.39/22.63 ((~((~(mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(c, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)))))) | (~((~(mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(c, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))))))),
% 22.39/22.63 inference(unit_resolution,[status(thm)],[4696, 27])).
% 22.39/22.63 tff(4698,plain,
% 22.39/22.63 (~((~(mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(c, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))))),
% 22.47/22.63 inference(unit_resolution,[status(thm)],[4697, 4686])).
% 22.47/22.63 tff(4699,plain,
% 22.47/22.63 (((~(mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(c, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))))) | (mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 22.47/22.63 inference(tautology,[status(thm)],[])).
% 22.47/22.63 tff(4700,plain,
% 22.47/22.63 (mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 22.47/22.63 inference(unit_resolution,[status(thm)],[4699, 4698])).
% 22.47/22.63 tff(4701,assumption,(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c))))), introduced(assumption)).
% 22.47/22.63 tff(4702,plain,
% 22.47/22.63 (mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a)),
% 22.47/22.63 inference(monotonicity,[status(thm)],[4701])).
% 22.47/22.63 tff(4703,plain,
% 22.47/22.63 (mult(mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a)),
% 22.47/22.63 inference(monotonicity,[status(thm)],[4530])).
% 22.47/22.63 tff(4704,plain,
% 22.47/22.63 (mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))), a)),
% 22.47/22.63 inference(symmetry,[status(thm)],[4703])).
% 22.47/22.63 tff(4705,plain,
% 22.47/22.63 (mult(mult(mult(mult(a, c), c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c)))),
% 22.47/22.63 inference(monotonicity,[status(thm)],[4667])).
% 22.47/22.63 tff(4706,plain,
% 22.47/22.63 (mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(mult(a, c), c), a), rd(mult(b, c), mult(a, c)))),
% 22.47/22.63 inference(symmetry,[status(thm)],[4705])).
% 22.47/22.63 tff(4707,plain,
% 22.47/22.63 ((mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a)) <=> (mult(mult(mult(mult(a, c), c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))), a))),
% 22.47/22.63 inference(monotonicity,[status(thm)],[4706, 4704])).
% 22.47/22.63 tff(4708,plain,
% 22.47/22.63 ((mult(mult(mult(mult(a, c), c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))), a)) <=> (mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a))),
% 22.47/22.63 inference(symmetry,[status(thm)],[4707])).
% 22.47/22.63 tff(4709,plain,
% 22.47/22.63 (mult(a, mult(mult(c, c), a)) = mult(a, mult(c, mult(c, a)))),
% 22.47/22.63 inference(monotonicity,[status(thm)],[3911])).
% 22.47/22.63 tff(4710,plain,
% 22.47/22.63 (mult(a, mult(c, mult(c, a))) = mult(a, mult(mult(c, c), a))),
% 22.47/22.63 inference(symmetry,[status(thm)],[4709])).
% 22.47/22.63 tff(4711,plain,
% 22.47/22.63 (mult(c, mult(c, a)) = mult(c, mult(a, c))),
% 22.47/22.63 inference(monotonicity,[status(thm)],[3885])).
% 22.47/22.63 tff(4712,plain,
% 22.47/22.63 (mult(a, mult(c, mult(c, a))) = mult(a, mult(c, mult(a, c)))),
% 22.47/22.63 inference(monotonicity,[status(thm)],[4711])).
% 22.47/22.63 tff(4713,plain,
% 22.47/22.63 (mult(a, mult(c, mult(a, c))) = mult(a, mult(c, mult(c, a)))),
% 22.47/22.63 inference(symmetry,[status(thm)],[4712])).
% 22.47/22.63 tff(4714,plain,
% 22.47/22.63 (mult(a, mult(c, mult(a, c))) = mult(a, mult(mult(c, a), c))),
% 22.47/22.63 inference(monotonicity,[status(thm)],[3877])).
% 22.47/22.63 tff(4715,plain,
% 22.47/22.63 (mult(a, mult(mult(c, a), c)) = mult(a, mult(c, mult(a, c)))),
% 22.47/22.63 inference(symmetry,[status(thm)],[4714])).
% 22.47/22.63 tff(4716,plain,
% 22.47/22.63 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(a, c), a), c) = mult(a, mult(mult(c, a), c)))),
% 22.47/22.63 inference(quant_inst,[status(thm)],[])).
% 22.47/22.63 tff(4717,plain,
% 22.47/22.63 (mult(mult(mult(a, c), a), c) = mult(a, mult(mult(c, a), c))),
% 22.47/22.63 inference(unit_resolution,[status(thm)],[4716, 56])).
% 22.47/22.64 tff(4718,plain,
% 22.47/22.64 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c)))),
% 22.47/22.64 inference(symmetry,[status(thm)],[4517])).
% 22.47/22.64 tff(4719,plain,
% 22.47/22.64 (ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) = ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))))),
% 22.47/22.64 inference(monotonicity,[status(thm)],[4718])).
% 22.47/22.64 tff(4720,plain,
% 22.47/22.64 (mult(mult(a, c), a) = mult(a, mult(a, c))),
% 22.47/22.64 inference(transitivity,[status(thm)],[4609, 4719, 4451])).
% 22.47/22.64 tff(4721,plain,
% 22.47/22.64 (mult(mult(mult(a, c), a), c) = mult(mult(a, mult(a, c)), c)),
% 22.47/22.64 inference(monotonicity,[status(thm)],[4720])).
% 22.47/22.64 tff(4722,plain,
% 22.47/22.64 (mult(mult(a, mult(a, c)), c) = mult(mult(mult(a, c), a), c)),
% 22.47/22.64 inference(symmetry,[status(thm)],[4721])).
% 22.47/22.64 tff(4723,plain,
% 22.47/22.64 ((mult(mult(a, c), mult(a, c)) = mult(mult(a, mult(a, c)), c)) <=> (mult(mult(a, mult(a, c)), c) = mult(mult(a, c), mult(a, c)))),
% 22.47/22.64 inference(commutativity,[status(thm)],[])).
% 22.47/22.64 tff(4724,plain,
% 22.47/22.64 (mult(a, mult(mult(c, a), c)) = mult(mult(mult(a, c), a), c)),
% 22.47/22.64 inference(symmetry,[status(thm)],[4717])).
% 22.47/22.64 tff(4725,plain,
% 22.47/22.64 (mult(a, mult(c, mult(a, c))) = mult(mult(a, mult(a, c)), c)),
% 22.47/22.64 inference(transitivity,[status(thm)],[4714, 4724, 4721])).
% 22.47/22.64 tff(4726,plain,
% 22.47/22.64 ((mult(mult(a, c), mult(a, c)) = mult(a, mult(c, mult(a, c)))) <=> (mult(mult(a, c), mult(a, c)) = mult(mult(a, mult(a, c)), c))),
% 22.47/22.64 inference(monotonicity,[status(thm)],[4725])).
% 22.47/22.64 tff(4727,plain,
% 22.47/22.64 ((mult(mult(a, c), mult(a, c)) = mult(a, mult(c, mult(a, c)))) <=> (mult(mult(a, mult(a, c)), c) = mult(mult(a, c), mult(a, c)))),
% 22.47/22.64 inference(transitivity,[status(thm)],[4726, 4723])).
% 22.47/22.64 tff(4728,plain,
% 22.47/22.64 (mult(a, mult(c, mult(a, c))) = mult(a, mult(mult(a, c), c))),
% 22.47/22.64 inference(monotonicity,[status(thm)],[4122])).
% 22.47/22.64 tff(4729,plain,
% 22.47/22.64 (mult(a, mult(mult(a, c), c)) = mult(a, mult(c, mult(a, c)))),
% 22.47/22.64 inference(symmetry,[status(thm)],[4728])).
% 22.47/22.64 tff(4730,plain,
% 22.47/22.64 (mult(a, mult(mult(a, c), c)) = mult(a, mult(mult(c, a), c))),
% 22.47/22.64 inference(monotonicity,[status(thm)],[4066])).
% 22.47/22.64 tff(4731,plain,
% 22.47/22.64 (mult(a, mult(mult(c, a), c)) = mult(a, mult(mult(a, c), c))),
% 22.47/22.64 inference(symmetry,[status(thm)],[4730])).
% 22.47/22.64 tff(4732,plain,
% 22.47/22.64 (mult(mult(mult(a, c), a), c) = mult(mult(a, mult(a, c)), c)),
% 22.47/22.64 inference(monotonicity,[status(thm)],[4610])).
% 22.47/22.64 tff(4733,plain,
% 22.47/22.64 (mult(mult(a, mult(a, c)), c) = mult(mult(mult(a, c), a), c)),
% 22.47/22.64 inference(symmetry,[status(thm)],[4732])).
% 22.47/22.64 tff(4734,assumption,(~(mult(mult(a, c), mult(a, c)) = mult(a, mult(c, mult(a, c))))), introduced(assumption)).
% 22.47/22.64 tff(4735,plain,
% 22.47/22.64 (((~(mult(mult(a, mult(a, c)), c) = mult(a, mult(mult(a, c), c)))) | (~(mult(mult(a, c), mult(a, c)) = mult(a, mult(c, mult(a, c)))))) | (mult(mult(a, c), mult(a, c)) = mult(a, mult(c, mult(a, c))))),
% 22.47/22.64 inference(tautology,[status(thm)],[])).
% 22.47/22.64 tff(4736,plain,
% 22.47/22.64 ((~(mult(mult(a, mult(a, c)), c) = mult(a, mult(mult(a, c), c)))) | (~(mult(mult(a, c), mult(a, c)) = mult(a, mult(c, mult(a, c)))))),
% 22.47/22.64 inference(unit_resolution,[status(thm)],[4735, 4734])).
% 22.47/22.64 tff(4737,plain,
% 22.47/22.64 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(a, mult(mult(a, c), c)) = mult(a, mult(c, mult(a, c))))) | (~(mult(mult(a, mult(a, c)), c) = mult(mult(a, c), mult(a, c)))))) | (~((~(mult(mult(a, mult(a, c)), c) = mult(a, mult(mult(a, c), c)))) | (~(mult(mult(a, c), mult(a, c)) = mult(a, mult(c, mult(a, c))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(a, mult(mult(a, c), c)) = mult(a, mult(c, mult(a, c))))) | (~(mult(mult(a, mult(a, c)), c) = mult(mult(a, c), mult(a, c)))))) | (~((~(mult(mult(a, mult(a, c)), c) = mult(a, mult(mult(a, c), c)))) | (~(mult(mult(a, c), mult(a, c)) = mult(a, mult(c, mult(a, c))))))))),
% 22.47/22.64 inference(rewrite,[status(thm)],[])).
% 22.47/22.64 tff(4738,plain,
% 22.47/22.64 (((~((~(mult(mult(a, mult(a, c)), c) = mult(mult(a, c), mult(a, c)))) | (~(mult(a, mult(mult(a, c), c)) = mult(a, mult(c, mult(a, c))))))) | (~((~(mult(mult(a, mult(a, c)), c) = mult(a, mult(mult(a, c), c)))) | (~(mult(mult(a, c), mult(a, c)) = mult(a, mult(c, mult(a, c)))))))) <=> ((~((~(mult(a, mult(mult(a, c), c)) = mult(a, mult(c, mult(a, c))))) | (~(mult(mult(a, mult(a, c)), c) = mult(mult(a, c), mult(a, c)))))) | (~((~(mult(mult(a, mult(a, c)), c) = mult(a, mult(mult(a, c), c)))) | (~(mult(mult(a, c), mult(a, c)) = mult(a, mult(c, mult(a, c))))))))),
% 22.47/22.64 inference(rewrite,[status(thm)],[])).
% 22.47/22.64 tff(4739,plain,
% 22.47/22.64 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, mult(a, c)), c) = mult(mult(a, c), mult(a, c)))) | (~(mult(a, mult(mult(a, c), c)) = mult(a, mult(c, mult(a, c))))))) | (~((~(mult(mult(a, mult(a, c)), c) = mult(a, mult(mult(a, c), c)))) | (~(mult(mult(a, c), mult(a, c)) = mult(a, mult(c, mult(a, c))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(a, mult(mult(a, c), c)) = mult(a, mult(c, mult(a, c))))) | (~(mult(mult(a, mult(a, c)), c) = mult(mult(a, c), mult(a, c)))))) | (~((~(mult(mult(a, mult(a, c)), c) = mult(a, mult(mult(a, c), c)))) | (~(mult(mult(a, c), mult(a, c)) = mult(a, mult(c, mult(a, c)))))))))),
% 22.47/22.64 inference(monotonicity,[status(thm)],[4738])).
% 22.47/22.64 tff(4740,plain,
% 22.47/22.64 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, mult(a, c)), c) = mult(mult(a, c), mult(a, c)))) | (~(mult(a, mult(mult(a, c), c)) = mult(a, mult(c, mult(a, c))))))) | (~((~(mult(mult(a, mult(a, c)), c) = mult(a, mult(mult(a, c), c)))) | (~(mult(mult(a, c), mult(a, c)) = mult(a, mult(c, mult(a, c))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(a, mult(mult(a, c), c)) = mult(a, mult(c, mult(a, c))))) | (~(mult(mult(a, mult(a, c)), c) = mult(mult(a, c), mult(a, c)))))) | (~((~(mult(mult(a, mult(a, c)), c) = mult(a, mult(mult(a, c), c)))) | (~(mult(mult(a, c), mult(a, c)) = mult(a, mult(c, mult(a, c))))))))),
% 22.47/22.64 inference(transitivity,[status(thm)],[4739, 4737])).
% 22.47/22.64 tff(4741,plain,
% 22.47/22.64 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, mult(a, c)), c) = mult(mult(a, c), mult(a, c)))) | (~(mult(a, mult(mult(a, c), c)) = mult(a, mult(c, mult(a, c))))))) | (~((~(mult(mult(a, mult(a, c)), c) = mult(a, mult(mult(a, c), c)))) | (~(mult(mult(a, c), mult(a, c)) = mult(a, mult(c, mult(a, c))))))))),
% 22.47/22.64 inference(quant_inst,[status(thm)],[])).
% 22.47/22.64 tff(4742,plain,
% 22.47/22.64 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(a, mult(mult(a, c), c)) = mult(a, mult(c, mult(a, c))))) | (~(mult(mult(a, mult(a, c)), c) = mult(mult(a, c), mult(a, c)))))) | (~((~(mult(mult(a, mult(a, c)), c) = mult(a, mult(mult(a, c), c)))) | (~(mult(mult(a, c), mult(a, c)) = mult(a, mult(c, mult(a, c)))))))),
% 22.47/22.64 inference(modus_ponens,[status(thm)],[4741, 4740])).
% 22.47/22.64 tff(4743,plain,
% 22.47/22.64 ((~((~(mult(a, mult(mult(a, c), c)) = mult(a, mult(c, mult(a, c))))) | (~(mult(mult(a, mult(a, c)), c) = mult(mult(a, c), mult(a, c)))))) | (~((~(mult(mult(a, mult(a, c)), c) = mult(a, mult(mult(a, c), c)))) | (~(mult(mult(a, c), mult(a, c)) = mult(a, mult(c, mult(a, c)))))))),
% 22.47/22.64 inference(unit_resolution,[status(thm)],[4742, 27])).
% 22.47/22.64 tff(4744,plain,
% 22.47/22.64 (~((~(mult(a, mult(mult(a, c), c)) = mult(a, mult(c, mult(a, c))))) | (~(mult(mult(a, mult(a, c)), c) = mult(mult(a, c), mult(a, c)))))),
% 22.47/22.64 inference(unit_resolution,[status(thm)],[4743, 4736])).
% 22.47/22.64 tff(4745,plain,
% 22.47/22.64 (((~(mult(a, mult(mult(a, c), c)) = mult(a, mult(c, mult(a, c))))) | (~(mult(mult(a, mult(a, c)), c) = mult(mult(a, c), mult(a, c))))) | (mult(mult(a, mult(a, c)), c) = mult(mult(a, c), mult(a, c)))),
% 22.47/22.64 inference(tautology,[status(thm)],[])).
% 22.47/22.64 tff(4746,plain,
% 22.47/22.64 (mult(mult(a, mult(a, c)), c) = mult(mult(a, c), mult(a, c))),
% 22.47/22.64 inference(unit_resolution,[status(thm)],[4745, 4744])).
% 22.47/22.64 tff(4747,plain,
% 22.47/22.64 (mult(mult(a, c), mult(a, c)) = mult(mult(a, mult(a, c)), c)),
% 22.47/22.64 inference(symmetry,[status(thm)],[4746])).
% 22.47/22.64 tff(4748,plain,
% 22.47/22.64 (mult(mult(a, c), mult(a, c)) = mult(a, mult(c, mult(a, c)))),
% 22.47/22.64 inference(transitivity,[status(thm)],[4747, 4733, 4717, 4731, 4729])).
% 22.47/22.64 tff(4749,plain,
% 22.47/22.64 ($false),
% 22.47/22.64 inference(unit_resolution,[status(thm)],[4734, 4748])).
% 22.47/22.64 tff(4750,plain,((mult(mult(a, c), mult(a, c)) = mult(a, mult(c, mult(a, c)))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit))))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c))))), inference(lemma,lemma(discharge,[]))).
% 22.47/22.64 tff(4751,plain,
% 22.47/22.64 (mult(mult(a, c), mult(a, c)) = mult(a, mult(c, mult(a, c)))),
% 22.47/22.64 inference(unit_resolution,[status(thm)],[4750, 4517, 3865, 4003])).
% 22.47/22.64 tff(4752,plain,
% 22.47/22.64 (mult(mult(a, mult(a, c)), c) = mult(mult(a, c), mult(a, c))),
% 22.47/22.64 inference(modus_ponens,[status(thm)],[4751, 4727])).
% 22.47/22.64 tff(4753,plain,
% 22.47/22.64 (mult(mult(a, c), mult(a, c)) = mult(mult(a, mult(a, c)), c)),
% 22.47/22.64 inference(symmetry,[status(thm)],[4752])).
% 22.47/22.64 tff(4754,plain,
% 22.47/22.64 (mult(mult(a, c), mult(c, a)) = mult(mult(a, c), mult(a, c))),
% 22.47/22.64 inference(monotonicity,[status(thm)],[3885])).
% 22.47/22.64 tff(4755,plain,
% 22.47/22.64 (mult(mult(a, c), mult(c, a)) = mult(a, mult(mult(c, c), a))),
% 22.47/22.64 inference(transitivity,[status(thm)],[4754, 4753, 4722, 4717, 4715, 4713, 4710])).
% 22.47/22.64 tff(4756,plain,
% 22.47/22.64 ((mult(mult(mult(a, c), c), a) = mult(mult(a, c), mult(c, a))) <=> (mult(mult(a, mult(c, c)), a) = mult(a, mult(mult(c, c), a)))),
% 22.47/22.64 inference(monotonicity,[status(thm)],[4663, 4755])).
% 22.47/22.64 tff(4757,plain,
% 22.47/22.64 ((mult(mult(a, mult(c, c)), a) = mult(a, mult(mult(c, c), a))) <=> (mult(mult(mult(a, c), c), a) = mult(mult(a, c), mult(c, a)))),
% 22.47/22.64 inference(symmetry,[status(thm)],[4756])).
% 22.47/22.64 tff(4758,plain,
% 22.47/22.64 (mult(a, mult(mult(c, c), a)) = mult(mult(mult(a, c), a), c)),
% 22.47/22.64 inference(transitivity,[status(thm)],[4709, 4712, 4714, 4724])).
% 22.47/22.64 tff(4759,plain,
% 22.47/22.64 ((mult(mult(a, mult(c, c)), a) = mult(a, mult(mult(c, c), a))) <=> (mult(mult(mult(a, c), c), a) = mult(mult(mult(a, c), a), c))),
% 22.47/22.64 inference(monotonicity,[status(thm)],[4662, 4758])).
% 22.47/22.64 tff(4760,plain,
% 22.47/22.64 ((mult(mult(mult(a, c), c), a) = mult(mult(mult(a, c), a), c)) <=> (mult(mult(a, mult(c, c)), a) = mult(a, mult(mult(c, c), a)))),
% 22.47/22.64 inference(symmetry,[status(thm)],[4759])).
% 22.47/22.64 tff(4761,plain,
% 22.47/22.64 ((mult(mult(mult(a, c), c), a) = mult(mult(mult(a, c), a), c)) <=> (mult(mult(mult(a, c), c), a) = mult(mult(a, c), mult(c, a)))),
% 22.47/22.64 inference(transitivity,[status(thm)],[4760, 4757])).
% 22.47/22.64 tff(4762,assumption,(~(mult(mult(mult(a, c), c), a) = mult(mult(a, c), mult(c, a)))), introduced(assumption)).
% 22.47/22.64 tff(4763,plain,
% 22.47/22.64 (((~(mult(mult(mult(a, c), c), a) = mult(mult(a, c), mult(c, a)))) | (~(mult(mult(mult(a, c), a), c) = mult(mult(a, c), mult(a, c))))) | (mult(mult(mult(a, c), c), a) = mult(mult(a, c), mult(c, a)))),
% 22.47/22.64 inference(tautology,[status(thm)],[])).
% 22.47/22.64 tff(4764,plain,
% 22.47/22.64 ((~(mult(mult(mult(a, c), c), a) = mult(mult(a, c), mult(c, a)))) | (~(mult(mult(mult(a, c), a), c) = mult(mult(a, c), mult(a, c))))),
% 22.47/22.64 inference(unit_resolution,[status(thm)],[4763, 4762])).
% 22.47/22.64 tff(4765,plain,
% 22.47/22.64 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, c), c), a) = mult(mult(a, c), mult(c, a)))) | (~(mult(mult(mult(a, c), a), c) = mult(mult(a, c), mult(a, c)))))) | (~((~(mult(mult(mult(a, c), c), a) = mult(mult(mult(a, c), a), c))) | (~(mult(mult(a, c), mult(c, a)) = mult(mult(a, c), mult(a, c)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(a, c), c), a) = mult(mult(a, c), mult(c, a)))) | (~(mult(mult(mult(a, c), a), c) = mult(mult(a, c), mult(a, c)))))) | (~((~(mult(mult(mult(a, c), c), a) = mult(mult(mult(a, c), a), c))) | (~(mult(mult(a, c), mult(c, a)) = mult(mult(a, c), mult(a, c)))))))),
% 22.47/22.64 inference(rewrite,[status(thm)],[])).
% 22.47/22.64 tff(4766,plain,
% 22.47/22.64 (((~((~(mult(mult(mult(a, c), c), a) = mult(mult(mult(a, c), a), c))) | (~(mult(mult(a, c), mult(c, a)) = mult(mult(a, c), mult(a, c)))))) | (~((~(mult(mult(mult(a, c), c), a) = mult(mult(a, c), mult(c, a)))) | (~(mult(mult(mult(a, c), a), c) = mult(mult(a, c), mult(a, c))))))) <=> ((~((~(mult(mult(mult(a, c), c), a) = mult(mult(a, c), mult(c, a)))) | (~(mult(mult(mult(a, c), a), c) = mult(mult(a, c), mult(a, c)))))) | (~((~(mult(mult(mult(a, c), c), a) = mult(mult(mult(a, c), a), c))) | (~(mult(mult(a, c), mult(c, a)) = mult(mult(a, c), mult(a, c)))))))),
% 22.47/22.64 inference(rewrite,[status(thm)],[])).
% 22.47/22.64 tff(4767,plain,
% 22.47/22.64 ((~((~(mult(mult(mult(a, c), c), a) = mult(mult(a, c), mult(c, a)))) | (~(mult(mult(mult(a, c), a), c) = mult(mult(a, c), mult(a, c)))))) <=> (~((~(mult(mult(mult(a, c), c), a) = mult(mult(a, c), mult(c, a)))) | (~(mult(mult(mult(a, c), a), c) = mult(mult(a, c), mult(a, c))))))),
% 22.47/22.64 inference(rewrite,[status(thm)],[])).
% 22.47/22.64 tff(4768,plain,
% 22.47/22.64 ((~((~(mult(mult(mult(a, c), c), a) = mult(mult(mult(a, c), a), c))) | (~(mult(mult(a, c), mult(c, a)) = mult(mult(a, c), mult(a, c)))))) <=> (~((~(mult(mult(mult(a, c), c), a) = mult(mult(mult(a, c), a), c))) | (~(mult(mult(a, c), mult(c, a)) = mult(mult(a, c), mult(a, c))))))),
% 22.47/22.64 inference(rewrite,[status(thm)],[])).
% 22.47/22.64 tff(4769,plain,
% 22.47/22.64 (((~((~(mult(mult(mult(a, c), c), a) = mult(mult(mult(a, c), a), c))) | (~(mult(mult(a, c), mult(c, a)) = mult(mult(a, c), mult(a, c)))))) | (~((~(mult(mult(mult(a, c), c), a) = mult(mult(a, c), mult(c, a)))) | (~(mult(mult(mult(a, c), a), c) = mult(mult(a, c), mult(a, c))))))) <=> ((~((~(mult(mult(mult(a, c), c), a) = mult(mult(mult(a, c), a), c))) | (~(mult(mult(a, c), mult(c, a)) = mult(mult(a, c), mult(a, c)))))) | (~((~(mult(mult(mult(a, c), c), a) = mult(mult(a, c), mult(c, a)))) | (~(mult(mult(mult(a, c), a), c) = mult(mult(a, c), mult(a, c)))))))),
% 22.47/22.64 inference(monotonicity,[status(thm)],[4768, 4767])).
% 22.47/22.64 tff(4770,plain,
% 22.47/22.64 (((~((~(mult(mult(mult(a, c), c), a) = mult(mult(mult(a, c), a), c))) | (~(mult(mult(a, c), mult(c, a)) = mult(mult(a, c), mult(a, c)))))) | (~((~(mult(mult(mult(a, c), c), a) = mult(mult(a, c), mult(c, a)))) | (~(mult(mult(mult(a, c), a), c) = mult(mult(a, c), mult(a, c))))))) <=> ((~((~(mult(mult(mult(a, c), c), a) = mult(mult(a, c), mult(c, a)))) | (~(mult(mult(mult(a, c), a), c) = mult(mult(a, c), mult(a, c)))))) | (~((~(mult(mult(mult(a, c), c), a) = mult(mult(mult(a, c), a), c))) | (~(mult(mult(a, c), mult(c, a)) = mult(mult(a, c), mult(a, c)))))))),
% 22.47/22.65 inference(transitivity,[status(thm)],[4769, 4766])).
% 22.47/22.65 tff(4771,plain,
% 22.47/22.65 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, c), c), a) = mult(mult(mult(a, c), a), c))) | (~(mult(mult(a, c), mult(c, a)) = mult(mult(a, c), mult(a, c)))))) | (~((~(mult(mult(mult(a, c), c), a) = mult(mult(a, c), mult(c, a)))) | (~(mult(mult(mult(a, c), a), c) = mult(mult(a, c), mult(a, c)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, c), c), a) = mult(mult(a, c), mult(c, a)))) | (~(mult(mult(mult(a, c), a), c) = mult(mult(a, c), mult(a, c)))))) | (~((~(mult(mult(mult(a, c), c), a) = mult(mult(mult(a, c), a), c))) | (~(mult(mult(a, c), mult(c, a)) = mult(mult(a, c), mult(a, c))))))))),
% 22.47/22.65 inference(monotonicity,[status(thm)],[4770])).
% 22.47/22.65 tff(4772,plain,
% 22.47/22.65 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, c), c), a) = mult(mult(mult(a, c), a), c))) | (~(mult(mult(a, c), mult(c, a)) = mult(mult(a, c), mult(a, c)))))) | (~((~(mult(mult(mult(a, c), c), a) = mult(mult(a, c), mult(c, a)))) | (~(mult(mult(mult(a, c), a), c) = mult(mult(a, c), mult(a, c)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(a, c), c), a) = mult(mult(a, c), mult(c, a)))) | (~(mult(mult(mult(a, c), a), c) = mult(mult(a, c), mult(a, c)))))) | (~((~(mult(mult(mult(a, c), c), a) = mult(mult(mult(a, c), a), c))) | (~(mult(mult(a, c), mult(c, a)) = mult(mult(a, c), mult(a, c)))))))),
% 22.47/22.65 inference(transitivity,[status(thm)],[4771, 4765])).
% 22.47/22.65 tff(4773,plain,
% 22.47/22.65 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, c), c), a) = mult(mult(mult(a, c), a), c))) | (~(mult(mult(a, c), mult(c, a)) = mult(mult(a, c), mult(a, c)))))) | (~((~(mult(mult(mult(a, c), c), a) = mult(mult(a, c), mult(c, a)))) | (~(mult(mult(mult(a, c), a), c) = mult(mult(a, c), mult(a, c)))))))),
% 22.47/22.65 inference(quant_inst,[status(thm)],[])).
% 22.47/22.65 tff(4774,plain,
% 22.47/22.65 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(a, c), c), a) = mult(mult(a, c), mult(c, a)))) | (~(mult(mult(mult(a, c), a), c) = mult(mult(a, c), mult(a, c)))))) | (~((~(mult(mult(mult(a, c), c), a) = mult(mult(mult(a, c), a), c))) | (~(mult(mult(a, c), mult(c, a)) = mult(mult(a, c), mult(a, c))))))),
% 22.47/22.65 inference(modus_ponens,[status(thm)],[4773, 4772])).
% 22.47/22.65 tff(4775,plain,
% 22.47/22.65 ((~((~(mult(mult(mult(a, c), c), a) = mult(mult(a, c), mult(c, a)))) | (~(mult(mult(mult(a, c), a), c) = mult(mult(a, c), mult(a, c)))))) | (~((~(mult(mult(mult(a, c), c), a) = mult(mult(mult(a, c), a), c))) | (~(mult(mult(a, c), mult(c, a)) = mult(mult(a, c), mult(a, c))))))),
% 22.47/22.65 inference(unit_resolution,[status(thm)],[4774, 27])).
% 22.47/22.65 tff(4776,plain,
% 22.47/22.65 (~((~(mult(mult(mult(a, c), c), a) = mult(mult(mult(a, c), a), c))) | (~(mult(mult(a, c), mult(c, a)) = mult(mult(a, c), mult(a, c)))))),
% 22.47/22.65 inference(unit_resolution,[status(thm)],[4775, 4764])).
% 22.47/22.65 tff(4777,plain,
% 22.47/22.65 (((~(mult(mult(mult(a, c), c), a) = mult(mult(mult(a, c), a), c))) | (~(mult(mult(a, c), mult(c, a)) = mult(mult(a, c), mult(a, c))))) | (mult(mult(mult(a, c), c), a) = mult(mult(mult(a, c), a), c))),
% 22.47/22.65 inference(tautology,[status(thm)],[])).
% 22.47/22.65 tff(4778,plain,
% 22.47/22.65 (mult(mult(mult(a, c), c), a) = mult(mult(mult(a, c), a), c)),
% 22.47/22.65 inference(unit_resolution,[status(thm)],[4777, 4776])).
% 22.47/22.65 tff(4779,plain,
% 22.47/22.65 (mult(mult(mult(a, c), c), a) = mult(mult(a, c), mult(c, a))),
% 22.47/22.65 inference(modus_ponens,[status(thm)],[4778, 4761])).
% 22.47/22.65 tff(4780,plain,
% 22.47/22.65 ($false),
% 22.47/22.65 inference(unit_resolution,[status(thm)],[4762, 4779])).
% 22.47/22.65 tff(4781,plain,((mult(mult(mult(a, c), c), a) = mult(mult(a, c), mult(c, a))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit))))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))), inference(lemma,lemma(discharge,[]))).
% 22.47/22.65 tff(4782,plain,
% 22.47/22.65 (mult(mult(mult(a, c), c), a) = mult(mult(a, c), mult(c, a))),
% 22.47/22.65 inference(unit_resolution,[status(thm)],[4781, 4517, 3865])).
% 22.47/22.65 tff(4783,plain,
% 22.47/22.65 ((mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a)) <=> (mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 22.47/22.65 inference(commutativity,[status(thm)],[])).
% 22.47/22.65 tff(4784,plain,
% 22.47/22.65 (mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 22.47/22.65 inference(symmetry,[status(thm)],[4701])).
% 22.47/22.65 tff(4785,plain,
% 22.47/22.65 (mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a)),
% 22.47/22.65 inference(monotonicity,[status(thm)],[4784])).
% 22.47/22.65 tff(4786,plain,
% 22.47/22.65 (mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a)),
% 22.47/22.65 inference(symmetry,[status(thm)],[4785])).
% 22.47/22.65 tff(4787,plain,
% 22.47/22.65 (mult(mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))), a) = mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a)),
% 22.47/22.65 inference(transitivity,[status(thm)],[4703, 4786])).
% 22.47/22.65 tff(4788,plain,
% 22.47/22.65 (mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 22.47/22.65 inference(symmetry,[status(thm)],[4670])).
% 22.47/22.65 tff(4789,assumption,(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c))))), introduced(assumption)).
% 22.47/22.65 tff(4790,assumption,(mult(mult(mult(a, c), c), a) = mult(mult(a, c), mult(c, a))), introduced(assumption)).
% 22.47/22.65 tff(4791,plain,
% 22.47/22.65 (mult(mult(mult(a, c), c), a) = mult(mult(a, c), mult(a, c))),
% 22.47/22.65 inference(transitivity,[status(thm)],[4790, 4754])).
% 22.47/22.65 tff(4792,plain,
% 22.47/22.65 (mult(mult(mult(mult(a, c), c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 22.47/22.65 inference(monotonicity,[status(thm)],[4791])).
% 22.47/22.65 tff(4793,plain,
% 22.47/22.65 (mult(mult(mult(mult(a, c), c), a), rd(mult(b, c), mult(a, c))) = mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 22.47/22.65 inference(transitivity,[status(thm)],[4792, 4789, 4788])).
% 22.47/22.65 tff(4794,plain,
% 22.47/22.65 ((mult(mult(mult(mult(a, c), c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))), a)) <=> (mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a))),
% 22.47/22.65 inference(monotonicity,[status(thm)],[4793, 4787])).
% 22.47/22.65 tff(4795,plain,
% 22.47/22.65 ((mult(mult(mult(mult(a, c), c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))), a)) <=> (mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 22.47/22.65 inference(transitivity,[status(thm)],[4794, 4783])).
% 22.47/22.65 tff(4796,plain,
% 22.47/22.65 ((mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c))))) <=> (mult(mult(mult(mult(a, c), c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))), a))),
% 22.47/22.65 inference(symmetry,[status(thm)],[4795])).
% 22.47/22.65 tff(4797,assumption,(mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c))))), introduced(assumption)).
% 22.47/22.65 tff(4798,plain,
% 22.47/22.65 (mult(mult(mult(mult(a, c), c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))), a)),
% 22.47/22.65 inference(modus_ponens,[status(thm)],[4797, 4796])).
% 22.47/22.65 tff(4799,assumption,(~(mult(mult(mult(mult(a, c), c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))), a))), introduced(assumption)).
% 22.47/22.65 tff(4800,plain,
% 22.47/22.65 ($false),
% 22.47/22.65 inference(unit_resolution,[status(thm)],[4799, 4798])).
% 22.47/22.65 tff(4801,plain,((~(mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (mult(mult(mult(mult(a, c), c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))), a)) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit))))) | (~(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), c), a) = mult(mult(a, c), mult(c, a))))), inference(lemma,lemma(discharge,[]))).
% 22.47/22.65 tff(4802,plain,
% 22.47/22.65 (mult(mult(mult(mult(a, c), c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))), a)),
% 22.47/22.65 inference(unit_resolution,[status(thm)],[4801, 4700, 3865, 4782, 4701, 4603])).
% 22.47/22.65 tff(4803,plain,
% 22.47/22.65 (mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a)),
% 22.47/22.65 inference(modus_ponens,[status(thm)],[4802, 4708])).
% 22.47/22.65 tff(4804,plain,
% 22.47/22.65 (mult(mult(mult(mult(a, c), c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 22.47/22.65 inference(transitivity,[status(thm)],[4705, 4803, 4702, 4700, 4670, 4604])).
% 22.47/22.65 tff(4805,plain,
% 22.47/22.65 (rd(mult(mult(mult(mult(a, c), c), a), rd(mult(b, c), mult(a, c))), rd(mult(b, c), mult(a, c))) = rd(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))), rd(mult(b, c), mult(a, c)))),
% 22.47/22.65 inference(monotonicity,[status(thm)],[4804])).
% 22.47/22.65 tff(4806,plain,
% 22.47/22.65 (rd(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))), rd(mult(b, c), mult(a, c))) = rd(mult(mult(mult(mult(a, c), c), a), rd(mult(b, c), mult(a, c))), rd(mult(b, c), mult(a, c)))),
% 22.47/22.65 inference(symmetry,[status(thm)],[4805])).
% 22.47/22.65 tff(4807,plain,
% 22.47/22.65 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(a, c)))),
% 22.47/22.65 inference(quant_inst,[status(thm)],[])).
% 22.47/22.65 tff(4808,plain,
% 22.47/22.65 (rd(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(a, c))),
% 22.47/22.65 inference(unit_resolution,[status(thm)],[4807, 168])).
% 22.47/22.65 tff(4809,plain,
% 22.47/22.65 (mult(mult(a, c), mult(a, c)) = rd(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))), rd(mult(b, c), mult(a, c)))),
% 22.47/22.65 inference(symmetry,[status(thm)],[4808])).
% 22.47/22.65 tff(4810,plain,
% 22.47/22.65 (mult(mult(mult(a, c), unit), mult(a, c)) = mult(mult(c, mult(a, c)), a)),
% 22.47/22.65 inference(transitivity,[status(thm)],[2503, 4809, 4806, 4669, 4667])).
% 22.47/22.65 tff(4811,plain,
% 22.47/22.65 (mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), unit), mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(c, mult(a, c)), a))),
% 22.47/22.65 inference(monotonicity,[status(thm)],[4810])).
% 22.47/22.65 tff(4812,plain,
% 22.47/22.65 (mult(mult(b, c), unit) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), unit)),
% 22.47/22.65 inference(symmetry,[status(thm)],[2497])).
% 22.47/22.65 tff(4813,plain,
% 22.47/22.65 (mult(mult(mult(c, unit), b), unit) = mult(mult(b, c), unit)),
% 22.47/22.65 inference(symmetry,[status(thm)],[845])).
% 22.47/22.65 tff(4814,plain,
% 22.47/22.65 (mult(b, c) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), unit)),
% 22.47/22.65 inference(transitivity,[status(thm)],[843, 842, 239, 841, 840, 4813, 4812])).
% 22.47/22.65 tff(4815,plain,
% 22.47/22.65 (mult(mult(b, c), mult(a, c)) = mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), unit), mult(a, c))),
% 22.47/22.65 inference(monotonicity,[status(thm)],[4814])).
% 22.47/22.65 tff(4816,plain,
% 22.47/22.65 (mult(mult(b, mult(a, c)), c) = mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), c)),
% 22.47/22.65 inference(transitivity,[status(thm)],[4399, 4815, 2501, 4811, 4666, 4661, 4658, 4600, 4528, 4527])).
% 22.47/22.65 tff(4817,plain,
% 22.47/22.65 (rd(mult(mult(b, mult(a, c)), c), c) = rd(mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), c), c)),
% 22.47/22.65 inference(monotonicity,[status(thm)],[4816])).
% 22.47/22.65 tff(4818,plain,
% 22.47/22.65 (mult(b, mult(a, c)) = mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))),
% 22.47/22.65 inference(transitivity,[status(thm)],[2681, 4817, 4525])).
% 22.47/22.65 tff(4819,plain,
% 22.47/22.65 (mult(c, mult(b, mult(a, c))) = mult(c, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))))),
% 22.47/22.65 inference(monotonicity,[status(thm)],[4818])).
% 22.47/22.65 tff(4820,plain,
% 22.47/22.65 (mult(c, mult(b, mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))),
% 22.47/22.65 inference(transitivity,[status(thm)],[4819, 4675, 2698, 4673, 4672, 4611, 4607, 4549])).
% 22.47/22.65 tff(4821,plain,
% 22.47/22.65 (mult(mult(c, b), mult(a, c)) = mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 22.47/22.65 inference(transitivity,[status(thm)],[2429, 4815, 2501, 4811, 4666, 4661, 4658, 4702, 4700, 4670, 4604])).
% 22.47/22.65 tff(4822,plain,
% 22.47/22.65 ((mult(mult(c, b), mult(a, c)) = mult(c, mult(b, mult(a, c)))) <=> (mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 22.47/22.65 inference(monotonicity,[status(thm)],[4821, 4820])).
% 22.47/22.65 tff(4823,plain,
% 22.47/22.65 ((mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))) <=> (mult(mult(c, b), mult(a, c)) = mult(c, mult(b, mult(a, c))))),
% 22.47/22.65 inference(symmetry,[status(thm)],[4822])).
% 22.47/22.65 tff(4824,plain,
% 22.47/22.65 ((~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))) <=> (~(mult(mult(c, b), mult(a, c)) = mult(c, mult(b, mult(a, c)))))),
% 22.47/22.65 inference(monotonicity,[status(thm)],[4823])).
% 22.47/22.65 tff(4825,plain,
% 22.47/22.65 (~(mult(mult(c, b), mult(a, c)) = mult(c, mult(b, mult(a, c))))),
% 22.47/22.65 inference(modus_ponens,[status(thm)],[4620, 4824])).
% 22.47/22.65 tff(4826,plain,
% 22.47/22.65 ((~(mult(mult(c, mult(a, c)), b) = mult(c, mult(mult(a, c), b)))) | (~(mult(mult(c, b), mult(a, c)) = mult(c, mult(b, mult(a, c)))))),
% 22.47/22.65 inference(unit_resolution,[status(thm)],[2431, 4825])).
% 22.47/22.65 tff(4827,plain,
% 22.47/22.65 (~((~(mult(mult(c, mult(a, c)), b) = mult(mult(c, b), mult(a, c)))) | (~(mult(c, mult(mult(a, c), b)) = mult(c, mult(b, mult(a, c))))))),
% 22.47/22.65 inference(unit_resolution,[status(thm)],[2436, 4826])).
% 22.47/22.65 tff(4828,plain,
% 22.47/22.65 (mult(c, mult(mult(a, c), b)) = mult(c, mult(b, mult(a, c)))),
% 22.47/22.65 inference(unit_resolution,[status(thm)],[2710, 4827])).
% 22.47/22.65 tff(4829,plain,
% 22.47/22.65 (mult(c, mult(mult(a, b), c)) = mult(c, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))))),
% 22.47/22.65 inference(transitivity,[status(thm)],[4024, 4828, 4819])).
% 22.47/22.65 tff(4830,plain,
% 22.47/22.65 (ld(c, mult(c, mult(mult(a, b), c))) = ld(c, mult(c, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))))),
% 22.47/22.65 inference(monotonicity,[status(thm)],[4829])).
% 22.47/22.65 tff(4831,plain,
% 22.47/22.65 (mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 22.47/22.65 inference(transitivity,[status(thm)],[214, 4032, 4830, 4523, 4521])).
% 22.47/22.65 tff(4832,plain,
% 22.47/22.65 (mult(mult(mult(c, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(mult(b, c), a), c)),
% 22.47/22.65 inference(transitivity,[status(thm)],[3187, 4127, 4828, 4819, 4675, 2698, 4673, 4672, 4611, 4607, 4549, 4548, 138, 266, 4544])).
% 22.47/22.66 tff(4833,plain,
% 22.47/22.66 (rd(mult(mult(mult(c, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c), c) = rd(mult(mult(mult(b, c), a), c), c)),
% 22.47/22.66 inference(monotonicity,[status(thm)],[4832])).
% 22.47/22.66 tff(4834,plain,
% 22.47/22.66 (mult(mult(c, c), mult(mult(unit, ld(c, mult(a, b))), unit)) = rd(mult(mult(mult(c, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c), c)),
% 22.47/22.66 inference(symmetry,[status(thm)],[4121])).
% 22.47/22.66 tff(4835,plain,
% 22.47/22.66 (mult(mult(c, c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))),
% 22.47/22.66 inference(transitivity,[status(thm)],[4834, 4833, 2676, 4397, 4502, 4414])).
% 22.47/22.66 tff(4836,plain,
% 22.47/22.66 ((mult(mult(c, c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), c)) <=> (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))))),
% 22.47/22.66 inference(monotonicity,[status(thm)],[4835, 4831])).
% 22.47/22.66 tff(4837,plain,
% 22.47/22.66 ((mult(mult(c, c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), c)) <=> (mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 22.47/22.66 inference(transitivity,[status(thm)],[4836, 4516])).
% 22.47/22.66 tff(4838,plain,
% 22.47/22.66 ((mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))) <=> (mult(mult(c, c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), c))),
% 22.47/22.66 inference(symmetry,[status(thm)],[4837])).
% 22.47/22.66 tff(4839,plain,
% 22.47/22.66 ((mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))) <=> (mult(mult(c, mult(mult(unit, c), unit)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(c, mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit))))),
% 22.47/22.66 inference(transitivity,[status(thm)],[4838, 4515, 4223])).
% 22.47/22.66 tff(4840,plain,
% 22.47/22.66 ((~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))) <=> (~(mult(mult(c, mult(mult(unit, c), unit)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(c, mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit)))))),
% 22.47/22.66 inference(monotonicity,[status(thm)],[4839])).
% 22.47/22.66 tff(4841,plain,
% 22.47/22.66 (~(mult(mult(c, mult(mult(unit, c), unit)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(c, mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit))))),
% 22.47/22.66 inference(modus_ponens,[status(thm)],[301, 4840])).
% 22.47/22.66 tff(4842,plain,
% 22.47/22.66 (mult(mult(c, mult(mult(unit, c), unit)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(c, mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit)))),
% 22.47/22.66 inference(unit_resolution,[status(thm)],[4237, 4511, 3865])).
% 22.47/22.66 tff(4843,plain,
% 22.47/22.66 ($false),
% 22.47/22.66 inference(unit_resolution,[status(thm)],[4842, 4841])).
% 22.47/22.66 tff(4844,plain,((~(mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))) | (~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit))))) | (~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)))) | (~(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a))) | (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))), inference(lemma,lemma(discharge,[]))).
% 22.47/22.66 tff(4845,plain,
% 22.47/22.66 (~(mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))),
% 22.47/22.66 inference(unit_resolution,[status(thm)],[4844, 4487, 285, 3865, 3842, 4360, 4495, 4448, 4432, 4400, 279, 4499, 4390, 281])).
% 22.47/22.66 tff(4846,plain,
% 22.47/22.66 ((~(mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c))))),
% 22.47/22.66 inference(unit_resolution,[status(thm)],[2215, 4845])).
% 22.47/22.66 tff(4847,plain,
% 22.47/22.66 (~((~(mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))))),
% 22.47/22.66 inference(unit_resolution,[status(thm)],[2213, 4846])).
% 22.47/22.66 tff(4848,plain,
% 22.47/22.66 (mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))),
% 22.47/22.66 inference(unit_resolution,[status(thm)],[2201, 4847])).
% 22.47/22.66 tff(4849,plain,
% 22.47/22.66 (mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c)),
% 22.47/22.66 inference(symmetry,[status(thm)],[4848])).
% 22.47/22.66 tff(4850,plain,
% 22.47/22.66 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), unit) = mult(mult(mult(mult(a, c), unit), rd(mult(b, c), mult(a, c))), unit)),
% 22.47/22.66 inference(symmetry,[status(thm)],[2178])).
% 22.47/22.66 tff(4851,plain,
% 22.47/22.66 (mult(mult(mult(a, c), unit), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), unit)),
% 22.47/22.66 inference(symmetry,[status(thm)],[2177])).
% 22.47/22.66 tff(4852,plain,
% 22.47/22.66 (mult(mult(a, c), rd(mult(b, c), mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), c), a)),
% 22.47/22.66 inference(transitivity,[status(thm)],[2167, 4851, 4850, 2171, 4849, 4493, 4492, 4490, 4489, 4488])).
% 22.47/22.66 tff(4853,plain,
% 22.47/22.66 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c)),
% 22.47/22.66 inference(monotonicity,[status(thm)],[4852])).
% 22.47/22.66 tff(4854,plain,
% 22.47/22.66 (mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)),
% 22.47/22.66 inference(symmetry,[status(thm)],[4853])).
% 22.47/22.66 tff(4855,plain,
% 22.47/22.66 (mult(rd(mult(b, c), mult(a, c)), mult(mult(c, a), c)) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c)),
% 22.47/22.66 inference(symmetry,[status(thm)],[2627])).
% 22.47/22.66 tff(4856,plain,
% 22.47/22.66 (rd(mult(b, c), mult(a, c)) = mult(unit, rd(mult(b, c), mult(a, c)))),
% 22.47/22.66 inference(symmetry,[status(thm)],[1893])).
% 22.47/22.66 tff(4857,plain,
% 22.47/22.66 (mult(rd(mult(b, c), mult(a, c)), mult(mult(c, a), c)) = mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(mult(c, a), c))),
% 22.47/22.66 inference(monotonicity,[status(thm)],[4856])).
% 22.47/22.66 tff(4858,plain,
% 22.47/22.66 (mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(mult(c, a), c)) = mult(rd(mult(b, c), mult(a, c)), mult(mult(c, a), c))),
% 22.47/22.66 inference(symmetry,[status(thm)],[4857])).
% 22.47/22.66 tff(4859,plain,
% 22.47/22.66 (mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(mult(c, a), c)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))),
% 22.47/22.66 inference(monotonicity,[status(thm)],[1893, 2690])).
% 22.47/22.66 tff(4860,plain,
% 22.47/22.66 (mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))) = mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(mult(c, a), c))),
% 22.47/22.66 inference(symmetry,[status(thm)],[4859])).
% 22.47/22.66 tff(4861,plain,
% 22.47/22.66 (mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)),
% 22.47/22.66 inference(transitivity,[status(thm)],[4860, 4858, 4855, 4854])).
% 22.47/22.66 tff(4862,plain,
% 22.47/22.66 (mult(mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))), a) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a)),
% 22.47/22.66 inference(monotonicity,[status(thm)],[4861])).
% 22.47/22.66 tff(4863,plain,
% 22.47/22.66 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), unit) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))),
% 22.47/22.66 inference(transitivity,[status(thm)],[1875, 1871, 4340, 4491, 2189, 4848, 2172, 2178, 2177, 2162])).
% 22.47/22.66 tff(4864,plain,
% 22.47/22.66 (mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), unit), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)),
% 22.47/22.66 inference(monotonicity,[status(thm)],[4863])).
% 22.47/22.66 tff(4865,plain,
% 22.47/22.66 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))),
% 22.47/22.66 inference(transitivity,[status(thm)],[4656, 4655, 4864, 4853, 2627, 4857, 4859])).
% 22.47/22.66 tff(4866,plain,
% 22.47/22.66 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)), a) = mult(mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))), a)),
% 22.47/22.66 inference(monotonicity,[status(thm)],[4865])).
% 22.47/22.66 tff(4867,plain,
% 22.47/22.66 (mult(mult(mult(a, c), c), a) = mult(mult(c, mult(a, c)), a)),
% 22.47/22.66 inference(monotonicity,[status(thm)],[4529])).
% 22.47/22.66 tff(4868,plain,
% 22.47/22.66 (mult(mult(c, mult(a, c)), a) = mult(mult(mult(a, c), c), a)),
% 22.47/22.66 inference(symmetry,[status(thm)],[4867])).
% 22.47/22.66 tff(4869,plain,
% 22.47/22.66 (mult(mult(c, mult(a, c)), a) = mult(mult(a, mult(c, c)), a)),
% 22.47/22.66 inference(transitivity,[status(thm)],[4868, 4663])).
% 22.47/22.66 tff(4870,plain,
% 22.47/22.66 (mult(rd(mult(b, c), mult(a, c)), mult(mult(c, mult(a, c)), a)) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(c, c)), a))),
% 22.47/22.66 inference(monotonicity,[status(thm)],[4869])).
% 22.47/22.66 tff(4871,plain,
% 22.47/22.66 (mult(mult(c, mult(a, c)), a) = mult(mult(mult(c, a), c), a)),
% 22.47/22.66 inference(monotonicity,[status(thm)],[3877])).
% 22.47/22.66 tff(4872,plain,
% 22.47/22.66 (mult(mult(mult(c, a), c), a) = mult(mult(c, mult(a, c)), a)),
% 22.47/22.66 inference(symmetry,[status(thm)],[4871])).
% 22.47/22.66 tff(4873,plain,
% 22.47/22.66 (ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) = ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))))),
% 22.47/22.66 inference(symmetry,[status(thm)],[4449])).
% 22.47/22.66 tff(4874,plain,
% 22.47/22.66 (mult(mult(a, c), a) = mult(a, mult(a, c))),
% 22.47/22.66 inference(transitivity,[status(thm)],[4609, 4873, 4451])).
% 22.47/22.66 tff(4875,plain,
% 22.47/22.66 (mult(c, mult(mult(a, c), a)) = mult(c, mult(a, mult(a, c)))),
% 22.47/22.66 inference(monotonicity,[status(thm)],[4874])).
% 22.47/22.66 tff(4876,plain,
% 22.47/22.66 (mult(c, mult(a, mult(a, c))) = mult(c, mult(mult(a, c), a))),
% 22.47/22.66 inference(symmetry,[status(thm)],[4875])).
% 22.47/22.66 tff(4877,plain,
% 22.47/22.66 ((mult(mult(a, c), mult(c, a)) = mult(mult(mult(a, c), c), a)) <=> (mult(mult(mult(a, c), c), a) = mult(mult(a, c), mult(c, a)))),
% 22.47/22.66 inference(commutativity,[status(thm)],[])).
% 22.47/22.66 tff(4878,plain,
% 22.47/22.66 (mult(c, mult(a, mult(a, c))) = mult(mult(mult(a, c), c), a)),
% 22.47/22.66 inference(transitivity,[status(thm)],[4876, 2562, 4872, 4868])).
% 22.47/22.66 tff(4879,plain,
% 22.47/22.66 (mult(mult(a, c), mult(a, c)) = mult(mult(a, c), mult(c, a))),
% 22.47/22.66 inference(symmetry,[status(thm)],[4754])).
% 22.47/22.66 tff(4880,plain,
% 22.47/22.66 (mult(mult(c, a), mult(a, c)) = mult(mult(a, c), mult(a, c))),
% 22.47/22.66 inference(monotonicity,[status(thm)],[3885])).
% 22.47/22.66 tff(4881,plain,
% 22.47/22.66 (mult(mult(c, a), mult(a, c)) = mult(mult(a, c), mult(c, a))),
% 22.47/22.66 inference(transitivity,[status(thm)],[4880, 4879])).
% 22.47/22.66 tff(4882,plain,
% 22.47/22.66 ((mult(mult(c, a), mult(a, c)) = mult(c, mult(a, mult(a, c)))) <=> (mult(mult(a, c), mult(c, a)) = mult(mult(mult(a, c), c), a))),
% 22.47/22.66 inference(monotonicity,[status(thm)],[4881, 4878])).
% 22.47/22.66 tff(4883,plain,
% 22.47/22.66 ((mult(mult(c, a), mult(a, c)) = mult(c, mult(a, mult(a, c)))) <=> (mult(mult(mult(a, c), c), a) = mult(mult(a, c), mult(c, a)))),
% 22.47/22.66 inference(transitivity,[status(thm)],[4882, 4877])).
% 22.47/22.66 tff(4884,plain,
% 22.47/22.66 ((mult(mult(mult(a, c), c), a) = mult(mult(a, c), mult(c, a))) <=> (mult(mult(c, a), mult(a, c)) = mult(c, mult(a, mult(a, c))))),
% 22.47/22.66 inference(symmetry,[status(thm)],[4883])).
% 22.47/22.66 tff(4885,plain,
% 22.47/22.66 (mult(mult(mult(a, c), c), a) = mult(mult(a, c), mult(c, a))),
% 22.47/22.66 inference(unit_resolution,[status(thm)],[4781, 4448, 3865])).
% 22.47/22.66 tff(4886,plain,
% 22.47/22.66 (mult(mult(c, a), mult(a, c)) = mult(c, mult(a, mult(a, c)))),
% 22.47/22.66 inference(modus_ponens,[status(thm)],[4885, 4884])).
% 22.47/22.66 tff(4887,plain,
% 22.47/22.66 (mult(mult(a, c), mult(a, c)) = mult(mult(c, a), mult(a, c))),
% 22.47/22.66 inference(symmetry,[status(thm)],[4880])).
% 22.47/22.66 tff(4888,plain,
% 22.47/22.66 (mult(mult(mult(a, c), unit), mult(a, c)) = mult(mult(c, mult(a, c)), a)),
% 22.47/22.66 inference(transitivity,[status(thm)],[2503, 4887, 4886, 4876, 2562, 4872])).
% 22.47/22.66 tff(4889,plain,
% 22.47/22.66 (mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), unit), mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(c, mult(a, c)), a))),
% 22.47/22.66 inference(monotonicity,[status(thm)],[4888])).
% 22.47/22.66 tff(4890,plain,
% 22.47/22.66 (mult(mult(b, mult(a, c)), c) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c)),
% 22.47/22.66 inference(transitivity,[status(thm)],[4399, 4815, 2501, 4889, 4870, 4661, 4866, 4862, 4487])).
% 22.47/22.66 tff(4891,plain,
% 22.47/22.66 (rd(mult(mult(b, mult(a, c)), c), c) = rd(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c), c)),
% 22.47/22.66 inference(monotonicity,[status(thm)],[4890])).
% 22.47/22.66 tff(4892,plain,
% 22.47/22.66 (rd(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c), c) = rd(mult(mult(b, mult(a, c)), c), c)),
% 22.47/22.66 inference(symmetry,[status(thm)],[4891])).
% 22.47/22.66 tff(4893,plain,
% 22.47/22.66 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(b, mult(a, c))),
% 22.47/22.66 inference(transitivity,[status(thm)],[322, 4892, 2680])).
% 22.47/22.66 tff(4894,plain,
% 22.47/22.66 (mult(mult(unit, c), mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)) = mult(c, mult(b, mult(a, c)))),
% 22.47/22.66 inference(monotonicity,[status(thm)],[73, 4893])).
% 22.47/22.66 tff(4895,plain,
% 22.47/22.66 (mult(c, mult(b, mult(a, c))) = mult(mult(unit, c), mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))),
% 22.47/22.66 inference(symmetry,[status(thm)],[4894])).
% 22.47/22.66 tff(4896,plain,
% 22.47/22.66 (mult(b, mult(c, a)) = mult(b, mult(a, c))),
% 22.47/22.66 inference(monotonicity,[status(thm)],[3885])).
% 22.47/22.66 tff(4897,plain,
% 22.47/22.66 (mult(b, mult(a, c)) = mult(b, mult(c, a))),
% 22.47/22.66 inference(symmetry,[status(thm)],[4896])).
% 22.47/22.66 tff(4898,plain,
% 22.47/22.66 (mult(c, mult(b, mult(a, c))) = mult(c, mult(b, mult(c, a)))),
% 22.47/22.66 inference(monotonicity,[status(thm)],[4897])).
% 22.47/22.66 tff(4899,plain,
% 22.47/22.66 (mult(c, mult(b, mult(c, a))) = mult(c, mult(b, mult(a, c)))),
% 22.47/22.66 inference(symmetry,[status(thm)],[4898])).
% 22.47/22.66 tff(4900,plain,
% 22.47/22.66 (mult(unit, rd(mult(b, c), mult(a, c))) = mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)),
% 22.47/22.66 inference(symmetry,[status(thm)],[1895])).
% 22.47/22.66 tff(4901,plain,
% 22.47/22.66 (mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), mult(a, c))),
% 22.47/22.66 inference(monotonicity,[status(thm)],[4900])).
% 22.47/22.66 tff(4902,plain,
% 22.47/22.66 (mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), mult(a, c)) = mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(a, c))),
% 22.47/22.66 inference(symmetry,[status(thm)],[4901])).
% 22.47/22.66 tff(4903,plain,
% 22.47/22.66 (mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), mult(a, c)) = mult(rd(mult(b, c), mult(a, c)), mult(a, c))),
% 22.47/22.66 inference(monotonicity,[status(thm)],[1896])).
% 22.47/22.66 tff(4904,plain,
% 22.47/22.66 (mult(rd(mult(b, c), mult(a, c)), mult(a, c)) = mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), mult(a, c))),
% 22.47/22.66 inference(symmetry,[status(thm)],[4903])).
% 22.47/22.66 tff(4905,plain,
% 22.47/22.66 (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(mult(a, b), c)),
% 22.47/22.66 inference(transitivity,[status(thm)],[1332, 3892, 3891, 3886, 161])).
% 22.47/22.66 tff(4906,plain,
% 22.47/22.66 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(a, mult(b, c))),
% 22.47/22.66 inference(transitivity,[status(thm)],[4414, 287, 142])).
% 22.47/22.66 tff(4907,plain,
% 22.47/22.66 ((mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a)) <=> (mult(a, mult(b, c)) = mult(mult(a, b), c))),
% 22.47/22.66 inference(monotonicity,[status(thm)],[4906, 4905])).
% 22.47/22.66 tff(4908,plain,
% 22.47/22.66 ((mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a)) <=> (mult(mult(a, b), c) = mult(a, mult(b, c)))),
% 22.47/22.66 inference(transitivity,[status(thm)],[4907, 143])).
% 22.47/22.66 tff(4909,plain,
% 22.47/22.66 ((mult(mult(a, b), c) = mult(a, mult(b, c))) <=> (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a))),
% 22.47/22.66 inference(symmetry,[status(thm)],[4908])).
% 22.47/22.66 tff(4910,plain,
% 22.47/22.66 ((~(mult(mult(a, b), c) = mult(a, mult(b, c)))) <=> (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a)))),
% 22.47/22.66 inference(monotonicity,[status(thm)],[4909])).
% 22.47/22.66 tff(4911,plain,
% 22.47/22.66 (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a))),
% 22.47/22.66 inference(modus_ponens,[status(thm)],[146, 4910])).
% 22.47/22.66 tff(4912,plain,
% 22.47/22.66 ((~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))),
% 22.47/22.67 inference(unit_resolution,[status(thm)],[4297, 4911])).
% 22.47/22.67 tff(4913,plain,
% 22.47/22.67 (~((~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))))),
% 22.47/22.67 inference(unit_resolution,[status(thm)],[4295, 4912])).
% 22.47/22.67 tff(4914,plain,
% 22.47/22.67 (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))),
% 22.47/22.67 inference(unit_resolution,[status(thm)],[4290, 4913])).
% 22.47/22.67 tff(4915,plain,
% 22.47/22.67 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a)),
% 22.47/22.67 inference(symmetry,[status(thm)],[4914])).
% 22.47/22.67 tff(4916,plain,
% 22.47/22.67 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a) = mult(mult(b, c), a)),
% 22.47/22.67 inference(transitivity,[status(thm)],[1168, 4915, 1332])).
% 22.47/22.67 tff(4917,plain,
% 22.47/22.67 (rd(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a), a) = rd(mult(mult(b, c), a), a)),
% 22.47/22.67 inference(monotonicity,[status(thm)],[4916])).
% 22.47/22.67 tff(4918,plain,
% 22.47/22.67 (mult(mult(rd(mult(b, c), mult(a, c)), a), c) = mult(b, c)),
% 22.47/22.67 inference(transitivity,[status(thm)],[1377, 4917, 1370])).
% 22.47/22.67 tff(4919,plain,
% 22.47/22.67 (rd(mult(mult(rd(mult(b, c), mult(a, c)), a), c), c) = rd(mult(b, c), c)),
% 22.47/22.67 inference(monotonicity,[status(thm)],[4918])).
% 22.47/22.67 tff(4920,plain,
% 22.47/22.67 (rd(mult(b, c), c) = rd(mult(mult(rd(mult(b, c), mult(a, c)), a), c), c)),
% 22.47/22.67 inference(symmetry,[status(thm)],[4919])).
% 22.47/22.67 tff(4921,plain,
% 22.47/22.67 (b = mult(a, rd(mult(b, c), mult(a, c)))),
% 22.47/22.67 inference(transitivity,[status(thm)],[2727, 4920, 174, 4412, 4409, 358])).
% 22.47/22.67 tff(4922,plain,
% 22.47/22.67 (mult(b, mult(a, c)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))),
% 22.47/22.67 inference(monotonicity,[status(thm)],[4921])).
% 22.47/22.67 tff(4923,plain,
% 22.47/22.67 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(b, mult(a, c))),
% 22.47/22.67 inference(symmetry,[status(thm)],[4922])).
% 22.47/22.67 tff(4924,plain,
% 22.47/22.67 (mult(a, mult(b, c)) = mult(b, mult(a, c))),
% 22.47/22.67 inference(transitivity,[status(thm)],[289, 288, 4923])).
% 22.47/22.67 tff(4925,plain,
% 22.47/22.67 (mult(mult(a, mult(b, c)), c) = mult(mult(b, mult(a, c)), c)),
% 22.47/22.67 inference(monotonicity,[status(thm)],[4924])).
% 22.47/22.67 tff(4926,plain,
% 22.47/22.67 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(b, c), mult(a, c))),
% 22.47/22.67 inference(transitivity,[status(thm)],[1039, 138, 266, 4925, 4399])).
% 22.47/22.67 tff(4927,plain,
% 22.47/22.67 (rd(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)), mult(a, c)) = rd(mult(mult(b, c), mult(a, c)), mult(a, c))),
% 22.47/22.67 inference(monotonicity,[status(thm)],[4926])).
% 22.47/22.67 tff(4928,plain,
% 22.47/22.67 (mult(mult(unit, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))),
% 22.47/22.67 inference(monotonicity,[status(thm)],[1549])).
% 22.47/22.67 tff(4929,plain,
% 22.47/22.67 (mult(mult(unit, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(a, c))),
% 22.47/22.67 inference(transitivity,[status(thm)],[4928, 4423, 4927, 4402, 267, 4904, 4902])).
% 22.47/22.67 tff(4930,plain,
% 22.47/22.67 ((mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(unit, mult(a, c)), rd(mult(b, c), mult(a, c)))) <=> (mult(mult(unit, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 22.47/22.67 inference(commutativity,[status(thm)],[])).
% 22.47/22.67 tff(4931,plain,
% 22.47/22.67 (mult(mult(a, c), rd(mult(b, c), mult(a, c))) = mult(mult(unit, mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 22.47/22.67 inference(symmetry,[status(thm)],[4928])).
% 22.47/22.67 tff(4932,assumption,(mult(mult(c, b), a) = mult(mult(c, a), b)), introduced(assumption)).
% 22.47/22.67 tff(4933,plain,
% 22.47/22.67 (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(mult(a, b), c)),
% 22.47/22.67 inference(transitivity,[status(thm)],[1332, 3892, 4932, 3886, 161])).
% 22.47/22.67 tff(4934,plain,
% 22.47/22.67 (ld(mult(a, c), mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))) = ld(mult(a, c), mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))),
% 22.47/22.67 inference(monotonicity,[status(thm)],[404])).
% 22.47/22.67 tff(4935,plain,
% 22.47/22.67 (mult(rd(mult(b, c), mult(a, c)), a) = mult(a, rd(mult(b, c), mult(a, c)))),
% 22.47/22.67 inference(transitivity,[status(thm)],[4412, 4934, 358])).
% 22.47/22.67 tff(4936,plain,
% 22.47/22.67 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))),
% 22.47/22.67 inference(monotonicity,[status(thm)],[4935])).
% 22.47/22.67 tff(4937,plain,
% 22.47/22.67 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(a, mult(b, c))),
% 22.47/22.67 inference(transitivity,[status(thm)],[4936, 287, 142])).
% 22.47/22.67 tff(4938,plain,
% 22.47/22.67 ((mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a)) <=> (mult(a, mult(b, c)) = mult(mult(a, b), c))),
% 22.47/22.67 inference(monotonicity,[status(thm)],[4937, 4933])).
% 22.47/22.67 tff(4939,plain,
% 22.47/22.67 ((mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a)) <=> (mult(mult(a, b), c) = mult(a, mult(b, c)))),
% 22.47/22.67 inference(transitivity,[status(thm)],[4938, 143])).
% 22.47/22.67 tff(4940,plain,
% 22.47/22.67 ((mult(mult(a, b), c) = mult(a, mult(b, c))) <=> (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a))),
% 22.47/22.67 inference(symmetry,[status(thm)],[4939])).
% 22.47/22.67 tff(4941,plain,
% 22.47/22.67 ((~(mult(mult(a, b), c) = mult(a, mult(b, c)))) <=> (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a)))),
% 22.47/22.67 inference(monotonicity,[status(thm)],[4940])).
% 22.47/22.67 tff(4942,plain,
% 22.47/22.67 (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a))),
% 22.47/22.67 inference(modus_ponens,[status(thm)],[146, 4941])).
% 22.47/22.67 tff(4943,plain,
% 22.47/22.67 ((~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))),
% 22.47/22.67 inference(unit_resolution,[status(thm)],[4297, 4942])).
% 22.47/22.67 tff(4944,assumption,(mult(mult(a, rd(mult(b, c), mult(a, c))), c) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))), introduced(assumption)).
% 22.47/22.67 tff(4945,plain,
% 22.47/22.67 (mult(mult(unit, rd(mult(b, c), mult(a, c))), a) = mult(rd(mult(b, c), mult(a, c)), a)),
% 22.47/22.67 inference(monotonicity,[status(thm)],[1893])).
% 22.47/22.67 tff(4946,plain,
% 22.47/22.67 (mult(rd(mult(b, c), mult(a, c)), a) = mult(mult(unit, rd(mult(b, c), mult(a, c))), a)),
% 22.47/22.67 inference(symmetry,[status(thm)],[4945])).
% 22.47/22.67 tff(4947,plain,
% 22.47/22.67 (ld(mult(a, c), mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = ld(mult(a, c), mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))),
% 22.47/22.67 inference(symmetry,[status(thm)],[4934])).
% 22.47/22.67 tff(4948,plain,
% 22.47/22.67 (mult(mult(unit, a), rd(mult(b, c), mult(a, c))) = mult(mult(unit, rd(mult(b, c), mult(a, c))), a)),
% 22.47/22.67 inference(transitivity,[status(thm)],[2890, 471, 4947, 4411, 4946])).
% 22.47/22.67 tff(4949,plain,
% 22.47/22.67 (mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), a) = mult(rd(mult(b, c), mult(a, c)), a)),
% 22.47/22.67 inference(monotonicity,[status(thm)],[1896])).
% 22.47/22.67 tff(4950,plain,
% 22.47/22.67 (mult(mult(unit, rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), a)),
% 22.47/22.67 inference(monotonicity,[status(thm)],[4900])).
% 22.47/22.67 tff(4951,assumption,(mult(mult(unit, a), rd(mult(b, c), mult(a, c))) = mult(mult(unit, rd(mult(b, c), mult(a, c))), a)), introduced(assumption)).
% 22.47/22.67 tff(4952,plain,
% 22.47/22.67 (mult(a, rd(mult(b, c), mult(a, c))) = mult(mult(unit, a), rd(mult(b, c), mult(a, c)))),
% 22.47/22.67 inference(monotonicity,[status(thm)],[245])).
% 22.47/22.67 tff(4953,plain,
% 22.47/22.67 (mult(a, rd(mult(b, c), mult(a, c))) = b),
% 22.47/22.67 inference(transitivity,[status(thm)],[4952, 4951, 4950, 4949, 175, 2183, 170])).
% 22.47/22.67 tff(4954,plain,
% 22.47/22.67 (mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(b, a)),
% 22.47/22.67 inference(monotonicity,[status(thm)],[4953])).
% 22.47/22.67 tff(4955,plain,
% 22.47/22.67 (mult(b, a) = mult(mult(a, rd(mult(b, c), mult(a, c))), a)),
% 22.47/22.67 inference(symmetry,[status(thm)],[4954])).
% 22.47/22.67 tff(4956,plain,
% 22.47/22.67 (ld(c, mult(c, mult(b, a))) = ld(c, mult(c, mult(a, b)))),
% 22.47/22.67 inference(monotonicity,[status(thm)],[4211])).
% 22.47/22.67 tff(4957,plain,
% 22.47/22.67 (ld(c, mult(c, mult(a, b))) = ld(c, mult(c, mult(b, a)))),
% 22.47/22.67 inference(symmetry,[status(thm)],[4956])).
% 22.47/22.67 tff(4958,plain,
% 22.47/22.67 (mult(c, ld(c, mult(a, b))) = mult(mult(a, rd(mult(b, c), mult(a, c))), a)),
% 22.47/22.67 inference(transitivity,[status(thm)],[204, 2235, 4957, 1472, 4955])).
% 22.47/22.67 tff(4959,plain,
% 22.47/22.67 (mult(c, mult(c, ld(c, mult(a, b)))) = mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), a))),
% 22.47/22.67 inference(monotonicity,[status(thm)],[4958])).
% 22.47/22.67 tff(4960,plain,
% 22.47/22.67 (mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), a)) = mult(c, mult(c, ld(c, mult(a, b))))),
% 22.47/22.67 inference(symmetry,[status(thm)],[4959])).
% 22.47/22.67 tff(4961,plain,
% 22.47/22.67 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(c, a), rd(mult(b, c), mult(a, c))), a) = mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), a)))),
% 22.47/22.67 inference(quant_inst,[status(thm)],[])).
% 22.47/22.67 tff(4962,plain,
% 22.47/22.67 (mult(mult(mult(c, a), rd(mult(b, c), mult(a, c))), a) = mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), a))),
% 22.47/22.67 inference(unit_resolution,[status(thm)],[4961, 56])).
% 22.47/22.67 tff(4963,assumption,(mult(c, mult(c, a)) = mult(c, mult(a, c))), introduced(assumption)).
% 22.47/22.67 tff(4964,plain,
% 22.47/22.67 (ld(c, mult(c, mult(c, a))) = ld(c, mult(c, mult(a, c)))),
% 22.47/22.67 inference(monotonicity,[status(thm)],[4963])).
% 22.47/22.67 tff(4965,plain,
% 22.47/22.67 (mult(c, a) = mult(a, c)),
% 22.47/22.67 inference(transitivity,[status(thm)],[2468, 4964, 2452])).
% 22.47/22.67 tff(4966,plain,
% 22.47/22.67 (mult(mult(c, a), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))),
% 22.47/22.67 inference(monotonicity,[status(thm)],[4965])).
% 22.47/22.67 tff(4967,plain,
% 22.47/22.67 (mult(mult(mult(c, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)),
% 22.47/22.67 inference(monotonicity,[status(thm)],[4966])).
% 22.47/22.67 tff(4968,plain,
% 22.47/22.67 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(c, a), rd(mult(b, c), mult(a, c))), a)),
% 22.47/22.67 inference(symmetry,[status(thm)],[4967])).
% 22.47/22.67 tff(4969,plain,
% 22.47/22.67 (mult(a, rd(mult(b, c), mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), a)),
% 22.47/22.67 inference(transitivity,[status(thm)],[4952, 4951, 4950, 4949])).
% 22.47/22.67 tff(4970,plain,
% 22.47/22.67 (mult(mult(a, rd(mult(b, c), mult(a, c))), c) = mult(mult(rd(mult(b, c), mult(a, c)), a), c)),
% 22.47/22.67 inference(monotonicity,[status(thm)],[4969])).
% 22.47/22.67 tff(4971,plain,
% 22.47/22.67 (mult(mult(a, c), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), c)),
% 22.47/22.67 inference(symmetry,[status(thm)],[4944])).
% 22.47/22.67 tff(4972,plain,
% 22.47/22.67 (mult(mult(a, c), rd(mult(b, c), mult(a, c))) = mult(b, c)),
% 22.47/22.67 inference(transitivity,[status(thm)],[4971, 4970, 1377, 2181, 1370])).
% 22.47/22.67 tff(4973,plain,
% 22.47/22.67 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(b, c), a)),
% 22.47/22.67 inference(monotonicity,[status(thm)],[4972])).
% 22.47/22.67 tff(4974,plain,
% 22.47/22.67 (mult(mult(b, c), a) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)),
% 22.47/22.67 inference(symmetry,[status(thm)],[4973])).
% 22.47/22.67 tff(4975,plain,
% 22.47/22.67 (mult(mult(c, b), a) = mult(mult(b, c), a)),
% 22.47/22.67 inference(symmetry,[status(thm)],[3892])).
% 22.47/22.67 tff(4976,plain,
% 22.47/22.67 (mult(mult(c, a), b) = mult(mult(c, b), a)),
% 22.47/22.67 inference(symmetry,[status(thm)],[4218])).
% 22.47/22.67 tff(4977,plain,
% 22.47/22.67 (mult(mult(c, a), b) = mult(c, mult(a, b))),
% 22.47/22.67 inference(transitivity,[status(thm)],[4976, 4975, 4974, 4968, 4962, 4960, 1443])).
% 22.47/22.67 tff(4978,plain,
% 22.47/22.67 ($false),
% 22.47/22.67 inference(unit_resolution,[status(thm)],[4025, 4977])).
% 22.47/22.67 tff(4979,plain,((~(mult(mult(a, rd(mult(b, c), mult(a, c))), c) = mult(mult(a, c), rd(mult(b, c), mult(a, c))))) | (mult(mult(c, a), b) = mult(c, mult(a, b))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) | (~(mult(mult(unit, a), rd(mult(b, c), mult(a, c))) = mult(mult(unit, rd(mult(b, c), mult(a, c))), a))) | (~(mult(c, mult(c, a)) = mult(c, mult(a, c))))), inference(lemma,lemma(discharge,[]))).
% 22.47/22.67 tff(4980,plain,
% 22.47/22.67 (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))),
% 22.47/22.67 inference(unit_resolution,[status(thm)],[4979, 4948, 4711, 4025, 4944])).
% 22.47/22.67 tff(4981,plain,
% 22.47/22.67 ((~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))),
% 22.47/22.67 inference(unit_resolution,[status(thm)],[4290, 4980])).
% 22.47/22.67 tff(4982,plain,
% 22.47/22.67 ($false),
% 22.47/22.67 inference(unit_resolution,[status(thm)],[4295, 4981, 4943])).
% 22.47/22.67 tff(4983,plain,((~(mult(mult(a, rd(mult(b, c), mult(a, c))), c) = mult(mult(a, c), rd(mult(b, c), mult(a, c))))) | (mult(mult(c, a), b) = mult(c, mult(a, b))) | (~(mult(mult(c, b), a) = mult(mult(c, a), b))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))))), inference(lemma,lemma(discharge,[]))).
% 22.47/22.67 tff(4984,plain,
% 22.47/22.67 (~(mult(mult(a, rd(mult(b, c), mult(a, c))), c) = mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 22.47/22.67 inference(unit_resolution,[status(thm)],[4983, 4019, 3891, 3865, 287, 359])).
% 22.47/22.67 tff(4985,plain,
% 22.47/22.67 (((~(mult(mult(a, rd(mult(b, c), mult(a, c))), c) = mult(mult(a, c), rd(mult(b, c), mult(a, c))))) | (~(mult(a, mult(rd(mult(b, c), mult(a, c)), c)) = mult(a, mult(c, rd(mult(b, c), mult(a, c))))))) | (mult(mult(a, rd(mult(b, c), mult(a, c))), c) = mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 22.47/22.67 inference(tautology,[status(thm)],[])).
% 22.47/22.67 tff(4986,plain,
% 22.47/22.67 ((~(mult(mult(a, rd(mult(b, c), mult(a, c))), c) = mult(mult(a, c), rd(mult(b, c), mult(a, c))))) | (~(mult(a, mult(rd(mult(b, c), mult(a, c)), c)) = mult(a, mult(c, rd(mult(b, c), mult(a, c))))))),
% 22.47/22.67 inference(unit_resolution,[status(thm)],[4985, 4984])).
% 22.47/22.67 tff(4987,plain,
% 22.47/22.67 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, rd(mult(b, c), mult(a, c))), c) = mult(mult(a, c), rd(mult(b, c), mult(a, c))))) | (~(mult(a, mult(rd(mult(b, c), mult(a, c)), c)) = mult(a, mult(c, rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(a, rd(mult(b, c), mult(a, c))), c) = mult(a, mult(rd(mult(b, c), mult(a, c)), c)))) | (~(mult(mult(a, c), rd(mult(b, c), mult(a, c))) = mult(a, mult(c, rd(mult(b, c), mult(a, c)))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, rd(mult(b, c), mult(a, c))), c) = mult(mult(a, c), rd(mult(b, c), mult(a, c))))) | (~(mult(a, mult(rd(mult(b, c), mult(a, c)), c)) = mult(a, mult(c, rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(a, rd(mult(b, c), mult(a, c))), c) = mult(a, mult(rd(mult(b, c), mult(a, c)), c)))) | (~(mult(mult(a, c), rd(mult(b, c), mult(a, c))) = mult(a, mult(c, rd(mult(b, c), mult(a, c)))))))))),
% 22.47/22.67 inference(rewrite,[status(thm)],[])).
% 22.47/22.67 tff(4988,plain,
% 22.47/22.67 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, rd(mult(b, c), mult(a, c))), c) = mult(mult(a, c), rd(mult(b, c), mult(a, c))))) | (~(mult(a, mult(rd(mult(b, c), mult(a, c)), c)) = mult(a, mult(c, rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(a, rd(mult(b, c), mult(a, c))), c) = mult(a, mult(rd(mult(b, c), mult(a, c)), c)))) | (~(mult(mult(a, c), rd(mult(b, c), mult(a, c))) = mult(a, mult(c, rd(mult(b, c), mult(a, c)))))))))),
% 22.47/22.67 inference(quant_inst,[status(thm)],[])).
% 22.47/22.67 tff(4989,plain,
% 22.47/22.67 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, rd(mult(b, c), mult(a, c))), c) = mult(mult(a, c), rd(mult(b, c), mult(a, c))))) | (~(mult(a, mult(rd(mult(b, c), mult(a, c)), c)) = mult(a, mult(c, rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(a, rd(mult(b, c), mult(a, c))), c) = mult(a, mult(rd(mult(b, c), mult(a, c)), c)))) | (~(mult(mult(a, c), rd(mult(b, c), mult(a, c))) = mult(a, mult(c, rd(mult(b, c), mult(a, c))))))))),
% 22.47/22.67 inference(modus_ponens,[status(thm)],[4988, 4987])).
% 22.47/22.67 tff(4990,plain,
% 22.47/22.67 ((~((~(mult(mult(a, rd(mult(b, c), mult(a, c))), c) = mult(mult(a, c), rd(mult(b, c), mult(a, c))))) | (~(mult(a, mult(rd(mult(b, c), mult(a, c)), c)) = mult(a, mult(c, rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(a, rd(mult(b, c), mult(a, c))), c) = mult(a, mult(rd(mult(b, c), mult(a, c)), c)))) | (~(mult(mult(a, c), rd(mult(b, c), mult(a, c))) = mult(a, mult(c, rd(mult(b, c), mult(a, c))))))))),
% 22.47/22.67 inference(unit_resolution,[status(thm)],[4989, 27])).
% 22.47/22.67 tff(4991,plain,
% 22.47/22.67 (~((~(mult(mult(a, rd(mult(b, c), mult(a, c))), c) = mult(a, mult(rd(mult(b, c), mult(a, c)), c)))) | (~(mult(mult(a, c), rd(mult(b, c), mult(a, c))) = mult(a, mult(c, rd(mult(b, c), mult(a, c)))))))),
% 22.47/22.67 inference(unit_resolution,[status(thm)],[4990, 4986])).
% 22.47/22.67 tff(4992,plain,
% 22.47/22.67 (((~(mult(mult(a, rd(mult(b, c), mult(a, c))), c) = mult(a, mult(rd(mult(b, c), mult(a, c)), c)))) | (~(mult(mult(a, c), rd(mult(b, c), mult(a, c))) = mult(a, mult(c, rd(mult(b, c), mult(a, c))))))) | (mult(mult(a, c), rd(mult(b, c), mult(a, c))) = mult(a, mult(c, rd(mult(b, c), mult(a, c)))))),
% 22.47/22.67 inference(tautology,[status(thm)],[])).
% 22.47/22.67 tff(4993,plain,
% 22.47/22.67 (mult(mult(a, c), rd(mult(b, c), mult(a, c))) = mult(a, mult(c, rd(mult(b, c), mult(a, c))))),
% 22.47/22.67 inference(unit_resolution,[status(thm)],[4992, 4991])).
% 22.47/22.67 tff(4994,plain,
% 22.47/22.67 (mult(a, mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))),
% 22.47/22.67 inference(symmetry,[status(thm)],[4993])).
% 22.47/22.67 tff(4995,plain,
% 22.47/22.67 (mult(a, mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(unit, mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 22.47/22.67 inference(transitivity,[status(thm)],[4994, 4931])).
% 22.47/22.67 tff(4996,plain,
% 22.47/22.67 (mult(a, rd(mult(b, c), mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), a)),
% 22.47/22.67 inference(transitivity,[status(thm)],[471, 4408, 4411])).
% 22.47/22.67 tff(4997,plain,
% 22.47/22.67 (mult(mult(a, rd(mult(b, c), mult(a, c))), c) = mult(mult(rd(mult(b, c), mult(a, c)), a), c)),
% 22.47/22.67 inference(monotonicity,[status(thm)],[4996])).
% 22.47/22.67 tff(4998,plain,
% 22.47/22.67 (((~(mult(mult(a, rd(mult(b, c), mult(a, c))), c) = mult(a, mult(rd(mult(b, c), mult(a, c)), c)))) | (~(mult(mult(a, c), rd(mult(b, c), mult(a, c))) = mult(a, mult(c, rd(mult(b, c), mult(a, c))))))) | (mult(mult(a, rd(mult(b, c), mult(a, c))), c) = mult(a, mult(rd(mult(b, c), mult(a, c)), c)))),
% 22.47/22.67 inference(tautology,[status(thm)],[])).
% 22.47/22.67 tff(4999,plain,
% 22.47/22.67 (mult(mult(a, rd(mult(b, c), mult(a, c))), c) = mult(a, mult(rd(mult(b, c), mult(a, c)), c))),
% 22.47/22.67 inference(unit_resolution,[status(thm)],[4998, 4991])).
% 22.47/22.67 tff(5000,plain,
% 22.47/22.68 (mult(a, mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, rd(mult(b, c), mult(a, c))), c)),
% 22.47/22.68 inference(symmetry,[status(thm)],[4999])).
% 22.47/22.68 tff(5001,plain,
% 22.47/22.68 (mult(a, mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(a, c))),
% 22.47/22.68 inference(transitivity,[status(thm)],[5000, 4997, 1377, 4917, 1370, 267, 4904, 4902])).
% 22.47/22.68 tff(5002,plain,
% 22.47/22.68 ((mult(a, mult(rd(mult(b, c), mult(a, c)), c)) = mult(a, mult(c, rd(mult(b, c), mult(a, c))))) <=> (mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(unit, mult(a, c)), rd(mult(b, c), mult(a, c))))),
% 22.47/22.68 inference(monotonicity,[status(thm)],[5001, 4995])).
% 22.47/22.68 tff(5003,plain,
% 22.47/22.68 ((mult(a, mult(rd(mult(b, c), mult(a, c)), c)) = mult(a, mult(c, rd(mult(b, c), mult(a, c))))) <=> (mult(mult(unit, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 22.47/22.68 inference(transitivity,[status(thm)],[5002, 4930])).
% 22.47/22.68 tff(5004,plain,
% 22.47/22.68 ((~(mult(a, mult(rd(mult(b, c), mult(a, c)), c)) = mult(a, mult(c, rd(mult(b, c), mult(a, c)))))) <=> (~(mult(mult(unit, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(a, c))))),
% 22.47/22.68 inference(monotonicity,[status(thm)],[5003])).
% 22.47/22.68 tff(5005,plain,
% 22.47/22.68 ((mult(mult(a, rd(mult(b, c), mult(a, c))), c) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))) <=> (mult(a, mult(rd(mult(b, c), mult(a, c)), c)) = mult(a, mult(c, rd(mult(b, c), mult(a, c)))))),
% 22.47/22.68 inference(monotonicity,[status(thm)],[4999, 4993])).
% 22.47/22.68 tff(5006,plain,
% 22.47/22.68 ((~(mult(mult(a, rd(mult(b, c), mult(a, c))), c) = mult(mult(a, c), rd(mult(b, c), mult(a, c))))) <=> (~(mult(a, mult(rd(mult(b, c), mult(a, c)), c)) = mult(a, mult(c, rd(mult(b, c), mult(a, c))))))),
% 22.47/22.68 inference(monotonicity,[status(thm)],[5005])).
% 22.47/22.68 tff(5007,plain,
% 22.47/22.68 (~(mult(a, mult(rd(mult(b, c), mult(a, c)), c)) = mult(a, mult(c, rd(mult(b, c), mult(a, c)))))),
% 22.47/22.68 inference(modus_ponens,[status(thm)],[4984, 5006])).
% 22.47/22.68 tff(5008,plain,
% 22.47/22.68 (~(mult(mult(unit, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 22.47/22.68 inference(modus_ponens,[status(thm)],[5007, 5004])).
% 22.47/22.68 tff(5009,plain,
% 22.47/22.68 ($false),
% 22.47/22.68 inference(unit_resolution,[status(thm)],[5008, 4929])).
% 22.47/22.68 tff(5010,plain,((mult(mult(c, b), a) = mult(c, mult(b, a))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit)))))), inference(lemma,lemma(discharge,[]))).
% 22.47/22.68 tff(5011,plain,
% 22.47/22.68 (mult(mult(c, b), a) = mult(c, mult(b, a))),
% 22.47/22.68 inference(unit_resolution,[status(thm)],[5010, 4400, 279, 1039, 3865])).
% 22.47/22.68 tff(5012,plain,
% 22.47/22.68 (mult(mult(c, a), b) = mult(c, mult(a, b))),
% 22.47/22.68 inference(unit_resolution,[status(thm)],[4220, 5011])).
% 22.47/22.68 tff(5013,plain,
% 22.47/22.68 (mult(unit, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))) = mult(unit, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))),
% 22.47/22.68 inference(monotonicity,[status(thm)],[3842])).
% 22.47/22.68 tff(5014,plain,
% 22.47/22.68 ((~![A: $i] : (mult(unit, A) = A)) | (mult(unit, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 22.47/22.68 inference(quant_inst,[status(thm)],[])).
% 22.47/22.68 tff(5015,plain,
% 22.47/22.68 (mult(unit, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))),
% 22.47/22.68 inference(unit_resolution,[status(thm)],[5014, 71])).
% 22.47/22.68 tff(5016,plain,
% 22.47/22.68 (mult(mult(unit, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)),
% 22.47/22.68 inference(monotonicity,[status(thm)],[5015])).
% 22.47/22.68 tff(5017,plain,
% 22.47/22.68 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(unit, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a)),
% 22.47/22.68 inference(symmetry,[status(thm)],[5016])).
% 22.47/22.68 tff(5018,plain,
% 22.47/22.68 (mult(mult(mult(unit, a), unit), c) = mult(a, c)),
% 22.47/22.68 inference(monotonicity,[status(thm)],[507])).
% 22.47/22.68 tff(5019,plain,
% 22.47/22.68 (mult(unit, a) = mult(mult(unit, a), unit)),
% 22.47/22.68 inference(symmetry,[status(thm)],[506])).
% 22.47/22.68 tff(5020,plain,
% 22.47/22.68 (mult(mult(unit, a), c) = mult(mult(mult(unit, a), unit), c)),
% 22.47/22.68 inference(monotonicity,[status(thm)],[5019])).
% 22.47/22.68 tff(5021,plain,
% 22.47/22.68 (mult(mult(unit, a), c) = mult(a, c)),
% 22.47/22.68 inference(transitivity,[status(thm)],[5020, 5018])).
% 22.47/22.68 tff(5022,plain,
% 22.47/22.68 (mult(mult(mult(unit, a), c), a) = mult(mult(a, c), a)),
% 22.47/22.68 inference(monotonicity,[status(thm)],[5021])).
% 22.47/22.68 tff(5023,plain,
% 22.47/22.68 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(unit, a), c), a) = mult(unit, mult(mult(a, c), a)))),
% 22.47/22.68 inference(quant_inst,[status(thm)],[])).
% 22.47/22.68 tff(5024,plain,
% 22.47/22.68 (mult(mult(mult(unit, a), c), a) = mult(unit, mult(mult(a, c), a))),
% 22.47/22.68 inference(unit_resolution,[status(thm)],[5023, 56])).
% 22.47/22.68 tff(5025,plain,
% 22.47/22.68 (mult(unit, mult(mult(a, c), a)) = mult(mult(mult(unit, a), c), a)),
% 22.47/22.68 inference(symmetry,[status(thm)],[5024])).
% 22.47/22.68 tff(5026,plain,
% 22.47/22.68 (mult(unit, mult(mult(a, c), a)) = mult(mult(a, c), a)),
% 22.47/22.68 inference(transitivity,[status(thm)],[5025, 5022])).
% 22.47/22.68 tff(5027,plain,
% 22.47/22.68 (mult(mult(unit, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))),
% 22.47/22.68 inference(monotonicity,[status(thm)],[5026])).
% 22.47/22.68 tff(5028,plain,
% 22.47/22.68 (mult(mult(unit, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(mult(unit, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a)),
% 22.47/22.68 inference(transitivity,[status(thm)],[5027, 3842, 5017])).
% 22.47/22.68 tff(5029,plain,
% 22.47/22.68 ((mult(mult(unit, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(unit, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))))) <=> (mult(mult(unit, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(unit, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)))),
% 22.47/22.68 inference(monotonicity,[status(thm)],[5028, 5013])).
% 22.47/22.68 tff(5030,plain,
% 22.47/22.68 ((~![A: $i] : (mult(unit, A) = A)) | (mult(unit, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))))),
% 22.47/22.68 inference(quant_inst,[status(thm)],[])).
% 22.47/22.68 tff(5031,plain,
% 22.47/22.68 (mult(unit, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))),
% 22.47/22.68 inference(unit_resolution,[status(thm)],[5030, 71])).
% 22.47/22.68 tff(5032,plain,
% 22.47/22.68 (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(unit, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))))),
% 22.47/22.68 inference(symmetry,[status(thm)],[5031])).
% 22.47/22.68 tff(5033,plain,
% 22.47/22.68 (mult(mult(unit, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(unit, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))))),
% 22.47/22.68 inference(transitivity,[status(thm)],[5027, 5032])).
% 22.47/22.68 tff(5034,assumption,(~(mult(mult(unit, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(unit, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))))), introduced(assumption)).
% 22.47/22.68 tff(5035,plain,
% 22.47/22.68 ($false),
% 22.47/22.68 inference(unit_resolution,[status(thm)],[5034, 5033])).
% 22.47/22.68 tff(5036,plain,(mult(mult(unit, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(unit, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))))), inference(lemma,lemma(discharge,[]))).
% 22.47/22.68 tff(5037,plain,
% 22.47/22.68 (mult(mult(unit, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(unit, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))),
% 22.47/22.68 inference(modus_ponens,[status(thm)],[5036, 5029])).
% 22.47/22.68 tff(5038,plain,
% 22.47/22.68 (mult(c, mult(b, mult(c, a))) = mult(c, mult(b, mult(a, c)))),
% 22.47/22.68 inference(monotonicity,[status(thm)],[4896])).
% 22.47/22.68 tff(5039,plain,
% 22.47/22.68 (mult(mult(b, c), mult(c, a)) = mult(mult(b, c), mult(a, c))),
% 22.47/22.68 inference(monotonicity,[status(thm)],[3885])).
% 22.47/22.68 tff(5040,plain,
% 22.47/22.68 (mult(mult(c, b), mult(c, a)) = mult(mult(c, b), mult(a, c))),
% 22.47/22.68 inference(transitivity,[status(thm)],[2231, 5039, 2742])).
% 22.47/22.68 tff(5041,plain,
% 22.47/22.68 ((mult(mult(c, b), mult(c, a)) = mult(c, mult(b, mult(c, a)))) <=> (mult(mult(c, b), mult(a, c)) = mult(c, mult(b, mult(a, c))))),
% 22.47/22.68 inference(monotonicity,[status(thm)],[5040, 5038])).
% 22.47/22.68 tff(5042,plain,
% 22.47/22.68 ((mult(mult(c, b), mult(a, c)) = mult(c, mult(b, mult(a, c)))) <=> (mult(mult(c, b), mult(c, a)) = mult(c, mult(b, mult(c, a))))),
% 22.47/22.68 inference(symmetry,[status(thm)],[5041])).
% 22.47/22.68 tff(5043,plain,
% 22.47/22.68 ((mult(mult(unit, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)), c) = mult(mult(unit, c), mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))) <=> (mult(mult(unit, c), mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)) = mult(mult(unit, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)), c))),
% 22.47/22.68 inference(commutativity,[status(thm)],[])).
% 22.47/22.68 tff(5044,plain,
% 22.47/22.68 (mult(mult(rd(mult(b, c), mult(a, c)), a), c) = mult(mult(a, rd(mult(b, c), mult(a, c))), c)),
% 22.47/22.68 inference(monotonicity,[status(thm)],[4413])).
% 22.47/22.68 tff(5045,plain,
% 22.47/22.68 (mult(mult(a, rd(mult(b, c), mult(a, c))), c) = mult(mult(rd(mult(b, c), mult(a, c)), a), c)),
% 22.47/22.68 inference(symmetry,[status(thm)],[5044])).
% 22.47/22.68 tff(5046,plain,
% 22.47/22.68 (mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c)),
% 22.47/22.68 inference(symmetry,[status(thm)],[2187])).
% 22.47/22.68 tff(5047,plain,
% 22.47/22.68 (mult(mult(a, c), rd(mult(b, c), mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), c), a)),
% 22.47/22.68 inference(transitivity,[status(thm)],[2167, 4851, 4850, 2171, 5046, 4493, 5045, 4490, 4489, 4488])).
% 22.47/22.68 tff(5048,plain,
% 22.47/22.68 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c)),
% 22.47/22.68 inference(monotonicity,[status(thm)],[5047])).
% 22.47/22.68 tff(5049,plain,
% 22.47/22.68 (mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)),
% 22.47/22.68 inference(symmetry,[status(thm)],[5048])).
% 22.47/22.68 tff(5050,plain,
% 22.47/22.68 (mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)),
% 22.47/22.68 inference(transitivity,[status(thm)],[4860, 4858, 4855, 5049])).
% 22.47/22.68 tff(5051,plain,
% 22.47/22.68 (mult(mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))), a) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a)),
% 22.47/22.68 inference(monotonicity,[status(thm)],[5050])).
% 22.47/22.68 tff(5052,plain,
% 22.47/22.68 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), unit) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))),
% 22.47/22.68 inference(transitivity,[status(thm)],[1875, 1871, 4340, 5044, 2189, 2187, 2172, 2178, 2177, 2162])).
% 22.47/22.68 tff(5053,plain,
% 22.47/22.68 (mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), unit), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)),
% 22.47/22.68 inference(monotonicity,[status(thm)],[5052])).
% 22.47/22.68 tff(5054,plain,
% 22.47/22.68 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))),
% 22.47/22.68 inference(transitivity,[status(thm)],[4656, 4655, 5053, 5048, 2627, 4857, 4859])).
% 22.47/22.68 tff(5055,plain,
% 22.47/22.68 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)), a) = mult(mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))), a)),
% 22.47/22.68 inference(monotonicity,[status(thm)],[5054])).
% 22.47/22.68 tff(5056,plain,
% 22.47/22.68 (mult(c, mult(mult(a, c), a)) = mult(c, mult(a, mult(a, c)))),
% 22.47/22.68 inference(monotonicity,[status(thm)],[4610])).
% 22.47/22.68 tff(5057,plain,
% 22.47/22.68 (mult(c, mult(a, mult(a, c))) = mult(c, mult(mult(a, c), a))),
% 22.47/22.68 inference(symmetry,[status(thm)],[5056])).
% 22.47/22.68 tff(5058,plain,
% 22.47/22.68 (mult(c, mult(a, mult(a, c))) = mult(mult(mult(a, c), c), a)),
% 22.47/22.68 inference(transitivity,[status(thm)],[5057, 2562, 4872, 4868])).
% 22.47/22.68 tff(5059,plain,
% 22.47/22.68 ((mult(mult(c, a), mult(a, c)) = mult(c, mult(a, mult(a, c)))) <=> (mult(mult(a, c), mult(c, a)) = mult(mult(mult(a, c), c), a))),
% 22.47/22.68 inference(monotonicity,[status(thm)],[4881, 5058])).
% 22.47/22.68 tff(5060,plain,
% 22.47/22.68 ((mult(mult(c, a), mult(a, c)) = mult(c, mult(a, mult(a, c)))) <=> (mult(mult(mult(a, c), c), a) = mult(mult(a, c), mult(c, a)))),
% 22.47/22.68 inference(transitivity,[status(thm)],[5059, 4877])).
% 22.47/22.68 tff(5061,plain,
% 22.47/22.68 ((mult(mult(mult(a, c), c), a) = mult(mult(a, c), mult(c, a))) <=> (mult(mult(c, a), mult(a, c)) = mult(c, mult(a, mult(a, c))))),
% 22.47/22.68 inference(symmetry,[status(thm)],[5060])).
% 22.47/22.68 tff(5062,plain,
% 22.47/22.68 (mult(mult(c, a), mult(a, c)) = mult(c, mult(a, mult(a, c)))),
% 22.47/22.68 inference(modus_ponens,[status(thm)],[4782, 5061])).
% 22.47/22.68 tff(5063,plain,
% 22.47/22.68 (mult(mult(mult(a, c), unit), mult(a, c)) = mult(mult(c, mult(a, c)), a)),
% 22.47/22.68 inference(transitivity,[status(thm)],[2503, 4887, 5062, 5057, 2562, 4872])).
% 22.47/22.68 tff(5064,plain,
% 22.47/22.68 (mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), unit), mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(c, mult(a, c)), a))),
% 22.47/22.68 inference(monotonicity,[status(thm)],[5063])).
% 22.47/22.68 tff(5065,plain,
% 22.47/22.68 (mult(mult(b, mult(a, c)), c) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c)),
% 22.47/22.68 inference(transitivity,[status(thm)],[4399, 4815, 2501, 5064, 4870, 4661, 5055, 5051, 4528])).
% 22.47/22.68 tff(5066,plain,
% 22.47/22.68 (rd(mult(mult(b, mult(a, c)), c), c) = rd(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c), c)),
% 22.47/22.68 inference(monotonicity,[status(thm)],[5065])).
% 22.47/22.68 tff(5067,plain,
% 22.47/22.68 (rd(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c), c) = rd(mult(mult(b, mult(a, c)), c), c)),
% 22.47/22.68 inference(symmetry,[status(thm)],[5066])).
% 22.47/22.68 tff(5068,plain,
% 22.47/22.68 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(b, mult(a, c))),
% 22.47/22.68 inference(transitivity,[status(thm)],[322, 5067, 2680])).
% 22.47/22.68 tff(5069,plain,
% 22.47/22.68 (mult(mult(unit, c), mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)) = mult(c, mult(b, mult(a, c)))),
% 22.47/22.68 inference(monotonicity,[status(thm)],[73, 5068])).
% 22.47/22.68 tff(5070,plain,
% 22.47/22.68 (mult(c, mult(b, mult(a, c))) = mult(mult(unit, c), mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))),
% 22.47/22.68 inference(symmetry,[status(thm)],[5069])).
% 22.47/22.68 tff(5071,assumption,(mult(mult(unit, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(unit, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))), introduced(assumption)).
% 22.47/22.68 tff(5072,plain,
% 22.47/22.68 (mult(unit, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)) = mult(mult(unit, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a)),
% 22.47/22.68 inference(symmetry,[status(thm)],[5071])).
% 22.47/22.68 tff(5073,plain,
% 22.47/22.68 (mult(unit, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)),
% 22.47/22.68 inference(transitivity,[status(thm)],[5072, 5016])).
% 22.47/22.68 tff(5074,plain,
% 22.47/22.68 (mult(mult(unit, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)), c) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c)),
% 22.47/22.68 inference(monotonicity,[status(thm)],[5073])).
% 22.47/22.68 tff(5075,plain,
% 22.47/22.68 (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(unit, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)), c)),
% 22.47/22.68 inference(symmetry,[status(thm)],[5074])).
% 22.47/22.68 tff(5076,plain,
% 22.47/22.68 (mult(mult(c, b), mult(a, c)) = mult(mult(unit, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)), c)),
% 22.47/22.68 inference(transitivity,[status(thm)],[2429, 4815, 2501, 5064, 4870, 4661, 5055, 5051, 4528, 5075])).
% 22.47/22.68 tff(5077,plain,
% 22.47/22.68 ((mult(mult(c, b), mult(a, c)) = mult(c, mult(b, mult(a, c)))) <=> (mult(mult(unit, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)), c) = mult(mult(unit, c), mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)))),
% 22.47/22.68 inference(monotonicity,[status(thm)],[5076, 5070])).
% 22.47/22.68 tff(5078,plain,
% 22.47/22.68 ((mult(mult(c, b), mult(a, c)) = mult(c, mult(b, mult(a, c)))) <=> (mult(mult(unit, c), mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)) = mult(mult(unit, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)), c))),
% 22.47/22.68 inference(transitivity,[status(thm)],[5077, 5043])).
% 22.47/22.68 tff(5079,plain,
% 22.47/22.68 ((mult(mult(unit, c), mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)) = mult(mult(unit, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)), c)) <=> (mult(mult(c, b), mult(a, c)) = mult(c, mult(b, mult(a, c))))),
% 22.47/22.68 inference(symmetry,[status(thm)],[5078])).
% 22.47/22.68 tff(5080,assumption,(~(mult(mult(c, b), mult(c, a)) = mult(c, mult(b, mult(c, a))))), introduced(assumption)).
% 22.47/22.68 tff(5081,plain,
% 22.47/22.68 (mult(mult(c, b), mult(c, a)) = mult(c, mult(b, mult(c, a)))),
% 22.47/22.68 inference(modus_ponens,[status(thm)],[2741, 5042])).
% 22.47/22.68 tff(5082,plain,
% 22.47/22.68 ($false),
% 22.47/22.68 inference(unit_resolution,[status(thm)],[5080, 5081])).
% 22.47/22.69 tff(5083,plain,((~(mult(mult(c, b), mult(a, c)) = mult(c, mult(b, mult(a, c))))) | (mult(mult(c, b), mult(c, a)) = mult(c, mult(b, mult(c, a)))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit)))))), inference(lemma,lemma(discharge,[]))).
% 22.47/22.69 tff(5084,plain,
% 22.47/22.69 (~(mult(mult(c, b), mult(a, c)) = mult(c, mult(b, mult(a, c))))),
% 22.47/22.69 inference(unit_resolution,[status(thm)],[5083, 5080, 3865])).
% 22.47/22.69 tff(5085,plain,
% 22.47/22.69 ((~(mult(mult(c, mult(a, c)), b) = mult(c, mult(mult(a, c), b)))) | (~(mult(mult(c, b), mult(a, c)) = mult(c, mult(b, mult(a, c)))))),
% 22.47/22.69 inference(unit_resolution,[status(thm)],[2431, 5084])).
% 22.47/22.69 tff(5086,plain,
% 22.47/22.69 (~((~(mult(mult(c, mult(a, c)), b) = mult(mult(c, b), mult(a, c)))) | (~(mult(c, mult(mult(a, c), b)) = mult(c, mult(b, mult(a, c))))))),
% 22.47/22.69 inference(unit_resolution,[status(thm)],[2436, 5085])).
% 22.47/22.69 tff(5087,plain,
% 22.47/22.69 (mult(c, mult(mult(a, c), b)) = mult(c, mult(b, mult(a, c)))),
% 22.47/22.69 inference(unit_resolution,[status(thm)],[2710, 5086])).
% 22.47/22.69 tff(5088,plain,
% 22.47/22.69 (mult(mult(c, c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(a, c), b)),
% 22.47/22.69 inference(transitivity,[status(thm)],[3183, 4277, 4010, 4225, 4224, 3886])).
% 22.47/22.69 tff(5089,plain,
% 22.47/22.69 (mult(mult(mult(c, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(mult(a, c), b), c)),
% 22.47/22.69 inference(monotonicity,[status(thm)],[5088])).
% 22.47/22.69 tff(5090,plain,
% 22.47/22.69 (mult(mult(mult(a, c), b), c) = mult(mult(mult(c, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c)),
% 22.47/22.69 inference(symmetry,[status(thm)],[5089])).
% 22.47/22.69 tff(5091,plain,
% 22.47/22.69 (mult(mult(c, mult(a, c)), b) = mult(mult(mult(a, c), c), b)),
% 22.47/22.69 inference(symmetry,[status(thm)],[4540])).
% 22.47/22.69 tff(5092,plain,
% 22.47/22.69 (mult(mult(c, mult(a, c)), b) = mult(mult(unit, c), mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))),
% 22.47/22.69 inference(transitivity,[status(thm)],[5091, 4104, 5090, 3187, 4274, 5087, 5070])).
% 22.47/22.69 tff(5093,plain,
% 22.47/22.69 ((mult(mult(c, mult(a, c)), b) = mult(mult(c, b), mult(a, c))) <=> (mult(mult(unit, c), mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)) = mult(mult(unit, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)), c))),
% 22.47/22.69 inference(monotonicity,[status(thm)],[5092, 5076])).
% 22.47/22.69 tff(5094,plain,
% 22.47/22.69 ((mult(mult(c, mult(a, c)), b) = mult(mult(c, b), mult(a, c))) <=> (mult(mult(c, b), mult(c, a)) = mult(c, mult(b, mult(c, a))))),
% 22.47/22.69 inference(transitivity,[status(thm)],[5093, 5079, 5042])).
% 22.47/22.69 tff(5095,plain,
% 22.47/22.69 (mult(mult(c, mult(a, c)), b) = mult(mult(c, b), mult(a, c))),
% 22.47/22.69 inference(unit_resolution,[status(thm)],[2438, 5086])).
% 22.47/22.69 tff(5096,plain,
% 22.47/22.69 (mult(mult(c, b), mult(c, a)) = mult(c, mult(b, mult(c, a)))),
% 22.47/22.69 inference(modus_ponens,[status(thm)],[5095, 5094])).
% 22.47/22.69 tff(5097,plain,
% 22.47/22.69 ($false),
% 22.47/22.69 inference(unit_resolution,[status(thm)],[5080, 5096])).
% 22.47/22.69 tff(5098,plain,((mult(mult(c, b), mult(c, a)) = mult(c, mult(b, mult(c, a)))) | (~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))) | (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit))))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) | (~(mult(mult(unit, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(unit, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)))) | (~(mult(mult(c, a), b) = mult(c, mult(a, b))))), inference(lemma,lemma(discharge,[]))).
% 22.47/22.69 tff(5099,plain,
% 22.47/22.69 (mult(mult(c, b), mult(c, a)) = mult(c, mult(b, mult(c, a)))),
% 22.47/22.69 inference(unit_resolution,[status(thm)],[5098, 4487, 4360, 4848, 4400, 3865, 4448, 5037, 5012])).
% 22.47/22.69 tff(5100,plain,
% 22.47/22.69 (mult(mult(b, c), mult(c, a)) = mult(mult(c, b), mult(c, a))),
% 22.47/22.69 inference(symmetry,[status(thm)],[2231])).
% 22.47/22.69 tff(5101,plain,
% 22.47/22.69 (mult(mult(b, c), mult(a, c)) = mult(mult(b, c), mult(c, a))),
% 22.47/22.69 inference(symmetry,[status(thm)],[5039])).
% 22.47/22.69 tff(5102,plain,
% 22.47/22.69 (mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), unit), mult(a, c)) = mult(mult(b, c), mult(a, c))),
% 22.47/22.69 inference(symmetry,[status(thm)],[4815])).
% 22.47/22.69 tff(5103,plain,
% 22.47/22.69 (mult(rd(mult(b, c), mult(a, c)), mult(mult(c, mult(a, c)), a)) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), unit), mult(a, c)))),
% 22.47/22.69 inference(symmetry,[status(thm)],[4889])).
% 22.47/22.69 tff(5104,plain,
% 22.47/22.69 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(c, c)), a)) = mult(rd(mult(b, c), mult(a, c)), mult(mult(c, mult(a, c)), a))),
% 22.47/22.69 inference(symmetry,[status(thm)],[4870])).
% 22.47/22.69 tff(5105,plain,
% 22.47/22.69 (mult(mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)), a)),
% 22.47/22.69 inference(symmetry,[status(thm)],[4866])).
% 22.47/22.69 tff(5106,plain,
% 22.47/22.69 ((~![A: $i] : (mult(unit, A) = A)) | (mult(unit, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))))),
% 22.47/22.69 inference(quant_inst,[status(thm)],[])).
% 22.47/22.69 tff(5107,plain,
% 22.47/22.69 (mult(unit, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))),
% 22.47/22.69 inference(unit_resolution,[status(thm)],[5106, 71])).
% 22.47/22.69 tff(5108,plain,
% 22.47/22.69 (mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))),
% 22.47/22.69 inference(monotonicity,[status(thm)],[1893])).
% 22.47/22.69 tff(5109,plain,
% 22.47/22.69 (mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))) = mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c)))),
% 22.47/22.69 inference(symmetry,[status(thm)],[5108])).
% 22.47/22.69 tff(5110,plain,
% 22.47/22.69 (mult(unit, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))) = mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c)))),
% 22.47/22.69 inference(transitivity,[status(thm)],[5107, 5109])).
% 22.47/22.69 tff(5111,plain,
% 22.47/22.69 (mult(mult(unit, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 22.47/22.69 inference(monotonicity,[status(thm)],[4367])).
% 22.47/22.69 tff(5112,plain,
% 22.47/22.69 (mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(unit, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c)))),
% 22.47/22.69 inference(symmetry,[status(thm)],[5111])).
% 22.47/22.69 tff(5113,plain,
% 22.47/22.69 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(a, mult(a, mult(c, rd(mult(b, c), mult(a, c))))) = mult(c, rd(mult(b, c), mult(a, c))))),
% 22.47/22.69 inference(quant_inst,[status(thm)],[])).
% 22.47/22.69 tff(5114,plain,
% 22.47/22.69 (ld(a, mult(a, mult(c, rd(mult(b, c), mult(a, c))))) = mult(c, rd(mult(b, c), mult(a, c)))),
% 22.47/22.69 inference(unit_resolution,[status(thm)],[5113, 7])).
% 22.47/22.69 tff(5115,plain,
% 22.47/22.69 (mult(rd(mult(b, c), mult(a, c)), c) = mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)),
% 22.47/22.69 inference(symmetry,[status(thm)],[2355])).
% 22.47/22.69 tff(5116,plain,
% 22.47/22.69 (mult(a, mult(rd(mult(b, c), mult(a, c)), c)) = mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c))),
% 22.47/22.69 inference(monotonicity,[status(thm)],[5115])).
% 22.47/22.69 tff(5117,plain,
% 22.47/22.69 (mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), c))),
% 22.47/22.69 inference(symmetry,[status(thm)],[5116])).
% 22.47/22.69 tff(5118,plain,
% 22.47/22.69 (((~(mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))),
% 22.47/22.69 inference(tautology,[status(thm)],[])).
% 22.47/22.69 tff(5119,plain,
% 22.47/22.69 (mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))),
% 22.47/22.69 inference(unit_resolution,[status(thm)],[5118, 4847])).
% 22.47/22.69 tff(5120,plain,
% 22.47/22.69 (mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))) = mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c))),
% 22.47/22.69 inference(symmetry,[status(thm)],[5119])).
% 22.47/22.69 tff(5121,plain,
% 22.47/22.69 (mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))) = mult(a, mult(c, rd(mult(b, c), mult(a, c))))),
% 22.47/22.69 inference(monotonicity,[status(thm)],[2218])).
% 22.47/22.69 tff(5122,plain,
% 22.47/22.69 (mult(a, mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))),
% 22.47/22.69 inference(symmetry,[status(thm)],[5121])).
% 22.47/22.69 tff(5123,plain,
% 22.47/22.69 (mult(a, mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), c))),
% 22.47/22.69 inference(transitivity,[status(thm)],[5122, 5120, 5117])).
% 22.47/22.69 tff(5124,plain,
% 22.47/22.69 (ld(a, mult(a, mult(c, rd(mult(b, c), mult(a, c))))) = ld(a, mult(a, mult(rd(mult(b, c), mult(a, c)), c)))),
% 22.47/22.69 inference(monotonicity,[status(thm)],[5123])).
% 22.47/22.69 tff(5125,plain,
% 22.47/22.69 (ld(a, mult(a, mult(rd(mult(b, c), mult(a, c)), c))) = ld(a, mult(a, mult(c, rd(mult(b, c), mult(a, c)))))),
% 22.47/22.69 inference(symmetry,[status(thm)],[5124])).
% 22.47/22.69 tff(5126,plain,
% 22.47/22.69 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(a, mult(a, mult(rd(mult(b, c), mult(a, c)), c))) = mult(rd(mult(b, c), mult(a, c)), c))),
% 22.47/22.69 inference(quant_inst,[status(thm)],[])).
% 22.47/22.69 tff(5127,plain,
% 22.47/22.69 (ld(a, mult(a, mult(rd(mult(b, c), mult(a, c)), c))) = mult(rd(mult(b, c), mult(a, c)), c)),
% 22.47/22.69 inference(unit_resolution,[status(thm)],[5126, 7])).
% 22.47/22.69 tff(5128,plain,
% 22.47/22.69 (mult(rd(mult(b, c), mult(a, c)), c) = ld(a, mult(a, mult(rd(mult(b, c), mult(a, c)), c)))),
% 22.47/22.69 inference(symmetry,[status(thm)],[5127])).
% 22.47/22.69 tff(5129,plain,
% 22.47/22.69 (mult(rd(mult(b, c), mult(a, c)), c) = mult(c, rd(mult(b, c), mult(a, c)))),
% 22.47/22.69 inference(transitivity,[status(thm)],[5128, 5125, 5114])).
% 22.47/22.69 tff(5130,plain,
% 22.47/22.69 (mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c))))),
% 22.47/22.69 inference(monotonicity,[status(thm)],[3874, 5129])).
% 22.47/22.69 tff(5131,plain,
% 22.47/22.69 (mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c))),
% 22.47/22.69 inference(symmetry,[status(thm)],[5130])).
% 22.47/22.69 tff(5132,plain,
% 22.47/22.69 (mult(mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a)),
% 22.47/22.69 inference(monotonicity,[status(thm)],[5131])).
% 22.47/22.69 tff(5133,plain,
% 22.47/22.69 (mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c)))), a)),
% 22.47/22.69 inference(symmetry,[status(thm)],[5132])).
% 22.47/22.69 tff(5134,plain,
% 22.47/22.69 ((mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), c)) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)), c)) <=> (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)), c) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), c)))),
% 22.47/22.69 inference(commutativity,[status(thm)],[])).
% 22.47/22.69 tff(5135,plain,
% 22.47/22.69 (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)), c) = mult(mult(a, mult(b, c)), c)),
% 22.47/22.69 inference(monotonicity,[status(thm)],[4286])).
% 22.47/22.69 tff(5136,plain,
% 22.47/22.69 (mult(mult(a, mult(b, c)), c) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)), c)),
% 22.47/22.69 inference(symmetry,[status(thm)],[5135])).
% 22.47/22.69 tff(5137,plain,
% 22.47/22.69 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)), c)),
% 22.47/22.69 inference(transitivity,[status(thm)],[1039, 138, 266, 5136])).
% 22.47/22.69 tff(5138,plain,
% 22.47/22.69 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), c))),
% 22.47/22.69 inference(monotonicity,[status(thm)],[4435, 3878])).
% 22.47/22.69 tff(5139,plain,
% 22.47/22.69 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(c, a), c)) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, mult(a, c)))),
% 22.47/22.69 inference(monotonicity,[status(thm)],[2690])).
% 22.47/22.69 tff(5140,plain,
% 22.47/22.69 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a), c) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(c, a), c)))),
% 22.47/22.69 inference(quant_inst,[status(thm)],[])).
% 22.47/22.69 tff(5141,plain,
% 22.47/22.69 (mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a), c) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(c, a), c))),
% 22.47/22.69 inference(unit_resolution,[status(thm)],[5140, 56])).
% 22.47/22.69 tff(5142,plain,
% 22.47/22.69 (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), c) = mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a), c)),
% 22.47/22.69 inference(monotonicity,[status(thm)],[1169])).
% 22.47/22.69 tff(5143,plain,
% 22.47/22.69 (mult(mult(rd(mult(b, c), mult(a, c)), a), c) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))),
% 22.47/22.69 inference(transitivity,[status(thm)],[4491, 2189, 4848, 2172, 2178, 2177, 2162])).
% 22.47/22.69 tff(5144,plain,
% 22.47/22.69 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)),
% 22.47/22.69 inference(monotonicity,[status(thm)],[5143])).
% 22.47/22.69 tff(5145,plain,
% 22.47/22.69 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a)),
% 22.47/22.69 inference(symmetry,[status(thm)],[5144])).
% 22.47/22.69 tff(5146,plain,
% 22.47/22.69 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))),
% 22.47/22.69 inference(transitivity,[status(thm)],[5145, 1168])).
% 22.47/22.69 tff(5147,plain,
% 22.47/22.69 (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), c)),
% 22.47/22.69 inference(monotonicity,[status(thm)],[5146])).
% 22.47/22.69 tff(5148,plain,
% 22.47/22.69 (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), c))),
% 22.47/22.69 inference(transitivity,[status(thm)],[5147, 5142, 5141, 5139, 5138])).
% 22.47/22.69 tff(5149,plain,
% 22.47/22.69 ((mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))) <=> (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), c)) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)), c))),
% 22.47/22.69 inference(monotonicity,[status(thm)],[5148, 5137])).
% 22.47/22.69 tff(5150,plain,
% 22.47/22.69 ((mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))) <=> (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)), c) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), c)))),
% 22.47/22.69 inference(transitivity,[status(thm)],[5149, 5134])).
% 22.47/22.69 tff(5151,plain,
% 22.47/22.69 ((~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))) <=> (~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)), c) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), c))))),
% 22.47/22.69 inference(monotonicity,[status(thm)],[5150])).
% 22.47/22.69 tff(5152,plain,
% 22.47/22.69 (~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)), c) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), c)))),
% 22.47/22.69 inference(modus_ponens,[status(thm)],[4482, 5151])).
% 22.47/22.69 tff(5153,plain,
% 22.47/22.69 (mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))) = mult(mult(unit, mult(c, mult(a, c))), b)),
% 22.47/22.69 inference(transitivity,[status(thm)],[4539, 4372, 234, 4371, 4370, 4369])).
% 22.47/22.69 tff(5154,plain,
% 22.47/22.69 (mult(mult(rd(mult(b, c), mult(a, c)), c), a) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))),
% 22.47/22.69 inference(transitivity,[status(thm)],[83, 4360, 4340, 5044, 2189, 2187, 2172, 2178, 2177, 2162])).
% 22.47/22.69 tff(5155,plain,
% 22.47/22.69 (mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)) = mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 22.47/22.69 inference(monotonicity,[status(thm)],[5154])).
% 22.47/22.69 tff(5156,assumption,(~((~(mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a))) | (~(mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)))))), introduced(assumption)).
% 22.47/22.69 tff(5157,plain,
% 22.47/22.69 (((~(mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a))) | (~(mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a))))) | (mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)))),
% 22.54/22.70 inference(tautology,[status(thm)],[])).
% 22.54/22.70 tff(5158,plain,
% 22.54/22.70 (mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a))),
% 22.54/22.70 inference(unit_resolution,[status(thm)],[5157, 5156])).
% 22.54/22.70 tff(5159,assumption,(mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))), introduced(assumption)).
% 22.54/22.70 tff(5160,plain,
% 22.54/22.70 (mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))) = mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c))),
% 22.54/22.70 inference(symmetry,[status(thm)],[5159])).
% 22.54/22.70 tff(5161,plain,
% 22.54/22.70 (mult(a, mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), c))),
% 22.54/22.70 inference(transitivity,[status(thm)],[5122, 5160, 5117])).
% 22.54/22.70 tff(5162,plain,
% 22.54/22.70 (mult(mult(c, a), mult(a, mult(c, rd(mult(b, c), mult(a, c))))) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c)))),
% 22.54/22.70 inference(monotonicity,[status(thm)],[3885, 5161])).
% 22.54/22.70 tff(5163,plain,
% 22.54/22.70 (mult(mult(a, c), mult(a, mult(c, rd(mult(b, c), mult(a, c))))) = mult(mult(c, a), mult(a, mult(c, rd(mult(b, c), mult(a, c)))))),
% 22.54/22.70 inference(monotonicity,[status(thm)],[3874])).
% 22.54/22.70 tff(5164,plain,
% 22.54/22.70 (mult(mult(a, c), mult(a, mult(c, rd(mult(b, c), mult(a, c))))) = mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 22.54/22.70 inference(transitivity,[status(thm)],[5163, 5162, 5158, 5155])).
% 22.54/22.70 tff(5165,plain,
% 22.54/22.70 (ld(mult(a, c), mult(mult(a, c), mult(a, mult(c, rd(mult(b, c), mult(a, c)))))) = ld(mult(a, c), mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 22.54/22.70 inference(monotonicity,[status(thm)],[5164])).
% 22.54/22.70 tff(5166,plain,
% 22.54/22.70 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(a, c), mult(mult(a, c), mult(a, mult(c, rd(mult(b, c), mult(a, c)))))) = mult(a, mult(c, rd(mult(b, c), mult(a, c)))))),
% 22.54/22.70 inference(quant_inst,[status(thm)],[])).
% 22.54/22.70 tff(5167,plain,
% 22.54/22.70 (ld(mult(a, c), mult(mult(a, c), mult(a, mult(c, rd(mult(b, c), mult(a, c)))))) = mult(a, mult(c, rd(mult(b, c), mult(a, c))))),
% 22.54/22.70 inference(unit_resolution,[status(thm)],[5166, 7])).
% 22.54/22.70 tff(5168,plain,
% 22.54/22.70 (mult(a, mult(c, rd(mult(b, c), mult(a, c)))) = ld(mult(a, c), mult(mult(a, c), mult(a, mult(c, rd(mult(b, c), mult(a, c))))))),
% 22.54/22.70 inference(symmetry,[status(thm)],[5167])).
% 22.54/22.70 tff(5169,plain,
% 22.54/22.70 (mult(a, mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))),
% 22.54/22.70 inference(transitivity,[status(thm)],[5168, 5165, 295])).
% 22.54/22.70 tff(5170,plain,
% 22.54/22.70 (mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))),
% 22.54/22.70 inference(monotonicity,[status(thm)],[5169])).
% 22.54/22.70 tff(5171,plain,
% 22.54/22.70 (mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(mult(unit, b), mult(c, mult(a, c)))),
% 22.54/22.70 inference(transitivity,[status(thm)],[5170, 1039, 138, 266, 4544, 2570, 4396, 4395])).
% 22.54/22.70 tff(5172,plain,
% 22.54/22.70 ((mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))) <=> (mult(mult(unit, b), mult(c, mult(a, c))) = mult(mult(unit, mult(c, mult(a, c))), b))),
% 22.54/22.70 inference(monotonicity,[status(thm)],[5171, 5153])).
% 22.54/22.70 tff(5173,plain,
% 22.54/22.70 ((mult(mult(unit, b), mult(c, mult(a, c))) = mult(mult(unit, mult(c, mult(a, c))), b)) <=> (mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))),
% 22.54/22.70 inference(symmetry,[status(thm)],[5172])).
% 22.54/22.70 tff(5174,plain,
% 22.54/22.70 ((~(mult(mult(unit, b), mult(c, mult(a, c))) = mult(mult(unit, mult(c, mult(a, c))), b))) <=> (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))))),
% 22.54/22.70 inference(monotonicity,[status(thm)],[5173])).
% 22.54/22.70 tff(5175,plain,
% 22.54/22.70 (mult(a, mult(mult(b, c), c)) = mult(mult(unit, mult(c, mult(a, c))), b)),
% 22.54/22.70 inference(transitivity,[status(thm)],[4372, 234, 4371, 4370, 4369])).
% 22.54/22.70 tff(5176,plain,
% 22.54/22.70 ((mult(mult(a, mult(b, c)), c) = mult(a, mult(mult(b, c), c))) <=> (mult(mult(unit, b), mult(c, mult(a, c))) = mult(mult(unit, mult(c, mult(a, c))), b))),
% 22.54/22.70 inference(monotonicity,[status(thm)],[4555, 5175])).
% 22.54/22.70 tff(5177,plain,
% 22.54/22.70 ((~(mult(mult(a, mult(b, c)), c) = mult(a, mult(mult(b, c), c)))) <=> (~(mult(mult(unit, b), mult(c, mult(a, c))) = mult(mult(unit, mult(c, mult(a, c))), b)))),
% 22.54/22.70 inference(monotonicity,[status(thm)],[5176])).
% 22.54/22.70 tff(5178,plain,
% 22.54/22.70 (~(mult(mult(unit, b), mult(c, mult(a, c))) = mult(mult(unit, mult(c, mult(a, c))), b))),
% 22.54/22.70 inference(modus_ponens,[status(thm)],[258, 5177])).
% 22.54/22.70 tff(5179,plain,
% 22.54/22.70 (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))),
% 22.54/22.70 inference(modus_ponens,[status(thm)],[5178, 5174])).
% 22.54/22.70 tff(5180,plain,
% 22.54/22.70 ((~(mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))))),
% 22.54/22.70 inference(unit_resolution,[status(thm)],[4560, 5179])).
% 22.54/22.70 tff(5181,plain,
% 22.54/22.70 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(a, mult(b, c))),
% 22.54/22.70 inference(transitivity,[status(thm)],[287, 142])).
% 22.54/22.70 tff(5182,plain,
% 22.54/22.70 (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)), c) = mult(mult(a, mult(b, c)), c)),
% 22.54/22.70 inference(monotonicity,[status(thm)],[5181])).
% 22.54/22.70 tff(5183,plain,
% 22.54/22.70 (mult(mult(a, mult(b, c)), c) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)), c)),
% 22.54/22.70 inference(symmetry,[status(thm)],[5182])).
% 22.54/22.70 tff(5184,plain,
% 22.54/22.70 (mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)), c)),
% 22.54/22.70 inference(transitivity,[status(thm)],[5170, 1039, 138, 266, 5183])).
% 22.54/22.70 tff(5185,plain,
% 22.54/22.70 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), c))),
% 22.54/22.70 inference(monotonicity,[status(thm)],[4413, 3878])).
% 22.54/22.70 tff(5186,plain,
% 22.54/22.70 (mult(mult(rd(mult(b, c), mult(a, c)), a), c) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))),
% 22.54/22.70 inference(transitivity,[status(thm)],[5044, 2189, 2187, 2172, 2178, 2177, 2162])).
% 22.54/22.70 tff(5187,plain,
% 22.54/22.70 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)),
% 22.54/22.70 inference(monotonicity,[status(thm)],[5186])).
% 22.54/22.70 tff(5188,plain,
% 22.54/22.70 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a)),
% 22.54/22.70 inference(symmetry,[status(thm)],[5187])).
% 22.54/22.70 tff(5189,plain,
% 22.54/22.70 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))),
% 22.54/22.70 inference(transitivity,[status(thm)],[5188, 1168])).
% 22.54/22.70 tff(5190,plain,
% 22.54/22.70 (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), c)),
% 22.54/22.70 inference(monotonicity,[status(thm)],[5189])).
% 22.54/22.70 tff(5191,plain,
% 22.54/22.70 (mult(a, mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))),
% 22.54/22.70 inference(transitivity,[status(thm)],[5116, 5159, 5121, 5168, 5165, 295])).
% 22.54/22.70 tff(5192,plain,
% 22.54/22.70 (mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)),
% 22.54/22.70 inference(monotonicity,[status(thm)],[5191])).
% 22.54/22.70 tff(5193,plain,
% 22.54/22.70 (mult(c, mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a)) = mult(mult(unit, c), mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))),
% 22.54/22.70 inference(monotonicity,[status(thm)],[74, 5192])).
% 22.54/22.70 tff(5194,plain,
% 22.54/22.70 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(c, a), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(c, mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a)))),
% 22.54/22.70 inference(quant_inst,[status(thm)],[])).
% 22.54/22.70 tff(5195,plain,
% 22.54/22.70 (mult(mult(mult(c, a), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(c, mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a))),
% 22.54/22.70 inference(unit_resolution,[status(thm)],[5194, 56])).
% 22.54/22.70 tff(5196,plain,
% 22.54/22.70 (mult(mult(c, a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c))),
% 22.54/22.70 inference(monotonicity,[status(thm)],[3885])).
% 22.54/22.70 tff(5197,plain,
% 22.54/22.70 (mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(c, a), mult(rd(mult(b, c), mult(a, c)), c))),
% 22.54/22.70 inference(symmetry,[status(thm)],[5196])).
% 22.54/22.70 tff(5198,plain,
% 22.54/22.70 (mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(c, a), mult(rd(mult(b, c), mult(a, c)), c)), a)),
% 22.54/22.70 inference(monotonicity,[status(thm)],[5197])).
% 22.54/22.70 tff(5199,plain,
% 22.54/22.70 (((~(mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a))) | (~(mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a))))) | (mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a))),
% 22.54/22.70 inference(tautology,[status(thm)],[])).
% 22.54/22.70 tff(5200,plain,
% 22.54/22.70 (mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a)),
% 22.54/22.70 inference(unit_resolution,[status(thm)],[5199, 5156])).
% 22.54/22.70 tff(5201,plain,
% 22.54/22.70 (ld(a, mult(a, mult(c, rd(mult(b, c), mult(a, c))))) = ld(a, mult(a, mult(rd(mult(b, c), mult(a, c)), c)))),
% 22.54/22.70 inference(monotonicity,[status(thm)],[5161])).
% 22.54/22.70 tff(5202,plain,
% 22.54/22.70 (mult(c, rd(mult(b, c), mult(a, c))) = ld(a, mult(a, mult(c, rd(mult(b, c), mult(a, c)))))),
% 22.54/22.70 inference(symmetry,[status(thm)],[5114])).
% 22.54/22.70 tff(5203,plain,
% 22.54/22.70 (mult(c, rd(mult(b, c), mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), c)),
% 22.54/22.70 inference(transitivity,[status(thm)],[5202, 5201, 5127])).
% 22.54/22.70 tff(5204,plain,
% 22.54/22.70 (mult(mult(mult(a, c), a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c))),
% 22.54/22.70 inference(monotonicity,[status(thm)],[5203])).
% 22.54/22.70 tff(5205,plain,
% 22.54/22.70 (mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, c), a), mult(c, rd(mult(b, c), mult(a, c))))),
% 22.54/22.70 inference(monotonicity,[status(thm)],[4519])).
% 22.54/22.70 tff(5206,plain,
% 22.54/22.70 (mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), c))),
% 22.54/22.70 inference(transitivity,[status(thm)],[5205, 5204, 5200, 5198, 5195, 5193, 5069, 4898, 2830, 2231, 5039, 4815, 2501, 5064, 4870, 4661, 5055, 5051, 4528, 5190, 5142, 5141, 5139, 5185])).
% 22.54/22.70 tff(5207,plain,
% 22.54/22.70 ((mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c))) <=> (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), c)) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)), c))),
% 22.54/22.70 inference(monotonicity,[status(thm)],[5206, 5184])).
% 22.54/22.70 tff(5208,plain,
% 22.54/22.70 ((mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c))) <=> (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)), c) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), c)))),
% 22.54/22.70 inference(transitivity,[status(thm)],[5207, 5134])).
% 22.54/22.70 tff(5209,plain,
% 22.54/22.70 ((mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)), c) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), c))) <=> (mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)))),
% 22.54/22.70 inference(symmetry,[status(thm)],[5208])).
% 22.54/22.70 tff(5210,plain,
% 22.54/22.70 ((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)), c) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), c)))) <=> (~(mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c))))),
% 22.54/22.70 inference(monotonicity,[status(thm)],[5209])).
% 22.54/22.70 tff(5211,assumption,(~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)), c) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), c)))), introduced(assumption)).
% 22.54/22.71 tff(5212,plain,
% 22.54/22.71 (~(mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)))),
% 22.54/22.71 inference(modus_ponens,[status(thm)],[5211, 5210])).
% 22.54/22.71 tff(5213,plain,
% 22.54/22.71 ((~(mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)))) | (~(mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))))),
% 22.54/22.71 inference(unit_resolution,[status(thm)],[4606, 5212])).
% 22.54/22.71 tff(5214,plain,
% 22.54/22.71 ($false),
% 22.54/22.71 inference(unit_resolution,[status(thm)],[4565, 5213, 5180])).
% 22.54/22.71 tff(5215,plain,(((~(mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a))) | (~(mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a))))) | (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)), c) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), c))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))) | (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (~(mult(mult(c, b), mult(c, a)) = mult(c, mult(b, mult(c, a))))) | (~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a)))), inference(lemma,lemma(discharge,[]))).
% 22.54/22.71 tff(5216,plain,
% 22.54/22.71 ((~(mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a))) | (~(mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a))))),
% 22.54/22.71 inference(unit_resolution,[status(thm)],[5215, 5152, 1039, 4360, 4848, 4400, 5119, 3865, 279, 5099, 4487, 4448, 4390, 4432])).
% 22.54/22.71 tff(5217,plain,
% 22.54/22.71 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a))) | (~(mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)))))) | (~((~(mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))) | (~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a))) | (~(mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)))))) | (~((~(mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))) | (~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)))))))),
% 22.54/22.71 inference(rewrite,[status(thm)],[])).
% 22.54/22.71 tff(5218,plain,
% 22.54/22.71 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a))) | (~(mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)))))) | (~((~(mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))) | (~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)))))))),
% 22.54/22.71 inference(quant_inst,[status(thm)],[])).
% 22.54/22.71 tff(5219,plain,
% 22.54/22.71 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a))) | (~(mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)))))) | (~((~(mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))) | (~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a))))))),
% 22.54/22.71 inference(modus_ponens,[status(thm)],[5218, 5217])).
% 22.54/22.71 tff(5220,plain,
% 22.54/22.71 ((~((~(mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a))) | (~(mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)))))) | (~((~(mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))) | (~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a))))))),
% 22.54/22.71 inference(unit_resolution,[status(thm)],[5219, 27])).
% 22.54/22.71 tff(5221,plain,
% 22.54/22.71 (~((~(mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))) | (~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)))))),
% 22.54/22.71 inference(unit_resolution,[status(thm)],[5220, 5216])).
% 22.54/22.71 tff(5222,plain,
% 22.54/22.71 (((~(mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))) | (~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a))))) | (mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)))),
% 22.54/22.71 inference(tautology,[status(thm)],[])).
% 22.54/22.71 tff(5223,plain,
% 22.54/22.71 (mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a))),
% 22.54/22.71 inference(unit_resolution,[status(thm)],[5222, 5221])).
% 22.54/22.71 tff(5224,plain,
% 22.54/22.71 (mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a)),
% 22.54/22.71 inference(symmetry,[status(thm)],[5223])).
% 22.54/22.71 tff(5225,plain,
% 22.54/22.71 (mult(mult(rd(mult(b, c), mult(a, c)), c), a) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))),
% 22.54/22.71 inference(transitivity,[status(thm)],[83, 4360, 4340, 4491, 2189, 4848, 2172, 2178, 2177, 2162])).
% 22.54/22.71 tff(5226,plain,
% 22.54/22.71 (mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)) = mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 22.54/22.71 inference(monotonicity,[status(thm)],[5225])).
% 22.54/22.71 tff(5227,plain,
% 22.54/22.71 (mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a))),
% 22.54/22.71 inference(symmetry,[status(thm)],[5226])).
% 22.54/22.71 tff(5228,plain,
% 22.54/22.71 (mult(mult(a, c), mult(a, c)) = mult(mult(mult(a, c), c), a)),
% 22.54/22.71 inference(transitivity,[status(thm)],[4887, 4886, 4876, 2562, 4872, 4868])).
% 22.54/22.71 tff(5229,plain,
% 22.54/22.71 (mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(mult(a, c), c), a), rd(mult(b, c), mult(a, c)))),
% 22.54/22.71 inference(monotonicity,[status(thm)],[5228])).
% 22.54/22.71 tff(5230,plain,
% 22.54/22.71 (mult(mult(mult(mult(a, c), c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 22.54/22.71 inference(symmetry,[status(thm)],[5229])).
% 22.54/22.71 tff(5231,plain,
% 22.54/22.71 (mult(mult(mult(mult(a, c), c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c)))),
% 22.54/22.71 inference(monotonicity,[status(thm)],[4867])).
% 22.54/22.71 tff(5232,plain,
% 22.54/22.71 (mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(mult(a, c), c), a), rd(mult(b, c), mult(a, c)))),
% 22.54/22.71 inference(symmetry,[status(thm)],[5231])).
% 22.54/22.71 tff(5233,plain,
% 22.54/22.71 (mult(c, mult(a, mult(a, c))) = mult(mult(c, a), mult(a, c))),
% 22.54/22.71 inference(symmetry,[status(thm)],[5062])).
% 22.54/22.71 tff(5234,plain,
% 22.54/22.71 (mult(mult(mult(a, c), c), a) = mult(mult(a, c), mult(a, c))),
% 22.54/22.71 inference(transitivity,[status(thm)],[4867, 4871, 2561, 5056, 5233, 4880])).
% 22.54/22.71 tff(5235,plain,
% 22.54/22.71 (mult(mult(mult(mult(a, c), c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 22.54/22.71 inference(monotonicity,[status(thm)],[5234])).
% 22.54/22.71 tff(5236,plain,
% 22.54/22.71 (mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(mult(a, c), c), a), rd(mult(b, c), mult(a, c)))),
% 22.54/22.71 inference(monotonicity,[status(thm)],[4868])).
% 22.54/22.71 tff(5237,plain,
% 22.54/22.71 (mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))) = mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 22.54/22.71 inference(transitivity,[status(thm)],[5236, 5235, 4789, 4788])).
% 22.54/22.71 tff(5238,plain,
% 22.54/22.71 ((mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c)))) <=> (mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 22.54/22.71 inference(monotonicity,[status(thm)],[4786, 5237])).
% 22.54/22.71 tff(5239,plain,
% 22.54/22.71 ((mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c))))) <=> (mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))))),
% 22.54/22.71 inference(symmetry,[status(thm)],[5238])).
% 22.54/22.71 tff(5240,assumption,(~(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))))), introduced(assumption)).
% 22.54/22.71 tff(5241,plain,
% 22.54/22.71 (((~(mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c)))))) | (mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))))),
% 22.54/22.71 inference(tautology,[status(thm)],[])).
% 22.54/22.71 tff(5242,plain,
% 22.54/22.71 ((~(mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c)))))),
% 22.54/22.71 inference(unit_resolution,[status(thm)],[5241, 5240])).
% 22.54/22.71 tff(5243,plain,
% 22.54/22.71 ((~((~(mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))))))) | (~((~(mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a))))))),
% 22.54/22.71 inference(unit_resolution,[status(thm)],[2402, 27])).
% 22.54/22.71 tff(5244,plain,
% 22.54/22.71 (~((~(mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)))))),
% 22.54/22.71 inference(unit_resolution,[status(thm)],[5243, 5242])).
% 22.54/22.71 tff(5245,plain,
% 22.54/22.71 (mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a))),
% 22.54/22.71 inference(unit_resolution,[status(thm)],[2408, 5244])).
% 22.54/22.71 tff(5246,plain,
% 22.54/22.71 (mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a)),
% 22.54/22.71 inference(symmetry,[status(thm)],[5245])).
% 22.54/22.71 tff(5247,plain,
% 22.54/22.71 (mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c))))),
% 22.54/22.71 inference(monotonicity,[status(thm)],[4413])).
% 22.54/22.71 tff(5248,plain,
% 22.54/22.71 (mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a))),
% 22.54/22.71 inference(symmetry,[status(thm)],[5247])).
% 22.54/22.71 tff(5249,plain,
% 22.54/22.71 (mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a)),
% 22.54/22.71 inference(transitivity,[status(thm)],[5248, 5246, 4786])).
% 22.54/22.71 tff(5250,plain,
% 22.54/22.71 ((mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c))))) <=> (mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a))),
% 22.54/22.71 inference(monotonicity,[status(thm)],[5237, 5249])).
% 22.54/22.71 tff(5251,plain,
% 22.54/22.71 ((mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c))))) <=> (mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 22.54/22.71 inference(transitivity,[status(thm)],[5250, 4783])).
% 22.54/22.71 tff(5252,plain,
% 22.54/22.71 ((mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c))))) <=> (mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))))),
% 22.54/22.71 inference(transitivity,[status(thm)],[5251, 5239])).
% 22.54/22.71 tff(5253,plain,
% 22.54/22.71 (((~(mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a))))) | (mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))),
% 22.54/22.71 inference(tautology,[status(thm)],[])).
% 22.54/22.71 tff(5254,plain,
% 22.54/22.71 (mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c))))),
% 22.54/22.72 inference(unit_resolution,[status(thm)],[5253, 5244])).
% 22.54/22.72 tff(5255,plain,
% 22.54/22.72 (mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c)))),
% 22.54/22.72 inference(modus_ponens,[status(thm)],[5254, 5252])).
% 22.54/22.72 tff(5256,plain,
% 22.54/22.72 ($false),
% 22.54/22.72 inference(unit_resolution,[status(thm)],[5240, 5255])).
% 22.54/22.72 tff(5257,plain,((mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c)))) | (~(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit))))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))), inference(lemma,lemma(discharge,[]))).
% 22.54/22.72 tff(5258,plain,
% 22.54/22.72 (mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c)))),
% 22.54/22.72 inference(unit_resolution,[status(thm)],[5257, 4448, 4400, 4789, 3865, 4495])).
% 22.54/22.72 tff(5259,plain,
% 22.54/22.72 (mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c)))), a)),
% 22.54/22.72 inference(transitivity,[status(thm)],[5258, 5232, 5230, 4789, 5227, 5224, 5133])).
% 22.54/22.72 tff(5260,plain,
% 22.54/22.72 (rd(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a), a) = rd(mult(mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c)))), a), a)),
% 22.54/22.72 inference(monotonicity,[status(thm)],[5259])).
% 22.54/22.72 tff(5261,plain,
% 22.54/22.72 (rd(mult(mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c)))), a), a) = rd(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a), a)),
% 22.54/22.72 inference(symmetry,[status(thm)],[5260])).
% 22.54/22.72 tff(5262,plain,
% 22.54/22.72 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c)))), a), a) = mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c)))))),
% 22.54/22.72 inference(quant_inst,[status(thm)],[])).
% 22.54/22.72 tff(5263,plain,
% 22.54/22.72 (rd(mult(mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c)))), a), a) = mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c))))),
% 22.54/22.72 inference(unit_resolution,[status(thm)],[5262, 168])).
% 22.54/22.72 tff(5264,plain,
% 22.54/22.72 (mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c)))) = rd(mult(mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c)))), a), a)),
% 22.54/22.72 inference(symmetry,[status(thm)],[5263])).
% 22.54/22.72 tff(5265,plain,
% 22.54/22.72 (mult(c, a) = mult(unit, mult(a, c))),
% 22.54/22.72 inference(transitivity,[status(thm)],[3884, 3869, 3872, 1551])).
% 22.54/22.72 tff(5266,plain,
% 22.54/22.72 (mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(unit, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c))))),
% 22.54/22.72 inference(monotonicity,[status(thm)],[5265])).
% 22.54/22.72 tff(5267,plain,
% 22.54/22.72 (mult(mult(unit, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c))))),
% 22.54/22.72 inference(symmetry,[status(thm)],[5266])).
% 22.54/22.72 tff(5268,plain,
% 22.54/22.72 (mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))),
% 22.54/22.72 inference(monotonicity,[status(thm)],[5129])).
% 22.54/22.72 tff(5269,plain,
% 22.54/22.72 ((~![A: $i] : (mult(unit, A) = A)) | (mult(unit, mult(rd(mult(b, c), mult(a, c)), c)) = mult(rd(mult(b, c), mult(a, c)), c))),
% 22.54/22.72 inference(quant_inst,[status(thm)],[])).
% 22.54/22.72 tff(5270,plain,
% 22.54/22.72 (mult(unit, mult(rd(mult(b, c), mult(a, c)), c)) = mult(rd(mult(b, c), mult(a, c)), c)),
% 22.54/22.72 inference(unit_resolution,[status(thm)],[5269, 71])).
% 22.54/22.72 tff(5271,plain,
% 22.54/22.72 (mult(c, rd(mult(b, c), mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), c)),
% 22.54/22.72 inference(transitivity,[status(thm)],[5202, 5124, 5127])).
% 22.54/22.72 tff(5272,plain,
% 22.54/22.72 (mult(unit, mult(c, rd(mult(b, c), mult(a, c)))) = mult(unit, mult(rd(mult(b, c), mult(a, c)), c))),
% 22.54/22.72 inference(monotonicity,[status(thm)],[5271])).
% 22.54/22.72 tff(5273,plain,
% 22.54/22.72 (mult(unit, mult(c, rd(mult(b, c), mult(a, c)))) = mult(rd(mult(b, c), mult(a, c)), c)),
% 22.54/22.72 inference(transitivity,[status(thm)],[5272, 5270])).
% 22.54/22.72 tff(5274,plain,
% 22.54/22.72 (mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c))),
% 22.54/22.72 inference(monotonicity,[status(thm)],[5273])).
% 22.54/22.72 tff(5275,plain,
% 22.54/22.72 (mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))),
% 22.54/22.72 inference(transitivity,[status(thm)],[5274, 5268])).
% 22.54/22.72 tff(5276,plain,
% 22.54/22.72 (mult(mult(unit, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 22.54/22.72 inference(transitivity,[status(thm)],[5267, 5264, 5261, 2786])).
% 22.54/22.72 tff(5277,plain,
% 22.54/22.72 ((mult(mult(unit, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c))) <=> (mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 22.54/22.72 inference(monotonicity,[status(thm)],[5276, 5275])).
% 22.54/22.72 tff(5278,plain,
% 22.54/22.72 ((mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))) <=> (mult(mult(unit, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)))),
% 22.54/22.72 inference(symmetry,[status(thm)],[5277])).
% 22.54/22.72 tff(5279,plain,
% 22.54/22.72 ((~(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))) <=> (~(mult(mult(unit, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c))))),
% 22.54/22.72 inference(monotonicity,[status(thm)],[5278])).
% 22.54/22.72 tff(5280,plain,
% 22.54/22.72 (~(mult(mult(unit, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)))),
% 22.54/22.72 inference(modus_ponens,[status(thm)],[4499, 5279])).
% 22.54/22.72 tff(5281,plain,
% 22.54/22.72 (((~(mult(mult(unit, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)))) | (~(mult(unit, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(unit, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))))) | (mult(mult(unit, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)))),
% 22.54/22.72 inference(tautology,[status(thm)],[])).
% 22.54/22.72 tff(5282,plain,
% 22.54/22.72 ((~(mult(mult(unit, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)))) | (~(mult(unit, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(unit, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))))),
% 22.54/22.72 inference(unit_resolution,[status(thm)],[5281, 5280])).
% 22.54/22.72 tff(5283,plain,
% 22.54/22.72 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(unit, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)))) | (~(mult(unit, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(unit, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))))) | (~((~(mult(mult(unit, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(unit, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(unit, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(unit, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)))) | (~(mult(unit, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(unit, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))))) | (~((~(mult(mult(unit, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(unit, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(unit, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))))))),
% 22.54/22.72 inference(rewrite,[status(thm)],[])).
% 22.54/22.72 tff(5284,plain,
% 22.54/22.72 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(unit, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)))) | (~(mult(unit, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(unit, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))))) | (~((~(mult(mult(unit, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(unit, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(unit, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))))))),
% 22.54/22.72 inference(quant_inst,[status(thm)],[])).
% 22.54/22.72 tff(5285,plain,
% 22.54/22.72 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(unit, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)))) | (~(mult(unit, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(unit, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))))) | (~((~(mult(mult(unit, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(unit, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(unit, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))))))),
% 22.54/22.72 inference(modus_ponens,[status(thm)],[5284, 5283])).
% 22.54/22.72 tff(5286,plain,
% 22.54/22.72 ((~((~(mult(mult(unit, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)))) | (~(mult(unit, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(unit, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))))) | (~((~(mult(mult(unit, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(unit, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(unit, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))))))),
% 22.54/22.72 inference(unit_resolution,[status(thm)],[5285, 27])).
% 22.54/22.72 tff(5287,plain,
% 22.54/22.72 (~((~(mult(mult(unit, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(unit, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(unit, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))))),
% 22.54/22.72 inference(unit_resolution,[status(thm)],[5286, 5282])).
% 22.54/22.72 tff(5288,plain,
% 22.54/22.72 (((~(mult(mult(unit, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(unit, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(unit, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(unit, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))))) | (mult(mult(unit, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(unit, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))))),
% 22.54/22.72 inference(tautology,[status(thm)],[])).
% 22.54/22.72 tff(5289,plain,
% 22.54/22.72 (mult(mult(unit, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(unit, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))),
% 22.54/22.72 inference(unit_resolution,[status(thm)],[5288, 5287])).
% 22.54/22.72 tff(5290,plain,
% 22.54/22.72 (mult(unit, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(mult(unit, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c))))),
% 22.54/22.72 inference(symmetry,[status(thm)],[5289])).
% 22.54/22.72 tff(5291,plain,
% 22.54/22.72 (mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 22.54/22.72 inference(transitivity,[status(thm)],[4531, 5264, 5261, 2786])).
% 22.54/22.72 tff(5292,plain,
% 22.54/22.72 (mult(unit, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(unit, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))))),
% 22.54/22.72 inference(monotonicity,[status(thm)],[5291])).
% 22.54/22.72 tff(5293,plain,
% 22.54/22.72 (mult(unit, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))) = mult(unit, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))),
% 22.54/22.72 inference(symmetry,[status(thm)],[5292])).
% 22.54/22.72 tff(5294,plain,
% 22.54/22.72 (mult(unit, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))) = mult(mult(unit, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c)))),
% 22.54/22.72 inference(transitivity,[status(thm)],[5293, 5290, 5267, 5264, 5261, 2786, 5112])).
% 22.54/22.72 tff(5295,plain,
% 22.54/22.72 ((mult(unit, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))) = mult(unit, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))))) <=> (mult(mult(unit, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))))),
% 22.54/22.72 inference(monotonicity,[status(thm)],[5294, 5110])).
% 22.54/22.72 tff(5296,plain,
% 22.54/22.72 ((mult(mult(unit, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c)))) <=> (mult(unit, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))) = mult(unit, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))))),
% 22.54/22.72 inference(symmetry,[status(thm)],[5295])).
% 22.54/22.72 tff(5297,plain,
% 22.54/22.72 ((mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)) <=> (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))))),
% 22.54/22.72 inference(commutativity,[status(thm)],[])).
% 22.54/22.72 tff(5298,plain,
% 22.54/22.72 (mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)),
% 22.54/22.72 inference(transitivity,[status(thm)],[5108, 4860, 4858, 4855, 4854])).
% 22.54/22.72 tff(5299,plain,
% 22.54/22.72 (mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c)))),
% 22.54/22.72 inference(symmetry,[status(thm)],[4530])).
% 22.54/22.72 tff(5300,plain,
% 22.54/22.72 (mult(mult(unit, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c)))),
% 22.54/22.72 inference(transitivity,[status(thm)],[5111, 5299])).
% 22.54/22.72 tff(5301,plain,
% 22.54/22.72 ((mult(mult(unit, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c)))) <=> (mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c))),
% 22.54/22.72 inference(monotonicity,[status(thm)],[5300, 5298])).
% 22.54/22.72 tff(5302,plain,
% 22.54/22.72 ((mult(mult(unit, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c)))) <=> (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))))),
% 22.54/22.72 inference(transitivity,[status(thm)],[5301, 5297])).
% 22.54/22.72 tff(5303,plain,
% 22.54/22.72 ((mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c)))) <=> (mult(mult(unit, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))))),
% 22.54/22.72 inference(symmetry,[status(thm)],[5302])).
% 22.54/22.72 tff(5304,assumption,(~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))))), introduced(assumption)).
% 22.54/22.72 tff(5305,plain,
% 22.54/22.72 ((~(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c)))))),
% 22.54/22.72 inference(unit_resolution,[status(thm)],[4596, 5304])).
% 22.54/22.72 tff(5306,plain,
% 22.54/22.72 (~((~(mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)))))),
% 22.54/22.73 inference(unit_resolution,[status(thm)],[4594, 5305])).
% 22.54/22.73 tff(5307,plain,
% 22.54/22.73 (mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))),
% 22.54/22.73 inference(unit_resolution,[status(thm)],[4582, 5306])).
% 22.54/22.73 tff(5308,plain,
% 22.54/22.73 (mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c)))),
% 22.54/22.73 inference(symmetry,[status(thm)],[5307])).
% 22.54/22.73 tff(5309,plain,
% 22.54/22.73 (mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(c, a), mult(rd(mult(b, c), mult(a, c)), c))),
% 22.54/22.73 inference(monotonicity,[status(thm)],[5203])).
% 22.54/22.73 tff(5310,plain,
% 22.54/22.73 (mult(mult(c, a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c))))),
% 22.54/22.73 inference(symmetry,[status(thm)],[5309])).
% 22.54/22.73 tff(5311,plain,
% 22.54/22.73 (((~(mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c))))) | (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)))),
% 22.54/22.73 inference(tautology,[status(thm)],[])).
% 22.54/22.73 tff(5312,plain,
% 22.54/22.73 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c))),
% 22.54/22.73 inference(unit_resolution,[status(thm)],[5311, 5306])).
% 22.54/22.73 tff(5313,plain,
% 22.54/22.73 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c)))),
% 22.54/22.73 inference(transitivity,[status(thm)],[5312, 5197, 5310, 4569, 5308])).
% 22.54/22.73 tff(5314,plain,
% 22.54/22.73 ($false),
% 22.54/22.73 inference(unit_resolution,[status(thm)],[5304, 5313])).
% 22.54/22.73 tff(5315,plain,((mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c)))) | (~(mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit)))))), inference(lemma,lemma(discharge,[]))).
% 22.54/22.73 tff(5316,plain,
% 22.54/22.73 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c)))),
% 22.54/22.73 inference(unit_resolution,[status(thm)],[5315, 5119, 3865])).
% 22.54/22.73 tff(5317,plain,
% 22.54/22.73 (mult(mult(unit, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c)))),
% 22.54/22.73 inference(modus_ponens,[status(thm)],[5316, 5303])).
% 22.54/22.73 tff(5318,plain,
% 22.54/22.73 (mult(unit, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))) = mult(unit, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))))),
% 22.54/22.73 inference(modus_ponens,[status(thm)],[5317, 5296])).
% 22.54/22.73 tff(5319,plain,
% 22.54/22.73 (mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))),
% 22.54/22.73 inference(transitivity,[status(thm)],[2787, 5260, 5263, 5266, 5289, 5292, 5318, 5107])).
% 22.54/22.73 tff(5320,plain,
% 22.54/22.73 (mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))), a)),
% 22.54/22.73 inference(monotonicity,[status(thm)],[5319])).
% 22.54/22.73 tff(5321,plain,
% 22.54/22.73 (mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a)),
% 22.54/22.73 inference(symmetry,[status(thm)],[5258])).
% 22.54/22.73 tff(5322,plain,
% 22.54/22.73 (mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 22.54/22.73 inference(symmetry,[status(thm)],[4789])).
% 22.54/22.73 tff(5323,plain,
% 22.54/22.73 (mult(mult(mult(c, a), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a)),
% 22.54/22.73 inference(monotonicity,[status(thm)],[5196])).
% 22.54/22.73 tff(5324,plain,
% 22.54/22.73 (mult(c, mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a)) = mult(mult(mult(c, a), mult(rd(mult(b, c), mult(a, c)), c)), a)),
% 22.54/22.73 inference(symmetry,[status(thm)],[5195])).
% 22.54/22.73 tff(5325,plain,
% 22.54/22.73 (mult(c, mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a)) = mult(c, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))),
% 22.54/22.73 inference(transitivity,[status(thm)],[5324, 5323, 5223, 5226, 5322, 5229, 5231, 5321, 5320, 5105, 4660, 5104, 5103, 2502, 5102, 5101, 5100, 5099, 4899, 4895, 4445])).
% 22.54/22.73 tff(5326,plain,
% 22.54/22.73 (ld(c, mult(c, mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a))) = ld(c, mult(c, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)))),
% 22.54/22.73 inference(monotonicity,[status(thm)],[5325])).
% 22.54/22.73 tff(5327,plain,
% 22.54/22.73 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(c, mult(c, mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a))) = mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a))),
% 22.54/22.73 inference(quant_inst,[status(thm)],[])).
% 22.54/22.73 tff(5328,plain,
% 22.54/22.73 (ld(c, mult(c, mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a))) = mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a)),
% 22.54/22.73 inference(unit_resolution,[status(thm)],[5327, 7])).
% 22.54/22.73 tff(5329,plain,
% 22.54/22.73 (mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a) = ld(c, mult(c, mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a)))),
% 22.54/22.73 inference(symmetry,[status(thm)],[5328])).
% 22.54/22.73 tff(5330,plain,
% 22.54/22.73 (mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a)),
% 22.54/22.73 inference(monotonicity,[status(thm)],[5123])).
% 22.54/22.73 tff(5331,plain,
% 22.54/22.73 (mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)),
% 22.54/22.73 inference(transitivity,[status(thm)],[5330, 5329, 5326, 4443])).
% 22.54/22.73 tff(5332,plain,
% 22.54/22.73 (rd(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a), a) = rd(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), a)),
% 22.54/22.73 inference(monotonicity,[status(thm)],[5331])).
% 22.54/22.73 tff(5333,plain,
% 22.54/22.73 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a), a) = mult(a, mult(c, rd(mult(b, c), mult(a, c)))))),
% 22.54/22.73 inference(quant_inst,[status(thm)],[])).
% 22.54/22.73 tff(5334,plain,
% 22.54/22.73 (rd(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a), a) = mult(a, mult(c, rd(mult(b, c), mult(a, c))))),
% 22.54/22.73 inference(unit_resolution,[status(thm)],[5333, 168])).
% 22.54/22.73 tff(5335,plain,
% 22.54/22.73 (mult(a, mult(c, rd(mult(b, c), mult(a, c)))) = rd(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a), a)),
% 22.54/22.73 inference(symmetry,[status(thm)],[5334])).
% 22.54/22.73 tff(5336,plain,
% 22.54/22.73 (mult(a, mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))),
% 22.54/22.73 inference(transitivity,[status(thm)],[5335, 5332, 4441])).
% 22.54/22.73 tff(5337,plain,
% 22.54/22.73 (mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))),
% 22.54/22.73 inference(monotonicity,[status(thm)],[5336])).
% 22.54/22.73 tff(5338,plain,
% 22.54/22.73 (mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(mult(unit, b), mult(c, mult(a, c)))),
% 22.54/22.73 inference(transitivity,[status(thm)],[5337, 1039, 138, 266, 4439, 2570, 4396, 4395])).
% 22.54/22.73 tff(5339,plain,
% 22.54/22.73 ((mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))) <=> (mult(mult(unit, b), mult(c, mult(a, c))) = mult(mult(unit, mult(c, mult(a, c))), b))),
% 22.54/22.73 inference(monotonicity,[status(thm)],[5338, 4393])).
% 22.54/22.73 tff(5340,plain,
% 22.54/22.73 ((mult(mult(unit, b), mult(c, mult(a, c))) = mult(mult(unit, mult(c, mult(a, c))), b)) <=> (mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))),
% 22.54/22.73 inference(symmetry,[status(thm)],[5339])).
% 22.54/22.73 tff(5341,plain,
% 22.54/22.73 ((~(mult(mult(unit, b), mult(c, mult(a, c))) = mult(mult(unit, mult(c, mult(a, c))), b))) <=> (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))))),
% 22.54/22.73 inference(monotonicity,[status(thm)],[5340])).
% 22.54/22.73 tff(5342,plain,
% 22.54/22.73 (mult(mult(a, mult(b, c)), c) = mult(mult(unit, b), mult(c, mult(a, c)))),
% 22.54/22.73 inference(transitivity,[status(thm)],[4439, 2570, 4396, 4395])).
% 22.54/22.73 tff(5343,plain,
% 22.54/22.73 ((mult(mult(a, mult(b, c)), c) = mult(a, mult(mult(b, c), c))) <=> (mult(mult(unit, b), mult(c, mult(a, c))) = mult(mult(unit, mult(c, mult(a, c))), b))),
% 22.54/22.73 inference(monotonicity,[status(thm)],[5342, 5175])).
% 22.54/22.73 tff(5344,plain,
% 22.54/22.73 ((~(mult(mult(a, mult(b, c)), c) = mult(a, mult(mult(b, c), c)))) <=> (~(mult(mult(unit, b), mult(c, mult(a, c))) = mult(mult(unit, mult(c, mult(a, c))), b)))),
% 22.54/22.73 inference(monotonicity,[status(thm)],[5343])).
% 22.54/22.73 tff(5345,plain,
% 22.54/22.73 (~(mult(mult(unit, b), mult(c, mult(a, c))) = mult(mult(unit, mult(c, mult(a, c))), b))),
% 22.54/22.73 inference(modus_ponens,[status(thm)],[258, 5344])).
% 22.54/22.73 tff(5346,plain,
% 22.54/22.73 (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))),
% 22.54/22.73 inference(modus_ponens,[status(thm)],[5345, 5341])).
% 22.54/22.73 tff(5347,plain,
% 22.54/22.73 ((~(mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))))),
% 22.54/22.73 inference(unit_resolution,[status(thm)],[4560, 5346])).
% 22.54/22.73 tff(5348,plain,
% 22.54/22.73 (mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)), c)),
% 22.54/22.73 inference(transitivity,[status(thm)],[5337, 1039, 138, 266, 5136])).
% 22.54/22.73 tff(5349,plain,
% 22.54/22.73 (mult(mult(c, a), mult(a, mult(c, rd(mult(b, c), mult(a, c))))) = mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 22.54/22.73 inference(monotonicity,[status(thm)],[3885, 5336])).
% 22.54/22.73 tff(5350,plain,
% 22.54/22.73 (mult(a, mult(rd(mult(b, c), mult(a, c)), c)) = mult(a, mult(c, rd(mult(b, c), mult(a, c))))),
% 22.54/22.73 inference(transitivity,[status(thm)],[5116, 5119, 5121])).
% 22.54/22.73 tff(5351,plain,
% 22.54/22.73 (mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))) = mult(mult(c, a), mult(a, mult(c, rd(mult(b, c), mult(a, c)))))),
% 22.54/22.73 inference(monotonicity,[status(thm)],[3874, 5350])).
% 22.54/22.73 tff(5352,plain,
% 22.54/22.73 (((~(mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))) | (~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a))))) | (mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))),
% 22.54/22.73 inference(tautology,[status(thm)],[])).
% 22.54/22.73 tff(5353,plain,
% 22.54/22.73 (mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c)))),
% 22.54/22.73 inference(unit_resolution,[status(thm)],[5352, 5221])).
% 22.54/22.73 tff(5354,plain,
% 22.54/22.73 (mult(mult(mult(a, c), a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c))),
% 22.54/22.73 inference(monotonicity,[status(thm)],[5271])).
% 22.54/22.73 tff(5355,plain,
% 22.54/22.73 (mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, c), a), mult(c, rd(mult(b, c), mult(a, c))))),
% 22.54/22.73 inference(monotonicity,[status(thm)],[4453])).
% 22.54/22.73 tff(5356,plain,
% 22.54/22.73 (mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), c))),
% 22.54/22.73 inference(transitivity,[status(thm)],[5355, 5354, 5353, 5351, 5349, 5322, 5229, 5231, 5321, 5320, 4862, 4487, 5147, 5142, 5141, 5139, 5138])).
% 22.54/22.73 tff(5357,plain,
% 22.54/22.73 ((mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c))) <=> (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), c)) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)), c))),
% 22.54/22.73 inference(monotonicity,[status(thm)],[5356, 5348])).
% 22.54/22.73 tff(5358,plain,
% 22.54/22.73 ((mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c))) <=> (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)), c) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), c)))),
% 22.54/22.74 inference(transitivity,[status(thm)],[5357, 5134])).
% 22.54/22.74 tff(5359,plain,
% 22.54/22.74 ((mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)), c) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), c))) <=> (mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)))),
% 22.54/22.74 inference(symmetry,[status(thm)],[5358])).
% 22.54/22.74 tff(5360,plain,
% 22.54/22.74 ((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)), c) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), c)))) <=> (~(mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c))))),
% 22.54/22.74 inference(monotonicity,[status(thm)],[5359])).
% 22.54/22.74 tff(5361,plain,
% 22.54/22.74 (~(mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)))),
% 22.54/22.74 inference(modus_ponens,[status(thm)],[5152, 5360])).
% 22.54/22.74 tff(5362,plain,
% 22.54/22.74 ((~(mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)))) | (~(mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))))),
% 22.54/22.74 inference(unit_resolution,[status(thm)],[4606, 5361])).
% 22.54/22.74 tff(5363,plain,
% 22.54/22.74 ($false),
% 22.54/22.74 inference(unit_resolution,[status(thm)],[4565, 5362, 5347])).
% 22.54/22.74 tff(5364,plain,((mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)))) | (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))), inference(lemma,lemma(discharge,[]))).
% 22.54/22.74 tff(5365,plain,
% 22.54/22.74 (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))),
% 22.54/22.74 inference(unit_resolution,[status(thm)],[5364, 4355, 329, 3865, 4360, 4353])).
% 22.54/22.74 tff(5366,plain,
% 22.54/22.74 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(b, c), mult(a, c))),
% 22.54/22.74 inference(monotonicity,[status(thm)],[1491])).
% 22.54/22.74 tff(5367,plain,
% 22.54/22.74 (mult(mult(b, c), mult(a, c)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))),
% 22.54/22.74 inference(symmetry,[status(thm)],[5366])).
% 22.54/22.74 tff(5368,plain,
% 22.54/22.74 (mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(mult(a, c), mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), unit), mult(a, c)))),
% 22.54/22.74 inference(monotonicity,[status(thm)],[1893, 2504])).
% 22.54/22.74 tff(5369,plain,
% 22.54/22.74 (mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(mult(a, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))),
% 22.54/22.74 inference(transitivity,[status(thm)],[5368, 2502, 2499, 5367])).
% 22.54/22.74 tff(5370,plain,
% 22.54/22.74 ((~![A: $i] : (mult(A, unit) = A)) | (mult(mult(unit, mult(a, c)), unit) = mult(unit, mult(a, c)))),
% 22.54/22.74 inference(quant_inst,[status(thm)],[])).
% 22.54/22.74 tff(5371,plain,
% 22.54/22.74 (mult(mult(unit, mult(a, c)), unit) = mult(unit, mult(a, c))),
% 22.54/22.74 inference(unit_resolution,[status(thm)],[5370, 43])).
% 22.54/22.74 tff(5372,plain,
% 22.54/22.74 (mult(mult(unit, mult(a, c)), unit) = mult(a, c)),
% 22.54/22.74 inference(transitivity,[status(thm)],[5371, 1549])).
% 22.54/22.74 tff(5373,plain,
% 22.54/22.74 (mult(mult(mult(unit, mult(a, c)), unit), mult(a, c)) = mult(mult(a, c), mult(a, c))),
% 22.54/22.74 inference(monotonicity,[status(thm)],[5372])).
% 22.54/22.74 tff(5374,plain,
% 22.54/22.74 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(unit, mult(a, c)), unit), mult(a, c)) = mult(unit, mult(mult(mult(a, c), unit), mult(a, c))))),
% 22.54/22.74 inference(quant_inst,[status(thm)],[])).
% 22.54/22.74 tff(5375,plain,
% 22.54/22.74 (mult(mult(mult(unit, mult(a, c)), unit), mult(a, c)) = mult(unit, mult(mult(mult(a, c), unit), mult(a, c)))),
% 22.54/22.74 inference(unit_resolution,[status(thm)],[5374, 56])).
% 22.54/22.74 tff(5376,plain,
% 22.54/22.74 (mult(unit, mult(mult(mult(a, c), unit), mult(a, c))) = mult(mult(mult(unit, mult(a, c)), unit), mult(a, c))),
% 22.54/22.74 inference(symmetry,[status(thm)],[5375])).
% 22.54/22.74 tff(5377,plain,
% 22.54/22.74 (mult(unit, mult(mult(a, c), mult(a, c))) = mult(unit, mult(mult(mult(a, c), unit), mult(a, c)))),
% 22.54/22.74 inference(monotonicity,[status(thm)],[2504])).
% 22.54/22.74 tff(5378,plain,
% 22.54/22.74 (mult(unit, mult(mult(a, c), mult(a, c))) = mult(mult(a, c), mult(a, c))),
% 22.54/22.74 inference(transitivity,[status(thm)],[5377, 5376, 5373])).
% 22.54/22.74 tff(5379,plain,
% 22.54/22.74 (mult(mult(unit, mult(mult(a, c), mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 22.54/22.74 inference(monotonicity,[status(thm)],[5378])).
% 22.54/22.74 tff(5380,plain,
% 22.54/22.74 ((mult(mult(unit, mult(mult(a, c), mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(mult(a, c), mult(a, c)))) <=> (mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 22.54/22.74 inference(monotonicity,[status(thm)],[5379, 5369])).
% 22.54/22.74 tff(5381,plain,
% 22.54/22.74 ((mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))) <=> (mult(mult(unit, mult(mult(a, c), mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(mult(a, c), mult(a, c))))),
% 22.54/22.74 inference(symmetry,[status(thm)],[5380])).
% 22.54/22.74 tff(5382,plain,
% 22.54/22.74 ((~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))) <=> (~(mult(mult(unit, mult(mult(a, c), mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(mult(a, c), mult(a, c)))))),
% 22.54/22.74 inference(monotonicity,[status(thm)],[5381])).
% 22.54/22.74 tff(5383,assumption,(~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))), introduced(assumption)).
% 22.54/22.74 tff(5384,plain,
% 22.54/22.74 (~(mult(mult(unit, mult(mult(a, c), mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(mult(a, c), mult(a, c))))),
% 22.54/22.74 inference(modus_ponens,[status(thm)],[5383, 5382])).
% 22.54/22.74 tff(5385,plain,
% 22.54/22.74 (mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), unit), mult(a, c))) = mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(mult(a, c), mult(a, c)))),
% 22.54/22.74 inference(symmetry,[status(thm)],[5368])).
% 22.54/22.74 tff(5386,plain,
% 22.54/22.74 (mult(mult(b, c), mult(a, c)) = mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), unit), mult(a, c))),
% 22.54/22.74 inference(symmetry,[status(thm)],[2499])).
% 22.54/22.74 tff(5387,plain,
% 22.54/22.74 (mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))),
% 22.54/22.74 inference(symmetry,[status(thm)],[1039])).
% 22.54/22.74 tff(5388,plain,
% 22.54/22.74 (mult(mult(unit, mult(mult(a, c), mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(mult(a, c), mult(a, c)))),
% 22.54/22.74 inference(transitivity,[status(thm)],[5379, 4789, 2257, 268, 5387, 5366, 5386, 2501, 5385])).
% 22.54/22.74 tff(5389,plain,
% 22.54/22.74 ($false),
% 22.54/22.74 inference(unit_resolution,[status(thm)],[5388, 5384])).
% 22.54/22.74 tff(5390,plain,((~(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))) | (~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))), inference(lemma,lemma(discharge,[]))).
% 22.54/22.74 tff(5391,plain,
% 22.54/22.74 (mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))),
% 22.54/22.74 inference(unit_resolution,[status(thm)],[5390, 5365, 4355, 4353])).
% 22.54/22.74 tff(5392,plain,
% 22.54/22.74 ($false),
% 22.54/22.74 inference(unit_resolution,[status(thm)],[5391, 4359])).
% 22.54/22.74 tff(5393,plain,((mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))) | (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit))))), inference(lemma,lemma(discharge,[]))).
% 22.54/22.74 tff(5394,plain,
% 22.54/22.74 (mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))),
% 22.54/22.74 inference(unit_resolution,[status(thm)],[5393, 4347, 329, 4349])).
% 22.54/22.74 tff(5395,plain,
% 22.54/22.74 (mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(b, c))),
% 22.54/22.74 inference(transitivity,[status(thm)],[5394, 138])).
% 22.54/22.74 tff(5396,plain,
% 22.54/22.74 (ld(mult(a, c), mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c))))) = ld(mult(a, c), mult(mult(a, c), mult(b, c)))),
% 22.54/22.74 inference(monotonicity,[status(thm)],[5395])).
% 22.54/22.74 tff(5397,plain,
% 22.54/22.74 (mult(mult(a, c), rd(mult(b, c), mult(a, c))) = mult(b, c)),
% 22.54/22.74 inference(transitivity,[status(thm)],[1642, 5396, 291])).
% 22.54/22.74 tff(5398,plain,
% 22.54/22.74 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(b, c), a)),
% 22.54/22.74 inference(monotonicity,[status(thm)],[5397])).
% 22.54/22.74 tff(5399,plain,
% 22.54/22.74 (mult(rd(mult(b, c), mult(a, c)), mult(c, a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, c))),
% 22.54/22.74 inference(transitivity,[status(thm)],[3867, 4347, 61])).
% 22.54/22.74 tff(5400,plain,
% 22.54/22.74 (ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(c, a))) = ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))),
% 22.54/22.74 inference(monotonicity,[status(thm)],[5399])).
% 22.54/22.74 tff(5401,plain,
% 22.54/22.74 (mult(c, a) = mult(a, c)),
% 22.54/22.74 inference(transitivity,[status(thm)],[3884, 5400, 3872])).
% 22.54/22.74 tff(5402,plain,
% 22.54/22.74 (mult(mult(c, a), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))),
% 22.54/22.74 inference(monotonicity,[status(thm)],[5401])).
% 22.54/22.74 tff(5403,plain,
% 22.54/22.74 (mult(mult(mult(c, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)),
% 22.54/22.74 inference(monotonicity,[status(thm)],[5402])).
% 22.54/22.74 tff(5404,plain,
% 22.54/22.74 (mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), a)) = mult(mult(mult(c, a), rd(mult(b, c), mult(a, c))), a)),
% 22.54/22.74 inference(symmetry,[status(thm)],[4962])).
% 22.54/22.74 tff(5405,plain,
% 22.54/22.74 (mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), a)) = mult(c, mult(b, a))),
% 22.54/22.74 inference(transitivity,[status(thm)],[5404, 5403, 5398, 3057, 4348])).
% 22.54/22.74 tff(5406,plain,
% 22.54/22.74 (ld(c, mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), a))) = ld(c, mult(c, mult(b, a)))),
% 22.54/22.74 inference(monotonicity,[status(thm)],[5405])).
% 22.54/22.74 tff(5407,plain,
% 22.54/22.74 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(c, mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), a))) = mult(mult(a, rd(mult(b, c), mult(a, c))), a))),
% 22.54/22.74 inference(quant_inst,[status(thm)],[])).
% 22.54/22.74 tff(5408,plain,
% 22.54/22.74 (ld(c, mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), a))) = mult(mult(a, rd(mult(b, c), mult(a, c))), a)),
% 22.54/22.74 inference(unit_resolution,[status(thm)],[5407, 7])).
% 22.54/22.74 tff(5409,plain,
% 22.54/22.74 (mult(mult(a, rd(mult(b, c), mult(a, c))), a) = ld(c, mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), a)))),
% 22.54/22.74 inference(symmetry,[status(thm)],[5408])).
% 22.54/22.74 tff(5410,plain,
% 22.54/22.74 (mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(b, a)),
% 22.54/22.74 inference(transitivity,[status(thm)],[5409, 5406, 1472])).
% 22.54/22.74 tff(5411,plain,
% 22.54/22.74 (rd(mult(mult(a, rd(mult(b, c), mult(a, c))), a), a) = rd(mult(b, a), a)),
% 22.54/22.74 inference(monotonicity,[status(thm)],[5410])).
% 22.54/22.74 tff(5412,plain,
% 22.54/22.74 (mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))),
% 22.54/22.74 inference(symmetry,[status(thm)],[4400])).
% 22.54/22.74 tff(5413,plain,
% 22.54/22.74 (ld(mult(a, c), mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))) = ld(mult(a, c), mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))),
% 22.54/22.74 inference(monotonicity,[status(thm)],[5412])).
% 22.54/22.74 tff(5414,plain,
% 22.54/22.74 (mult(rd(mult(b, c), mult(a, c)), a) = b),
% 22.54/22.74 inference(transitivity,[status(thm)],[4412, 5413, 358, 1456, 5411, 1451])).
% 22.54/22.74 tff(5415,plain,
% 22.54/22.74 (mult(mult(rd(mult(b, c), mult(a, c)), a), c) = mult(b, c)),
% 22.54/22.74 inference(monotonicity,[status(thm)],[5414])).
% 22.54/22.74 tff(5416,plain,
% 22.54/22.74 (mult(mult(rd(mult(b, c), mult(a, c)), a), c) = mult(rd(mult(b, c), mult(a, c)), mult(a, c))),
% 22.54/22.74 inference(transitivity,[status(thm)],[5415, 267])).
% 22.54/22.74 tff(5417,plain,
% 22.54/22.74 ($false),
% 22.54/22.74 inference(unit_resolution,[status(thm)],[5416, 4344])).
% 22.54/22.74 tff(5418,plain,((mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit)))) | (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))), inference(lemma,lemma(discharge,[]))).
% 22.54/22.74 tff(5419,plain,
% 22.54/22.74 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit)))),
% 22.54/22.74 inference(unit_resolution,[status(thm)],[5418, 329])).
% 22.54/22.74 tff(5420,plain,
% 22.54/22.74 (~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))),
% 22.54/22.74 inference(unit_resolution,[status(thm)],[3846, 329, 4400])).
% 22.54/22.74 tff(5421,plain,
% 22.54/22.74 (~(mult(mult(unit, b), a) = mult(mult(unit, a), b))),
% 22.54/22.74 inference(unit_resolution,[status(thm)],[937, 97, 898, 359])).
% 22.54/22.74 tff(5422,plain,
% 22.54/22.74 (mult(b, mult(a, b)) = mult(b, mult(b, a))),
% 22.54/22.74 inference(unit_resolution,[status(thm)],[725, 97, 359, 723])).
% 22.54/22.74 tff(5423,plain,
% 22.54/22.74 ($false),
% 22.54/22.74 inference(unit_resolution,[status(thm)],[943, 5422, 5421])).
% 22.54/22.74 tff(5424,plain,((~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit))))) | (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))) | (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) | (mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a)))), inference(lemma,lemma(discharge,[]))).
% 22.54/22.74 tff(5425,plain,
% 22.54/22.74 (mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a))),
% 22.54/22.74 inference(unit_resolution,[status(thm)],[5424, 4400, 5420, 5419])).
% 22.54/22.74 tff(5426,plain,
% 22.54/22.74 ((mult(mult(c, mult(mult(unit, c), unit)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(c, mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit)))) <=> (mult(mult(c, c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(c, mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))),
% 22.54/22.74 inference(monotonicity,[status(thm)],[4239, 4011])).
% 22.54/22.74 tff(5427,plain,
% 22.54/22.74 ((mult(mult(c, c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(c, mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)))) <=> (mult(mult(c, mult(mult(unit, c), unit)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(c, mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit))))),
% 22.54/22.74 inference(symmetry,[status(thm)],[5426])).
% 22.54/22.74 tff(5428,plain,
% 22.54/22.74 (mult(c, mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(unit, c), unit)))),
% 22.54/22.74 inference(unit_resolution,[status(thm)],[4088, 4221, 3862])).
% 22.54/22.74 tff(5429,plain,
% 22.54/22.74 (mult(c, mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), c))),
% 22.54/22.74 inference(transitivity,[status(thm)],[4006, 4241, 5428, 4004])).
% 22.54/22.74 tff(5430,plain,
% 22.54/22.74 (mult(mult(c, c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), c)),
% 22.54/22.74 inference(transitivity,[status(thm)],[3183, 4282, 3179, 3178, 3175, 864, 858, 856, 161, 215])).
% 22.54/22.74 tff(5431,plain,
% 22.54/22.74 ((mult(mult(c, c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(c, mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)))) <=> (mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)))),
% 22.54/22.74 inference(monotonicity,[status(thm)],[5430, 5429])).
% 22.54/22.74 tff(5432,plain,
% 22.54/22.74 ((mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), c))) <=> (mult(mult(c, c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(c, mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))),
% 22.54/22.74 inference(symmetry,[status(thm)],[5431])).
% 22.54/22.74 tff(5433,plain,
% 22.54/22.74 ((mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)) = mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), c)) <=> (mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)))),
% 22.54/22.74 inference(commutativity,[status(thm)],[])).
% 22.54/22.74 tff(5434,plain,
% 22.54/22.74 (mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c))),
% 22.54/22.75 inference(unit_resolution,[status(thm)],[4002, 3862])).
% 22.54/22.75 tff(5435,plain,
% 22.54/22.75 (mult(mult(b, mult(a, c)), c) = mult(mult(b, c), mult(a, c))),
% 22.54/22.75 inference(unit_resolution,[status(thm)],[2601, 5434])).
% 22.54/22.75 tff(5436,plain,
% 22.54/22.75 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(b, mult(a, c))),
% 22.54/22.75 inference(symmetry,[status(thm)],[367])).
% 22.54/22.75 tff(5437,plain,
% 22.54/22.75 (mult(a, mult(b, c)) = mult(b, mult(a, c))),
% 22.54/22.75 inference(transitivity,[status(thm)],[289, 4416, 5436])).
% 22.54/22.75 tff(5438,plain,
% 22.54/22.75 (mult(mult(a, mult(b, c)), c) = mult(mult(b, mult(a, c)), c)),
% 22.54/22.75 inference(monotonicity,[status(thm)],[5437])).
% 22.54/22.75 tff(5439,plain,
% 22.54/22.75 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(b, c), mult(a, c))),
% 22.54/22.75 inference(transitivity,[status(thm)],[4467, 138, 266, 5438, 4403])).
% 22.54/22.75 tff(5440,plain,
% 22.54/22.75 (rd(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)), mult(a, c)) = rd(mult(mult(b, c), mult(a, c)), mult(a, c))),
% 22.54/22.75 inference(monotonicity,[status(thm)],[5439])).
% 22.54/22.75 tff(5441,plain,
% 22.54/22.75 (mult(mult(a, c), rd(mult(b, c), mult(a, c))) = mult(b, c)),
% 22.54/22.75 inference(transitivity,[status(thm)],[4423, 5440, 4402])).
% 22.54/22.75 tff(5442,plain,
% 22.54/22.75 (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(b, c))),
% 22.54/22.75 inference(monotonicity,[status(thm)],[5441])).
% 22.54/22.75 tff(5443,plain,
% 22.54/22.75 (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))),
% 22.54/22.75 inference(transitivity,[status(thm)],[5442, 289])).
% 22.54/22.75 tff(5444,plain,
% 22.54/22.75 ($false),
% 22.54/22.75 inference(unit_resolution,[status(thm)],[270, 5443])).
% 22.54/22.75 tff(5445,plain,((~(mult(mult(b, mult(a, c)), c) = mult(mult(b, c), mult(a, c)))) | (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))) | (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit)))))), inference(lemma,lemma(discharge,[]))).
% 22.54/22.75 tff(5446,plain,
% 22.54/22.75 ((mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))) | (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit)))))),
% 22.54/22.75 inference(unit_resolution,[status(thm)],[5445, 5435])).
% 22.54/22.75 tff(5447,plain,
% 22.54/22.75 (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))),
% 22.54/22.75 inference(unit_resolution,[status(thm)],[5446, 5419, 4400])).
% 22.54/22.75 tff(5448,plain,
% 22.54/22.75 (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(b, c))),
% 22.54/22.75 inference(transitivity,[status(thm)],[5447, 142])).
% 22.54/22.75 tff(5449,plain,
% 22.54/22.75 (ld(a, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))) = ld(a, mult(a, mult(b, c)))),
% 22.54/22.75 inference(monotonicity,[status(thm)],[5448])).
% 22.54/22.75 tff(5450,assumption,(ld(a, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))), introduced(assumption)).
% 22.54/22.75 tff(5451,plain,
% 22.54/22.75 (mult(mult(a, c), rd(mult(b, c), mult(a, c))) = ld(a, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 22.54/22.75 inference(symmetry,[status(thm)],[5450])).
% 22.54/22.75 tff(5452,plain,
% 22.54/22.75 (mult(mult(a, c), rd(mult(b, c), mult(a, c))) = mult(b, c)),
% 22.54/22.75 inference(transitivity,[status(thm)],[5451, 5449, 141])).
% 22.54/22.75 tff(5453,plain,
% 22.54/22.75 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(b, c), a)),
% 22.54/22.75 inference(monotonicity,[status(thm)],[5452])).
% 22.54/22.75 tff(5454,plain,
% 22.54/22.75 ((mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(mult(unit, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c)))) <=> (mult(mult(unit, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)))),
% 22.54/22.75 inference(commutativity,[status(thm)],[])).
% 22.54/22.75 tff(5455,plain,
% 22.54/22.75 ((mult(mult(unit, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a))) <=> (mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(mult(unit, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))))),
% 22.54/22.75 inference(symmetry,[status(thm)],[5454])).
% 22.54/22.75 tff(5456,plain,
% 22.54/22.75 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)) = mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a))),
% 22.54/22.75 inference(monotonicity,[status(thm)],[4856])).
% 22.54/22.75 tff(5457,plain,
% 22.54/22.75 (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(unit, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c)))),
% 22.54/22.75 inference(symmetry,[status(thm)],[5027])).
% 22.54/22.75 tff(5458,plain,
% 22.54/22.75 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))),
% 22.54/22.75 inference(symmetry,[status(thm)],[1683])).
% 22.54/22.75 tff(5459,plain,
% 22.54/22.75 (mult(mult(b, c), a) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)),
% 22.54/22.75 inference(symmetry,[status(thm)],[5453])).
% 22.54/22.75 tff(5460,plain,
% 22.54/22.75 (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(mult(unit, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c)))),
% 22.54/22.75 inference(transitivity,[status(thm)],[1332, 5459, 5458, 5457])).
% 22.54/22.75 tff(5461,plain,
% 22.54/22.75 ((mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) <=> (mult(mult(unit, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)))),
% 22.54/22.75 inference(monotonicity,[status(thm)],[5460, 5456])).
% 22.54/22.75 tff(5462,plain,
% 22.54/22.75 ((mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) <=> (mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(mult(unit, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))))),
% 22.54/22.75 inference(transitivity,[status(thm)],[5461, 5455])).
% 22.54/22.75 tff(5463,plain,
% 22.54/22.75 (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))),
% 22.54/22.75 inference(unit_resolution,[status(thm)],[1367, 5419])).
% 22.54/22.75 tff(5464,plain,
% 22.54/22.75 (mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(mult(unit, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c)))),
% 22.54/22.75 inference(modus_ponens,[status(thm)],[5463, 5462])).
% 22.54/22.75 tff(5465,plain,
% 22.54/22.75 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a) = mult(mult(b, c), a)),
% 22.54/22.75 inference(transitivity,[status(thm)],[1168, 5456, 5464, 5027, 1683, 5453])).
% 22.54/22.75 tff(5466,plain,
% 22.54/22.75 (rd(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a), a) = rd(mult(mult(b, c), a), a)),
% 22.54/22.75 inference(monotonicity,[status(thm)],[5465])).
% 22.54/22.75 tff(5467,plain,
% 22.54/22.75 (ld(mult(a, c), mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = ld(mult(a, c), mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))),
% 22.54/22.75 inference(symmetry,[status(thm)],[5413])).
% 22.54/22.75 tff(5468,plain,
% 22.54/22.75 (mult(a, rd(mult(b, c), mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), a)),
% 22.54/22.75 inference(transitivity,[status(thm)],[471, 5467, 4411])).
% 22.54/22.75 tff(5469,plain,
% 22.54/22.75 (mult(mult(a, rd(mult(b, c), mult(a, c))), c) = mult(mult(rd(mult(b, c), mult(a, c)), a), c)),
% 22.54/22.75 inference(monotonicity,[status(thm)],[5468])).
% 22.54/22.75 tff(5470,plain,
% 22.54/22.75 (mult(mult(a, rd(mult(b, c), mult(a, c))), c) = mult(b, c)),
% 22.54/22.75 inference(transitivity,[status(thm)],[5469, 1377, 5466, 1370])).
% 22.54/22.75 tff(5471,plain,
% 22.54/22.75 (rd(mult(mult(a, rd(mult(b, c), mult(a, c))), c), c) = rd(mult(b, c), c)),
% 22.54/22.75 inference(monotonicity,[status(thm)],[5470])).
% 22.54/22.75 tff(5472,plain,
% 22.54/22.75 (mult(a, rd(mult(b, c), mult(a, c))) = b),
% 22.54/22.75 inference(transitivity,[status(thm)],[2194, 5471, 170])).
% 22.54/22.75 tff(5473,plain,
% 22.54/22.75 (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), b)),
% 22.54/22.75 inference(monotonicity,[status(thm)],[5472])).
% 22.54/22.75 tff(5474,plain,
% 22.54/22.75 (mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), c)),
% 22.54/22.75 inference(transitivity,[status(thm)],[5412, 5473, 161, 215])).
% 22.54/22.75 tff(5475,plain,
% 22.54/22.75 (rd(mult(b, c), c) = rd(mult(mult(a, rd(mult(b, c), mult(a, c))), c), c)),
% 22.54/22.75 inference(symmetry,[status(thm)],[5471])).
% 22.54/22.75 tff(5476,plain,
% 22.54/22.75 (b = mult(a, rd(mult(b, c), mult(a, c)))),
% 22.54/22.75 inference(transitivity,[status(thm)],[2727, 5475, 2193])).
% 22.54/22.75 tff(5477,plain,
% 22.54/22.75 (mult(b, a) = mult(mult(a, rd(mult(b, c), mult(a, c))), a)),
% 22.54/22.75 inference(monotonicity,[status(thm)],[5476])).
% 22.54/22.75 tff(5478,plain,
% 22.54/22.75 (mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(b, a)),
% 22.54/22.75 inference(symmetry,[status(thm)],[5477])).
% 22.54/22.75 tff(5479,plain,
% 22.54/22.75 (mult(rd(mult(b, c), mult(a, c)), a) = mult(a, rd(mult(b, c), mult(a, c)))),
% 22.54/22.75 inference(transitivity,[status(thm)],[4412, 5413, 358])).
% 22.54/22.75 tff(5480,plain,
% 22.54/22.75 (mult(a, mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(a, rd(mult(b, c), mult(a, c))))),
% 22.54/22.75 inference(monotonicity,[status(thm)],[5479])).
% 22.54/22.75 tff(5481,plain,
% 22.54/22.75 (mult(a, mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), a))),
% 22.54/22.75 inference(symmetry,[status(thm)],[5480])).
% 22.54/22.75 tff(5482,plain,
% 22.54/22.75 (mult(a, mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, b)),
% 22.54/22.75 inference(monotonicity,[status(thm)],[5472])).
% 22.54/22.75 tff(5483,plain,
% 22.54/22.75 (mult(a, b) = mult(a, mult(a, rd(mult(b, c), mult(a, c))))),
% 22.54/22.75 inference(symmetry,[status(thm)],[5482])).
% 22.54/22.75 tff(5484,plain,
% 22.54/22.75 (mult(c, ld(c, mult(a, b))) = mult(b, a)),
% 22.54/22.75 inference(transitivity,[status(thm)],[204, 5483, 5481, 1334, 5478])).
% 22.54/22.75 tff(5485,plain,
% 22.54/22.75 (mult(c, mult(c, ld(c, mult(a, b)))) = mult(c, mult(b, a))),
% 22.54/22.75 inference(monotonicity,[status(thm)],[5484])).
% 22.54/22.75 tff(5486,plain,
% 22.54/22.75 (mult(c, mult(b, a)) = mult(c, mult(c, ld(c, mult(a, b))))),
% 22.54/22.75 inference(symmetry,[status(thm)],[5485])).
% 22.54/22.75 tff(5487,plain,
% 22.54/22.75 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), c))),
% 22.54/22.75 inference(transitivity,[status(thm)],[5453, 3057, 4208, 5486, 4241, 5428, 4004])).
% 22.54/22.75 tff(5488,plain,
% 22.54/22.75 ((mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))) <=> (mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)) = mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), c))),
% 22.54/22.75 inference(monotonicity,[status(thm)],[5487, 5474])).
% 22.54/22.75 tff(5489,plain,
% 22.54/22.75 ((mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))) <=> (mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)))),
% 22.54/22.75 inference(transitivity,[status(thm)],[5488, 5433])).
% 22.54/22.75 tff(5490,plain,
% 22.54/22.75 ((mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))) <=> (mult(mult(c, mult(mult(unit, c), unit)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(c, mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit))))),
% 22.54/22.75 inference(transitivity,[status(thm)],[5489, 5432, 5427])).
% 22.54/22.75 tff(5491,plain,
% 22.54/22.75 ((~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))) <=> (~(mult(mult(c, mult(mult(unit, c), unit)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(c, mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit)))))),
% 22.54/22.75 inference(monotonicity,[status(thm)],[5490])).
% 22.54/22.75 tff(5492,plain,
% 22.54/22.75 (~(mult(mult(c, mult(mult(unit, c), unit)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(c, mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit))))),
% 22.54/22.75 inference(modus_ponens,[status(thm)],[329, 5491])).
% 22.54/22.75 tff(5493,plain,
% 22.54/22.75 ($false),
% 22.54/22.75 inference(unit_resolution,[status(thm)],[4238, 5492])).
% 22.54/22.75 tff(5494,plain,((~(ld(a, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))) = mult(mult(a, c), rd(mult(b, c), mult(a, c))))) | (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))) | (~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a))))), inference(lemma,lemma(discharge,[]))).
% 22.54/22.75 tff(5495,plain,
% 22.54/22.75 ($false),
% 22.54/22.75 inference(unit_resolution,[status(thm)],[5494, 3842, 5425, 4336, 329])).
% 22.54/22.75 tff(5496,plain,(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))), inference(lemma,lemma(discharge,[]))).
% 22.54/22.75 tff(5497,plain,
% 22.54/22.75 (mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)),
% 22.54/22.75 inference(symmetry,[status(thm)],[5496])).
% 22.54/22.75 tff(5498,plain,
% 22.54/22.75 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a)),
% 22.54/22.75 inference(symmetry,[status(thm)],[4331])).
% 22.54/22.75 tff(5499,plain,
% 22.54/22.75 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a) = mult(mult(b, c), a)),
% 22.54/22.75 inference(transitivity,[status(thm)],[1168, 5498, 1332])).
% 22.54/22.75 tff(5500,plain,
% 22.54/22.75 (rd(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a), a) = rd(mult(mult(b, c), a), a)),
% 22.54/22.75 inference(monotonicity,[status(thm)],[5499])).
% 22.54/22.75 tff(5501,plain,
% 22.54/22.75 (mult(mult(rd(mult(b, c), mult(a, c)), a), c) = mult(b, c)),
% 22.54/22.75 inference(transitivity,[status(thm)],[1377, 5500, 1370])).
% 22.54/22.75 tff(5502,plain,
% 22.54/22.75 (rd(mult(mult(rd(mult(b, c), mult(a, c)), a), c), c) = rd(mult(b, c), c)),
% 22.54/22.75 inference(monotonicity,[status(thm)],[5501])).
% 22.54/22.75 tff(5503,plain,
% 22.54/22.75 (mult(rd(mult(b, c), mult(a, c)), a) = b),
% 22.54/22.75 inference(transitivity,[status(thm)],[175, 5502, 170])).
% 22.54/22.75 tff(5504,plain,
% 22.54/22.75 (mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, c), b)),
% 22.54/22.75 inference(monotonicity,[status(thm)],[5503])).
% 22.54/22.75 tff(5505,plain,
% 22.54/22.75 (mult(mult(a, c), b) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))),
% 22.54/22.75 inference(symmetry,[status(thm)],[5504])).
% 22.54/22.75 tff(5506,plain,
% 22.54/22.75 (mult(mult(unit, mult(a, c)), b) = mult(mult(a, c), b)),
% 22.54/22.75 inference(monotonicity,[status(thm)],[1549])).
% 22.54/22.75 tff(5507,plain,
% 22.54/22.75 (mult(mult(unit, mult(a, c)), b) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))),
% 22.54/22.75 inference(transitivity,[status(thm)],[5506, 5505, 5497, 4339, 1431, 4331])).
% 22.54/22.75 tff(5508,plain,
% 22.54/22.75 (rd(mult(b, c), c) = rd(mult(mult(rd(mult(b, c), mult(a, c)), a), c), c)),
% 22.54/22.75 inference(symmetry,[status(thm)],[5502])).
% 22.54/22.75 tff(5509,plain,
% 22.54/22.75 (b = mult(rd(mult(b, c), mult(a, c)), a)),
% 22.54/22.75 inference(transitivity,[status(thm)],[2727, 5508, 174])).
% 22.54/22.75 tff(5510,plain,
% 22.54/22.75 (mult(b, mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c))),
% 22.54/22.75 inference(monotonicity,[status(thm)],[5509])).
% 22.54/22.75 tff(5511,plain,
% 22.54/22.75 (mult(mult(unit, b), mult(a, c)) = mult(b, mult(a, c))),
% 22.54/22.75 inference(monotonicity,[status(thm)],[184])).
% 22.54/22.75 tff(5512,plain,
% 22.54/22.75 (mult(mult(unit, b), mult(a, c)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c)))),
% 22.54/22.75 inference(transitivity,[status(thm)],[5511, 5510, 4333])).
% 22.54/22.75 tff(5513,plain,
% 22.54/22.75 ((mult(mult(unit, b), mult(a, c)) = mult(mult(unit, mult(a, c)), b)) <=> (mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))),
% 22.54/22.75 inference(monotonicity,[status(thm)],[5512, 5507])).
% 22.54/22.75 tff(5514,plain,
% 22.54/22.75 ((mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) <=> (mult(mult(unit, b), mult(a, c)) = mult(mult(unit, mult(a, c)), b))),
% 22.54/22.75 inference(symmetry,[status(thm)],[5513])).
% 22.54/22.75 tff(5515,plain,
% 22.54/22.75 ((~(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) <=> (~(mult(mult(unit, b), mult(a, c)) = mult(mult(unit, mult(a, c)), b)))),
% 22.54/22.75 inference(monotonicity,[status(thm)],[5514])).
% 22.54/22.75 tff(5516,plain,
% 22.54/22.75 (~(mult(mult(unit, b), mult(a, c)) = mult(mult(unit, mult(a, c)), b))),
% 22.54/22.75 inference(modus_ponens,[status(thm)],[4327, 5515])).
% 22.54/22.75 tff(5517,plain,
% 22.54/22.75 (mult(mult(a, c), b) = mult(mult(unit, mult(a, c)), b)),
% 22.54/22.75 inference(symmetry,[status(thm)],[5506])).
% 22.54/22.75 tff(5518,plain,
% 22.54/22.75 (mult(mult(b, c), a) = mult(mult(a, b), c)),
% 22.54/22.75 inference(transitivity,[status(thm)],[4338, 5496, 2232, 161])).
% 22.54/22.75 tff(5519,plain,
% 22.54/22.75 (mult(mult(mult(b, c), a), b) = mult(mult(mult(a, b), c), b)),
% 22.54/22.75 inference(monotonicity,[status(thm)],[5518])).
% 22.54/22.75 tff(5520,assumption,(mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a)), introduced(assumption)).
% 22.54/22.75 tff(5521,plain,
% 22.54/22.75 (mult(mult(mult(b, c), b), a) = mult(mult(mult(b, c), a), b)),
% 22.54/22.75 inference(symmetry,[status(thm)],[5520])).
% 22.54/22.75 tff(5522,plain,
% 22.54/22.75 (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), b) = mult(mult(b, c), b)),
% 22.54/22.75 inference(monotonicity,[status(thm)],[137])).
% 22.54/22.75 tff(5523,assumption,(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c)))), introduced(assumption)).
% 22.54/22.75 tff(5524,assumption,(~(mult(mult(unit, b), mult(a, c)) = mult(mult(unit, mult(a, c)), b))), introduced(assumption)).
% 22.54/22.75 tff(5525,plain,
% 22.54/22.75 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c))) = mult(mult(a, b), c))),
% 22.54/22.75 inference(quant_inst,[status(thm)],[])).
% 22.54/22.75 tff(5526,plain,
% 22.54/22.75 (ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c))) = mult(mult(a, b), c)),
% 22.54/22.75 inference(unit_resolution,[status(thm)],[5525, 7])).
% 22.54/22.75 tff(5527,plain,
% 22.54/22.75 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), b))),
% 22.54/22.75 inference(monotonicity,[status(thm)],[227])).
% 22.54/22.75 tff(5528,plain,
% 22.54/22.75 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), b)) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c))),
% 22.54/22.75 inference(symmetry,[status(thm)],[5527])).
% 22.54/22.75 tff(5529,assumption,(mult(rd(mult(b, c), mult(a, c)), mult(b, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), b))), introduced(assumption)).
% 22.54/22.75 tff(5530,plain,
% 22.54/22.75 (mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c))),
% 22.54/22.75 inference(symmetry,[status(thm)],[5523])).
% 22.54/22.75 tff(5531,plain,
% 22.54/22.75 (mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(b, mult(a, c))),
% 22.54/22.75 inference(transitivity,[status(thm)],[5530, 4407])).
% 22.54/22.75 tff(5532,plain,
% 22.54/22.75 (mult(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c)))) = mult(rd(mult(b, c), mult(a, c)), mult(b, mult(a, c)))),
% 22.54/22.75 inference(monotonicity,[status(thm)],[5531])).
% 22.54/22.75 tff(5533,plain,
% 22.54/22.75 (mult(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c)))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c))),
% 22.54/22.75 inference(transitivity,[status(thm)],[5532, 5529, 5528])).
% 22.54/22.75 tff(5534,plain,
% 22.54/22.75 (ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))))) = ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)))),
% 22.54/22.75 inference(monotonicity,[status(thm)],[5533])).
% 22.54/22.75 tff(5535,plain,
% 22.54/22.75 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))))) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))))),
% 22.54/22.75 inference(quant_inst,[status(thm)],[])).
% 22.54/22.75 tff(5536,plain,
% 22.54/22.75 (ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))))) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c)))),
% 22.54/22.75 inference(unit_resolution,[status(thm)],[5535, 7])).
% 22.54/22.75 tff(5537,plain,
% 22.54/22.75 (mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c)))))),
% 22.54/22.76 inference(symmetry,[status(thm)],[5536])).
% 22.54/22.76 tff(5538,plain,
% 22.54/22.76 (mult(mult(unit, b), mult(a, c)) = mult(mult(unit, mult(a, c)), b)),
% 22.54/22.76 inference(transitivity,[status(thm)],[5511, 4406, 5523, 5537, 5534, 5526, 227, 5517])).
% 22.54/22.76 tff(5539,plain,
% 22.54/22.76 ($false),
% 22.54/22.76 inference(unit_resolution,[status(thm)],[5524, 5538])).
% 22.54/22.76 tff(5540,plain,((~(mult(rd(mult(b, c), mult(a, c)), mult(b, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), b)))) | (mult(mult(unit, b), mult(a, c)) = mult(mult(unit, mult(a, c)), b)) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))), inference(lemma,lemma(discharge,[]))).
% 22.54/22.76 tff(5541,plain,
% 22.54/22.76 (~(mult(rd(mult(b, c), mult(a, c)), mult(b, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), b)))),
% 22.54/22.76 inference(unit_resolution,[status(thm)],[5540, 5524, 5523, 1371])).
% 22.54/22.76 tff(5542,plain,
% 22.54/22.76 (((~(mult(mult(rd(mult(b, c), mult(a, c)), b), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), b))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(b, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), b))))) | (mult(rd(mult(b, c), mult(a, c)), mult(b, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), b)))),
% 22.54/22.76 inference(tautology,[status(thm)],[])).
% 22.54/22.76 tff(5543,plain,
% 22.54/22.76 ((~(mult(mult(rd(mult(b, c), mult(a, c)), b), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), b))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(b, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), b))))),
% 22.54/22.76 inference(unit_resolution,[status(thm)],[5542, 5541])).
% 22.54/22.76 tff(5544,plain,
% 22.54/22.76 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(rd(mult(b, c), mult(a, c)), b), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), b))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(b, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), b)))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), b), mult(a, c)) = mult(rd(mult(b, c), mult(a, c)), mult(b, mult(a, c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), b) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), b)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), b), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), b))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(b, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), b)))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), b), mult(a, c)) = mult(rd(mult(b, c), mult(a, c)), mult(b, mult(a, c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), b) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), b)))))))),
% 22.54/22.76 inference(rewrite,[status(thm)],[])).
% 22.54/22.76 tff(5545,plain,
% 22.54/22.76 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(rd(mult(b, c), mult(a, c)), b), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), b))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(b, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), b)))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), b), mult(a, c)) = mult(rd(mult(b, c), mult(a, c)), mult(b, mult(a, c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), b) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), b)))))))),
% 22.60/22.76 inference(quant_inst,[status(thm)],[])).
% 22.60/22.76 tff(5546,plain,
% 22.60/22.76 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), b), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), b))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(b, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), b)))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), b), mult(a, c)) = mult(rd(mult(b, c), mult(a, c)), mult(b, mult(a, c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), b) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), b))))))),
% 22.60/22.76 inference(modus_ponens,[status(thm)],[5545, 5544])).
% 22.60/22.76 tff(5547,plain,
% 22.60/22.76 ((~((~(mult(mult(rd(mult(b, c), mult(a, c)), b), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), b))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(b, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), b)))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), b), mult(a, c)) = mult(rd(mult(b, c), mult(a, c)), mult(b, mult(a, c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), b) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), b))))))),
% 22.60/22.76 inference(unit_resolution,[status(thm)],[5546, 27])).
% 22.60/22.76 tff(5548,plain,
% 22.60/22.76 (~((~(mult(mult(rd(mult(b, c), mult(a, c)), b), mult(a, c)) = mult(rd(mult(b, c), mult(a, c)), mult(b, mult(a, c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), b) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), b)))))),
% 22.60/22.76 inference(unit_resolution,[status(thm)],[5547, 5543])).
% 22.60/22.76 tff(5549,plain,
% 22.60/22.76 (((~(mult(mult(rd(mult(b, c), mult(a, c)), b), mult(a, c)) = mult(rd(mult(b, c), mult(a, c)), mult(b, mult(a, c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), b) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), b))))) | (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), b) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), b)))),
% 22.60/22.76 inference(tautology,[status(thm)],[])).
% 22.60/22.76 tff(5550,plain,
% 22.60/22.76 (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), b) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), b))),
% 22.60/22.76 inference(unit_resolution,[status(thm)],[5549, 5548])).
% 22.60/22.76 tff(5551,plain,
% 22.60/22.76 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), b)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), b)),
% 22.60/22.76 inference(symmetry,[status(thm)],[5550])).
% 22.60/22.76 tff(5552,plain,
% 22.60/22.76 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)) = mult(mult(b, c), b)),
% 22.60/22.76 inference(transitivity,[status(thm)],[5527, 5551, 5522])).
% 22.60/22.76 tff(5553,plain,
% 22.60/22.76 (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)), a) = mult(mult(mult(b, c), b), a)),
% 22.60/22.76 inference(monotonicity,[status(thm)],[5552])).
% 22.60/22.76 tff(5554,plain,
% 22.60/22.76 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, b), c), a))) = mult(mult(mult(a, b), c), a))),
% 22.60/22.76 inference(quant_inst,[status(thm)],[])).
% 22.60/22.76 tff(5555,plain,
% 22.60/22.76 (ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, b), c), a))) = mult(mult(mult(a, b), c), a)),
% 22.60/22.76 inference(unit_resolution,[status(thm)],[5554, 7])).
% 22.60/22.76 tff(5556,assumption,(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, b), c), a))), introduced(assumption)).
% 22.60/22.76 tff(5557,assumption,(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), b) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), b))), introduced(assumption)).
% 22.60/22.76 tff(5558,plain,
% 22.60/22.76 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), b)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), b)),
% 22.60/22.76 inference(symmetry,[status(thm)],[5557])).
% 22.60/22.76 tff(5559,plain,
% 22.60/22.76 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)) = mult(mult(b, c), b)),
% 22.60/22.76 inference(transitivity,[status(thm)],[5527, 5558, 5522])).
% 22.60/22.76 tff(5560,plain,
% 22.60/22.76 (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)), a) = mult(mult(mult(b, c), b), a)),
% 22.60/22.76 inference(monotonicity,[status(thm)],[5559])).
% 22.60/22.76 tff(5561,plain,
% 22.60/22.76 (mult(mult(mult(b, c), b), a) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)), a)),
% 22.60/22.76 inference(symmetry,[status(thm)],[5560])).
% 22.60/22.76 tff(5562,plain,
% 22.60/22.76 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(a, mult(a, mult(mult(b, c), b))) = mult(mult(b, c), b))),
% 22.60/22.76 inference(quant_inst,[status(thm)],[])).
% 22.60/22.76 tff(5563,plain,
% 22.60/22.76 (ld(a, mult(a, mult(mult(b, c), b))) = mult(mult(b, c), b)),
% 22.60/22.76 inference(unit_resolution,[status(thm)],[5562, 7])).
% 22.60/22.76 tff(5564,plain,
% 22.60/22.76 (((~(mult(mult(a, b), mult(b, c)) = mult(mult(a, mult(b, c)), b))) | (~(mult(a, mult(b, mult(b, c))) = mult(a, mult(mult(b, c), b))))) | (mult(a, mult(b, mult(b, c))) = mult(a, mult(mult(b, c), b)))),
% 22.60/22.76 inference(tautology,[status(thm)],[])).
% 22.60/22.76 tff(5565,plain,
% 22.60/22.76 (mult(a, mult(b, mult(b, c))) = mult(a, mult(mult(b, c), b))),
% 22.60/22.76 inference(unit_resolution,[status(thm)],[5564, 803])).
% 22.60/22.76 tff(5566,plain,
% 22.60/22.76 (ld(a, mult(a, mult(b, mult(b, c)))) = ld(a, mult(a, mult(mult(b, c), b)))),
% 22.60/22.76 inference(monotonicity,[status(thm)],[5565])).
% 22.60/22.76 tff(5567,plain,
% 22.60/22.76 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(a, mult(a, mult(b, mult(b, c)))) = mult(b, mult(b, c)))),
% 22.60/22.76 inference(quant_inst,[status(thm)],[])).
% 22.60/22.76 tff(5568,plain,
% 22.60/22.76 (ld(a, mult(a, mult(b, mult(b, c)))) = mult(b, mult(b, c))),
% 22.60/22.76 inference(unit_resolution,[status(thm)],[5567, 7])).
% 22.60/22.76 tff(5569,plain,
% 22.60/22.76 (mult(b, mult(b, c)) = ld(a, mult(a, mult(b, mult(b, c))))),
% 22.60/22.76 inference(symmetry,[status(thm)],[5568])).
% 22.60/22.76 tff(5570,plain,
% 22.60/22.76 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(b, c)) = mult(b, mult(b, c))),
% 22.60/22.76 inference(monotonicity,[status(thm)],[1380])).
% 22.60/22.76 tff(5571,plain,
% 22.60/22.76 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(b, c)) = mult(mult(b, c), b)),
% 22.60/22.76 inference(transitivity,[status(thm)],[5570, 5569, 5566, 5563])).
% 22.60/22.76 tff(5572,plain,
% 22.60/22.76 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(b, c)), a) = mult(mult(mult(b, c), b), a)),
% 22.60/22.76 inference(monotonicity,[status(thm)],[5571])).
% 22.60/22.76 tff(5573,plain,
% 22.60/22.76 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(b, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(b, c)), a)))),
% 22.60/22.76 inference(quant_inst,[status(thm)],[])).
% 22.60/22.76 tff(5574,plain,
% 22.60/22.76 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(b, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(b, c)), a))),
% 22.60/22.76 inference(unit_resolution,[status(thm)],[5573, 56])).
% 22.60/22.76 tff(5575,plain,
% 22.60/22.76 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(b, c)), a)) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(b, c)), a)),
% 22.60/22.76 inference(symmetry,[status(thm)],[5574])).
% 22.60/22.76 tff(5576,plain,
% 22.60/22.76 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(b, c)), a)) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, b), c), a))),
% 22.60/22.76 inference(transitivity,[status(thm)],[5575, 5572, 5561, 5556])).
% 22.60/22.76 tff(5577,plain,
% 22.60/22.76 (ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(b, c)), a))) = ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, b), c), a)))),
% 22.60/22.76 inference(monotonicity,[status(thm)],[5576])).
% 22.60/22.76 tff(5578,plain,
% 22.60/22.76 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(b, c)), a))) = mult(mult(a, mult(b, c)), a))),
% 22.60/22.76 inference(quant_inst,[status(thm)],[])).
% 22.60/22.76 tff(5579,plain,
% 22.60/22.76 (ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(b, c)), a))) = mult(mult(a, mult(b, c)), a)),
% 22.60/22.76 inference(unit_resolution,[status(thm)],[5578, 7])).
% 22.60/22.76 tff(5580,plain,
% 22.60/22.76 (mult(mult(a, mult(b, c)), a) = ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(b, c)), a)))),
% 22.60/22.76 inference(symmetry,[status(thm)],[5579])).
% 22.60/22.76 tff(5581,plain,
% 22.60/22.76 (mult(mult(a, mult(b, c)), a) = mult(mult(mult(a, b), c), a)),
% 22.60/22.76 inference(transitivity,[status(thm)],[5580, 5577, 5555])).
% 22.60/22.77 tff(5582,plain,
% 22.60/22.77 (rd(mult(mult(a, mult(b, c)), a), a) = rd(mult(mult(mult(a, b), c), a), a)),
% 22.60/22.77 inference(monotonicity,[status(thm)],[5581])).
% 22.60/22.77 tff(5583,plain,
% 22.60/22.77 (rd(mult(mult(mult(a, b), c), a), a) = rd(mult(mult(a, mult(b, c)), a), a)),
% 22.60/22.77 inference(symmetry,[status(thm)],[5582])).
% 22.60/22.77 tff(5584,plain,
% 22.60/22.77 (mult(mult(a, b), c) = mult(a, mult(b, c))),
% 22.60/22.77 inference(transitivity,[status(thm)],[1151, 5583, 1034])).
% 22.60/22.77 tff(5585,plain,
% 22.60/22.77 ($false),
% 22.60/22.77 inference(unit_resolution,[status(thm)],[146, 5584])).
% 22.60/22.77 tff(5586,plain,((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, b), c), a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), b) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), b))))), inference(lemma,lemma(discharge,[]))).
% 22.60/22.77 tff(5587,plain,
% 22.60/22.77 (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, b), c), a)))),
% 22.60/22.77 inference(unit_resolution,[status(thm)],[5586, 5550, 1371])).
% 22.60/22.77 tff(5588,plain,
% 22.60/22.77 (((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, b), c), a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, b), c)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(a, b), c)))))) | (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, b), c), a)))),
% 22.60/22.77 inference(tautology,[status(thm)],[])).
% 22.60/22.77 tff(5589,plain,
% 22.60/22.77 ((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, b), c), a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, b), c)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(a, b), c)))))),
% 22.60/22.77 inference(unit_resolution,[status(thm)],[5588, 5587])).
% 22.60/22.77 tff(5590,plain,
% 22.60/22.77 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, b), c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(a, b), c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, b), c)))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, b), c), a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, b), c)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(a, b), c))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, b), c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(a, b), c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, b), c)))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, b), c), a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, b), c)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(a, b), c))))))))),
% 22.60/22.77 inference(rewrite,[status(thm)],[])).
% 22.60/22.77 tff(5591,plain,
% 22.60/22.77 (((~((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, b), c)))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, b), c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(a, b), c))))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, b), c), a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, b), c)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(a, b), c)))))))) <=> ((~((~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, b), c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(a, b), c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, b), c)))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, b), c), a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, b), c)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(a, b), c))))))))),
% 22.60/22.77 inference(rewrite,[status(thm)],[])).
% 22.60/22.77 tff(5592,plain,
% 22.60/22.77 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, b), c)))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, b), c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(a, b), c))))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, b), c), a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, b), c)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(a, b), c))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, b), c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(a, b), c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, b), c)))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, b), c), a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, b), c)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(a, b), c)))))))))),
% 22.60/22.77 inference(monotonicity,[status(thm)],[5591])).
% 22.60/22.77 tff(5593,plain,
% 22.60/22.77 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, b), c)))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, b), c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(a, b), c))))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, b), c), a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, b), c)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(a, b), c))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, b), c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(a, b), c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, b), c)))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, b), c), a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, b), c)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(a, b), c))))))))),
% 22.60/22.77 inference(transitivity,[status(thm)],[5592, 5590])).
% 22.60/22.77 tff(5594,plain,
% 22.60/22.77 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, b), c)))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, b), c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(a, b), c))))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, b), c), a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, b), c)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(a, b), c))))))))),
% 22.60/22.77 inference(quant_inst,[status(thm)],[])).
% 22.60/22.77 tff(5595,plain,
% 22.60/22.77 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, b), c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(a, b), c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, b), c)))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, b), c), a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, b), c)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(a, b), c)))))))),
% 22.60/22.77 inference(modus_ponens,[status(thm)],[5594, 5593])).
% 22.60/22.77 tff(5596,plain,
% 22.60/22.77 ((~((~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, b), c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(a, b), c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, b), c)))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, b), c), a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, b), c)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(a, b), c)))))))),
% 22.60/22.77 inference(unit_resolution,[status(thm)],[5595, 27])).
% 22.60/22.77 tff(5597,plain,
% 22.60/22.77 (~((~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, b), c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(a, b), c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, b), c)))))),
% 22.60/22.77 inference(unit_resolution,[status(thm)],[5596, 5589])).
% 22.60/22.77 tff(5598,plain,
% 22.60/22.77 (((~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, b), c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(a, b), c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, b), c))))) | (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, b), c)))),
% 22.60/22.77 inference(tautology,[status(thm)],[])).
% 22.60/22.77 tff(5599,plain,
% 22.60/22.77 (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, b), c))),
% 22.60/22.77 inference(unit_resolution,[status(thm)],[5598, 5597])).
% 22.60/22.77 tff(5600,plain,
% 22.60/22.77 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, b), c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)), a)),
% 22.60/22.77 inference(symmetry,[status(thm)],[5599])).
% 22.60/22.77 tff(5601,plain,
% 22.60/22.77 (mult(unit, b) = mult(rd(mult(b, c), mult(a, c)), a)),
% 22.60/22.77 inference(transitivity,[status(thm)],[184, 2727, 4404, 174])).
% 22.60/22.77 tff(5602,plain,
% 22.60/22.77 (mult(mult(unit, b), mult(mult(a, b), c)) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, b), c))),
% 22.60/22.77 inference(monotonicity,[status(thm)],[5601])).
% 22.60/22.77 tff(5603,plain,
% 22.60/22.77 (mult(b, mult(mult(a, c), b)) = mult(mult(unit, b), mult(mult(a, b), c))),
% 22.60/22.77 inference(monotonicity,[status(thm)],[3386, 161])).
% 22.60/22.77 tff(5604,plain,
% 22.60/22.77 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(b, mult(b, mult(mult(a, b), c))) = mult(mult(a, b), c))),
% 22.60/22.77 inference(quant_inst,[status(thm)],[])).
% 22.60/22.77 tff(5605,plain,
% 22.60/22.77 (ld(b, mult(b, mult(mult(a, b), c))) = mult(mult(a, b), c)),
% 22.60/22.77 inference(unit_resolution,[status(thm)],[5604, 7])).
% 22.60/22.77 tff(5606,assumption,(mult(b, mult(mult(a, c), b)) = mult(b, mult(b, mult(a, c)))), introduced(assumption)).
% 22.60/22.77 tff(5607,plain,
% 22.60/22.77 (mult(b, mult(b, mult(a, c))) = mult(b, mult(mult(a, c), b))),
% 22.60/22.77 inference(symmetry,[status(thm)],[5606])).
% 22.60/22.77 tff(5608,plain,
% 22.60/22.77 (mult(b, mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c)))) = mult(b, mult(b, mult(a, c)))),
% 22.60/22.77 inference(monotonicity,[status(thm)],[5531])).
% 22.60/22.77 tff(5609,plain,
% 22.60/22.77 (mult(b, mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c)))) = mult(b, mult(mult(a, b), c))),
% 22.60/22.77 inference(transitivity,[status(thm)],[5608, 5607, 5603, 3388])).
% 22.60/22.77 tff(5610,plain,
% 22.60/22.77 (ld(b, mult(b, mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))))) = ld(b, mult(b, mult(mult(a, b), c)))),
% 22.60/22.77 inference(monotonicity,[status(thm)],[5609])).
% 22.60/22.77 tff(5611,plain,
% 22.60/22.77 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(b, mult(b, mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))))) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))))),
% 22.60/22.77 inference(quant_inst,[status(thm)],[])).
% 22.60/22.77 tff(5612,plain,
% 22.60/22.77 (ld(b, mult(b, mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))))) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c)))),
% 22.60/22.77 inference(unit_resolution,[status(thm)],[5611, 7])).
% 22.60/22.77 tff(5613,plain,
% 22.60/22.77 (mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = ld(b, mult(b, mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c)))))),
% 22.60/22.77 inference(symmetry,[status(thm)],[5612])).
% 22.60/22.77 tff(5614,plain,
% 22.60/22.77 (mult(mult(unit, b), mult(a, c)) = mult(mult(unit, mult(a, c)), b)),
% 22.60/22.77 inference(transitivity,[status(thm)],[5511, 4406, 5523, 5613, 5610, 5605, 227, 5517])).
% 22.60/22.77 tff(5615,plain,
% 22.60/22.77 ($false),
% 22.60/22.77 inference(unit_resolution,[status(thm)],[5524, 5614])).
% 22.60/22.77 tff(5616,plain,((~(mult(b, mult(mult(a, c), b)) = mult(b, mult(b, mult(a, c))))) | (mult(mult(unit, b), mult(a, c)) = mult(mult(unit, mult(a, c)), b)) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))), inference(lemma,lemma(discharge,[]))).
% 22.60/22.77 tff(5617,plain,
% 22.60/22.77 (~(mult(b, mult(mult(a, c), b)) = mult(b, mult(b, mult(a, c))))),
% 22.60/22.77 inference(unit_resolution,[status(thm)],[5616, 5524, 5523, 1371])).
% 22.60/22.77 tff(5618,plain,
% 22.60/22.77 (((~(mult(mult(b, mult(a, c)), b) = mult(mult(b, b), mult(a, c)))) | (~(mult(b, mult(mult(a, c), b)) = mult(b, mult(b, mult(a, c)))))) | (mult(b, mult(mult(a, c), b)) = mult(b, mult(b, mult(a, c))))),
% 22.60/22.77 inference(tautology,[status(thm)],[])).
% 22.60/22.77 tff(5619,plain,
% 22.60/22.77 ((~(mult(mult(b, mult(a, c)), b) = mult(mult(b, b), mult(a, c)))) | (~(mult(b, mult(mult(a, c), b)) = mult(b, mult(b, mult(a, c)))))),
% 22.60/22.77 inference(unit_resolution,[status(thm)],[5618, 5617])).
% 22.60/22.77 tff(5620,plain,
% 22.60/22.77 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(b, b), mult(a, c)) = mult(b, mult(b, mult(a, c))))) | (~(mult(mult(b, mult(a, c)), b) = mult(b, mult(mult(a, c), b)))))) | (~((~(mult(mult(b, mult(a, c)), b) = mult(mult(b, b), mult(a, c)))) | (~(mult(b, mult(mult(a, c), b)) = mult(b, mult(b, mult(a, c))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(b, b), mult(a, c)) = mult(b, mult(b, mult(a, c))))) | (~(mult(mult(b, mult(a, c)), b) = mult(b, mult(mult(a, c), b)))))) | (~((~(mult(mult(b, mult(a, c)), b) = mult(mult(b, b), mult(a, c)))) | (~(mult(b, mult(mult(a, c), b)) = mult(b, mult(b, mult(a, c))))))))),
% 22.60/22.78 inference(rewrite,[status(thm)],[])).
% 22.60/22.78 tff(5621,plain,
% 22.60/22.78 (((~((~(mult(mult(b, mult(a, c)), b) = mult(mult(b, b), mult(a, c)))) | (~(mult(b, mult(mult(a, c), b)) = mult(b, mult(b, mult(a, c))))))) | (~((~(mult(mult(b, b), mult(a, c)) = mult(b, mult(b, mult(a, c))))) | (~(mult(mult(b, mult(a, c)), b) = mult(b, mult(mult(a, c), b))))))) <=> ((~((~(mult(mult(b, b), mult(a, c)) = mult(b, mult(b, mult(a, c))))) | (~(mult(mult(b, mult(a, c)), b) = mult(b, mult(mult(a, c), b)))))) | (~((~(mult(mult(b, mult(a, c)), b) = mult(mult(b, b), mult(a, c)))) | (~(mult(b, mult(mult(a, c), b)) = mult(b, mult(b, mult(a, c))))))))),
% 22.60/22.78 inference(rewrite,[status(thm)],[])).
% 22.60/22.78 tff(5622,plain,
% 22.60/22.78 ((~((~(mult(mult(b, mult(a, c)), b) = mult(b, mult(mult(a, c), b)))) | (~(mult(mult(b, b), mult(a, c)) = mult(b, mult(b, mult(a, c))))))) <=> (~((~(mult(mult(b, b), mult(a, c)) = mult(b, mult(b, mult(a, c))))) | (~(mult(mult(b, mult(a, c)), b) = mult(b, mult(mult(a, c), b))))))),
% 22.60/22.78 inference(rewrite,[status(thm)],[])).
% 22.60/22.78 tff(5623,plain,
% 22.60/22.78 ((~((~(mult(mult(b, mult(a, c)), b) = mult(mult(b, b), mult(a, c)))) | (~(mult(b, mult(mult(a, c), b)) = mult(b, mult(b, mult(a, c))))))) <=> (~((~(mult(mult(b, mult(a, c)), b) = mult(mult(b, b), mult(a, c)))) | (~(mult(b, mult(mult(a, c), b)) = mult(b, mult(b, mult(a, c)))))))),
% 22.60/22.78 inference(rewrite,[status(thm)],[])).
% 22.60/22.78 tff(5624,plain,
% 22.60/22.78 (((~((~(mult(mult(b, mult(a, c)), b) = mult(mult(b, b), mult(a, c)))) | (~(mult(b, mult(mult(a, c), b)) = mult(b, mult(b, mult(a, c))))))) | (~((~(mult(mult(b, mult(a, c)), b) = mult(b, mult(mult(a, c), b)))) | (~(mult(mult(b, b), mult(a, c)) = mult(b, mult(b, mult(a, c)))))))) <=> ((~((~(mult(mult(b, mult(a, c)), b) = mult(mult(b, b), mult(a, c)))) | (~(mult(b, mult(mult(a, c), b)) = mult(b, mult(b, mult(a, c))))))) | (~((~(mult(mult(b, b), mult(a, c)) = mult(b, mult(b, mult(a, c))))) | (~(mult(mult(b, mult(a, c)), b) = mult(b, mult(mult(a, c), b)))))))),
% 22.60/22.78 inference(monotonicity,[status(thm)],[5623, 5622])).
% 22.60/22.78 tff(5625,plain,
% 22.60/22.78 (((~((~(mult(mult(b, mult(a, c)), b) = mult(mult(b, b), mult(a, c)))) | (~(mult(b, mult(mult(a, c), b)) = mult(b, mult(b, mult(a, c))))))) | (~((~(mult(mult(b, mult(a, c)), b) = mult(b, mult(mult(a, c), b)))) | (~(mult(mult(b, b), mult(a, c)) = mult(b, mult(b, mult(a, c)))))))) <=> ((~((~(mult(mult(b, b), mult(a, c)) = mult(b, mult(b, mult(a, c))))) | (~(mult(mult(b, mult(a, c)), b) = mult(b, mult(mult(a, c), b)))))) | (~((~(mult(mult(b, mult(a, c)), b) = mult(mult(b, b), mult(a, c)))) | (~(mult(b, mult(mult(a, c), b)) = mult(b, mult(b, mult(a, c))))))))),
% 22.60/22.78 inference(transitivity,[status(thm)],[5624, 5621])).
% 22.60/22.78 tff(5626,plain,
% 22.60/22.78 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(b, mult(a, c)), b) = mult(mult(b, b), mult(a, c)))) | (~(mult(b, mult(mult(a, c), b)) = mult(b, mult(b, mult(a, c))))))) | (~((~(mult(mult(b, mult(a, c)), b) = mult(b, mult(mult(a, c), b)))) | (~(mult(mult(b, b), mult(a, c)) = mult(b, mult(b, mult(a, c))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(b, b), mult(a, c)) = mult(b, mult(b, mult(a, c))))) | (~(mult(mult(b, mult(a, c)), b) = mult(b, mult(mult(a, c), b)))))) | (~((~(mult(mult(b, mult(a, c)), b) = mult(mult(b, b), mult(a, c)))) | (~(mult(b, mult(mult(a, c), b)) = mult(b, mult(b, mult(a, c)))))))))),
% 22.60/22.78 inference(monotonicity,[status(thm)],[5625])).
% 22.60/22.78 tff(5627,plain,
% 22.60/22.78 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(b, mult(a, c)), b) = mult(mult(b, b), mult(a, c)))) | (~(mult(b, mult(mult(a, c), b)) = mult(b, mult(b, mult(a, c))))))) | (~((~(mult(mult(b, mult(a, c)), b) = mult(b, mult(mult(a, c), b)))) | (~(mult(mult(b, b), mult(a, c)) = mult(b, mult(b, mult(a, c))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(b, b), mult(a, c)) = mult(b, mult(b, mult(a, c))))) | (~(mult(mult(b, mult(a, c)), b) = mult(b, mult(mult(a, c), b)))))) | (~((~(mult(mult(b, mult(a, c)), b) = mult(mult(b, b), mult(a, c)))) | (~(mult(b, mult(mult(a, c), b)) = mult(b, mult(b, mult(a, c))))))))),
% 22.60/22.78 inference(transitivity,[status(thm)],[5626, 5620])).
% 22.60/22.78 tff(5628,plain,
% 22.60/22.78 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(b, mult(a, c)), b) = mult(mult(b, b), mult(a, c)))) | (~(mult(b, mult(mult(a, c), b)) = mult(b, mult(b, mult(a, c))))))) | (~((~(mult(mult(b, mult(a, c)), b) = mult(b, mult(mult(a, c), b)))) | (~(mult(mult(b, b), mult(a, c)) = mult(b, mult(b, mult(a, c))))))))),
% 22.60/22.78 inference(quant_inst,[status(thm)],[])).
% 22.60/22.78 tff(5629,plain,
% 22.60/22.78 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(b, b), mult(a, c)) = mult(b, mult(b, mult(a, c))))) | (~(mult(mult(b, mult(a, c)), b) = mult(b, mult(mult(a, c), b)))))) | (~((~(mult(mult(b, mult(a, c)), b) = mult(mult(b, b), mult(a, c)))) | (~(mult(b, mult(mult(a, c), b)) = mult(b, mult(b, mult(a, c)))))))),
% 22.60/22.78 inference(modus_ponens,[status(thm)],[5628, 5627])).
% 22.60/22.78 tff(5630,plain,
% 22.60/22.78 ((~((~(mult(mult(b, b), mult(a, c)) = mult(b, mult(b, mult(a, c))))) | (~(mult(mult(b, mult(a, c)), b) = mult(b, mult(mult(a, c), b)))))) | (~((~(mult(mult(b, mult(a, c)), b) = mult(mult(b, b), mult(a, c)))) | (~(mult(b, mult(mult(a, c), b)) = mult(b, mult(b, mult(a, c)))))))),
% 22.60/22.78 inference(unit_resolution,[status(thm)],[5629, 27])).
% 22.60/22.78 tff(5631,plain,
% 22.60/22.78 (~((~(mult(mult(b, b), mult(a, c)) = mult(b, mult(b, mult(a, c))))) | (~(mult(mult(b, mult(a, c)), b) = mult(b, mult(mult(a, c), b)))))),
% 22.60/22.78 inference(unit_resolution,[status(thm)],[5630, 5619])).
% 22.60/22.78 tff(5632,plain,
% 22.60/22.78 (((~(mult(mult(b, b), mult(a, c)) = mult(b, mult(b, mult(a, c))))) | (~(mult(mult(b, mult(a, c)), b) = mult(b, mult(mult(a, c), b))))) | (mult(mult(b, mult(a, c)), b) = mult(b, mult(mult(a, c), b)))),
% 22.60/22.78 inference(tautology,[status(thm)],[])).
% 22.60/22.78 tff(5633,plain,
% 22.60/22.78 (mult(mult(b, mult(a, c)), b) = mult(b, mult(mult(a, c), b))),
% 22.60/22.78 inference(unit_resolution,[status(thm)],[5632, 5631])).
% 22.60/22.78 tff(5634,plain,
% 22.60/22.78 (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))), b) = mult(mult(b, mult(a, c)), b)),
% 22.60/22.78 inference(monotonicity,[status(thm)],[5531])).
% 22.60/22.78 tff(5635,plain,
% 22.60/22.78 (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))), b) = mult(mult(mult(a, b), c), b)),
% 22.60/22.78 inference(transitivity,[status(thm)],[5634, 5633, 5603, 5602, 5600, 5553, 5521, 5519])).
% 22.60/22.78 tff(5636,plain,
% 22.60/22.78 (rd(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))), b), b) = rd(mult(mult(mult(a, b), c), b), b)),
% 22.60/22.78 inference(monotonicity,[status(thm)],[5635])).
% 22.60/22.78 tff(5637,plain,
% 22.60/22.78 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))), b), b) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))))),
% 22.60/22.78 inference(quant_inst,[status(thm)],[])).
% 22.60/22.78 tff(5638,plain,
% 22.60/22.78 (rd(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))), b), b) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c)))),
% 22.60/22.78 inference(unit_resolution,[status(thm)],[5637, 168])).
% 22.60/22.78 tff(5639,plain,
% 22.60/22.78 (mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = rd(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))), b), b)),
% 22.60/22.78 inference(symmetry,[status(thm)],[5638])).
% 22.60/22.78 tff(5640,plain,
% 22.60/22.78 (mult(mult(unit, b), mult(a, c)) = mult(mult(unit, mult(a, c)), b)),
% 22.60/22.78 inference(transitivity,[status(thm)],[5511, 4406, 5523, 5639, 5636, 793, 227, 5517])).
% 22.60/22.78 tff(5641,plain,
% 22.60/22.78 ($false),
% 22.60/22.78 inference(unit_resolution,[status(thm)],[5524, 5640])).
% 22.60/22.78 tff(5642,plain,((~(mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a))) | (mult(mult(unit, b), mult(a, c)) = mult(mult(unit, mult(a, c)), b)) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))))) | (~(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))), inference(lemma,lemma(discharge,[]))).
% 22.60/22.78 tff(5643,plain,
% 22.60/22.78 (~(mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a))),
% 22.60/22.78 inference(unit_resolution,[status(thm)],[5642, 5516, 4333, 1488, 4331])).
% 22.60/22.78 tff(5644,plain,
% 22.60/22.78 (mult(b, mult(mult(unit, mult(b, a)), unit)) = mult(b, mult(b, a))),
% 22.60/22.78 inference(monotonicity,[status(thm)],[4321])).
% 22.60/22.78 tff(5645,plain,
% 22.60/22.78 (mult(c, mult(b, mult(mult(unit, mult(b, a)), unit))) = mult(c, mult(b, mult(b, a)))),
% 22.60/22.78 inference(monotonicity,[status(thm)],[5644])).
% 22.60/22.78 tff(5646,plain,
% 22.60/22.78 ((mult(mult(c, b), mult(mult(unit, mult(b, a)), unit)) = mult(c, mult(b, mult(mult(unit, mult(b, a)), unit)))) <=> (mult(mult(c, b), mult(b, a)) = mult(c, mult(b, mult(b, a))))),
% 22.60/22.78 inference(monotonicity,[status(thm)],[4323, 5645])).
% 22.60/22.78 tff(5647,plain,
% 22.60/22.78 ((mult(mult(c, b), mult(b, a)) = mult(c, mult(b, mult(b, a)))) <=> (mult(mult(c, b), mult(mult(unit, mult(b, a)), unit)) = mult(c, mult(b, mult(mult(unit, mult(b, a)), unit))))),
% 22.60/22.78 inference(symmetry,[status(thm)],[5646])).
% 22.60/22.78 tff(5648,plain,
% 22.60/22.78 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(b, c), mult(mult(b, c), mult(a, c))) = mult(a, c))),
% 22.60/22.78 inference(quant_inst,[status(thm)],[])).
% 22.60/22.78 tff(5649,plain,
% 22.60/22.78 (ld(mult(b, c), mult(mult(b, c), mult(a, c))) = mult(a, c)),
% 22.60/22.78 inference(unit_resolution,[status(thm)],[5648, 7])).
% 22.60/22.78 tff(5650,plain,
% 22.60/22.78 (mult(mult(a, c), rd(mult(b, c), mult(a, c))) = ld(a, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 22.60/22.78 inference(symmetry,[status(thm)],[4336])).
% 22.60/22.78 tff(5651,plain,
% 22.60/22.78 (mult(mult(a, c), rd(mult(b, c), mult(a, c))) = mult(b, c)),
% 22.60/22.78 inference(transitivity,[status(thm)],[5650, 1490, 141])).
% 22.60/22.78 tff(5652,plain,
% 22.60/22.78 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(b, c), mult(a, c))),
% 22.60/22.78 inference(monotonicity,[status(thm)],[5651])).
% 22.60/22.78 tff(5653,plain,
% 22.60/22.78 (mult(mult(b, c), mult(a, c)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))),
% 22.60/22.78 inference(symmetry,[status(thm)],[5652])).
% 22.60/22.78 tff(5654,plain,
% 22.60/22.78 (mult(c, mult(mult(a, c), b)) = mult(c, mult(mult(a, b), c))),
% 22.60/22.78 inference(symmetry,[status(thm)],[4024])).
% 22.60/22.78 tff(5655,plain,
% 22.60/22.78 (mult(c, mult(b, mult(a, c))) = mult(c, mult(mult(a, b), c))),
% 22.60/22.78 inference(transitivity,[status(thm)],[2740, 5654])).
% 22.60/22.78 tff(5656,plain,
% 22.60/22.78 (ld(c, mult(c, mult(b, mult(a, c)))) = ld(c, mult(c, mult(mult(a, b), c)))),
% 22.60/22.78 inference(monotonicity,[status(thm)],[5655])).
% 22.60/22.78 tff(5657,plain,
% 22.60/22.78 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(c, mult(c, mult(b, mult(a, c)))) = mult(b, mult(a, c)))),
% 22.60/22.78 inference(quant_inst,[status(thm)],[])).
% 22.60/22.78 tff(5658,plain,
% 22.60/22.78 (ld(c, mult(c, mult(b, mult(a, c)))) = mult(b, mult(a, c))),
% 22.60/22.78 inference(unit_resolution,[status(thm)],[5657, 7])).
% 22.60/22.78 tff(5659,plain,
% 22.60/22.78 (mult(b, mult(a, c)) = ld(c, mult(c, mult(b, mult(a, c))))),
% 22.60/22.78 inference(symmetry,[status(thm)],[5658])).
% 22.60/22.78 tff(5660,plain,
% 22.60/22.78 (mult(mult(unit, b), mult(a, c)) = mult(mult(unit, mult(a, c)), b)),
% 22.60/22.78 inference(transitivity,[status(thm)],[5511, 5659, 5656, 4031, 227, 5517])).
% 22.60/22.78 tff(5661,plain,
% 22.60/22.78 ($false),
% 22.60/22.78 inference(unit_resolution,[status(thm)],[5524, 5660])).
% 22.60/22.78 tff(5662,plain,((~(mult(c, mult(mult(a, c), b)) = mult(c, mult(b, mult(a, c))))) | (mult(mult(unit, b), mult(a, c)) = mult(mult(unit, mult(a, c)), b))), inference(lemma,lemma(discharge,[]))).
% 22.60/22.78 tff(5663,plain,
% 22.60/22.78 (~(mult(c, mult(mult(a, c), b)) = mult(c, mult(b, mult(a, c))))),
% 22.60/22.78 inference(unit_resolution,[status(thm)],[5662, 5516])).
% 22.60/22.78 tff(5664,plain,
% 22.60/22.78 ((~(mult(mult(c, mult(a, c)), b) = mult(mult(c, b), mult(a, c)))) | (~(mult(c, mult(mult(a, c), b)) = mult(c, mult(b, mult(a, c)))))),
% 22.60/22.78 inference(unit_resolution,[status(thm)],[2710, 5663])).
% 22.60/22.78 tff(5665,plain,
% 22.60/22.78 (~((~(mult(mult(c, mult(a, c)), b) = mult(c, mult(mult(a, c), b)))) | (~(mult(mult(c, b), mult(a, c)) = mult(c, mult(b, mult(a, c))))))),
% 22.60/22.78 inference(unit_resolution,[status(thm)],[2436, 5664])).
% 22.60/22.78 tff(5666,plain,
% 22.60/22.78 (mult(mult(c, b), mult(a, c)) = mult(c, mult(b, mult(a, c)))),
% 22.60/22.78 inference(unit_resolution,[status(thm)],[2431, 5665])).
% 22.60/22.78 tff(5667,plain,
% 22.60/22.78 (mult(c, mult(b, mult(a, c))) = mult(mult(c, b), mult(a, c))),
% 22.60/22.78 inference(symmetry,[status(thm)],[5666])).
% 22.60/22.78 tff(5668,plain,
% 22.60/22.78 (mult(c, mult(b, mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))),
% 22.60/22.78 inference(transitivity,[status(thm)],[5667, 2429, 5653])).
% 22.60/22.78 tff(5669,plain,
% 22.60/22.78 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), b)),
% 22.60/22.78 inference(transitivity,[status(thm)],[5496, 5504])).
% 22.60/22.78 tff(5670,plain,
% 22.60/22.78 (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(a, c), b), c)),
% 22.60/22.78 inference(monotonicity,[status(thm)],[5669])).
% 22.60/22.78 tff(5671,plain,
% 22.60/22.78 (mult(mult(mult(a, c), b), c) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c)),
% 22.60/22.78 inference(symmetry,[status(thm)],[5670])).
% 22.60/22.78 tff(5672,plain,
% 22.60/22.78 (mult(c, mult(mult(a, c), b)) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c)),
% 22.60/22.78 inference(transitivity,[status(thm)],[3190, 3188, 4284, 5671])).
% 22.60/22.78 tff(5673,plain,
% 22.60/22.78 ((mult(c, mult(mult(a, c), b)) = mult(c, mult(b, mult(a, c)))) <=> (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 22.60/22.78 inference(monotonicity,[status(thm)],[5672, 5668])).
% 22.60/22.78 tff(5674,plain,
% 22.60/22.78 ((~(mult(c, mult(mult(a, c), b)) = mult(c, mult(b, mult(a, c))))) <=> (~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))))),
% 22.60/22.78 inference(monotonicity,[status(thm)],[5673])).
% 22.60/22.78 tff(5675,plain,
% 22.60/22.78 (~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 22.60/22.78 inference(modus_ponens,[status(thm)],[5663, 5674])).
% 22.60/22.78 tff(5676,plain,
% 22.60/22.78 ((~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)))) | (~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))))),
% 22.60/22.78 inference(unit_resolution,[status(thm)],[121, 5675])).
% 22.60/22.78 tff(5677,plain,
% 22.60/22.78 (~((~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))))),
% 22.60/22.78 inference(unit_resolution,[status(thm)],[4484, 5676])).
% 22.60/22.78 tff(5678,plain,
% 22.60/22.78 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))),
% 22.60/22.78 inference(unit_resolution,[status(thm)],[115, 5677])).
% 22.60/22.78 tff(5679,plain,
% 22.60/22.78 (mult(mult(b, c), mult(c, a)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a))),
% 22.60/22.78 inference(monotonicity,[status(thm)],[4337])).
% 22.60/22.78 tff(5680,plain,
% 22.60/22.78 (mult(mult(b, c), mult(c, a)) = mult(mult(b, c), mult(a, c))),
% 22.60/22.78 inference(transitivity,[status(thm)],[5679, 5678, 5652])).
% 22.60/22.78 tff(5681,plain,
% 22.60/22.78 (ld(mult(b, c), mult(mult(b, c), mult(c, a))) = ld(mult(b, c), mult(mult(b, c), mult(a, c)))),
% 22.60/22.78 inference(monotonicity,[status(thm)],[5680])).
% 22.60/22.78 tff(5682,plain,
% 22.60/22.78 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(b, c), mult(mult(b, c), mult(c, a))) = mult(c, a))),
% 22.60/22.78 inference(quant_inst,[status(thm)],[])).
% 22.60/22.78 tff(5683,plain,
% 22.60/22.78 (ld(mult(b, c), mult(mult(b, c), mult(c, a))) = mult(c, a)),
% 22.60/22.78 inference(unit_resolution,[status(thm)],[5682, 7])).
% 22.60/22.78 tff(5684,plain,
% 22.60/22.78 (mult(c, a) = ld(mult(b, c), mult(mult(b, c), mult(c, a)))),
% 22.60/22.78 inference(symmetry,[status(thm)],[5683])).
% 22.60/22.78 tff(5685,plain,
% 22.60/22.78 (mult(c, a) = mult(a, c)),
% 22.60/22.78 inference(transitivity,[status(thm)],[5684, 5681, 5649])).
% 22.60/22.78 tff(5686,plain,
% 22.60/22.78 (mult(mult(c, a), b) = mult(mult(a, c), b)),
% 22.60/22.78 inference(monotonicity,[status(thm)],[5685])).
% 22.60/22.78 tff(5687,plain,
% 22.60/22.78 (mult(mult(a, c), b) = mult(mult(c, a), b)),
% 22.60/22.78 inference(symmetry,[status(thm)],[5686])).
% 22.60/22.78 tff(5688,plain,
% 22.60/22.78 (mult(c, mult(b, a)) = mult(c, mult(a, b))),
% 22.60/22.78 inference(transitivity,[status(thm)],[4304, 2298, 4338, 5496, 5504, 5687, 4221])).
% 22.60/22.78 tff(5689,plain,
% 22.60/22.78 (ld(c, mult(c, mult(b, a))) = ld(c, mult(c, mult(a, b)))),
% 22.60/22.78 inference(monotonicity,[status(thm)],[5688])).
% 22.60/22.78 tff(5690,plain,
% 22.60/22.78 (mult(b, a) = mult(a, b)),
% 22.60/22.78 inference(transitivity,[status(thm)],[1473, 5689, 1468])).
% 22.60/22.78 tff(5691,plain,
% 22.60/22.78 (mult(b, mult(b, a)) = mult(b, mult(a, b))),
% 22.60/22.78 inference(monotonicity,[status(thm)],[5690])).
% 22.60/22.78 tff(5692,plain,
% 22.60/22.78 (mult(c, mult(b, mult(b, a))) = mult(c, mult(b, mult(a, b)))),
% 22.60/22.78 inference(monotonicity,[status(thm)],[5691])).
% 22.60/22.78 tff(5693,plain,
% 22.60/22.78 (mult(c, mult(b, mult(a, b))) = mult(c, mult(b, mult(b, a)))),
% 22.60/22.78 inference(symmetry,[status(thm)],[5692])).
% 22.60/22.78 tff(5694,plain,
% 22.60/22.78 (ld(c, mult(c, mult(a, b))) = ld(c, mult(c, mult(b, a)))),
% 22.60/22.78 inference(symmetry,[status(thm)],[5689])).
% 22.60/22.78 tff(5695,plain,
% 22.60/22.78 (mult(a, b) = mult(b, a)),
% 22.60/22.78 inference(transitivity,[status(thm)],[2235, 5694, 1472])).
% 22.60/22.78 tff(5696,plain,
% 22.60/22.78 (mult(mult(a, b), rd(mult(b, c), mult(a, c))) = mult(mult(b, a), rd(mult(b, c), mult(a, c)))),
% 22.60/22.78 inference(monotonicity,[status(thm)],[5695])).
% 22.60/22.78 tff(5697,plain,
% 22.60/22.78 (mult(a, mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, b)),
% 22.60/22.78 inference(monotonicity,[status(thm)],[5503])).
% 22.60/22.78 tff(5698,plain,
% 22.60/22.78 (mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))),
% 22.60/22.78 inference(unit_resolution,[status(thm)],[4328, 4296])).
% 22.60/22.78 tff(5699,plain,
% 22.60/22.78 (ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c)))) = ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))),
% 22.60/22.78 inference(monotonicity,[status(thm)],[5698])).
% 22.60/22.78 tff(5700,plain,
% 22.60/22.78 (mult(c, a) = mult(a, c)),
% 22.60/22.78 inference(transitivity,[status(thm)],[3884, 4263, 3872])).
% 22.60/22.78 tff(5701,plain,
% 22.60/22.78 (mult(a, mult(c, a)) = mult(a, mult(a, c))),
% 22.60/22.78 inference(monotonicity,[status(thm)],[5700])).
% 22.60/22.78 tff(5702,plain,
% 22.60/22.78 (mult(a, mult(c, a)) = mult(mult(a, c), a)),
% 22.60/22.78 inference(transitivity,[status(thm)],[5701, 4452, 5699, 4447])).
% 22.60/22.78 tff(5703,plain,
% 22.60/22.78 (mult(mult(a, mult(c, a)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))),
% 22.60/22.78 inference(monotonicity,[status(thm)],[5702])).
% 22.60/22.78 tff(5704,plain,
% 22.60/22.78 (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, mult(c, a)), rd(mult(b, c), mult(a, c)))),
% 22.60/22.78 inference(symmetry,[status(thm)],[5703])).
% 22.60/22.78 tff(5705,plain,
% 22.60/22.78 (ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) = ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))))),
% 22.60/22.78 inference(symmetry,[status(thm)],[5699])).
% 22.60/22.78 tff(5706,plain,
% 22.60/22.78 (mult(mult(a, c), a) = mult(a, mult(a, c))),
% 22.60/22.78 inference(transitivity,[status(thm)],[4609, 5705, 4451])).
% 22.60/22.78 tff(5707,plain,
% 22.60/22.78 (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 22.60/22.78 inference(monotonicity,[status(thm)],[5706])).
% 22.60/22.78 tff(5708,plain,
% 22.60/22.78 (mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))),
% 22.60/22.78 inference(symmetry,[status(thm)],[5707])).
% 22.60/22.78 tff(5709,plain,
% 22.60/22.79 (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))),
% 22.60/22.79 inference(unit_resolution,[status(thm)],[1814, 5496])).
% 22.60/22.79 tff(5710,plain,
% 22.60/22.79 (mult(mult(c, a), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))),
% 22.60/22.79 inference(monotonicity,[status(thm)],[3885])).
% 22.60/22.79 tff(5711,plain,
% 22.60/22.79 (mult(mult(mult(c, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)),
% 22.60/22.79 inference(monotonicity,[status(thm)],[5710])).
% 22.60/22.79 tff(5712,assumption,(~((~(mult(mult(a, a), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), a))) | (~(mult(a, mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), a)))))), introduced(assumption)).
% 22.60/22.79 tff(5713,plain,
% 22.60/22.79 (((~(mult(mult(a, a), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), a))) | (~(mult(a, mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), a))))) | (mult(mult(a, a), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), a))),
% 22.60/22.79 inference(tautology,[status(thm)],[])).
% 22.60/22.79 tff(5714,plain,
% 22.60/22.79 (mult(mult(a, a), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), a)),
% 22.60/22.79 inference(unit_resolution,[status(thm)],[5713, 5712])).
% 22.60/22.79 tff(5715,plain,
% 22.60/22.79 (mult(c, mult(mult(a, a), rd(mult(b, c), mult(a, c)))) = mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), a))),
% 22.60/22.79 inference(monotonicity,[status(thm)],[5714])).
% 22.60/22.79 tff(5716,plain,
% 22.60/22.79 (mult(c, mult(mult(a, a), rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)),
% 22.60/22.79 inference(transitivity,[status(thm)],[5715, 5404, 5711])).
% 22.60/22.79 tff(5717,plain,
% 22.60/22.79 (mult(c, mult(mult(a, unit), a)) = mult(c, mult(a, a))),
% 22.60/22.79 inference(symmetry,[status(thm)],[2656])).
% 22.60/22.79 tff(5718,plain,
% 22.60/22.79 ((~![A: $i] : (mult(A, unit) = A)) | (mult(mult(c, a), unit) = mult(c, a))),
% 22.60/22.79 inference(quant_inst,[status(thm)],[])).
% 22.60/22.79 tff(5719,plain,
% 22.60/22.79 (mult(mult(c, a), unit) = mult(c, a)),
% 22.60/22.79 inference(unit_resolution,[status(thm)],[5718, 43])).
% 22.60/22.79 tff(5720,plain,
% 22.60/22.79 (mult(mult(c, a), unit) = mult(a, c)),
% 22.60/22.79 inference(transitivity,[status(thm)],[5719, 3884, 3869, 3872])).
% 22.60/22.79 tff(5721,plain,
% 22.60/22.79 (mult(mult(mult(c, a), unit), a) = mult(mult(a, c), a)),
% 22.60/22.79 inference(monotonicity,[status(thm)],[5720])).
% 22.60/22.79 tff(5722,plain,
% 22.60/22.79 (mult(mult(a, c), a) = mult(mult(mult(c, a), unit), a)),
% 22.60/22.79 inference(symmetry,[status(thm)],[5721])).
% 22.60/22.79 tff(5723,plain,
% 22.60/22.79 (mult(mult(a, c), a) = mult(c, mult(a, a))),
% 22.60/22.79 inference(transitivity,[status(thm)],[5722, 2654, 5717])).
% 22.60/22.79 tff(5724,plain,
% 22.60/22.79 (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(c, mult(a, a)), rd(mult(b, c), mult(a, c)))),
% 22.60/22.79 inference(monotonicity,[status(thm)],[5723])).
% 22.60/22.79 tff(5725,plain,
% 22.60/22.79 (mult(mult(c, mult(a, a)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))),
% 22.60/22.79 inference(symmetry,[status(thm)],[5724])).
% 22.60/22.79 tff(5726,plain,
% 22.60/22.79 ((mult(mult(c, mult(a, a)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, a), rd(mult(b, c), mult(a, c))))) <=> (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))),
% 22.60/22.79 inference(monotonicity,[status(thm)],[5725, 5716])).
% 22.60/22.79 tff(5727,plain,
% 22.60/22.79 ((mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)) <=> (mult(mult(c, mult(a, a)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, a), rd(mult(b, c), mult(a, c)))))),
% 22.60/22.79 inference(symmetry,[status(thm)],[5726])).
% 22.60/22.79 tff(5728,plain,
% 22.60/22.79 ((~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))) <=> (~(mult(mult(c, mult(a, a)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, a), rd(mult(b, c), mult(a, c))))))),
% 22.60/22.79 inference(monotonicity,[status(thm)],[5727])).
% 22.60/22.79 tff(5729,plain,
% 22.60/22.79 (~(mult(mult(c, mult(a, a)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, a), rd(mult(b, c), mult(a, c)))))),
% 22.60/22.79 inference(modus_ponens,[status(thm)],[2331, 5728])).
% 22.60/22.79 tff(5730,plain,
% 22.60/22.79 (((~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, a))))) | (~(mult(mult(c, mult(a, a)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, a), rd(mult(b, c), mult(a, c))))))) | (mult(mult(c, mult(a, a)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, a), rd(mult(b, c), mult(a, c)))))),
% 22.60/22.79 inference(tautology,[status(thm)],[])).
% 22.60/22.79 tff(5731,plain,
% 22.60/22.79 ((~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, a))))) | (~(mult(mult(c, mult(a, a)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, a), rd(mult(b, c), mult(a, c))))))),
% 22.60/22.79 inference(unit_resolution,[status(thm)],[5730, 5729])).
% 22.60/22.79 tff(5732,plain,
% 22.60/22.79 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(mult(c, mult(a, a)), rd(mult(b, c), mult(a, c))))) | (~(mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, a))) = mult(c, mult(mult(a, a), rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, a))))) | (~(mult(mult(c, mult(a, a)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, a), rd(mult(b, c), mult(a, c)))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(mult(c, mult(a, a)), rd(mult(b, c), mult(a, c))))) | (~(mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, a))) = mult(c, mult(mult(a, a), rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, a))))) | (~(mult(mult(c, mult(a, a)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, a), rd(mult(b, c), mult(a, c)))))))))),
% 22.60/22.79 inference(rewrite,[status(thm)],[])).
% 22.60/22.79 tff(5733,plain,
% 22.60/22.79 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(mult(c, mult(a, a)), rd(mult(b, c), mult(a, c))))) | (~(mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, a))) = mult(c, mult(mult(a, a), rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, a))))) | (~(mult(mult(c, mult(a, a)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, a), rd(mult(b, c), mult(a, c)))))))))),
% 22.60/22.79 inference(quant_inst,[status(thm)],[])).
% 22.60/22.79 tff(5734,plain,
% 22.60/22.79 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(mult(c, mult(a, a)), rd(mult(b, c), mult(a, c))))) | (~(mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, a))) = mult(c, mult(mult(a, a), rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, a))))) | (~(mult(mult(c, mult(a, a)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, a), rd(mult(b, c), mult(a, c))))))))),
% 22.60/22.79 inference(modus_ponens,[status(thm)],[5733, 5732])).
% 22.60/22.79 tff(5735,plain,
% 22.60/22.79 ((~((~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(mult(c, mult(a, a)), rd(mult(b, c), mult(a, c))))) | (~(mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, a))) = mult(c, mult(mult(a, a), rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, a))))) | (~(mult(mult(c, mult(a, a)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, a), rd(mult(b, c), mult(a, c))))))))),
% 22.60/22.79 inference(unit_resolution,[status(thm)],[5734, 27])).
% 22.60/22.79 tff(5736,plain,
% 22.60/22.79 (~((~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(mult(c, mult(a, a)), rd(mult(b, c), mult(a, c))))) | (~(mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, a))) = mult(c, mult(mult(a, a), rd(mult(b, c), mult(a, c)))))))),
% 22.60/22.79 inference(unit_resolution,[status(thm)],[5735, 5731])).
% 22.60/22.79 tff(5737,plain,
% 22.60/22.79 (((~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(mult(c, mult(a, a)), rd(mult(b, c), mult(a, c))))) | (~(mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, a))) = mult(c, mult(mult(a, a), rd(mult(b, c), mult(a, c))))))) | (mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, a))) = mult(c, mult(mult(a, a), rd(mult(b, c), mult(a, c)))))),
% 22.60/22.79 inference(tautology,[status(thm)],[])).
% 22.60/22.79 tff(5738,plain,
% 22.60/22.79 (mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, a))) = mult(c, mult(mult(a, a), rd(mult(b, c), mult(a, c))))),
% 22.60/22.79 inference(unit_resolution,[status(thm)],[5737, 5736])).
% 22.60/22.79 tff(5739,plain,
% 22.60/22.79 (mult(c, mult(mult(a, a), rd(mult(b, c), mult(a, c)))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, a)))),
% 22.60/22.79 inference(symmetry,[status(thm)],[5738])).
% 22.60/22.79 tff(5740,plain,
% 22.60/22.79 (mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), a)) = mult(c, mult(mult(a, a), rd(mult(b, c), mult(a, c))))),
% 22.60/22.79 inference(symmetry,[status(thm)],[5715])).
% 22.60/22.79 tff(5741,plain,
% 22.60/22.79 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(c, a), rd(mult(b, c), mult(a, c))), a)),
% 22.60/22.79 inference(symmetry,[status(thm)],[5711])).
% 22.60/22.79 tff(5742,plain,
% 22.60/22.79 (mult(a, mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), a))),
% 22.60/22.79 inference(unit_resolution,[status(thm)],[909, 5712])).
% 22.60/22.79 tff(5743,plain,
% 22.60/22.79 (ld(a, mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = ld(a, mult(a, mult(rd(mult(b, c), mult(a, c)), a)))),
% 22.60/22.79 inference(monotonicity,[status(thm)],[5742])).
% 22.60/22.79 tff(5744,plain,
% 22.60/22.79 (ld(a, mult(a, mult(rd(mult(b, c), mult(a, c)), a))) = ld(a, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))),
% 22.60/22.79 inference(symmetry,[status(thm)],[5743])).
% 22.60/22.79 tff(5745,plain,
% 22.60/22.79 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(a, mult(a, mult(rd(mult(b, c), mult(a, c)), a))) = mult(rd(mult(b, c), mult(a, c)), a))),
% 22.60/22.79 inference(quant_inst,[status(thm)],[])).
% 22.60/22.79 tff(5746,plain,
% 22.60/22.79 (ld(a, mult(a, mult(rd(mult(b, c), mult(a, c)), a))) = mult(rd(mult(b, c), mult(a, c)), a)),
% 22.60/22.79 inference(unit_resolution,[status(thm)],[5745, 7])).
% 22.60/22.79 tff(5747,plain,
% 22.60/22.79 (mult(rd(mult(b, c), mult(a, c)), a) = ld(a, mult(a, mult(rd(mult(b, c), mult(a, c)), a)))),
% 22.60/22.79 inference(symmetry,[status(thm)],[5746])).
% 22.60/22.79 tff(5748,plain,
% 22.60/22.79 (mult(rd(mult(b, c), mult(a, c)), a) = mult(a, rd(mult(b, c), mult(a, c)))),
% 22.60/22.79 inference(transitivity,[status(thm)],[5747, 5744, 918])).
% 22.60/22.79 tff(5749,plain,
% 22.60/22.79 (mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))),
% 22.60/22.79 inference(monotonicity,[status(thm)],[5748])).
% 22.60/22.79 tff(5750,plain,
% 22.60/22.79 (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))),
% 22.60/22.79 inference(symmetry,[status(thm)],[5749])).
% 22.60/22.79 tff(5751,plain,
% 22.60/22.79 (((~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(mult(c, mult(a, a)), rd(mult(b, c), mult(a, c))))) | (~(mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, a))) = mult(c, mult(mult(a, a), rd(mult(b, c), mult(a, c))))))) | (mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(mult(c, mult(a, a)), rd(mult(b, c), mult(a, c))))),
% 22.60/22.79 inference(tautology,[status(thm)],[])).
% 22.60/22.79 tff(5752,plain,
% 22.60/22.79 (mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(mult(c, mult(a, a)), rd(mult(b, c), mult(a, c)))),
% 22.60/22.79 inference(unit_resolution,[status(thm)],[5751, 5736])).
% 22.60/22.79 tff(5753,plain,
% 22.60/22.79 (mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, a)))),
% 22.60/22.79 inference(transitivity,[status(thm)],[5752, 5725, 2319, 5750, 1800, 5741, 4962, 5740, 5739])).
% 22.60/22.79 tff(5754,plain,
% 22.60/22.79 (mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, a))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)),
% 22.60/22.79 inference(transitivity,[status(thm)],[5738, 5715, 5404, 5711])).
% 22.60/22.79 tff(5755,plain,
% 22.60/22.79 (mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))),
% 22.60/22.79 inference(transitivity,[status(thm)],[5752, 5725])).
% 22.60/22.79 tff(5756,plain,
% 22.60/22.79 ((mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, a)))) <=> (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))),
% 22.60/22.79 inference(monotonicity,[status(thm)],[5755, 5754])).
% 22.60/22.79 tff(5757,plain,
% 22.60/22.79 ((mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)) <=> (mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, a))))),
% 22.60/22.79 inference(symmetry,[status(thm)],[5756])).
% 22.60/22.79 tff(5758,plain,
% 22.60/22.79 ((~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))) <=> (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, a)))))),
% 22.60/22.79 inference(monotonicity,[status(thm)],[5757])).
% 22.60/22.79 tff(5759,plain,
% 22.60/22.79 (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, a))))),
% 22.60/22.79 inference(modus_ponens,[status(thm)],[2331, 5758])).
% 22.60/22.79 tff(5760,plain,
% 22.60/22.79 ($false),
% 22.60/22.79 inference(unit_resolution,[status(thm)],[5759, 5753])).
% 22.60/22.79 tff(5761,plain,(((~(mult(mult(a, a), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), a))) | (~(mult(a, mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), a))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit))))) | (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))), inference(lemma,lemma(discharge,[]))).
% 22.60/22.79 tff(5762,plain,
% 22.60/22.79 (((~(mult(mult(a, a), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), a))) | (~(mult(a, mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), a))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))) | (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))),
% 22.60/22.79 inference(unit_resolution,[status(thm)],[5761, 3862])).
% 22.60/22.79 tff(5763,plain,
% 22.60/22.79 (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)),
% 22.60/22.79 inference(unit_resolution,[status(thm)],[5762, 908, 5709, 5496])).
% 22.60/22.79 tff(5764,plain,
% 22.60/22.79 (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))),
% 22.60/22.79 inference(unit_resolution,[status(thm)],[2329, 5763])).
% 22.60/22.79 tff(5765,plain,
% 22.60/22.79 (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), c)),
% 22.60/22.79 inference(monotonicity,[status(thm)],[5458])).
% 22.60/22.79 tff(5766,plain,
% 22.60/22.79 (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))),
% 22.60/22.79 inference(transitivity,[status(thm)],[4455, 4520])).
% 22.60/22.79 tff(5767,plain,
% 22.60/22.79 (mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))) = mult(c, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))))),
% 22.60/22.79 inference(monotonicity,[status(thm)],[5766])).
% 22.60/22.79 tff(5768,plain,
% 22.64/22.80 (mult(c, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 22.64/22.80 inference(symmetry,[status(thm)],[5767])).
% 22.64/22.80 tff(5769,plain,
% 22.64/22.80 (mult(mult(unit, c), mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)) = mult(c, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))))),
% 22.64/22.80 inference(monotonicity,[status(thm)],[73, 5458])).
% 22.64/22.80 tff(5770,plain,
% 22.64/22.80 (mult(c, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 22.64/22.80 inference(transitivity,[status(thm)],[4444, 5769, 5768])).
% 22.64/22.80 tff(5771,plain,
% 22.64/22.80 (~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 22.64/22.80 inference(unit_resolution,[status(thm)],[4481, 5770, 270])).
% 22.64/22.80 tff(5772,plain,
% 22.64/22.80 ((~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)))) | (~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))))),
% 22.64/22.80 inference(unit_resolution,[status(thm)],[121, 5771])).
% 22.64/22.80 tff(5773,plain,
% 22.64/22.80 (~((~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))))),
% 22.64/22.80 inference(unit_resolution,[status(thm)],[4484, 5772])).
% 22.64/22.80 tff(5774,plain,
% 22.64/22.80 (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c)),
% 22.64/22.80 inference(unit_resolution,[status(thm)],[4486, 5773])).
% 22.64/22.80 tff(5775,plain,
% 22.64/22.80 ((mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))) <=> (mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 22.64/22.80 inference(monotonicity,[status(thm)],[4455, 4416])).
% 22.64/22.80 tff(5776,plain,
% 22.64/22.80 ((~(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) <=> (~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))))),
% 22.64/22.80 inference(monotonicity,[status(thm)],[5775])).
% 22.64/22.80 tff(5777,plain,
% 22.64/22.80 (~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 22.64/22.80 inference(modus_ponens,[status(thm)],[270, 5776])).
% 22.64/22.80 tff(5778,plain,
% 22.64/22.80 (~(mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))),
% 22.64/22.80 inference(unit_resolution,[status(thm)],[4844, 5777, 5774, 3865, 1683, 4360, 4495, 4517, 4501, 359, 279, 4499, 4390, 281])).
% 22.64/22.80 tff(5779,plain,
% 22.64/22.80 ((~(mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c))))),
% 22.64/22.80 inference(unit_resolution,[status(thm)],[2215, 5778])).
% 22.64/22.80 tff(5780,plain,
% 22.64/22.80 (~((~(mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))))),
% 22.64/22.80 inference(unit_resolution,[status(thm)],[2213, 5779])).
% 22.64/22.80 tff(5781,plain,
% 22.64/22.80 (mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))),
% 22.64/22.80 inference(unit_resolution,[status(thm)],[2201, 5780])).
% 22.64/22.80 tff(5782,plain,
% 22.64/22.80 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), unit) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))),
% 22.64/22.80 inference(transitivity,[status(thm)],[1875, 1871, 4340, 5044, 2189, 5781, 2172, 2178, 2177, 2162])).
% 22.64/22.80 tff(5783,plain,
% 22.64/22.80 (mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), unit), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)),
% 22.64/22.80 inference(monotonicity,[status(thm)],[5782])).
% 22.64/22.80 tff(5784,plain,
% 22.64/22.80 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)),
% 22.64/22.80 inference(transitivity,[status(thm)],[4656, 4655, 5783])).
% 22.64/22.80 tff(5785,plain,
% 22.64/22.80 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)), a) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a)),
% 22.64/22.80 inference(monotonicity,[status(thm)],[5784])).
% 22.64/22.80 tff(5786,plain,
% 22.64/22.80 (mult(mult(b, mult(a, c)), c) = mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), c)),
% 22.64/22.80 inference(transitivity,[status(thm)],[4399, 4815, 2501, 5064, 4870, 4661, 5785, 5774, 5765])).
% 22.64/22.80 tff(5787,plain,
% 22.64/22.80 (rd(mult(mult(b, mult(a, c)), c), c) = rd(mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), c), c)),
% 22.64/22.80 inference(monotonicity,[status(thm)],[5786])).
% 22.64/22.80 tff(5788,plain,
% 22.64/22.80 (rd(mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), c), c) = rd(mult(mult(b, mult(a, c)), c), c)),
% 22.64/22.80 inference(symmetry,[status(thm)],[5787])).
% 22.64/22.80 tff(5789,plain,
% 22.64/22.80 (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = rd(mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), c), c)),
% 22.64/22.80 inference(symmetry,[status(thm)],[4525])).
% 22.64/22.80 tff(5790,plain,
% 22.64/22.80 (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(b, mult(a, c))),
% 22.64/22.80 inference(transitivity,[status(thm)],[5789, 5788, 2680])).
% 22.64/22.80 tff(5791,plain,
% 22.64/22.80 (mult(c, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))) = mult(c, mult(b, mult(a, c)))),
% 22.64/22.80 inference(monotonicity,[status(thm)],[5790])).
% 22.64/22.80 tff(5792,plain,
% 22.64/22.80 (mult(c, mult(b, mult(a, c))) = mult(c, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))))),
% 22.64/22.80 inference(symmetry,[status(thm)],[5791])).
% 22.64/22.80 tff(5793,assumption,(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a)), introduced(assumption)).
% 22.64/22.80 tff(5794,plain,
% 22.64/22.80 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), c), c) = mult(a, mult(rd(mult(b, c), mult(a, c)), a)))),
% 22.64/22.80 inference(quant_inst,[status(thm)],[])).
% 22.64/22.80 tff(5795,plain,
% 22.64/22.80 (rd(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), c), c) = mult(a, mult(rd(mult(b, c), mult(a, c)), a))),
% 22.64/22.80 inference(unit_resolution,[status(thm)],[5794, 168])).
% 22.64/22.80 tff(5796,plain,
% 22.64/22.80 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c)),
% 22.64/22.80 inference(symmetry,[status(thm)],[5793])).
% 22.64/22.80 tff(5797,plain,
% 22.64/22.80 (mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), c)) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 22.64/22.80 inference(monotonicity,[status(thm)],[5186])).
% 22.64/22.80 tff(5798,plain,
% 22.64/22.80 (mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), c))),
% 22.64/22.80 inference(monotonicity,[status(thm)],[5045])).
% 22.64/22.80 tff(5799,assumption,(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c))), introduced(assumption)).
% 22.64/22.80 tff(5800,plain,
% 22.64/22.80 (mult(a, mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), a))),
% 22.64/22.80 inference(monotonicity,[status(thm)],[4996])).
% 22.64/22.80 tff(5801,plain,
% 22.64/22.80 (mult(a, mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(a, rd(mult(b, c), mult(a, c))))),
% 22.64/22.80 inference(symmetry,[status(thm)],[5800])).
% 22.64/22.80 tff(5802,plain,
% 22.64/22.80 (mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), c) = mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)),
% 22.64/22.80 inference(monotonicity,[status(thm)],[5801])).
% 22.64/22.80 tff(5803,plain,
% 22.64/22.80 (mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), c) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c)),
% 22.64/22.80 inference(transitivity,[status(thm)],[5802, 5799, 5798, 5797, 4676, 4520, 1683, 5188, 5796])).
% 22.64/22.80 tff(5804,plain,
% 22.64/22.80 (rd(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), c), c) = rd(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c), c)),
% 22.64/22.80 inference(monotonicity,[status(thm)],[5803])).
% 22.64/22.80 tff(5805,plain,
% 22.64/22.80 (rd(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c), c) = rd(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), c), c)),
% 22.64/22.80 inference(symmetry,[status(thm)],[5804])).
% 22.64/22.80 tff(5806,plain,
% 22.64/22.80 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c), c) = mult(mult(rd(mult(b, c), mult(a, c)), a), a))),
% 22.64/22.80 inference(quant_inst,[status(thm)],[])).
% 22.64/22.80 tff(5807,plain,
% 22.64/22.80 (rd(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c), c) = mult(mult(rd(mult(b, c), mult(a, c)), a), a)),
% 22.64/22.80 inference(unit_resolution,[status(thm)],[5806, 168])).
% 22.64/22.80 tff(5808,plain,
% 22.64/22.80 (mult(mult(rd(mult(b, c), mult(a, c)), a), a) = rd(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c), c)),
% 22.64/22.80 inference(symmetry,[status(thm)],[5807])).
% 22.64/22.80 tff(5809,plain,
% 22.64/22.80 (mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), a)),
% 22.64/22.80 inference(monotonicity,[status(thm)],[4996])).
% 22.64/22.80 tff(5810,plain,
% 22.64/22.80 (mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a))),
% 22.64/22.80 inference(transitivity,[status(thm)],[5809, 5808, 5805, 5795])).
% 22.64/22.80 tff(5811,plain,
% 22.64/22.80 ($false),
% 22.64/22.80 inference(unit_resolution,[status(thm)],[898, 5810])).
% 22.64/22.80 tff(5812,plain,((~(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c)))) | (mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a))) | (~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a))) | (~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))) | (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))))), inference(lemma,lemma(discharge,[]))).
% 22.64/22.80 tff(5813,plain,
% 22.64/22.80 (~(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c)))),
% 22.64/22.80 inference(unit_resolution,[status(thm)],[5812, 281, 898, 5793, 1683, 4517, 5781, 359])).
% 22.64/22.80 tff(5814,plain,
% 22.64/22.80 (((~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c))))) | (mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c)))),
% 22.64/22.80 inference(tautology,[status(thm)],[])).
% 22.64/22.80 tff(5815,plain,
% 22.64/22.80 ((~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c))))),
% 22.64/22.80 inference(unit_resolution,[status(thm)],[5814, 5813])).
% 22.64/22.80 tff(5816,plain,
% 22.64/22.80 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c)))))))),
% 22.64/22.81 inference(rewrite,[status(thm)],[])).
% 22.64/22.81 tff(5817,plain,
% 22.64/22.81 (((~((~(mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c))))))) <=> ((~((~(mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c)))))))),
% 22.64/22.81 inference(rewrite,[status(thm)],[])).
% 22.64/22.81 tff(5818,plain,
% 22.64/22.81 ((~((~(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c)))) | (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c))))))))) <=> (~((~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c))))))),
% 22.64/22.81 inference(rewrite,[status(thm)],[])).
% 22.64/22.81 tff(5819,plain,
% 22.64/22.81 ((~((~(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c))))))))) <=> (~((~(mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))))))),
% 22.64/22.81 inference(rewrite,[status(thm)],[])).
% 22.64/22.81 tff(5820,plain,
% 22.64/22.81 (((~((~(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c))))))))) | (~((~(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c)))) | (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c)))))))))) <=> ((~((~(mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c)))))))),
% 22.64/22.81 inference(monotonicity,[status(thm)],[5819, 5818])).
% 22.64/22.81 tff(5821,plain,
% 22.64/22.81 (((~((~(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c))))))))) | (~((~(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c)))) | (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c)))))))))) <=> ((~((~(mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c)))))))),
% 22.64/22.81 inference(transitivity,[status(thm)],[5820, 5817])).
% 22.64/22.81 tff(5822,plain,
% 22.64/22.81 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c))))))))) | (~((~(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c)))) | (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c))))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c))))))))),
% 22.64/22.81 inference(monotonicity,[status(thm)],[5821])).
% 22.64/22.81 tff(5823,plain,
% 22.64/22.81 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c))))))))) | (~((~(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c)))) | (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c))))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c)))))))),
% 22.64/22.81 inference(transitivity,[status(thm)],[5822, 5816])).
% 22.64/22.81 tff(5824,plain,
% 22.64/22.81 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c))))))))) | (~((~(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c)))) | (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c))))))))))),
% 22.64/22.81 inference(quant_inst,[status(thm)],[])).
% 22.64/22.81 tff(5825,plain,
% 22.64/22.81 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c))))))),
% 22.64/22.81 inference(modus_ponens,[status(thm)],[5824, 5823])).
% 22.64/22.81 tff(5826,plain,
% 22.64/22.81 ((~((~(mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c))))))),
% 22.64/22.81 inference(unit_resolution,[status(thm)],[5825, 27])).
% 22.64/22.81 tff(5827,plain,
% 22.64/22.81 (~((~(mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))))),
% 22.64/22.81 inference(unit_resolution,[status(thm)],[5826, 5815])).
% 22.64/22.81 tff(5828,plain,
% 22.64/22.81 (((~(mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))))) | (mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c))))))),
% 22.64/22.81 inference(tautology,[status(thm)],[])).
% 22.64/22.81 tff(5829,plain,
% 22.64/22.81 (mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c)))))),
% 22.64/22.81 inference(unit_resolution,[status(thm)],[5828, 5827])).
% 22.64/22.81 tff(5830,plain,
% 22.64/22.81 (mult(mult(c, b), a) = mult(a, mult(b, c))),
% 22.64/22.81 inference(transitivity,[status(thm)],[2298, 4397, 4502, 4414, 279, 142])).
% 22.64/22.81 tff(5831,plain,
% 22.64/22.81 ((mult(mult(c, b), a) = mult(mult(c, a), b)) <=> (mult(a, mult(b, c)) = mult(mult(a, b), c))),
% 22.64/22.81 inference(monotonicity,[status(thm)],[5830, 4500])).
% 22.64/22.81 tff(5832,plain,
% 22.64/22.81 ((mult(mult(c, b), a) = mult(mult(c, a), b)) <=> (mult(mult(a, b), c) = mult(a, mult(b, c)))),
% 22.64/22.81 inference(transitivity,[status(thm)],[5831, 143])).
% 22.64/22.81 tff(5833,plain,
% 22.64/22.81 ((mult(mult(a, b), c) = mult(a, mult(b, c))) <=> (mult(mult(c, b), a) = mult(mult(c, a), b))),
% 22.64/22.81 inference(symmetry,[status(thm)],[5832])).
% 22.64/22.81 tff(5834,plain,
% 22.64/22.81 ((~(mult(mult(a, b), c) = mult(a, mult(b, c)))) <=> (~(mult(mult(c, b), a) = mult(mult(c, a), b)))),
% 22.64/22.81 inference(monotonicity,[status(thm)],[5833])).
% 22.64/22.81 tff(5835,plain,
% 22.64/22.81 (~(mult(mult(c, b), a) = mult(mult(c, a), b))),
% 22.64/22.81 inference(modus_ponens,[status(thm)],[146, 5834])).
% 22.64/22.81 tff(5836,plain,
% 22.64/22.81 ((~(mult(mult(c, b), a) = mult(mult(c, a), b))) | (~(mult(c, mult(b, a)) = mult(c, mult(a, b))))),
% 22.64/22.81 inference(unit_resolution,[status(thm)],[3890, 5835])).
% 22.64/22.81 tff(5837,plain,
% 22.64/22.81 (~((~(mult(mult(c, b), a) = mult(c, mult(b, a)))) | (~(mult(mult(c, a), b) = mult(c, mult(a, b)))))),
% 22.64/22.81 inference(unit_resolution,[status(thm)],[2249, 5836])).
% 22.64/22.81 tff(5838,plain,
% 22.64/22.81 (mult(mult(c, a), b) = mult(c, mult(a, b))),
% 22.64/22.81 inference(unit_resolution,[status(thm)],[2279, 5837])).
% 22.64/22.81 tff(5839,plain,
% 22.64/22.81 (mult(mult(rd(mult(b, c), mult(a, c)), a), c) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))),
% 22.64/22.81 inference(transitivity,[status(thm)],[5044, 2189, 5781, 2172, 2178, 2177, 2162])).
% 22.64/22.81 tff(5840,plain,
% 22.64/22.81 (mult(c, mult(mult(rd(mult(b, c), mult(a, c)), a), c)) = mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 22.64/22.81 inference(monotonicity,[status(thm)],[5839])).
% 22.64/22.81 tff(5841,plain,
% 22.64/22.81 (mult(c, mult(mult(rd(mult(b, c), mult(a, c)), a), c)) = mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c)))),
% 22.64/22.81 inference(transitivity,[status(thm)],[5840, 4496, 5299])).
% 22.64/22.81 tff(5842,plain,
% 22.64/22.81 (mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), c)) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 22.64/22.81 inference(monotonicity,[status(thm)],[5839])).
% 22.64/22.81 tff(5843,plain,
% 22.64/22.81 (mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c))),
% 22.64/22.81 inference(symmetry,[status(thm)],[5829])).
% 22.64/22.81 tff(5844,plain,
% 22.64/22.81 (mult(c, mult(a, rd(mult(b, c), mult(a, c)))) = mult(c, mult(rd(mult(b, c), mult(a, c)), a))),
% 22.64/22.81 inference(monotonicity,[status(thm)],[4996])).
% 22.64/22.81 tff(5845,plain,
% 22.64/22.81 (mult(c, mult(rd(mult(b, c), mult(a, c)), a)) = mult(c, mult(a, rd(mult(b, c), mult(a, c))))),
% 22.64/22.81 inference(symmetry,[status(thm)],[5844])).
% 22.64/22.81 tff(5846,plain,
% 22.64/22.81 (mult(a, mult(c, mult(rd(mult(b, c), mult(a, c)), a))) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c)))))),
% 22.64/22.81 inference(monotonicity,[status(thm)],[5845])).
% 22.64/22.81 tff(5847,plain,
% 22.64/22.81 (mult(a, mult(c, mult(rd(mult(b, c), mult(a, c)), a))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 22.64/22.81 inference(transitivity,[status(thm)],[5846, 5843, 5798, 5842])).
% 22.64/22.81 tff(5848,plain,
% 22.64/22.81 (ld(a, mult(a, mult(c, mult(rd(mult(b, c), mult(a, c)), a)))) = ld(a, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 22.64/22.81 inference(monotonicity,[status(thm)],[5847])).
% 22.64/22.81 tff(5849,plain,
% 22.64/22.81 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(a, mult(a, mult(c, mult(rd(mult(b, c), mult(a, c)), a)))) = mult(c, mult(rd(mult(b, c), mult(a, c)), a)))),
% 22.64/22.81 inference(quant_inst,[status(thm)],[])).
% 22.64/22.81 tff(5850,plain,
% 22.64/22.81 (ld(a, mult(a, mult(c, mult(rd(mult(b, c), mult(a, c)), a)))) = mult(c, mult(rd(mult(b, c), mult(a, c)), a))),
% 22.64/22.81 inference(unit_resolution,[status(thm)],[5849, 7])).
% 22.64/22.81 tff(5851,plain,
% 22.64/22.81 (mult(c, mult(rd(mult(b, c), mult(a, c)), a)) = ld(a, mult(a, mult(c, mult(rd(mult(b, c), mult(a, c)), a))))),
% 22.64/22.81 inference(symmetry,[status(thm)],[5850])).
% 22.64/22.81 tff(5852,plain,
% 22.64/22.81 (mult(c, mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))),
% 22.64/22.81 inference(transitivity,[status(thm)],[5851, 5848, 733])).
% 22.64/22.81 tff(5853,plain,
% 22.64/22.81 (mult(mult(c, mult(rd(mult(b, c), mult(a, c)), a)), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)),
% 22.64/22.81 inference(monotonicity,[status(thm)],[5852])).
% 22.64/22.81 tff(5854,plain,
% 22.64/22.81 ((mult(mult(c, mult(rd(mult(b, c), mult(a, c)), a)), c) = mult(c, mult(mult(rd(mult(b, c), mult(a, c)), a), c))) <=> (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))))),
% 22.64/22.81 inference(monotonicity,[status(thm)],[5853, 5841])).
% 22.64/22.81 tff(5855,plain,
% 22.64/22.81 ((mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c)))) <=> (mult(mult(c, mult(rd(mult(b, c), mult(a, c)), a)), c) = mult(c, mult(mult(rd(mult(b, c), mult(a, c)), a), c)))),
% 22.64/22.81 inference(symmetry,[status(thm)],[5854])).
% 22.64/22.81 tff(5856,plain,
% 22.64/22.81 (mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))),
% 22.64/22.81 inference(unit_resolution,[status(thm)],[5118, 5780])).
% 22.64/22.81 tff(5857,plain,
% 22.64/22.81 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c)))),
% 22.64/22.81 inference(unit_resolution,[status(thm)],[5315, 5856, 3865])).
% 22.64/22.81 tff(5858,plain,
% 22.64/22.81 (mult(mult(c, mult(rd(mult(b, c), mult(a, c)), a)), c) = mult(c, mult(mult(rd(mult(b, c), mult(a, c)), a), c))),
% 22.64/22.82 inference(modus_ponens,[status(thm)],[5857, 5855])).
% 22.64/22.82 tff(5859,plain,
% 22.64/22.82 (mult(c, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))) = mult(mult(unit, c), mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))),
% 22.64/22.82 inference(symmetry,[status(thm)],[5769])).
% 22.64/22.82 tff(5860,plain,
% 22.64/22.82 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)),
% 22.64/22.82 inference(transitivity,[status(thm)],[4656, 4655, 5053])).
% 22.64/22.82 tff(5861,plain,
% 22.64/22.82 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)), a) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a)),
% 22.64/22.82 inference(monotonicity,[status(thm)],[5860])).
% 22.64/22.82 tff(5862,plain,
% 22.64/22.82 (mult(mult(b, mult(a, c)), c) = mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), c)),
% 22.64/22.82 inference(transitivity,[status(thm)],[4399, 4815, 2501, 5064, 4870, 4661, 5861, 4528, 5765])).
% 22.64/22.82 tff(5863,plain,
% 22.64/22.82 (rd(mult(mult(b, mult(a, c)), c), c) = rd(mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), c), c)),
% 22.64/22.82 inference(monotonicity,[status(thm)],[5862])).
% 22.64/22.82 tff(5864,plain,
% 22.64/22.82 (mult(b, mult(a, c)) = mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))),
% 22.64/22.82 inference(transitivity,[status(thm)],[2681, 5863, 4525])).
% 22.64/22.82 tff(5865,plain,
% 22.64/22.82 (mult(c, mult(b, mult(a, c))) = mult(c, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))))),
% 22.64/22.82 inference(monotonicity,[status(thm)],[5864])).
% 22.64/22.82 tff(5866,plain,
% 22.64/22.82 (mult(c, mult(b, mult(a, c))) = mult(mult(unit, c), mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))),
% 22.64/22.82 inference(transitivity,[status(thm)],[5865, 5859])).
% 22.64/22.82 tff(5867,plain,
% 22.64/22.82 (mult(unit, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))) = mult(unit, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))),
% 22.64/22.82 inference(monotonicity,[status(thm)],[1683])).
% 22.64/22.82 tff(5868,plain,
% 22.64/22.82 (mult(unit, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)) = mult(unit, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))))),
% 22.64/22.82 inference(symmetry,[status(thm)],[5867])).
% 22.64/22.82 tff(5869,plain,
% 22.64/22.82 (mult(mult(unit, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(unit, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c)))),
% 22.64/22.82 inference(transitivity,[status(thm)],[5016, 5458, 5457])).
% 22.64/22.82 tff(5870,plain,
% 22.64/22.82 ((mult(mult(unit, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(unit, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))) <=> (mult(mult(unit, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(unit, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))))),
% 22.64/22.82 inference(monotonicity,[status(thm)],[5869, 5868])).
% 22.64/22.82 tff(5871,plain,
% 22.64/22.82 ((mult(mult(unit, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(unit, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))))) <=> (mult(mult(unit, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(unit, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)))),
% 22.64/22.82 inference(symmetry,[status(thm)],[5870])).
% 22.64/22.82 tff(5872,plain,
% 22.64/22.82 (mult(mult(unit, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(unit, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))),
% 22.64/22.82 inference(modus_ponens,[status(thm)],[5036, 5871])).
% 22.64/22.82 tff(5873,plain,
% 22.64/22.82 (mult(unit, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)) = mult(mult(unit, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a)),
% 22.64/22.82 inference(symmetry,[status(thm)],[5872])).
% 22.64/22.82 tff(5874,plain,
% 22.64/22.82 (mult(unit, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)) = mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))),
% 22.64/22.82 inference(transitivity,[status(thm)],[5873, 5016, 5458])).
% 22.64/22.82 tff(5875,plain,
% 22.64/22.82 (mult(mult(unit, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)), c) = mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), c)),
% 22.64/22.82 inference(monotonicity,[status(thm)],[5874])).
% 22.64/22.82 tff(5876,plain,
% 22.64/22.82 (mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), c) = mult(mult(unit, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)), c)),
% 22.64/22.82 inference(symmetry,[status(thm)],[5875])).
% 22.64/22.82 tff(5877,plain,
% 22.64/22.82 (mult(mult(c, b), mult(a, c)) = mult(mult(unit, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)), c)),
% 22.64/22.82 inference(transitivity,[status(thm)],[2429, 4815, 2501, 5064, 4870, 4661, 5861, 4528, 5765, 5876])).
% 22.64/22.82 tff(5878,plain,
% 22.64/22.82 ((mult(mult(c, b), mult(a, c)) = mult(c, mult(b, mult(a, c)))) <=> (mult(mult(unit, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)), c) = mult(mult(unit, c), mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)))),
% 22.64/22.82 inference(monotonicity,[status(thm)],[5877, 5866])).
% 22.64/22.82 tff(5879,plain,
% 22.64/22.82 ((mult(mult(c, b), mult(a, c)) = mult(c, mult(b, mult(a, c)))) <=> (mult(mult(unit, c), mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)) = mult(mult(unit, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)), c))),
% 22.64/22.82 inference(transitivity,[status(thm)],[5878, 5043])).
% 22.64/22.82 tff(5880,plain,
% 22.64/22.82 ((mult(mult(unit, c), mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)) = mult(mult(unit, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)), c)) <=> (mult(mult(c, b), mult(a, c)) = mult(c, mult(b, mult(a, c))))),
% 22.64/22.82 inference(symmetry,[status(thm)],[5879])).
% 22.64/22.82 tff(5881,plain,
% 22.64/22.82 (mult(c, mult(a, b)) = mult(mult(a, c), b)),
% 22.64/22.82 inference(transitivity,[status(thm)],[4224, 3886])).
% 22.64/22.82 tff(5882,plain,
% 22.64/22.82 (mult(c, mult(c, mult(a, b))) = mult(c, mult(mult(a, c), b))),
% 22.64/22.82 inference(monotonicity,[status(thm)],[5881])).
% 22.64/22.82 tff(5883,plain,
% 22.64/22.82 (mult(c, mult(c, mult(a, b))) = mult(mult(unit, c), mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))),
% 22.64/22.82 inference(transitivity,[status(thm)],[5882, 2711, 5865, 5859])).
% 22.64/22.82 tff(5884,assumption,(mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c)))))), introduced(assumption)).
% 22.64/22.82 tff(5885,plain,
% 22.64/22.82 (mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c))),
% 22.64/22.82 inference(symmetry,[status(thm)],[5884])).
% 22.64/22.82 tff(5886,plain,
% 22.64/22.82 (mult(a, mult(c, mult(rd(mult(b, c), mult(a, c)), a))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 22.64/22.82 inference(transitivity,[status(thm)],[5846, 5885, 5798, 5797])).
% 22.64/22.82 tff(5887,plain,
% 22.64/22.82 (ld(a, mult(a, mult(c, mult(rd(mult(b, c), mult(a, c)), a)))) = ld(a, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 22.64/22.82 inference(monotonicity,[status(thm)],[5886])).
% 22.64/22.82 tff(5888,plain,
% 22.64/22.82 (mult(c, mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))),
% 22.64/22.82 inference(transitivity,[status(thm)],[5851, 5887, 733])).
% 22.64/22.82 tff(5889,plain,
% 22.64/22.82 (mult(mult(c, mult(rd(mult(b, c), mult(a, c)), a)), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)),
% 22.64/22.82 inference(monotonicity,[status(thm)],[5888])).
% 22.64/22.82 tff(5890,assumption,(mult(mult(c, mult(rd(mult(b, c), mult(a, c)), a)), c) = mult(c, mult(mult(rd(mult(b, c), mult(a, c)), a), c))), introduced(assumption)).
% 22.64/22.82 tff(5891,plain,
% 22.64/22.82 (mult(c, mult(mult(rd(mult(b, c), mult(a, c)), a), c)) = mult(mult(c, mult(rd(mult(b, c), mult(a, c)), a)), c)),
% 22.64/22.82 inference(symmetry,[status(thm)],[5890])).
% 22.64/22.82 tff(5892,plain,
% 22.64/22.82 (mult(mult(a, c), rd(mult(b, c), mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), a), c)),
% 22.64/22.82 inference(transitivity,[status(thm)],[2167, 4851, 4850, 2171, 5046, 4493, 5045])).
% 22.64/22.82 tff(5893,plain,
% 22.64/22.82 (mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(mult(rd(mult(b, c), mult(a, c)), a), c))),
% 22.64/22.82 inference(monotonicity,[status(thm)],[5892])).
% 22.64/22.82 tff(5894,plain,
% 22.64/22.82 (mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)),
% 22.64/22.82 inference(transitivity,[status(thm)],[4701, 5893, 5891, 5889])).
% 22.64/22.82 tff(5895,plain,
% 22.64/22.82 (mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a)),
% 22.64/22.82 inference(monotonicity,[status(thm)],[5894])).
% 22.64/22.82 tff(5896,plain,
% 22.64/22.82 (mult(mult(c, c), a) = mult(c, mult(a, c))),
% 22.64/22.82 inference(transitivity,[status(thm)],[3911, 4711])).
% 22.64/22.82 tff(5897,plain,
% 22.64/22.82 (mult(mult(mult(c, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 22.64/22.82 inference(monotonicity,[status(thm)],[5896])).
% 22.64/22.82 tff(5898,plain,
% 22.64/22.82 (mult(mult(mult(mult(c, c), a), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a)),
% 22.64/22.82 inference(monotonicity,[status(thm)],[5897])).
% 22.64/22.82 tff(5899,plain,
% 22.64/22.82 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(c, c), a), rd(mult(b, c), mult(a, c))), a) = mult(mult(c, c), mult(mult(a, rd(mult(b, c), mult(a, c))), a)))),
% 22.64/22.82 inference(quant_inst,[status(thm)],[])).
% 22.64/22.82 tff(5900,plain,
% 22.64/22.82 (mult(mult(mult(mult(c, c), a), rd(mult(b, c), mult(a, c))), a) = mult(mult(c, c), mult(mult(a, rd(mult(b, c), mult(a, c))), a))),
% 22.64/22.82 inference(unit_resolution,[status(thm)],[5899, 56])).
% 22.64/22.82 tff(5901,plain,
% 22.64/22.82 (mult(mult(c, c), mult(mult(a, rd(mult(b, c), mult(a, c))), a)) = mult(mult(mult(mult(c, c), a), rd(mult(b, c), mult(a, c))), a)),
% 22.64/22.82 inference(symmetry,[status(thm)],[5900])).
% 22.64/22.82 tff(5902,plain,
% 22.64/22.82 (mult(mult(rd(mult(b, c), mult(a, c)), a), a) = mult(mult(a, rd(mult(b, c), mult(a, c))), a)),
% 22.64/22.82 inference(symmetry,[status(thm)],[5809])).
% 22.64/22.82 tff(5903,plain,
% 22.64/22.82 (mult(mult(c, c), mult(mult(rd(mult(b, c), mult(a, c)), a), a)) = mult(mult(c, c), mult(mult(a, rd(mult(b, c), mult(a, c))), a))),
% 22.64/22.82 inference(monotonicity,[status(thm)],[5902])).
% 22.64/22.82 tff(5904,plain,
% 22.64/22.82 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), mult(c, c)), mult(c, c)) = mult(mult(rd(mult(b, c), mult(a, c)), a), a))),
% 22.64/22.82 inference(quant_inst,[status(thm)],[])).
% 22.64/22.82 tff(5905,plain,
% 22.64/22.82 (rd(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), mult(c, c)), mult(c, c)) = mult(mult(rd(mult(b, c), mult(a, c)), a), a)),
% 22.64/22.82 inference(unit_resolution,[status(thm)],[5904, 168])).
% 22.64/22.82 tff(5906,plain,
% 22.64/22.82 (mult(mult(a, b), mult(c, c)) = mult(mult(a, b), mult(mult(c, unit), c))),
% 22.64/22.82 inference(monotonicity,[status(thm)],[2617])).
% 22.64/22.82 tff(5907,plain,
% 22.64/22.82 (mult(mult(a, b), mult(mult(c, unit), c)) = mult(mult(a, b), mult(c, c))),
% 22.64/22.82 inference(symmetry,[status(thm)],[5906])).
% 22.64/22.82 tff(5908,plain,
% 22.64/22.82 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(a, b), c), unit), c) = mult(mult(a, b), mult(mult(c, unit), c)))),
% 22.64/22.82 inference(quant_inst,[status(thm)],[])).
% 22.64/22.82 tff(5909,plain,
% 22.64/22.82 (mult(mult(mult(mult(a, b), c), unit), c) = mult(mult(a, b), mult(mult(c, unit), c))),
% 22.64/22.82 inference(unit_resolution,[status(thm)],[5908, 56])).
% 22.64/22.82 tff(5910,plain,
% 22.64/22.82 (mult(mult(mult(a, b), c), unit) = mult(mult(mult(a, c), b), unit)),
% 22.64/22.82 inference(monotonicity,[status(thm)],[227])).
% 22.64/22.82 tff(5911,plain,
% 22.64/22.82 (mult(mult(mult(a, b), c), unit) = mult(mult(a, c), b)),
% 22.64/22.82 inference(transitivity,[status(thm)],[5910, 864, 858, 856])).
% 22.64/22.82 tff(5912,plain,
% 22.64/22.82 (mult(mult(mult(mult(a, b), c), unit), c) = mult(mult(mult(a, c), b), c)),
% 22.64/22.82 inference(monotonicity,[status(thm)],[5911])).
% 22.64/22.82 tff(5913,plain,
% 22.64/22.82 (mult(mult(mult(a, c), b), c) = mult(mult(mult(mult(a, b), c), unit), c)),
% 22.64/22.82 inference(symmetry,[status(thm)],[5912])).
% 22.64/22.82 tff(5914,plain,
% 22.64/22.82 (mult(mult(c, b), mult(a, c)) = mult(mult(c, mult(a, c)), b)),
% 22.64/22.82 inference(symmetry,[status(thm)],[2439])).
% 22.64/22.82 tff(5915,plain,
% 22.64/22.82 (mult(rd(mult(b, c), mult(a, c)), mult(mult(c, mult(a, c)), a)) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), unit), mult(a, c)))),
% 22.64/22.82 inference(symmetry,[status(thm)],[5064])).
% 22.64/22.82 tff(5916,plain,
% 22.64/22.82 ((mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(c, c))) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(c, c))) <=> (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(c, c)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(c, c))))),
% 22.64/22.82 inference(commutativity,[status(thm)],[])).
% 22.64/22.82 tff(5917,plain,
% 22.64/22.82 (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(c, c)) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), mult(c, c))),
% 22.64/22.82 inference(monotonicity,[status(thm)],[5809])).
% 22.64/22.82 tff(5918,plain,
% 22.64/22.82 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), mult(c, c)) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(c, c))),
% 22.64/22.82 inference(symmetry,[status(thm)],[5917])).
% 22.64/22.82 tff(5919,plain,
% 22.64/22.82 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(c, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), c))),
% 22.64/22.82 inference(monotonicity,[status(thm)],[2619])).
% 22.64/22.82 tff(5920,plain,
% 22.64/22.82 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), c)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(c, c)))),
% 22.64/22.82 inference(symmetry,[status(thm)],[5919])).
% 22.64/22.82 tff(5921,plain,
% 22.64/22.82 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), c)) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, mult(a, c)))),
% 22.64/22.82 inference(monotonicity,[status(thm)],[4996, 4529])).
% 22.64/22.82 tff(5922,plain,
% 22.64/22.82 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), c))),
% 22.64/22.82 inference(symmetry,[status(thm)],[5921])).
% 22.64/22.82 tff(5923,plain,
% 22.64/22.82 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(c, a), c))),
% 22.64/22.82 inference(monotonicity,[status(thm)],[3877])).
% 22.64/22.82 tff(5924,plain,
% 22.64/22.82 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(c, a), c)) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, mult(a, c)))),
% 22.64/22.82 inference(symmetry,[status(thm)],[5923])).
% 22.64/22.82 tff(5925,plain,
% 22.64/22.82 (mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a), c) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), c)),
% 22.64/22.82 inference(monotonicity,[status(thm)],[1168])).
% 22.64/22.82 tff(5926,plain,
% 22.64/22.82 (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), c) = mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a), c)),
% 22.64/22.82 inference(symmetry,[status(thm)],[5925])).
% 22.64/22.82 tff(5927,plain,
% 22.64/22.82 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)) = mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))),
% 22.64/22.82 inference(transitivity,[status(thm)],[1169, 5187, 5458])).
% 22.64/22.82 tff(5928,plain,
% 22.64/22.82 (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), c) = mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), c)),
% 22.64/22.82 inference(monotonicity,[status(thm)],[5927])).
% 22.64/22.82 tff(5929,plain,
% 22.64/22.82 (mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), c) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), c)),
% 22.64/22.82 inference(symmetry,[status(thm)],[5928])).
% 22.64/22.82 tff(5930,plain,
% 22.64/22.82 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)), a) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(c, c)))),
% 22.64/22.82 inference(transitivity,[status(thm)],[5861, 4528, 5765, 5929, 5926, 5141, 5924, 5922, 5920])).
% 22.64/22.82 tff(5931,plain,
% 22.64/22.82 ((mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), mult(c, c))) <=> (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(c, c))) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(c, c)))),
% 22.64/22.82 inference(monotonicity,[status(thm)],[5930, 5918])).
% 22.64/22.82 tff(5932,plain,
% 22.64/22.82 ((mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), mult(c, c))) <=> (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(c, c)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(c, c))))),
% 22.64/22.82 inference(transitivity,[status(thm)],[5931, 5916])).
% 22.64/22.82 tff(5933,plain,
% 22.64/22.82 ((mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(c, c)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(c, c)))) <=> (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), mult(c, c)))),
% 22.64/22.82 inference(symmetry,[status(thm)],[5932])).
% 22.64/22.82 tff(5934,plain,
% 22.64/22.82 ((mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)), a) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(c, c))) <=> (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(c, c)) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)), a))),
% 22.64/22.82 inference(commutativity,[status(thm)],[])).
% 22.64/22.82 tff(5935,plain,
% 22.64/22.82 ((mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(c, c)) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)), a)) <=> (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)), a) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(c, c)))),
% 22.64/22.82 inference(symmetry,[status(thm)],[5934])).
% 22.64/22.82 tff(5936,plain,
% 22.64/22.82 (mult(mult(a, rd(mult(b, c), mult(a, c))), c) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))),
% 22.64/22.83 inference(transitivity,[status(thm)],[2189, 2187, 2172, 2178, 2177, 2162])).
% 22.64/22.83 tff(5937,plain,
% 22.64/22.83 (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), unit) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), unit)),
% 22.64/22.83 inference(monotonicity,[status(thm)],[5936])).
% 22.64/22.83 tff(5938,plain,
% 22.64/22.83 (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), unit) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))),
% 22.64/22.83 inference(transitivity,[status(thm)],[5937, 2177, 2162])).
% 22.64/22.83 tff(5939,plain,
% 22.64/22.83 (mult(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), unit), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)),
% 22.64/22.83 inference(monotonicity,[status(thm)],[5938])).
% 22.64/22.83 tff(5940,plain,
% 22.64/22.83 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), unit), c) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(c, unit), c)))),
% 22.64/22.83 inference(quant_inst,[status(thm)],[])).
% 22.64/22.83 tff(5941,plain,
% 22.64/22.83 (mult(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), unit), c) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(c, unit), c))),
% 22.64/22.83 inference(unit_resolution,[status(thm)],[5940, 56])).
% 22.64/22.83 tff(5942,plain,
% 22.64/22.83 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(c, unit), c)) = mult(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), unit), c)),
% 22.64/22.83 inference(symmetry,[status(thm)],[5941])).
% 22.64/22.83 tff(5943,plain,
% 22.64/22.83 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(c, unit), c))),
% 22.64/22.83 inference(monotonicity,[status(thm)],[2617])).
% 22.64/22.83 tff(5944,plain,
% 22.64/22.83 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)),
% 22.64/22.83 inference(transitivity,[status(thm)],[5943, 5942, 5939])).
% 22.64/22.83 tff(5945,plain,
% 22.64/22.83 (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)), a) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a)),
% 22.64/22.83 inference(monotonicity,[status(thm)],[5944])).
% 22.64/22.83 tff(5946,plain,
% 22.64/22.83 (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)), a)),
% 22.64/22.83 inference(symmetry,[status(thm)],[5945])).
% 22.64/22.83 tff(5947,plain,
% 22.64/22.83 (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a)),
% 22.64/22.83 inference(symmetry,[status(thm)],[4528])).
% 22.64/22.83 tff(5948,plain,
% 22.64/22.83 (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)),
% 22.64/22.83 inference(monotonicity,[status(thm)],[5936])).
% 22.64/22.83 tff(5949,plain,
% 22.64/22.83 (mult(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), a), c) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c)),
% 22.64/22.83 inference(monotonicity,[status(thm)],[5948])).
% 22.64/22.83 tff(5950,plain,
% 22.64/22.83 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), a), c) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(c, a), c)))),
% 22.64/22.83 inference(quant_inst,[status(thm)],[])).
% 22.64/22.83 tff(5951,plain,
% 22.64/22.83 (mult(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), a), c) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(c, a), c))),
% 22.64/22.83 inference(unit_resolution,[status(thm)],[5950, 56])).
% 22.64/22.83 tff(5952,plain,
% 22.64/22.83 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(c, a), c)) = mult(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), a), c)),
% 22.64/22.83 inference(symmetry,[status(thm)],[5951])).
% 22.64/22.83 tff(5953,plain,
% 22.64/22.83 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), c)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(c, a), c))),
% 22.64/22.83 inference(monotonicity,[status(thm)],[3875])).
% 22.64/22.83 tff(5954,plain,
% 22.64/22.83 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(c, c))) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)), a)),
% 22.64/22.83 inference(transitivity,[status(thm)],[5919, 5953, 5952, 5949, 5947, 5946])).
% 22.64/22.83 tff(5955,plain,
% 22.64/22.83 ((mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(c, c)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(c, c)))) <=> (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(c, c)) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)), a))),
% 22.64/22.83 inference(monotonicity,[status(thm)],[5954])).
% 22.64/22.83 tff(5956,plain,
% 22.64/22.83 ((mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(c, c)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(c, c)))) <=> (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)), a) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(c, c)))),
% 22.64/22.83 inference(transitivity,[status(thm)],[5955, 5935])).
% 22.64/22.83 tff(5957,plain,
% 22.64/22.83 ((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(c, c)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(c, c))))) <=> (~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)), a) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(c, c))))),
% 22.64/22.83 inference(monotonicity,[status(thm)],[5956])).
% 22.64/22.83 tff(5958,assumption,(~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(c, c)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(c, c))))), introduced(assumption)).
% 22.64/22.83 tff(5959,plain,
% 22.64/22.83 (~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)), a) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(c, c)))),
% 22.64/22.83 inference(modus_ponens,[status(thm)],[5958, 5957])).
% 22.64/22.83 tff(5960,plain,
% 22.64/22.83 (((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)), a) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(c, c), a)))) | (~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(c, c)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(c, c)))))) | (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(c, c)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(c, c))))),
% 22.64/22.83 inference(tautology,[status(thm)],[])).
% 22.64/22.83 tff(5961,plain,
% 22.64/22.83 ((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)), a) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(c, c), a)))) | (~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(c, c)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(c, c)))))),
% 22.64/22.83 inference(unit_resolution,[status(thm)],[5960, 5958])).
% 22.64/22.83 tff(5962,plain,
% 22.64/22.83 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)), a) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(c, c)))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(c, c), a)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(c, c))))))) | (~((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)), a) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(c, c), a)))) | (~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(c, c)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(c, c))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)), a) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(c, c)))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(c, c), a)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(c, c))))))) | (~((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)), a) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(c, c), a)))) | (~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(c, c)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(c, c))))))))),
% 22.64/22.83 inference(rewrite,[status(thm)],[])).
% 22.64/22.83 tff(5963,plain,
% 22.64/22.83 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)), a) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(c, c)))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(c, c), a)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(c, c))))))) | (~((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)), a) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(c, c), a)))) | (~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(c, c)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(c, c))))))))),
% 22.67/22.83 inference(quant_inst,[status(thm)],[])).
% 22.67/22.83 tff(5964,plain,
% 22.67/22.83 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)), a) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(c, c)))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(c, c), a)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(c, c))))))) | (~((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)), a) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(c, c), a)))) | (~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(c, c)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(c, c)))))))),
% 22.67/22.83 inference(modus_ponens,[status(thm)],[5963, 5962])).
% 22.67/22.83 tff(5965,plain,
% 22.67/22.83 ((~((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)), a) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(c, c)))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(c, c), a)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(c, c))))))) | (~((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)), a) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(c, c), a)))) | (~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(c, c)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(c, c)))))))),
% 22.67/22.83 inference(unit_resolution,[status(thm)],[5964, 27])).
% 22.67/22.83 tff(5966,plain,
% 22.67/22.83 (~((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)), a) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(c, c)))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(c, c), a)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(c, c))))))),
% 22.67/22.83 inference(unit_resolution,[status(thm)],[5965, 5961])).
% 22.67/22.83 tff(5967,plain,
% 22.67/22.83 (((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)), a) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(c, c)))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(c, c), a)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(c, c)))))) | (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)), a) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(c, c)))),
% 22.67/22.83 inference(tautology,[status(thm)],[])).
% 22.67/22.83 tff(5968,plain,
% 22.67/22.83 (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)), a) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(c, c))),
% 22.67/22.83 inference(unit_resolution,[status(thm)],[5967, 5966])).
% 22.67/22.83 tff(5969,plain,
% 22.67/22.83 ($false),
% 22.67/22.83 inference(unit_resolution,[status(thm)],[5968, 5959])).
% 22.67/22.83 tff(5970,plain,((mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(c, c)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(c, c)))) | (~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit)))))), inference(lemma,lemma(discharge,[]))).
% 22.67/22.83 tff(5971,plain,
% 22.67/22.83 (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(c, c)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(c, c)))),
% 22.67/22.83 inference(unit_resolution,[status(thm)],[5970, 2187, 3865, 4528])).
% 22.67/22.83 tff(5972,plain,
% 22.67/22.83 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), mult(c, c))),
% 22.67/22.83 inference(modus_ponens,[status(thm)],[5971, 5933])).
% 22.67/22.83 tff(5973,plain,
% 22.67/22.83 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), mult(c, c)) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)), a)),
% 22.67/22.83 inference(symmetry,[status(thm)],[5972])).
% 22.67/22.83 tff(5974,plain,
% 22.67/22.83 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), mult(c, c)) = mult(mult(a, b), mult(c, c))),
% 22.67/22.83 inference(transitivity,[status(thm)],[5973, 4660, 5104, 5915, 2502, 5102, 2742, 5914, 5091, 4104, 5913, 5909, 5907])).
% 22.67/22.83 tff(5975,plain,
% 22.67/22.83 (rd(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), mult(c, c)), mult(c, c)) = rd(mult(mult(a, b), mult(c, c)), mult(c, c))),
% 22.67/22.83 inference(monotonicity,[status(thm)],[5974])).
% 22.67/22.83 tff(5976,plain,
% 22.67/22.83 (rd(mult(mult(a, b), mult(c, c)), mult(c, c)) = rd(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), mult(c, c)), mult(c, c))),
% 22.67/22.83 inference(symmetry,[status(thm)],[5975])).
% 22.67/22.83 tff(5977,plain,
% 22.67/22.83 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(a, b), mult(c, c)), mult(c, c)) = mult(a, b))),
% 22.67/22.83 inference(quant_inst,[status(thm)],[])).
% 22.67/22.83 tff(5978,plain,
% 22.67/22.83 (rd(mult(mult(a, b), mult(c, c)), mult(c, c)) = mult(a, b)),
% 22.67/22.83 inference(unit_resolution,[status(thm)],[5977, 168])).
% 22.67/22.83 tff(5979,plain,
% 22.67/22.83 (mult(a, b) = rd(mult(mult(a, b), mult(c, c)), mult(c, c))),
% 22.67/22.83 inference(symmetry,[status(thm)],[5978])).
% 22.67/22.83 tff(5980,plain,
% 22.67/22.83 (mult(a, b) = mult(mult(rd(mult(b, c), mult(a, c)), a), a)),
% 22.67/22.83 inference(transitivity,[status(thm)],[5979, 5976, 5905])).
% 22.67/22.83 tff(5981,plain,
% 22.67/22.83 (mult(mult(c, c), mult(a, b)) = mult(mult(c, c), mult(mult(rd(mult(b, c), mult(a, c)), a), a))),
% 22.67/22.83 inference(monotonicity,[status(thm)],[5980])).
% 22.67/22.83 tff(5982,plain,
% 22.67/22.83 (mult(mult(c, c), mult(a, b)) = mult(mult(unit, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)), c)),
% 22.67/22.83 inference(transitivity,[status(thm)],[5981, 5903, 5901, 5898, 5895, 4528, 5765, 5876])).
% 22.67/22.83 tff(5983,plain,
% 22.67/22.83 ((mult(mult(c, c), mult(a, b)) = mult(c, mult(c, mult(a, b)))) <=> (mult(mult(unit, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)), c) = mult(mult(unit, c), mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)))),
% 22.67/22.83 inference(monotonicity,[status(thm)],[5982, 5883])).
% 22.67/22.83 tff(5984,plain,
% 22.67/22.83 ((mult(mult(c, c), mult(a, b)) = mult(c, mult(c, mult(a, b)))) <=> (mult(mult(unit, c), mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)) = mult(mult(unit, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)), c))),
% 22.67/22.83 inference(transitivity,[status(thm)],[5983, 5043])).
% 22.67/22.83 tff(5985,plain,
% 22.67/22.83 ((mult(mult(c, c), mult(a, b)) = mult(c, mult(c, mult(a, b)))) <=> (mult(mult(c, b), mult(a, c)) = mult(c, mult(b, mult(a, c))))),
% 22.67/22.83 inference(transitivity,[status(thm)],[5984, 5880])).
% 22.67/22.83 tff(5986,plain,
% 22.67/22.83 (mult(mult(c, c), mult(a, b)) = mult(c, mult(c, mult(a, b)))),
% 22.67/22.83 inference(unit_resolution,[status(thm)],[4259, 4277])).
% 22.67/22.83 tff(5987,plain,
% 22.67/22.83 (mult(mult(c, b), mult(a, c)) = mult(c, mult(b, mult(a, c)))),
% 22.67/22.83 inference(modus_ponens,[status(thm)],[5986, 5985])).
% 22.67/22.83 tff(5988,plain,
% 22.67/22.83 ($false),
% 22.67/22.83 inference(unit_resolution,[status(thm)],[2430, 5987])).
% 22.67/22.83 tff(5989,plain,((mult(mult(c, b), mult(a, c)) = mult(c, mult(b, mult(a, c)))) | (~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))) | (~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))) | (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit))))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) | (~(mult(mult(c, a), b) = mult(c, mult(a, b)))) | (~(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(c, mult(rd(mult(b, c), mult(a, c)), a)), c) = mult(c, mult(mult(rd(mult(b, c), mult(a, c)), a), c)))) | (~(mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c)))))))), inference(lemma,lemma(discharge,[]))).
% 22.67/22.84 tff(5990,plain,
% 22.67/22.84 (mult(mult(c, b), mult(a, c)) = mult(c, mult(b, mult(a, c)))),
% 22.67/22.84 inference(unit_resolution,[status(thm)],[5989, 5858, 5774, 5781, 359, 3865, 4517, 5838, 4495, 1683, 5829])).
% 22.67/22.84 tff(5991,plain,
% 22.67/22.84 (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)), a)),
% 22.67/22.84 inference(symmetry,[status(thm)],[5785])).
% 22.67/22.84 tff(5992,plain,
% 22.67/22.84 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(a, mult(a, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c))),
% 22.67/22.84 inference(quant_inst,[status(thm)],[])).
% 22.67/22.84 tff(5993,plain,
% 22.67/22.84 (ld(a, mult(a, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)),
% 22.67/22.84 inference(unit_resolution,[status(thm)],[5992, 7])).
% 22.67/22.84 tff(5994,plain,
% 22.67/22.84 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(c, unit), c)) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))),
% 22.67/22.84 inference(symmetry,[status(thm)],[4656])).
% 22.67/22.84 tff(5995,plain,
% 22.67/22.84 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), unit), c)),
% 22.67/22.84 inference(symmetry,[status(thm)],[5783])).
% 22.67/22.84 tff(5996,plain,
% 22.67/22.84 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))),
% 22.67/22.84 inference(transitivity,[status(thm)],[5995, 4654, 5994])).
% 22.67/22.84 tff(5997,plain,
% 22.67/22.84 (mult(a, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)))),
% 22.67/22.84 inference(monotonicity,[status(thm)],[5996])).
% 22.67/22.84 tff(5998,plain,
% 22.67/22.84 (mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))) = mult(a, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c))),
% 22.67/22.84 inference(symmetry,[status(thm)],[5997])).
% 22.67/22.84 tff(5999,plain,
% 22.67/22.84 (~(mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))),
% 22.67/22.84 inference(unit_resolution,[status(thm)],[303, 5777, 281, 279])).
% 22.67/22.84 tff(6000,plain,
% 22.67/22.84 ((~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))),
% 22.67/22.84 inference(unit_resolution,[status(thm)],[308, 5999])).
% 22.67/22.84 tff(6001,plain,
% 22.67/22.84 (~((~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))),
% 22.67/22.84 inference(unit_resolution,[status(thm)],[313, 6000])).
% 22.67/22.84 tff(6002,plain,
% 22.67/22.84 (mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 22.67/22.84 inference(unit_resolution,[status(thm)],[4354, 6001])).
% 22.67/22.84 tff(6003,plain,
% 22.67/22.84 (mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c)))),
% 22.67/22.84 inference(unit_resolution,[status(thm)],[5257, 4495, 359, 6002, 3865, 4517])).
% 22.67/22.84 tff(6004,plain,
% 22.67/22.84 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)), mult(c, c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), a)))),
% 22.67/22.84 inference(quant_inst,[status(thm)],[])).
% 22.67/22.84 tff(6005,plain,
% 22.67/22.84 (rd(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)), mult(c, c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), a))),
% 22.67/22.84 inference(unit_resolution,[status(thm)],[6004, 168])).
% 22.67/22.84 tff(6006,plain,
% 22.67/22.84 (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)), a)),
% 22.67/22.84 inference(symmetry,[status(thm)],[5861])).
% 22.67/22.84 tff(6007,plain,
% 22.67/22.84 (mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c)),
% 22.67/22.84 inference(symmetry,[status(thm)],[5765])).
% 22.67/22.84 tff(6008,plain,
% 22.67/22.84 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(c, a), c)) = mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a), c)),
% 22.67/22.84 inference(symmetry,[status(thm)],[5141])).
% 22.67/22.84 tff(6009,plain,
% 22.67/22.84 ((~![A: $i] : (mult(A, unit) = A)) | (mult(mult(c, mult(a, c)), unit) = mult(c, mult(a, c)))),
% 22.67/22.84 inference(quant_inst,[status(thm)],[])).
% 22.67/22.84 tff(6010,plain,
% 22.67/22.84 (mult(mult(c, mult(a, c)), unit) = mult(c, mult(a, c))),
% 22.67/22.84 inference(unit_resolution,[status(thm)],[6009, 43])).
% 22.67/22.84 tff(6011,plain,
% 22.67/22.84 (mult(unit, mult(mult(a, c), c)) = mult(unit, mult(c, mult(a, c)))),
% 22.67/22.84 inference(monotonicity,[status(thm)],[4529])).
% 22.67/22.84 tff(6012,plain,
% 22.67/22.84 (mult(unit, mult(mult(a, c), c)) = mult(c, mult(a, c))),
% 22.67/22.84 inference(transitivity,[status(thm)],[6011, 4366, 4365, 4362, 2690])).
% 22.67/22.84 tff(6013,plain,
% 22.67/22.84 (mult(mult(unit, mult(mult(a, c), c)), unit) = mult(mult(c, mult(a, c)), unit)),
% 22.67/22.84 inference(monotonicity,[status(thm)],[6012])).
% 22.67/22.84 tff(6014,plain,
% 22.67/22.84 (mult(mult(unit, mult(mult(a, c), c)), unit) = mult(mult(a, c), c)),
% 22.67/22.84 inference(transitivity,[status(thm)],[6013, 6010, 3877, 3876])).
% 22.67/22.84 tff(6015,plain,
% 22.67/22.84 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(unit, mult(mult(a, c), c)), unit)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), c))),
% 22.67/22.84 inference(monotonicity,[status(thm)],[6014])).
% 22.67/22.84 tff(6016,assumption,(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c)))), introduced(assumption)).
% 22.67/22.84 tff(6017,assumption,(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c)))), introduced(assumption)).
% 22.67/22.84 tff(6018,assumption,(~(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)))), introduced(assumption)).
% 22.67/22.84 tff(6019,plain,
% 22.67/22.84 ((~![A: $i] : (mult(unit, A) = A)) | (mult(unit, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c))),
% 22.67/22.84 inference(quant_inst,[status(thm)],[])).
% 22.67/22.84 tff(6020,plain,
% 22.67/22.84 (mult(unit, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)),
% 22.67/22.84 inference(unit_resolution,[status(thm)],[6019, 71])).
% 22.67/22.84 tff(6021,plain,
% 22.67/22.84 (mult(mult(unit, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)), unit) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), unit)),
% 22.67/22.84 inference(monotonicity,[status(thm)],[6020])).
% 22.67/22.84 tff(6022,plain,
% 22.67/22.84 (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), unit) = mult(mult(unit, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)), unit)),
% 22.67/22.84 inference(symmetry,[status(thm)],[6021])).
% 22.67/22.84 tff(6023,plain,
% 22.67/22.84 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), unit) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))),
% 22.67/22.84 inference(transitivity,[status(thm)],[2177, 2162])).
% 22.67/22.84 tff(6024,plain,
% 22.67/22.84 (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), unit), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)),
% 22.67/22.84 inference(monotonicity,[status(thm)],[6023])).
% 22.67/22.84 tff(6025,plain,
% 22.67/22.84 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), unit), c)),
% 22.67/22.84 inference(symmetry,[status(thm)],[6024])).
% 22.67/22.84 tff(6026,plain,
% 22.67/22.84 (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), unit) = mult(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), unit), c), unit)),
% 22.67/22.84 inference(monotonicity,[status(thm)],[6025])).
% 22.67/22.84 tff(6027,plain,
% 22.67/22.84 (mult(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), unit), c), unit) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), unit)),
% 22.67/22.84 inference(symmetry,[status(thm)],[6026])).
% 22.67/22.84 tff(6028,plain,
% 22.67/22.84 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), unit), c), unit) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(mult(unit, c), unit)))),
% 22.67/22.84 inference(quant_inst,[status(thm)],[])).
% 22.67/22.84 tff(6029,plain,
% 22.67/22.84 (mult(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), unit), c), unit) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(mult(unit, c), unit))),
% 22.67/22.84 inference(unit_resolution,[status(thm)],[6028, 56])).
% 22.67/22.84 tff(6030,plain,
% 22.67/22.84 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(mult(unit, c), unit)) = mult(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), unit), c), unit)),
% 22.67/22.84 inference(symmetry,[status(thm)],[6029])).
% 22.67/22.84 tff(6031,plain,
% 22.67/22.84 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(mult(unit, c), unit)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)),
% 22.67/22.84 inference(monotonicity,[status(thm)],[78])).
% 22.67/22.84 tff(6032,plain,
% 22.67/22.84 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(mult(unit, c), unit))),
% 22.67/22.84 inference(symmetry,[status(thm)],[6031])).
% 22.67/22.84 tff(6033,plain,
% 22.67/22.84 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(unit, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)), unit)),
% 22.67/22.84 inference(transitivity,[status(thm)],[6032, 6030, 6027, 6022])).
% 22.67/22.84 tff(6034,plain,
% 22.67/22.84 (mult(a, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(mult(unit, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)), unit))),
% 22.67/22.84 inference(monotonicity,[status(thm)],[6033])).
% 22.67/22.84 tff(6035,plain,
% 22.67/22.84 (mult(a, mult(mult(unit, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)), unit)) = mult(a, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c))),
% 22.67/22.84 inference(symmetry,[status(thm)],[6034])).
% 22.67/22.84 tff(6036,plain,
% 22.67/22.84 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(a, unit), mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)), unit) = mult(a, mult(mult(unit, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)), unit)))),
% 22.67/22.84 inference(quant_inst,[status(thm)],[])).
% 22.67/22.84 tff(6037,plain,
% 22.67/22.84 (mult(mult(mult(a, unit), mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)), unit) = mult(a, mult(mult(unit, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)), unit))),
% 22.67/22.84 inference(unit_resolution,[status(thm)],[6036, 56])).
% 22.67/22.84 tff(6038,plain,
% 22.67/22.84 (mult(mult(a, unit), mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c))),
% 22.67/22.84 inference(monotonicity,[status(thm)],[47])).
% 22.67/22.84 tff(6039,plain,
% 22.67/22.84 (mult(mult(mult(a, unit), mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)), unit) = mult(mult(a, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)), unit)),
% 22.67/22.84 inference(monotonicity,[status(thm)],[6038])).
% 22.67/22.84 tff(6040,plain,
% 22.67/22.84 (mult(mult(a, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)), unit) = mult(mult(mult(a, unit), mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)), unit)),
% 22.67/22.84 inference(symmetry,[status(thm)],[6039])).
% 22.67/22.84 tff(6041,plain,
% 22.67/22.84 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), c), unit), c) = mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(mult(c, unit), c)))),
% 22.67/22.84 inference(quant_inst,[status(thm)],[])).
% 22.67/22.84 tff(6042,plain,
% 22.67/22.84 (mult(mult(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), c), unit), c) = mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(mult(c, unit), c))),
% 22.67/22.84 inference(unit_resolution,[status(thm)],[6041, 56])).
% 22.67/22.84 tff(6043,plain,
% 22.67/22.84 (mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(mult(c, unit), c)) = mult(mult(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), c), unit), c)),
% 22.67/22.84 inference(symmetry,[status(thm)],[6042])).
% 22.67/22.84 tff(6044,plain,
% 22.67/22.84 (mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(mult(c, unit), c)) = mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c))),
% 22.67/22.84 inference(monotonicity,[status(thm)],[2616])).
% 22.67/22.84 tff(6045,plain,
% 22.67/22.84 (mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(mult(c, unit), c))),
% 22.67/22.84 inference(symmetry,[status(thm)],[6044])).
% 22.67/22.84 tff(6046,plain,
% 22.67/22.84 (((~(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a)))))) | (mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)))),
% 22.67/22.84 inference(tautology,[status(thm)],[])).
% 22.67/22.84 tff(6047,plain,
% 22.67/22.84 ((~(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a)))))),
% 22.67/22.84 inference(unit_resolution,[status(thm)],[6046, 6018])).
% 22.67/22.84 tff(6048,assumption,((~(mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))))) | (~(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)))))), introduced(assumption)).
% 22.67/22.84 tff(6049,plain,
% 22.67/22.84 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))))) | (~(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))))))) | (~((~(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))))) | (~(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))))))) | (~((~(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))))))))),
% 22.67/22.84 inference(rewrite,[status(thm)],[])).
% 22.67/22.84 tff(6050,plain,
% 22.67/22.84 (((~((~(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))))))) | (~((~(mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))))) | (~(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)))))))) <=> ((~((~(mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))))) | (~(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))))))) | (~((~(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))))))))),
% 22.67/22.85 inference(rewrite,[status(thm)],[])).
% 22.67/22.85 tff(6051,plain,
% 22.67/22.85 ((~((~(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))))) | (~(mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))))))) <=> (~((~(mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))))) | (~(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)))))))),
% 22.67/22.85 inference(rewrite,[status(thm)],[])).
% 22.67/22.85 tff(6052,plain,
% 22.67/22.85 ((~((~(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))))))) <=> (~((~(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a)))))))),
% 22.67/22.85 inference(rewrite,[status(thm)],[])).
% 22.67/22.85 tff(6053,plain,
% 22.67/22.85 (((~((~(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))))))) | (~((~(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))))) | (~(mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a)))))))) <=> ((~((~(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))))))) | (~((~(mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))))) | (~(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))))))))),
% 22.67/22.85 inference(monotonicity,[status(thm)],[6052, 6051])).
% 22.67/22.85 tff(6054,plain,
% 22.67/22.85 (((~((~(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))))))) | (~((~(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))))) | (~(mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a)))))))) <=> ((~((~(mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))))) | (~(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))))))) | (~((~(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))))))))),
% 22.67/22.85 inference(transitivity,[status(thm)],[6053, 6050])).
% 22.67/22.85 tff(6055,plain,
% 22.67/22.85 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))))))) | (~((~(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))))) | (~(mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))))) | (~(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))))))) | (~((~(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a)))))))))),
% 22.67/22.85 inference(monotonicity,[status(thm)],[6054])).
% 22.67/22.85 tff(6056,plain,
% 22.67/22.85 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))))))) | (~((~(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))))) | (~(mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))))) | (~(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))))))) | (~((~(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))))))))),
% 22.67/22.85 inference(transitivity,[status(thm)],[6055, 6049])).
% 22.67/22.85 tff(6057,plain,
% 22.67/22.85 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))))))) | (~((~(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))))) | (~(mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))))))))),
% 22.67/22.85 inference(quant_inst,[status(thm)],[])).
% 22.67/22.85 tff(6058,plain,
% 22.67/22.85 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))))) | (~(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))))))) | (~((~(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a)))))))),
% 22.67/22.85 inference(modus_ponens,[status(thm)],[6057, 6056])).
% 22.67/22.85 tff(6059,plain,
% 22.67/22.85 ($false),
% 22.67/22.85 inference(unit_resolution,[status(thm)],[6058, 27, 6048, 6047])).
% 22.67/22.85 tff(6060,plain,((~((~(mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))))) | (~(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))))))) | (mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)))), inference(lemma,lemma(discharge,[]))).
% 22.67/22.85 tff(6061,plain,
% 22.67/22.85 (~((~(mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))))) | (~(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))))))),
% 22.67/22.85 inference(unit_resolution,[status(thm)],[6060, 6018])).
% 22.67/22.85 tff(6062,plain,
% 22.67/22.85 (((~(mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))))) | (~(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)))))) | (mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))))),
% 22.67/22.85 inference(tautology,[status(thm)],[])).
% 22.67/22.85 tff(6063,plain,
% 22.67/22.85 (mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)))),
% 22.67/22.85 inference(unit_resolution,[status(thm)],[6062, 6061])).
% 22.67/22.85 tff(6064,plain,
% 22.67/22.85 (mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))) = mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c))),
% 22.67/22.85 inference(symmetry,[status(thm)],[6063])).
% 22.67/22.85 tff(6065,plain,
% 22.67/22.85 (mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))) = mult(a, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c))),
% 22.67/22.85 inference(monotonicity,[status(thm)],[5860])).
% 22.67/22.85 tff(6066,plain,
% 22.67/22.85 (mult(a, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)))),
% 22.67/22.85 inference(symmetry,[status(thm)],[6065])).
% 22.67/22.85 tff(6067,plain,
% 22.67/22.85 (mult(a, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)) = mult(mult(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), c), unit), c)),
% 22.67/22.85 inference(transitivity,[status(thm)],[6066, 6064, 6045, 6043])).
% 22.67/22.85 tff(6068,plain,
% 22.67/22.85 (mult(mult(a, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)), unit) = mult(mult(mult(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), c), unit), c), unit)),
% 22.67/22.85 inference(monotonicity,[status(thm)],[6067])).
% 22.67/22.85 tff(6069,plain,
% 22.67/22.85 (mult(mult(mult(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), c), unit), c), unit) = mult(mult(a, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)), unit)),
% 22.67/22.85 inference(symmetry,[status(thm)],[6068])).
% 22.67/22.85 tff(6070,plain,
% 22.67/22.85 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), c), unit), c), unit) = mult(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), c), mult(mult(unit, c), unit)))),
% 22.67/22.85 inference(quant_inst,[status(thm)],[])).
% 22.67/22.85 tff(6071,plain,
% 22.67/22.85 (mult(mult(mult(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), c), unit), c), unit) = mult(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), c), mult(mult(unit, c), unit))),
% 22.67/22.86 inference(unit_resolution,[status(thm)],[6070, 56])).
% 22.67/22.86 tff(6072,plain,
% 22.67/22.86 (mult(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), c), mult(mult(unit, c), unit)) = mult(mult(mult(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), c), unit), c), unit)),
% 22.67/22.86 inference(symmetry,[status(thm)],[6071])).
% 22.67/22.86 tff(6073,plain,
% 22.67/22.86 (c = mult(c, unit)),
% 22.67/22.86 inference(symmetry,[status(thm)],[206])).
% 22.67/22.86 tff(6074,plain,
% 22.67/22.86 (mult(mult(unit, c), unit) = mult(c, unit)),
% 22.67/22.86 inference(transitivity,[status(thm)],[63, 73, 6073])).
% 22.67/22.86 tff(6075,plain,
% 22.67/22.86 (mult(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), c), mult(mult(unit, c), unit)) = mult(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), c), mult(c, unit))),
% 22.67/22.86 inference(monotonicity,[status(thm)],[6074])).
% 22.67/22.86 tff(6076,plain,
% 22.67/22.86 (mult(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), c), mult(c, unit)) = mult(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), c), mult(mult(unit, c), unit))),
% 22.67/22.86 inference(symmetry,[status(thm)],[6075])).
% 22.67/22.86 tff(6077,assumption,(~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(unit, mult(mult(a, c), c)), unit)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, mult(mult(a, c), c)), unit))))), introduced(assumption)).
% 22.67/22.86 tff(6078,plain,
% 22.67/22.86 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))),
% 22.67/22.86 inference(monotonicity,[status(thm)],[4529])).
% 22.67/22.86 tff(6079,plain,
% 22.67/22.86 (mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c))),
% 22.67/22.86 inference(symmetry,[status(thm)],[6078])).
% 22.67/22.86 tff(6080,plain,
% 22.67/22.86 (mult(mult(unit, mult(mult(a, c), c)), unit) = mult(c, mult(a, c))),
% 22.67/22.86 inference(transitivity,[status(thm)],[6013, 6010])).
% 22.67/22.86 tff(6081,plain,
% 22.67/22.86 (mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, mult(mult(a, c), c)), unit)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))),
% 22.67/22.86 inference(monotonicity,[status(thm)],[6080])).
% 22.67/22.86 tff(6082,plain,
% 22.67/22.86 (mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, mult(mult(a, c), c)), unit)) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c))),
% 22.67/22.86 inference(transitivity,[status(thm)],[6081, 6079])).
% 22.67/22.86 tff(6083,plain,
% 22.67/22.86 (mult(a, mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, mult(mult(a, c), c)), unit))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c)))),
% 22.67/22.86 inference(monotonicity,[status(thm)],[6082])).
% 22.67/22.86 tff(6084,plain,
% 22.67/22.86 ((mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(unit, mult(mult(a, c), c)), unit)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, mult(mult(a, c), c)), unit)))) <=> (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c))))),
% 22.67/22.86 inference(monotonicity,[status(thm)],[6015, 6083])).
% 22.67/22.86 tff(6085,plain,
% 22.67/22.86 ((mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c)))) <=> (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(unit, mult(mult(a, c), c)), unit)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, mult(mult(a, c), c)), unit))))),
% 22.67/22.86 inference(symmetry,[status(thm)],[6084])).
% 22.67/22.86 tff(6086,plain,
% 22.67/22.86 (mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)),
% 22.67/22.86 inference(monotonicity,[status(thm)],[5154])).
% 22.67/22.86 tff(6087,plain,
% 22.67/22.86 (mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(mult(c, a), c)) = mult(rd(mult(b, c), mult(a, c)), mult(mult(c, a), c))),
% 22.67/22.86 inference(monotonicity,[status(thm)],[1893])).
% 22.67/22.86 tff(6088,plain,
% 22.67/22.86 (mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))) = mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(mult(c, a), c))),
% 22.67/22.86 inference(monotonicity,[status(thm)],[4856, 3877])).
% 22.67/22.86 tff(6089,plain,
% 22.67/22.86 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)),
% 22.67/22.86 inference(transitivity,[status(thm)],[6078, 6088, 6087, 4855, 6086])).
% 22.67/22.86 tff(6090,plain,
% 22.67/22.86 (mult(a, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c))) = mult(a, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c))),
% 22.67/22.86 inference(monotonicity,[status(thm)],[6089])).
% 22.67/22.86 tff(6091,plain,
% 22.67/22.86 (mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), c) = mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), c)),
% 22.67/22.86 inference(monotonicity,[status(thm)],[4677])).
% 22.67/22.86 tff(6092,plain,
% 22.67/22.86 (mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), c) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), c)),
% 22.67/22.86 inference(symmetry,[status(thm)],[6091])).
% 22.67/22.86 tff(6093,plain,
% 22.67/22.86 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), c)) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), c)),
% 22.67/22.86 inference(transitivity,[status(thm)],[5921, 5923, 6008, 5925, 5928, 6092])).
% 22.67/22.86 tff(6094,plain,
% 22.67/22.86 ((mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c)))) <=> (mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), c) = mult(a, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)))),
% 22.67/22.86 inference(monotonicity,[status(thm)],[6093, 6090])).
% 22.67/22.86 tff(6095,plain,
% 22.67/22.86 ((mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), c) = mult(a, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c))) <=> (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c))))),
% 22.67/22.86 inference(symmetry,[status(thm)],[6094])).
% 22.67/22.86 tff(6096,plain,
% 22.67/22.86 ((mult(a, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), c)) <=> (mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), c) = mult(a, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)))),
% 22.67/22.86 inference(commutativity,[status(thm)],[])).
% 22.67/22.86 tff(6097,plain,
% 22.67/22.86 (mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)),
% 22.67/22.86 inference(symmetry,[status(thm)],[6016])).
% 22.67/22.86 tff(6098,plain,
% 22.67/22.86 (mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c)))),
% 22.67/22.86 inference(monotonicity,[status(thm)],[3878])).
% 22.67/22.86 tff(6099,plain,
% 22.67/22.86 (mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)),
% 22.67/22.86 inference(transitivity,[status(thm)],[6098, 6097])).
% 22.67/22.86 tff(6100,plain,
% 22.67/22.86 (mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a)),
% 22.67/22.86 inference(monotonicity,[status(thm)],[6099])).
% 22.67/22.86 tff(6101,plain,
% 22.67/22.86 (mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a)),
% 22.67/22.86 inference(symmetry,[status(thm)],[6017])).
% 22.67/22.86 tff(6102,plain,
% 22.67/22.86 (mult(mult(a, c), mult(a, c)) = mult(mult(mult(a, c), c), a)),
% 22.67/22.86 inference(transitivity,[status(thm)],[4887, 5062, 5057, 2562, 4872, 4868])).
% 22.67/22.86 tff(6103,plain,
% 22.67/22.86 (mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(mult(a, c), c), a), rd(mult(b, c), mult(a, c)))),
% 22.67/22.86 inference(monotonicity,[status(thm)],[6102])).
% 22.67/22.86 tff(6104,plain,
% 22.67/22.86 (mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), a), c)) = mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 22.67/22.86 inference(monotonicity,[status(thm)],[5186])).
% 22.67/22.86 tff(6105,plain,
% 22.67/22.86 (mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), a), c)) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), c)),
% 22.67/22.86 inference(transitivity,[status(thm)],[6104, 5322, 6103, 5231, 6101, 6100, 4528, 5765, 6092])).
% 22.67/22.86 tff(6106,plain,
% 22.67/22.86 (mult(mult(unit, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)), unit) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)),
% 22.67/22.86 inference(transitivity,[status(thm)],[6021, 6026, 6029, 6031])).
% 22.67/22.86 tff(6107,plain,
% 22.67/22.86 (mult(a, mult(mult(unit, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)), unit)) = mult(a, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c))),
% 22.67/22.86 inference(monotonicity,[status(thm)],[6106])).
% 22.67/22.86 tff(6108,plain,
% 22.67/22.86 (mult(a, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)) = mult(mult(a, unit), mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c))),
% 22.67/22.86 inference(symmetry,[status(thm)],[6038])).
% 22.67/22.86 tff(6109,plain,
% 22.67/22.86 (mult(mult(a, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)), unit) = mult(mult(mult(a, unit), mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)), unit)),
% 22.67/22.86 inference(monotonicity,[status(thm)],[6108])).
% 22.67/22.86 tff(6110,plain,
% 22.67/22.86 (mult(mult(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), c), unit), c) = mult(a, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c))),
% 22.67/22.86 inference(transitivity,[status(thm)],[6042, 6044, 6063, 6065])).
% 22.67/22.86 tff(6111,plain,
% 22.67/22.86 (mult(mult(mult(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), c), unit), c), unit) = mult(mult(a, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)), unit)),
% 22.67/22.86 inference(monotonicity,[status(thm)],[6110])).
% 22.67/22.86 tff(6112,plain,
% 22.67/22.86 (mult(c, unit) = mult(mult(unit, c), unit)),
% 22.67/22.86 inference(transitivity,[status(thm)],[206, 74, 64])).
% 22.67/22.86 tff(6113,plain,
% 22.67/22.86 (mult(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), c), mult(c, unit)) = mult(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), c), mult(mult(unit, c), unit))),
% 22.67/22.86 inference(monotonicity,[status(thm)],[6112])).
% 22.67/22.86 tff(6114,plain,
% 22.67/22.86 (mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), c)),
% 22.67/22.86 inference(symmetry,[status(thm)],[5802])).
% 22.67/22.86 tff(6115,assumption,(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))), introduced(assumption)).
% 22.67/22.86 tff(6116,plain,
% 22.67/22.86 (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)),
% 22.67/22.86 inference(symmetry,[status(thm)],[6115])).
% 22.67/22.86 tff(6117,plain,
% 22.67/22.86 (mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), c)),
% 22.67/22.86 inference(transitivity,[status(thm)],[404, 6116, 6114])).
% 22.67/22.86 tff(6118,plain,
% 22.67/22.86 (mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c) = mult(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), c), mult(c, unit))),
% 22.67/22.86 inference(monotonicity,[status(thm)],[6117, 6073])).
% 22.67/22.86 tff(6119,plain,
% 22.67/22.86 (mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c) = mult(a, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c))),
% 22.67/22.86 inference(transitivity,[status(thm)],[6118, 6113, 6072, 6111, 6109, 6037, 6107])).
% 22.67/22.86 tff(6120,plain,
% 22.67/22.86 ((mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), a), c))) <=> (mult(a, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), c))),
% 22.67/22.86 inference(monotonicity,[status(thm)],[6119, 6105])).
% 22.67/22.86 tff(6121,plain,
% 22.67/22.86 ((mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), a), c))) <=> (mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), c) = mult(a, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)))),
% 22.67/22.86 inference(transitivity,[status(thm)],[6120, 6096])).
% 22.67/22.86 tff(6122,plain,
% 22.67/22.86 ((mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), a), c))) <=> (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(unit, mult(mult(a, c), c)), unit)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, mult(mult(a, c), c)), unit))))),
% 22.67/22.86 inference(transitivity,[status(thm)],[6121, 6095, 6085])).
% 22.67/22.86 tff(6123,plain,
% 22.67/22.86 ((mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c))) <=> (mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)))),
% 22.67/22.86 inference(commutativity,[status(thm)],[])).
% 22.67/22.86 tff(6124,plain,
% 22.67/22.86 (mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c) = mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c))),
% 22.67/22.86 inference(transitivity,[status(thm)],[6118, 6113, 6072, 6111, 6109, 6037, 6107, 6066, 6064])).
% 22.67/22.86 tff(6125,plain,
% 22.67/22.86 (mult(a, mult(c, c)) = mult(c, mult(a, c))),
% 22.67/22.86 inference(transitivity,[status(thm)],[2618, 2615, 2612, 3875, 2690])).
% 22.67/22.86 tff(6126,plain,
% 22.67/22.86 (mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a))),
% 22.67/22.86 inference(monotonicity,[status(thm)],[6125])).
% 22.67/22.86 tff(6127,plain,
% 22.67/22.86 (mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a))),
% 22.67/22.86 inference(symmetry,[status(thm)],[6126])).
% 22.67/22.86 tff(6128,plain,
% 22.67/22.86 (mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a))),
% 22.67/22.86 inference(monotonicity,[status(thm)],[4529])).
% 22.67/22.86 tff(6129,plain,
% 22.67/22.86 (mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a))),
% 22.67/22.86 inference(transitivity,[status(thm)],[6128, 6127])).
% 22.67/22.86 tff(6130,plain,
% 22.67/22.86 ((mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c)) <=> (mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)))),
% 22.67/22.86 inference(monotonicity,[status(thm)],[6129, 6124])).
% 22.67/22.86 tff(6131,plain,
% 22.67/22.86 ((mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c)) <=> (mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)))),
% 22.67/22.86 inference(transitivity,[status(thm)],[6130, 6123])).
% 22.67/22.86 tff(6132,plain,
% 22.67/22.86 ((mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a))) <=> (mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c))),
% 22.67/22.86 inference(symmetry,[status(thm)],[6131])).
% 22.67/22.86 tff(6133,plain,
% 22.67/22.86 ((~(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)))) <=> (~(mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c)))),
% 22.67/22.86 inference(monotonicity,[status(thm)],[6132])).
% 22.67/22.86 tff(6134,plain,
% 22.67/22.86 (~(mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c))),
% 22.67/22.86 inference(modus_ponens,[status(thm)],[6018, 6133])).
% 22.67/22.86 tff(6135,plain,
% 22.67/22.86 (((~(mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c))) | (~(mult(mult(a, c), mult(c, mult(rd(mult(b, c), mult(a, c)), a))) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), a), c))))) | (mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c))),
% 22.67/22.86 inference(tautology,[status(thm)],[])).
% 22.67/22.86 tff(6136,plain,
% 22.67/22.86 ((~(mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c))) | (~(mult(mult(a, c), mult(c, mult(rd(mult(b, c), mult(a, c)), a))) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), a), c))))),
% 22.67/22.86 inference(unit_resolution,[status(thm)],[6135, 6134])).
% 22.67/22.86 tff(6137,plain,
% 22.67/22.86 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, c), mult(c, mult(rd(mult(b, c), mult(a, c)), a))))) | (~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), a), c)))))) | (~((~(mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c))) | (~(mult(mult(a, c), mult(c, mult(rd(mult(b, c), mult(a, c)), a))) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), a), c)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, c), mult(c, mult(rd(mult(b, c), mult(a, c)), a))))) | (~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), a), c)))))) | (~((~(mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c))) | (~(mult(mult(a, c), mult(c, mult(rd(mult(b, c), mult(a, c)), a))) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), a), c)))))))),
% 22.67/22.87 inference(rewrite,[status(thm)],[])).
% 22.67/22.87 tff(6138,plain,
% 22.67/22.87 (((~((~(mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c))) | (~(mult(mult(a, c), mult(c, mult(rd(mult(b, c), mult(a, c)), a))) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), a), c)))))) | (~((~(mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, c), mult(c, mult(rd(mult(b, c), mult(a, c)), a))))) | (~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), a), c))))))) <=> ((~((~(mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, c), mult(c, mult(rd(mult(b, c), mult(a, c)), a))))) | (~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), a), c)))))) | (~((~(mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c))) | (~(mult(mult(a, c), mult(c, mult(rd(mult(b, c), mult(a, c)), a))) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), a), c)))))))),
% 22.67/22.87 inference(rewrite,[status(thm)],[])).
% 22.67/22.87 tff(6139,plain,
% 22.67/22.87 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c))) | (~(mult(mult(a, c), mult(c, mult(rd(mult(b, c), mult(a, c)), a))) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), a), c)))))) | (~((~(mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, c), mult(c, mult(rd(mult(b, c), mult(a, c)), a))))) | (~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), a), c)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, c), mult(c, mult(rd(mult(b, c), mult(a, c)), a))))) | (~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), a), c)))))) | (~((~(mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c))) | (~(mult(mult(a, c), mult(c, mult(rd(mult(b, c), mult(a, c)), a))) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), a), c))))))))),
% 22.67/22.87 inference(monotonicity,[status(thm)],[6138])).
% 22.67/22.87 tff(6140,plain,
% 22.67/22.87 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c))) | (~(mult(mult(a, c), mult(c, mult(rd(mult(b, c), mult(a, c)), a))) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), a), c)))))) | (~((~(mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, c), mult(c, mult(rd(mult(b, c), mult(a, c)), a))))) | (~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), a), c)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, c), mult(c, mult(rd(mult(b, c), mult(a, c)), a))))) | (~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), a), c)))))) | (~((~(mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c))) | (~(mult(mult(a, c), mult(c, mult(rd(mult(b, c), mult(a, c)), a))) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), a), c)))))))),
% 22.67/22.87 inference(transitivity,[status(thm)],[6139, 6137])).
% 22.67/22.87 tff(6141,plain,
% 22.67/22.87 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c))) | (~(mult(mult(a, c), mult(c, mult(rd(mult(b, c), mult(a, c)), a))) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), a), c)))))) | (~((~(mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, c), mult(c, mult(rd(mult(b, c), mult(a, c)), a))))) | (~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), a), c)))))))),
% 22.67/22.87 inference(quant_inst,[status(thm)],[])).
% 22.67/22.87 tff(6142,plain,
% 22.67/22.87 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, c), mult(c, mult(rd(mult(b, c), mult(a, c)), a))))) | (~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), a), c)))))) | (~((~(mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c))) | (~(mult(mult(a, c), mult(c, mult(rd(mult(b, c), mult(a, c)), a))) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), a), c))))))),
% 22.67/22.87 inference(modus_ponens,[status(thm)],[6141, 6140])).
% 22.67/22.87 tff(6143,plain,
% 22.67/22.87 ((~((~(mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, c), mult(c, mult(rd(mult(b, c), mult(a, c)), a))))) | (~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), a), c)))))) | (~((~(mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c))) | (~(mult(mult(a, c), mult(c, mult(rd(mult(b, c), mult(a, c)), a))) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), a), c))))))),
% 22.67/22.87 inference(unit_resolution,[status(thm)],[6142, 27])).
% 22.67/22.87 tff(6144,plain,
% 22.67/22.87 (~((~(mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, c), mult(c, mult(rd(mult(b, c), mult(a, c)), a))))) | (~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), a), c)))))),
% 22.67/22.87 inference(unit_resolution,[status(thm)],[6143, 6136])).
% 22.67/22.87 tff(6145,plain,
% 22.67/22.87 (((~(mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, c), mult(c, mult(rd(mult(b, c), mult(a, c)), a))))) | (~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), a), c))))) | (mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), a), c)))),
% 22.67/22.87 inference(tautology,[status(thm)],[])).
% 22.67/22.87 tff(6146,plain,
% 22.67/22.87 (mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), a), c))),
% 22.67/22.87 inference(unit_resolution,[status(thm)],[6145, 6144])).
% 22.67/22.87 tff(6147,plain,
% 22.67/22.87 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(unit, mult(mult(a, c), c)), unit)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, mult(mult(a, c), c)), unit)))),
% 22.67/22.87 inference(modus_ponens,[status(thm)],[6146, 6122])).
% 22.67/22.87 tff(6148,plain,
% 22.67/22.87 ($false),
% 22.67/22.87 inference(unit_resolution,[status(thm)],[6077, 6147])).
% 22.67/22.87 tff(6149,plain,((~(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))) | (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(unit, mult(mult(a, c), c)), unit)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, mult(mult(a, c), c)), unit)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))) | (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit))))) | (~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) | (~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))) | (~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))))) | (~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))))) | (mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)))), inference(lemma,lemma(discharge,[]))).
% 22.67/22.87 tff(6150,plain,
% 22.67/22.87 (~(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))),
% 22.67/22.87 inference(unit_resolution,[status(thm)],[6149, 6077, 4360, 2187, 359, 3865, 299, 4517, 1683, 4789, 6017, 4528, 6016, 6018])).
% 22.67/22.87 tff(6151,plain,
% 22.67/22.87 (((~(mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))))) | (mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))),
% 22.67/22.87 inference(tautology,[status(thm)],[])).
% 22.67/22.87 tff(6152,plain,
% 22.67/22.87 ((~(mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))))),
% 22.67/22.87 inference(unit_resolution,[status(thm)],[6151, 6150])).
% 22.67/22.87 tff(6153,plain,
% 22.67/22.87 (~((~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c)))))),
% 22.67/22.88 inference(unit_resolution,[status(thm)],[5826, 6152])).
% 22.67/22.88 tff(6154,plain,
% 22.67/22.88 (mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c))),
% 22.67/22.88 inference(unit_resolution,[status(thm)],[5814, 6153])).
% 22.67/22.88 tff(6155,plain,
% 22.67/22.88 (mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), c) = mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))),
% 22.67/22.88 inference(transitivity,[status(thm)],[5802, 6154, 5798, 5797, 4676, 4520])).
% 22.67/22.88 tff(6156,plain,
% 22.67/22.88 (mult(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), c), mult(c, unit)) = mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), c)),
% 22.67/22.88 inference(monotonicity,[status(thm)],[6155, 206])).
% 22.67/22.88 tff(6157,plain,
% 22.67/22.88 (mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), c), mult(c, unit))),
% 22.67/22.88 inference(symmetry,[status(thm)],[6156])).
% 22.67/22.88 tff(6158,plain,
% 22.67/22.88 (mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), c) = mult(a, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c))),
% 22.67/22.88 inference(transitivity,[status(thm)],[6091, 6157, 6076, 6072, 6069, 6040, 6037, 6035])).
% 22.67/22.88 tff(6159,plain,
% 22.67/22.88 ((mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(unit, mult(mult(a, c), c)), unit)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, mult(mult(a, c), c)), unit)))) <=> (mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), c) = mult(a, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)))),
% 22.67/22.88 inference(transitivity,[status(thm)],[6084, 6094])).
% 22.67/22.88 tff(6160,plain,
% 22.67/22.88 ((~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(unit, mult(mult(a, c), c)), unit)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, mult(mult(a, c), c)), unit))))) <=> (~(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), c) = mult(a, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c))))),
% 22.67/22.88 inference(monotonicity,[status(thm)],[6159])).
% 22.67/22.88 tff(6161,plain,
% 22.67/22.88 (~(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), c) = mult(a, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)))),
% 22.67/22.88 inference(modus_ponens,[status(thm)],[6077, 6160])).
% 22.67/22.88 tff(6162,plain,
% 22.67/22.88 ($false),
% 22.67/22.88 inference(unit_resolution,[status(thm)],[6161, 6158])).
% 22.67/22.88 tff(6163,plain,((mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(unit, mult(mult(a, c), c)), unit)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, mult(mult(a, c), c)), unit)))) | (~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))) | (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit))))) | (~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))) | (~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))))) | (~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))))) | (mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)))), inference(lemma,lemma(discharge,[]))).
% 22.67/22.88 tff(6164,plain,
% 22.67/22.88 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(unit, mult(mult(a, c), c)), unit)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, mult(mult(a, c), c)), unit)))),
% 22.67/22.88 inference(unit_resolution,[status(thm)],[6163, 6018, 4517, 2187, 359, 4360, 3865, 1683, 4789, 6017, 4528, 6016, 299])).
% 22.67/22.88 tff(6165,plain,
% 22.67/22.88 (mult(a, mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, mult(mult(a, c), c)), unit))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(unit, mult(mult(a, c), c)), unit))),
% 22.67/22.88 inference(symmetry,[status(thm)],[6164])).
% 22.67/22.88 tff(6166,plain,
% 22.67/22.88 (mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, mult(mult(a, c), c)), unit))),
% 22.67/22.88 inference(symmetry,[status(thm)],[6081])).
% 22.67/22.88 tff(6167,plain,
% 22.67/22.88 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c)) = mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, mult(mult(a, c), c)), unit))),
% 22.67/22.88 inference(transitivity,[status(thm)],[6078, 6166])).
% 22.67/22.88 tff(6168,plain,
% 22.67/22.88 (mult(a, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, mult(mult(a, c), c)), unit)))),
% 22.67/22.88 inference(monotonicity,[status(thm)],[6167])).
% 22.67/22.88 tff(6169,plain,
% 22.67/22.88 (mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(mult(c, a), c)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))),
% 22.67/22.88 inference(symmetry,[status(thm)],[6088])).
% 22.67/22.88 tff(6170,plain,
% 22.67/22.88 (mult(rd(mult(b, c), mult(a, c)), mult(mult(c, a), c)) = mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(mult(c, a), c))),
% 22.67/22.88 inference(symmetry,[status(thm)],[6087])).
% 22.67/22.88 tff(6171,plain,
% 22.67/22.88 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c)),
% 22.67/22.88 inference(symmetry,[status(thm)],[6086])).
% 22.67/22.88 tff(6172,plain,
% 22.67/22.88 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c))),
% 22.67/22.88 inference(transitivity,[status(thm)],[6171, 2627, 6170, 6169, 6079])).
% 22.67/22.88 tff(6173,plain,
% 22.67/22.88 (mult(a, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c)))),
% 22.67/22.88 inference(monotonicity,[status(thm)],[6172])).
% 22.67/22.88 tff(6174,plain,
% 22.67/22.88 (mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), mult(c, c))),
% 22.67/22.88 inference(transitivity,[status(thm)],[6063, 6065, 6173, 6168, 6165, 6015, 5921, 5923, 6008, 5925, 5928, 6007, 5947, 6006, 5972])).
% 22.67/22.88 tff(6175,plain,
% 22.67/22.88 (rd(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)), mult(c, c)) = rd(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), mult(c, c)), mult(c, c))),
% 22.67/22.88 inference(monotonicity,[status(thm)],[6174])).
% 22.67/22.88 tff(6176,plain,
% 22.67/22.88 (rd(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), mult(c, c)), mult(c, c)) = rd(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)), mult(c, c))),
% 22.67/22.88 inference(symmetry,[status(thm)],[6175])).
% 22.67/22.88 tff(6177,plain,
% 22.67/22.88 (mult(mult(rd(mult(b, c), mult(a, c)), a), a) = rd(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), mult(c, c)), mult(c, c))),
% 22.67/22.88 inference(symmetry,[status(thm)],[5905])).
% 22.67/22.88 tff(6178,plain,
% 22.67/22.88 (mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a))),
% 22.67/22.88 inference(transitivity,[status(thm)],[5809, 6177, 6176, 6005])).
% 22.67/22.88 tff(6179,plain,
% 22.67/22.88 ($false),
% 22.67/22.88 inference(unit_resolution,[status(thm)],[898, 6178])).
% 22.67/22.88 tff(6180,plain,((mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a))) | (mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a))) | (~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c))) | (~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)))) | (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) | (~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))))) | (~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))), inference(lemma,lemma(discharge,[]))).
% 22.67/22.88 tff(6181,plain,
% 22.67/22.88 (mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a))),
% 22.67/22.88 inference(unit_resolution,[status(thm)],[6180, 6003, 5774, 1683, 5781, 3865, 4360, 359, 4517, 6002, 5857, 898, 281])).
% 22.67/22.88 tff(6182,plain,
% 22.67/22.88 ((~(mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)))) <=> (~(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a))))),
% 22.67/22.88 inference(monotonicity,[status(thm)],[6123])).
% 22.67/22.88 tff(6183,assumption,(~(mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)))), introduced(assumption)).
% 22.67/22.88 tff(6184,plain,
% 22.67/22.88 (~(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)))),
% 22.67/22.88 inference(modus_ponens,[status(thm)],[6183, 6182])).
% 22.67/22.88 tff(6185,assumption,(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a))), introduced(assumption)).
% 22.67/22.88 tff(6186,plain,
% 22.67/22.88 ($false),
% 22.67/22.88 inference(unit_resolution,[status(thm)],[6185, 6184])).
% 22.67/22.88 tff(6187,plain,((mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c))) | (~(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a))))), inference(lemma,lemma(discharge,[]))).
% 22.67/22.88 tff(6188,plain,
% 22.67/22.88 (mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c))),
% 22.67/22.88 inference(unit_resolution,[status(thm)],[6187, 6181])).
% 22.67/22.88 tff(6189,assumption,(mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c))), introduced(assumption)).
% 22.67/22.88 tff(6190,assumption,(~(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))))), introduced(assumption)).
% 22.67/22.88 tff(6191,plain,
% 22.67/22.88 ((~(mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))))) | (~(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)))))),
% 22.67/22.88 inference(unit_resolution,[status(thm)],[6062, 6190])).
% 22.67/22.88 tff(6192,plain,
% 22.67/22.88 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))))) | (~(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))))))) | (~((~(mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)))) | (~(mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))))) | (~(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))))))) | (~((~(mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)))) | (~(mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))))))))),
% 22.67/22.88 inference(rewrite,[status(thm)],[])).
% 22.67/22.88 tff(6193,plain,
% 22.67/22.88 (((~((~(mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)))) | (~(mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))))))) | (~((~(mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))))) | (~(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)))))))) <=> ((~((~(mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))))) | (~(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))))))) | (~((~(mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)))) | (~(mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))))))))),
% 22.67/22.88 inference(rewrite,[status(thm)],[])).
% 22.67/22.88 tff(6194,plain,
% 22.67/22.88 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)))) | (~(mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))))))) | (~((~(mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))))) | (~(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))))) | (~(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))))))) | (~((~(mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)))) | (~(mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)))))))))),
% 22.67/22.88 inference(monotonicity,[status(thm)],[6193])).
% 22.67/22.88 tff(6195,plain,
% 22.67/22.88 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)))) | (~(mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))))))) | (~((~(mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))))) | (~(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))))) | (~(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))))))) | (~((~(mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)))) | (~(mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))))))))),
% 22.67/22.89 inference(transitivity,[status(thm)],[6194, 6192])).
% 22.67/22.89 tff(6196,plain,
% 22.67/22.89 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)))) | (~(mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))))))) | (~((~(mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))))) | (~(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))))))))),
% 22.67/22.89 inference(quant_inst,[status(thm)],[])).
% 22.67/22.89 tff(6197,plain,
% 22.67/22.89 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))))) | (~(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))))))) | (~((~(mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)))) | (~(mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)))))))),
% 22.67/22.89 inference(modus_ponens,[status(thm)],[6196, 6195])).
% 22.67/22.89 tff(6198,plain,
% 22.67/22.89 ((~((~(mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))))) | (~(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))))))) | (~((~(mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)))) | (~(mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)))))))),
% 22.67/22.89 inference(unit_resolution,[status(thm)],[6197, 27])).
% 22.67/22.89 tff(6199,plain,
% 22.67/22.89 (~((~(mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)))) | (~(mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))))))),
% 22.67/22.89 inference(unit_resolution,[status(thm)],[6198, 6191])).
% 22.67/22.89 tff(6200,plain,
% 22.67/22.89 (((~(mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)))) | (~(mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)))))) | (mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))))),
% 22.67/22.89 inference(tautology,[status(thm)],[])).
% 22.67/22.89 tff(6201,plain,
% 22.67/22.89 (mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)))),
% 22.67/22.89 inference(unit_resolution,[status(thm)],[6200, 6199])).
% 22.67/22.89 tff(6202,plain,
% 22.67/22.89 (mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a)))),
% 22.67/22.89 inference(symmetry,[status(thm)],[6201])).
% 22.67/22.89 tff(6203,plain,
% 22.67/22.89 (mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a))),
% 22.67/22.89 inference(symmetry,[status(thm)],[6189])).
% 22.67/22.89 tff(6204,plain,
% 22.67/22.89 ((mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)))) <=> (mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))))),
% 22.67/22.89 inference(monotonicity,[status(thm)],[6203, 6202])).
% 22.67/22.89 tff(6205,plain,
% 22.67/22.89 ((~(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))))) <=> (~(mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a)))))),
% 22.67/22.89 inference(monotonicity,[status(thm)],[6204])).
% 22.67/22.89 tff(6206,plain,
% 22.67/22.89 (~(mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))))),
% 22.67/22.89 inference(modus_ponens,[status(thm)],[6190, 6205])).
% 22.67/22.89 tff(6207,assumption,(mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)))), introduced(assumption)).
% 22.67/22.89 tff(6208,plain,
% 22.67/22.89 (mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a)))),
% 22.67/22.89 inference(symmetry,[status(thm)],[6207])).
% 22.67/22.89 tff(6209,assumption,(~((~(mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))))), introduced(assumption)).
% 22.67/22.89 tff(6210,plain,
% 22.67/22.89 (mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c)))))),
% 22.67/22.89 inference(unit_resolution,[status(thm)],[5828, 6209])).
% 22.67/22.89 tff(6211,plain,
% 22.67/22.89 (mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c))),
% 22.67/22.89 inference(symmetry,[status(thm)],[6210])).
% 22.67/22.89 tff(6212,plain,
% 22.67/22.89 (mult(a, mult(c, mult(rd(mult(b, c), mult(a, c)), a))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 22.67/22.89 inference(transitivity,[status(thm)],[5846, 6211, 5798, 5797])).
% 22.67/22.89 tff(6213,plain,
% 22.67/22.89 (ld(a, mult(a, mult(c, mult(rd(mult(b, c), mult(a, c)), a)))) = ld(a, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 22.67/22.89 inference(monotonicity,[status(thm)],[6212])).
% 22.67/22.89 tff(6214,plain,
% 22.67/22.89 (mult(c, mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))),
% 22.67/22.89 inference(transitivity,[status(thm)],[5851, 6213, 733])).
% 22.67/22.89 tff(6215,plain,
% 22.67/22.89 (mult(mult(c, mult(rd(mult(b, c), mult(a, c)), a)), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)),
% 22.67/22.89 inference(monotonicity,[status(thm)],[6214])).
% 22.67/22.89 tff(6216,plain,
% 22.67/22.89 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(c, mult(rd(mult(b, c), mult(a, c)), a)), c)),
% 22.67/22.89 inference(symmetry,[status(thm)],[6215])).
% 22.67/22.89 tff(6217,plain,
% 22.67/22.89 (mult(a, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(mult(c, mult(rd(mult(b, c), mult(a, c)), a)), c))),
% 22.67/22.89 inference(monotonicity,[status(thm)],[6216])).
% 22.67/22.89 tff(6218,plain,
% 22.67/22.89 (mult(a, mult(mult(c, mult(rd(mult(b, c), mult(a, c)), a)), c)) = mult(a, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c))),
% 22.67/22.89 inference(symmetry,[status(thm)],[6217])).
% 22.67/22.89 tff(6219,plain,
% 22.67/22.89 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c) = mult(a, mult(mult(c, mult(rd(mult(b, c), mult(a, c)), a)), c)))),
% 22.67/22.89 inference(quant_inst,[status(thm)],[])).
% 22.67/22.89 tff(6220,plain,
% 22.67/22.89 (mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c) = mult(a, mult(mult(c, mult(rd(mult(b, c), mult(a, c)), a)), c))),
% 22.67/22.89 inference(unit_resolution,[status(thm)],[6219, 56])).
% 22.67/22.89 tff(6221,plain,
% 22.67/22.89 (mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))),
% 22.67/22.89 inference(unit_resolution,[status(thm)],[6151, 6209])).
% 22.67/22.89 tff(6222,plain,
% 22.67/22.89 (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)),
% 22.67/22.89 inference(symmetry,[status(thm)],[6221])).
% 22.67/22.89 tff(6223,plain,
% 22.67/22.89 (mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), c)),
% 22.67/22.89 inference(transitivity,[status(thm)],[404, 6222, 6114])).
% 22.67/22.89 tff(6224,plain,
% 22.67/22.89 (mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c) = mult(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), c), mult(c, unit))),
% 22.67/22.89 inference(monotonicity,[status(thm)],[6223, 6073])).
% 22.67/22.89 tff(6225,plain,
% 22.67/22.89 (mult(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), c), mult(c, unit)) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c)),
% 22.67/22.89 inference(symmetry,[status(thm)],[6224])).
% 22.67/22.89 tff(6226,plain,
% 22.67/22.89 (mult(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), c), mult(mult(unit, c), unit)) = mult(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), c), mult(c, unit))),
% 22.67/22.89 inference(symmetry,[status(thm)],[6113])).
% 22.67/22.89 tff(6227,plain,
% 22.67/22.89 (mult(mult(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), c), unit), c) = mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a))),
% 22.67/22.89 inference(transitivity,[status(thm)],[6042, 6044, 6203, 6126])).
% 22.67/22.89 tff(6228,plain,
% 22.67/22.89 (mult(mult(mult(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), c), unit), c), unit) = mult(mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)), unit)),
% 22.67/22.89 inference(monotonicity,[status(thm)],[6227])).
% 22.67/22.89 tff(6229,plain,
% 22.67/22.89 (mult(mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)), unit) = mult(mult(mult(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), c), unit), c), unit)),
% 22.67/22.89 inference(symmetry,[status(thm)],[6228])).
% 22.67/22.89 tff(6230,plain,
% 22.67/22.89 (mult(mult(mult(c, mult(a, c)), unit), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a))),
% 22.67/22.89 inference(monotonicity,[status(thm)],[6010])).
% 22.67/22.89 tff(6231,plain,
% 22.67/22.89 (mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(c, mult(a, c)), unit), mult(rd(mult(b, c), mult(a, c)), a))),
% 22.67/22.89 inference(symmetry,[status(thm)],[6230])).
% 22.67/22.89 tff(6232,plain,
% 22.67/22.89 (mult(mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)), unit) = mult(mult(mult(mult(c, mult(a, c)), unit), mult(rd(mult(b, c), mult(a, c)), a)), unit)),
% 22.67/22.89 inference(monotonicity,[status(thm)],[6231])).
% 22.67/22.89 tff(6233,plain,
% 22.67/22.89 (mult(mult(mult(mult(c, mult(a, c)), unit), mult(rd(mult(b, c), mult(a, c)), a)), unit) = mult(mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)), unit)),
% 22.67/22.89 inference(symmetry,[status(thm)],[6232])).
% 22.67/22.89 tff(6234,plain,
% 22.67/22.89 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(c, mult(a, c)), unit), mult(rd(mult(b, c), mult(a, c)), a)), unit) = mult(mult(c, mult(a, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit)))),
% 22.67/22.89 inference(quant_inst,[status(thm)],[])).
% 22.67/22.89 tff(6235,plain,
% 22.67/22.89 (mult(mult(mult(mult(c, mult(a, c)), unit), mult(rd(mult(b, c), mult(a, c)), a)), unit) = mult(mult(c, mult(a, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit))),
% 22.67/22.89 inference(unit_resolution,[status(thm)],[6234, 56])).
% 22.67/22.89 tff(6236,plain,
% 22.67/22.89 (mult(mult(c, mult(a, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit)) = mult(mult(mult(mult(c, mult(a, c)), unit), mult(rd(mult(b, c), mult(a, c)), a)), unit)),
% 22.67/22.89 inference(symmetry,[status(thm)],[6235])).
% 22.67/22.89 tff(6237,plain,
% 22.67/22.89 ((~![A: $i] : (mult(unit, A) = A)) | (mult(unit, mult(rd(mult(b, c), mult(a, c)), a)) = mult(rd(mult(b, c), mult(a, c)), a))),
% 22.67/22.89 inference(quant_inst,[status(thm)],[])).
% 22.67/22.89 tff(6238,plain,
% 22.67/22.89 (mult(unit, mult(rd(mult(b, c), mult(a, c)), a)) = mult(rd(mult(b, c), mult(a, c)), a)),
% 22.67/22.89 inference(unit_resolution,[status(thm)],[6237, 71])).
% 22.67/22.89 tff(6239,plain,
% 22.67/22.89 (mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit) = mult(mult(rd(mult(b, c), mult(a, c)), a), unit)),
% 22.67/22.89 inference(monotonicity,[status(thm)],[6238])).
% 22.67/22.89 tff(6240,plain,
% 22.67/22.89 (mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit) = mult(rd(mult(b, c), mult(a, c)), a)),
% 22.67/22.89 inference(transitivity,[status(thm)],[6239, 535, 530, 528])).
% 22.67/22.89 tff(6241,plain,
% 22.67/22.89 (mult(mult(c, mult(a, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit)) = mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a))),
% 22.67/22.89 inference(monotonicity,[status(thm)],[6240])).
% 22.67/22.89 tff(6242,plain,
% 22.67/22.89 (mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(c, mult(a, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit))),
% 22.67/22.89 inference(symmetry,[status(thm)],[6241])).
% 22.67/22.89 tff(6243,plain,
% 22.67/22.89 (mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a)))),
% 22.67/22.89 inference(transitivity,[status(thm)],[6126, 6242, 6236, 6233, 6229, 6071, 6226, 6225, 6220, 6218, 6066, 6208])).
% 22.67/22.89 tff(6244,assumption,(~(mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))))), introduced(assumption)).
% 22.67/22.89 tff(6245,plain,
% 22.67/22.89 ($false),
% 22.67/22.89 inference(unit_resolution,[status(thm)],[6244, 6243])).
% 22.67/22.89 tff(6246,plain,(((~(mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))))) | (mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))))) | (~(mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)))) | (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit)))))), inference(lemma,lemma(discharge,[]))).
% 22.67/22.89 tff(6247,plain,
% 22.67/22.89 ((~(mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))))),
% 22.67/22.89 inference(unit_resolution,[status(thm)],[6246, 6206, 6201, 6189, 359, 2187, 3865])).
% 22.67/22.89 tff(6248,plain,
% 22.67/22.89 (~((~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c)))))),
% 22.67/22.89 inference(unit_resolution,[status(thm)],[5826, 6247])).
% 22.67/22.89 tff(6249,plain,
% 22.67/22.89 (mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c))),
% 22.67/22.90 inference(unit_resolution,[status(thm)],[5814, 6248])).
% 22.67/22.90 tff(6250,plain,
% 22.67/22.90 (mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), c) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c)),
% 22.67/22.90 inference(transitivity,[status(thm)],[5802, 6249, 5798, 5797, 4676, 4520, 1683, 5188, 5796])).
% 22.67/22.90 tff(6251,plain,
% 22.67/22.90 (rd(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), c), c) = rd(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c), c)),
% 22.67/22.90 inference(monotonicity,[status(thm)],[6250])).
% 22.67/22.90 tff(6252,plain,
% 22.67/22.90 (rd(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c), c) = rd(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), c), c)),
% 22.67/22.90 inference(symmetry,[status(thm)],[6251])).
% 22.67/22.90 tff(6253,plain,
% 22.67/22.90 (mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a))),
% 22.67/22.90 inference(transitivity,[status(thm)],[5809, 5808, 6252, 5795])).
% 22.67/22.90 tff(6254,plain,
% 22.67/22.90 ($false),
% 22.67/22.90 inference(unit_resolution,[status(thm)],[898, 6253])).
% 22.67/22.90 tff(6255,plain,((mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)))) | (mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a))) | (~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a))) | (~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))) | (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit)))))), inference(lemma,lemma(discharge,[]))).
% 22.67/22.90 tff(6256,plain,
% 22.67/22.90 (mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)))),
% 22.67/22.90 inference(unit_resolution,[status(thm)],[6255, 281, 898, 5793, 1683, 4517, 5781, 359, 6188, 3865])).
% 22.67/22.90 tff(6257,plain,
% 22.67/22.90 (mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))),
% 22.67/22.90 inference(unit_resolution,[status(thm)],[6151, 5827])).
% 22.67/22.90 tff(6258,plain,
% 22.67/22.90 ((mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a)))) <=> (mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))))),
% 22.67/22.90 inference(commutativity,[status(thm)],[])).
% 22.67/22.90 tff(6259,plain,
% 22.67/22.90 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(c, mult(rd(mult(b, c), mult(a, c)), a)), c)),
% 22.67/22.90 inference(symmetry,[status(thm)],[5889])).
% 22.67/22.90 tff(6260,plain,
% 22.67/22.90 (mult(a, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(mult(c, mult(rd(mult(b, c), mult(a, c)), a)), c))),
% 22.67/22.90 inference(monotonicity,[status(thm)],[6259])).
% 22.67/22.90 tff(6261,plain,
% 22.67/22.90 (mult(a, mult(mult(c, mult(rd(mult(b, c), mult(a, c)), a)), c)) = mult(a, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c))),
% 22.67/22.90 inference(symmetry,[status(thm)],[6260])).
% 22.67/22.90 tff(6262,plain,
% 22.67/22.90 (mult(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), c), mult(c, unit)) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c)),
% 22.67/22.90 inference(symmetry,[status(thm)],[6118])).
% 22.67/22.90 tff(6263,plain,
% 22.67/22.90 (mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)))),
% 22.67/22.90 inference(transitivity,[status(thm)],[6126, 6242, 6236, 6233, 6229, 6071, 6226, 6262, 6220, 6261, 6066])).
% 22.67/22.90 tff(6264,plain,
% 22.67/22.90 ((mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a)))) <=> (mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))))),
% 22.67/22.90 inference(monotonicity,[status(thm)],[6263])).
% 22.67/22.90 tff(6265,plain,
% 22.67/22.90 ((mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a)))) <=> (mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))))),
% 22.67/22.90 inference(transitivity,[status(thm)],[6264, 6258])).
% 22.67/22.90 tff(6266,assumption,(~(mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))))), introduced(assumption)).
% 22.67/22.90 tff(6267,plain,
% 22.67/22.90 ((~(mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)))) | (~(mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)))))),
% 22.67/22.90 inference(unit_resolution,[status(thm)],[6200, 6266])).
% 22.67/22.90 tff(6268,plain,
% 22.67/22.90 (~((~(mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))))) | (~(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))))))),
% 22.67/22.90 inference(unit_resolution,[status(thm)],[6198, 6267])).
% 22.67/22.90 tff(6269,plain,
% 22.67/22.90 (((~(mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))))) | (~(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)))))) | (mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))))),
% 22.67/22.90 inference(tautology,[status(thm)],[])).
% 22.67/22.90 tff(6270,plain,
% 22.67/22.90 (mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a)))),
% 22.67/22.90 inference(unit_resolution,[status(thm)],[6269, 6268])).
% 22.67/22.90 tff(6271,plain,
% 22.67/22.90 (mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)))),
% 22.67/22.90 inference(modus_ponens,[status(thm)],[6270, 6265])).
% 22.67/22.90 tff(6272,plain,
% 22.67/22.90 ($false),
% 22.67/22.90 inference(unit_resolution,[status(thm)],[6266, 6271])).
% 22.67/22.90 tff(6273,plain,((mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit))))) | (~(mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)))) | (~(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))), inference(lemma,lemma(discharge,[]))).
% 22.67/22.90 tff(6274,plain,
% 22.67/22.90 (mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)))),
% 22.67/22.90 inference(unit_resolution,[status(thm)],[6273, 6257, 6188, 3865, 359, 5829, 5781])).
% 22.67/22.90 tff(6275,plain,
% 22.67/22.90 (mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a)))),
% 22.67/22.90 inference(unit_resolution,[status(thm)],[6246, 6274, 5827, 6188, 359, 5781, 3865])).
% 22.67/22.90 tff(6276,plain,
% 22.67/22.90 (mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))) = mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a))),
% 22.67/22.90 inference(symmetry,[status(thm)],[6275])).
% 22.67/22.90 tff(6277,plain,
% 22.67/22.90 (mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))) = mult(a, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c))),
% 22.67/22.90 inference(transitivity,[status(thm)],[6276, 6188, 6256, 5998])).
% 22.67/22.90 tff(6278,plain,
% 22.67/22.90 (ld(a, mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a)))) = ld(a, mult(a, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)))),
% 22.67/22.90 inference(monotonicity,[status(thm)],[6277])).
% 22.67/22.90 tff(6279,plain,
% 22.67/22.90 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(a, mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a)))) = mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a)))),
% 22.67/22.90 inference(quant_inst,[status(thm)],[])).
% 22.67/22.90 tff(6280,plain,
% 22.67/22.90 (ld(a, mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a)))) = mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))),
% 22.67/22.90 inference(unit_resolution,[status(thm)],[6279, 7])).
% 22.67/22.90 tff(6281,plain,
% 22.67/22.90 (mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a)) = ld(a, mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))))),
% 22.67/22.90 inference(symmetry,[status(thm)],[6280])).
% 22.67/22.90 tff(6282,plain,
% 22.67/22.90 (ld(a, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))) = ld(a, mult(a, mult(c, mult(rd(mult(b, c), mult(a, c)), a))))),
% 22.67/22.90 inference(symmetry,[status(thm)],[5848])).
% 22.67/22.90 tff(6283,plain,
% 22.67/22.90 (mult(mult(a, c), rd(mult(b, c), mult(a, c))) = mult(c, mult(rd(mult(b, c), mult(a, c)), a))),
% 22.67/22.90 inference(transitivity,[status(thm)],[734, 6282, 5850])).
% 22.67/22.90 tff(6284,plain,
% 22.67/22.90 (mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(c, mult(rd(mult(b, c), mult(a, c)), a)))),
% 22.67/22.90 inference(monotonicity,[status(thm)],[6283])).
% 22.67/22.90 tff(6285,plain,
% 22.67/22.90 (mult(c, mult(c, mult(rd(mult(b, c), mult(a, c)), a))) = mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 22.67/22.90 inference(symmetry,[status(thm)],[6284])).
% 22.67/22.90 tff(6286,plain,
% 22.67/22.90 (mult(c, mult(c, mult(rd(mult(b, c), mult(a, c)), a))) = mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c)))),
% 22.67/22.90 inference(transitivity,[status(thm)],[6285, 4496, 5299])).
% 22.67/22.90 tff(6287,plain,
% 22.67/22.90 (mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)),
% 22.67/22.90 inference(transitivity,[status(thm)],[6281, 6278, 5993])).
% 22.67/22.90 tff(6288,plain,
% 22.67/22.90 ((mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(c, mult(c, mult(rd(mult(b, c), mult(a, c)), a)))) <=> (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))))),
% 22.67/22.90 inference(monotonicity,[status(thm)],[6287, 6286])).
% 22.67/22.90 tff(6289,plain,
% 22.67/22.90 ((mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c)))) <=> (mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(c, mult(c, mult(rd(mult(b, c), mult(a, c)), a))))),
% 22.67/22.90 inference(symmetry,[status(thm)],[6288])).
% 22.67/22.90 tff(6290,plain,
% 22.67/22.90 (mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(c, mult(c, mult(rd(mult(b, c), mult(a, c)), a)))),
% 22.67/22.90 inference(modus_ponens,[status(thm)],[5857, 6289])).
% 22.67/22.90 tff(6291,plain,
% 22.67/22.90 (mult(c, mult(c, mult(rd(mult(b, c), mult(a, c)), a))) = mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))),
% 22.67/22.90 inference(symmetry,[status(thm)],[6290])).
% 22.67/22.90 tff(6292,plain,
% 22.67/22.90 (mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)),
% 22.67/22.90 inference(transitivity,[status(thm)],[4495, 6284, 6291, 6281, 6278, 5993])).
% 22.67/22.90 tff(6293,plain,
% 22.67/22.90 (mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a)),
% 22.67/22.90 inference(monotonicity,[status(thm)],[6292])).
% 22.67/22.90 tff(6294,plain,
% 22.67/22.90 (mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a)),
% 22.67/22.90 inference(symmetry,[status(thm)],[6003])).
% 22.67/22.90 tff(6295,plain,
% 22.67/22.90 (mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 22.67/22.90 inference(symmetry,[status(thm)],[6002])).
% 22.67/22.90 tff(6296,plain,
% 22.67/22.90 (mult(mult(rd(mult(b, c), mult(a, c)), c), a) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))),
% 22.67/22.90 inference(transitivity,[status(thm)],[83, 4360, 4340, 5044, 2189, 5781, 2172, 2178, 2177, 2162])).
% 22.67/22.90 tff(6297,plain,
% 22.67/22.90 (mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)) = mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 22.67/22.90 inference(monotonicity,[status(thm)],[6296])).
% 22.67/22.90 tff(6298,plain,
% 22.67/22.90 (mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))),
% 22.67/22.90 inference(transitivity,[status(thm)],[2172, 2178, 2177, 2162])).
% 22.67/22.90 tff(6299,plain,
% 22.67/22.90 ((mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))) <=> (mult(mult(a, c), rd(mult(b, c), mult(a, c))) = mult(a, mult(c, rd(mult(b, c), mult(a, c)))))),
% 22.67/22.90 inference(monotonicity,[status(thm)],[6298, 5121])).
% 22.67/22.90 tff(6300,plain,
% 22.67/22.90 ((~(mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) <=> (~(mult(mult(a, c), rd(mult(b, c), mult(a, c))) = mult(a, mult(c, rd(mult(b, c), mult(a, c))))))),
% 22.67/22.90 inference(monotonicity,[status(thm)],[6299])).
% 22.67/22.90 tff(6301,plain,
% 22.67/22.90 (~(mult(mult(a, c), rd(mult(b, c), mult(a, c))) = mult(a, mult(c, rd(mult(b, c), mult(a, c)))))),
% 22.67/22.90 inference(modus_ponens,[status(thm)],[5778, 6300])).
% 22.67/22.90 tff(6302,assumption,(mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a))), introduced(assumption)).
% 22.67/22.90 tff(6303,plain,
% 22.67/22.90 (mult(mult(a, c), mult(a, mult(c, rd(mult(b, c), mult(a, c))))) = mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 22.67/22.90 inference(transitivity,[status(thm)],[5163, 5162, 6302, 5155])).
% 22.67/22.90 tff(6304,plain,
% 22.67/22.90 (ld(mult(a, c), mult(mult(a, c), mult(a, mult(c, rd(mult(b, c), mult(a, c)))))) = ld(mult(a, c), mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 22.67/22.90 inference(monotonicity,[status(thm)],[6303])).
% 22.67/22.90 tff(6305,plain,
% 22.67/22.90 (ld(mult(a, c), mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c))))) = ld(mult(a, c), mult(mult(a, c), mult(a, mult(c, rd(mult(b, c), mult(a, c))))))),
% 22.67/22.90 inference(symmetry,[status(thm)],[6304])).
% 22.67/22.90 tff(6306,plain,
% 22.67/22.90 (mult(mult(a, c), rd(mult(b, c), mult(a, c))) = mult(a, mult(c, rd(mult(b, c), mult(a, c))))),
% 22.67/22.90 inference(transitivity,[status(thm)],[296, 6305, 5167])).
% 22.67/22.90 tff(6307,assumption,(~(mult(mult(a, c), rd(mult(b, c), mult(a, c))) = mult(a, mult(c, rd(mult(b, c), mult(a, c)))))), introduced(assumption)).
% 22.67/22.90 tff(6308,plain,
% 22.67/22.90 ($false),
% 22.67/22.90 inference(unit_resolution,[status(thm)],[6307, 6306])).
% 22.67/22.90 tff(6309,plain,((~(mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)))) | (mult(mult(a, c), rd(mult(b, c), mult(a, c))) = mult(a, mult(c, rd(mult(b, c), mult(a, c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))) | (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit)))))), inference(lemma,lemma(discharge,[]))).
% 22.67/22.90 tff(6310,plain,
% 22.67/22.90 (~(mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)))),
% 22.67/22.90 inference(unit_resolution,[status(thm)],[6309, 6301, 4360, 5781, 359, 5856, 3865])).
% 22.67/22.90 tff(6311,plain,
% 22.67/22.90 ((~(mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a))) | (~(mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a))))),
% 22.67/22.91 inference(unit_resolution,[status(thm)],[5157, 6310])).
% 22.67/22.91 tff(6312,plain,
% 22.67/22.91 (~((~(mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))) | (~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)))))),
% 22.67/22.91 inference(unit_resolution,[status(thm)],[5220, 6311])).
% 22.67/22.91 tff(6313,plain,
% 22.67/22.91 (mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a))),
% 22.67/22.91 inference(unit_resolution,[status(thm)],[5222, 6312])).
% 22.67/22.91 tff(6314,plain,
% 22.67/22.91 (mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(c, a), mult(rd(mult(b, c), mult(a, c)), c))),
% 22.67/22.91 inference(monotonicity,[status(thm)],[3874])).
% 22.67/22.91 tff(6315,plain,
% 22.67/22.91 (mult(mult(c, a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c))),
% 22.67/22.91 inference(symmetry,[status(thm)],[6314])).
% 22.67/22.91 tff(6316,plain,
% 22.67/22.91 (mult(mult(mult(c, a), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a)),
% 22.67/22.91 inference(monotonicity,[status(thm)],[6315])).
% 22.67/22.91 tff(6317,plain,
% 22.67/22.91 (mult(c, mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a)) = mult(c, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))))),
% 22.67/22.91 inference(transitivity,[status(thm)],[5324, 6316, 6313, 6297, 6295, 6103, 5231, 6294, 6293, 5991, 4660, 5104, 5915, 2502, 5102, 2742, 5990, 5792])).
% 22.67/22.91 tff(6318,plain,
% 22.67/22.91 (ld(c, mult(c, mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a))) = ld(c, mult(c, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))))),
% 22.67/22.91 inference(monotonicity,[status(thm)],[6317])).
% 22.67/22.91 tff(6319,plain,
% 22.67/22.91 (mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))) = mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c))),
% 22.67/22.91 inference(symmetry,[status(thm)],[5856])).
% 22.67/22.91 tff(6320,plain,
% 22.67/22.91 (mult(a, mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), c))),
% 22.67/22.91 inference(transitivity,[status(thm)],[5122, 6319, 5117])).
% 22.67/22.91 tff(6321,plain,
% 22.67/22.91 (mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a)),
% 22.67/22.91 inference(monotonicity,[status(thm)],[6320])).
% 22.67/22.91 tff(6322,plain,
% 22.67/22.91 (mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)),
% 22.67/22.91 inference(transitivity,[status(thm)],[6321, 5329, 6318, 4523, 1683])).
% 22.67/22.91 tff(6323,plain,
% 22.67/22.91 (rd(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a), a) = rd(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), a)),
% 22.67/22.91 inference(monotonicity,[status(thm)],[6322])).
% 22.67/22.91 tff(6324,plain,
% 22.67/22.91 (rd(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), a) = rd(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a), a)),
% 22.67/22.91 inference(symmetry,[status(thm)],[6323])).
% 22.67/22.91 tff(6325,plain,
% 22.67/22.91 (mult(mult(a, c), rd(mult(b, c), mult(a, c))) = rd(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), a)),
% 22.67/22.91 inference(symmetry,[status(thm)],[4441])).
% 22.67/22.91 tff(6326,plain,
% 22.67/22.91 (mult(mult(a, c), rd(mult(b, c), mult(a, c))) = mult(a, mult(c, rd(mult(b, c), mult(a, c))))),
% 22.67/22.91 inference(transitivity,[status(thm)],[6325, 6324, 5334])).
% 22.67/22.91 tff(6327,plain,
% 22.67/22.91 ($false),
% 22.67/22.91 inference(unit_resolution,[status(thm)],[6301, 6326])).
% 22.67/22.91 tff(6328,plain,((mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))) | (~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))) | (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit))))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)))) | (mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a)))), inference(lemma,lemma(discharge,[]))).
% 22.67/22.91 tff(6329,plain,
% 22.67/22.91 (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a))),
% 22.67/22.91 inference(unit_resolution,[status(thm)],[6328, 5698, 270, 3865, 359, 4360, 1683, 898, 4298])).
% 22.67/22.91 tff(6330,plain,
% 22.67/22.91 (((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, a))))) | (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a))),
% 22.67/22.91 inference(tautology,[status(thm)],[])).
% 22.67/22.91 tff(6331,plain,
% 22.67/22.91 ((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, a))))),
% 22.67/22.91 inference(unit_resolution,[status(thm)],[6330, 6329])).
% 22.67/22.91 tff(6332,plain,
% 22.67/22.91 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, a)))))) | (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, a)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, a)))))) | (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, a)))))))),
% 22.67/22.91 inference(rewrite,[status(thm)],[])).
% 22.67/22.91 tff(6333,plain,
% 22.67/22.91 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, a)))))) | (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, a)))))))),
% 22.67/22.91 inference(quant_inst,[status(thm)],[])).
% 22.67/22.91 tff(6334,plain,
% 22.67/22.91 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, a)))))) | (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, a))))))),
% 22.67/22.91 inference(modus_ponens,[status(thm)],[6333, 6332])).
% 22.67/22.91 tff(6335,plain,
% 22.67/22.91 ((~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, a)))))) | (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, a))))))),
% 22.67/22.91 inference(unit_resolution,[status(thm)],[6334, 27])).
% 22.67/22.91 tff(6336,plain,
% 22.67/22.91 (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, a)))))),
% 22.67/22.91 inference(unit_resolution,[status(thm)],[6335, 6331])).
% 22.67/22.91 tff(6337,plain,
% 22.67/22.91 (((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, a))))) | (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, a)))),
% 22.67/22.91 inference(tautology,[status(thm)],[])).
% 22.67/22.91 tff(6338,plain,
% 22.67/22.91 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, a))),
% 22.67/22.91 inference(unit_resolution,[status(thm)],[6337, 6336])).
% 22.67/22.91 tff(6339,plain,
% 22.67/22.91 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, a)) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a)),
% 22.67/22.91 inference(symmetry,[status(thm)],[6338])).
% 22.67/22.91 tff(6340,plain,
% 22.67/22.91 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, a)) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c))),
% 22.67/22.91 inference(monotonicity,[status(thm)],[3885])).
% 22.67/22.91 tff(6341,plain,
% 22.67/22.91 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, a))),
% 22.67/22.91 inference(symmetry,[status(thm)],[6340])).
% 22.67/22.91 tff(6342,plain,
% 22.67/22.91 (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c))),
% 22.67/22.91 inference(symmetry,[status(thm)],[4298])).
% 22.67/22.91 tff(6343,plain,
% 22.67/22.91 (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))),
% 22.67/22.91 inference(transitivity,[status(thm)],[6342, 6341, 6339, 1168])).
% 22.67/22.91 tff(6344,plain,
% 22.67/22.91 ($false),
% 22.67/22.91 inference(unit_resolution,[status(thm)],[1364, 6343])).
% 22.67/22.91 tff(6345,plain,((mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit))))) | (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))) | (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)))) | (~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))) | (mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a)))), inference(lemma,lemma(discharge,[]))).
% 22.67/22.91 tff(6346,plain,
% 22.67/22.91 ((mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) | (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))) | (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)))) | (~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))) | (mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a)))),
% 22.67/22.91 inference(unit_resolution,[status(thm)],[6345, 3862])).
% 22.67/22.91 tff(6347,plain,
% 22.67/22.91 (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))),
% 22.67/22.91 inference(unit_resolution,[status(thm)],[6346, 4303, 898, 5763, 1364, 5764])).
% 22.67/22.91 tff(6348,plain,
% 22.67/22.91 (mult(mult(c, a), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))),
% 22.67/22.91 inference(monotonicity,[status(thm)],[5700])).
% 22.67/22.91 tff(6349,plain,
% 22.67/22.91 (mult(mult(mult(c, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)),
% 22.67/22.91 inference(monotonicity,[status(thm)],[6348])).
% 22.67/22.91 tff(6350,plain,
% 22.67/22.91 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)), mult(a, c)) = mult(rd(mult(b, c), mult(a, c)), a))),
% 22.67/22.91 inference(quant_inst,[status(thm)],[])).
% 22.67/22.91 tff(6351,plain,
% 22.67/22.91 (rd(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)), mult(a, c)) = mult(rd(mult(b, c), mult(a, c)), a)),
% 22.67/22.91 inference(unit_resolution,[status(thm)],[6350, 168])).
% 22.67/22.91 tff(6352,plain,
% 22.67/22.91 (mult(a, mult(a, c)) = mult(mult(a, c), a)),
% 22.67/22.91 inference(transitivity,[status(thm)],[4452, 5699, 4447])).
% 22.67/22.91 tff(6353,plain,
% 22.67/22.91 (mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))),
% 22.67/22.91 inference(monotonicity,[status(thm)],[6352])).
% 22.67/22.91 tff(6354,assumption,(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))), introduced(assumption)).
% 22.67/22.91 tff(6355,plain,
% 22.67/22.91 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 22.67/22.91 inference(symmetry,[status(thm)],[6354])).
% 22.67/22.91 tff(6356,plain,
% 22.67/22.91 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c))),
% 22.67/22.91 inference(transitivity,[status(thm)],[6355, 6353, 5709, 359, 5497, 4339, 1431, 6342])).
% 22.67/22.91 tff(6357,plain,
% 22.67/22.91 (rd(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)), mult(a, c)) = rd(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)), mult(a, c))),
% 22.67/22.91 inference(monotonicity,[status(thm)],[6356])).
% 22.67/22.91 tff(6358,plain,
% 22.67/22.91 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)), mult(a, c)) = mult(a, rd(mult(b, c), mult(a, c))))),
% 22.67/22.91 inference(quant_inst,[status(thm)],[])).
% 22.67/22.91 tff(6359,plain,
% 22.67/22.91 (rd(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)), mult(a, c)) = mult(a, rd(mult(b, c), mult(a, c)))),
% 22.67/22.91 inference(unit_resolution,[status(thm)],[6358, 168])).
% 22.67/22.91 tff(6360,plain,
% 22.67/22.91 (mult(a, rd(mult(b, c), mult(a, c))) = rd(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)), mult(a, c))),
% 22.67/22.91 inference(symmetry,[status(thm)],[6359])).
% 22.67/22.91 tff(6361,plain,
% 22.67/22.91 (mult(a, rd(mult(b, c), mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), a)),
% 22.67/22.91 inference(transitivity,[status(thm)],[6360, 6357, 6351])).
% 22.67/22.91 tff(6362,plain,
% 22.67/22.91 (mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), a)),
% 22.67/22.91 inference(monotonicity,[status(thm)],[6361])).
% 22.67/22.91 tff(6363,plain,
% 22.67/22.91 (mult(mult(rd(mult(b, c), mult(a, c)), a), a) = mult(mult(a, rd(mult(b, c), mult(a, c))), a)),
% 22.67/22.91 inference(symmetry,[status(thm)],[6362])).
% 22.67/22.91 tff(6364,plain,
% 22.67/22.91 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), unit), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), a)),
% 22.67/22.91 inference(monotonicity,[status(thm)],[1872])).
% 22.67/22.91 tff(6365,plain,
% 22.67/22.92 (mult(rd(mult(b, c), mult(a, c)), mult(a, a)) = mult(mult(a, rd(mult(b, c), mult(a, c))), a)),
% 22.67/22.92 inference(transitivity,[status(thm)],[541, 540, 6364, 6363])).
% 22.67/22.92 tff(6366,plain,
% 22.67/22.92 (mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, a))) = mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), a))),
% 22.67/22.92 inference(monotonicity,[status(thm)],[6365])).
% 22.67/22.92 tff(6367,plain,
% 22.67/22.92 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, a))),
% 22.67/22.92 inference(symmetry,[status(thm)],[541])).
% 22.67/22.92 tff(6368,plain,
% 22.67/22.92 (mult(mult(rd(mult(b, c), mult(a, c)), a), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), unit), a)),
% 22.67/22.92 inference(symmetry,[status(thm)],[6364])).
% 22.67/22.92 tff(6369,plain,
% 22.67/22.92 (mult(mult(rd(mult(b, c), mult(a, c)), a), a) = mult(rd(mult(b, c), mult(a, c)), mult(a, a))),
% 22.67/22.92 inference(transitivity,[status(thm)],[6368, 539, 6367])).
% 22.67/22.92 tff(6370,plain,
% 22.67/22.92 (mult(c, mult(mult(rd(mult(b, c), mult(a, c)), a), a)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, a)))),
% 22.67/22.92 inference(monotonicity,[status(thm)],[6369])).
% 22.67/22.92 tff(6371,plain,
% 22.67/22.92 (mult(c, mult(mult(rd(mult(b, c), mult(a, c)), a), a)) = mult(c, mult(b, a))),
% 22.67/22.92 inference(transitivity,[status(thm)],[6370, 6366, 5404, 6349, 4339, 3057, 4208])).
% 22.67/22.92 tff(6372,plain,
% 22.67/22.92 (ld(c, mult(c, mult(mult(rd(mult(b, c), mult(a, c)), a), a))) = ld(c, mult(c, mult(b, a)))),
% 22.67/22.92 inference(monotonicity,[status(thm)],[6371])).
% 22.67/22.92 tff(6373,plain,
% 22.67/22.92 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(c, mult(c, mult(mult(rd(mult(b, c), mult(a, c)), a), a))) = mult(mult(rd(mult(b, c), mult(a, c)), a), a))),
% 22.67/22.92 inference(quant_inst,[status(thm)],[])).
% 22.67/22.92 tff(6374,plain,
% 22.67/22.92 (ld(c, mult(c, mult(mult(rd(mult(b, c), mult(a, c)), a), a))) = mult(mult(rd(mult(b, c), mult(a, c)), a), a)),
% 22.67/22.92 inference(unit_resolution,[status(thm)],[6373, 7])).
% 22.67/22.92 tff(6375,plain,
% 22.67/22.92 (mult(mult(rd(mult(b, c), mult(a, c)), a), a) = ld(c, mult(c, mult(mult(rd(mult(b, c), mult(a, c)), a), a)))),
% 22.67/22.92 inference(symmetry,[status(thm)],[6374])).
% 22.67/22.92 tff(6376,plain,
% 22.67/22.92 (mult(mult(rd(mult(b, c), mult(a, c)), a), a) = mult(b, a)),
% 22.67/22.92 inference(transitivity,[status(thm)],[6375, 6372, 1472])).
% 22.67/22.92 tff(6377,plain,
% 22.67/22.92 (rd(mult(mult(rd(mult(b, c), mult(a, c)), a), a), a) = rd(mult(b, a), a)),
% 22.67/22.92 inference(monotonicity,[status(thm)],[6376])).
% 22.67/22.92 tff(6378,plain,
% 22.67/22.92 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(rd(mult(b, c), mult(a, c)), a), a), a) = mult(rd(mult(b, c), mult(a, c)), a))),
% 22.67/22.92 inference(quant_inst,[status(thm)],[])).
% 22.67/22.92 tff(6379,plain,
% 22.67/22.92 (rd(mult(mult(rd(mult(b, c), mult(a, c)), a), a), a) = mult(rd(mult(b, c), mult(a, c)), a)),
% 22.67/22.92 inference(unit_resolution,[status(thm)],[6378, 168])).
% 22.67/22.92 tff(6380,plain,
% 22.67/22.92 (mult(rd(mult(b, c), mult(a, c)), a) = rd(mult(mult(rd(mult(b, c), mult(a, c)), a), a), a)),
% 22.67/22.92 inference(symmetry,[status(thm)],[6379])).
% 22.67/22.92 tff(6381,plain,
% 22.67/22.92 (mult(rd(mult(b, c), mult(a, c)), a) = b),
% 22.67/22.92 inference(transitivity,[status(thm)],[6380, 6377, 1451])).
% 22.67/22.92 tff(6382,plain,
% 22.67/22.92 (mult(mult(rd(mult(b, c), mult(a, c)), a), c) = mult(b, c)),
% 22.67/22.92 inference(monotonicity,[status(thm)],[6381])).
% 22.67/22.92 tff(6383,plain,
% 22.67/22.92 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a) = mult(mult(b, c), a)),
% 22.67/22.92 inference(monotonicity,[status(thm)],[6382])).
% 22.67/22.92 tff(6384,plain,
% 22.67/22.92 (mult(mult(b, c), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a)),
% 22.67/22.92 inference(symmetry,[status(thm)],[6383])).
% 22.67/22.92 tff(6385,plain,
% 22.67/22.92 (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))),
% 22.67/22.92 inference(transitivity,[status(thm)],[1332, 6384, 1168])).
% 22.67/22.92 tff(6386,plain,
% 22.67/22.92 ($false),
% 22.67/22.92 inference(unit_resolution,[status(thm)],[1364, 6385])).
% 22.67/22.92 tff(6387,plain,((~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))) | (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) | (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))), inference(lemma,lemma(discharge,[]))).
% 22.67/22.92 tff(6388,plain,
% 22.67/22.92 (~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 22.67/22.92 inference(unit_resolution,[status(thm)],[6387, 1364, 5764, 6347])).
% 22.67/22.92 tff(6389,plain,
% 22.67/22.92 (((~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))) | (mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 22.67/22.92 inference(tautology,[status(thm)],[])).
% 22.67/22.92 tff(6390,plain,
% 22.67/22.92 ((~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))),
% 22.67/22.92 inference(unit_resolution,[status(thm)],[6389, 6388])).
% 22.67/22.92 tff(6391,plain,
% 22.67/22.92 (~((~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))),
% 22.67/22.92 inference(unit_resolution,[status(thm)],[276, 6390])).
% 22.67/22.92 tff(6392,plain,
% 22.67/22.92 (mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 22.67/22.92 inference(unit_resolution,[status(thm)],[280, 6391])).
% 22.67/22.92 tff(6393,plain,
% 22.67/22.92 (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 22.67/22.92 inference(symmetry,[status(thm)],[6392])).
% 22.67/22.92 tff(6394,plain,
% 22.67/22.92 (mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 22.67/22.92 inference(symmetry,[status(thm)],[6347])).
% 22.67/22.92 tff(6395,plain,
% 22.67/22.92 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))),
% 22.67/22.92 inference(unit_resolution,[status(thm)],[278, 6391])).
% 22.67/22.92 tff(6396,plain,
% 22.67/22.92 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))),
% 22.67/22.92 inference(monotonicity,[status(thm)],[5700])).
% 22.67/22.92 tff(6397,plain,
% 22.67/22.92 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(a, mult(c, a)), rd(mult(b, c), mult(a, c)))),
% 22.67/22.92 inference(transitivity,[status(thm)],[6396, 6395, 6394, 6393, 5708, 5704])).
% 22.67/22.92 tff(6398,plain,
% 22.67/22.92 ((mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(a, mult(c, a)), rd(mult(b, c), mult(a, c)))) <=> (mult(mult(a, mult(c, a)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, a)))),
% 22.67/22.92 inference(commutativity,[status(thm)],[])).
% 22.67/22.92 tff(6399,plain,
% 22.67/22.92 ((mult(mult(a, mult(c, a)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, a))) <=> (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(a, mult(c, a)), rd(mult(b, c), mult(a, c))))),
% 22.67/22.92 inference(symmetry,[status(thm)],[6398])).
% 22.67/22.92 tff(6400,plain,
% 22.67/22.92 (mult(mult(a, mult(c, a)), rd(mult(b, c), mult(a, c))) = mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 22.67/22.92 inference(transitivity,[status(thm)],[5703, 5707])).
% 22.67/22.92 tff(6401,plain,
% 22.67/22.92 ((mult(mult(a, mult(c, a)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, a))) <=> (mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 22.67/22.92 inference(monotonicity,[status(thm)],[6400, 6396])).
% 22.67/22.92 tff(6402,plain,
% 22.67/22.92 ((mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))) <=> (mult(mult(a, mult(c, a)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, a)))),
% 22.67/22.92 inference(symmetry,[status(thm)],[6401])).
% 22.67/22.92 tff(6403,plain,
% 22.67/22.92 ((mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))) <=> (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(a, mult(c, a)), rd(mult(b, c), mult(a, c))))),
% 22.67/22.92 inference(transitivity,[status(thm)],[6402, 6399])).
% 22.67/22.92 tff(6404,plain,
% 22.67/22.92 ((~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))) <=> (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(a, mult(c, a)), rd(mult(b, c), mult(a, c)))))),
% 22.67/22.92 inference(monotonicity,[status(thm)],[6403])).
% 22.67/22.92 tff(6405,plain,
% 22.67/22.92 (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(a, mult(c, a)), rd(mult(b, c), mult(a, c))))),
% 22.67/22.92 inference(modus_ponens,[status(thm)],[6388, 6404])).
% 22.67/22.92 tff(6406,plain,
% 22.67/22.92 ($false),
% 22.67/22.92 inference(unit_resolution,[status(thm)],[6405, 6397])).
% 22.67/22.92 tff(6407,plain,((mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) | (mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a)))), inference(lemma,lemma(discharge,[]))).
% 22.67/22.92 tff(6408,plain,
% 22.67/22.92 (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))),
% 22.67/22.92 inference(unit_resolution,[status(thm)],[6407, 898])).
% 22.67/22.92 tff(6409,plain,
% 22.67/22.92 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a)),
% 22.67/22.92 inference(symmetry,[status(thm)],[6408])).
% 22.67/22.92 tff(6410,plain,
% 22.67/22.92 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a) = mult(mult(b, c), a)),
% 22.67/22.92 inference(transitivity,[status(thm)],[1168, 6409, 1332])).
% 22.67/22.92 tff(6411,plain,
% 22.67/22.92 (rd(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a), a) = rd(mult(mult(b, c), a), a)),
% 22.67/22.92 inference(monotonicity,[status(thm)],[6410])).
% 22.67/22.92 tff(6412,plain,
% 22.67/22.92 (mult(mult(rd(mult(b, c), mult(a, c)), a), c) = mult(b, c)),
% 22.67/22.92 inference(transitivity,[status(thm)],[1377, 6411, 1370])).
% 22.67/22.92 tff(6413,plain,
% 22.67/22.92 (rd(mult(mult(rd(mult(b, c), mult(a, c)), a), c), c) = rd(mult(b, c), c)),
% 22.67/22.92 inference(monotonicity,[status(thm)],[6412])).
% 22.67/22.92 tff(6414,plain,
% 22.67/22.92 (mult(rd(mult(b, c), mult(a, c)), a) = b),
% 22.67/22.92 inference(transitivity,[status(thm)],[175, 6413, 170])).
% 22.67/22.92 tff(6415,plain,
% 22.67/22.92 (mult(a, mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, b)),
% 22.67/22.92 inference(monotonicity,[status(thm)],[6414])).
% 22.67/22.92 tff(6416,plain,
% 22.67/22.92 (mult(a, mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(unit, a), b)),
% 22.67/22.92 inference(transitivity,[status(thm)],[6415, 927])).
% 22.67/22.92 tff(6417,plain,
% 22.67/22.92 (mult(mult(rd(mult(b, c), mult(a, c)), a), a) = mult(b, a)),
% 22.67/22.92 inference(monotonicity,[status(thm)],[6414])).
% 22.67/22.92 tff(6418,plain,
% 22.67/22.92 (ld(mult(a, c), mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = ld(mult(a, c), mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))),
% 22.67/22.92 inference(monotonicity,[status(thm)],[5764])).
% 22.67/22.92 tff(6419,plain,
% 22.67/22.92 (mult(a, rd(mult(b, c), mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), a)),
% 22.67/22.92 inference(transitivity,[status(thm)],[471, 6418, 4411])).
% 22.67/22.92 tff(6420,plain,
% 22.67/22.92 (mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), a)),
% 22.67/22.92 inference(monotonicity,[status(thm)],[6419])).
% 22.67/22.92 tff(6421,plain,
% 22.67/22.92 (mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(mult(unit, b), a)),
% 22.67/22.92 inference(transitivity,[status(thm)],[6420, 6417, 930])).
% 22.67/22.92 tff(6422,plain,
% 22.67/22.92 ((mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a))) <=> (mult(mult(unit, b), a) = mult(mult(unit, a), b))),
% 22.67/22.92 inference(monotonicity,[status(thm)],[6421, 6416])).
% 22.67/22.92 tff(6423,plain,
% 22.67/22.92 ((mult(mult(unit, b), a) = mult(mult(unit, a), b)) <=> (mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a)))),
% 22.67/22.92 inference(symmetry,[status(thm)],[6422])).
% 22.67/22.92 tff(6424,plain,
% 22.67/22.92 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(a, c), rd(mult(b, c), mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(a, c))),
% 22.67/22.92 inference(quant_inst,[status(thm)],[])).
% 22.67/22.92 tff(6425,plain,
% 22.67/22.92 (rd(mult(mult(a, c), rd(mult(b, c), mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(a, c)),
% 22.67/22.92 inference(unit_resolution,[status(thm)],[6424, 168])).
% 22.67/22.92 tff(6426,plain,
% 22.67/22.92 (mult(mult(rd(mult(b, c), mult(a, c)), a), a) = mult(b, a)),
% 22.67/22.92 inference(monotonicity,[status(thm)],[1380])).
% 22.67/22.92 tff(6427,plain,
% 22.67/22.92 (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))),
% 22.67/22.92 inference(unit_resolution,[status(thm)],[2329, 1683])).
% 22.67/22.92 tff(6428,plain,
% 22.67/22.92 (ld(mult(a, c), mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = ld(mult(a, c), mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))),
% 22.67/22.92 inference(monotonicity,[status(thm)],[6427])).
% 22.67/22.92 tff(6429,plain,
% 22.67/22.92 (mult(a, rd(mult(b, c), mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), a)),
% 22.67/22.92 inference(transitivity,[status(thm)],[471, 6428, 4411])).
% 22.67/22.92 tff(6430,plain,
% 22.67/22.92 (mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), a)),
% 22.67/22.92 inference(monotonicity,[status(thm)],[6429])).
% 22.67/22.92 tff(6431,plain,
% 22.67/22.92 (mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(b, a)),
% 22.67/22.92 inference(transitivity,[status(thm)],[6430, 6426])).
% 22.67/22.92 tff(6432,plain,
% 22.67/22.92 (mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), a)) = mult(c, mult(b, a))),
% 22.67/22.92 inference(monotonicity,[status(thm)],[6431])).
% 22.67/22.92 tff(6433,plain,
% 22.67/22.92 (mult(mult(mult(c, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(b, c), a)),
% 22.67/22.92 inference(transitivity,[status(thm)],[4962, 6432, 4304, 2298])).
% 22.67/22.92 tff(6434,plain,
% 22.67/22.92 (rd(mult(mult(mult(c, a), rd(mult(b, c), mult(a, c))), a), a) = rd(mult(mult(b, c), a), a)),
% 22.67/22.92 inference(monotonicity,[status(thm)],[6433])).
% 22.67/22.92 tff(6435,plain,
% 22.67/22.92 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(c, a), rd(mult(b, c), mult(a, c))), a), a) = mult(mult(c, a), rd(mult(b, c), mult(a, c))))),
% 22.67/22.92 inference(quant_inst,[status(thm)],[])).
% 22.67/22.92 tff(6436,plain,
% 22.67/22.92 (rd(mult(mult(mult(c, a), rd(mult(b, c), mult(a, c))), a), a) = mult(mult(c, a), rd(mult(b, c), mult(a, c)))),
% 22.67/22.92 inference(unit_resolution,[status(thm)],[6435, 168])).
% 22.67/22.92 tff(6437,plain,
% 22.67/22.92 (mult(mult(c, a), rd(mult(b, c), mult(a, c))) = rd(mult(mult(mult(c, a), rd(mult(b, c), mult(a, c))), a), a)),
% 22.67/22.92 inference(symmetry,[status(thm)],[6436])).
% 22.67/22.92 tff(6438,plain,
% 22.67/22.92 (mult(mult(c, a), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))),
% 22.67/22.92 inference(transitivity,[status(thm)],[6437, 6434, 1370, 843, 2124, 4336])).
% 22.67/22.92 tff(6439,plain,
% 22.67/22.92 (rd(mult(mult(c, a), rd(mult(b, c), mult(a, c))), rd(mult(b, c), mult(a, c))) = rd(mult(mult(a, c), rd(mult(b, c), mult(a, c))), rd(mult(b, c), mult(a, c)))),
% 22.67/22.92 inference(monotonicity,[status(thm)],[6438])).
% 22.67/22.92 tff(6440,plain,
% 22.67/22.92 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(c, a), rd(mult(b, c), mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(c, a))),
% 22.67/22.92 inference(quant_inst,[status(thm)],[])).
% 22.67/22.92 tff(6441,plain,
% 22.67/22.92 (rd(mult(mult(c, a), rd(mult(b, c), mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(c, a)),
% 22.67/22.92 inference(unit_resolution,[status(thm)],[6440, 168])).
% 22.67/22.92 tff(6442,plain,
% 22.67/22.92 (mult(c, a) = rd(mult(mult(c, a), rd(mult(b, c), mult(a, c))), rd(mult(b, c), mult(a, c)))),
% 22.67/22.92 inference(symmetry,[status(thm)],[6441])).
% 22.67/22.92 tff(6443,plain,
% 22.67/22.92 (mult(c, a) = mult(a, c)),
% 22.67/22.92 inference(transitivity,[status(thm)],[6442, 6439, 6425])).
% 22.67/22.92 tff(6444,plain,
% 22.67/22.92 (mult(mult(c, a), b) = mult(mult(a, c), b)),
% 22.67/22.92 inference(monotonicity,[status(thm)],[6443])).
% 22.67/22.92 tff(6445,plain,
% 22.67/22.92 (mult(mult(a, c), b) = mult(mult(c, a), b)),
% 22.67/22.92 inference(symmetry,[status(thm)],[6444])).
% 22.67/22.92 tff(6446,plain,
% 22.67/22.92 (mult(c, mult(b, a)) = mult(c, mult(a, b))),
% 22.67/22.92 inference(transitivity,[status(thm)],[4304, 2298, 4338, 5458, 5709, 6427, 2232, 6445, 4221])).
% 22.67/22.92 tff(6447,plain,
% 22.67/22.92 (ld(c, mult(c, mult(b, a))) = ld(c, mult(c, mult(a, b)))),
% 22.67/22.92 inference(monotonicity,[status(thm)],[6446])).
% 22.67/22.92 tff(6448,plain,
% 22.67/22.92 (mult(mult(unit, b), a) = mult(mult(unit, a), b)),
% 22.67/22.92 inference(transitivity,[status(thm)],[929, 1473, 6447, 1468, 927])).
% 22.67/22.92 tff(6449,plain,
% 22.67/22.92 ($false),
% 22.67/22.92 inference(unit_resolution,[status(thm)],[941, 6448])).
% 22.67/22.92 tff(6450,plain,((mult(mult(unit, b), a) = mult(mult(unit, a), b)) | (~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) | (~(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))), inference(lemma,lemma(discharge,[]))).
% 22.67/22.93 tff(6451,plain,
% 22.67/22.93 (mult(mult(unit, b), a) = mult(mult(unit, a), b)),
% 22.67/22.93 inference(unit_resolution,[status(thm)],[6450, 1488, 6408, 5763])).
% 22.67/22.93 tff(6452,plain,
% 22.67/22.93 (mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a))),
% 22.67/22.93 inference(modus_ponens,[status(thm)],[6451, 6423])).
% 22.67/22.93 tff(6453,plain,
% 22.67/22.93 ($false),
% 22.67/22.93 inference(unit_resolution,[status(thm)],[898, 6452])).
% 22.67/22.93 tff(6454,plain,((~(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a)))), inference(lemma,lemma(discharge,[]))).
% 22.67/22.93 tff(6455,plain,
% 22.67/22.93 (~(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))),
% 22.67/22.93 inference(unit_resolution,[status(thm)],[6454, 898])).
% 22.67/22.93 tff(6456,plain,
% 22.67/22.93 (~(mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))),
% 22.67/22.93 inference(unit_resolution,[status(thm)],[306, 6455])).
% 22.67/22.93 tff(6457,plain,
% 22.67/22.93 ((~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))),
% 22.67/22.93 inference(unit_resolution,[status(thm)],[308, 6456])).
% 22.67/22.93 tff(6458,plain,
% 22.67/22.93 ((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) | (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))))),
% 22.67/22.93 inference(unit_resolution,[status(thm)],[4428, 5435])).
% 22.67/22.93 tff(6459,plain,
% 22.67/22.93 (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))),
% 22.67/22.93 inference(unit_resolution,[status(thm)],[6458, 6455, 5764, 6408])).
% 22.67/22.93 tff(6460,plain,
% 22.67/22.93 ((~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))),
% 22.67/22.93 inference(unit_resolution,[status(thm)],[315, 6459])).
% 22.67/22.93 tff(6461,plain,
% 22.67/22.93 ($false),
% 22.67/22.93 inference(unit_resolution,[status(thm)],[313, 6460, 6457])).
% 22.67/22.93 tff(6462,plain,(mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a))), inference(lemma,lemma(discharge,[]))).
% 22.67/22.93 tff(6463,plain,
% 22.67/22.93 (mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, b)),
% 22.67/22.93 inference(transitivity,[status(thm)],[6462, 5697])).
% 22.67/22.93 tff(6464,plain,
% 22.67/22.93 (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, b), rd(mult(b, c), mult(a, c)))),
% 22.67/22.93 inference(monotonicity,[status(thm)],[6463])).
% 22.67/22.93 tff(6465,plain,
% 22.67/22.93 (mult(mult(rd(mult(b, c), mult(a, c)), a), rd(mult(b, c), mult(a, c))) = mult(b, rd(mult(b, c), mult(a, c)))),
% 22.67/22.93 inference(monotonicity,[status(thm)],[5503])).
% 22.67/22.93 tff(6466,plain,
% 22.67/22.93 (mult(b, rd(mult(b, c), mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), a), rd(mult(b, c), mult(a, c)))),
% 22.67/22.93 inference(symmetry,[status(thm)],[6465])).
% 22.67/22.93 tff(6467,plain,
% 22.67/22.93 (mult(a, mult(b, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), rd(mult(b, c), mult(a, c))))),
% 22.67/22.93 inference(monotonicity,[status(thm)],[6466])).
% 22.67/22.93 tff(6468,plain,
% 22.67/22.93 (mult(a, mult(b, rd(mult(b, c), mult(a, c)))) = mult(mult(b, a), rd(mult(b, c), mult(a, c)))),
% 22.67/22.93 inference(transitivity,[status(thm)],[6467, 694, 6464, 5696])).
% 22.67/22.93 tff(6469,plain,
% 22.67/22.93 (mult(mult(a, mult(b, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a)),
% 22.67/22.93 inference(monotonicity,[status(thm)],[6468])).
% 22.67/22.93 tff(6470,plain,
% 22.67/22.93 (mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, mult(b, rd(mult(b, c), mult(a, c)))), a)),
% 22.67/22.93 inference(symmetry,[status(thm)],[6469])).
% 22.67/22.93 tff(6471,plain,
% 22.67/22.93 (mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), a)) = mult(b, mult(a, b))),
% 22.67/22.93 inference(monotonicity,[status(thm)],[6463])).
% 22.67/22.93 tff(6472,plain,
% 22.67/22.93 (mult(b, mult(a, b)) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), a))),
% 22.67/22.93 inference(symmetry,[status(thm)],[6471])).
% 22.67/22.93 tff(6473,plain,
% 22.67/22.93 (mult(b, mult(a, b)) = mult(mult(a, mult(b, rd(mult(b, c), mult(a, c)))), a)),
% 22.67/22.93 inference(transitivity,[status(thm)],[6472, 470, 6470])).
% 22.67/22.93 tff(6474,plain,
% 22.67/22.93 (mult(c, mult(b, mult(a, b))) = mult(c, mult(mult(a, mult(b, rd(mult(b, c), mult(a, c)))), a))),
% 22.67/22.93 inference(monotonicity,[status(thm)],[6473])).
% 22.67/22.93 tff(6475,plain,
% 22.67/22.93 (mult(c, mult(mult(a, mult(b, rd(mult(b, c), mult(a, c)))), a)) = mult(c, mult(b, mult(a, b)))),
% 22.67/22.93 inference(symmetry,[status(thm)],[6474])).
% 22.67/22.93 tff(6476,plain,
% 22.67/22.93 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(c, a), mult(b, rd(mult(b, c), mult(a, c)))), a) = mult(c, mult(mult(a, mult(b, rd(mult(b, c), mult(a, c)))), a)))),
% 22.67/22.93 inference(quant_inst,[status(thm)],[])).
% 22.67/22.93 tff(6477,plain,
% 22.67/22.93 (mult(mult(mult(c, a), mult(b, rd(mult(b, c), mult(a, c)))), a) = mult(c, mult(mult(a, mult(b, rd(mult(b, c), mult(a, c)))), a))),
% 22.67/22.93 inference(unit_resolution,[status(thm)],[6476, 56])).
% 22.67/22.93 tff(6478,plain,
% 22.67/22.93 (mult(mult(a, b), c) = mult(mult(b, c), a)),
% 22.67/22.93 inference(transitivity,[status(thm)],[227, 5505, 5497, 4339])).
% 22.67/22.93 tff(6479,plain,
% 22.67/22.93 (mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))) = mult(mult(mult(b, c), a), rd(mult(b, c), mult(a, c)))),
% 22.67/22.93 inference(monotonicity,[status(thm)],[6478])).
% 22.67/22.93 tff(6480,plain,
% 22.67/22.93 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, b), c)),
% 22.67/22.93 inference(transitivity,[status(thm)],[5496, 5504, 161])).
% 22.67/22.93 tff(6481,plain,
% 22.67/22.93 (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))),
% 22.67/22.93 inference(monotonicity,[status(thm)],[6480])).
% 22.67/22.93 tff(6482,plain,
% 22.67/22.93 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), a), rd(mult(b, c), mult(a, c)))))),
% 22.67/22.93 inference(quant_inst,[status(thm)],[])).
% 22.67/22.93 tff(6483,plain,
% 22.67/22.93 (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), a), rd(mult(b, c), mult(a, c))))),
% 22.67/22.93 inference(unit_resolution,[status(thm)],[6482, 56])).
% 22.67/22.93 tff(6484,plain,
% 22.67/22.93 (mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), a), rd(mult(b, c), mult(a, c)))) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), rd(mult(b, c), mult(a, c)))),
% 22.67/22.93 inference(symmetry,[status(thm)],[6483])).
% 22.67/22.93 tff(6485,plain,
% 22.67/22.93 (mult(mult(a, c), mult(b, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), a), rd(mult(b, c), mult(a, c))))),
% 22.67/22.93 inference(monotonicity,[status(thm)],[6466])).
% 22.67/22.93 tff(6486,plain,
% 22.67/22.93 (mult(mult(c, a), mult(b, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(b, rd(mult(b, c), mult(a, c))))),
% 22.67/22.93 inference(monotonicity,[status(thm)],[5685])).
% 22.67/22.93 tff(6487,plain,
% 22.67/22.93 (mult(mult(c, a), mult(b, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(b, c), a), rd(mult(b, c), mult(a, c)))),
% 22.67/22.93 inference(transitivity,[status(thm)],[6486, 6485, 6484, 6481, 6479])).
% 22.67/22.93 tff(6488,plain,
% 22.67/22.93 (mult(mult(mult(c, a), mult(b, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(mult(b, c), a), rd(mult(b, c), mult(a, c))), a)),
% 22.67/22.93 inference(monotonicity,[status(thm)],[6487])).
% 22.67/22.93 tff(6489,plain,
% 22.67/22.93 (mult(mult(mult(mult(b, c), a), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(c, a), mult(b, rd(mult(b, c), mult(a, c)))), a)),
% 22.67/22.93 inference(symmetry,[status(thm)],[6488])).
% 22.67/22.93 tff(6490,plain,
% 22.67/22.93 (mult(mult(b, c), mult(mult(a, rd(mult(b, c), mult(a, c))), a)) = mult(mult(b, c), mult(a, b))),
% 22.67/22.93 inference(monotonicity,[status(thm)],[6463])).
% 22.67/22.93 tff(6491,plain,
% 22.67/22.93 (mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(mult(a, rd(mult(b, c), mult(a, c))), a))),
% 22.67/22.93 inference(symmetry,[status(thm)],[6490])).
% 22.67/22.93 tff(6492,plain,
% 22.67/22.93 (mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a))),
% 22.67/22.93 inference(monotonicity,[status(thm)],[5695])).
% 22.67/22.93 tff(6493,plain,
% 22.67/22.93 (mult(mult(b, c), mult(b, a)) = mult(mult(b, c), mult(a, b))),
% 22.67/22.93 inference(symmetry,[status(thm)],[6492])).
% 22.67/22.93 tff(6494,plain,
% 22.67/22.93 (mult(mult(c, b), mult(b, a)) = mult(c, mult(b, mult(b, a)))),
% 22.67/22.93 inference(transitivity,[status(thm)],[3422, 6493, 6491, 1597, 6489, 6477, 6475, 5693])).
% 22.67/22.93 tff(6495,plain,
% 22.67/22.93 (mult(mult(c, b), mult(mult(unit, mult(b, a)), unit)) = mult(c, mult(b, mult(mult(unit, mult(b, a)), unit)))),
% 22.67/22.93 inference(modus_ponens,[status(thm)],[6494, 5647])).
% 22.67/22.93 tff(6496,plain,
% 22.67/22.93 (mult(mult(c, b), mult(a, b)) = mult(mult(b, c), mult(a, b))),
% 22.67/22.93 inference(monotonicity,[status(thm)],[241])).
% 22.67/22.93 tff(6497,plain,
% 22.67/22.93 (mult(mult(c, b), mult(a, b)) = mult(mult(c, b), mult(b, a))),
% 22.67/22.93 inference(transitivity,[status(thm)],[6496, 6492, 3468])).
% 22.67/22.93 tff(6498,plain,
% 22.67/22.93 ((mult(mult(c, b), mult(a, b)) = mult(c, mult(b, mult(a, b)))) <=> (mult(mult(c, b), mult(b, a)) = mult(c, mult(b, mult(b, a))))),
% 22.67/22.93 inference(monotonicity,[status(thm)],[6497, 5693])).
% 22.67/22.93 tff(6499,plain,
% 22.67/22.93 ((mult(mult(c, b), mult(b, a)) = mult(c, mult(b, mult(b, a)))) <=> (mult(mult(c, b), mult(a, b)) = mult(c, mult(b, mult(a, b))))),
% 22.67/22.93 inference(symmetry,[status(thm)],[6498])).
% 22.67/22.93 tff(6500,plain,
% 22.67/22.93 (mult(mult(c, b), mult(a, b)) = mult(c, mult(b, mult(a, b)))),
% 22.67/22.93 inference(modus_ponens,[status(thm)],[6494, 6499])).
% 22.67/22.93 tff(6501,plain,
% 22.67/22.93 (mult(b, mult(a, b)) = mult(b, mult(b, a))),
% 22.67/22.93 inference(symmetry,[status(thm)],[5691])).
% 22.67/22.93 tff(6502,plain,
% 22.67/22.93 ((~(mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a))) | (~(mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a))))),
% 22.67/22.93 inference(unit_resolution,[status(thm)],[1568, 5643])).
% 22.67/22.93 tff(6503,plain,
% 22.67/22.93 (~((~(mult(mult(mult(b, c), a), b) = mult(mult(b, c), mult(a, b)))) | (~(mult(mult(mult(b, c), b), a) = mult(mult(b, c), mult(b, a)))))),
% 22.67/22.93 inference(unit_resolution,[status(thm)],[1205, 6502])).
% 22.67/22.93 tff(6504,plain,
% 22.67/22.93 (mult(mult(mult(b, c), a), b) = mult(mult(b, c), mult(a, b))),
% 22.67/22.93 inference(unit_resolution,[status(thm)],[1229, 6503])).
% 22.67/22.93 tff(6505,plain,
% 22.67/22.93 (mult(mult(mult(b, c), b), a) = mult(mult(b, c), mult(b, a))),
% 22.67/22.93 inference(unit_resolution,[status(thm)],[1207, 6503])).
% 22.67/22.93 tff(6506,plain,
% 22.67/22.93 (mult(unit, mult(b, a)) = mult(mult(unit, mult(b, a)), unit)),
% 22.67/22.93 inference(symmetry,[status(thm)],[4320])).
% 22.67/22.93 tff(6507,plain,
% 22.67/22.93 (mult(b, a) = mult(unit, mult(b, a))),
% 22.67/22.93 inference(symmetry,[status(thm)],[4318])).
% 22.67/22.93 tff(6508,plain,
% 22.67/22.93 (mult(b, a) = mult(mult(unit, mult(b, a)), unit)),
% 22.67/22.93 inference(transitivity,[status(thm)],[6507, 6506])).
% 22.67/22.93 tff(6509,plain,
% 22.77/22.93 (mult(mult(b, c), mult(b, a)) = mult(mult(c, b), mult(mult(unit, mult(b, a)), unit))),
% 22.77/22.93 inference(monotonicity,[status(thm)],[1399, 6508])).
% 22.77/22.93 tff(6510,plain,
% 22.77/22.93 (mult(mult(c, b), mult(mult(unit, mult(b, a)), unit)) = mult(mult(b, c), mult(b, a))),
% 22.77/22.93 inference(symmetry,[status(thm)],[6509])).
% 22.77/22.93 tff(6511,assumption,(mult(mult(c, b), mult(mult(unit, mult(b, a)), unit)) = mult(c, mult(b, mult(mult(unit, mult(b, a)), unit)))), introduced(assumption)).
% 22.77/22.93 tff(6512,plain,
% 22.77/22.93 (mult(c, mult(b, mult(mult(unit, mult(b, a)), unit))) = mult(mult(c, b), mult(mult(unit, mult(b, a)), unit))),
% 22.77/22.93 inference(symmetry,[status(thm)],[6511])).
% 22.77/22.93 tff(6513,plain,
% 22.77/22.93 (mult(c, mult(b, mult(b, a))) = mult(c, mult(b, mult(mult(unit, mult(b, a)), unit)))),
% 22.77/22.93 inference(symmetry,[status(thm)],[5645])).
% 22.77/22.93 tff(6514,plain,
% 22.77/22.93 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(c, mult(c, mult(mult(b, a), b))) = mult(mult(b, a), b))),
% 22.77/22.93 inference(quant_inst,[status(thm)],[])).
% 22.77/22.93 tff(6515,plain,
% 22.77/22.93 (ld(c, mult(c, mult(mult(b, a), b))) = mult(mult(b, a), b)),
% 22.77/22.93 inference(unit_resolution,[status(thm)],[6514, 7])).
% 22.77/22.93 tff(6516,plain,
% 22.77/22.93 (mult(mult(mult(c, b), a), b) = mult(mult(mult(b, c), a), b)),
% 22.77/22.93 inference(monotonicity,[status(thm)],[2298])).
% 22.77/22.93 tff(6517,plain,
% 22.77/22.93 (mult(mult(mult(b, c), a), b) = mult(mult(mult(c, b), a), b)),
% 22.77/22.93 inference(symmetry,[status(thm)],[6516])).
% 22.77/22.93 tff(6518,assumption,(mult(mult(c, b), mult(a, b)) = mult(c, mult(b, mult(a, b)))), introduced(assumption)).
% 22.77/22.93 tff(6519,plain,
% 22.77/22.93 (mult(c, mult(b, mult(a, b))) = mult(mult(c, b), mult(a, b))),
% 22.77/22.93 inference(symmetry,[status(thm)],[6518])).
% 22.77/22.93 tff(6520,plain,
% 22.77/22.93 (mult(c, mult(b, mult(a, b))) = mult(c, mult(mult(b, a), b))),
% 22.77/22.93 inference(transitivity,[status(thm)],[6519, 6496, 1312, 6517, 3429])).
% 22.77/22.93 tff(6521,plain,
% 22.77/22.93 (ld(c, mult(c, mult(b, mult(a, b)))) = ld(c, mult(c, mult(mult(b, a), b)))),
% 22.77/22.93 inference(monotonicity,[status(thm)],[6520])).
% 22.77/22.93 tff(6522,plain,
% 22.77/22.93 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(c, mult(c, mult(b, mult(a, b)))) = mult(b, mult(a, b)))),
% 22.77/22.93 inference(quant_inst,[status(thm)],[])).
% 22.77/22.93 tff(6523,plain,
% 22.77/22.93 (ld(c, mult(c, mult(b, mult(a, b)))) = mult(b, mult(a, b))),
% 22.77/22.93 inference(unit_resolution,[status(thm)],[6522, 7])).
% 22.77/22.93 tff(6524,plain,
% 22.77/22.93 (mult(b, mult(a, b)) = ld(c, mult(c, mult(b, mult(a, b))))),
% 22.77/22.93 inference(symmetry,[status(thm)],[6523])).
% 22.77/22.93 tff(6525,plain,
% 22.77/22.93 (mult(b, mult(b, a)) = mult(mult(b, a), b)),
% 22.77/22.93 inference(transitivity,[status(thm)],[392, 6524, 6521, 6515])).
% 22.77/22.93 tff(6526,plain,
% 22.77/22.93 (mult(c, mult(b, mult(b, a))) = mult(c, mult(mult(b, a), b))),
% 22.77/22.93 inference(monotonicity,[status(thm)],[6525])).
% 22.77/22.93 tff(6527,plain,
% 22.77/22.93 (mult(c, mult(mult(b, a), b)) = mult(c, mult(b, mult(b, a)))),
% 22.77/22.93 inference(symmetry,[status(thm)],[6526])).
% 22.77/22.93 tff(6528,plain,
% 22.77/22.93 (mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a)),
% 22.77/22.93 inference(transitivity,[status(thm)],[6517, 3429, 6527, 6513, 6512, 6510, 3107])).
% 22.77/22.93 tff(6529,assumption,(~(mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a))), introduced(assumption)).
% 22.77/22.93 tff(6530,plain,
% 22.77/22.93 ($false),
% 22.77/22.93 inference(unit_resolution,[status(thm)],[6529, 6528])).
% 22.77/22.93 tff(6531,plain,((~(mult(b, mult(a, b)) = mult(b, mult(b, a)))) | (mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a)) | (~(mult(mult(mult(b, c), b), a) = mult(mult(b, c), mult(b, a)))) | (~(mult(mult(c, b), mult(mult(unit, mult(b, a)), unit)) = mult(c, mult(b, mult(mult(unit, mult(b, a)), unit))))) | (~(mult(mult(c, b), mult(a, b)) = mult(c, mult(b, mult(a, b))))) | (~(mult(mult(mult(b, c), a), b) = mult(mult(b, c), mult(a, b))))), inference(lemma,lemma(discharge,[]))).
% 22.77/22.93 tff(6532,plain,
% 22.77/22.93 ($false),
% 22.77/22.93 inference(unit_resolution,[status(thm)],[6531, 6505, 6504, 6501, 6500, 6495, 5643])).
% 22.77/22.93 tff(6533,plain,((~(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))), inference(lemma,lemma(discharge,[]))).
% 22.77/22.93 tff(6534,plain,
% 22.77/22.93 (~(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))),
% 22.77/22.93 inference(unit_resolution,[status(thm)],[6533, 4327])).
% 22.77/22.93 tff(6535,plain,
% 22.77/22.93 (~(mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))),
% 22.77/22.93 inference(unit_resolution,[status(thm)],[306, 6534])).
% 22.77/22.93 tff(6536,plain,
% 22.77/22.93 ((~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))),
% 22.77/22.93 inference(unit_resolution,[status(thm)],[308, 6535])).
% 22.77/22.93 tff(6537,plain,
% 22.77/22.93 (~((~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))),
% 22.77/22.93 inference(unit_resolution,[status(thm)],[313, 6536])).
% 22.77/22.94 tff(6538,plain,
% 22.77/22.94 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))),
% 22.77/22.94 inference(unit_resolution,[status(thm)],[315, 6537])).
% 22.77/22.94 tff(6539,plain,
% 22.77/22.94 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, mult(b, c)), c)),
% 22.77/22.94 inference(transitivity,[status(thm)],[6538, 138, 266])).
% 22.77/22.94 tff(6540,plain,
% 22.77/22.94 (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(a, mult(mult(b, c), c))),
% 22.77/22.94 inference(transitivity,[status(thm)],[5670, 233, 2414])).
% 22.77/22.94 tff(6541,plain,
% 22.77/22.94 ((mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))) <=> (mult(a, mult(mult(b, c), c)) = mult(mult(a, mult(b, c)), c))),
% 22.77/22.94 inference(monotonicity,[status(thm)],[6540, 6539])).
% 22.77/22.94 tff(6542,plain,
% 22.77/22.94 ((mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))) <=> (mult(mult(a, mult(b, c)), c) = mult(a, mult(mult(b, c), c)))),
% 22.77/22.94 inference(transitivity,[status(thm)],[6541, 2412])).
% 22.77/22.94 tff(6543,plain,
% 22.77/22.94 ((mult(mult(a, mult(b, c)), c) = mult(a, mult(mult(b, c), c))) <=> (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 22.77/22.94 inference(symmetry,[status(thm)],[6542])).
% 22.77/22.94 tff(6544,plain,
% 22.77/22.94 ((~(mult(mult(a, mult(b, c)), c) = mult(a, mult(mult(b, c), c)))) <=> (~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))))),
% 22.77/22.94 inference(monotonicity,[status(thm)],[6543])).
% 22.77/22.94 tff(6545,plain,
% 22.77/22.94 (~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 22.77/22.94 inference(modus_ponens,[status(thm)],[258, 6544])).
% 22.77/22.94 tff(6546,plain,
% 22.77/22.94 ((~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)))) | (~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))))),
% 22.77/22.94 inference(unit_resolution,[status(thm)],[121, 6545])).
% 22.77/22.94 tff(6547,plain,
% 22.77/22.94 (~((~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))))),
% 22.77/22.94 inference(unit_resolution,[status(thm)],[4484, 6546])).
% 22.77/22.94 tff(6548,plain,
% 22.77/22.94 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))),
% 22.77/22.94 inference(unit_resolution,[status(thm)],[115, 6547])).
% 22.77/22.94 tff(6549,plain,
% 22.77/22.94 ((mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit))) <=> (mult(mult(rd(mult(b, c), mult(a, c)), c), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), c))),
% 22.77/22.94 inference(monotonicity,[status(thm)],[4488, 4340])).
% 22.77/22.94 tff(6550,plain,
% 22.77/22.94 ((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)))) <=> (~(mult(mult(rd(mult(b, c), mult(a, c)), c), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), c)))),
% 22.77/22.94 inference(monotonicity,[status(thm)],[6549])).
% 22.77/22.94 tff(6551,assumption,(~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)))), introduced(assumption)).
% 22.77/22.94 tff(6552,plain,
% 22.77/22.94 (~(mult(mult(rd(mult(b, c), mult(a, c)), c), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), c))),
% 22.77/22.94 inference(modus_ponens,[status(thm)],[6551, 6550])).
% 22.77/22.94 tff(6553,plain,
% 22.77/22.94 ((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit)))))),
% 22.77/22.94 inference(unit_resolution,[status(thm)],[4302, 6551])).
% 22.77/22.94 tff(6554,plain,
% 22.77/22.94 (~((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit))))))),
% 22.77/22.94 inference(unit_resolution,[status(thm)],[31, 6553])).
% 22.77/22.94 tff(6555,plain,
% 22.77/22.94 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit)))),
% 22.77/22.94 inference(unit_resolution,[status(thm)],[33, 6554])).
% 22.77/22.94 tff(6556,plain,
% 22.77/22.94 (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a))),
% 22.77/22.94 inference(unit_resolution,[status(thm)],[35, 6554])).
% 22.77/22.94 tff(6557,plain,
% 22.77/22.94 (mult(mult(rd(mult(b, c), mult(a, c)), c), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), c)),
% 22.77/22.94 inference(unit_resolution,[status(thm)],[113, 6556, 102, 6555])).
% 22.77/22.94 tff(6558,plain,
% 22.77/22.94 ($false),
% 22.77/22.94 inference(unit_resolution,[status(thm)],[6557, 6552])).
% 22.77/22.94 tff(6559,plain,((mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))))), inference(lemma,lemma(discharge,[]))).
% 22.77/22.94 tff(6560,plain,
% 22.77/22.94 (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit))),
% 22.77/22.94 inference(unit_resolution,[status(thm)],[6559, 6548])).
% 22.77/22.94 tff(6561,assumption,(~((~(mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a))) | (~(mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a)))))), introduced(assumption)).
% 22.77/22.94 tff(6562,plain,
% 22.77/22.94 (mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a))),
% 22.77/22.94 inference(unit_resolution,[status(thm)],[1194, 6561])).
% 22.77/22.94 tff(6563,plain,
% 22.77/22.94 (mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a)),
% 22.77/22.94 inference(unit_resolution,[status(thm)],[1568, 6561])).
% 22.77/22.94 tff(6564,plain,
% 22.77/22.94 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(rd(mult(b, c), mult(a, c)), a), mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))),
% 22.77/22.94 inference(quant_inst,[status(thm)],[])).
% 22.77/22.94 tff(6565,plain,
% 22.77/22.94 (ld(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(rd(mult(b, c), mult(a, c)), a), mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))),
% 22.77/22.94 inference(unit_resolution,[status(thm)],[6564, 7])).
% 22.77/22.94 tff(6566,plain,
% 22.77/22.94 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, c), b)) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, b), c))),
% 22.77/22.94 inference(monotonicity,[status(thm)],[161])).
% 22.77/22.94 tff(6567,plain,
% 22.77/22.94 ((mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, b), c))) <=> (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, b), c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)), a))),
% 22.77/22.94 inference(commutativity,[status(thm)],[])).
% 22.77/22.94 tff(6568,plain,
% 22.77/22.94 (ld(a, mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = ld(a, mult(a, mult(rd(mult(b, c), mult(a, c)), a)))),
% 22.77/22.94 inference(monotonicity,[status(thm)],[910])).
% 22.77/22.94 tff(6569,plain,
% 22.77/22.94 (ld(a, mult(a, mult(rd(mult(b, c), mult(a, c)), a))) = ld(a, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))),
% 22.77/22.94 inference(symmetry,[status(thm)],[6568])).
% 22.77/22.94 tff(6570,plain,
% 22.77/22.94 (mult(rd(mult(b, c), mult(a, c)), a) = mult(a, rd(mult(b, c), mult(a, c)))),
% 22.77/22.94 inference(transitivity,[status(thm)],[5747, 6569, 918])).
% 22.77/22.94 tff(6571,plain,
% 22.77/22.94 (mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))),
% 22.77/22.94 inference(monotonicity,[status(thm)],[6570])).
% 22.77/22.94 tff(6572,plain,
% 22.77/22.94 (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))),
% 22.77/22.94 inference(symmetry,[status(thm)],[6571])).
% 22.77/22.94 tff(6573,plain,
% 22.77/22.94 (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))),
% 22.77/22.94 inference(unit_resolution,[status(thm)],[4428, 6572, 1039, 4399, 270])).
% 22.77/22.94 tff(6574,plain,
% 22.77/22.94 (~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))),
% 22.77/22.94 inference(unit_resolution,[status(thm)],[6345, 6573, 270, 898, 4360, 6572, 3865])).
% 22.77/22.94 tff(6575,plain,
% 22.77/22.94 (~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))),
% 22.77/22.94 inference(unit_resolution,[status(thm)],[5761, 6574, 3865, 908, 1799])).
% 22.77/22.94 tff(6576,plain,
% 22.77/22.94 ((~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))) | (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))))),
% 22.77/22.94 inference(unit_resolution,[status(thm)],[346, 6574])).
% 22.77/22.94 tff(6577,plain,
% 22.77/22.94 (~((~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))))),
% 22.77/22.94 inference(unit_resolution,[status(thm)],[1805, 6576])).
% 22.77/22.94 tff(6578,plain,
% 22.77/22.94 ($false),
% 22.77/22.94 inference(unit_resolution,[status(thm)],[1801, 6577, 6575])).
% 22.77/22.94 tff(6579,plain,((mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))) | (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))), inference(lemma,lemma(discharge,[]))).
% 22.77/22.94 tff(6580,plain,
% 22.77/22.94 ((mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))) | (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))),
% 22.77/22.94 inference(unit_resolution,[status(thm)],[6579, 3862])).
% 22.77/22.94 tff(6581,plain,
% 22.77/22.94 (mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a))),
% 22.77/22.94 inference(unit_resolution,[status(thm)],[6580, 316, 1799, 4360, 270])).
% 22.77/22.94 tff(6582,plain,
% 22.77/22.94 (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))),
% 22.77/22.94 inference(unit_resolution,[status(thm)],[1814, 1799])).
% 22.77/22.94 tff(6583,plain,
% 22.77/22.94 (mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 22.77/22.94 inference(unit_resolution,[status(thm)],[4354, 314])).
% 22.77/22.94 tff(6584,plain,
% 22.77/22.94 (~(mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))),
% 22.77/22.94 inference(unit_resolution,[status(thm)],[2390, 2330, 1799, 6582])).
% 22.77/22.94 tff(6585,plain,
% 22.77/22.94 ((mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a)) <=> (mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))))),
% 22.77/22.94 inference(commutativity,[status(thm)],[])).
% 22.77/22.94 tff(6586,plain,
% 22.77/22.94 ((mult(mult(mult(mult(a, c), c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))), a)) <=> (mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a))),
% 22.77/22.94 inference(monotonicity,[status(thm)],[4705, 4703])).
% 22.77/22.94 tff(6587,plain,
% 22.77/22.94 ((mult(mult(mult(mult(a, c), c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))), a)) <=> (mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))))),
% 22.77/22.94 inference(transitivity,[status(thm)],[6586, 6585])).
% 22.77/22.94 tff(6588,plain,
% 22.77/22.94 ((mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c)))) <=> (mult(mult(mult(mult(a, c), c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))), a))),
% 22.77/22.94 inference(symmetry,[status(thm)],[6587])).
% 22.77/22.94 tff(6589,plain,
% 22.77/22.94 (~((~(mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)))))),
% 22.77/22.94 inference(unit_resolution,[status(thm)],[2406, 2393])).
% 22.77/22.94 tff(6590,plain,
% 22.77/22.94 (mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c))))),
% 22.77/22.94 inference(unit_resolution,[status(thm)],[5253, 6589])).
% 22.77/22.94 tff(6591,plain,
% 22.77/22.94 (mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a))),
% 22.77/22.94 inference(unit_resolution,[status(thm)],[2408, 6589])).
% 22.77/22.94 tff(6592,plain,
% 22.77/22.94 ((mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c)))) <=> (mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))),
% 22.77/22.94 inference(monotonicity,[status(thm)],[6591, 6590])).
% 22.77/22.94 tff(6593,plain,
% 22.77/22.94 ((mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c))))) <=> (mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))))),
% 22.77/22.94 inference(symmetry,[status(thm)],[6592])).
% 22.77/22.94 tff(6594,plain,
% 22.77/22.94 ((mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c))))) <=> (mult(mult(mult(mult(a, c), c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))), a))),
% 22.77/22.94 inference(transitivity,[status(thm)],[6593, 6588])).
% 22.77/22.94 tff(6595,plain,
% 22.77/22.94 ((~(mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))) <=> (~(mult(mult(mult(mult(a, c), c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))), a)))),
% 22.77/22.94 inference(monotonicity,[status(thm)],[6594])).
% 22.77/22.94 tff(6596,plain,
% 22.77/22.94 (~(mult(mult(mult(mult(a, c), c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))), a))),
% 22.77/22.94 inference(modus_ponens,[status(thm)],[2393, 6595])).
% 22.77/22.94 tff(6597,assumption,(mult(mult(mult(mult(a, c), c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))), a)), introduced(assumption)).
% 22.77/22.94 tff(6598,plain,
% 22.77/22.94 ($false),
% 22.77/22.94 inference(unit_resolution,[status(thm)],[6597, 6596])).
% 22.77/22.94 tff(6599,plain,((~(mult(mult(mult(mult(a, c), c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))), a))) | (mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c))))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit)))))), inference(lemma,lemma(discharge,[]))).
% 22.77/22.95 tff(6600,plain,
% 22.77/22.95 ((~(mult(mult(mult(mult(a, c), c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))), a))) | (mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))),
% 22.77/22.95 inference(unit_resolution,[status(thm)],[6599, 3862])).
% 22.77/22.95 tff(6601,plain,
% 22.77/22.95 (~(mult(mult(mult(mult(a, c), c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))), a))),
% 22.77/22.95 inference(unit_resolution,[status(thm)],[6600, 6584])).
% 22.77/22.95 tff(6602,plain,
% 22.77/22.95 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a) = mult(mult(b, c), a)),
% 22.77/22.95 inference(transitivity,[status(thm)],[1168, 1372, 4398])).
% 22.77/22.95 tff(6603,plain,
% 22.77/22.95 (rd(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a), a) = rd(mult(mult(b, c), a), a)),
% 22.77/22.95 inference(monotonicity,[status(thm)],[6602])).
% 22.77/22.95 tff(6604,plain,
% 22.77/22.95 (mult(mult(rd(mult(b, c), mult(a, c)), c), a) = mult(b, c)),
% 22.77/22.95 inference(transitivity,[status(thm)],[83, 4360, 4340, 1377, 6603, 1370])).
% 22.77/22.95 tff(6605,plain,
% 22.77/22.95 (mult(a, mult(mult(rd(mult(b, c), mult(a, c)), c), a)) = mult(a, mult(b, c))),
% 22.77/22.95 inference(monotonicity,[status(thm)],[6604])).
% 22.77/22.95 tff(6606,plain,
% 22.77/22.95 (mult(mult(rd(mult(b, c), mult(a, c)), a), c) = mult(b, c)),
% 22.77/22.95 inference(transitivity,[status(thm)],[1377, 6603, 1370])).
% 22.77/22.95 tff(6607,plain,
% 22.77/22.95 (rd(mult(mult(rd(mult(b, c), mult(a, c)), a), c), c) = rd(mult(b, c), c)),
% 22.77/22.95 inference(monotonicity,[status(thm)],[6606])).
% 22.77/22.95 tff(6608,plain,
% 22.77/22.95 (mult(rd(mult(b, c), mult(a, c)), a) = b),
% 22.77/22.95 inference(transitivity,[status(thm)],[175, 6607, 170])).
% 22.77/22.95 tff(6609,plain,
% 22.77/22.95 (mult(a, mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, b)),
% 22.77/22.95 inference(monotonicity,[status(thm)],[6608])).
% 22.77/22.95 tff(6610,plain,
% 22.77/22.95 (mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, b)),
% 22.77/22.95 inference(transitivity,[status(thm)],[1287, 6609])).
% 22.77/22.95 tff(6611,plain,
% 22.77/22.95 (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), c) = mult(mult(a, b), c)),
% 22.77/22.95 inference(monotonicity,[status(thm)],[6610])).
% 22.77/22.95 tff(6612,plain,
% 22.77/22.95 ((mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), c) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))) <=> (mult(mult(a, b), c) = mult(a, mult(b, c)))),
% 22.77/22.95 inference(monotonicity,[status(thm)],[6611, 4286])).
% 22.77/22.95 tff(6613,plain,
% 22.77/22.95 ((mult(mult(a, b), c) = mult(a, mult(b, c))) <=> (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), c) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 22.77/22.95 inference(symmetry,[status(thm)],[6612])).
% 22.77/22.95 tff(6614,plain,
% 22.77/22.95 ((~(mult(mult(a, b), c) = mult(a, mult(b, c)))) <=> (~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), c) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))))),
% 22.77/22.95 inference(monotonicity,[status(thm)],[6613])).
% 22.77/22.95 tff(6615,plain,
% 22.77/22.95 (~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), c) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 22.77/22.95 inference(modus_ponens,[status(thm)],[146, 6614])).
% 22.77/22.95 tff(6616,plain,
% 22.77/22.95 ((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), a) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, a)))) | (~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), c) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))))),
% 22.77/22.95 inference(unit_resolution,[status(thm)],[764, 6615])).
% 22.77/22.95 tff(6617,plain,
% 22.77/22.95 (~((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), c))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))))),
% 22.77/22.95 inference(unit_resolution,[status(thm)],[762, 6616])).
% 22.77/22.95 tff(6618,plain,
% 22.77/22.95 (((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), c))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))))) | (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), c))),
% 22.77/22.95 inference(tautology,[status(thm)],[])).
% 22.77/22.95 tff(6619,plain,
% 22.77/22.95 (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), c)),
% 22.77/22.95 inference(unit_resolution,[status(thm)],[6618, 6617])).
% 22.77/22.95 tff(6620,plain,
% 22.77/22.95 (mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, rd(mult(b, c), mult(a, c))), c)),
% 22.77/22.95 inference(monotonicity,[status(thm)],[1897])).
% 22.77/22.95 tff(6621,assumption,(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c))), introduced(assumption)).
% 22.77/22.95 tff(6622,plain,
% 22.77/22.95 (mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)) = mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c)),
% 22.77/22.95 inference(symmetry,[status(thm)],[6621])).
% 22.77/22.95 tff(6623,plain,
% 22.77/22.95 (mult(a, mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, rd(mult(b, c), mult(a, c))), c)),
% 22.77/22.95 inference(transitivity,[status(thm)],[5116, 6622, 6620])).
% 22.77/22.95 tff(6624,plain,
% 22.77/22.95 (mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), a)),
% 22.77/22.95 inference(monotonicity,[status(thm)],[6623])).
% 22.77/22.95 tff(6625,plain,
% 22.77/22.95 (mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(a, b), c)),
% 22.77/22.95 inference(transitivity,[status(thm)],[6624, 6619, 6611])).
% 22.77/22.95 tff(6626,plain,
% 22.77/22.95 ((mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), c), a))) <=> (mult(mult(a, b), c) = mult(a, mult(b, c)))),
% 22.77/22.95 inference(monotonicity,[status(thm)],[6625, 6605])).
% 22.77/22.95 tff(6627,plain,
% 22.77/22.95 ((mult(mult(a, b), c) = mult(a, mult(b, c))) <=> (mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), c), a)))),
% 22.77/22.95 inference(symmetry,[status(thm)],[6626])).
% 22.77/22.95 tff(6628,plain,
% 22.77/22.95 ((~(mult(mult(a, b), c) = mult(a, mult(b, c)))) <=> (~(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), c), a))))),
% 22.77/22.95 inference(monotonicity,[status(thm)],[6627])).
% 22.77/22.95 tff(6629,plain,
% 22.77/22.95 (~(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), c), a)))),
% 22.77/22.95 inference(modus_ponens,[status(thm)],[146, 6628])).
% 22.77/22.95 tff(6630,plain,
% 22.77/22.95 (((~(mult(mult(a, a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(a, mult(a, mult(rd(mult(b, c), mult(a, c)), c))))) | (~(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), c), a))))) | (mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), c), a)))),
% 22.77/22.95 inference(tautology,[status(thm)],[])).
% 22.77/22.95 tff(6631,plain,
% 22.77/22.95 ((~(mult(mult(a, a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(a, mult(a, mult(rd(mult(b, c), mult(a, c)), c))))) | (~(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), c), a))))),
% 22.77/22.95 inference(unit_resolution,[status(thm)],[6630, 6629])).
% 22.77/22.95 tff(6632,plain,
% 22.77/22.95 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a))) | (~(mult(a, mult(a, mult(rd(mult(b, c), mult(a, c)), c))) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), c), a)))))) | (~((~(mult(mult(a, a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(a, mult(a, mult(rd(mult(b, c), mult(a, c)), c))))) | (~(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), c), a)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a))) | (~(mult(a, mult(a, mult(rd(mult(b, c), mult(a, c)), c))) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), c), a)))))) | (~((~(mult(mult(a, a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(a, mult(a, mult(rd(mult(b, c), mult(a, c)), c))))) | (~(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), c), a)))))))),
% 22.77/22.95 inference(rewrite,[status(thm)],[])).
% 22.77/22.95 tff(6633,plain,
% 22.77/22.95 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a))) | (~(mult(a, mult(a, mult(rd(mult(b, c), mult(a, c)), c))) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), c), a)))))) | (~((~(mult(mult(a, a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(a, mult(a, mult(rd(mult(b, c), mult(a, c)), c))))) | (~(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), c), a)))))))),
% 22.77/22.95 inference(quant_inst,[status(thm)],[])).
% 22.77/22.95 tff(6634,plain,
% 22.77/22.95 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a))) | (~(mult(a, mult(a, mult(rd(mult(b, c), mult(a, c)), c))) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), c), a)))))) | (~((~(mult(mult(a, a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(a, mult(a, mult(rd(mult(b, c), mult(a, c)), c))))) | (~(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), c), a))))))),
% 22.77/22.95 inference(modus_ponens,[status(thm)],[6633, 6632])).
% 22.77/22.95 tff(6635,plain,
% 22.77/22.95 ((~((~(mult(mult(a, a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a))) | (~(mult(a, mult(a, mult(rd(mult(b, c), mult(a, c)), c))) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), c), a)))))) | (~((~(mult(mult(a, a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(a, mult(a, mult(rd(mult(b, c), mult(a, c)), c))))) | (~(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), c), a))))))),
% 22.77/22.95 inference(unit_resolution,[status(thm)],[6634, 27])).
% 22.77/22.95 tff(6636,plain,
% 22.77/22.95 (~((~(mult(mult(a, a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a))) | (~(mult(a, mult(a, mult(rd(mult(b, c), mult(a, c)), c))) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), c), a)))))),
% 22.77/22.95 inference(unit_resolution,[status(thm)],[6635, 6631])).
% 22.77/22.95 tff(6637,plain,
% 22.77/22.95 (((~(mult(mult(a, a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a))) | (~(mult(a, mult(a, mult(rd(mult(b, c), mult(a, c)), c))) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), c), a))))) | (mult(a, mult(a, mult(rd(mult(b, c), mult(a, c)), c))) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), c), a)))),
% 22.77/22.95 inference(tautology,[status(thm)],[])).
% 22.77/22.95 tff(6638,plain,
% 22.77/22.95 (mult(a, mult(a, mult(rd(mult(b, c), mult(a, c)), c))) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), c), a))),
% 22.77/22.95 inference(unit_resolution,[status(thm)],[6637, 6636])).
% 22.77/22.95 tff(6639,plain,
% 22.77/22.95 (mult(mult(a, rd(mult(b, c), mult(a, c))), c) = mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c)),
% 22.77/22.95 inference(symmetry,[status(thm)],[6620])).
% 22.77/22.95 tff(6640,plain,
% 22.77/22.95 (mult(mult(a, rd(mult(b, c), mult(a, c))), c) = mult(a, mult(rd(mult(b, c), mult(a, c)), c))),
% 22.77/22.95 inference(transitivity,[status(thm)],[6639, 6621, 5117])).
% 22.77/22.95 tff(6641,plain,
% 22.77/22.95 (mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(a, mult(rd(mult(b, c), mult(a, c)), c)))),
% 22.77/22.95 inference(monotonicity,[status(thm)],[6640])).
% 22.77/22.95 tff(6642,plain,
% 22.77/22.95 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), a), a) = mult(mult(a, rd(mult(b, c), mult(a, c))), c))),
% 22.77/22.96 inference(quant_inst,[status(thm)],[])).
% 22.77/22.96 tff(6643,plain,
% 22.77/22.96 (rd(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), a), a) = mult(mult(a, rd(mult(b, c), mult(a, c))), c)),
% 22.77/22.96 inference(unit_resolution,[status(thm)],[6642, 168])).
% 22.77/22.96 tff(6644,plain,
% 22.77/22.96 (mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, c), b)),
% 22.77/22.96 inference(monotonicity,[status(thm)],[6608])).
% 22.77/22.96 tff(6645,plain,
% 22.77/22.96 (mult(mult(a, c), b) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))),
% 22.77/22.96 inference(symmetry,[status(thm)],[6644])).
% 22.77/22.96 tff(6646,plain,
% 22.77/22.96 (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)),
% 22.77/22.96 inference(transitivity,[status(thm)],[6619, 6611, 227, 6645, 1800])).
% 22.77/22.96 tff(6647,plain,
% 22.77/22.96 (rd(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), a), a) = rd(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), a)),
% 22.77/22.96 inference(monotonicity,[status(thm)],[6646])).
% 22.77/22.96 tff(6648,plain,
% 22.77/22.96 (rd(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), a) = rd(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), a), a)),
% 22.77/22.96 inference(symmetry,[status(thm)],[6647])).
% 22.77/22.96 tff(6649,plain,
% 22.77/22.96 (mult(mult(a, c), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), c)),
% 22.77/22.96 inference(transitivity,[status(thm)],[6325, 6648, 6643])).
% 22.77/22.96 tff(6650,plain,
% 22.77/22.96 (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c))),
% 22.77/22.96 inference(monotonicity,[status(thm)],[6649])).
% 22.77/22.96 tff(6651,plain,
% 22.77/22.96 (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))),
% 22.77/22.96 inference(transitivity,[status(thm)],[6650, 6641, 6638, 6605, 289])).
% 22.77/22.96 tff(6652,plain,
% 22.77/22.96 ($false),
% 22.77/22.96 inference(unit_resolution,[status(thm)],[270, 6651])).
% 22.77/22.96 tff(6653,plain,((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) | (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a))))), inference(lemma,lemma(discharge,[]))).
% 22.77/22.96 tff(6654,plain,
% 22.77/22.96 (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))),
% 22.77/22.96 inference(unit_resolution,[status(thm)],[6653, 4289, 4360, 270, 1799, 1287])).
% 22.77/22.96 tff(6655,plain,
% 22.77/22.96 ((~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))),
% 22.77/22.96 inference(unit_resolution,[status(thm)],[4290, 6654])).
% 22.77/22.96 tff(6656,plain,
% 22.77/22.96 (~((~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))))),
% 22.77/22.96 inference(unit_resolution,[status(thm)],[4295, 6655])).
% 22.77/22.96 tff(6657,plain,
% 22.77/22.96 (mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))),
% 22.77/22.96 inference(unit_resolution,[status(thm)],[4328, 6656])).
% 22.77/22.96 tff(6658,plain,
% 22.77/22.96 ((mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))) <=> (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))),
% 22.77/22.96 inference(commutativity,[status(thm)],[])).
% 22.77/22.96 tff(6659,plain,
% 22.77/22.96 (ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c)))) = ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))),
% 22.77/22.96 inference(monotonicity,[status(thm)],[6657])).
% 22.77/22.96 tff(6660,plain,
% 22.77/22.96 (mult(a, mult(a, c)) = mult(mult(a, c), a)),
% 22.77/22.96 inference(transitivity,[status(thm)],[4452, 6659, 4447])).
% 22.77/22.96 tff(6661,plain,
% 22.77/22.96 (mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))),
% 22.77/22.96 inference(monotonicity,[status(thm)],[6660])).
% 22.77/22.96 tff(6662,plain,
% 22.77/22.96 (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 22.77/22.96 inference(symmetry,[status(thm)],[6661])).
% 22.77/22.96 tff(6663,plain,
% 22.77/22.96 (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))),
% 22.77/22.96 inference(symmetry,[status(thm)],[2319])).
% 22.77/22.96 tff(6664,plain,
% 22.77/22.96 (mult(mult(unit, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))),
% 22.77/22.96 inference(monotonicity,[status(thm)],[1549])).
% 22.77/22.96 tff(6665,plain,
% 22.77/22.96 (mult(mult(unit, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 22.77/22.96 inference(transitivity,[status(thm)],[6664, 6663, 6662, 281])).
% 22.77/22.96 tff(6666,plain,
% 22.77/22.96 ((~![A: $i] : (mult(unit, A) = A)) | (mult(unit, mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, rd(mult(b, c), mult(a, c))))),
% 22.77/22.96 inference(quant_inst,[status(thm)],[])).
% 22.77/22.96 tff(6667,plain,
% 22.77/22.96 (mult(unit, mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, rd(mult(b, c), mult(a, c)))),
% 22.77/22.96 inference(unit_resolution,[status(thm)],[6666, 71])).
% 22.77/22.96 tff(6668,plain,
% 22.77/22.96 ((~![A: $i] : (mult(A, unit) = A)) | (mult(mult(unit, mult(a, rd(mult(b, c), mult(a, c)))), unit) = mult(unit, mult(a, rd(mult(b, c), mult(a, c)))))),
% 22.77/22.96 inference(quant_inst,[status(thm)],[])).
% 22.77/22.96 tff(6669,plain,
% 22.77/22.96 (mult(mult(unit, mult(a, rd(mult(b, c), mult(a, c)))), unit) = mult(unit, mult(a, rd(mult(b, c), mult(a, c))))),
% 22.77/22.96 inference(unit_resolution,[status(thm)],[6668, 43])).
% 22.77/22.96 tff(6670,plain,
% 22.77/22.96 (mult(mult(unit, mult(a, rd(mult(b, c), mult(a, c)))), unit) = mult(a, rd(mult(b, c), mult(a, c)))),
% 22.77/22.96 inference(transitivity,[status(thm)],[6669, 6667])).
% 22.77/22.96 tff(6671,plain,
% 22.77/22.96 (mult(mult(mult(unit, mult(a, rd(mult(b, c), mult(a, c)))), unit), mult(a, c)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))),
% 22.77/22.96 inference(monotonicity,[status(thm)],[6670])).
% 22.77/22.96 tff(6672,plain,
% 22.77/22.96 (mult(unit, mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(unit, mult(a, rd(mult(b, c), mult(a, c)))), unit)),
% 22.77/22.96 inference(symmetry,[status(thm)],[6669])).
% 22.77/22.96 tff(6673,plain,
% 22.77/22.96 (mult(mult(unit, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(mult(mult(unit, mult(a, rd(mult(b, c), mult(a, c)))), unit), mult(a, c))),
% 22.77/22.96 inference(monotonicity,[status(thm)],[6672])).
% 22.77/22.96 tff(6674,plain,
% 22.77/22.96 (mult(mult(unit, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))),
% 22.77/22.96 inference(transitivity,[status(thm)],[6673, 6671, 279])).
% 22.77/22.96 tff(6675,plain,
% 22.77/22.96 ((mult(mult(unit, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(mult(unit, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c))))) <=> (mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 22.77/22.96 inference(monotonicity,[status(thm)],[6674, 6665])).
% 22.77/22.96 tff(6676,plain,
% 22.77/22.96 ((mult(mult(unit, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(mult(unit, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c))))) <=> (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))),
% 22.77/22.96 inference(transitivity,[status(thm)],[6675, 6658])).
% 22.77/22.96 tff(6677,plain,
% 22.77/22.96 ((mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))) <=> (mult(mult(unit, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(mult(unit, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))),
% 22.77/22.96 inference(symmetry,[status(thm)],[6676])).
% 22.77/22.96 tff(6678,plain,
% 22.77/22.96 ((~(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) <=> (~(mult(mult(unit, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(mult(unit, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c))))))),
% 22.77/22.96 inference(monotonicity,[status(thm)],[6677])).
% 22.77/22.96 tff(6679,plain,
% 22.77/22.96 (~(mult(mult(unit, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(mult(unit, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))),
% 22.77/22.96 inference(modus_ponens,[status(thm)],[270, 6678])).
% 22.77/22.96 tff(6680,plain,
% 22.77/22.96 (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(unit, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c))))),
% 22.77/22.96 inference(symmetry,[status(thm)],[6664])).
% 22.77/22.96 tff(6681,plain,
% 22.77/22.96 (ld(c, mult(c, mult(b, c))) = ld(c, mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 22.77/22.96 inference(symmetry,[status(thm)],[4377])).
% 22.77/22.96 tff(6682,plain,
% 22.77/22.96 (mult(b, c) = ld(c, mult(c, mult(b, c)))),
% 22.77/22.96 inference(symmetry,[status(thm)],[4374])).
% 22.77/22.96 tff(6683,plain,
% 22.77/22.96 (mult(b, c) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))),
% 22.77/22.96 inference(transitivity,[status(thm)],[6682, 6681, 4379])).
% 22.77/22.96 tff(6684,plain,
% 22.77/22.96 (mult(a, mult(b, c)) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 22.77/22.96 inference(monotonicity,[status(thm)],[6683])).
% 22.77/22.96 tff(6685,plain,
% 22.77/22.96 (mult(mult(unit, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(mult(unit, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c))))),
% 22.77/22.96 inference(transitivity,[status(thm)],[6673, 6671, 287, 142, 6684, 4676, 4520, 2319, 6680])).
% 22.77/22.96 tff(6686,assumption,(~(mult(mult(unit, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(mult(unit, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))), introduced(assumption)).
% 22.77/22.96 tff(6687,plain,
% 22.77/22.96 ($false),
% 22.77/22.96 inference(unit_resolution,[status(thm)],[6686, 6685])).
% 22.77/22.96 tff(6688,plain,((~(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (mult(mult(unit, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(mult(unit, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))), inference(lemma,lemma(discharge,[]))).
% 22.77/22.96 tff(6689,plain,
% 22.77/22.96 (~(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))),
% 22.77/22.96 inference(unit_resolution,[status(thm)],[6688, 6679, 279, 281, 2319, 6657])).
% 22.77/22.96 tff(6690,plain,
% 22.77/22.96 ((~(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))),
% 22.77/22.96 inference(unit_resolution,[status(thm)],[4387, 6689])).
% 22.77/22.96 tff(6691,plain,
% 22.77/22.96 (~((~(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))),
% 22.77/22.96 inference(unit_resolution,[status(thm)],[2797, 6690])).
% 22.77/22.96 tff(6692,plain,
% 22.77/22.96 (mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))),
% 22.77/22.96 inference(unit_resolution,[status(thm)],[2799, 6691])).
% 22.77/22.96 tff(6693,plain,
% 22.77/22.96 (mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))),
% 22.77/22.96 inference(symmetry,[status(thm)],[6692])).
% 22.77/22.96 tff(6694,plain,
% 22.77/22.96 (mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(b, c), c)),
% 22.77/22.96 inference(transitivity,[status(thm)],[6692, 2802, 4179, 4176, 4173])).
% 22.77/22.96 tff(6695,plain,
% 22.77/22.96 (mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))) = mult(a, mult(mult(b, c), c))),
% 22.77/22.96 inference(monotonicity,[status(thm)],[6694])).
% 22.77/22.96 tff(6696,plain,
% 22.77/22.96 (mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))) = mult(a, mult(c, rd(mult(b, c), mult(a, c))))),
% 22.77/22.96 inference(symmetry,[status(thm)],[2220])).
% 22.77/22.96 tff(6697,plain,
% 22.77/22.96 (mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))),
% 22.77/22.96 inference(unit_resolution,[status(thm)],[2215, 4288])).
% 22.77/22.96 tff(6698,plain,
% 22.77/22.96 (mult(mult(a, c), rd(mult(b, c), mult(a, c))) = mult(a, mult(c, rd(mult(b, c), mult(a, c))))),
% 22.77/22.96 inference(transitivity,[status(thm)],[2167, 4851, 4850, 2171, 6697, 6696])).
% 22.77/22.96 tff(6699,plain,
% 22.77/22.96 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c))),
% 22.77/22.96 inference(monotonicity,[status(thm)],[6698])).
% 22.77/22.96 tff(6700,plain,
% 22.77/22.96 (mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))),
% 22.77/22.96 inference(symmetry,[status(thm)],[6699])).
% 22.77/22.96 tff(6701,plain,
% 22.77/22.96 (mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(mult(a, mult(b, c)), c)),
% 22.77/22.96 inference(transitivity,[status(thm)],[6700, 1039, 269, 266])).
% 22.77/22.96 tff(6702,plain,
% 22.77/22.96 ((mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))) <=> (mult(mult(a, mult(b, c)), c) = mult(a, mult(mult(b, c), c)))),
% 22.77/22.96 inference(monotonicity,[status(thm)],[6701, 6695])).
% 22.77/22.96 tff(6703,plain,
% 22.77/22.96 ((mult(mult(a, mult(b, c)), c) = mult(a, mult(mult(b, c), c))) <=> (mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))),
% 22.77/22.96 inference(symmetry,[status(thm)],[6702])).
% 22.77/22.96 tff(6704,plain,
% 22.77/22.96 ((~(mult(mult(a, mult(b, c)), c) = mult(a, mult(mult(b, c), c)))) <=> (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))))),
% 22.77/22.96 inference(monotonicity,[status(thm)],[6703])).
% 22.77/22.96 tff(6705,plain,
% 22.77/22.96 (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))),
% 22.77/22.96 inference(modus_ponens,[status(thm)],[258, 6704])).
% 22.77/22.96 tff(6706,plain,
% 22.77/22.96 ((~(mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))))),
% 22.77/22.96 inference(unit_resolution,[status(thm)],[4560, 6705])).
% 22.77/22.96 tff(6707,plain,
% 22.77/22.96 (~((~(mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)))) | (~(mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))))),
% 22.77/22.96 inference(unit_resolution,[status(thm)],[4565, 6706])).
% 22.77/22.96 tff(6708,plain,
% 22.77/22.96 (mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 22.77/22.96 inference(unit_resolution,[status(thm)],[4567, 6707])).
% 22.77/22.96 tff(6709,plain,
% 22.77/22.96 (mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 22.77/22.96 inference(unit_resolution,[status(thm)],[2810, 6691])).
% 22.77/22.96 tff(6710,plain,
% 22.77/22.96 (mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a)),
% 22.77/22.96 inference(monotonicity,[status(thm)],[6709])).
% 22.77/22.96 tff(6711,plain,
% 22.77/22.96 (mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a)),
% 22.77/22.96 inference(symmetry,[status(thm)],[6710])).
% 22.77/22.96 tff(6712,plain,
% 22.77/22.96 (mult(mult(mult(a, c), c), a) = mult(mult(a, c), mult(c, a))),
% 22.77/22.96 inference(unit_resolution,[status(thm)],[4781, 6657, 3865])).
% 22.77/22.96 tff(6713,plain,
% 22.77/22.96 (~(mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 22.77/22.96 inference(unit_resolution,[status(thm)],[4801, 6709, 3865, 4799, 4789, 6712])).
% 22.77/22.96 tff(6714,plain,
% 22.77/22.96 ((~(mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(c, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))))),
% 22.77/22.97 inference(unit_resolution,[status(thm)],[4699, 6713])).
% 22.77/22.97 tff(6715,plain,
% 22.77/22.97 (~((~(mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(c, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)))))),
% 22.77/22.97 inference(unit_resolution,[status(thm)],[4697, 6714])).
% 22.77/22.97 tff(6716,plain,
% 22.77/22.97 (((~(mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(c, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))))) | (mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(c, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)))),
% 22.77/22.97 inference(tautology,[status(thm)],[])).
% 22.77/22.97 tff(6717,plain,
% 22.77/22.97 (mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(c, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))),
% 22.77/22.97 inference(unit_resolution,[status(thm)],[6716, 6715])).
% 22.77/22.97 tff(6718,plain,
% 22.77/22.97 (mult(c, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)) = mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a)),
% 22.77/22.97 inference(symmetry,[status(thm)],[6717])).
% 22.77/22.97 tff(6719,plain,
% 22.77/22.97 (mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))),
% 22.77/22.97 inference(symmetry,[status(thm)],[6697])).
% 22.77/22.97 tff(6720,plain,
% 22.77/22.97 (mult(a, mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))),
% 22.77/22.97 inference(transitivity,[status(thm)],[2220, 6719, 2172, 2178, 2177, 2162])).
% 22.77/22.97 tff(6721,plain,
% 22.77/22.97 (mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)),
% 22.77/22.97 inference(monotonicity,[status(thm)],[6720])).
% 22.77/22.97 tff(6722,plain,
% 22.77/22.97 (mult(c, mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), a)) = mult(mult(unit, c), mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))),
% 22.77/22.97 inference(monotonicity,[status(thm)],[74, 6721])).
% 22.77/22.97 tff(6723,plain,
% 22.77/22.97 (mult(mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a)),
% 22.77/22.97 inference(transitivity,[status(thm)],[2697, 6722, 4445, 6718, 6711])).
% 22.77/22.97 tff(6724,plain,
% 22.77/22.97 (rd(mult(mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c)))), a), a) = rd(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a), a)),
% 22.77/22.97 inference(monotonicity,[status(thm)],[6723])).
% 22.77/22.97 tff(6725,plain,
% 22.77/22.97 (rd(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a), a) = rd(mult(mult(mult(c, a), mult(c, rd(mult(b, c), mult(a, c)))), a), a)),
% 22.77/22.97 inference(symmetry,[status(thm)],[6724])).
% 22.77/22.97 tff(6726,plain,
% 22.77/22.97 (mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))),
% 22.77/22.97 inference(transitivity,[status(thm)],[4530, 2787, 6725, 5263, 4569])).
% 22.77/22.97 tff(6727,plain,
% 22.77/22.97 (mult(a, mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))),
% 22.77/22.97 inference(monotonicity,[status(thm)],[6726])).
% 22.77/22.97 tff(6728,plain,
% 22.77/22.97 (mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))))),
% 22.77/22.97 inference(monotonicity,[status(thm)],[5299])).
% 22.77/22.97 tff(6729,plain,
% 22.77/22.97 (mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(b, c), c))),
% 22.77/22.97 inference(transitivity,[status(thm)],[6728, 6727, 6708, 6695])).
% 22.77/22.97 tff(6730,plain,
% 22.77/22.97 (ld(a, mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))))) = ld(a, mult(a, mult(mult(b, c), c)))),
% 22.77/22.97 inference(monotonicity,[status(thm)],[6729])).
% 22.77/22.97 tff(6731,plain,
% 22.77/22.97 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(a, mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))))) = mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))))),
% 22.77/22.97 inference(quant_inst,[status(thm)],[])).
% 22.77/22.97 tff(6732,plain,
% 22.77/22.97 (ld(a, mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))))) = mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 22.77/22.97 inference(unit_resolution,[status(thm)],[6731, 7])).
% 22.77/22.97 tff(6733,plain,
% 22.77/22.97 (mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = ld(a, mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))))),
% 22.77/22.97 inference(symmetry,[status(thm)],[6732])).
% 22.77/22.97 tff(6734,plain,
% 22.77/22.97 (mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))),
% 22.77/22.97 inference(transitivity,[status(thm)],[6733, 6730, 4537, 4178, 2803, 6693])).
% 22.77/22.97 tff(6735,plain,
% 22.77/22.97 (mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 22.77/22.97 inference(symmetry,[status(thm)],[6709])).
% 22.77/22.97 tff(6736,plain,
% 22.77/22.97 ((mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))) <=> (mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 22.77/22.97 inference(monotonicity,[status(thm)],[6735, 6693])).
% 22.77/22.97 tff(6737,plain,
% 22.77/22.97 ((~(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) <=> (~(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))),
% 22.77/22.97 inference(monotonicity,[status(thm)],[6736])).
% 22.77/22.97 tff(6738,plain,
% 22.77/22.97 (~(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 22.77/22.97 inference(modus_ponens,[status(thm)],[6689, 6737])).
% 22.77/22.97 tff(6739,plain,
% 22.77/22.97 ($false),
% 22.77/22.97 inference(unit_resolution,[status(thm)],[6738, 6734])).
% 22.77/22.97 tff(6740,plain,(((~(mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c))))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (mult(mult(mult(mult(a, c), c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))), a)) | (~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))) | (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a))))), inference(lemma,lemma(discharge,[]))).
% 22.77/22.97 tff(6741,plain,
% 22.77/22.97 (((~(mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (mult(mult(mult(mult(a, c), c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))), a)) | (~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))) | (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a))))),
% 22.77/22.97 inference(unit_resolution,[status(thm)],[6740, 3862])).
% 22.77/22.97 tff(6742,plain,
% 22.77/22.97 ((~(mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c))))),
% 22.77/22.97 inference(unit_resolution,[status(thm)],[6741, 6601, 270, 6583, 6582, 316, 4360, 1799, 6581])).
% 22.77/22.97 tff(6743,plain,
% 22.77/22.97 (~((~(mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))))),
% 22.77/22.97 inference(unit_resolution,[status(thm)],[2213, 6742])).
% 22.77/22.97 tff(6744,plain,
% 22.77/22.97 (mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))),
% 22.77/22.97 inference(unit_resolution,[status(thm)],[5118, 6743])).
% 22.77/22.97 tff(6745,plain,
% 22.77/22.97 (mult(b, a) = mult(c, ld(c, mult(a, b)))),
% 22.77/22.97 inference(transitivity,[status(thm)],[1444, 1182, 1185, 1441])).
% 22.77/22.97 tff(6746,plain,
% 22.77/22.97 (mult(c, mult(b, a)) = mult(c, mult(c, ld(c, mult(a, b))))),
% 22.77/22.97 inference(monotonicity,[status(thm)],[6745])).
% 22.77/22.97 tff(6747,plain,
% 22.77/22.97 (mult(c, mult(b, a)) = mult(c, mult(a, b))),
% 22.77/22.97 inference(transitivity,[status(thm)],[6746, 4225])).
% 22.77/22.97 tff(6748,plain,
% 22.77/22.97 (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))),
% 22.77/22.97 inference(unit_resolution,[status(thm)],[2242, 330, 6747, 6581])).
% 22.77/22.97 tff(6749,plain,
% 22.77/22.97 ((~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))),
% 22.77/22.97 inference(unit_resolution,[status(thm)],[4290, 6748])).
% 22.77/22.97 tff(6750,plain,
% 22.77/22.97 (~((~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))))),
% 22.77/22.97 inference(unit_resolution,[status(thm)],[4295, 6749])).
% 22.77/22.97 tff(6751,plain,
% 22.77/22.97 (mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))),
% 22.77/22.97 inference(unit_resolution,[status(thm)],[4328, 6750])).
% 22.77/22.97 tff(6752,plain,
% 22.77/22.97 ((mult(mult(mult(a, c), c), a) = mult(mult(a, c), mult(c, a))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))),
% 22.77/22.97 inference(unit_resolution,[status(thm)],[4781, 3862])).
% 22.77/22.97 tff(6753,plain,
% 22.77/22.97 (mult(mult(mult(a, c), c), a) = mult(mult(a, c), mult(c, a))),
% 22.77/22.97 inference(unit_resolution,[status(thm)],[6752, 6751])).
% 22.77/22.97 tff(6754,plain,
% 22.77/22.97 ((~(mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (mult(mult(mult(mult(a, c), c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))), a)) | (~(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), c), a) = mult(mult(a, c), mult(c, a))))),
% 22.77/22.97 inference(unit_resolution,[status(thm)],[4801, 3862])).
% 22.77/22.97 tff(6755,plain,
% 22.77/22.97 (~(mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 22.77/22.97 inference(unit_resolution,[status(thm)],[6754, 6753, 6601, 4495, 6583])).
% 22.77/22.97 tff(6756,plain,
% 22.77/22.97 ((~(mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(c, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))))),
% 22.77/22.97 inference(unit_resolution,[status(thm)],[4699, 6755])).
% 22.77/22.97 tff(6757,plain,
% 22.77/22.97 (~((~(mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(c, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)))))),
% 22.77/22.97 inference(unit_resolution,[status(thm)],[4697, 6756])).
% 22.77/22.97 tff(6758,plain,
% 22.77/22.97 (mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 22.77/22.97 inference(unit_resolution,[status(thm)],[4685, 6757])).
% 22.77/22.97 tff(6759,plain,
% 22.77/22.97 (mult(mult(c, a), mult(b, c)) = mult(mult(a, c), mult(b, c))),
% 22.77/22.97 inference(monotonicity,[status(thm)],[5700])).
% 22.77/22.97 tff(6760,plain,
% 22.77/22.97 (mult(mult(c, a), mult(b, c)) = mult(mult(a, mult(b, c)), c)),
% 22.77/22.97 inference(transitivity,[status(thm)],[6759, 266])).
% 22.77/22.97 tff(6761,plain,
% 22.77/22.97 (mult(mult(c, a), b) = mult(mult(a, c), b)),
% 22.77/22.97 inference(monotonicity,[status(thm)],[5700])).
% 22.77/22.97 tff(6762,plain,
% 22.77/22.97 (mult(mult(b, c), a) = mult(mult(a, c), b)),
% 22.77/22.97 inference(transitivity,[status(thm)],[3892, 4208, 6746, 4225, 4270, 6761])).
% 22.77/22.97 tff(6763,plain,
% 22.77/22.97 (mult(mult(mult(b, c), a), c) = mult(mult(mult(a, c), b), c)),
% 22.77/22.97 inference(monotonicity,[status(thm)],[6762])).
% 22.77/22.97 tff(6764,plain,
% 22.77/22.97 (mult(mult(mult(a, c), c), mult(c, a)) = mult(mult(mult(a, c), c), mult(a, c))),
% 22.77/22.97 inference(monotonicity,[status(thm)],[5700])).
% 22.77/22.97 tff(6765,plain,
% 22.77/22.97 ((mult(b, mult(c, mult(a, c))) = mult(mult(b, c), mult(a, c))) <=> (mult(mult(b, c), mult(a, c)) = mult(b, mult(c, mult(a, c))))),
% 22.77/22.97 inference(commutativity,[status(thm)],[])).
% 22.77/22.97 tff(6766,plain,
% 22.77/22.97 (mult(mult(mult(b, c), a), c) = mult(b, mult(c, mult(a, c)))),
% 22.77/22.97 inference(transitivity,[status(thm)],[2570, 4396])).
% 22.77/22.97 tff(6767,plain,
% 22.77/22.97 ((mult(mult(mult(b, c), a), c) = mult(mult(b, c), mult(a, c))) <=> (mult(b, mult(c, mult(a, c))) = mult(mult(b, c), mult(a, c)))),
% 22.77/22.97 inference(monotonicity,[status(thm)],[6766])).
% 22.77/22.97 tff(6768,plain,
% 22.77/22.97 ((mult(mult(mult(b, c), a), c) = mult(mult(b, c), mult(a, c))) <=> (mult(mult(b, c), mult(a, c)) = mult(b, mult(c, mult(a, c))))),
% 22.77/22.97 inference(transitivity,[status(thm)],[6767, 6765])).
% 22.77/22.97 tff(6769,plain,
% 22.77/22.97 (mult(mult(mult(b, c), a), c) = mult(mult(b, c), mult(a, c))),
% 22.77/22.97 inference(unit_resolution,[status(thm)],[2576, 4164])).
% 22.77/22.97 tff(6770,plain,
% 22.77/22.97 (mult(mult(b, c), mult(a, c)) = mult(b, mult(c, mult(a, c)))),
% 22.77/22.97 inference(modus_ponens,[status(thm)],[6769, 6768])).
% 22.77/22.97 tff(6771,plain,
% 22.77/22.97 (~(mult(mult(b, c), mult(a, c)) = mult(b, mult(c, mult(a, c))))),
% 22.77/22.97 inference(unit_resolution,[status(thm)],[4170, 4162, 4155])).
% 22.77/22.97 tff(6772,plain,
% 22.77/22.97 ($false),
% 22.77/22.97 inference(unit_resolution,[status(thm)],[6771, 6770])).
% 22.77/22.97 tff(6773,plain,((mult(mult(mult(b, c), c), a) = mult(mult(mult(b, c), a), c)) | (~(mult(mult(mult(a, c), c), mult(c, a)) = mult(mult(mult(a, c), c), mult(a, c))))), inference(lemma,lemma(discharge,[]))).
% 22.77/22.97 tff(6774,plain,
% 22.77/22.97 (mult(mult(mult(b, c), c), a) = mult(mult(mult(b, c), a), c)),
% 22.77/22.97 inference(unit_resolution,[status(thm)],[6773, 6764])).
% 22.77/22.97 tff(6775,plain,
% 22.77/22.97 (mult(mult(c, mult(b, c)), a) = mult(a, mult(mult(b, c), c))),
% 22.77/22.97 inference(transitivity,[status(thm)],[4181, 6774, 6763, 233, 2414])).
% 22.77/22.97 tff(6776,plain,
% 22.77/22.97 ((mult(mult(c, mult(b, c)), a) = mult(mult(c, a), mult(b, c))) <=> (mult(a, mult(mult(b, c), c)) = mult(mult(a, mult(b, c)), c))),
% 22.77/22.97 inference(monotonicity,[status(thm)],[6775, 6760])).
% 22.77/22.97 tff(6777,plain,
% 22.77/22.97 ((mult(mult(c, mult(b, c)), a) = mult(mult(c, a), mult(b, c))) <=> (mult(mult(a, mult(b, c)), c) = mult(a, mult(mult(b, c), c)))),
% 22.77/22.98 inference(transitivity,[status(thm)],[6776, 2412])).
% 22.77/22.98 tff(6778,plain,
% 22.77/22.98 ((mult(mult(a, mult(b, c)), c) = mult(a, mult(mult(b, c), c))) <=> (mult(mult(c, mult(b, c)), a) = mult(mult(c, a), mult(b, c)))),
% 22.77/22.98 inference(symmetry,[status(thm)],[6777])).
% 22.77/22.98 tff(6779,plain,
% 22.77/22.98 ((~(mult(mult(a, mult(b, c)), c) = mult(a, mult(mult(b, c), c)))) <=> (~(mult(mult(c, mult(b, c)), a) = mult(mult(c, a), mult(b, c))))),
% 22.77/22.98 inference(monotonicity,[status(thm)],[6778])).
% 22.77/22.98 tff(6780,plain,
% 22.77/22.98 (~(mult(mult(c, mult(b, c)), a) = mult(mult(c, a), mult(b, c)))),
% 22.77/22.98 inference(modus_ponens,[status(thm)],[258, 6779])).
% 22.77/22.98 tff(6781,plain,
% 22.77/22.98 ((~(mult(mult(c, mult(b, c)), a) = mult(mult(c, a), mult(b, c)))) | (~(mult(c, mult(mult(b, c), a)) = mult(c, mult(a, mult(b, c)))))),
% 22.77/22.98 inference(unit_resolution,[status(thm)],[4194, 6780])).
% 22.77/22.98 tff(6782,plain,
% 22.77/22.98 (~((~(mult(mult(c, mult(b, c)), a) = mult(c, mult(mult(b, c), a)))) | (~(mult(mult(c, a), mult(b, c)) = mult(c, mult(a, mult(b, c))))))),
% 22.77/22.98 inference(unit_resolution,[status(thm)],[4199, 6781])).
% 22.77/22.98 tff(6783,plain,
% 22.77/22.98 (((~(mult(mult(c, mult(b, c)), a) = mult(c, mult(mult(b, c), a)))) | (~(mult(mult(c, a), mult(b, c)) = mult(c, mult(a, mult(b, c)))))) | (mult(mult(c, a), mult(b, c)) = mult(c, mult(a, mult(b, c))))),
% 22.77/22.98 inference(tautology,[status(thm)],[])).
% 22.77/22.98 tff(6784,plain,
% 22.77/22.98 (mult(mult(c, a), mult(b, c)) = mult(c, mult(a, mult(b, c)))),
% 22.77/22.98 inference(unit_resolution,[status(thm)],[6783, 6782])).
% 22.77/22.98 tff(6785,plain,
% 22.77/22.98 (mult(c, mult(a, mult(b, c))) = mult(mult(c, a), mult(b, c))),
% 22.77/22.98 inference(symmetry,[status(thm)],[6784])).
% 22.77/22.98 tff(6786,plain,
% 22.77/22.98 (mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))) = mult(c, mult(a, mult(b, c)))),
% 22.77/22.98 inference(monotonicity,[status(thm)],[4286])).
% 22.77/22.98 tff(6787,plain,
% 22.77/22.98 (mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))),
% 22.77/22.98 inference(transitivity,[status(thm)],[6786, 6785, 6759, 139])).
% 22.77/22.98 tff(6788,plain,
% 22.77/22.98 (mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 22.77/22.98 inference(monotonicity,[status(thm)],[5700])).
% 22.77/22.98 tff(6789,plain,
% 22.77/22.98 (mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))) = mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 22.77/22.98 inference(symmetry,[status(thm)],[6758])).
% 22.77/22.98 tff(6790,plain,
% 22.77/22.98 (ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c)))) = ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))),
% 22.77/22.98 inference(monotonicity,[status(thm)],[6751])).
% 22.77/22.98 tff(6791,plain,
% 22.77/22.98 (mult(a, mult(a, c)) = mult(mult(a, c), a)),
% 22.77/22.98 inference(transitivity,[status(thm)],[4452, 6790, 4447])).
% 22.77/22.98 tff(6792,plain,
% 22.77/22.98 (mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))),
% 22.77/22.98 inference(monotonicity,[status(thm)],[6791])).
% 22.77/22.98 tff(6793,plain,
% 22.77/22.98 (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 22.77/22.98 inference(symmetry,[status(thm)],[6792])).
% 22.77/22.98 tff(6794,plain,
% 22.77/22.98 (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 22.77/22.98 inference(transitivity,[status(thm)],[6793, 281])).
% 22.77/22.98 tff(6795,plain,
% 22.77/22.98 (mult(c, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 22.77/22.98 inference(monotonicity,[status(thm)],[6794])).
% 22.77/22.98 tff(6796,plain,
% 22.77/22.98 (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))),
% 22.77/22.98 inference(symmetry,[status(thm)],[6582])).
% 22.77/22.98 tff(6797,plain,
% 22.77/22.98 (mult(c, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))))),
% 22.77/22.98 inference(monotonicity,[status(thm)],[6796])).
% 22.77/22.98 tff(6798,plain,
% 22.77/22.98 (mult(c, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 22.77/22.98 inference(transitivity,[status(thm)],[6797, 6795, 6789, 6788])).
% 22.77/22.98 tff(6799,plain,
% 22.77/22.98 ((mult(c, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))) <=> (mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))),
% 22.77/22.98 inference(monotonicity,[status(thm)],[6798, 6787])).
% 22.77/22.98 tff(6800,plain,
% 22.77/22.98 ((mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))) <=> (mult(c, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))))),
% 22.77/22.98 inference(symmetry,[status(thm)],[6799])).
% 22.77/22.98 tff(6801,plain,
% 22.77/22.98 ((~(mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) <=> (~(mult(c, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))))),
% 22.77/22.98 inference(monotonicity,[status(thm)],[6800])).
% 22.77/22.98 tff(6802,plain,
% 22.77/22.98 (~(mult(c, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))))),
% 22.77/22.98 inference(modus_ponens,[status(thm)],[307, 6801])).
% 22.77/22.98 tff(6803,plain,
% 22.77/22.98 (((~(mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c)))) | (~(mult(c, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))))) | (mult(c, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))))),
% 22.77/22.98 inference(tautology,[status(thm)],[])).
% 22.77/22.98 tff(6804,plain,
% 22.77/22.98 ((~(mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c)))) | (~(mult(c, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))))),
% 22.77/22.98 inference(unit_resolution,[status(thm)],[6803, 6802])).
% 22.77/22.98 tff(6805,plain,
% 22.77/22.98 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c)))) | (~(mult(c, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))))))) | (~((~(mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(c, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c)))) | (~(mult(c, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))))))) | (~((~(mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(c, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))))))))),
% 22.77/22.98 inference(rewrite,[status(thm)],[])).
% 22.77/22.98 tff(6806,plain,
% 22.77/22.98 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c)))) | (~(mult(c, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))))))) | (~((~(mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(c, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))))))))),
% 22.77/22.98 inference(quant_inst,[status(thm)],[])).
% 22.77/22.98 tff(6807,plain,
% 22.77/22.98 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c)))) | (~(mult(c, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))))))) | (~((~(mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(c, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))))))),
% 22.77/22.98 inference(modus_ponens,[status(thm)],[6806, 6805])).
% 22.77/22.98 tff(6808,plain,
% 22.77/22.98 ((~((~(mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c)))) | (~(mult(c, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))))))) | (~((~(mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(c, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))))))),
% 22.77/22.98 inference(unit_resolution,[status(thm)],[6807, 27])).
% 22.77/22.98 tff(6809,plain,
% 22.77/22.98 (~((~(mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(c, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))))))),
% 22.77/22.98 inference(unit_resolution,[status(thm)],[6808, 6804])).
% 22.77/22.98 tff(6810,plain,
% 22.77/22.98 (((~(mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(c, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))))) | (mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(c, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))))),
% 22.77/22.98 inference(tautology,[status(thm)],[])).
% 22.77/22.98 tff(6811,plain,
% 22.77/22.98 (mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(c, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))),
% 22.77/22.98 inference(unit_resolution,[status(thm)],[6810, 6809])).
% 22.77/22.98 tff(6812,plain,
% 22.77/22.98 (~((~(mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)))))),
% 22.77/22.98 inference(unit_resolution,[status(thm)],[2406, 6584])).
% 22.77/22.98 tff(6813,plain,
% 22.77/22.98 (mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c))))),
% 22.77/22.98 inference(unit_resolution,[status(thm)],[5253, 6812])).
% 22.77/22.98 tff(6814,plain,
% 22.77/22.98 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))),
% 22.77/22.98 inference(quant_inst,[status(thm)],[])).
% 22.77/22.98 tff(6815,plain,
% 22.77/22.98 (ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))),
% 22.77/22.98 inference(unit_resolution,[status(thm)],[6814, 7])).
% 22.77/22.98 tff(6816,plain,
% 22.77/22.98 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c)))),
% 22.77/22.98 inference(symmetry,[status(thm)],[5698])).
% 22.77/22.98 tff(6817,plain,
% 22.77/22.98 (mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))))),
% 22.77/22.98 inference(monotonicity,[status(thm)],[6816])).
% 22.77/22.98 tff(6818,plain,
% 22.77/22.98 (mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c)))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))),
% 22.77/22.98 inference(symmetry,[status(thm)],[6817])).
% 22.77/22.98 tff(6819,assumption,(mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c))))), introduced(assumption)).
% 22.77/22.98 tff(6820,assumption,(mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(c, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))), introduced(assumption)).
% 22.77/22.98 tff(6821,plain,
% 22.77/22.98 (mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))))),
% 22.77/22.98 inference(monotonicity,[status(thm)],[4718])).
% 22.77/22.98 tff(6822,plain,
% 22.77/22.98 (mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c)))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))),
% 22.77/22.98 inference(symmetry,[status(thm)],[6821])).
% 22.77/22.98 tff(6823,assumption,(~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, mult(a, c))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c)))))), introduced(assumption)).
% 22.77/22.98 tff(6824,plain,
% 22.77/22.98 (((~(mult(mult(c, mult(a, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, mult(a, c))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))))))) | (mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, mult(a, c))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c)))))),
% 22.77/22.98 inference(tautology,[status(thm)],[])).
% 22.77/22.98 tff(6825,plain,
% 22.77/22.98 ((~(mult(mult(c, mult(a, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, mult(a, c))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))))))),
% 22.77/22.98 inference(unit_resolution,[status(thm)],[6824, 6823])).
% 22.77/22.98 tff(6826,plain,
% 22.77/22.98 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c)))) = mult(c, mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, mult(a, c))) = mult(mult(c, mult(a, mult(a, c))), rd(mult(b, c), mult(a, c))))))) | (~((~(mult(mult(c, mult(a, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, mult(a, c))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c)))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c)))) = mult(c, mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, mult(a, c))) = mult(mult(c, mult(a, mult(a, c))), rd(mult(b, c), mult(a, c))))))) | (~((~(mult(mult(c, mult(a, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, mult(a, c))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c)))))))))),
% 22.77/22.99 inference(rewrite,[status(thm)],[])).
% 22.77/22.99 tff(6827,plain,
% 22.77/22.99 (((~((~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, mult(a, c))) = mult(mult(c, mult(a, mult(a, c))), rd(mult(b, c), mult(a, c))))) | (~(mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c)))) = mult(c, mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, mult(a, c))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c)))))) | (~(mult(mult(c, mult(a, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))))))))) <=> ((~((~(mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c)))) = mult(c, mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, mult(a, c))) = mult(mult(c, mult(a, mult(a, c))), rd(mult(b, c), mult(a, c))))))) | (~((~(mult(mult(c, mult(a, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, mult(a, c))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c)))))))))),
% 22.77/22.99 inference(rewrite,[status(thm)],[])).
% 22.77/22.99 tff(6828,plain,
% 22.77/22.99 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, mult(a, c))) = mult(mult(c, mult(a, mult(a, c))), rd(mult(b, c), mult(a, c))))) | (~(mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c)))) = mult(c, mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, mult(a, c))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c)))))) | (~(mult(mult(c, mult(a, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c)))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c)))) = mult(c, mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, mult(a, c))) = mult(mult(c, mult(a, mult(a, c))), rd(mult(b, c), mult(a, c))))))) | (~((~(mult(mult(c, mult(a, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, mult(a, c))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))))))))))),
% 22.77/22.99 inference(monotonicity,[status(thm)],[6827])).
% 22.77/22.99 tff(6829,plain,
% 22.77/22.99 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, mult(a, c))) = mult(mult(c, mult(a, mult(a, c))), rd(mult(b, c), mult(a, c))))) | (~(mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c)))) = mult(c, mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, mult(a, c))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c)))))) | (~(mult(mult(c, mult(a, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c)))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c)))) = mult(c, mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, mult(a, c))) = mult(mult(c, mult(a, mult(a, c))), rd(mult(b, c), mult(a, c))))))) | (~((~(mult(mult(c, mult(a, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, mult(a, c))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c)))))))))),
% 22.77/22.99 inference(transitivity,[status(thm)],[6828, 6826])).
% 22.77/22.99 tff(6830,plain,
% 22.77/22.99 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, mult(a, c))) = mult(mult(c, mult(a, mult(a, c))), rd(mult(b, c), mult(a, c))))) | (~(mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c)))) = mult(c, mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, mult(a, c))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c)))))) | (~(mult(mult(c, mult(a, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c)))))))))),
% 22.77/22.99 inference(quant_inst,[status(thm)],[])).
% 22.77/22.99 tff(6831,plain,
% 22.77/22.99 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c)))) = mult(c, mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, mult(a, c))) = mult(mult(c, mult(a, mult(a, c))), rd(mult(b, c), mult(a, c))))))) | (~((~(mult(mult(c, mult(a, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, mult(a, c))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))))))))),
% 22.77/22.99 inference(modus_ponens,[status(thm)],[6830, 6829])).
% 22.77/22.99 tff(6832,plain,
% 22.77/22.99 ((~((~(mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c)))) = mult(c, mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, mult(a, c))) = mult(mult(c, mult(a, mult(a, c))), rd(mult(b, c), mult(a, c))))))) | (~((~(mult(mult(c, mult(a, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, mult(a, c))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))))))))),
% 22.77/22.99 inference(unit_resolution,[status(thm)],[6831, 27])).
% 22.77/22.99 tff(6833,plain,
% 22.77/22.99 (~((~(mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c)))) = mult(c, mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, mult(a, c))) = mult(mult(c, mult(a, mult(a, c))), rd(mult(b, c), mult(a, c))))))),
% 22.77/22.99 inference(unit_resolution,[status(thm)],[6832, 6825])).
% 22.77/22.99 tff(6834,plain,
% 22.77/22.99 (((~(mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c)))) = mult(c, mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, mult(a, c))) = mult(mult(c, mult(a, mult(a, c))), rd(mult(b, c), mult(a, c)))))) | (mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c)))) = mult(c, mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c)))))),
% 22.77/22.99 inference(tautology,[status(thm)],[])).
% 22.77/22.99 tff(6835,plain,
% 22.77/22.99 (mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c)))) = mult(c, mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))))),
% 22.77/22.99 inference(unit_resolution,[status(thm)],[6834, 6833])).
% 22.77/22.99 tff(6836,plain,
% 22.77/22.99 (mult(c, mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c)))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))))),
% 22.77/22.99 inference(symmetry,[status(thm)],[6835])).
% 22.77/22.99 tff(6837,plain,
% 22.77/22.99 (mult(c, mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 22.77/22.99 inference(monotonicity,[status(thm)],[299])).
% 22.77/22.99 tff(6838,plain,
% 22.77/22.99 (mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))) = mult(c, mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))))),
% 22.77/22.99 inference(symmetry,[status(thm)],[6837])).
% 22.77/22.99 tff(6839,plain,
% 22.77/22.99 (mult(c, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 22.77/22.99 inference(symmetry,[status(thm)],[4678])).
% 22.77/22.99 tff(6840,plain,
% 22.77/22.99 (mult(c, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))) = mult(c, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))),
% 22.77/22.99 inference(monotonicity,[status(thm)],[2319])).
% 22.77/22.99 tff(6841,plain,
% 22.77/22.99 (mult(c, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))))),
% 22.77/22.99 inference(symmetry,[status(thm)],[6840])).
% 22.77/22.99 tff(6842,plain,
% 22.77/22.99 (mult(mult(mult(c, a), c), a) = mult(mult(c, mult(a, c)), a)),
% 22.77/22.99 inference(monotonicity,[status(thm)],[2690])).
% 22.77/22.99 tff(6843,plain,
% 22.77/22.99 (mult(mult(c, mult(a, c)), a) = mult(mult(mult(c, a), c), a)),
% 22.77/22.99 inference(symmetry,[status(thm)],[6842])).
% 22.77/22.99 tff(6844,plain,
% 22.77/22.99 (mult(mult(c, mult(a, c)), a) = mult(c, mult(mult(a, c), a))),
% 22.77/22.99 inference(transitivity,[status(thm)],[6843, 2561])).
% 22.77/22.99 tff(6845,plain,
% 22.77/22.99 (mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))) = mult(mult(c, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c)))),
% 22.77/22.99 inference(monotonicity,[status(thm)],[6844])).
% 22.77/22.99 tff(6846,plain,
% 22.77/22.99 (mult(mult(c, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c)))),
% 22.77/22.99 inference(symmetry,[status(thm)],[6845])).
% 22.77/22.99 tff(6847,plain,
% 22.77/22.99 (mult(c, mult(a, mult(a, c))) = mult(c, mult(mult(a, c), a))),
% 22.77/22.99 inference(monotonicity,[status(thm)],[4519])).
% 22.77/22.99 tff(6848,plain,
% 22.77/22.99 (mult(c, mult(mult(a, c), a)) = mult(c, mult(a, mult(a, c)))),
% 22.77/22.99 inference(symmetry,[status(thm)],[6847])).
% 22.77/22.99 tff(6849,plain,
% 22.77/22.99 (mult(mult(c, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(mult(c, mult(a, mult(a, c))), rd(mult(b, c), mult(a, c)))),
% 22.77/22.99 inference(monotonicity,[status(thm)],[6848])).
% 22.77/22.99 tff(6850,plain,
% 22.77/22.99 (mult(mult(c, mult(a, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(c, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c)))),
% 22.77/22.99 inference(symmetry,[status(thm)],[6849])).
% 22.77/22.99 tff(6851,plain,
% 22.77/22.99 (((~(mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c)))) = mult(c, mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, mult(a, c))) = mult(mult(c, mult(a, mult(a, c))), rd(mult(b, c), mult(a, c)))))) | (mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, mult(a, c))) = mult(mult(c, mult(a, mult(a, c))), rd(mult(b, c), mult(a, c))))),
% 22.77/22.99 inference(tautology,[status(thm)],[])).
% 22.77/22.99 tff(6852,plain,
% 22.77/22.99 (mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, mult(a, c))) = mult(mult(c, mult(a, mult(a, c))), rd(mult(b, c), mult(a, c)))),
% 22.77/22.99 inference(unit_resolution,[status(thm)],[6851, 6833])).
% 22.77/22.99 tff(6853,plain,
% 22.77/22.99 (mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, mult(a, c))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a))),
% 22.77/22.99 inference(monotonicity,[status(thm)],[4519])).
% 22.77/22.99 tff(6854,plain,
% 22.77/22.99 (mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, mult(a, c)))),
% 22.77/22.99 inference(symmetry,[status(thm)],[6853])).
% 22.77/22.99 tff(6855,plain,
% 22.77/22.99 (mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))),
% 22.77/22.99 inference(transitivity,[status(thm)],[6854, 6852, 6850, 6846, 6819, 6820, 6841, 6839, 6838, 6836, 6822])).
% 22.77/22.99 tff(6856,plain,
% 22.77/22.99 ((mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, mult(a, c))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))))) <=> (mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))),
% 22.77/22.99 inference(monotonicity,[status(thm)],[6853, 6822])).
% 22.77/22.99 tff(6857,plain,
% 22.77/22.99 ((~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, mult(a, c))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c)))))) <=> (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))))),
% 22.77/22.99 inference(monotonicity,[status(thm)],[6856])).
% 22.77/22.99 tff(6858,plain,
% 22.77/22.99 (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))),
% 22.77/22.99 inference(modus_ponens,[status(thm)],[6823, 6857])).
% 22.77/22.99 tff(6859,plain,
% 22.77/22.99 ($false),
% 22.77/22.99 inference(unit_resolution,[status(thm)],[6858, 6855])).
% 22.77/22.99 tff(6860,plain,((mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, mult(a, c))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))))) | (~(mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(c, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))), inference(lemma,lemma(discharge,[]))).
% 22.77/22.99 tff(6861,plain,
% 22.77/22.99 (mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, mult(a, c))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))))),
% 22.77/22.99 inference(unit_resolution,[status(thm)],[6860, 6820, 6819, 2319, 299, 5698])).
% 22.77/22.99 tff(6862,plain,
% 22.77/22.99 (mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, mult(a, c))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a))),
% 22.77/22.99 inference(monotonicity,[status(thm)],[6352])).
% 22.77/22.99 tff(6863,plain,
% 22.77/22.99 (mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, mult(a, c)))),
% 22.77/22.99 inference(symmetry,[status(thm)],[6862])).
% 22.77/22.99 tff(6864,plain,
% 22.77/22.99 (mult(mult(c, a), a) = mult(mult(a, c), a)),
% 22.77/22.99 inference(monotonicity,[status(thm)],[5700])).
% 22.77/22.99 tff(6865,plain,
% 22.77/22.99 (mult(mult(a, c), a) = mult(mult(c, a), a)),
% 22.77/22.99 inference(symmetry,[status(thm)],[6864])).
% 22.77/22.99 tff(6866,plain,
% 22.77/22.99 (mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(c, a), a))),
% 22.77/22.99 inference(monotonicity,[status(thm)],[5203, 6865])).
% 22.77/22.99 tff(6867,plain,
% 22.77/22.99 (mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(c, a), a)) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a))),
% 22.77/22.99 inference(symmetry,[status(thm)],[6866])).
% 22.77/22.99 tff(6868,plain,
% 22.77/22.99 (mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(c, a), a)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a))),
% 22.77/22.99 inference(monotonicity,[status(thm)],[6864])).
% 22.77/22.99 tff(6869,plain,
% 22.77/22.99 (mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(c, a), a))),
% 22.77/22.99 inference(symmetry,[status(thm)],[6868])).
% 22.77/22.99 tff(6870,plain,
% 22.77/22.99 (mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))),
% 22.77/22.99 inference(transitivity,[status(thm)],[2627, 4857, 4859])).
% 22.77/22.99 tff(6871,plain,
% 22.77/22.99 (mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c), a) = mult(mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))), a)),
% 22.77/22.99 inference(monotonicity,[status(thm)],[6870])).
% 22.77/22.99 tff(6872,plain,
% 22.77/22.99 (mult(mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))), a) = mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c), a)),
% 22.77/22.99 inference(symmetry,[status(thm)],[6871])).
% 22.77/22.99 tff(6873,plain,
% 22.77/22.99 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), unit) = mult(mult(rd(mult(b, c), mult(a, c)), c), a)),
% 22.77/22.99 inference(transitivity,[status(thm)],[1875, 1871, 4489, 4488])).
% 22.77/22.99 tff(6874,plain,
% 22.77/22.99 (mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), unit), c) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c)),
% 22.84/23.00 inference(monotonicity,[status(thm)],[6873])).
% 22.84/23.00 tff(6875,plain,
% 22.84/23.00 (mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c) = mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), unit), c)),
% 22.84/23.00 inference(symmetry,[status(thm)],[6874])).
% 22.84/23.00 tff(6876,plain,
% 22.84/23.00 (mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))),
% 22.84/23.00 inference(transitivity,[status(thm)],[4860, 4858, 4855, 6875, 4654, 5994])).
% 22.84/23.00 tff(6877,plain,
% 22.84/23.00 (mult(mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)), a)),
% 22.84/23.00 inference(monotonicity,[status(thm)],[6876])).
% 22.84/23.00 tff(6878,plain,
% 22.84/23.00 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)), a) = mult(mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))), a)),
% 22.84/23.00 inference(symmetry,[status(thm)],[6877])).
% 22.84/23.00 tff(6879,assumption,(mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))), introduced(assumption)).
% 22.84/23.00 tff(6880,plain,
% 22.84/23.00 (mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))) = mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 22.84/23.00 inference(symmetry,[status(thm)],[6879])).
% 22.84/23.00 tff(6881,plain,
% 22.84/23.00 (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 22.84/23.00 inference(symmetry,[status(thm)],[6353])).
% 22.84/23.00 tff(6882,plain,
% 22.84/23.00 (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 22.84/23.00 inference(transitivity,[status(thm)],[6881, 299])).
% 22.84/23.00 tff(6883,plain,
% 22.84/23.00 (mult(c, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 22.84/23.00 inference(monotonicity,[status(thm)],[6882])).
% 22.84/23.00 tff(6884,plain,
% 22.84/23.00 (mult(c, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))))),
% 22.84/23.00 inference(monotonicity,[status(thm)],[6663])).
% 22.84/23.00 tff(6885,plain,
% 22.84/23.00 (mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 22.84/23.00 inference(transitivity,[status(thm)],[6819, 6820, 6884, 6883, 6880, 6788, 5322])).
% 22.84/23.00 tff(6886,plain,
% 22.84/23.00 (rd(mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))), rd(mult(b, c), mult(a, c))) = rd(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))), rd(mult(b, c), mult(a, c)))),
% 22.84/23.00 inference(monotonicity,[status(thm)],[6885])).
% 22.84/23.00 tff(6887,plain,
% 22.84/23.00 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(c, mult(a, c)), a))),
% 22.84/23.00 inference(quant_inst,[status(thm)],[])).
% 22.84/23.00 tff(6888,plain,
% 22.84/23.00 (rd(mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(c, mult(a, c)), a)),
% 22.84/23.00 inference(unit_resolution,[status(thm)],[6887, 168])).
% 22.84/23.00 tff(6889,plain,
% 22.84/23.00 (mult(mult(c, mult(a, c)), a) = rd(mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))), rd(mult(b, c), mult(a, c)))),
% 22.84/23.00 inference(symmetry,[status(thm)],[6888])).
% 22.84/23.00 tff(6890,plain,
% 22.84/23.00 (ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(a, c))) = ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(c, a)))),
% 22.84/23.00 inference(symmetry,[status(thm)],[4263])).
% 22.84/23.00 tff(6891,plain,
% 22.84/23.00 (mult(a, c) = mult(c, a)),
% 22.84/23.00 inference(transitivity,[status(thm)],[3873, 6890, 3864])).
% 22.84/23.00 tff(6892,plain,
% 22.84/23.00 (mult(mult(a, c), c) = mult(mult(c, a), c)),
% 22.84/23.00 inference(monotonicity,[status(thm)],[6891])).
% 22.84/23.00 tff(6893,plain,
% 22.84/23.00 (mult(mult(a, c), c) = mult(c, mult(a, c))),
% 22.84/23.00 inference(transitivity,[status(thm)],[6892, 2690])).
% 22.84/23.00 tff(6894,plain,
% 22.84/23.00 (mult(mult(mult(a, c), c), a) = mult(mult(c, mult(a, c)), a)),
% 22.84/23.00 inference(monotonicity,[status(thm)],[6893])).
% 22.84/23.00 tff(6895,plain,
% 22.84/23.00 (mult(mult(a, mult(c, c)), a) = mult(mult(mult(a, c), unit), mult(a, c))),
% 22.84/23.00 inference(transitivity,[status(thm)],[4662, 6894, 6889, 6886, 4808, 2504])).
% 22.84/23.00 tff(6896,plain,
% 22.84/23.00 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(c, c)), a)) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), unit), mult(a, c)))),
% 22.84/23.00 inference(monotonicity,[status(thm)],[6895])).
% 22.84/23.00 tff(6897,plain,
% 22.84/23.00 (mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), unit), mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(c, c)), a))),
% 22.84/23.00 inference(symmetry,[status(thm)],[6896])).
% 22.84/23.00 tff(6898,plain,
% 22.84/23.00 (mult(b, mult(c, a)) = mult(b, mult(a, c))),
% 22.84/23.00 inference(monotonicity,[status(thm)],[5700])).
% 22.84/23.00 tff(6899,plain,
% 22.84/23.00 (mult(c, mult(b, mult(c, a))) = mult(c, mult(b, mult(a, c)))),
% 22.84/23.00 inference(monotonicity,[status(thm)],[6898])).
% 22.84/23.00 tff(6900,plain,
% 22.84/23.00 (mult(mult(b, c), mult(c, a)) = mult(mult(b, c), mult(a, c))),
% 22.84/23.00 inference(monotonicity,[status(thm)],[5700])).
% 22.84/23.00 tff(6901,plain,
% 22.84/23.00 (mult(mult(c, b), mult(c, a)) = mult(mult(c, b), mult(a, c))),
% 22.84/23.00 inference(transitivity,[status(thm)],[2231, 6900, 2742])).
% 22.84/23.00 tff(6902,plain,
% 22.84/23.00 ((mult(mult(c, b), mult(c, a)) = mult(c, mult(b, mult(c, a)))) <=> (mult(mult(c, b), mult(a, c)) = mult(c, mult(b, mult(a, c))))),
% 22.84/23.00 inference(monotonicity,[status(thm)],[6901, 6899])).
% 22.84/23.00 tff(6903,plain,
% 22.84/23.00 ((mult(mult(c, b), mult(a, c)) = mult(mult(c, mult(a, c)), b)) <=> (mult(mult(c, mult(a, c)), b) = mult(mult(c, b), mult(a, c)))),
% 22.84/23.00 inference(commutativity,[status(thm)],[])).
% 22.84/23.00 tff(6904,plain,
% 22.84/23.00 (mult(c, mult(mult(c, a), b)) = mult(c, mult(mult(a, c), b))),
% 22.84/23.00 inference(monotonicity,[status(thm)],[3886])).
% 22.84/23.00 tff(6905,plain,
% 22.84/23.00 (((~(mult(mult(c, mult(c, a)), b) = mult(c, mult(mult(c, a), b)))) | (~(mult(mult(c, b), mult(c, a)) = mult(c, mult(b, mult(c, a)))))) | (mult(mult(c, b), mult(c, a)) = mult(c, mult(b, mult(c, a))))),
% 22.84/23.00 inference(tautology,[status(thm)],[])).
% 22.84/23.00 tff(6906,plain,
% 22.84/23.00 ((~(mult(mult(c, mult(c, a)), b) = mult(c, mult(mult(c, a), b)))) | (~(mult(mult(c, b), mult(c, a)) = mult(c, mult(b, mult(c, a)))))),
% 22.84/23.00 inference(unit_resolution,[status(thm)],[6905, 5080])).
% 22.84/23.00 tff(6907,plain,
% 22.84/23.00 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(c, mult(c, a)), b) = mult(mult(c, b), mult(c, a)))) | (~(mult(c, mult(mult(c, a), b)) = mult(c, mult(b, mult(c, a))))))) | (~((~(mult(mult(c, mult(c, a)), b) = mult(c, mult(mult(c, a), b)))) | (~(mult(mult(c, b), mult(c, a)) = mult(c, mult(b, mult(c, a))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(c, mult(c, a)), b) = mult(mult(c, b), mult(c, a)))) | (~(mult(c, mult(mult(c, a), b)) = mult(c, mult(b, mult(c, a))))))) | (~((~(mult(mult(c, mult(c, a)), b) = mult(c, mult(mult(c, a), b)))) | (~(mult(mult(c, b), mult(c, a)) = mult(c, mult(b, mult(c, a))))))))),
% 22.84/23.00 inference(rewrite,[status(thm)],[])).
% 22.84/23.00 tff(6908,plain,
% 22.84/23.00 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(c, mult(c, a)), b) = mult(mult(c, b), mult(c, a)))) | (~(mult(c, mult(mult(c, a), b)) = mult(c, mult(b, mult(c, a))))))) | (~((~(mult(mult(c, mult(c, a)), b) = mult(c, mult(mult(c, a), b)))) | (~(mult(mult(c, b), mult(c, a)) = mult(c, mult(b, mult(c, a))))))))),
% 22.84/23.00 inference(quant_inst,[status(thm)],[])).
% 22.84/23.00 tff(6909,plain,
% 22.84/23.00 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(c, mult(c, a)), b) = mult(mult(c, b), mult(c, a)))) | (~(mult(c, mult(mult(c, a), b)) = mult(c, mult(b, mult(c, a))))))) | (~((~(mult(mult(c, mult(c, a)), b) = mult(c, mult(mult(c, a), b)))) | (~(mult(mult(c, b), mult(c, a)) = mult(c, mult(b, mult(c, a)))))))),
% 22.84/23.00 inference(modus_ponens,[status(thm)],[6908, 6907])).
% 22.84/23.00 tff(6910,plain,
% 22.84/23.00 ((~((~(mult(mult(c, mult(c, a)), b) = mult(mult(c, b), mult(c, a)))) | (~(mult(c, mult(mult(c, a), b)) = mult(c, mult(b, mult(c, a))))))) | (~((~(mult(mult(c, mult(c, a)), b) = mult(c, mult(mult(c, a), b)))) | (~(mult(mult(c, b), mult(c, a)) = mult(c, mult(b, mult(c, a)))))))),
% 22.84/23.00 inference(unit_resolution,[status(thm)],[6909, 27])).
% 22.84/23.00 tff(6911,plain,
% 22.84/23.00 (~((~(mult(mult(c, mult(c, a)), b) = mult(mult(c, b), mult(c, a)))) | (~(mult(c, mult(mult(c, a), b)) = mult(c, mult(b, mult(c, a))))))),
% 22.84/23.00 inference(unit_resolution,[status(thm)],[6910, 6906])).
% 22.84/23.00 tff(6912,plain,
% 22.84/23.00 (((~(mult(mult(c, mult(c, a)), b) = mult(mult(c, b), mult(c, a)))) | (~(mult(c, mult(mult(c, a), b)) = mult(c, mult(b, mult(c, a)))))) | (mult(c, mult(mult(c, a), b)) = mult(c, mult(b, mult(c, a))))),
% 22.84/23.00 inference(tautology,[status(thm)],[])).
% 22.84/23.00 tff(6913,plain,
% 22.84/23.00 (mult(c, mult(mult(c, a), b)) = mult(c, mult(b, mult(c, a)))),
% 22.84/23.00 inference(unit_resolution,[status(thm)],[6912, 6911])).
% 22.84/23.00 tff(6914,plain,
% 22.84/23.00 (mult(c, mult(b, mult(c, a))) = mult(c, mult(mult(c, a), b))),
% 22.84/23.00 inference(symmetry,[status(thm)],[6913])).
% 22.84/23.00 tff(6915,plain,
% 22.84/23.00 (mult(c, mult(b, mult(a, c))) = mult(mult(c, mult(a, c)), b)),
% 22.84/23.00 inference(transitivity,[status(thm)],[4898, 6914, 6904, 3190, 3188, 3185, 4371, 4370])).
% 22.84/23.00 tff(6916,plain,
% 22.84/23.00 ((mult(mult(c, b), mult(a, c)) = mult(c, mult(b, mult(a, c)))) <=> (mult(mult(c, b), mult(a, c)) = mult(mult(c, mult(a, c)), b))),
% 22.84/23.00 inference(monotonicity,[status(thm)],[6915])).
% 22.84/23.00 tff(6917,plain,
% 22.84/23.00 ((mult(mult(c, b), mult(a, c)) = mult(c, mult(b, mult(a, c)))) <=> (mult(mult(c, mult(a, c)), b) = mult(mult(c, b), mult(a, c)))),
% 22.84/23.00 inference(transitivity,[status(thm)],[6916, 6903])).
% 22.84/23.00 tff(6918,plain,
% 22.84/23.00 ((mult(mult(c, mult(a, c)), b) = mult(mult(c, b), mult(a, c))) <=> (mult(mult(c, b), mult(a, c)) = mult(c, mult(b, mult(a, c))))),
% 22.84/23.00 inference(symmetry,[status(thm)],[6917])).
% 22.84/23.00 tff(6919,plain,
% 22.84/23.00 (mult(mult(c, b), mult(a, c)) = mult(c, mult(b, mult(a, c)))),
% 22.84/23.00 inference(modus_ponens,[status(thm)],[5095, 6918])).
% 22.84/23.00 tff(6920,plain,
% 22.84/23.00 ($false),
% 22.84/23.00 inference(unit_resolution,[status(thm)],[5084, 6919])).
% 22.84/23.00 tff(6921,plain,((mult(mult(c, b), mult(c, a)) = mult(c, mult(b, mult(c, a)))) | (~(mult(mult(c, mult(mult(unit, c), unit)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(mult(unit, c), unit)))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit)))))), inference(lemma,lemma(discharge,[]))).
% 22.84/23.00 tff(6922,plain,
% 22.84/23.00 (mult(mult(c, b), mult(c, a)) = mult(c, mult(b, mult(c, a)))),
% 22.84/23.00 inference(unit_resolution,[status(thm)],[6921, 4282, 3862])).
% 22.84/23.00 tff(6923,plain,
% 22.84/23.00 (mult(mult(c, b), mult(a, c)) = mult(c, mult(b, mult(a, c)))),
% 22.84/23.00 inference(modus_ponens,[status(thm)],[6922, 6902])).
% 22.84/23.00 tff(6924,plain,
% 22.84/23.00 (mult(c, mult(b, mult(a, c))) = mult(mult(c, b), mult(a, c))),
% 22.84/23.00 inference(symmetry,[status(thm)],[6923])).
% 22.84/23.00 tff(6925,plain,
% 22.84/23.00 (mult(c, mult(b, mult(a, c))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))),
% 22.84/23.00 inference(transitivity,[status(thm)],[6924, 2429, 5386, 2501, 6897, 4661, 6878, 6872, 2631, 6869, 6867, 6863, 6861, 6818])).
% 22.84/23.00 tff(6926,plain,
% 22.84/23.00 (ld(c, mult(c, mult(b, mult(a, c)))) = ld(c, mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))),
% 22.84/23.00 inference(monotonicity,[status(thm)],[6925])).
% 22.84/23.00 tff(6927,plain,
% 22.84/23.00 (ld(c, mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) = ld(c, mult(c, mult(b, mult(a, c))))),
% 22.84/23.00 inference(symmetry,[status(thm)],[6926])).
% 22.84/23.00 tff(6928,plain,
% 22.84/23.00 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(c, mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))),
% 22.84/23.00 inference(quant_inst,[status(thm)],[])).
% 22.84/23.00 tff(6929,plain,
% 22.84/23.00 (ld(c, mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))),
% 22.84/23.00 inference(unit_resolution,[status(thm)],[6928, 7])).
% 22.84/23.00 tff(6930,plain,
% 22.84/23.00 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)) = ld(c, mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))),
% 22.84/23.00 inference(symmetry,[status(thm)],[6929])).
% 22.84/23.00 tff(6931,plain,
% 22.84/23.00 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)) = mult(b, mult(a, c))),
% 22.84/23.00 inference(transitivity,[status(thm)],[6930, 6927, 5658])).
% 22.84/23.00 tff(6932,plain,
% 22.84/23.00 (mult(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) = mult(rd(mult(b, c), mult(a, c)), mult(b, mult(a, c)))),
% 22.84/23.00 inference(monotonicity,[status(thm)],[6931])).
% 22.84/23.00 tff(6933,plain,
% 22.84/23.00 (mult(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c))),
% 22.84/23.00 inference(transitivity,[status(thm)],[6932, 5529, 5528])).
% 22.84/23.00 tff(6934,plain,
% 22.84/23.00 (ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) = ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)))),
% 22.84/23.00 inference(monotonicity,[status(thm)],[6933])).
% 22.84/23.00 tff(6935,plain,
% 22.84/23.00 (ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c))) = ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))),
% 22.84/23.00 inference(symmetry,[status(thm)],[6934])).
% 22.84/23.00 tff(6936,plain,
% 22.84/23.00 (mult(mult(a, b), c) = ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)))),
% 22.84/23.00 inference(symmetry,[status(thm)],[5526])).
% 22.84/23.00 tff(6937,plain,
% 22.84/23.00 (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))),
% 22.84/23.00 inference(transitivity,[status(thm)],[1332, 3892, 4208, 6746, 4225, 4270, 6761, 161, 6936, 6935, 6815])).
% 22.84/23.00 tff(6938,plain,
% 22.84/23.00 ($false),
% 22.84/23.00 inference(unit_resolution,[status(thm)],[1364, 6937])).
% 22.84/23.00 tff(6939,plain,((~(mult(rd(mult(b, c), mult(a, c)), mult(b, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), b)))) | (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) | (~(mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a)))) | (~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(c, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)))) | (~(mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))))), inference(lemma,lemma(discharge,[]))).
% 22.84/23.00 tff(6940,plain,
% 22.84/23.00 (~(mult(rd(mult(b, c), mult(a, c)), mult(b, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), b)))),
% 22.84/23.00 inference(unit_resolution,[status(thm)],[6939, 6748, 1180, 6583, 6813, 6811, 6758, 281, 6582, 4360, 6744])).
% 22.84/23.00 tff(6941,plain,
% 22.84/23.00 ((~(mult(mult(rd(mult(b, c), mult(a, c)), b), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), b))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(b, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), b))))),
% 22.84/23.00 inference(unit_resolution,[status(thm)],[5542, 6940])).
% 22.84/23.01 tff(6942,plain,
% 22.84/23.01 (~((~(mult(mult(rd(mult(b, c), mult(a, c)), b), mult(a, c)) = mult(rd(mult(b, c), mult(a, c)), mult(b, mult(a, c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), b) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), b)))))),
% 22.84/23.01 inference(unit_resolution,[status(thm)],[5547, 6941])).
% 22.84/23.01 tff(6943,plain,
% 22.84/23.01 (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), b) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), b))),
% 22.84/23.01 inference(unit_resolution,[status(thm)],[5549, 6942])).
% 22.84/23.01 tff(6944,plain,
% 22.84/23.01 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), b)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), b)),
% 22.84/23.01 inference(symmetry,[status(thm)],[6943])).
% 22.84/23.01 tff(6945,plain,
% 22.84/23.01 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)) = mult(mult(b, c), b)),
% 22.84/23.01 inference(transitivity,[status(thm)],[5527, 6944, 5522])).
% 22.84/23.01 tff(6946,plain,
% 22.84/23.01 (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)), a) = mult(mult(mult(b, c), b), a)),
% 22.84/23.01 inference(monotonicity,[status(thm)],[6945])).
% 22.84/23.01 tff(6947,plain,
% 22.84/23.01 (mult(mult(mult(b, c), b), a) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)), a)),
% 22.84/23.01 inference(symmetry,[status(thm)],[6946])).
% 22.84/23.01 tff(6948,plain,
% 22.84/23.01 (mult(mult(b, c), a) = mult(mult(a, b), c)),
% 22.84/23.01 inference(transitivity,[status(thm)],[3892, 4208, 6746, 4225, 4270, 6761, 161])).
% 22.84/23.01 tff(6949,plain,
% 22.84/23.01 (mult(mult(mult(b, c), a), b) = mult(mult(mult(a, b), c), b)),
% 22.84/23.01 inference(monotonicity,[status(thm)],[6948])).
% 22.84/23.01 tff(6950,plain,
% 22.84/23.01 (mult(mult(mult(a, b), c), b) = mult(mult(mult(b, c), a), b)),
% 22.84/23.01 inference(symmetry,[status(thm)],[6949])).
% 22.84/23.01 tff(6951,plain,
% 22.84/23.01 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a)),
% 22.84/23.01 inference(unit_resolution,[status(thm)],[4297, 6750])).
% 22.84/23.01 tff(6952,plain,
% 22.84/23.01 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(a, b), c)),
% 22.84/23.01 inference(transitivity,[status(thm)],[6951, 1332, 3892, 4208, 6746, 4225, 4270, 6761, 161])).
% 22.84/23.01 tff(6953,plain,
% 22.84/23.01 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)), b) = mult(mult(mult(a, b), c), b)),
% 22.84/23.01 inference(monotonicity,[status(thm)],[6952])).
% 22.84/23.01 tff(6954,plain,
% 22.84/23.01 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)), b) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)), a)),
% 22.84/23.01 inference(transitivity,[status(thm)],[6953, 6950, 5520, 6947])).
% 22.84/23.01 tff(6955,plain,
% 22.84/23.01 ((mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)), b) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, c), b))) <=> (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, b), c)))),
% 22.84/23.01 inference(monotonicity,[status(thm)],[6954, 6566])).
% 22.84/23.01 tff(6956,plain,
% 22.84/23.01 ((mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)), b) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, c), b))) <=> (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, b), c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)), a))),
% 22.84/23.01 inference(transitivity,[status(thm)],[6955, 6567])).
% 22.84/23.01 tff(6957,plain,
% 22.84/23.01 ((mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, b), c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)), a)) <=> (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)), b) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, c), b)))),
% 22.84/23.01 inference(symmetry,[status(thm)],[6956])).
% 22.84/23.01 tff(6958,plain,
% 22.84/23.01 ((~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, b), c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)), a))) <=> (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)), b) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, c), b))))),
% 22.84/23.01 inference(monotonicity,[status(thm)],[6957])).
% 22.84/23.01 tff(6959,plain,
% 22.84/23.01 ((mult(mult(a, b), mult(b, c)) = mult(mult(mult(a, b), b), c)) <=> (mult(mult(mult(a, b), b), c) = mult(mult(a, b), mult(b, c)))),
% 22.84/23.01 inference(commutativity,[status(thm)],[])).
% 22.84/23.01 tff(6960,plain,
% 22.84/23.01 (mult(b, mult(b, c)) = mult(mult(b, c), b)),
% 22.84/23.01 inference(transitivity,[status(thm)],[5569, 5566, 5563])).
% 22.84/23.01 tff(6961,plain,
% 22.84/23.01 (mult(mult(b, mult(b, c)), a) = mult(mult(mult(b, c), b), a)),
% 22.84/23.01 inference(monotonicity,[status(thm)],[6960])).
% 22.84/23.01 tff(6962,plain,
% 22.84/23.01 (mult(mult(b, mult(b, c)), a) = mult(mult(mult(a, b), b), c)),
% 22.84/23.01 inference(transitivity,[status(thm)],[6961, 5521, 6949, 827])).
% 22.84/23.01 tff(6963,plain,
% 22.84/23.01 (mult(mult(b, a), mult(b, c)) = mult(mult(a, b), mult(b, c))),
% 22.84/23.01 inference(monotonicity,[status(thm)],[1664])).
% 22.84/23.01 tff(6964,plain,
% 22.84/23.01 ((mult(mult(b, a), mult(b, c)) = mult(mult(b, mult(b, c)), a)) <=> (mult(mult(a, b), mult(b, c)) = mult(mult(mult(a, b), b), c))),
% 22.84/23.01 inference(monotonicity,[status(thm)],[6963, 6962])).
% 22.84/23.01 tff(6965,plain,
% 22.84/23.01 ((mult(mult(b, a), mult(b, c)) = mult(mult(b, mult(b, c)), a)) <=> (mult(mult(mult(a, b), b), c) = mult(mult(a, b), mult(b, c)))),
% 22.84/23.01 inference(transitivity,[status(thm)],[6964, 6959])).
% 22.84/23.01 tff(6966,plain,
% 22.84/23.01 ((mult(mult(mult(a, b), b), c) = mult(mult(a, b), mult(b, c))) <=> (mult(mult(b, a), mult(b, c)) = mult(mult(b, mult(b, c)), a))),
% 22.84/23.01 inference(symmetry,[status(thm)],[6965])).
% 22.84/23.01 tff(6967,plain,
% 22.84/23.01 ((~(mult(mult(mult(a, b), b), c) = mult(mult(a, b), mult(b, c)))) <=> (~(mult(mult(b, a), mult(b, c)) = mult(mult(b, mult(b, c)), a)))),
% 22.84/23.01 inference(monotonicity,[status(thm)],[6966])).
% 22.84/23.01 tff(6968,plain,
% 22.84/23.01 (~(mult(mult(b, a), mult(b, c)) = mult(mult(b, mult(b, c)), a))),
% 22.84/23.01 inference(modus_ponens,[status(thm)],[1729, 6967])).
% 22.84/23.01 tff(6969,plain,
% 22.84/23.01 (((~(mult(mult(b, a), mult(b, c)) = mult(mult(b, mult(b, c)), a))) | (~(mult(b, mult(a, mult(b, c))) = mult(b, mult(mult(b, c), a))))) | (mult(mult(b, a), mult(b, c)) = mult(mult(b, mult(b, c)), a))),
% 22.84/23.01 inference(tautology,[status(thm)],[])).
% 22.84/23.01 tff(6970,plain,
% 22.84/23.01 ((~(mult(mult(b, a), mult(b, c)) = mult(mult(b, mult(b, c)), a))) | (~(mult(b, mult(a, mult(b, c))) = mult(b, mult(mult(b, c), a))))),
% 22.84/23.01 inference(unit_resolution,[status(thm)],[6969, 6968])).
% 22.84/23.01 tff(6971,plain,
% 22.84/23.01 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(b, a), mult(b, c)) = mult(mult(b, mult(b, c)), a))) | (~(mult(b, mult(a, mult(b, c))) = mult(b, mult(mult(b, c), a)))))) | (~((~(mult(mult(b, a), mult(b, c)) = mult(b, mult(a, mult(b, c))))) | (~(mult(mult(b, mult(b, c)), a) = mult(b, mult(mult(b, c), a)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(b, a), mult(b, c)) = mult(mult(b, mult(b, c)), a))) | (~(mult(b, mult(a, mult(b, c))) = mult(b, mult(mult(b, c), a)))))) | (~((~(mult(mult(b, a), mult(b, c)) = mult(b, mult(a, mult(b, c))))) | (~(mult(mult(b, mult(b, c)), a) = mult(b, mult(mult(b, c), a)))))))),
% 22.84/23.01 inference(rewrite,[status(thm)],[])).
% 22.84/23.01 tff(6972,plain,
% 22.84/23.01 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(b, a), mult(b, c)) = mult(mult(b, mult(b, c)), a))) | (~(mult(b, mult(a, mult(b, c))) = mult(b, mult(mult(b, c), a)))))) | (~((~(mult(mult(b, a), mult(b, c)) = mult(b, mult(a, mult(b, c))))) | (~(mult(mult(b, mult(b, c)), a) = mult(b, mult(mult(b, c), a)))))))),
% 22.84/23.01 inference(quant_inst,[status(thm)],[])).
% 22.84/23.01 tff(6973,plain,
% 22.84/23.01 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(b, a), mult(b, c)) = mult(mult(b, mult(b, c)), a))) | (~(mult(b, mult(a, mult(b, c))) = mult(b, mult(mult(b, c), a)))))) | (~((~(mult(mult(b, a), mult(b, c)) = mult(b, mult(a, mult(b, c))))) | (~(mult(mult(b, mult(b, c)), a) = mult(b, mult(mult(b, c), a))))))),
% 22.84/23.01 inference(modus_ponens,[status(thm)],[6972, 6971])).
% 22.84/23.01 tff(6974,plain,
% 22.84/23.01 ((~((~(mult(mult(b, a), mult(b, c)) = mult(mult(b, mult(b, c)), a))) | (~(mult(b, mult(a, mult(b, c))) = mult(b, mult(mult(b, c), a)))))) | (~((~(mult(mult(b, a), mult(b, c)) = mult(b, mult(a, mult(b, c))))) | (~(mult(mult(b, mult(b, c)), a) = mult(b, mult(mult(b, c), a))))))),
% 22.84/23.01 inference(unit_resolution,[status(thm)],[6973, 27])).
% 22.84/23.01 tff(6975,plain,
% 22.84/23.01 (~((~(mult(mult(b, a), mult(b, c)) = mult(b, mult(a, mult(b, c))))) | (~(mult(mult(b, mult(b, c)), a) = mult(b, mult(mult(b, c), a)))))),
% 22.84/23.01 inference(unit_resolution,[status(thm)],[6974, 6970])).
% 22.84/23.01 tff(6976,plain,
% 22.84/23.01 (((~(mult(mult(b, a), mult(b, c)) = mult(b, mult(a, mult(b, c))))) | (~(mult(mult(b, mult(b, c)), a) = mult(b, mult(mult(b, c), a))))) | (mult(mult(b, mult(b, c)), a) = mult(b, mult(mult(b, c), a)))),
% 22.84/23.01 inference(tautology,[status(thm)],[])).
% 22.84/23.01 tff(6977,plain,
% 22.84/23.01 (mult(mult(b, mult(b, c)), a) = mult(b, mult(mult(b, c), a))),
% 22.84/23.01 inference(unit_resolution,[status(thm)],[6976, 6975])).
% 22.84/23.01 tff(6978,plain,
% 22.84/23.01 (mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c)))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, mult(a, c)))),
% 22.84/23.01 inference(symmetry,[status(thm)],[6861])).
% 22.84/23.01 tff(6979,plain,
% 22.84/23.01 (mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) = mult(c, mult(b, mult(a, c)))),
% 22.84/23.01 inference(transitivity,[status(thm)],[6817, 6978, 6862, 6866, 6868, 2632, 6871, 6877, 4660, 6896, 2502, 2499, 2742, 6923])).
% 22.84/23.01 tff(6980,plain,
% 22.84/23.01 (ld(c, mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) = ld(c, mult(c, mult(b, mult(a, c))))),
% 22.84/23.01 inference(monotonicity,[status(thm)],[6979])).
% 22.84/23.01 tff(6981,plain,
% 22.84/23.01 (ld(c, mult(c, mult(b, mult(a, c)))) = ld(c, mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))),
% 22.84/23.01 inference(symmetry,[status(thm)],[6980])).
% 22.84/23.01 tff(6982,plain,
% 22.84/23.01 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, b), c)), mult(mult(a, b), c)) = mult(rd(mult(b, c), mult(a, c)), a))),
% 22.84/23.01 inference(quant_inst,[status(thm)],[])).
% 22.84/23.01 tff(6983,plain,
% 22.84/23.01 (rd(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, b), c)), mult(mult(a, b), c)) = mult(rd(mult(b, c), mult(a, c)), a)),
% 22.84/23.01 inference(unit_resolution,[status(thm)],[6982, 168])).
% 22.84/23.01 tff(6984,plain,
% 22.84/23.01 (mult(c, mult(c, ld(c, mult(a, b)))) = mult(c, mult(b, a))),
% 22.84/23.01 inference(symmetry,[status(thm)],[6746])).
% 22.84/23.01 tff(6985,plain,
% 22.84/23.01 (mult(c, mult(a, b)) = mult(c, mult(c, ld(c, mult(a, b))))),
% 22.84/23.01 inference(symmetry,[status(thm)],[4225])).
% 22.84/23.01 tff(6986,plain,
% 22.84/23.01 (mult(mult(a, c), b) = mult(mult(c, a), b)),
% 22.84/23.01 inference(symmetry,[status(thm)],[6761])).
% 22.84/23.01 tff(6987,plain,
% 22.84/23.01 (mult(mult(a, b), c) = mult(mult(b, c), a)),
% 22.84/23.01 inference(transitivity,[status(thm)],[227, 6986, 4221, 6985, 6984, 4304, 4975])).
% 22.84/23.01 tff(6988,plain,
% 22.84/23.01 (mult(mult(unit, b), mult(mult(a, b), c)) = mult(b, mult(mult(b, c), a))),
% 22.84/23.01 inference(monotonicity,[status(thm)],[184, 6987])).
% 22.84/23.01 tff(6989,plain,
% 22.84/23.01 (mult(b, mult(mult(b, c), a)) = mult(mult(unit, b), mult(mult(a, b), c))),
% 22.84/23.01 inference(symmetry,[status(thm)],[6988])).
% 22.84/23.01 tff(6990,assumption,(mult(mult(b, mult(b, c)), a) = mult(b, mult(mult(b, c), a))), introduced(assumption)).
% 22.84/23.01 tff(6991,plain,
% 22.84/23.01 (mult(mult(mult(b, c), b), a) = mult(mult(b, mult(b, c)), a)),
% 22.84/23.01 inference(symmetry,[status(thm)],[6961])).
% 22.84/23.01 tff(6992,plain,
% 22.84/23.01 (~(mult(rd(mult(b, c), mult(a, c)), mult(b, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), b)))),
% 22.84/23.01 inference(unit_resolution,[status(thm)],[6939, 1364, 1180, 4789, 6819, 6820, 6879, 299, 2319, 4360, 5159])).
% 22.84/23.01 tff(6993,plain,
% 22.84/23.01 ((~(mult(mult(rd(mult(b, c), mult(a, c)), b), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), b))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(b, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), b))))),
% 22.84/23.01 inference(unit_resolution,[status(thm)],[5542, 6992])).
% 22.84/23.01 tff(6994,plain,
% 22.84/23.01 (~((~(mult(mult(rd(mult(b, c), mult(a, c)), b), mult(a, c)) = mult(rd(mult(b, c), mult(a, c)), mult(b, mult(a, c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), b) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), b)))))),
% 22.84/23.01 inference(unit_resolution,[status(thm)],[5547, 6993])).
% 22.84/23.01 tff(6995,plain,
% 22.84/23.01 (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), b) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), b))),
% 22.84/23.01 inference(unit_resolution,[status(thm)],[5549, 6994])).
% 22.84/23.01 tff(6996,plain,
% 22.84/23.01 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), b)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), b)),
% 22.84/23.01 inference(symmetry,[status(thm)],[6995])).
% 22.84/23.01 tff(6997,plain,
% 22.84/23.01 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)) = mult(mult(b, c), b)),
% 22.84/23.01 inference(transitivity,[status(thm)],[5527, 6996, 5522])).
% 22.84/23.01 tff(6998,plain,
% 22.84/23.01 (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)), a) = mult(mult(mult(b, c), b), a)),
% 22.84/23.01 inference(monotonicity,[status(thm)],[6997])).
% 22.84/23.01 tff(6999,assumption,(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, b), c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)), a)), introduced(assumption)).
% 22.84/23.01 tff(7000,plain,
% 22.84/23.01 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, b), c)) = mult(b, mult(mult(a, b), c))),
% 22.84/23.01 inference(transitivity,[status(thm)],[6999, 6998, 6991, 6990, 6989, 3388])).
% 22.84/23.01 tff(7001,plain,
% 22.84/23.01 (rd(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, b), c)), mult(mult(a, b), c)) = rd(mult(b, mult(mult(a, b), c)), mult(mult(a, b), c))),
% 22.84/23.01 inference(monotonicity,[status(thm)],[7000])).
% 22.84/23.01 tff(7002,plain,
% 22.84/23.01 (rd(mult(b, mult(mult(a, b), c)), mult(mult(a, b), c)) = rd(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, b), c)), mult(mult(a, b), c))),
% 22.84/23.01 inference(symmetry,[status(thm)],[7001])).
% 22.84/23.01 tff(7003,plain,
% 22.84/23.01 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(b, mult(mult(a, b), c)), mult(mult(a, b), c)) = b)),
% 22.84/23.01 inference(quant_inst,[status(thm)],[])).
% 22.84/23.01 tff(7004,plain,
% 22.84/23.01 (rd(mult(b, mult(mult(a, b), c)), mult(mult(a, b), c)) = b),
% 22.84/23.01 inference(unit_resolution,[status(thm)],[7003, 168])).
% 22.84/23.01 tff(7005,plain,
% 22.84/23.01 (b = rd(mult(b, mult(mult(a, b), c)), mult(mult(a, b), c))),
% 22.84/23.01 inference(symmetry,[status(thm)],[7004])).
% 22.84/23.01 tff(7006,plain,
% 22.84/23.01 (b = mult(rd(mult(b, c), mult(a, c)), a)),
% 22.84/23.01 inference(transitivity,[status(thm)],[7005, 7002, 6983])).
% 22.84/23.01 tff(7007,plain,
% 22.84/23.01 (mult(b, mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c))),
% 22.84/23.01 inference(monotonicity,[status(thm)],[7006])).
% 22.84/23.01 tff(7008,plain,
% 22.84/23.01 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(b, mult(a, c))),
% 22.84/23.01 inference(symmetry,[status(thm)],[7007])).
% 22.84/23.01 tff(7009,plain,
% 22.84/23.01 (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))),
% 22.84/23.01 inference(transitivity,[status(thm)],[6342, 7008, 5659, 6981, 6929])).
% 22.84/23.01 tff(7010,plain,
% 22.84/23.01 ($false),
% 22.84/23.01 inference(unit_resolution,[status(thm)],[1364, 7009])).
% 22.84/23.01 tff(7011,plain,((~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, b), c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)), a))) | (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) | (~(mult(mult(b, mult(b, c)), a) = mult(b, mult(mult(b, c), a)))) | (~(mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a)))) | (~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(c, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)))) | (~(mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))))), inference(lemma,lemma(discharge,[]))).
% 22.84/23.02 tff(7012,plain,
% 22.84/23.02 (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, b), c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)), a))),
% 22.84/23.02 inference(unit_resolution,[status(thm)],[7011, 6748, 6977, 1180, 6583, 6813, 6811, 6758, 281, 6582, 4360, 6744])).
% 22.84/23.02 tff(7013,plain,
% 22.84/23.02 (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)), b) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, c), b)))),
% 22.84/23.02 inference(modus_ponens,[status(thm)],[7012, 6958])).
% 22.84/23.02 tff(7014,plain,
% 22.84/23.02 (((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), b), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(b, mult(a, c))))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)), b) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, c), b))))) | (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)), b) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, c), b)))),
% 22.84/23.02 inference(tautology,[status(thm)],[])).
% 22.84/23.02 tff(7015,plain,
% 22.84/23.02 ((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), b), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(b, mult(a, c))))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)), b) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, c), b))))),
% 22.84/23.02 inference(unit_resolution,[status(thm)],[7014, 7013])).
% 22.84/23.02 tff(7016,plain,
% 22.84/23.02 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), b), mult(a, c)) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)), b))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(b, mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, c), b)))))) | (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), b), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(b, mult(a, c))))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)), b) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, c), b)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), b), mult(a, c)) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)), b))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(b, mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, c), b)))))) | (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), b), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(b, mult(a, c))))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)), b) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, c), b)))))))),
% 22.84/23.02 inference(rewrite,[status(thm)],[])).
% 22.84/23.02 tff(7017,plain,
% 22.84/23.02 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), b), mult(a, c)) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)), b))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(b, mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, c), b)))))) | (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), b), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(b, mult(a, c))))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)), b) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, c), b)))))))),
% 22.84/23.02 inference(quant_inst,[status(thm)],[])).
% 22.84/23.02 tff(7018,plain,
% 22.84/23.02 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), b), mult(a, c)) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)), b))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(b, mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, c), b)))))) | (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), b), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(b, mult(a, c))))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)), b) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, c), b))))))),
% 22.84/23.02 inference(modus_ponens,[status(thm)],[7017, 7016])).
% 22.84/23.02 tff(7019,plain,
% 22.84/23.02 ((~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), b), mult(a, c)) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)), b))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(b, mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, c), b)))))) | (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), b), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(b, mult(a, c))))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)), b) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, c), b))))))),
% 22.84/23.02 inference(unit_resolution,[status(thm)],[7018, 27])).
% 22.84/23.02 tff(7020,plain,
% 22.84/23.02 (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), b), mult(a, c)) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)), b))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(b, mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, c), b)))))),
% 22.84/23.02 inference(unit_resolution,[status(thm)],[7019, 7015])).
% 22.84/23.02 tff(7021,plain,
% 22.84/23.02 (((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), b), mult(a, c)) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)), b))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(b, mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, c), b))))) | (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(b, mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, c), b)))),
% 22.84/23.02 inference(tautology,[status(thm)],[])).
% 22.84/23.02 tff(7022,plain,
% 22.84/23.02 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(b, mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, c), b))),
% 22.84/23.02 inference(unit_resolution,[status(thm)],[7021, 7020])).
% 22.84/23.02 tff(7023,plain,
% 22.84/23.02 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c)))),
% 22.84/23.02 inference(symmetry,[status(thm)],[6751])).
% 22.84/23.02 tff(7024,plain,
% 22.84/23.02 (mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))))),
% 22.84/23.02 inference(monotonicity,[status(thm)],[7023])).
% 22.84/23.02 tff(7025,plain,
% 22.84/23.02 (mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c)))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))),
% 22.84/23.02 inference(symmetry,[status(thm)],[7024])).
% 22.84/23.02 tff(7026,plain,
% 22.84/23.02 (mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, mult(a, c))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))))),
% 22.84/23.02 inference(unit_resolution,[status(thm)],[6860, 6811, 6813, 6582, 281, 6751])).
% 22.84/23.02 tff(7027,plain,
% 22.84/23.02 (mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, mult(a, c))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a))),
% 22.84/23.02 inference(monotonicity,[status(thm)],[6791])).
% 22.84/23.02 tff(7028,plain,
% 22.84/23.02 (mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, mult(a, c)))),
% 22.84/23.02 inference(symmetry,[status(thm)],[7027])).
% 22.84/23.02 tff(7029,plain,
% 22.84/23.02 (mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))) = mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c))),
% 22.84/23.02 inference(symmetry,[status(thm)],[6744])).
% 22.84/23.02 tff(7030,plain,
% 22.84/23.02 (mult(a, mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), c))),
% 22.84/23.02 inference(transitivity,[status(thm)],[5122, 7029, 5117])).
% 22.84/23.02 tff(7031,plain,
% 22.84/23.02 (ld(a, mult(a, mult(c, rd(mult(b, c), mult(a, c))))) = ld(a, mult(a, mult(rd(mult(b, c), mult(a, c)), c)))),
% 22.84/23.02 inference(monotonicity,[status(thm)],[7030])).
% 22.84/23.02 tff(7032,plain,
% 22.84/23.02 (mult(c, rd(mult(b, c), mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), c)),
% 22.84/23.02 inference(transitivity,[status(thm)],[5202, 7031, 5127])).
% 22.84/23.02 tff(7033,plain,
% 22.84/23.02 (mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(c, a), a))),
% 22.84/23.02 inference(monotonicity,[status(thm)],[7032, 6865])).
% 22.84/23.02 tff(7034,plain,
% 22.84/23.02 (mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(c, a), a)) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a))),
% 22.84/23.02 inference(symmetry,[status(thm)],[7033])).
% 22.84/23.02 tff(7035,plain,
% 22.84/23.02 (mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 22.84/23.02 inference(symmetry,[status(thm)],[6583])).
% 22.84/23.02 tff(7036,plain,
% 22.84/23.02 (mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 22.84/23.02 inference(transitivity,[status(thm)],[6813, 6811, 6797, 6795, 6789, 6788, 7035])).
% 22.84/23.02 tff(7037,plain,
% 22.84/23.02 (rd(mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))), rd(mult(b, c), mult(a, c))) = rd(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))), rd(mult(b, c), mult(a, c)))),
% 22.84/23.02 inference(monotonicity,[status(thm)],[7036])).
% 22.84/23.02 tff(7038,plain,
% 22.84/23.02 (mult(mult(a, mult(c, c)), a) = mult(mult(mult(a, c), unit), mult(a, c))),
% 22.84/23.02 inference(transitivity,[status(thm)],[4662, 6894, 6889, 7037, 4808, 2504])).
% 22.84/23.02 tff(7039,plain,
% 22.84/23.02 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(c, c)), a)) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), unit), mult(a, c)))),
% 22.84/23.02 inference(monotonicity,[status(thm)],[7038])).
% 22.84/23.02 tff(7040,plain,
% 22.84/23.02 (mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), unit), mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(c, c)), a))),
% 22.84/23.02 inference(symmetry,[status(thm)],[7039])).
% 22.84/23.02 tff(7041,plain,
% 22.84/23.02 (mult(c, mult(b, mult(a, c))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))),
% 22.84/23.02 inference(transitivity,[status(thm)],[6924, 2429, 5386, 2501, 7040, 4661, 6878, 6872, 2631, 6869, 7034, 7028, 7026, 7025])).
% 22.84/23.02 tff(7042,plain,
% 22.84/23.02 (ld(c, mult(c, mult(b, mult(a, c)))) = ld(c, mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))),
% 22.84/23.02 inference(monotonicity,[status(thm)],[7041])).
% 22.84/23.02 tff(7043,plain,
% 22.84/23.02 (ld(c, mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) = ld(c, mult(c, mult(b, mult(a, c))))),
% 22.84/23.02 inference(symmetry,[status(thm)],[7042])).
% 22.84/23.02 tff(7044,plain,
% 22.84/23.02 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)) = mult(b, mult(a, c))),
% 22.84/23.02 inference(transitivity,[status(thm)],[6930, 7043, 5658])).
% 22.84/23.02 tff(7045,plain,
% 22.84/23.02 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(b, mult(a, c)))),
% 22.84/23.02 inference(monotonicity,[status(thm)],[7044])).
% 22.84/23.02 tff(7046,plain,
% 22.84/23.02 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, b), c))),
% 22.84/23.02 inference(transitivity,[status(thm)],[7045, 7022, 6566])).
% 22.84/23.02 tff(7047,plain,
% 22.84/23.02 (ld(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(rd(mult(b, c), mult(a, c)), a), mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) = ld(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, b), c)))),
% 22.84/23.02 inference(monotonicity,[status(thm)],[7046])).
% 22.84/23.02 tff(7048,plain,
% 22.84/23.02 (ld(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, b), c))) = ld(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(rd(mult(b, c), mult(a, c)), a), mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))),
% 22.84/23.02 inference(symmetry,[status(thm)],[7047])).
% 22.84/23.02 tff(7049,plain,
% 22.84/23.02 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, b), c))) = mult(mult(a, b), c))),
% 22.84/23.02 inference(quant_inst,[status(thm)],[])).
% 22.84/23.02 tff(7050,plain,
% 22.84/23.02 (ld(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, b), c))) = mult(mult(a, b), c)),
% 22.84/23.02 inference(unit_resolution,[status(thm)],[7049, 7])).
% 22.84/23.02 tff(7051,plain,
% 22.84/23.02 (mult(mult(a, b), c) = ld(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, b), c)))),
% 22.84/23.02 inference(symmetry,[status(thm)],[7050])).
% 22.84/23.02 tff(7052,plain,
% 22.84/23.02 (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))),
% 22.84/23.02 inference(transitivity,[status(thm)],[1332, 3892, 4208, 6746, 4225, 4270, 6761, 161, 7051, 7048, 6565])).
% 22.84/23.02 tff(7053,plain,
% 22.84/23.02 ($false),
% 22.84/23.02 inference(unit_resolution,[status(thm)],[6748, 7052])).
% 22.84/23.02 tff(7054,plain,((mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))) | (~(mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)))) | (~(mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a))) | (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))))), inference(lemma,lemma(discharge,[]))).
% 22.84/23.02 tff(7055,plain,
% 22.84/23.02 (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))),
% 22.84/23.02 inference(unit_resolution,[status(thm)],[7054, 6562, 4360, 6563, 270, 1799])).
% 22.84/23.02 tff(7056,plain,
% 22.84/23.02 (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))),
% 22.84/23.02 inference(unit_resolution,[status(thm)],[6458, 7055, 270, 316])).
% 22.84/23.02 tff(7057,plain,
% 22.84/23.02 ((~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))),
% 22.84/23.02 inference(unit_resolution,[status(thm)],[4290, 7056])).
% 22.84/23.02 tff(7058,plain,
% 22.84/23.02 (~((~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))))),
% 22.84/23.02 inference(unit_resolution,[status(thm)],[4295, 7057])).
% 22.84/23.02 tff(7059,plain,
% 22.84/23.02 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a)),
% 22.84/23.02 inference(unit_resolution,[status(thm)],[4297, 7058])).
% 22.84/23.02 tff(7060,plain,
% 22.84/23.02 (mult(a, mult(b, c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))),
% 22.84/23.02 inference(monotonicity,[status(thm)],[267])).
% 22.84/23.02 tff(7061,plain,
% 22.84/23.02 (mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))) = mult(a, mult(b, c))),
% 22.84/23.02 inference(symmetry,[status(thm)],[7060])).
% 22.84/23.02 tff(7062,plain,
% 22.84/23.02 (ld(mult(c, mult(a, c)), mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a))) = ld(mult(c, mult(a, c)), mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))),
% 22.84/23.02 inference(monotonicity,[status(thm)],[2378])).
% 22.84/23.02 tff(7063,plain,
% 22.84/23.02 (ld(mult(c, mult(a, c)), mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c))))) = ld(mult(c, mult(a, c)), mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)))),
% 22.84/23.02 inference(symmetry,[status(thm)],[7062])).
% 22.84/23.02 tff(7064,plain,
% 22.84/23.02 (mult(a, rd(mult(b, c), mult(a, c))) = ld(mult(c, mult(a, c)), mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))),
% 22.84/23.02 inference(symmetry,[status(thm)],[2377])).
% 22.84/23.02 tff(7065,plain,
% 22.84/23.02 (mult(a, rd(mult(b, c), mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), a)),
% 22.84/23.02 inference(transitivity,[status(thm)],[7064, 7063, 2383])).
% 22.84/23.02 tff(7066,plain,
% 22.84/23.02 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c))),
% 22.84/23.03 inference(monotonicity,[status(thm)],[7065])).
% 22.84/23.03 tff(7067,plain,
% 22.84/23.03 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))),
% 22.84/23.03 inference(symmetry,[status(thm)],[7066])).
% 22.84/23.03 tff(7068,plain,
% 22.84/23.03 (mult(mult(a, b), c) = mult(a, mult(b, c))),
% 22.84/23.03 inference(transitivity,[status(thm)],[227, 6986, 4221, 6985, 6984, 4304, 4975, 1431, 4502, 7067, 287, 7061])).
% 22.84/23.03 tff(7069,plain,
% 22.84/23.03 ($false),
% 22.84/23.03 inference(unit_resolution,[status(thm)],[146, 7068])).
% 22.84/23.03 tff(7070,plain,((~(mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a))) | (~(mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a))))), inference(lemma,lemma(discharge,[]))).
% 22.84/23.03 tff(7071,plain,
% 22.84/23.03 (~(mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))),
% 22.84/23.03 inference(unit_resolution,[status(thm)],[7070, 7059, 279, 6562])).
% 22.84/23.03 tff(7072,plain,
% 22.84/23.03 (~((~(mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)))))),
% 22.84/23.03 inference(unit_resolution,[status(thm)],[2406, 7071])).
% 22.84/23.03 tff(7073,plain,
% 22.84/23.03 (mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c))))),
% 22.84/23.03 inference(unit_resolution,[status(thm)],[5253, 7072])).
% 22.84/23.03 tff(7074,plain,
% 22.84/23.03 (mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a))),
% 22.84/23.03 inference(unit_resolution,[status(thm)],[2408, 7072])).
% 22.84/23.03 tff(7075,plain,
% 22.84/23.03 ((mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c)))) <=> (mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))),
% 22.84/23.03 inference(monotonicity,[status(thm)],[7074, 7073])).
% 22.84/23.03 tff(7076,plain,
% 22.84/23.03 ((mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c))))) <=> (mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))))),
% 22.84/23.03 inference(symmetry,[status(thm)],[7075])).
% 22.84/23.03 tff(7077,plain,
% 22.84/23.03 ((~(mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))) <=> (~(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c)))))),
% 22.84/23.03 inference(monotonicity,[status(thm)],[7076])).
% 22.84/23.03 tff(7078,plain,
% 22.84/23.03 (~(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))))),
% 22.84/23.03 inference(modus_ponens,[status(thm)],[7071, 7077])).
% 22.84/23.03 tff(7079,plain,
% 22.84/23.03 (mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))),
% 22.84/23.03 inference(unit_resolution,[status(thm)],[4328, 7058])).
% 22.84/23.03 tff(7080,plain,
% 22.84/23.03 ((mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c)))) | (~(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))),
% 22.84/23.03 inference(unit_resolution,[status(thm)],[5257, 3862])).
% 22.84/23.03 tff(7081,plain,
% 22.84/23.03 (mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c)))),
% 22.84/23.03 inference(unit_resolution,[status(thm)],[7080, 7079, 7055, 6583, 4495])).
% 22.84/23.03 tff(7082,plain,
% 22.84/23.03 ($false),
% 22.84/23.03 inference(unit_resolution,[status(thm)],[7081, 7078])).
% 22.84/23.03 tff(7083,plain,(((~(mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a))) | (~(mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a))))) | (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))))), inference(lemma,lemma(discharge,[]))).
% 22.84/23.03 tff(7084,plain,
% 22.84/23.03 (((~(mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a))) | (~(mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a))))) | (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit))))),
% 22.84/23.03 inference(unit_resolution,[status(thm)],[7083, 5496])).
% 22.84/23.03 tff(7085,plain,
% 22.84/23.03 ((~(mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a))) | (~(mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a))))),
% 22.84/23.03 inference(unit_resolution,[status(thm)],[7084, 6560, 6534])).
% 22.84/23.03 tff(7086,plain,
% 22.84/23.03 (~((~(mult(mult(mult(b, c), a), b) = mult(mult(b, c), mult(a, b)))) | (~(mult(mult(mult(b, c), b), a) = mult(mult(b, c), mult(b, a)))))),
% 22.84/23.03 inference(unit_resolution,[status(thm)],[1205, 7085])).
% 22.84/23.03 tff(7087,plain,
% 22.84/23.03 (mult(mult(mult(b, c), b), a) = mult(mult(b, c), mult(b, a))),
% 22.84/23.03 inference(unit_resolution,[status(thm)],[1207, 7086])).
% 22.84/23.03 tff(7088,plain,
% 22.84/23.03 (mult(mult(mult(b, c), b), a) = mult(mult(c, b), mult(b, a))),
% 22.84/23.03 inference(transitivity,[status(thm)],[7087, 3468])).
% 22.84/23.03 tff(7089,plain,
% 22.84/23.03 ((mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a)) <=> (mult(mult(c, mult(b, a)), b) = mult(mult(c, b), mult(b, a)))),
% 22.84/23.03 inference(monotonicity,[status(thm)],[4307, 7088])).
% 22.84/23.03 tff(7090,plain,
% 22.84/23.03 ((mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a)) <=> (mult(mult(c, b), mult(b, a)) = mult(mult(c, mult(b, a)), b))),
% 22.84/23.03 inference(transitivity,[status(thm)],[7089, 4326])).
% 22.84/23.03 tff(7091,plain,
% 22.84/23.03 ((mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a)) <=> (mult(mult(c, b), mult(mult(unit, mult(b, a)), unit)) = mult(mult(c, mult(mult(unit, mult(b, a)), unit)), b))),
% 22.84/23.03 inference(transitivity,[status(thm)],[7090, 4325])).
% 22.84/23.03 tff(7092,plain,
% 22.84/23.03 ((mult(mult(c, b), mult(b, a)) = mult(mult(c, mult(b, a)), b)) <=> (mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a))),
% 22.84/23.03 inference(symmetry,[status(thm)],[7090])).
% 22.84/23.03 tff(7093,plain,
% 22.84/23.03 ((mult(mult(c, b), mult(mult(unit, mult(b, a)), unit)) = mult(mult(c, mult(mult(unit, mult(b, a)), unit)), b)) <=> (mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a))),
% 22.84/23.03 inference(transitivity,[status(thm)],[4324, 7092])).
% 22.84/23.03 tff(7094,plain,
% 22.84/23.03 ((mult(mult(b, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(mult(b, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a))) <=> (mult(mult(b, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(mult(b, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))))),
% 22.84/23.03 inference(commutativity,[status(thm)],[])).
% 22.84/23.03 tff(7095,plain,
% 22.84/23.03 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(b, rd(mult(b, c), mult(a, c))), a), c), a) = mult(mult(b, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)))),
% 22.84/23.03 inference(quant_inst,[status(thm)],[])).
% 22.84/23.03 tff(7096,plain,
% 22.84/23.03 (mult(mult(mult(mult(b, rd(mult(b, c), mult(a, c))), a), c), a) = mult(mult(b, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a))),
% 22.84/23.03 inference(unit_resolution,[status(thm)],[7095, 56])).
% 22.84/23.03 tff(7097,plain,
% 22.84/23.03 (mult(mult(unit, mult(mult(b, unit), b)), c) = mult(mult(b, b), c)),
% 22.84/23.03 inference(monotonicity,[status(thm)],[1106])).
% 22.84/23.03 tff(7098,plain,
% 22.84/23.03 (mult(mult(b, b), c) = mult(mult(unit, mult(mult(b, unit), b)), c)),
% 22.84/23.03 inference(symmetry,[status(thm)],[7097])).
% 22.84/23.03 tff(7099,plain,
% 22.84/23.03 (mult(a, mult(mult(b, b), c)) = mult(a, mult(mult(unit, mult(mult(b, unit), b)), c))),
% 22.84/23.03 inference(monotonicity,[status(thm)],[7098])).
% 22.84/23.03 tff(7100,plain,
% 22.84/23.03 (mult(a, mult(mult(b, b), c)) = mult(a, mult(mult(b, c), b))),
% 22.84/23.03 inference(transitivity,[status(thm)],[7099, 893, 833, 828, 781])).
% 22.84/23.03 tff(7101,plain,
% 22.84/23.03 (ld(a, mult(a, mult(mult(b, b), c))) = ld(a, mult(a, mult(mult(b, c), b)))),
% 22.84/23.03 inference(monotonicity,[status(thm)],[7100])).
% 22.84/23.03 tff(7102,plain,
% 22.84/23.03 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(a, mult(a, mult(mult(b, b), c))) = mult(mult(b, b), c))),
% 22.84/23.03 inference(quant_inst,[status(thm)],[])).
% 22.84/23.03 tff(7103,plain,
% 22.84/23.03 (ld(a, mult(a, mult(mult(b, b), c))) = mult(mult(b, b), c)),
% 22.84/23.03 inference(unit_resolution,[status(thm)],[7102, 7])).
% 22.84/23.03 tff(7104,plain,
% 22.84/23.03 (mult(mult(b, b), c) = ld(a, mult(a, mult(mult(b, b), c)))),
% 22.84/23.03 inference(symmetry,[status(thm)],[7103])).
% 22.84/23.03 tff(7105,plain,
% 22.84/23.03 (mult(rd(mult(b, c), mult(a, c)), a) = mult(b, unit)),
% 22.84/23.03 inference(transitivity,[status(thm)],[175, 5502, 170, 431])).
% 22.84/23.03 tff(7106,plain,
% 22.84/23.03 (mult(mult(rd(mult(b, c), mult(a, c)), a), b) = mult(mult(b, unit), b)),
% 22.84/23.03 inference(monotonicity,[status(thm)],[7105])).
% 22.84/23.03 tff(7107,plain,
% 22.84/23.03 (mult(mult(rd(mult(b, c), mult(a, c)), a), b) = mult(unit, mult(mult(b, unit), b))),
% 22.84/23.03 inference(transitivity,[status(thm)],[7106, 430])).
% 22.84/23.03 tff(7108,plain,
% 22.84/23.03 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), b), a) = mult(mult(unit, mult(mult(b, unit), b)), a)),
% 22.84/23.03 inference(monotonicity,[status(thm)],[7107])).
% 22.84/23.03 tff(7109,plain,
% 22.84/23.03 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), a)) = mult(mult(b, b), a)),
% 22.84/23.03 inference(transitivity,[status(thm)],[2011, 7108, 435])).
% 22.84/23.03 tff(7110,plain,
% 22.84/23.03 ((~(mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a))) | (~(mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a))))),
% 22.84/23.03 inference(unit_resolution,[status(thm)],[7083, 270, 4360, 1799])).
% 22.84/23.03 tff(7111,plain,
% 22.84/23.03 (~((~(mult(mult(mult(b, c), a), b) = mult(mult(b, c), mult(a, b)))) | (~(mult(mult(mult(b, c), b), a) = mult(mult(b, c), mult(b, a)))))),
% 22.84/23.03 inference(unit_resolution,[status(thm)],[1205, 7110])).
% 22.84/23.03 tff(7112,plain,
% 22.84/23.03 (mult(mult(mult(b, c), a), b) = mult(mult(b, c), mult(a, b))),
% 22.84/23.03 inference(unit_resolution,[status(thm)],[1229, 7111])).
% 22.84/23.03 tff(7113,plain,
% 22.84/23.03 (mult(mult(mult(b, c), b), a) = mult(mult(b, c), mult(b, a))),
% 22.84/23.03 inference(unit_resolution,[status(thm)],[1207, 7111])).
% 22.84/23.03 tff(7114,plain,
% 22.84/23.03 (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))),
% 22.84/23.03 inference(unit_resolution,[status(thm)],[6458, 4331, 270, 316])).
% 22.84/23.03 tff(7115,plain,
% 22.84/23.03 (~(mult(c, mult(b, a)) = mult(c, mult(a, b)))),
% 22.84/23.03 inference(unit_resolution,[status(thm)],[2242, 7114, 4331, 6581])).
% 22.84/23.03 tff(7116,plain,
% 22.84/23.03 (mult(c, mult(a, b)) = mult(mult(a, b), c)),
% 22.84/23.03 inference(transitivity,[status(thm)],[4270, 6761, 161])).
% 22.84/23.03 tff(7117,plain,
% 22.84/23.03 (mult(mult(c, mult(a, b)), b) = mult(mult(mult(a, b), c), b)),
% 22.84/23.03 inference(monotonicity,[status(thm)],[7116])).
% 22.84/23.03 tff(7118,assumption,(mult(mult(c, b), mult(a, b)) = mult(mult(c, mult(a, b)), b)), introduced(assumption)).
% 22.84/23.03 tff(7119,plain,
% 22.84/23.03 (mult(mult(b, c), mult(a, b)) = mult(mult(c, b), mult(a, b))),
% 22.84/23.03 inference(monotonicity,[status(thm)],[1399])).
% 22.84/23.03 tff(7120,plain,
% 22.84/23.03 (mult(mult(mult(b, c), a), b) = mult(mult(mult(a, b), c), b)),
% 22.84/23.03 inference(transitivity,[status(thm)],[1311, 7119, 7118, 7117])).
% 22.84/23.03 tff(7121,plain,
% 22.84/23.03 (rd(mult(mult(mult(b, c), a), b), b) = rd(mult(mult(mult(a, b), c), b), b)),
% 22.84/23.03 inference(monotonicity,[status(thm)],[7120])).
% 22.84/23.03 tff(7122,plain,
% 22.84/23.03 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(b, c), a), b), b) = mult(mult(b, c), a))),
% 22.84/23.03 inference(quant_inst,[status(thm)],[])).
% 22.84/23.03 tff(7123,plain,
% 22.84/23.03 (rd(mult(mult(mult(b, c), a), b), b) = mult(mult(b, c), a)),
% 22.84/23.03 inference(unit_resolution,[status(thm)],[7122, 168])).
% 22.84/23.03 tff(7124,plain,
% 22.84/23.03 (mult(mult(b, c), a) = rd(mult(mult(mult(b, c), a), b), b)),
% 22.84/23.03 inference(symmetry,[status(thm)],[7123])).
% 22.84/23.03 tff(7125,plain,
% 22.84/23.03 (mult(c, mult(b, a)) = mult(c, mult(a, b))),
% 22.84/23.03 inference(transitivity,[status(thm)],[4304, 2298, 7124, 7121, 793, 227, 6986, 4221])).
% 22.84/23.03 tff(7126,plain,
% 22.84/23.03 ($false),
% 22.84/23.03 inference(unit_resolution,[status(thm)],[2302, 7125])).
% 22.84/23.03 tff(7127,plain,((~(mult(mult(c, b), mult(a, b)) = mult(mult(c, mult(a, b)), b))) | (mult(c, mult(b, a)) = mult(c, mult(a, b))) | (~(mult(mult(mult(b, c), a), b) = mult(mult(b, c), mult(a, b))))), inference(lemma,lemma(discharge,[]))).
% 22.84/23.03 tff(7128,plain,
% 22.84/23.03 (~(mult(mult(c, b), mult(a, b)) = mult(mult(c, mult(a, b)), b))),
% 22.84/23.03 inference(unit_resolution,[status(thm)],[7127, 7115, 7112])).
% 22.84/23.03 tff(7129,plain,
% 22.84/23.03 (((~(mult(mult(c, b), mult(a, b)) = mult(mult(c, mult(a, b)), b))) | (~(mult(c, mult(b, mult(a, b))) = mult(c, mult(mult(a, b), b))))) | (mult(mult(c, b), mult(a, b)) = mult(mult(c, mult(a, b)), b))),
% 22.84/23.03 inference(tautology,[status(thm)],[])).
% 22.84/23.03 tff(7130,plain,
% 22.84/23.03 ((~(mult(mult(c, b), mult(a, b)) = mult(mult(c, mult(a, b)), b))) | (~(mult(c, mult(b, mult(a, b))) = mult(c, mult(mult(a, b), b))))),
% 22.84/23.03 inference(unit_resolution,[status(thm)],[7129, 7128])).
% 22.84/23.03 tff(7131,plain,
% 22.84/23.03 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(c, b), mult(a, b)) = mult(mult(c, mult(a, b)), b))) | (~(mult(c, mult(b, mult(a, b))) = mult(c, mult(mult(a, b), b)))))) | (~((~(mult(mult(c, b), mult(a, b)) = mult(c, mult(b, mult(a, b))))) | (~(mult(mult(c, mult(a, b)), b) = mult(c, mult(mult(a, b), b)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(c, b), mult(a, b)) = mult(mult(c, mult(a, b)), b))) | (~(mult(c, mult(b, mult(a, b))) = mult(c, mult(mult(a, b), b)))))) | (~((~(mult(mult(c, b), mult(a, b)) = mult(c, mult(b, mult(a, b))))) | (~(mult(mult(c, mult(a, b)), b) = mult(c, mult(mult(a, b), b)))))))),
% 22.84/23.03 inference(rewrite,[status(thm)],[])).
% 22.84/23.03 tff(7132,plain,
% 22.84/23.03 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(c, b), mult(a, b)) = mult(mult(c, mult(a, b)), b))) | (~(mult(c, mult(b, mult(a, b))) = mult(c, mult(mult(a, b), b)))))) | (~((~(mult(mult(c, b), mult(a, b)) = mult(c, mult(b, mult(a, b))))) | (~(mult(mult(c, mult(a, b)), b) = mult(c, mult(mult(a, b), b)))))))),
% 22.84/23.03 inference(quant_inst,[status(thm)],[])).
% 22.84/23.03 tff(7133,plain,
% 22.84/23.03 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(c, b), mult(a, b)) = mult(mult(c, mult(a, b)), b))) | (~(mult(c, mult(b, mult(a, b))) = mult(c, mult(mult(a, b), b)))))) | (~((~(mult(mult(c, b), mult(a, b)) = mult(c, mult(b, mult(a, b))))) | (~(mult(mult(c, mult(a, b)), b) = mult(c, mult(mult(a, b), b))))))),
% 22.84/23.03 inference(modus_ponens,[status(thm)],[7132, 7131])).
% 22.84/23.03 tff(7134,plain,
% 22.84/23.03 ((~((~(mult(mult(c, b), mult(a, b)) = mult(mult(c, mult(a, b)), b))) | (~(mult(c, mult(b, mult(a, b))) = mult(c, mult(mult(a, b), b)))))) | (~((~(mult(mult(c, b), mult(a, b)) = mult(c, mult(b, mult(a, b))))) | (~(mult(mult(c, mult(a, b)), b) = mult(c, mult(mult(a, b), b))))))),
% 22.84/23.03 inference(unit_resolution,[status(thm)],[7133, 27])).
% 22.84/23.04 tff(7135,plain,
% 22.84/23.04 (~((~(mult(mult(c, b), mult(a, b)) = mult(c, mult(b, mult(a, b))))) | (~(mult(mult(c, mult(a, b)), b) = mult(c, mult(mult(a, b), b)))))),
% 22.84/23.04 inference(unit_resolution,[status(thm)],[7134, 7130])).
% 22.84/23.04 tff(7136,plain,
% 22.84/23.04 (((~(mult(mult(c, b), mult(a, b)) = mult(c, mult(b, mult(a, b))))) | (~(mult(mult(c, mult(a, b)), b) = mult(c, mult(mult(a, b), b))))) | (mult(mult(c, b), mult(a, b)) = mult(c, mult(b, mult(a, b))))),
% 22.84/23.04 inference(tautology,[status(thm)],[])).
% 22.84/23.04 tff(7137,plain,
% 22.84/23.04 (mult(mult(c, b), mult(a, b)) = mult(c, mult(b, mult(a, b)))),
% 22.84/23.04 inference(unit_resolution,[status(thm)],[7136, 7135])).
% 22.84/23.04 tff(7138,plain,
% 22.84/23.04 (~(mult(b, mult(a, b)) = mult(b, mult(b, a)))),
% 22.84/23.04 inference(unit_resolution,[status(thm)],[6531, 7137, 7113, 6511, 6529, 7112])).
% 22.84/23.04 tff(7139,plain,
% 22.84/23.04 ((~(mult(mult(b, a), b) = mult(mult(b, b), a))) | (~(mult(b, mult(a, b)) = mult(b, mult(b, a))))),
% 22.84/23.04 inference(unit_resolution,[status(thm)],[413, 7138])).
% 22.84/23.04 tff(7140,plain,
% 22.84/23.04 (~((~(mult(mult(b, a), b) = mult(b, mult(a, b)))) | (~(mult(mult(b, b), a) = mult(b, mult(b, a)))))),
% 22.84/23.04 inference(unit_resolution,[status(thm)],[418, 7139])).
% 22.84/23.04 tff(7141,plain,
% 22.84/23.04 (mult(mult(b, a), b) = mult(b, mult(a, b))),
% 22.84/23.04 inference(unit_resolution,[status(thm)],[420, 7140])).
% 22.84/23.04 tff(7142,plain,
% 22.84/23.04 (mult(b, mult(a, b)) = mult(mult(b, a), b)),
% 22.84/23.04 inference(symmetry,[status(thm)],[7141])).
% 22.84/23.04 tff(7143,plain,
% 22.84/23.04 (mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, b)),
% 22.84/23.04 inference(transitivity,[status(thm)],[6581, 5697])).
% 22.84/23.04 tff(7144,plain,
% 22.84/23.04 (mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), a)) = mult(b, mult(a, b))),
% 22.84/23.04 inference(monotonicity,[status(thm)],[7143])).
% 22.84/23.04 tff(7145,plain,
% 22.84/23.04 (mult(b, mult(mult(a, a), rd(mult(b, c), mult(a, c)))) = mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))),
% 22.84/23.04 inference(monotonicity,[status(thm)],[1361])).
% 22.84/23.04 tff(7146,plain,
% 22.84/23.04 ((mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a)) <=> (mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c))))),
% 22.84/23.04 inference(commutativity,[status(thm)],[])).
% 22.84/23.04 tff(7147,plain,
% 22.84/23.04 (mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, b)),
% 22.84/23.04 inference(transitivity,[status(thm)],[1287, 1381])).
% 22.84/23.04 tff(7148,plain,
% 22.84/23.04 (mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), a)) = mult(b, mult(a, b))),
% 22.84/23.04 inference(monotonicity,[status(thm)],[7147])).
% 22.84/23.04 tff(7149,plain,
% 22.84/23.04 (mult(b, mult(a, b)) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), a))),
% 22.84/23.04 inference(symmetry,[status(thm)],[7148])).
% 22.84/23.04 tff(7150,plain,
% 22.84/23.04 (mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(b, a), b)),
% 22.84/23.04 inference(monotonicity,[status(thm)],[1380])).
% 22.84/23.04 tff(7151,assumption,(~(mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c))) = mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))))), introduced(assumption)).
% 22.84/23.04 tff(7152,plain,
% 22.84/23.04 (((~(mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c))) = mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), a))))) | (mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c))) = mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))))),
% 22.84/23.04 inference(tautology,[status(thm)],[])).
% 22.84/23.04 tff(7153,plain,
% 22.84/23.04 ((~(mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c))) = mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), a))))),
% 22.84/23.04 inference(unit_resolution,[status(thm)],[7152, 7151])).
% 22.84/23.04 tff(7154,plain,
% 22.84/23.04 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a))) | (~(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), a)))))) | (~((~(mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c))) = mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), a)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a))) | (~(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), a)))))) | (~((~(mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c))) = mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), a)))))))),
% 22.84/23.04 inference(rewrite,[status(thm)],[])).
% 22.84/23.04 tff(7155,plain,
% 22.84/23.04 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a))) | (~(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), a)))))) | (~((~(mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c))) = mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), a)))))))),
% 22.84/23.04 inference(quant_inst,[status(thm)],[])).
% 22.84/23.04 tff(7156,plain,
% 22.84/23.04 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a))) | (~(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), a)))))) | (~((~(mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c))) = mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), a))))))),
% 22.84/23.04 inference(modus_ponens,[status(thm)],[7155, 7154])).
% 22.84/23.04 tff(7157,plain,
% 22.84/23.04 ((~((~(mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a))) | (~(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), a)))))) | (~((~(mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c))) = mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), a))))))),
% 22.84/23.04 inference(unit_resolution,[status(thm)],[7156, 27])).
% 22.84/23.04 tff(7158,plain,
% 22.84/23.04 (~((~(mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a))) | (~(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), a)))))),
% 22.84/23.04 inference(unit_resolution,[status(thm)],[7157, 7153])).
% 22.84/23.04 tff(7159,plain,
% 22.84/23.04 (((~(mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a))) | (~(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), a))))) | (mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), a)))),
% 22.84/23.04 inference(tautology,[status(thm)],[])).
% 22.84/23.04 tff(7160,plain,
% 22.84/23.04 (mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), a))),
% 22.84/23.04 inference(unit_resolution,[status(thm)],[7159, 7158])).
% 22.84/23.04 tff(7161,plain,
% 22.84/23.04 (mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a)),
% 22.84/23.04 inference(transitivity,[status(thm)],[7160, 7150, 607, 7149, 470])).
% 22.84/23.04 tff(7162,plain,
% 22.84/23.04 ((mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c))) = mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c))))) <=> (mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a))),
% 22.84/23.04 inference(monotonicity,[status(thm)],[7161])).
% 22.84/23.04 tff(7163,plain,
% 22.84/23.04 ((mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c))) = mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c))))) <=> (mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c))))),
% 22.84/23.04 inference(transitivity,[status(thm)],[7162, 7146])).
% 22.84/23.04 tff(7164,plain,
% 22.84/23.04 ((mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c)))) <=> (mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c))) = mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))))),
% 22.84/23.04 inference(symmetry,[status(thm)],[7163])).
% 22.84/23.04 tff(7165,plain,
% 22.84/23.04 (~((~(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c))))) | (~(mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))))))),
% 22.84/23.04 inference(unit_resolution,[status(thm)],[500, 7153])).
% 22.84/23.04 tff(7166,plain,
% 22.84/23.04 (mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c)))),
% 22.84/23.04 inference(unit_resolution,[status(thm)],[502, 7165])).
% 22.84/23.04 tff(7167,plain,
% 22.84/23.04 (mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c))) = mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c))))),
% 22.84/23.04 inference(modus_ponens,[status(thm)],[7166, 7164])).
% 22.84/23.04 tff(7168,plain,
% 22.84/23.04 ($false),
% 22.84/23.04 inference(unit_resolution,[status(thm)],[7151, 7167])).
% 22.84/23.04 tff(7169,plain,((mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c))) = mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c))))) | (~(mult(mult(b, a), b) = mult(b, mult(a, b)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a))))), inference(lemma,lemma(discharge,[]))).
% 22.84/23.04 tff(7170,plain,
% 22.84/23.04 (mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c))) = mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c))))),
% 22.84/23.04 inference(unit_resolution,[status(thm)],[7169, 1371, 421, 1287])).
% 22.84/23.04 tff(7171,plain,
% 22.84/23.04 (mult(b, mult(a, a)) = mult(mult(b, a), a)),
% 22.84/23.04 inference(transitivity,[status(thm)],[521, 518, 515])).
% 22.84/23.04 tff(7172,plain,
% 22.84/23.04 (mult(mult(b, mult(a, a)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(b, a), a), rd(mult(b, c), mult(a, c)))),
% 22.84/23.04 inference(monotonicity,[status(thm)],[7171])).
% 22.84/23.04 tff(7173,plain,
% 22.84/23.04 (mult(mult(b, mult(a, a)), rd(mult(b, c), mult(a, c))) = mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c))))),
% 22.84/23.04 inference(transitivity,[status(thm)],[7172, 7170])).
% 22.84/23.04 tff(7174,plain,
% 22.84/23.04 ((mult(mult(b, mult(a, a)), rd(mult(b, c), mult(a, c))) = mult(b, mult(mult(a, a), rd(mult(b, c), mult(a, c))))) <=> (mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))),
% 22.84/23.04 inference(monotonicity,[status(thm)],[7173, 7145])).
% 22.84/23.04 tff(7175,plain,
% 22.84/23.04 (mult(mult(rd(mult(b, c), mult(a, c)), a), unit) = b),
% 22.84/23.04 inference(transitivity,[status(thm)],[535, 530, 528, 175, 1379, 170])).
% 22.84/23.04 tff(7176,plain,
% 22.84/23.04 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), unit), a) = mult(b, a)),
% 22.84/23.04 inference(monotonicity,[status(thm)],[7175])).
% 22.84/23.04 tff(7177,plain,
% 22.84/23.04 (mult(rd(mult(b, c), mult(a, c)), mult(a, a)) = mult(b, a)),
% 22.84/23.04 inference(transitivity,[status(thm)],[541, 540, 7176])).
% 22.84/23.04 tff(7178,plain,
% 22.84/23.04 (mult(b, mult(rd(mult(b, c), mult(a, c)), mult(a, a))) = mult(b, mult(b, a))),
% 22.84/23.04 inference(monotonicity,[status(thm)],[7177])).
% 22.84/23.04 tff(7179,assumption,(~(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))), introduced(assumption)).
% 22.84/23.04 tff(7180,plain,
% 22.84/23.04 (((~(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(b, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), a))))) | (mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))),
% 22.84/23.04 inference(tautology,[status(thm)],[])).
% 22.84/23.04 tff(7181,plain,
% 22.84/23.04 ((~(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(b, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), a))))),
% 22.84/23.04 inference(unit_resolution,[status(thm)],[7180, 7179])).
% 22.84/23.04 tff(7182,plain,
% 22.84/23.04 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(b, mult(a, rd(mult(b, c), mult(a, c)))), a))) | (~(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), a)))))) | (~((~(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(b, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), a)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(b, mult(a, rd(mult(b, c), mult(a, c)))), a))) | (~(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), a)))))) | (~((~(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(b, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), a)))))))),
% 22.84/23.04 inference(rewrite,[status(thm)],[])).
% 22.84/23.04 tff(7183,plain,
% 22.84/23.04 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(b, mult(a, rd(mult(b, c), mult(a, c)))), a))) | (~(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), a)))))) | (~((~(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(b, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), a)))))))),
% 22.84/23.04 inference(quant_inst,[status(thm)],[])).
% 22.84/23.04 tff(7184,plain,
% 22.84/23.04 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(b, mult(a, rd(mult(b, c), mult(a, c)))), a))) | (~(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), a)))))) | (~((~(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(b, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), a))))))),
% 22.84/23.04 inference(modus_ponens,[status(thm)],[7183, 7182])).
% 22.84/23.04 tff(7185,plain,
% 22.84/23.04 ((~((~(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(b, mult(a, rd(mult(b, c), mult(a, c)))), a))) | (~(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), a)))))) | (~((~(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(b, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), a))))))),
% 22.84/23.05 inference(unit_resolution,[status(thm)],[7184, 27])).
% 22.84/23.05 tff(7186,plain,
% 22.84/23.05 (~((~(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(b, mult(a, rd(mult(b, c), mult(a, c)))), a))) | (~(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), a)))))),
% 22.84/23.05 inference(unit_resolution,[status(thm)],[7185, 7181])).
% 22.84/23.05 tff(7187,plain,
% 22.84/23.05 (((~(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(b, mult(a, rd(mult(b, c), mult(a, c)))), a))) | (~(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), a))))) | (mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), a)))),
% 22.84/23.05 inference(tautology,[status(thm)],[])).
% 22.84/23.05 tff(7188,plain,
% 22.84/23.05 (mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), a))),
% 22.84/23.05 inference(unit_resolution,[status(thm)],[7187, 7186])).
% 22.84/23.05 tff(7189,plain,
% 22.84/23.05 (mult(b, mult(mult(a, a), rd(mult(b, c), mult(a, c)))) = mult(b, mult(a, b))),
% 22.84/23.05 inference(transitivity,[status(thm)],[7145, 7188, 7148])).
% 22.84/23.05 tff(7190,plain,
% 22.84/23.05 ((mult(b, mult(mult(a, a), rd(mult(b, c), mult(a, c)))) = mult(b, mult(rd(mult(b, c), mult(a, c)), mult(a, a)))) <=> (mult(b, mult(a, b)) = mult(b, mult(b, a)))),
% 22.84/23.05 inference(monotonicity,[status(thm)],[7189, 7178])).
% 22.84/23.05 tff(7191,plain,
% 22.84/23.05 ((mult(b, mult(a, b)) = mult(b, mult(b, a))) <=> (mult(b, mult(mult(a, a), rd(mult(b, c), mult(a, c)))) = mult(b, mult(rd(mult(b, c), mult(a, c)), mult(a, a))))),
% 22.84/23.05 inference(symmetry,[status(thm)],[7190])).
% 22.84/23.05 tff(7192,plain,
% 22.84/23.05 ((~(mult(b, mult(a, b)) = mult(b, mult(b, a)))) <=> (~(mult(b, mult(mult(a, a), rd(mult(b, c), mult(a, c)))) = mult(b, mult(rd(mult(b, c), mult(a, c)), mult(a, a)))))),
% 22.84/23.05 inference(monotonicity,[status(thm)],[7191])).
% 22.84/23.05 tff(7193,plain,
% 22.84/23.05 (~(mult(b, mult(mult(a, a), rd(mult(b, c), mult(a, c)))) = mult(b, mult(rd(mult(b, c), mult(a, c)), mult(a, a))))),
% 22.84/23.05 inference(modus_ponens,[status(thm)],[412, 7192])).
% 22.84/23.05 tff(7194,plain,
% 22.84/23.05 (((~(mult(mult(b, mult(a, a)), rd(mult(b, c), mult(a, c))) = mult(mult(b, rd(mult(b, c), mult(a, c))), mult(a, a)))) | (~(mult(b, mult(mult(a, a), rd(mult(b, c), mult(a, c)))) = mult(b, mult(rd(mult(b, c), mult(a, c)), mult(a, a)))))) | (mult(b, mult(mult(a, a), rd(mult(b, c), mult(a, c)))) = mult(b, mult(rd(mult(b, c), mult(a, c)), mult(a, a))))),
% 22.84/23.05 inference(tautology,[status(thm)],[])).
% 22.84/23.05 tff(7195,plain,
% 22.84/23.05 ((~(mult(mult(b, mult(a, a)), rd(mult(b, c), mult(a, c))) = mult(mult(b, rd(mult(b, c), mult(a, c))), mult(a, a)))) | (~(mult(b, mult(mult(a, a), rd(mult(b, c), mult(a, c)))) = mult(b, mult(rd(mult(b, c), mult(a, c)), mult(a, a)))))),
% 22.84/23.05 inference(unit_resolution,[status(thm)],[7194, 7193])).
% 22.84/23.05 tff(7196,plain,
% 22.84/23.05 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(b, mult(a, a)), rd(mult(b, c), mult(a, c))) = mult(mult(b, rd(mult(b, c), mult(a, c))), mult(a, a)))) | (~(mult(b, mult(mult(a, a), rd(mult(b, c), mult(a, c)))) = mult(b, mult(rd(mult(b, c), mult(a, c)), mult(a, a))))))) | (~((~(mult(mult(b, mult(a, a)), rd(mult(b, c), mult(a, c))) = mult(b, mult(mult(a, a), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(b, rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(b, mult(rd(mult(b, c), mult(a, c)), mult(a, a))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(b, mult(a, a)), rd(mult(b, c), mult(a, c))) = mult(mult(b, rd(mult(b, c), mult(a, c))), mult(a, a)))) | (~(mult(b, mult(mult(a, a), rd(mult(b, c), mult(a, c)))) = mult(b, mult(rd(mult(b, c), mult(a, c)), mult(a, a))))))) | (~((~(mult(mult(b, mult(a, a)), rd(mult(b, c), mult(a, c))) = mult(b, mult(mult(a, a), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(b, rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(b, mult(rd(mult(b, c), mult(a, c)), mult(a, a))))))))),
% 22.84/23.05 inference(rewrite,[status(thm)],[])).
% 22.84/23.05 tff(7197,plain,
% 22.84/23.05 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(b, mult(a, a)), rd(mult(b, c), mult(a, c))) = mult(mult(b, rd(mult(b, c), mult(a, c))), mult(a, a)))) | (~(mult(b, mult(mult(a, a), rd(mult(b, c), mult(a, c)))) = mult(b, mult(rd(mult(b, c), mult(a, c)), mult(a, a))))))) | (~((~(mult(mult(b, mult(a, a)), rd(mult(b, c), mult(a, c))) = mult(b, mult(mult(a, a), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(b, rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(b, mult(rd(mult(b, c), mult(a, c)), mult(a, a))))))))),
% 22.84/23.05 inference(quant_inst,[status(thm)],[])).
% 22.84/23.05 tff(7198,plain,
% 22.84/23.05 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(b, mult(a, a)), rd(mult(b, c), mult(a, c))) = mult(mult(b, rd(mult(b, c), mult(a, c))), mult(a, a)))) | (~(mult(b, mult(mult(a, a), rd(mult(b, c), mult(a, c)))) = mult(b, mult(rd(mult(b, c), mult(a, c)), mult(a, a))))))) | (~((~(mult(mult(b, mult(a, a)), rd(mult(b, c), mult(a, c))) = mult(b, mult(mult(a, a), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(b, rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(b, mult(rd(mult(b, c), mult(a, c)), mult(a, a)))))))),
% 22.84/23.05 inference(modus_ponens,[status(thm)],[7197, 7196])).
% 22.84/23.05 tff(7199,plain,
% 22.84/23.05 ((~((~(mult(mult(b, mult(a, a)), rd(mult(b, c), mult(a, c))) = mult(mult(b, rd(mult(b, c), mult(a, c))), mult(a, a)))) | (~(mult(b, mult(mult(a, a), rd(mult(b, c), mult(a, c)))) = mult(b, mult(rd(mult(b, c), mult(a, c)), mult(a, a))))))) | (~((~(mult(mult(b, mult(a, a)), rd(mult(b, c), mult(a, c))) = mult(b, mult(mult(a, a), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(b, rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(b, mult(rd(mult(b, c), mult(a, c)), mult(a, a)))))))),
% 22.84/23.05 inference(unit_resolution,[status(thm)],[7198, 27])).
% 22.84/23.05 tff(7200,plain,
% 22.84/23.05 (~((~(mult(mult(b, mult(a, a)), rd(mult(b, c), mult(a, c))) = mult(b, mult(mult(a, a), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(b, rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(b, mult(rd(mult(b, c), mult(a, c)), mult(a, a))))))),
% 22.84/23.05 inference(unit_resolution,[status(thm)],[7199, 7195])).
% 22.84/23.05 tff(7201,plain,
% 22.84/23.05 (((~(mult(mult(b, mult(a, a)), rd(mult(b, c), mult(a, c))) = mult(b, mult(mult(a, a), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(b, rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(b, mult(rd(mult(b, c), mult(a, c)), mult(a, a)))))) | (mult(mult(b, mult(a, a)), rd(mult(b, c), mult(a, c))) = mult(b, mult(mult(a, a), rd(mult(b, c), mult(a, c)))))),
% 22.84/23.05 inference(tautology,[status(thm)],[])).
% 22.84/23.05 tff(7202,plain,
% 22.84/23.05 (mult(mult(b, mult(a, a)), rd(mult(b, c), mult(a, c))) = mult(b, mult(mult(a, a), rd(mult(b, c), mult(a, c))))),
% 22.84/23.05 inference(unit_resolution,[status(thm)],[7201, 7200])).
% 22.84/23.05 tff(7203,plain,
% 22.84/23.05 (mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))),
% 22.84/23.05 inference(modus_ponens,[status(thm)],[7202, 7174])).
% 22.84/23.05 tff(7204,plain,
% 22.84/23.05 ($false),
% 22.84/23.05 inference(unit_resolution,[status(thm)],[7179, 7203])).
% 22.84/23.05 tff(7205,plain,((mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))) | (mult(b, mult(a, b)) = mult(b, mult(b, a))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a))))), inference(lemma,lemma(discharge,[]))).
% 22.84/23.05 tff(7206,plain,
% 22.84/23.05 (mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))),
% 22.84/23.05 inference(unit_resolution,[status(thm)],[7205, 7138, 4331, 6581])).
% 22.84/23.05 tff(7207,assumption,(~(mult(mult(b, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), a)))), introduced(assumption)).
% 22.84/23.05 tff(7208,plain,
% 22.84/23.05 (((~(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(b, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), a))))) | (mult(mult(b, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), a)))),
% 22.84/23.05 inference(tautology,[status(thm)],[])).
% 22.84/23.05 tff(7209,plain,
% 22.84/23.05 ((~(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(b, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), a))))),
% 22.84/23.05 inference(unit_resolution,[status(thm)],[7208, 7207])).
% 22.84/23.05 tff(7210,plain,
% 22.84/23.05 (~((~(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(b, mult(a, rd(mult(b, c), mult(a, c)))), a))) | (~(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), a)))))),
% 22.84/23.05 inference(unit_resolution,[status(thm)],[7185, 7209])).
% 22.84/23.05 tff(7211,plain,
% 22.84/23.05 (mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), a))),
% 22.84/23.05 inference(unit_resolution,[status(thm)],[7187, 7210])).
% 22.84/23.05 tff(7212,assumption,(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))), introduced(assumption)).
% 22.84/23.05 tff(7213,plain,
% 22.84/23.05 (((~(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(b, mult(a, rd(mult(b, c), mult(a, c)))), a))) | (~(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), a))))) | (mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(b, mult(a, rd(mult(b, c), mult(a, c)))), a))),
% 22.84/23.05 inference(tautology,[status(thm)],[])).
% 22.84/23.05 tff(7214,plain,
% 22.84/23.05 (mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(b, mult(a, rd(mult(b, c), mult(a, c)))), a)),
% 22.84/23.05 inference(unit_resolution,[status(thm)],[7213, 7210])).
% 22.84/23.05 tff(7215,plain,
% 22.84/23.05 (mult(mult(b, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c))))),
% 22.84/23.05 inference(symmetry,[status(thm)],[7214])).
% 22.84/23.05 tff(7216,plain,
% 22.84/23.05 (mult(mult(b, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), a))),
% 22.84/23.05 inference(transitivity,[status(thm)],[7215, 7212, 7211])).
% 22.84/23.05 tff(7217,plain,
% 22.84/23.05 ($false),
% 22.84/23.05 inference(unit_resolution,[status(thm)],[7207, 7216])).
% 22.84/23.05 tff(7218,plain,((mult(mult(b, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), a))) | (~(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))), inference(lemma,lemma(discharge,[]))).
% 22.84/23.05 tff(7219,plain,
% 22.84/23.05 (mult(mult(b, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), a))),
% 22.84/23.05 inference(unit_resolution,[status(thm)],[7218, 7206])).
% 22.84/23.05 tff(7220,plain,
% 22.84/23.05 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(b, mult(a, rd(mult(b, c), mult(a, c))))),
% 22.84/23.05 inference(monotonicity,[status(thm)],[5503])).
% 22.84/23.05 tff(7221,plain,
% 22.84/23.05 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(mult(b, mult(a, rd(mult(b, c), mult(a, c)))), a)),
% 22.84/23.05 inference(monotonicity,[status(thm)],[7220])).
% 22.84/23.05 tff(7222,plain,
% 22.84/23.05 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), a)))),
% 22.84/23.05 inference(quant_inst,[status(thm)],[])).
% 22.84/23.05 tff(7223,plain,
% 22.84/23.05 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), a))),
% 22.84/23.05 inference(unit_resolution,[status(thm)],[7222, 56])).
% 22.84/23.05 tff(7224,plain,
% 22.84/23.05 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), a)) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, rd(mult(b, c), mult(a, c)))), a)),
% 22.84/23.05 inference(symmetry,[status(thm)],[7223])).
% 22.84/23.05 tff(7225,plain,
% 22.84/23.05 (mult(mult(a, a), rd(mult(b, c), mult(a, c))) = mult(a, mult(a, rd(mult(b, c), mult(a, c))))),
% 22.84/23.05 inference(unit_resolution,[status(thm)],[1360, 6581])).
% 22.84/23.05 tff(7226,plain,
% 22.84/23.05 (mult(a, mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, a), rd(mult(b, c), mult(a, c)))),
% 22.84/23.05 inference(symmetry,[status(thm)],[7225])).
% 22.84/23.05 tff(7227,plain,
% 22.84/23.05 (mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(a, a), rd(mult(b, c), mult(a, c))), a)),
% 22.84/23.05 inference(monotonicity,[status(thm)],[7226])).
% 22.84/23.05 tff(7228,plain,
% 22.84/23.05 (mult(mult(mult(a, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), a)),
% 22.84/23.05 inference(symmetry,[status(thm)],[7227])).
% 22.84/23.05 tff(7229,plain,
% 22.84/23.05 (mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), a)) = mult(a, mult(a, b))),
% 22.84/23.05 inference(monotonicity,[status(thm)],[7143])).
% 22.84/23.05 tff(7230,plain,
% 22.84/23.05 (mult(a, mult(a, b)) = mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), a))),
% 22.84/23.05 inference(symmetry,[status(thm)],[7229])).
% 22.84/23.05 tff(7231,plain,
% 22.84/23.05 (mult(a, mult(a, b)) = mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), a)),
% 22.84/23.05 inference(transitivity,[status(thm)],[7230, 1395, 7228])).
% 22.84/23.05 tff(7232,plain,
% 22.84/23.05 (mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, b))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), a))),
% 22.84/23.05 inference(monotonicity,[status(thm)],[7231])).
% 22.84/23.05 tff(7233,plain,
% 22.84/23.05 (mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, b))) = mult(mult(b, a), b)),
% 22.84/23.05 inference(transitivity,[status(thm)],[7232, 7224, 7221, 7219, 7144, 7142])).
% 22.84/23.05 tff(7234,plain,
% 22.84/23.05 ((mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, b))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), a))) <=> (mult(mult(b, a), b) = mult(mult(b, b), a))),
% 22.84/23.05 inference(monotonicity,[status(thm)],[7233, 7109])).
% 22.84/23.05 tff(7235,plain,
% 22.84/23.05 ((mult(mult(b, a), b) = mult(mult(b, b), a)) <=> (mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, b))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), a)))),
% 22.84/23.05 inference(symmetry,[status(thm)],[7234])).
% 22.84/23.05 tff(7236,plain,
% 22.84/23.05 ((~(mult(mult(b, a), b) = mult(mult(b, b), a))) <=> (~(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, b))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), a))))),
% 22.84/23.05 inference(monotonicity,[status(thm)],[7235])).
% 22.84/23.05 tff(7237,plain,
% 22.84/23.05 (mult(mult(b, b), a) = mult(b, mult(b, a))),
% 22.84/23.05 inference(unit_resolution,[status(thm)],[422, 7140])).
% 22.84/23.05 tff(7238,plain,
% 22.84/23.05 (mult(b, mult(b, a)) = mult(mult(b, b), a)),
% 22.84/23.05 inference(symmetry,[status(thm)],[7237])).
% 22.84/23.05 tff(7239,plain,
% 22.84/23.05 ((mult(b, mult(a, b)) = mult(b, mult(b, a))) <=> (mult(mult(b, a), b) = mult(mult(b, b), a))),
% 22.84/23.05 inference(monotonicity,[status(thm)],[7142, 7238])).
% 22.84/23.05 tff(7240,plain,
% 22.84/23.05 ((~(mult(b, mult(a, b)) = mult(b, mult(b, a)))) <=> (~(mult(mult(b, a), b) = mult(mult(b, b), a)))),
% 22.84/23.05 inference(monotonicity,[status(thm)],[7239])).
% 22.84/23.05 tff(7241,plain,
% 22.84/23.05 (~(mult(mult(b, a), b) = mult(mult(b, b), a))),
% 22.84/23.05 inference(modus_ponens,[status(thm)],[7138, 7240])).
% 22.84/23.05 tff(7242,plain,
% 22.84/23.05 (~(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, b))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), a)))),
% 22.84/23.05 inference(modus_ponens,[status(thm)],[7241, 7236])).
% 22.84/23.05 tff(7243,plain,
% 22.84/23.05 (((~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, b)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, b)), a))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, b))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), a))))) | (mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, b))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), a)))),
% 22.84/23.06 inference(tautology,[status(thm)],[])).
% 22.84/23.06 tff(7244,plain,
% 22.84/23.06 ((~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, b)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, b)), a))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, b))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), a))))),
% 22.84/23.06 inference(unit_resolution,[status(thm)],[7243, 7242])).
% 22.84/23.06 tff(7245,plain,
% 22.84/23.06 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, b)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, b)), a))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, b))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), a)))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, b)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, b))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, b)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), a)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, b)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, b)), a))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, b))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), a)))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, b)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, b))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, b)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), a)))))))),
% 22.84/23.06 inference(rewrite,[status(thm)],[])).
% 22.84/23.06 tff(7246,plain,
% 22.84/23.06 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, b)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, b)), a))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, b))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), a)))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, b)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, b))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, b)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), a)))))))),
% 22.84/23.06 inference(quant_inst,[status(thm)],[])).
% 22.84/23.06 tff(7247,plain,
% 22.84/23.06 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, b)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, b)), a))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, b))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), a)))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, b)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, b))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, b)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), a))))))),
% 22.84/23.06 inference(modus_ponens,[status(thm)],[7246, 7245])).
% 22.84/23.06 tff(7248,plain,
% 22.84/23.06 ((~((~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, b)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, b)), a))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, b))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), a)))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, b)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, b))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, b)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), a))))))),
% 22.90/23.06 inference(unit_resolution,[status(thm)],[7247, 27])).
% 22.90/23.06 tff(7249,plain,
% 22.90/23.06 (~((~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, b)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, b))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, b)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), a)))))),
% 22.90/23.06 inference(unit_resolution,[status(thm)],[7248, 7244])).
% 22.90/23.06 tff(7250,plain,
% 22.90/23.06 (((~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, b)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, b))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, b)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), a))))) | (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, b)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), a)))),
% 22.90/23.06 inference(tautology,[status(thm)],[])).
% 22.90/23.06 tff(7251,plain,
% 22.90/23.06 (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, b)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), a))),
% 22.90/23.06 inference(unit_resolution,[status(thm)],[7250, 7249])).
% 22.90/23.06 tff(7252,plain,
% 22.90/23.06 (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, b)), a) = mult(mult(unit, mult(mult(b, unit), b)), a)),
% 22.90/23.06 inference(transitivity,[status(thm)],[7251, 2011, 7108])).
% 22.90/23.06 tff(7253,plain,
% 22.90/23.06 (rd(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, b)), a), a) = rd(mult(mult(unit, mult(mult(b, unit), b)), a), a)),
% 22.90/23.06 inference(monotonicity,[status(thm)],[7252])).
% 22.90/23.06 tff(7254,plain,
% 22.90/23.06 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, b)), a), a) = mult(rd(mult(b, c), mult(a, c)), mult(a, b)))),
% 22.90/23.06 inference(quant_inst,[status(thm)],[])).
% 22.90/23.06 tff(7255,plain,
% 22.90/23.06 (rd(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, b)), a), a) = mult(rd(mult(b, c), mult(a, c)), mult(a, b))),
% 22.90/23.06 inference(unit_resolution,[status(thm)],[7254, 168])).
% 22.90/23.06 tff(7256,plain,
% 22.90/23.06 (mult(rd(mult(b, c), mult(a, c)), mult(a, b)) = rd(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, b)), a), a)),
% 22.90/23.06 inference(symmetry,[status(thm)],[7255])).
% 22.90/23.06 tff(7257,plain,
% 22.90/23.06 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, rd(mult(b, c), mult(a, c))), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, b))),
% 22.90/23.06 inference(monotonicity,[status(thm)],[7143])).
% 22.90/23.06 tff(7258,plain,
% 22.90/23.06 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), rd(mult(b, c), mult(a, c))), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, rd(mult(b, c), mult(a, c))), a)))),
% 22.90/23.06 inference(quant_inst,[status(thm)],[])).
% 22.90/23.06 tff(7259,plain,
% 22.90/23.06 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), rd(mult(b, c), mult(a, c))), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, rd(mult(b, c), mult(a, c))), a))),
% 22.90/23.06 inference(unit_resolution,[status(thm)],[7258, 56])).
% 22.90/23.06 tff(7260,plain,
% 22.90/23.06 (mult(mult(b, rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), rd(mult(b, c), mult(a, c))), a)),
% 22.90/23.06 inference(monotonicity,[status(thm)],[6466])).
% 22.90/23.06 tff(7261,plain,
% 22.90/23.06 (mult(mult(b, rd(mult(b, c), mult(a, c))), a) = mult(b, b)),
% 22.90/23.06 inference(transitivity,[status(thm)],[7260, 7259, 7257, 7256, 7253, 552, 429, 1105])).
% 22.90/23.06 tff(7262,plain,
% 22.90/23.06 (mult(mult(mult(b, rd(mult(b, c), mult(a, c))), a), c) = mult(mult(b, b), c)),
% 22.90/23.06 inference(monotonicity,[status(thm)],[7261])).
% 22.90/23.06 tff(7263,plain,
% 22.90/23.06 (mult(mult(mult(b, rd(mult(b, c), mult(a, c))), a), c) = mult(mult(b, c), b)),
% 22.90/23.06 inference(transitivity,[status(thm)],[7262, 7104, 7101, 5563])).
% 22.90/23.06 tff(7264,plain,
% 22.90/23.06 (mult(mult(mult(mult(b, rd(mult(b, c), mult(a, c))), a), c), a) = mult(mult(mult(b, c), b), a)),
% 22.90/23.06 inference(monotonicity,[status(thm)],[7263])).
% 22.90/23.06 tff(7265,plain,
% 22.90/23.06 (mult(mult(mult(b, c), b), a) = mult(mult(mult(mult(b, rd(mult(b, c), mult(a, c))), a), c), a)),
% 22.90/23.06 inference(symmetry,[status(thm)],[7264])).
% 22.90/23.06 tff(7266,plain,
% 22.90/23.06 ((mult(mult(c, b), mult(a, b)) = mult(mult(c, mult(a, b)), b)) <=> (mult(mult(c, mult(a, b)), b) = mult(mult(c, b), mult(a, b)))),
% 22.90/23.06 inference(commutativity,[status(thm)],[])).
% 22.90/23.06 tff(7267,plain,
% 22.90/23.06 ((~(mult(mult(c, b), mult(a, b)) = mult(mult(c, mult(a, b)), b))) <=> (~(mult(mult(c, mult(a, b)), b) = mult(mult(c, b), mult(a, b))))),
% 22.90/23.06 inference(monotonicity,[status(thm)],[7266])).
% 22.90/23.06 tff(7268,plain,
% 22.90/23.06 (~(mult(mult(c, mult(a, b)), b) = mult(mult(c, b), mult(a, b)))),
% 22.90/23.06 inference(modus_ponens,[status(thm)],[7128, 7267])).
% 22.90/23.06 tff(7269,plain,
% 22.90/23.06 (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)))),
% 22.90/23.06 inference(unit_resolution,[status(thm)],[6653, 4331, 4360, 1799, 270, 6581])).
% 22.90/23.06 tff(7270,plain,
% 22.90/23.06 ((~(mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c))))),
% 22.90/23.06 inference(unit_resolution,[status(thm)],[2357, 7269])).
% 22.90/23.06 tff(7271,plain,
% 22.90/23.06 (~((~(mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))))),
% 22.90/23.06 inference(unit_resolution,[status(thm)],[2213, 7270])).
% 22.90/23.06 tff(7272,plain,
% 22.90/23.06 (mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))),
% 22.90/23.06 inference(unit_resolution,[status(thm)],[2201, 7271])).
% 22.90/23.06 tff(7273,plain,
% 22.90/23.06 (mult(mult(b, c), mult(a, b)) = mult(mult(c, b), mult(a, b))),
% 22.90/23.06 inference(symmetry,[status(thm)],[6496])).
% 22.90/23.06 tff(7274,plain,
% 22.90/23.06 (mult(mult(mult(b, c), a), b) = mult(mult(mult(c, b), a), b)),
% 22.90/23.06 inference(monotonicity,[status(thm)],[3057])).
% 22.90/23.06 tff(7275,plain,
% 22.90/23.06 (mult(mult(mult(c, b), a), b) = mult(mult(mult(b, c), a), b)),
% 22.90/23.06 inference(symmetry,[status(thm)],[7274])).
% 22.90/23.06 tff(7276,plain,
% 22.90/23.06 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(a, c), mult(mult(a, c), mult(mult(unit, a), mult(mult(b, unit), b)))) = mult(mult(unit, a), mult(mult(b, unit), b)))),
% 22.90/23.06 inference(quant_inst,[status(thm)],[])).
% 22.90/23.06 tff(7277,plain,
% 22.90/23.06 (ld(mult(a, c), mult(mult(a, c), mult(mult(unit, a), mult(mult(b, unit), b)))) = mult(mult(unit, a), mult(mult(b, unit), b))),
% 22.90/23.06 inference(unit_resolution,[status(thm)],[7276, 7])).
% 22.90/23.06 tff(7278,assumption,(~(mult(mult(c, mult(a, b)), b) = mult(mult(c, b), mult(a, b)))), introduced(assumption)).
% 22.90/23.06 tff(7279,plain,
% 22.90/23.06 (((~(mult(mult(c, mult(a, b)), b) = mult(mult(c, b), mult(a, b)))) | (~(mult(c, mult(mult(a, b), b)) = mult(c, mult(b, mult(a, b)))))) | (mult(mult(c, mult(a, b)), b) = mult(mult(c, b), mult(a, b)))),
% 22.90/23.06 inference(tautology,[status(thm)],[])).
% 22.90/23.06 tff(7280,plain,
% 22.90/23.06 ((~(mult(mult(c, mult(a, b)), b) = mult(mult(c, b), mult(a, b)))) | (~(mult(c, mult(mult(a, b), b)) = mult(c, mult(b, mult(a, b)))))),
% 22.90/23.06 inference(unit_resolution,[status(thm)],[7279, 7278])).
% 22.90/23.06 tff(7281,plain,
% 22.90/23.06 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(c, b), mult(a, b)) = mult(c, mult(b, mult(a, b))))) | (~(mult(mult(c, mult(a, b)), b) = mult(c, mult(mult(a, b), b)))))) | (~((~(mult(mult(c, mult(a, b)), b) = mult(mult(c, b), mult(a, b)))) | (~(mult(c, mult(mult(a, b), b)) = mult(c, mult(b, mult(a, b))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(c, b), mult(a, b)) = mult(c, mult(b, mult(a, b))))) | (~(mult(mult(c, mult(a, b)), b) = mult(c, mult(mult(a, b), b)))))) | (~((~(mult(mult(c, mult(a, b)), b) = mult(mult(c, b), mult(a, b)))) | (~(mult(c, mult(mult(a, b), b)) = mult(c, mult(b, mult(a, b))))))))),
% 22.90/23.06 inference(rewrite,[status(thm)],[])).
% 22.90/23.06 tff(7282,plain,
% 22.90/23.06 (((~((~(mult(mult(c, mult(a, b)), b) = mult(mult(c, b), mult(a, b)))) | (~(mult(c, mult(mult(a, b), b)) = mult(c, mult(b, mult(a, b))))))) | (~((~(mult(mult(c, b), mult(a, b)) = mult(c, mult(b, mult(a, b))))) | (~(mult(mult(c, mult(a, b)), b) = mult(c, mult(mult(a, b), b))))))) <=> ((~((~(mult(mult(c, b), mult(a, b)) = mult(c, mult(b, mult(a, b))))) | (~(mult(mult(c, mult(a, b)), b) = mult(c, mult(mult(a, b), b)))))) | (~((~(mult(mult(c, mult(a, b)), b) = mult(mult(c, b), mult(a, b)))) | (~(mult(c, mult(mult(a, b), b)) = mult(c, mult(b, mult(a, b))))))))),
% 22.90/23.06 inference(rewrite,[status(thm)],[])).
% 22.90/23.06 tff(7283,plain,
% 22.90/23.06 ((~((~(mult(mult(c, mult(a, b)), b) = mult(c, mult(mult(a, b), b)))) | (~(mult(mult(c, b), mult(a, b)) = mult(c, mult(b, mult(a, b))))))) <=> (~((~(mult(mult(c, b), mult(a, b)) = mult(c, mult(b, mult(a, b))))) | (~(mult(mult(c, mult(a, b)), b) = mult(c, mult(mult(a, b), b))))))),
% 22.90/23.06 inference(rewrite,[status(thm)],[])).
% 22.90/23.06 tff(7284,plain,
% 22.90/23.06 ((~((~(mult(mult(c, mult(a, b)), b) = mult(mult(c, b), mult(a, b)))) | (~(mult(c, mult(mult(a, b), b)) = mult(c, mult(b, mult(a, b))))))) <=> (~((~(mult(mult(c, mult(a, b)), b) = mult(mult(c, b), mult(a, b)))) | (~(mult(c, mult(mult(a, b), b)) = mult(c, mult(b, mult(a, b)))))))),
% 22.90/23.06 inference(rewrite,[status(thm)],[])).
% 22.90/23.06 tff(7285,plain,
% 22.90/23.06 (((~((~(mult(mult(c, mult(a, b)), b) = mult(mult(c, b), mult(a, b)))) | (~(mult(c, mult(mult(a, b), b)) = mult(c, mult(b, mult(a, b))))))) | (~((~(mult(mult(c, mult(a, b)), b) = mult(c, mult(mult(a, b), b)))) | (~(mult(mult(c, b), mult(a, b)) = mult(c, mult(b, mult(a, b)))))))) <=> ((~((~(mult(mult(c, mult(a, b)), b) = mult(mult(c, b), mult(a, b)))) | (~(mult(c, mult(mult(a, b), b)) = mult(c, mult(b, mult(a, b))))))) | (~((~(mult(mult(c, b), mult(a, b)) = mult(c, mult(b, mult(a, b))))) | (~(mult(mult(c, mult(a, b)), b) = mult(c, mult(mult(a, b), b)))))))),
% 22.90/23.06 inference(monotonicity,[status(thm)],[7284, 7283])).
% 22.90/23.06 tff(7286,plain,
% 22.90/23.06 (((~((~(mult(mult(c, mult(a, b)), b) = mult(mult(c, b), mult(a, b)))) | (~(mult(c, mult(mult(a, b), b)) = mult(c, mult(b, mult(a, b))))))) | (~((~(mult(mult(c, mult(a, b)), b) = mult(c, mult(mult(a, b), b)))) | (~(mult(mult(c, b), mult(a, b)) = mult(c, mult(b, mult(a, b)))))))) <=> ((~((~(mult(mult(c, b), mult(a, b)) = mult(c, mult(b, mult(a, b))))) | (~(mult(mult(c, mult(a, b)), b) = mult(c, mult(mult(a, b), b)))))) | (~((~(mult(mult(c, mult(a, b)), b) = mult(mult(c, b), mult(a, b)))) | (~(mult(c, mult(mult(a, b), b)) = mult(c, mult(b, mult(a, b))))))))),
% 22.90/23.06 inference(transitivity,[status(thm)],[7285, 7282])).
% 22.90/23.06 tff(7287,plain,
% 22.90/23.06 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(c, mult(a, b)), b) = mult(mult(c, b), mult(a, b)))) | (~(mult(c, mult(mult(a, b), b)) = mult(c, mult(b, mult(a, b))))))) | (~((~(mult(mult(c, mult(a, b)), b) = mult(c, mult(mult(a, b), b)))) | (~(mult(mult(c, b), mult(a, b)) = mult(c, mult(b, mult(a, b))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(c, b), mult(a, b)) = mult(c, mult(b, mult(a, b))))) | (~(mult(mult(c, mult(a, b)), b) = mult(c, mult(mult(a, b), b)))))) | (~((~(mult(mult(c, mult(a, b)), b) = mult(mult(c, b), mult(a, b)))) | (~(mult(c, mult(mult(a, b), b)) = mult(c, mult(b, mult(a, b)))))))))),
% 22.90/23.06 inference(monotonicity,[status(thm)],[7286])).
% 22.90/23.06 tff(7288,plain,
% 22.90/23.06 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(c, mult(a, b)), b) = mult(mult(c, b), mult(a, b)))) | (~(mult(c, mult(mult(a, b), b)) = mult(c, mult(b, mult(a, b))))))) | (~((~(mult(mult(c, mult(a, b)), b) = mult(c, mult(mult(a, b), b)))) | (~(mult(mult(c, b), mult(a, b)) = mult(c, mult(b, mult(a, b))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(c, b), mult(a, b)) = mult(c, mult(b, mult(a, b))))) | (~(mult(mult(c, mult(a, b)), b) = mult(c, mult(mult(a, b), b)))))) | (~((~(mult(mult(c, mult(a, b)), b) = mult(mult(c, b), mult(a, b)))) | (~(mult(c, mult(mult(a, b), b)) = mult(c, mult(b, mult(a, b))))))))),
% 22.90/23.07 inference(transitivity,[status(thm)],[7287, 7281])).
% 22.90/23.07 tff(7289,plain,
% 22.90/23.07 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(c, mult(a, b)), b) = mult(mult(c, b), mult(a, b)))) | (~(mult(c, mult(mult(a, b), b)) = mult(c, mult(b, mult(a, b))))))) | (~((~(mult(mult(c, mult(a, b)), b) = mult(c, mult(mult(a, b), b)))) | (~(mult(mult(c, b), mult(a, b)) = mult(c, mult(b, mult(a, b))))))))),
% 22.90/23.07 inference(quant_inst,[status(thm)],[])).
% 22.90/23.07 tff(7290,plain,
% 22.90/23.07 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(c, b), mult(a, b)) = mult(c, mult(b, mult(a, b))))) | (~(mult(mult(c, mult(a, b)), b) = mult(c, mult(mult(a, b), b)))))) | (~((~(mult(mult(c, mult(a, b)), b) = mult(mult(c, b), mult(a, b)))) | (~(mult(c, mult(mult(a, b), b)) = mult(c, mult(b, mult(a, b)))))))),
% 22.90/23.07 inference(modus_ponens,[status(thm)],[7289, 7288])).
% 22.90/23.07 tff(7291,plain,
% 22.90/23.07 ((~((~(mult(mult(c, b), mult(a, b)) = mult(c, mult(b, mult(a, b))))) | (~(mult(mult(c, mult(a, b)), b) = mult(c, mult(mult(a, b), b)))))) | (~((~(mult(mult(c, mult(a, b)), b) = mult(mult(c, b), mult(a, b)))) | (~(mult(c, mult(mult(a, b), b)) = mult(c, mult(b, mult(a, b)))))))),
% 22.90/23.07 inference(unit_resolution,[status(thm)],[7290, 27])).
% 22.90/23.07 tff(7292,plain,
% 22.90/23.07 (~((~(mult(mult(c, b), mult(a, b)) = mult(c, mult(b, mult(a, b))))) | (~(mult(mult(c, mult(a, b)), b) = mult(c, mult(mult(a, b), b)))))),
% 22.90/23.07 inference(unit_resolution,[status(thm)],[7291, 7280])).
% 22.90/23.07 tff(7293,plain,
% 22.90/23.07 (mult(mult(c, b), mult(a, b)) = mult(c, mult(b, mult(a, b)))),
% 22.90/23.07 inference(unit_resolution,[status(thm)],[7136, 7292])).
% 22.90/23.07 tff(7294,plain,
% 22.90/23.07 (mult(c, mult(b, mult(a, b))) = mult(mult(c, b), mult(a, b))),
% 22.90/23.07 inference(symmetry,[status(thm)],[7293])).
% 22.90/23.07 tff(7295,plain,
% 22.90/23.07 (mult(c, mult(b, mult(a, b))) = mult(c, mult(mult(b, a), b))),
% 22.90/23.07 inference(transitivity,[status(thm)],[7294, 6496, 1312, 7274, 3429])).
% 22.90/23.07 tff(7296,plain,
% 22.90/23.07 (ld(c, mult(c, mult(b, mult(a, b)))) = ld(c, mult(c, mult(mult(b, a), b)))),
% 22.90/23.07 inference(monotonicity,[status(thm)],[7295])).
% 22.90/23.07 tff(7297,plain,
% 22.90/23.07 (ld(c, mult(c, mult(mult(b, a), b))) = ld(c, mult(c, mult(b, mult(a, b))))),
% 22.90/23.07 inference(symmetry,[status(thm)],[7296])).
% 22.90/23.07 tff(7298,plain,
% 22.90/23.07 (mult(mult(b, a), b) = ld(c, mult(c, mult(mult(b, a), b)))),
% 22.90/23.07 inference(symmetry,[status(thm)],[6515])).
% 22.90/23.07 tff(7299,plain,
% 22.90/23.07 (mult(mult(b, a), b) = mult(b, mult(a, b))),
% 22.90/23.07 inference(transitivity,[status(thm)],[7298, 7297, 6523])).
% 22.90/23.07 tff(7300,plain,
% 22.90/23.07 (mult(mult(a, c), mult(mult(b, a), b)) = mult(mult(a, c), mult(b, mult(a, b)))),
% 22.90/23.07 inference(monotonicity,[status(thm)],[7299])).
% 22.90/23.07 tff(7301,plain,
% 22.90/23.07 (mult(mult(a, c), mult(b, mult(a, b))) = mult(mult(a, c), mult(mult(b, a), b))),
% 22.90/23.07 inference(symmetry,[status(thm)],[7300])).
% 22.90/23.07 tff(7302,plain,
% 22.90/23.07 (mult(mult(a, c), mult(mult(a, b), b)) = mult(mult(a, c), mult(b, mult(a, b)))),
% 22.90/23.07 inference(symmetry,[status(thm)],[562])).
% 22.90/23.07 tff(7303,plain,
% 22.90/23.07 (mult(mult(a, c), mult(mult(unit, a), mult(mult(b, unit), b))) = mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b))))),
% 22.90/23.07 inference(monotonicity,[status(thm)],[830])).
% 22.90/23.07 tff(7304,plain,
% 22.90/23.07 (mult(mult(a, c), mult(mult(unit, a), mult(mult(b, unit), b))) = mult(mult(a, c), mult(mult(b, a), b))),
% 22.90/23.07 inference(transitivity,[status(thm)],[7303, 1093, 7302, 7301])).
% 22.90/23.07 tff(7305,plain,
% 22.90/23.07 (ld(mult(a, c), mult(mult(a, c), mult(mult(unit, a), mult(mult(b, unit), b)))) = ld(mult(a, c), mult(mult(a, c), mult(mult(b, a), b)))),
% 22.90/23.07 inference(monotonicity,[status(thm)],[7304])).
% 22.90/23.07 tff(7306,plain,
% 22.90/23.07 (ld(mult(a, c), mult(mult(a, c), mult(mult(b, a), b))) = ld(mult(a, c), mult(mult(a, c), mult(mult(unit, a), mult(mult(b, unit), b))))),
% 22.90/23.07 inference(symmetry,[status(thm)],[7305])).
% 22.90/23.07 tff(7307,plain,
% 22.90/23.07 (mult(mult(b, a), b) = mult(a, mult(unit, mult(mult(b, unit), b)))),
% 22.90/23.07 inference(transitivity,[status(thm)],[1102, 7306, 7277, 830])).
% 22.90/23.07 tff(7308,plain,
% 22.90/23.07 (mult(c, mult(mult(b, a), b)) = mult(c, mult(a, mult(unit, mult(mult(b, unit), b))))),
% 22.90/23.07 inference(monotonicity,[status(thm)],[7307])).
% 22.90/23.07 tff(7309,plain,
% 22.90/23.07 (mult(c, mult(a, mult(unit, mult(mult(b, unit), b)))) = mult(c, mult(mult(b, a), b))),
% 22.90/23.07 inference(symmetry,[status(thm)],[7308])).
% 22.90/23.07 tff(7310,plain,
% 22.90/23.07 (mult(c, mult(a, mult(unit, mult(mult(b, unit), b)))) = mult(c, mult(mult(a, b), b))),
% 22.90/23.07 inference(monotonicity,[status(thm)],[1092])).
% 22.90/23.07 tff(7311,plain,
% 22.90/23.07 (mult(c, mult(mult(a, b), b)) = mult(c, mult(a, mult(unit, mult(mult(b, unit), b))))),
% 22.90/23.07 inference(symmetry,[status(thm)],[7310])).
% 22.90/23.07 tff(7312,plain,
% 22.90/23.07 (((~(mult(mult(c, b), mult(a, b)) = mult(c, mult(b, mult(a, b))))) | (~(mult(mult(c, mult(a, b)), b) = mult(c, mult(mult(a, b), b))))) | (mult(mult(c, mult(a, b)), b) = mult(c, mult(mult(a, b), b)))),
% 22.90/23.07 inference(tautology,[status(thm)],[])).
% 22.90/23.07 tff(7313,plain,
% 22.90/23.07 (mult(mult(c, mult(a, b)), b) = mult(c, mult(mult(a, b), b))),
% 22.90/23.07 inference(unit_resolution,[status(thm)],[7312, 7292])).
% 22.90/23.07 tff(7314,plain,
% 22.90/23.07 (mult(mult(c, mult(a, b)), b) = mult(mult(c, b), mult(a, b))),
% 22.90/23.07 inference(transitivity,[status(thm)],[7313, 7311, 7309, 3430, 7275, 1311, 7273])).
% 22.90/23.07 tff(7315,plain,
% 22.90/23.07 ($false),
% 22.90/23.07 inference(unit_resolution,[status(thm)],[7278, 7314])).
% 22.90/23.07 tff(7316,plain,((~(mult(mult(a, c), mult(b, mult(a, b))) = mult(mult(a, c), mult(mult(a, b), b)))) | (mult(mult(c, mult(a, b)), b) = mult(mult(c, b), mult(a, b))) | (~(mult(mult(mult(b, c), a), b) = mult(mult(b, c), mult(a, b))))), inference(lemma,lemma(discharge,[]))).
% 22.90/23.07 tff(7317,plain,
% 22.90/23.07 (~(mult(mult(a, c), mult(b, mult(a, b))) = mult(mult(a, c), mult(mult(a, b), b)))),
% 22.90/23.07 inference(unit_resolution,[status(thm)],[7316, 7268, 7112])).
% 22.90/23.07 tff(7318,plain,
% 22.90/23.07 ((~(mult(mult(a, c), mult(b, mult(a, b))) = mult(mult(a, c), mult(mult(a, b), b)))) | (~(mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(mult(a, c), mult(a, b)), b)))),
% 22.90/23.07 inference(unit_resolution,[status(thm)],[576, 7317])).
% 22.90/23.07 tff(7319,plain,
% 22.90/23.07 (~((~(mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(a, c), mult(b, mult(a, b))))) | (~(mult(mult(mult(a, c), mult(a, b)), b) = mult(mult(a, c), mult(mult(a, b), b)))))),
% 22.90/23.07 inference(unit_resolution,[status(thm)],[584, 7318])).
% 22.90/23.07 tff(7320,plain,
% 22.90/23.07 (mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(a, c), mult(b, mult(a, b)))),
% 22.90/23.07 inference(unit_resolution,[status(thm)],[604, 7319])).
% 22.90/23.07 tff(7321,plain,
% 22.90/23.07 (mult(mult(a, c), mult(b, mult(a, b))) = mult(mult(mult(a, c), b), mult(a, b))),
% 22.90/23.07 inference(symmetry,[status(thm)],[7320])).
% 22.90/23.07 tff(7322,plain,
% 22.90/23.07 (mult(mult(a, c), mult(mult(b, a), b)) = mult(mult(a, c), mult(b, mult(a, b)))),
% 22.90/23.07 inference(monotonicity,[status(thm)],[7141])).
% 22.90/23.07 tff(7323,plain,
% 22.90/23.07 (mult(mult(mult(mult(a, b), c), a), b) = mult(mult(mult(a, b), c), mult(a, b))),
% 22.90/23.07 inference(transitivity,[status(thm)],[959, 956, 7322, 7321, 949])).
% 22.90/23.07 tff(7324,plain,
% 22.90/23.07 (~(mult(mult(a, c), mult(mult(b, a), b)) = mult(mult(a, c), mult(b, mult(b, a))))),
% 22.90/23.07 inference(unit_resolution,[status(thm)],[974, 7323, 7138, 7320])).
% 22.90/23.07 tff(7325,plain,
% 22.90/23.07 (mult(rd(mult(b, c), mult(a, c)), a) = mult(b, unit)),
% 22.90/23.07 inference(transitivity,[status(thm)],[175, 1379, 170, 431])).
% 22.90/23.07 tff(7326,plain,
% 22.90/23.07 (mult(mult(rd(mult(b, c), mult(a, c)), a), b) = mult(mult(b, unit), b)),
% 22.90/23.07 inference(monotonicity,[status(thm)],[7325])).
% 22.90/23.07 tff(7327,plain,
% 22.90/23.07 (mult(mult(b, unit), b) = mult(mult(rd(mult(b, c), mult(a, c)), a), b)),
% 22.90/23.07 inference(symmetry,[status(thm)],[7326])).
% 22.90/23.07 tff(7328,plain,
% 22.90/23.07 (mult(unit, mult(mult(b, unit), b)) = mult(mult(rd(mult(b, c), mult(a, c)), a), b)),
% 22.90/23.07 inference(transitivity,[status(thm)],[429, 7327])).
% 22.90/23.07 tff(7329,plain,
% 22.90/23.07 (mult(mult(unit, mult(mult(b, unit), b)), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), b), a)),
% 22.90/23.07 inference(monotonicity,[status(thm)],[7328])).
% 22.90/23.07 tff(7330,plain,
% 22.90/23.07 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), b), a) = mult(mult(unit, mult(mult(b, unit), b)), a)),
% 22.90/23.07 inference(symmetry,[status(thm)],[7329])).
% 22.90/23.07 tff(7331,plain,
% 22.90/23.07 (mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), a)) = mult(a, mult(a, b))),
% 22.90/23.07 inference(symmetry,[status(thm)],[1397])).
% 22.90/23.07 tff(7332,plain,
% 22.90/23.07 (mult(mult(mult(a, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), a)),
% 22.90/23.07 inference(monotonicity,[status(thm)],[1361])).
% 22.90/23.07 tff(7333,plain,
% 22.90/23.07 (mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(a, a), rd(mult(b, c), mult(a, c))), a)),
% 22.90/23.07 inference(symmetry,[status(thm)],[7332])).
% 22.90/23.07 tff(7334,plain,
% 22.90/23.07 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), a))) = mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), a))),
% 22.90/23.07 inference(quant_inst,[status(thm)],[])).
% 22.90/23.07 tff(7335,plain,
% 22.90/23.07 (ld(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), a))) = mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), a)),
% 22.90/23.07 inference(unit_resolution,[status(thm)],[7334, 7])).
% 22.90/23.07 tff(7336,plain,
% 22.90/23.07 (mult(a, mult(a, b)) = mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), a)),
% 22.90/23.07 inference(transitivity,[status(thm)],[1397, 1395, 7332])).
% 22.90/23.07 tff(7337,plain,
% 22.90/23.07 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(a, b))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), a))),
% 22.90/23.07 inference(monotonicity,[status(thm)],[7336])).
% 22.90/23.07 tff(7338,assumption,(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(a, b)))), introduced(assumption)).
% 22.90/23.07 tff(7339,plain,
% 22.90/23.07 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), a))),
% 22.90/23.07 inference(transitivity,[status(thm)],[7338, 7337])).
% 22.90/23.07 tff(7340,plain,
% 22.90/23.07 (ld(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a))) = ld(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), a)))),
% 22.90/23.07 inference(monotonicity,[status(thm)],[7339])).
% 22.90/23.07 tff(7341,plain,
% 22.90/23.07 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a))) = mult(mult(a, b), a))),
% 22.90/23.07 inference(quant_inst,[status(thm)],[])).
% 22.90/23.07 tff(7342,plain,
% 22.90/23.07 (ld(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a))) = mult(mult(a, b), a)),
% 22.90/23.07 inference(unit_resolution,[status(thm)],[7341, 7])).
% 22.90/23.07 tff(7343,plain,
% 22.90/23.07 (mult(mult(a, b), a) = ld(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a)))),
% 22.90/23.07 inference(symmetry,[status(thm)],[7342])).
% 22.90/23.07 tff(7344,plain,
% 22.90/23.07 (mult(mult(a, b), a) = mult(a, mult(a, b))),
% 22.90/23.07 inference(transitivity,[status(thm)],[7343, 7340, 7335, 7333, 1394, 7331])).
% 22.90/23.07 tff(7345,plain,
% 22.90/23.07 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, b)))),
% 22.90/23.07 inference(monotonicity,[status(thm)],[7344])).
% 22.90/23.07 tff(7346,plain,
% 22.90/23.07 (mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, b))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), a))),
% 22.90/23.07 inference(symmetry,[status(thm)],[7345])).
% 22.90/23.07 tff(7347,plain,
% 22.90/23.07 (mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, b))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), a))),
% 22.90/23.07 inference(monotonicity,[status(thm)],[7336])).
% 22.90/23.07 tff(7348,plain,
% 22.90/23.07 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, b)))),
% 22.90/23.07 inference(symmetry,[status(thm)],[7347])).
% 22.90/23.07 tff(7349,plain,
% 22.90/23.07 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(b, mult(a, rd(mult(b, c), mult(a, c))))),
% 22.90/23.07 inference(monotonicity,[status(thm)],[1380])).
% 22.90/23.07 tff(7350,plain,
% 22.90/23.07 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(mult(b, mult(a, rd(mult(b, c), mult(a, c)))), a)),
% 22.90/23.07 inference(monotonicity,[status(thm)],[7349])).
% 22.90/23.07 tff(7351,plain,
% 22.90/23.07 (mult(mult(b, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, rd(mult(b, c), mult(a, c)))), a)),
% 22.90/23.07 inference(symmetry,[status(thm)],[7350])).
% 22.90/23.07 tff(7352,assumption,(mult(mult(b, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), a))), introduced(assumption)).
% 22.90/23.07 tff(7353,plain,
% 22.90/23.07 (mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), a)) = mult(mult(b, mult(a, rd(mult(b, c), mult(a, c)))), a)),
% 22.90/23.07 inference(symmetry,[status(thm)],[7352])).
% 22.90/23.07 tff(7354,plain,
% 22.90/23.07 (mult(b, mult(a, b)) = mult(b, mult(b, a))),
% 22.90/23.07 inference(transitivity,[status(thm)],[7149, 7353, 7351, 7223, 7348, 7346, 2011, 7330, 435, 423])).
% 22.90/23.07 tff(7355,plain,
% 22.90/23.07 ($false),
% 22.90/23.07 inference(unit_resolution,[status(thm)],[412, 7354])).
% 22.90/23.07 tff(7356,plain,((~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(a, b))))) | (mult(b, mult(a, b)) = mult(b, mult(b, a))) | (~(mult(mult(b, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), a)))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))), inference(lemma,lemma(discharge,[]))).
% 22.90/23.07 tff(7357,plain,
% 22.90/23.07 (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(a, b))))),
% 22.90/23.07 inference(unit_resolution,[status(thm)],[7356, 7219, 6581, 7138, 4331])).
% 22.90/23.07 tff(7358,plain,
% 22.90/23.07 (((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, b)), a) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(a, b)))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(a, b)))))) | (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(a, b))))),
% 22.90/23.07 inference(tautology,[status(thm)],[])).
% 22.90/23.07 tff(7359,plain,
% 22.90/23.07 ((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, b)), a) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(a, b)))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(a, b)))))),
% 22.90/23.07 inference(unit_resolution,[status(thm)],[7358, 7357])).
% 22.90/23.07 tff(7360,plain,
% 22.90/23.07 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, b)), a) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(a, b)))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(a, b))))))) | (~((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, b)), a) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a)))) | (~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(a, b)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(a, b))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, b)), a) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(a, b)))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(a, b))))))) | (~((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, b)), a) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a)))) | (~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(a, b)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(a, b))))))))),
% 22.90/23.08 inference(rewrite,[status(thm)],[])).
% 22.90/23.08 tff(7361,plain,
% 22.90/23.08 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, b)), a) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(a, b)))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(a, b))))))) | (~((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, b)), a) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a)))) | (~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(a, b)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(a, b))))))))),
% 22.90/23.08 inference(quant_inst,[status(thm)],[])).
% 22.90/23.08 tff(7362,plain,
% 22.90/23.08 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, b)), a) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(a, b)))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(a, b))))))) | (~((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, b)), a) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a)))) | (~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(a, b)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(a, b)))))))),
% 22.90/23.08 inference(modus_ponens,[status(thm)],[7361, 7360])).
% 22.90/23.08 tff(7363,plain,
% 22.90/23.08 (~((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, b)), a) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a)))) | (~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(a, b)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(a, b))))))),
% 22.90/23.08 inference(unit_resolution,[status(thm)],[7362, 27, 7359])).
% 22.90/23.08 tff(7364,plain,
% 22.90/23.08 (((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, b)), a) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a)))) | (~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(a, b)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(a, b)))))) | (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(a, b)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(a, b))))),
% 22.90/23.08 inference(tautology,[status(thm)],[])).
% 22.90/23.08 tff(7365,plain,
% 22.90/23.08 (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(a, b)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(a, b)))),
% 22.90/23.08 inference(unit_resolution,[status(thm)],[7364, 7363])).
% 22.90/23.08 tff(7366,assumption,(~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, b)), a) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a)))), introduced(assumption)).
% 22.90/23.08 tff(7367,assumption,(~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(a, b))))), introduced(assumption)).
% 22.90/23.08 tff(7368,plain,
% 22.90/23.08 ((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, b)), a) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(a, b)))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(a, b)))))),
% 22.90/23.08 inference(unit_resolution,[status(thm)],[7358, 7367])).
% 22.90/23.08 tff(7369,plain,
% 22.90/23.08 (((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, b)), a) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a)))) | (~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(a, b)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(a, b)))))) | (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, b)), a) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a)))),
% 22.90/23.08 inference(tautology,[status(thm)],[])).
% 22.90/23.08 tff(7370,plain,
% 22.90/23.08 ((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, b)), a) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a)))) | (~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(a, b)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(a, b)))))),
% 22.90/23.08 inference(unit_resolution,[status(thm)],[7369, 7366])).
% 22.90/23.08 tff(7371,assumption,((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, b)), a) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(a, b)))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(a, b)))))), introduced(assumption)).
% 22.90/23.08 tff(7372,plain,
% 22.90/23.08 ($false),
% 22.90/23.08 inference(unit_resolution,[status(thm)],[7362, 27, 7371, 7370])).
% 22.90/23.08 tff(7373,plain,((~((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, b)), a) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(a, b)))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(a, b))))))) | (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, b)), a) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a)))), inference(lemma,lemma(discharge,[]))).
% 22.90/23.08 tff(7374,plain,
% 22.90/23.08 ($false),
% 22.90/23.08 inference(unit_resolution,[status(thm)],[7373, 7368, 7366])).
% 22.90/23.08 tff(7375,plain,((mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, b)), a) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a))) | (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(a, b))))), inference(lemma,lemma(discharge,[]))).
% 22.90/23.08 tff(7376,plain,
% 22.90/23.08 (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, b)), a) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a))),
% 22.90/23.08 inference(unit_resolution,[status(thm)],[7375, 7357])).
% 22.90/23.08 tff(7377,plain,
% 22.90/23.08 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(a, b))) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(a, b))),
% 22.90/23.08 inference(symmetry,[status(thm)],[7365])).
% 22.90/23.08 tff(7378,plain,
% 22.90/23.08 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a)) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, b)), a)),
% 22.90/23.08 inference(symmetry,[status(thm)],[7376])).
% 22.90/23.08 tff(7379,plain,
% 22.90/23.08 ((mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(a, b)))) <=> (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, b)), a) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(a, b)))),
% 22.90/23.08 inference(monotonicity,[status(thm)],[7378, 7377])).
% 22.90/23.08 tff(7380,plain,
% 22.90/23.08 ((~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(a, b))))) <=> (~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, b)), a) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(a, b))))),
% 22.90/23.08 inference(monotonicity,[status(thm)],[7379])).
% 22.90/23.08 tff(7381,plain,
% 22.90/23.08 (~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, b)), a) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(a, b)))),
% 22.90/23.08 inference(modus_ponens,[status(thm)],[7357, 7380])).
% 22.90/23.08 tff(7382,assumption,(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(a, b)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(a, b)))), introduced(assumption)).
% 22.90/23.08 tff(7383,plain,
% 22.90/23.08 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(a, b))) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(a, b))),
% 22.90/23.08 inference(symmetry,[status(thm)],[7382])).
% 22.90/23.08 tff(7384,plain,
% 22.90/23.08 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, b)))) = mult(a, mult(a, b)))),
% 22.90/23.08 inference(quant_inst,[status(thm)],[])).
% 22.90/23.08 tff(7385,plain,
% 22.90/23.08 (ld(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, b)))) = mult(a, mult(a, b))),
% 22.90/23.08 inference(unit_resolution,[status(thm)],[7384, 7])).
% 22.90/23.08 tff(7386,assumption,(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, b), a)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, b)))), introduced(assumption)).
% 22.90/23.08 tff(7387,plain,
% 22.90/23.08 (ld(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, b), a))) = ld(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, b))))),
% 22.90/23.08 inference(monotonicity,[status(thm)],[7386])).
% 22.90/23.08 tff(7388,plain,
% 22.90/23.08 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, b), a))) = mult(mult(a, b), a))),
% 22.90/23.08 inference(quant_inst,[status(thm)],[])).
% 22.90/23.08 tff(7389,plain,
% 22.90/23.08 (ld(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, b), a))) = mult(mult(a, b), a)),
% 22.90/23.08 inference(unit_resolution,[status(thm)],[7388, 7])).
% 22.90/23.08 tff(7390,plain,
% 22.90/23.08 (mult(mult(a, b), a) = ld(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, b), a)))),
% 22.90/23.08 inference(symmetry,[status(thm)],[7389])).
% 22.90/23.08 tff(7391,plain,
% 22.90/23.08 (mult(mult(a, b), a) = mult(a, mult(a, b))),
% 22.90/23.08 inference(transitivity,[status(thm)],[7390, 7387, 7385])).
% 22.90/23.08 tff(7392,plain,
% 22.90/23.08 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(a, b)))),
% 22.90/23.08 inference(monotonicity,[status(thm)],[7391])).
% 22.90/23.08 tff(7393,assumption,(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, b)), a) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a))), introduced(assumption)).
% 22.90/23.08 tff(7394,plain,
% 22.90/23.08 (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, b)), a) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(a, b))),
% 22.90/23.08 inference(transitivity,[status(thm)],[7393, 7392, 7383])).
% 22.90/23.08 tff(7395,assumption,(~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, b)), a) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(a, b)))), introduced(assumption)).
% 22.90/23.08 tff(7396,plain,
% 22.90/23.08 ($false),
% 22.90/23.08 inference(unit_resolution,[status(thm)],[7395, 7394])).
% 22.90/23.08 tff(7397,plain,((~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, b), a)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, b))))) | (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, b)), a) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(a, b))) | (~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, b)), a) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), a)))) | (~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(a, b)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(a, b)))))), inference(lemma,lemma(discharge,[]))).
% 22.90/23.08 tff(7398,plain,
% 22.90/23.08 (~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, b), a)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, b))))),
% 22.90/23.08 inference(unit_resolution,[status(thm)],[7397, 7381, 7376, 7365])).
% 22.90/23.08 tff(7399,plain,
% 22.90/23.08 (((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, b)), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, b)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, b), a)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, b)))))) | (mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, b), a)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, b))))),
% 22.90/23.09 inference(tautology,[status(thm)],[])).
% 22.90/23.09 tff(7400,plain,
% 22.90/23.09 ((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, b)), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, b)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, b), a)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, b)))))),
% 22.90/23.09 inference(unit_resolution,[status(thm)],[7399, 7398])).
% 22.90/23.09 tff(7401,plain,
% 22.90/23.09 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, b)), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, b)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, b), a)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, b))))))) | (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, b)), a) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, b), a)))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, b)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, b))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, b)), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, b)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, b), a)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, b))))))) | (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, b)), a) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, b), a)))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, b)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, b))))))))),
% 22.90/23.09 inference(rewrite,[status(thm)],[])).
% 22.90/23.09 tff(7402,plain,
% 22.90/23.09 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, b)), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, b)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, b), a)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, b))))))) | (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, b)), a) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, b), a)))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, b)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, b))))))))),
% 22.90/23.09 inference(quant_inst,[status(thm)],[])).
% 22.90/23.09 tff(7403,plain,
% 22.90/23.09 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, b)), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, b)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, b), a)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, b))))))) | (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, b)), a) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, b), a)))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, b)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, b)))))))),
% 22.90/23.09 inference(modus_ponens,[status(thm)],[7402, 7401])).
% 22.90/23.09 tff(7404,plain,
% 22.90/23.09 ((~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, b)), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, b)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, b), a)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, b))))))) | (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, b)), a) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, b), a)))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, b)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, b)))))))),
% 22.90/23.09 inference(unit_resolution,[status(thm)],[7403, 27])).
% 22.90/23.09 tff(7405,plain,
% 22.90/23.09 (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, b)), a) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, b), a)))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, b)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, b))))))),
% 22.90/23.09 inference(unit_resolution,[status(thm)],[7404, 7400])).
% 22.90/23.09 tff(7406,plain,
% 22.90/23.09 (((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, b)), a) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, b), a)))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, b)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, b)))))) | (mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, b)), a) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, b), a)))),
% 22.90/23.09 inference(tautology,[status(thm)],[])).
% 22.90/23.09 tff(7407,plain,
% 22.90/23.09 (mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, b)), a) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, b), a))),
% 22.90/23.09 inference(unit_resolution,[status(thm)],[7406, 7405])).
% 22.90/23.09 tff(7408,assumption,(~(mult(mult(a, c), mult(mult(b, a), b)) = mult(mult(a, c), mult(b, mult(b, a))))), introduced(assumption)).
% 22.90/23.09 tff(7409,plain,
% 22.90/23.09 ((~(mult(mult(mult(a, c), mult(b, a)), b) = mult(mult(mult(a, c), b), mult(b, a)))) | (~(mult(mult(a, c), mult(mult(b, a), b)) = mult(mult(a, c), mult(b, mult(b, a)))))),
% 22.90/23.09 inference(unit_resolution,[status(thm)],[617, 7408])).
% 22.90/23.09 tff(7410,plain,
% 22.90/23.09 (~((~(mult(mult(mult(a, c), mult(b, a)), b) = mult(mult(a, c), mult(mult(b, a), b)))) | (~(mult(mult(mult(a, c), b), mult(b, a)) = mult(mult(a, c), mult(b, mult(b, a))))))),
% 22.90/23.09 inference(unit_resolution,[status(thm)],[622, 7409])).
% 22.90/23.09 tff(7411,plain,
% 22.90/23.09 (mult(mult(mult(a, c), b), mult(b, a)) = mult(mult(a, c), mult(b, mult(b, a)))),
% 22.90/23.09 inference(unit_resolution,[status(thm)],[624, 7410])).
% 22.90/23.09 tff(7412,plain,
% 22.90/23.09 ((mult(mult(a, c), mult(b, mult(b, a))) = mult(mult(a, c), mult(mult(b, a), b))) <=> (mult(mult(a, c), mult(mult(b, a), b)) = mult(mult(a, c), mult(b, mult(b, a))))),
% 22.90/23.09 inference(commutativity,[status(thm)],[])).
% 22.90/23.09 tff(7413,plain,
% 22.90/23.09 (mult(mult(a, c), mult(b, mult(a, b))) = mult(mult(a, c), mult(mult(b, a), b))),
% 22.90/23.09 inference(symmetry,[status(thm)],[608])).
% 22.90/23.09 tff(7414,plain,
% 22.90/23.09 (mult(mult(mult(a, b), c), mult(a, b)) = mult(mult(a, c), mult(mult(b, a), b))),
% 22.90/23.09 inference(transitivity,[status(thm)],[574, 961, 7413])).
% 22.90/23.09 tff(7415,plain,
% 22.90/23.09 (mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(a, c), mult(b, mult(b, a)))),
% 22.90/23.09 inference(transitivity,[status(thm)],[626, 7411])).
% 22.90/23.09 tff(7416,plain,
% 22.90/23.09 ((mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(a, b))) <=> (mult(mult(a, c), mult(b, mult(b, a))) = mult(mult(a, c), mult(mult(b, a), b)))),
% 22.90/23.09 inference(monotonicity,[status(thm)],[7415, 7414])).
% 22.90/23.09 tff(7417,plain,
% 22.90/23.09 ((mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(a, b))) <=> (mult(mult(a, c), mult(mult(b, a), b)) = mult(mult(a, c), mult(b, mult(b, a))))),
% 22.90/23.09 inference(transitivity,[status(thm)],[7416, 7412])).
% 22.90/23.09 tff(7418,plain,
% 22.90/23.09 ((mult(mult(a, c), mult(mult(b, a), b)) = mult(mult(a, c), mult(b, mult(b, a)))) <=> (mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(a, b)))),
% 22.90/23.09 inference(symmetry,[status(thm)],[7417])).
% 22.90/23.09 tff(7419,plain,
% 22.90/23.09 ((~(mult(mult(a, c), mult(mult(b, a), b)) = mult(mult(a, c), mult(b, mult(b, a))))) <=> (~(mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(a, b))))),
% 22.90/23.09 inference(monotonicity,[status(thm)],[7418])).
% 22.90/23.09 tff(7420,plain,
% 22.90/23.09 (~(mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(a, b)))),
% 22.90/23.09 inference(modus_ponens,[status(thm)],[7408, 7419])).
% 22.90/23.09 tff(7421,plain,
% 22.90/23.09 ((~(mult(mult(mult(mult(a, b), c), b), a) = mult(mult(mult(mult(a, b), c), a), b))) | (~(mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(a, b))))),
% 22.90/23.09 inference(unit_resolution,[status(thm)],[637, 7420])).
% 22.90/23.09 tff(7422,plain,
% 22.90/23.09 (~((~(mult(mult(mult(mult(a, b), c), b), a) = mult(mult(mult(a, b), c), mult(b, a)))) | (~(mult(mult(mult(mult(a, b), c), a), b) = mult(mult(mult(a, b), c), mult(a, b)))))),
% 22.90/23.09 inference(unit_resolution,[status(thm)],[642, 7421])).
% 22.90/23.09 tff(7423,plain,
% 22.90/23.09 (mult(mult(mult(mult(a, b), c), b), a) = mult(mult(mult(a, b), c), mult(b, a))),
% 22.90/23.09 inference(unit_resolution,[status(thm)],[644, 7422])).
% 22.90/23.09 tff(7424,plain,
% 22.90/23.09 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(b, c), b), a), a) = mult(mult(b, c), b))),
% 22.90/23.09 inference(quant_inst,[status(thm)],[])).
% 22.90/23.09 tff(7425,plain,
% 22.90/23.09 (rd(mult(mult(mult(b, c), b), a), a) = mult(mult(b, c), b)),
% 22.90/23.09 inference(unit_resolution,[status(thm)],[7424, 168])).
% 22.90/23.09 tff(7426,plain,
% 22.90/23.09 (mult(mult(rd(mult(b, c), mult(a, c)), c), a) = mult(b, c)),
% 22.90/23.09 inference(transitivity,[status(thm)],[83, 4360, 4340, 1377, 1374, 1370])).
% 22.90/23.09 tff(7427,plain,
% 22.90/23.09 (mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), b) = mult(mult(b, c), b)),
% 22.90/23.09 inference(monotonicity,[status(thm)],[7426])).
% 22.90/23.09 tff(7428,plain,
% 22.90/23.09 (mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), b), a) = mult(mult(mult(b, c), b), a)),
% 22.90/23.09 inference(monotonicity,[status(thm)],[7427])).
% 22.90/23.09 tff(7429,plain,
% 22.90/23.09 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), b), a) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, b), a)))),
% 22.90/23.09 inference(quant_inst,[status(thm)],[])).
% 22.90/23.09 tff(7430,plain,
% 22.90/23.09 (mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), b), a) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, b), a))),
% 22.90/23.09 inference(unit_resolution,[status(thm)],[7429, 56])).
% 22.90/23.09 tff(7431,plain,
% 22.90/23.09 (mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, b), a)) = mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), b), a)),
% 22.90/23.09 inference(symmetry,[status(thm)],[7430])).
% 22.90/23.09 tff(7432,assumption,(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, b)), a) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, b), a))), introduced(assumption)).
% 22.90/23.09 tff(7433,plain,
% 22.90/23.09 (mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, b)), a) = mult(mult(mult(b, c), b), a)),
% 22.90/23.09 inference(transitivity,[status(thm)],[7432, 7431, 7428])).
% 22.90/23.09 tff(7434,plain,
% 22.90/23.09 (rd(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, b)), a), a) = rd(mult(mult(mult(b, c), b), a), a)),
% 22.90/23.09 inference(monotonicity,[status(thm)],[7433])).
% 22.90/23.09 tff(7435,plain,
% 22.90/23.09 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, b)), a), a) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, b)))),
% 22.90/23.09 inference(quant_inst,[status(thm)],[])).
% 22.90/23.09 tff(7436,plain,
% 22.90/23.09 (rd(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, b)), a), a) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, b))),
% 22.90/23.09 inference(unit_resolution,[status(thm)],[7435, 168])).
% 22.90/23.09 tff(7437,plain,
% 22.90/23.09 (mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, b)) = rd(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, b)), a), a)),
% 22.90/23.09 inference(symmetry,[status(thm)],[7436])).
% 22.90/23.09 tff(7438,plain,
% 22.90/23.09 (mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, rd(mult(b, c), mult(a, c))), a)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, b))),
% 22.90/23.09 inference(monotonicity,[status(thm)],[7147])).
% 22.90/23.09 tff(7439,plain,
% 22.90/23.09 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), rd(mult(b, c), mult(a, c))), a) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, rd(mult(b, c), mult(a, c))), a)))),
% 22.90/23.09 inference(quant_inst,[status(thm)],[])).
% 22.90/23.09 tff(7440,plain,
% 22.90/23.09 (mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), rd(mult(b, c), mult(a, c))), a) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, rd(mult(b, c), mult(a, c))), a))),
% 22.90/23.09 inference(unit_resolution,[status(thm)],[7439, 56])).
% 22.90/23.09 tff(7441,plain,
% 22.90/23.09 (mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), rd(mult(b, c), mult(a, c))) = mult(mult(b, c), rd(mult(b, c), mult(a, c)))),
% 22.90/23.09 inference(monotonicity,[status(thm)],[7426])).
% 22.90/23.09 tff(7442,plain,
% 22.90/23.09 (mult(mult(b, c), rd(mult(b, c), mult(a, c))) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), rd(mult(b, c), mult(a, c)))),
% 22.90/23.09 inference(symmetry,[status(thm)],[7441])).
% 22.90/23.09 tff(7443,plain,
% 22.90/23.09 (mult(mult(mult(b, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), rd(mult(b, c), mult(a, c))), a)),
% 22.90/23.09 inference(monotonicity,[status(thm)],[7442])).
% 22.90/23.09 tff(7444,plain,
% 22.90/23.09 (mult(mult(mult(b, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(b, c), b)),
% 22.90/23.09 inference(transitivity,[status(thm)],[7443, 7440, 7438, 7437, 7434, 7425])).
% 22.90/23.09 tff(7445,plain,
% 22.90/23.09 (mult(a, mult(mult(mult(b, c), rd(mult(b, c), mult(a, c))), a)) = mult(mult(unit, a), mult(mult(b, c), b))),
% 22.90/23.09 inference(monotonicity,[status(thm)],[245, 7444])).
% 22.90/23.09 tff(7446,plain,
% 22.90/23.09 (mult(mult(mult(a, b), c), b) = mult(mult(c, mult(a, b)), b)),
% 22.90/23.09 inference(symmetry,[status(thm)],[7117])).
% 22.90/23.09 tff(7447,plain,
% 22.90/23.09 (mult(a, mult(mult(mult(b, c), rd(mult(b, c), mult(a, c))), a)) = mult(mult(c, mult(a, b)), b)),
% 22.90/23.09 inference(transitivity,[status(thm)],[7445, 778, 783, 7446])).
% 22.90/23.09 tff(7448,plain,
% 22.90/23.09 (mult(mult(b, c), mult(mult(a, rd(mult(b, c), mult(a, c))), a)) = mult(mult(b, c), mult(a, b))),
% 22.90/23.09 inference(monotonicity,[status(thm)],[7147])).
% 22.90/23.09 tff(7449,plain,
% 22.90/23.09 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(b, mult(b, mult(mult(b, c), a))) = mult(mult(b, c), a))),
% 22.90/23.09 inference(quant_inst,[status(thm)],[])).
% 22.90/23.09 tff(7450,plain,
% 22.90/23.09 (ld(b, mult(b, mult(mult(b, c), a))) = mult(mult(b, c), a)),
% 22.90/23.09 inference(unit_resolution,[status(thm)],[7449, 7])).
% 22.90/23.09 tff(7451,assumption,(mult(b, mult(a, mult(b, c))) = mult(b, mult(mult(b, c), a))), introduced(assumption)).
% 22.90/23.09 tff(7452,plain,
% 22.90/23.09 (ld(b, mult(b, mult(a, mult(b, c)))) = ld(b, mult(b, mult(mult(b, c), a)))),
% 22.90/23.09 inference(monotonicity,[status(thm)],[7451])).
% 22.90/23.09 tff(7453,plain,
% 22.90/23.09 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(b, mult(b, mult(a, mult(b, c)))) = mult(a, mult(b, c)))),
% 22.90/23.09 inference(quant_inst,[status(thm)],[])).
% 22.90/23.09 tff(7454,plain,
% 22.90/23.09 (ld(b, mult(b, mult(a, mult(b, c)))) = mult(a, mult(b, c))),
% 22.90/23.09 inference(unit_resolution,[status(thm)],[7453, 7])).
% 22.90/23.09 tff(7455,plain,
% 22.90/23.09 (mult(a, mult(b, c)) = ld(b, mult(b, mult(a, mult(b, c))))),
% 22.90/23.09 inference(symmetry,[status(thm)],[7454])).
% 22.90/23.09 tff(7456,plain,
% 22.90/23.09 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(b, c), a)),
% 22.90/23.09 inference(transitivity,[status(thm)],[287, 142, 7455, 7452, 7450])).
% 22.90/23.09 tff(7457,plain,
% 22.90/23.09 (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(b, c), a), rd(mult(b, c), mult(a, c)))),
% 22.90/23.09 inference(monotonicity,[status(thm)],[7456])).
% 22.90/23.09 tff(7458,plain,
% 22.90/23.09 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), rd(mult(b, c), mult(a, c)))))),
% 22.90/23.09 inference(quant_inst,[status(thm)],[])).
% 22.90/23.09 tff(7459,plain,
% 22.90/23.09 (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), rd(mult(b, c), mult(a, c))))),
% 22.90/23.09 inference(unit_resolution,[status(thm)],[7458, 56])).
% 22.90/23.09 tff(7460,plain,
% 22.90/23.09 (mult(a, mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 22.90/23.09 inference(symmetry,[status(thm)],[7459])).
% 22.90/23.09 tff(7461,plain,
% 22.90/23.09 (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(b, c), rd(mult(b, c), mult(a, c)))),
% 22.90/23.09 inference(monotonicity,[status(thm)],[137])).
% 22.90/23.09 tff(7462,plain,
% 22.90/23.09 (mult(mult(b, c), rd(mult(b, c), mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 22.90/23.09 inference(symmetry,[status(thm)],[7461])).
% 22.90/23.09 tff(7463,plain,
% 22.90/23.09 (mult(rd(mult(b, c), mult(a, c)), mult(c, a)) = mult(b, c)),
% 22.90/23.09 inference(transitivity,[status(thm)],[3867, 3862, 61, 137])).
% 22.90/23.09 tff(7464,plain,
% 22.90/23.09 (mult(mult(rd(mult(b, c), mult(a, c)), mult(c, a)), rd(mult(b, c), mult(a, c))) = mult(mult(b, c), rd(mult(b, c), mult(a, c)))),
% 22.90/23.09 inference(monotonicity,[status(thm)],[7463])).
% 22.90/23.09 tff(7465,plain,
% 22.90/23.09 (mult(mult(rd(mult(b, c), mult(a, c)), mult(c, a)), rd(mult(b, c), mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 22.90/23.09 inference(transitivity,[status(thm)],[7464, 7462])).
% 22.90/23.09 tff(7466,plain,
% 22.90/23.09 (mult(a, mult(mult(rd(mult(b, c), mult(a, c)), mult(c, a)), rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), rd(mult(b, c), mult(a, c))))),
% 22.90/23.09 inference(monotonicity,[status(thm)],[7465])).
% 22.90/23.09 tff(7467,plain,
% 22.90/23.09 (mult(mult(b, c), rd(mult(b, c), mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), mult(c, a)), rd(mult(b, c), mult(a, c)))),
% 22.90/23.10 inference(symmetry,[status(thm)],[7464])).
% 22.90/23.10 tff(7468,plain,
% 22.90/23.10 (mult(a, mult(mult(b, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), mult(c, a)), rd(mult(b, c), mult(a, c))))),
% 22.90/23.10 inference(monotonicity,[status(thm)],[7467])).
% 22.90/23.10 tff(7469,plain,
% 22.90/23.10 (mult(a, mult(mult(b, c), rd(mult(b, c), mult(a, c)))) = mult(mult(mult(b, c), a), rd(mult(b, c), mult(a, c)))),
% 22.90/23.10 inference(transitivity,[status(thm)],[7468, 7466, 7460, 7457])).
% 22.90/23.10 tff(7470,plain,
% 22.90/23.10 (mult(mult(a, mult(mult(b, c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(mult(b, c), a), rd(mult(b, c), mult(a, c))), a)),
% 22.90/23.10 inference(monotonicity,[status(thm)],[7469])).
% 22.90/23.10 tff(7471,plain,
% 22.90/23.10 (mult(mult(a, mult(mult(b, c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(c, b), mult(a, b))),
% 22.90/23.10 inference(transitivity,[status(thm)],[7470, 1214, 7448, 7273])).
% 22.90/23.10 tff(7472,plain,
% 22.90/23.10 ((mult(mult(a, mult(mult(b, c), rd(mult(b, c), mult(a, c)))), a) = mult(a, mult(mult(mult(b, c), rd(mult(b, c), mult(a, c))), a))) <=> (mult(mult(c, b), mult(a, b)) = mult(mult(c, mult(a, b)), b))),
% 22.90/23.10 inference(monotonicity,[status(thm)],[7471, 7447])).
% 22.90/23.10 tff(7473,plain,
% 22.90/23.10 ((mult(mult(a, mult(mult(b, c), rd(mult(b, c), mult(a, c)))), a) = mult(a, mult(mult(mult(b, c), rd(mult(b, c), mult(a, c))), a))) <=> (mult(mult(c, mult(a, b)), b) = mult(mult(c, b), mult(a, b)))),
% 22.90/23.10 inference(transitivity,[status(thm)],[7472, 7266])).
% 22.90/23.10 tff(7474,plain,
% 22.90/23.10 ((mult(mult(c, mult(a, b)), b) = mult(mult(c, b), mult(a, b))) <=> (mult(mult(a, mult(mult(b, c), rd(mult(b, c), mult(a, c)))), a) = mult(a, mult(mult(mult(b, c), rd(mult(b, c), mult(a, c))), a)))),
% 22.90/23.10 inference(symmetry,[status(thm)],[7473])).
% 22.90/23.10 tff(7475,plain,
% 22.90/23.10 ((~(mult(mult(c, mult(a, b)), b) = mult(mult(c, b), mult(a, b)))) <=> (~(mult(mult(a, mult(mult(b, c), rd(mult(b, c), mult(a, c)))), a) = mult(a, mult(mult(mult(b, c), rd(mult(b, c), mult(a, c))), a))))),
% 22.90/23.10 inference(monotonicity,[status(thm)],[7474])).
% 22.90/23.10 tff(7476,plain,
% 22.90/23.10 (~(mult(mult(a, mult(mult(b, c), rd(mult(b, c), mult(a, c)))), a) = mult(a, mult(mult(mult(b, c), rd(mult(b, c), mult(a, c))), a)))),
% 22.90/23.10 inference(modus_ponens,[status(thm)],[7278, 7475])).
% 22.90/23.10 tff(7477,plain,
% 22.90/23.10 (((~(mult(mult(a, a), mult(mult(b, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(a, mult(mult(b, c), rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(mult(b, c), rd(mult(b, c), mult(a, c)))), a) = mult(a, mult(mult(mult(b, c), rd(mult(b, c), mult(a, c))), a))))) | (mult(mult(a, mult(mult(b, c), rd(mult(b, c), mult(a, c)))), a) = mult(a, mult(mult(mult(b, c), rd(mult(b, c), mult(a, c))), a)))),
% 22.90/23.10 inference(tautology,[status(thm)],[])).
% 22.90/23.10 tff(7478,plain,
% 22.90/23.10 ((~(mult(mult(a, a), mult(mult(b, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(a, mult(mult(b, c), rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(mult(b, c), rd(mult(b, c), mult(a, c)))), a) = mult(a, mult(mult(mult(b, c), rd(mult(b, c), mult(a, c))), a))))),
% 22.90/23.10 inference(unit_resolution,[status(thm)],[7477, 7476])).
% 22.90/23.10 tff(7479,plain,
% 22.90/23.10 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, a), mult(mult(b, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(mult(b, c), rd(mult(b, c), mult(a, c)))), a))) | (~(mult(a, mult(a, mult(mult(b, c), rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(mult(b, c), rd(mult(b, c), mult(a, c))), a)))))) | (~((~(mult(mult(a, a), mult(mult(b, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(a, mult(mult(b, c), rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(mult(b, c), rd(mult(b, c), mult(a, c)))), a) = mult(a, mult(mult(mult(b, c), rd(mult(b, c), mult(a, c))), a)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, a), mult(mult(b, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(mult(b, c), rd(mult(b, c), mult(a, c)))), a))) | (~(mult(a, mult(a, mult(mult(b, c), rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(mult(b, c), rd(mult(b, c), mult(a, c))), a)))))) | (~((~(mult(mult(a, a), mult(mult(b, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(a, mult(mult(b, c), rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(mult(b, c), rd(mult(b, c), mult(a, c)))), a) = mult(a, mult(mult(mult(b, c), rd(mult(b, c), mult(a, c))), a)))))))),
% 22.90/23.10 inference(rewrite,[status(thm)],[])).
% 22.90/23.10 tff(7480,plain,
% 22.90/23.10 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, a), mult(mult(b, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(mult(b, c), rd(mult(b, c), mult(a, c)))), a))) | (~(mult(a, mult(a, mult(mult(b, c), rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(mult(b, c), rd(mult(b, c), mult(a, c))), a)))))) | (~((~(mult(mult(a, a), mult(mult(b, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(a, mult(mult(b, c), rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(mult(b, c), rd(mult(b, c), mult(a, c)))), a) = mult(a, mult(mult(mult(b, c), rd(mult(b, c), mult(a, c))), a)))))))),
% 22.90/23.10 inference(quant_inst,[status(thm)],[])).
% 22.90/23.10 tff(7481,plain,
% 22.90/23.10 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, a), mult(mult(b, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(mult(b, c), rd(mult(b, c), mult(a, c)))), a))) | (~(mult(a, mult(a, mult(mult(b, c), rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(mult(b, c), rd(mult(b, c), mult(a, c))), a)))))) | (~((~(mult(mult(a, a), mult(mult(b, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(a, mult(mult(b, c), rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(mult(b, c), rd(mult(b, c), mult(a, c)))), a) = mult(a, mult(mult(mult(b, c), rd(mult(b, c), mult(a, c))), a))))))),
% 22.90/23.10 inference(modus_ponens,[status(thm)],[7480, 7479])).
% 22.90/23.10 tff(7482,plain,
% 22.90/23.10 ((~((~(mult(mult(a, a), mult(mult(b, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(mult(b, c), rd(mult(b, c), mult(a, c)))), a))) | (~(mult(a, mult(a, mult(mult(b, c), rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(mult(b, c), rd(mult(b, c), mult(a, c))), a)))))) | (~((~(mult(mult(a, a), mult(mult(b, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(a, mult(mult(b, c), rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(mult(b, c), rd(mult(b, c), mult(a, c)))), a) = mult(a, mult(mult(mult(b, c), rd(mult(b, c), mult(a, c))), a))))))),
% 22.90/23.10 inference(unit_resolution,[status(thm)],[7481, 27])).
% 22.90/23.10 tff(7483,plain,
% 22.90/23.10 (~((~(mult(mult(a, a), mult(mult(b, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(mult(b, c), rd(mult(b, c), mult(a, c)))), a))) | (~(mult(a, mult(a, mult(mult(b, c), rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(mult(b, c), rd(mult(b, c), mult(a, c))), a)))))),
% 22.90/23.10 inference(unit_resolution,[status(thm)],[7482, 7478])).
% 22.90/23.10 tff(7484,plain,
% 22.90/23.10 (((~(mult(mult(a, a), mult(mult(b, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(mult(b, c), rd(mult(b, c), mult(a, c)))), a))) | (~(mult(a, mult(a, mult(mult(b, c), rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(mult(b, c), rd(mult(b, c), mult(a, c))), a))))) | (mult(a, mult(a, mult(mult(b, c), rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(mult(b, c), rd(mult(b, c), mult(a, c))), a)))),
% 22.90/23.10 inference(tautology,[status(thm)],[])).
% 22.90/23.10 tff(7485,plain,
% 22.90/23.10 (mult(a, mult(a, mult(mult(b, c), rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(mult(b, c), rd(mult(b, c), mult(a, c))), a))),
% 22.90/23.10 inference(unit_resolution,[status(thm)],[7484, 7483])).
% 22.90/23.10 tff(7486,plain,
% 22.90/23.10 (mult(a, mult(mult(rd(mult(b, c), mult(a, c)), mult(c, a)), rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(b, c), rd(mult(b, c), mult(a, c))))),
% 22.90/23.10 inference(symmetry,[status(thm)],[7468])).
% 22.90/23.10 tff(7487,plain,
% 22.90/23.10 (mult(a, mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), mult(c, a)), rd(mult(b, c), mult(a, c))))),
% 22.90/23.10 inference(symmetry,[status(thm)],[7466])).
% 22.90/23.10 tff(7488,plain,
% 22.90/23.10 (mult(mult(mult(b, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 22.90/23.10 inference(symmetry,[status(thm)],[7457])).
% 22.90/23.10 tff(7489,plain,
% 22.90/23.10 (mult(mult(mult(b, c), a), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(b, c), rd(mult(b, c), mult(a, c))))),
% 22.90/23.10 inference(transitivity,[status(thm)],[7488, 7459, 7487, 7486])).
% 22.90/23.10 tff(7490,plain,
% 22.90/23.10 (mult(a, mult(mult(mult(b, c), a), rd(mult(b, c), mult(a, c)))) = mult(a, mult(a, mult(mult(b, c), rd(mult(b, c), mult(a, c)))))),
% 22.90/23.10 inference(monotonicity,[status(thm)],[7489])).
% 22.90/23.10 tff(7491,plain,
% 22.90/23.10 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)) = mult(mult(b, c), a)),
% 22.90/23.10 inference(transitivity,[status(thm)],[1372, 1332])).
% 22.90/23.10 tff(7492,plain,
% 22.90/23.10 (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(b, c), a), rd(mult(b, c), mult(a, c)))),
% 22.90/23.10 inference(monotonicity,[status(thm)],[7491])).
% 22.90/23.10 tff(7493,plain,
% 22.90/23.10 (mult(a, mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(mult(b, c), a), rd(mult(b, c), mult(a, c))))),
% 22.90/23.10 inference(monotonicity,[status(thm)],[7492])).
% 22.90/23.10 tff(7494,assumption,(~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), c))), introduced(assumption)).
% 22.90/23.10 tff(7495,plain,
% 22.90/23.10 ((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), c))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))))),
% 22.90/23.10 inference(unit_resolution,[status(thm)],[6618, 7494])).
% 22.90/23.10 tff(7496,plain,
% 22.90/23.10 (~((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), a) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, a)))) | (~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), c) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))))),
% 22.90/23.10 inference(unit_resolution,[status(thm)],[762, 7495])).
% 22.90/23.10 tff(7497,plain,
% 22.90/23.10 (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), c) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))),
% 22.90/23.10 inference(unit_resolution,[status(thm)],[764, 7496])).
% 22.90/23.10 tff(7498,plain,
% 22.90/23.10 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), c)),
% 22.90/23.10 inference(symmetry,[status(thm)],[7497])).
% 22.90/23.10 tff(7499,plain,
% 22.90/23.10 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))),
% 22.90/23.10 inference(monotonicity,[status(thm)],[3885])).
% 22.90/23.10 tff(7500,plain,
% 22.90/23.10 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), c)),
% 22.90/23.10 inference(transitivity,[status(thm)],[7499, 7498])).
% 22.90/23.10 tff(7501,plain,
% 22.90/23.10 ((mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), a) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, a))) <=> (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), c))),
% 22.90/23.10 inference(monotonicity,[status(thm)],[7500])).
% 22.90/23.10 tff(7502,plain,
% 22.90/23.10 ((mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), c)) <=> (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), a) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, a)))),
% 22.90/23.10 inference(symmetry,[status(thm)],[7501])).
% 22.90/23.10 tff(7503,plain,
% 22.90/23.10 ((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), c))) <=> (~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), a) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, a))))),
% 22.90/23.10 inference(monotonicity,[status(thm)],[7502])).
% 22.90/23.10 tff(7504,plain,
% 22.90/23.10 (~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), a) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, a)))),
% 22.90/23.10 inference(modus_ponens,[status(thm)],[7494, 7503])).
% 22.90/23.10 tff(7505,plain,
% 22.90/23.10 (((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), a) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, a)))) | (~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), c) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))))) | (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), a) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, a)))),
% 22.90/23.10 inference(tautology,[status(thm)],[])).
% 22.90/23.10 tff(7506,plain,
% 22.90/23.10 (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), a) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, a))),
% 22.90/23.10 inference(unit_resolution,[status(thm)],[7505, 7496])).
% 22.90/23.10 tff(7507,plain,
% 22.90/23.10 ($false),
% 22.90/23.10 inference(unit_resolution,[status(thm)],[7506, 7504])).
% 22.90/23.10 tff(7508,plain,((mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), c)) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit)))))), inference(lemma,lemma(discharge,[]))).
% 22.90/23.10 tff(7509,plain,
% 22.90/23.10 (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), c)),
% 22.90/23.10 inference(unit_resolution,[status(thm)],[7508, 3862])).
% 22.90/23.10 tff(7510,plain,
% 22.90/23.10 (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), a)),
% 22.90/23.10 inference(symmetry,[status(thm)],[7509])).
% 22.90/23.10 tff(7511,plain,
% 22.90/23.10 (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), c) = mult(mult(a, b), c)),
% 22.90/23.10 inference(transitivity,[status(thm)],[7510, 5948, 1799, 2232, 161])).
% 22.90/23.10 tff(7512,plain,
% 22.90/23.10 (mult(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), c), a) = mult(mult(mult(a, b), c), a)),
% 22.90/23.10 inference(monotonicity,[status(thm)],[7511])).
% 22.90/23.10 tff(7513,plain,
% 22.90/23.10 (mult(mult(mult(a, b), c), a) = mult(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), c), a)),
% 22.90/23.10 inference(symmetry,[status(thm)],[7512])).
% 22.90/23.10 tff(7514,plain,
% 22.90/23.10 (mult(mult(mult(a, b), c), a) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a))),
% 22.90/23.10 inference(transitivity,[status(thm)],[7513, 2135])).
% 22.90/23.10 tff(7515,plain,
% 22.90/23.10 (mult(mult(mult(mult(a, b), c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)), rd(mult(b, c), mult(a, c)))),
% 22.90/23.10 inference(monotonicity,[status(thm)],[7514])).
% 22.90/23.10 tff(7516,plain,
% 22.90/23.10 (mult(mult(mult(mult(a, b), c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, b), c), b)),
% 22.90/23.10 inference(transitivity,[status(thm)],[7515, 2140, 7493, 7490, 7485, 7445, 778, 783])).
% 22.90/23.10 tff(7517,plain,
% 22.90/23.10 (mult(mult(mult(mult(mult(a, b), c), a), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(mult(a, b), c), b), a)),
% 22.90/23.10 inference(monotonicity,[status(thm)],[7516])).
% 22.90/23.10 tff(7518,plain,
% 22.90/23.10 (mult(mult(mult(a, b), c), mult(mult(a, rd(mult(b, c), mult(a, c))), a)) = mult(mult(mult(mult(mult(a, b), c), a), rd(mult(b, c), mult(a, c))), a)),
% 22.90/23.11 inference(symmetry,[status(thm)],[649])).
% 22.90/23.11 tff(7519,plain,
% 22.90/23.11 (mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(mult(a, b), c), mult(mult(a, rd(mult(b, c), mult(a, c))), a))),
% 22.90/23.11 inference(monotonicity,[status(thm)],[161, 1396])).
% 22.90/23.11 tff(7520,plain,
% 22.90/23.11 (mult(mult(a, c), mult(mult(b, a), b)) = mult(mult(a, c), mult(b, mult(b, a)))),
% 22.90/23.11 inference(transitivity,[status(thm)],[608, 1095, 7519, 7518, 7517, 7423, 626, 7411])).
% 22.90/23.11 tff(7521,plain,
% 22.90/23.11 ($false),
% 22.90/23.11 inference(unit_resolution,[status(thm)],[7408, 7520])).
% 22.90/23.11 tff(7522,plain,((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, b)), a) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, b), a)))) | (mult(mult(a, c), mult(mult(b, a), b)) = mult(mult(a, c), mult(b, mult(b, a)))) | (~(mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(a, c), mult(b, mult(a, b))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (~(mult(b, mult(a, mult(b, c))) = mult(b, mult(mult(b, c), a)))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(b, a), b) = mult(b, mult(a, b)))) | (mult(mult(c, mult(a, b)), b) = mult(mult(c, b), mult(a, b)))), inference(lemma,lemma(discharge,[]))).
% 22.90/23.11 tff(7523,plain,
% 22.90/23.11 (~(mult(b, mult(a, mult(b, c))) = mult(b, mult(mult(b, c), a)))),
% 22.90/23.11 inference(unit_resolution,[status(thm)],[7522, 7407, 7320, 4360, 4331, 279, 7324, 1799, 7272, 6581, 7141, 7268])).
% 22.90/23.11 tff(7524,plain,
% 22.90/23.11 (((~(mult(mult(b, a), mult(b, c)) = mult(mult(b, mult(b, c)), a))) | (~(mult(b, mult(a, mult(b, c))) = mult(b, mult(mult(b, c), a))))) | (mult(b, mult(a, mult(b, c))) = mult(b, mult(mult(b, c), a)))),
% 22.90/23.11 inference(tautology,[status(thm)],[])).
% 22.90/23.11 tff(7525,plain,
% 22.90/23.11 ((~(mult(mult(b, a), mult(b, c)) = mult(mult(b, mult(b, c)), a))) | (~(mult(b, mult(a, mult(b, c))) = mult(b, mult(mult(b, c), a))))),
% 22.90/23.11 inference(unit_resolution,[status(thm)],[7524, 7523])).
% 22.90/23.11 tff(7526,plain,
% 22.90/23.11 (~((~(mult(mult(b, a), mult(b, c)) = mult(b, mult(a, mult(b, c))))) | (~(mult(mult(b, mult(b, c)), a) = mult(b, mult(mult(b, c), a)))))),
% 22.90/23.11 inference(unit_resolution,[status(thm)],[6974, 7525])).
% 22.90/23.11 tff(7527,plain,
% 22.90/23.11 (mult(mult(b, mult(b, c)), a) = mult(b, mult(mult(b, c), a))),
% 22.90/23.11 inference(unit_resolution,[status(thm)],[6976, 7526])).
% 22.90/23.11 tff(7528,plain,
% 22.90/23.11 (mult(b, mult(mult(b, c), a)) = mult(mult(b, mult(b, c)), a)),
% 22.90/23.11 inference(symmetry,[status(thm)],[7527])).
% 22.90/23.11 tff(7529,plain,
% 22.90/23.11 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)) = mult(mult(b, c), a)),
% 22.90/23.11 inference(transitivity,[status(thm)],[5498, 1332])).
% 22.90/23.11 tff(7530,plain,
% 22.90/23.11 (mult(b, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) = mult(b, mult(mult(b, c), a))),
% 22.90/23.11 inference(monotonicity,[status(thm)],[7529])).
% 22.90/23.11 tff(7531,plain,
% 22.90/23.11 (mult(mult(mult(b, c), a), mult(a, b)) = mult(mult(b, c), mult(a, mult(a, b)))),
% 22.90/23.11 inference(unit_resolution,[status(thm)],[1320, 7112])).
% 22.90/23.11 tff(7532,plain,
% 22.90/23.11 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, a)) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c))),
% 22.90/23.11 inference(monotonicity,[status(thm)],[5700])).
% 22.90/23.11 tff(7533,plain,
% 22.90/23.11 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a)),
% 22.90/23.11 inference(transitivity,[status(thm)],[1168, 5498])).
% 22.90/23.11 tff(7534,plain,
% 22.90/23.11 ((mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, a))) <=> (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)))),
% 22.90/23.11 inference(monotonicity,[status(thm)],[7533, 7532])).
% 22.90/23.11 tff(7535,plain,
% 22.90/23.11 ((mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, a))) <=> (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a))),
% 22.90/23.11 inference(transitivity,[status(thm)],[7534, 1429])).
% 22.90/23.11 tff(7536,plain,
% 22.90/23.11 ((mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a)) <=> (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, a)))),
% 22.90/23.11 inference(symmetry,[status(thm)],[7535])).
% 22.90/23.11 tff(7537,plain,
% 22.90/23.11 (mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c))),
% 22.90/23.11 inference(symmetry,[status(thm)],[4333])).
% 22.90/23.11 tff(7538,plain,
% 22.90/23.11 ((mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) <=> (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a))),
% 22.90/23.11 inference(monotonicity,[status(thm)],[7537, 5498])).
% 22.90/23.11 tff(7539,plain,
% 22.90/23.11 ((mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) <=> (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, a)))),
% 22.90/23.11 inference(transitivity,[status(thm)],[7538, 7536])).
% 22.90/23.11 tff(7540,plain,
% 22.90/23.11 ((~(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) <=> (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, a))))),
% 22.90/23.11 inference(monotonicity,[status(thm)],[7539])).
% 22.90/23.11 tff(7541,plain,
% 22.90/23.11 (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, a)))),
% 22.90/23.11 inference(modus_ponens,[status(thm)],[4327, 7540])).
% 22.90/23.11 tff(7542,plain,
% 22.90/23.11 ((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, a))))),
% 22.90/23.11 inference(unit_resolution,[status(thm)],[6337, 7541])).
% 22.90/23.11 tff(7543,plain,
% 22.90/23.11 (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, a)))))),
% 22.90/23.11 inference(unit_resolution,[status(thm)],[6335, 7542])).
% 22.90/23.11 tff(7544,plain,
% 22.90/23.11 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a)),
% 22.90/23.11 inference(unit_resolution,[status(thm)],[6330, 7543])).
% 22.90/23.11 tff(7545,plain,
% 22.90/23.11 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, b), c)) = mult(mult(unit, b), mult(mult(a, b), c))),
% 22.90/23.11 inference(symmetry,[status(thm)],[5602])).
% 22.90/23.11 tff(7546,plain,
% 22.90/23.11 (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, b), c), a)))),
% 22.90/23.11 inference(unit_resolution,[status(thm)],[5586, 5557, 1371])).
% 22.90/23.11 tff(7547,plain,
% 22.90/23.11 ((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, b), c), a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, b), c)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(a, b), c)))))),
% 22.90/23.11 inference(unit_resolution,[status(thm)],[5588, 7546])).
% 22.90/23.11 tff(7548,plain,
% 22.90/23.11 (~((~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, b), c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(a, b), c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, b), c)))))),
% 22.90/23.11 inference(unit_resolution,[status(thm)],[5596, 7547])).
% 22.90/23.11 tff(7549,plain,
% 22.90/23.11 (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, b), c))),
% 22.90/23.11 inference(unit_resolution,[status(thm)],[5598, 7548])).
% 22.90/23.11 tff(7550,plain,
% 22.90/23.11 (mult(b, mult(mult(b, c), a)) = mult(mult(b, mult(b, c)), a)),
% 22.90/23.11 inference(symmetry,[status(thm)],[6990])).
% 22.90/23.11 tff(7551,plain,
% 22.90/23.11 (mult(b, mult(mult(b, c), a)) = mult(b, mult(mult(a, b), c))),
% 22.90/23.11 inference(transitivity,[status(thm)],[7550, 6961, 5561, 7549, 7545, 3388])).
% 22.90/23.11 tff(7552,plain,
% 22.90/23.11 (ld(b, mult(b, mult(mult(b, c), a))) = ld(b, mult(b, mult(mult(a, b), c)))),
% 22.90/23.11 inference(monotonicity,[status(thm)],[7551])).
% 22.90/23.11 tff(7553,plain,
% 22.90/23.11 (mult(mult(b, c), a) = ld(b, mult(b, mult(mult(b, c), a)))),
% 22.90/23.11 inference(symmetry,[status(thm)],[7450])).
% 22.90/23.11 tff(7554,plain,
% 22.90/23.11 (mult(c, mult(b, a)) = mult(c, mult(a, b))),
% 22.90/23.11 inference(transitivity,[status(thm)],[4304, 2298, 7553, 7552, 5605, 227, 6986, 4221])).
% 22.90/23.11 tff(7555,plain,
% 22.90/23.11 ($false),
% 22.90/23.11 inference(unit_resolution,[status(thm)],[2302, 7554])).
% 22.90/23.11 tff(7556,plain,((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), b) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), b)))) | (mult(c, mult(b, a)) = mult(c, mult(a, b))) | (~(mult(mult(b, mult(b, c)), a) = mult(b, mult(mult(b, c), a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))), inference(lemma,lemma(discharge,[]))).
% 22.90/23.11 tff(7557,plain,
% 22.90/23.11 (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), b) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), b)))),
% 22.90/23.11 inference(unit_resolution,[status(thm)],[7556, 7115, 7527, 4331])).
% 22.90/23.11 tff(7558,plain,
% 22.90/23.11 ((~(mult(mult(rd(mult(b, c), mult(a, c)), b), mult(a, c)) = mult(rd(mult(b, c), mult(a, c)), mult(b, mult(a, c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), b) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), b))))),
% 22.90/23.11 inference(unit_resolution,[status(thm)],[5549, 7557])).
% 22.90/23.11 tff(7559,plain,
% 22.90/23.11 (~((~(mult(mult(rd(mult(b, c), mult(a, c)), b), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), b))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(b, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), b)))))),
% 22.90/23.11 inference(unit_resolution,[status(thm)],[5547, 7558])).
% 22.90/23.11 tff(7560,plain,
% 22.90/23.11 (mult(rd(mult(b, c), mult(a, c)), mult(b, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), b))),
% 22.90/23.11 inference(unit_resolution,[status(thm)],[5542, 7559])).
% 22.90/23.11 tff(7561,plain,
% 22.90/23.11 (((~(mult(mult(b, a), mult(b, c)) = mult(b, mult(a, mult(b, c))))) | (~(mult(mult(b, mult(b, c)), a) = mult(b, mult(mult(b, c), a))))) | (mult(mult(b, a), mult(b, c)) = mult(b, mult(a, mult(b, c))))),
% 22.90/23.11 inference(tautology,[status(thm)],[])).
% 22.90/23.11 tff(7562,plain,
% 22.90/23.11 (mult(mult(b, a), mult(b, c)) = mult(b, mult(a, mult(b, c)))),
% 22.90/23.11 inference(unit_resolution,[status(thm)],[7561, 7526])).
% 22.90/23.11 tff(7563,plain,
% 22.90/23.11 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), c)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c)))),
% 22.90/23.11 inference(monotonicity,[status(thm)],[6893])).
% 22.90/23.11 tff(7564,plain,
% 22.90/23.11 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), c))),
% 22.90/23.11 inference(symmetry,[status(thm)],[7563])).
% 22.90/23.11 tff(7565,plain,
% 22.90/23.11 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(c, a), c))),
% 22.90/23.11 inference(monotonicity,[status(thm)],[3877])).
% 22.90/23.11 tff(7566,plain,
% 22.90/23.11 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(c, a), c)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c)))),
% 22.90/23.11 inference(symmetry,[status(thm)],[7565])).
% 22.90/23.11 tff(7567,plain,
% 22.90/23.11 (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(mult(unit, c), unit)) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), c)),
% 22.90/23.11 inference(monotonicity,[status(thm)],[78])).
% 22.90/23.11 tff(7568,plain,
% 22.90/23.11 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), unit), c), unit) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(mult(unit, c), unit)))),
% 22.90/23.11 inference(quant_inst,[status(thm)],[])).
% 22.90/23.11 tff(7569,plain,
% 22.90/23.11 (mult(mult(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), unit), c), unit) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(mult(unit, c), unit))),
% 22.90/23.11 inference(unit_resolution,[status(thm)],[7568, 56])).
% 22.90/23.11 tff(7570,plain,
% 22.90/23.11 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(unit, a), unit)) = mult(mult(a, rd(mult(b, c), mult(a, c))), a)),
% 22.90/23.11 inference(monotonicity,[status(thm)],[507])).
% 22.90/23.11 tff(7571,plain,
% 22.90/23.11 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), unit), a), unit) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(unit, a), unit)))),
% 22.90/23.11 inference(quant_inst,[status(thm)],[])).
% 22.90/23.11 tff(7572,plain,
% 22.90/23.11 (mult(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), unit), a), unit) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(unit, a), unit))),
% 22.90/23.11 inference(unit_resolution,[status(thm)],[7571, 56])).
% 22.90/23.11 tff(7573,plain,
% 22.90/23.11 (mult(mult(a, rd(mult(b, c), mult(a, c))), unit) = mult(a, rd(mult(b, c), mult(a, c)))),
% 22.90/23.11 inference(transitivity,[status(thm)],[1902, 1899, 1897])).
% 22.90/23.11 tff(7574,plain,
% 22.90/23.11 (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), unit), a) = mult(mult(a, rd(mult(b, c), mult(a, c))), a)),
% 22.90/23.11 inference(monotonicity,[status(thm)],[7573])).
% 22.90/23.11 tff(7575,plain,
% 22.90/23.11 (mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), unit), a)),
% 22.90/23.11 inference(symmetry,[status(thm)],[7574])).
% 22.90/23.11 tff(7576,plain,
% 22.90/23.11 (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), unit) = mult(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), unit), a), unit)),
% 22.90/23.11 inference(monotonicity,[status(thm)],[7575])).
% 22.90/23.11 tff(7577,plain,
% 22.90/23.11 (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), unit) = mult(mult(a, rd(mult(b, c), mult(a, c))), a)),
% 22.90/23.11 inference(transitivity,[status(thm)],[7576, 7572, 7570])).
% 22.90/23.11 tff(7578,plain,
% 22.90/23.11 (mult(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), unit), c) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), c)),
% 22.90/23.11 inference(monotonicity,[status(thm)],[7577])).
% 22.90/23.11 tff(7579,plain,
% 22.90/23.11 (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), unit), c)),
% 22.90/23.11 inference(symmetry,[status(thm)],[7578])).
% 22.90/23.11 tff(7580,plain,
% 22.90/23.11 (mult(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), c), unit) = mult(mult(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), unit), c), unit)),
% 22.90/23.11 inference(monotonicity,[status(thm)],[7579])).
% 22.90/23.11 tff(7581,plain,
% 22.90/23.11 (mult(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), c), unit) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), a)),
% 22.90/23.11 inference(transitivity,[status(thm)],[7580, 7569, 7567, 7510])).
% 22.90/23.11 tff(7582,plain,
% 22.90/23.11 (mult(mult(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), c), unit), c) = mult(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), a), c)),
% 22.90/23.11 inference(monotonicity,[status(thm)],[7581])).
% 22.90/23.11 tff(7583,plain,
% 22.90/23.11 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), c), unit), c) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(mult(c, unit), c)))),
% 22.90/23.11 inference(quant_inst,[status(thm)],[])).
% 22.90/23.11 tff(7584,plain,
% 22.90/23.11 (mult(mult(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), c), unit), c) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(mult(c, unit), c))),
% 22.90/23.11 inference(unit_resolution,[status(thm)],[7583, 56])).
% 22.90/23.11 tff(7585,plain,
% 22.90/23.11 (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(mult(c, unit), c)) = mult(mult(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), c), unit), c)),
% 22.90/23.11 inference(symmetry,[status(thm)],[7584])).
% 22.90/23.11 tff(7586,plain,
% 22.90/23.11 (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(c, c)) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(mult(c, unit), c))),
% 22.90/23.11 inference(monotonicity,[status(thm)],[2617])).
% 22.90/23.11 tff(7587,plain,
% 22.90/23.11 (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(c, c)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(c, c)))),
% 22.90/23.11 inference(transitivity,[status(thm)],[7586, 7585, 7582, 5951, 7566, 7564, 5920])).
% 22.90/23.11 tff(7588,plain,
% 22.90/23.11 ((mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c) = mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a))) <=> (mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c))),
% 22.90/23.12 inference(commutativity,[status(thm)],[])).
% 22.90/23.12 tff(7589,plain,
% 22.90/23.12 (mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a))),
% 22.90/23.12 inference(monotonicity,[status(thm)],[3878])).
% 22.90/23.12 tff(7590,plain,
% 22.90/23.12 (mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a))),
% 22.90/23.12 inference(transitivity,[status(thm)],[6126, 7589])).
% 22.90/23.12 tff(7591,plain,
% 22.90/23.12 (mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c)),
% 22.90/23.12 inference(monotonicity,[status(thm)],[1800])).
% 22.90/23.12 tff(7592,plain,
% 22.90/23.12 (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c)),
% 22.90/23.12 inference(symmetry,[status(thm)],[7591])).
% 22.90/23.12 tff(7593,assumption,(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(c, c)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(c, c)))), introduced(assumption)).
% 22.90/23.12 tff(7594,plain,
% 22.90/23.12 (mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(c, c))),
% 22.90/23.12 inference(monotonicity,[status(thm)],[1334])).
% 22.90/23.12 tff(7595,plain,
% 22.90/23.12 (mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c)),
% 22.90/23.12 inference(transitivity,[status(thm)],[7594, 7593, 5919, 5953, 5952, 5949, 7592])).
% 22.90/23.12 tff(7596,plain,
% 22.90/23.12 ((mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a))) <=> (mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c) = mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a)))),
% 22.90/23.12 inference(monotonicity,[status(thm)],[7595, 7590])).
% 22.90/23.12 tff(7597,plain,
% 22.90/23.12 ((mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a))) <=> (mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c))),
% 22.90/23.12 inference(transitivity,[status(thm)],[7596, 7588])).
% 22.90/23.12 tff(7598,plain,
% 22.90/23.12 ((~(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)))) <=> (~(mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c)))),
% 22.90/23.12 inference(monotonicity,[status(thm)],[7597])).
% 22.90/23.12 tff(7599,plain,
% 22.90/23.12 (~(mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c))),
% 22.90/23.12 inference(modus_ponens,[status(thm)],[6018, 7598])).
% 22.90/23.12 tff(7600,plain,
% 22.90/23.12 ((~(mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c))) | (~(mult(mult(a, c), mult(c, mult(rd(mult(b, c), mult(a, c)), a))) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), a), c))))),
% 22.90/23.12 inference(unit_resolution,[status(thm)],[6135, 7599])).
% 22.90/23.12 tff(7601,plain,
% 22.90/23.12 (~((~(mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, c), mult(c, mult(rd(mult(b, c), mult(a, c)), a))))) | (~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), a), c)))))),
% 22.90/23.12 inference(unit_resolution,[status(thm)],[6143, 7600])).
% 22.90/23.12 tff(7602,plain,
% 22.90/23.12 (mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), a), c))),
% 22.90/23.12 inference(unit_resolution,[status(thm)],[6145, 7601])).
% 22.90/23.12 tff(7603,plain,
% 22.90/23.12 (mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), a), c)) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c)),
% 22.90/23.12 inference(symmetry,[status(thm)],[7602])).
% 22.90/23.12 tff(7604,plain,
% 22.90/23.12 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), c), c) = mult(mult(rd(mult(b, c), mult(a, c)), a), c))),
% 22.90/23.12 inference(quant_inst,[status(thm)],[])).
% 22.90/23.12 tff(7605,plain,
% 22.90/23.12 (rd(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), c), c) = mult(mult(rd(mult(b, c), mult(a, c)), a), c)),
% 22.90/23.12 inference(unit_resolution,[status(thm)],[7604, 168])).
% 22.90/23.12 tff(7606,plain,
% 22.90/23.12 (mult(mult(rd(mult(b, c), mult(a, c)), a), c) = mult(mult(rd(mult(b, c), mult(a, c)), c), a)),
% 22.90/23.12 inference(transitivity,[status(thm)],[4490, 4489, 4488])).
% 22.90/23.12 tff(7607,plain,
% 22.90/23.12 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), c) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c)),
% 22.90/23.12 inference(monotonicity,[status(thm)],[7606])).
% 22.90/23.12 tff(7608,plain,
% 22.90/23.12 (mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), c)),
% 22.90/23.12 inference(symmetry,[status(thm)],[7607])).
% 22.90/23.12 tff(7609,plain,
% 22.90/23.12 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(a, mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))))) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))))),
% 22.90/23.12 inference(quant_inst,[status(thm)],[])).
% 22.90/23.12 tff(7610,plain,
% 22.90/23.12 (ld(a, mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))))) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))),
% 22.90/23.12 inference(unit_resolution,[status(thm)],[7609, 7])).
% 22.90/23.12 tff(7611,plain,
% 22.90/23.12 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c)) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))),
% 22.90/23.12 inference(transitivity,[status(thm)],[6078, 4860, 4858, 4855, 6875, 4654, 5994])).
% 22.90/23.12 tff(7612,plain,
% 22.90/23.12 (mult(a, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c))) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)))),
% 22.90/23.12 inference(monotonicity,[status(thm)],[7611])).
% 22.90/23.12 tff(7613,plain,
% 22.90/23.12 (mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c)))),
% 22.90/23.12 inference(monotonicity,[status(thm)],[6079])).
% 22.90/23.12 tff(7614,plain,
% 22.90/23.12 (mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))) = mult(a, mult(mult(c, mult(rd(mult(b, c), mult(a, c)), a)), c))),
% 22.90/23.12 inference(transitivity,[status(thm)],[7613, 7612, 6064, 7594, 7593, 5919, 5953, 5952, 5949, 7592, 6220])).
% 22.90/23.12 tff(7615,plain,
% 22.90/23.12 (ld(a, mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))))) = ld(a, mult(a, mult(mult(c, mult(rd(mult(b, c), mult(a, c)), a)), c)))),
% 22.90/23.12 inference(monotonicity,[status(thm)],[7614])).
% 22.90/23.12 tff(7616,plain,
% 22.90/23.12 (ld(a, mult(a, mult(mult(c, mult(rd(mult(b, c), mult(a, c)), a)), c))) = ld(a, mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))))),
% 22.90/23.12 inference(symmetry,[status(thm)],[7615])).
% 22.90/23.12 tff(7617,plain,
% 22.90/23.12 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(a, mult(a, mult(mult(c, mult(rd(mult(b, c), mult(a, c)), a)), c))) = mult(mult(c, mult(rd(mult(b, c), mult(a, c)), a)), c))),
% 22.90/23.12 inference(quant_inst,[status(thm)],[])).
% 22.90/23.12 tff(7618,plain,
% 22.90/23.12 (ld(a, mult(a, mult(mult(c, mult(rd(mult(b, c), mult(a, c)), a)), c))) = mult(mult(c, mult(rd(mult(b, c), mult(a, c)), a)), c)),
% 22.90/23.12 inference(unit_resolution,[status(thm)],[7617, 7])).
% 22.90/23.12 tff(7619,plain,
% 22.90/23.12 (mult(mult(c, mult(rd(mult(b, c), mult(a, c)), a)), c) = ld(a, mult(a, mult(mult(c, mult(rd(mult(b, c), mult(a, c)), a)), c)))),
% 22.90/23.12 inference(symmetry,[status(thm)],[7618])).
% 22.90/23.12 tff(7620,plain,
% 22.90/23.12 (mult(mult(c, mult(rd(mult(b, c), mult(a, c)), a)), c) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), c)),
% 22.90/23.12 inference(transitivity,[status(thm)],[7619, 7616, 7610, 4860, 4858, 4855, 7608])).
% 22.90/23.12 tff(7621,plain,
% 22.90/23.12 (rd(mult(mult(c, mult(rd(mult(b, c), mult(a, c)), a)), c), c) = rd(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), c), c)),
% 22.90/23.12 inference(monotonicity,[status(thm)],[7620])).
% 22.90/23.12 tff(7622,plain,
% 22.90/23.12 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(c, mult(rd(mult(b, c), mult(a, c)), a)), c), c) = mult(c, mult(rd(mult(b, c), mult(a, c)), a)))),
% 22.90/23.12 inference(quant_inst,[status(thm)],[])).
% 22.90/23.12 tff(7623,plain,
% 22.90/23.12 (rd(mult(mult(c, mult(rd(mult(b, c), mult(a, c)), a)), c), c) = mult(c, mult(rd(mult(b, c), mult(a, c)), a))),
% 22.90/23.12 inference(unit_resolution,[status(thm)],[7622, 168])).
% 22.90/23.12 tff(7624,plain,
% 22.90/23.12 (mult(c, mult(rd(mult(b, c), mult(a, c)), a)) = rd(mult(mult(c, mult(rd(mult(b, c), mult(a, c)), a)), c), c)),
% 22.90/23.12 inference(symmetry,[status(thm)],[7623])).
% 22.90/23.12 tff(7625,plain,
% 22.90/23.12 (mult(c, mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(rd(mult(b, c), mult(a, c)), a), c)),
% 22.90/23.12 inference(transitivity,[status(thm)],[7624, 7621, 7605])).
% 22.90/23.12 tff(7626,plain,
% 22.90/23.12 (mult(mult(a, c), mult(c, mult(rd(mult(b, c), mult(a, c)), a))) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), a), c))),
% 22.90/23.12 inference(monotonicity,[status(thm)],[7625])).
% 22.90/23.12 tff(7627,plain,
% 22.90/23.12 (((~(mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, c), mult(c, mult(rd(mult(b, c), mult(a, c)), a))))) | (~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), a), c))))) | (mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, c), mult(c, mult(rd(mult(b, c), mult(a, c)), a))))),
% 22.90/23.12 inference(tautology,[status(thm)],[])).
% 22.90/23.12 tff(7628,plain,
% 22.90/23.12 (mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, c), mult(c, mult(rd(mult(b, c), mult(a, c)), a)))),
% 22.90/23.12 inference(unit_resolution,[status(thm)],[7627, 7601])).
% 22.90/23.12 tff(7629,plain,
% 22.90/23.12 (mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c)),
% 22.90/23.12 inference(transitivity,[status(thm)],[7628, 7626, 7603])).
% 22.90/23.12 tff(7630,plain,
% 22.90/23.12 ($false),
% 22.90/23.12 inference(unit_resolution,[status(thm)],[7599, 7629])).
% 22.90/23.12 tff(7631,plain,((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(c, c)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(c, c))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))) | (mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)))), inference(lemma,lemma(discharge,[]))).
% 22.90/23.12 tff(7632,plain,
% 22.90/23.12 ((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(c, c)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(c, c))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))) | (mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)))),
% 22.90/23.12 inference(unit_resolution,[status(thm)],[7631, 3862])).
% 22.90/23.12 tff(7633,plain,
% 22.90/23.12 (mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a))),
% 22.90/23.12 inference(unit_resolution,[status(thm)],[7632, 7272, 1799, 4360, 6581, 7587])).
% 22.90/23.12 tff(7634,plain,
% 22.90/23.12 (mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c))),
% 22.90/23.12 inference(unit_resolution,[status(thm)],[6187, 7633])).
% 22.90/23.12 tff(7635,plain,
% 22.90/23.12 (~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))),
% 22.90/23.12 inference(unit_resolution,[status(thm)],[2329, 7114])).
% 22.90/23.12 tff(7636,plain,
% 22.90/23.12 (~(mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))),
% 22.90/23.12 inference(unit_resolution,[status(thm)],[2390, 7635, 1799, 6582])).
% 22.90/23.12 tff(7637,plain,
% 22.90/23.12 (~((~(mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)))))),
% 22.90/23.12 inference(unit_resolution,[status(thm)],[2406, 7636])).
% 22.90/23.12 tff(7638,plain,
% 22.90/23.12 (mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a))),
% 22.90/23.12 inference(unit_resolution,[status(thm)],[2408, 7637])).
% 22.90/23.12 tff(7639,plain,
% 22.90/23.12 ((mult(a, mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a)) = mult(a, mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)))) <=> (mult(a, mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c))) = mult(a, mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a)))),
% 22.90/23.12 inference(commutativity,[status(thm)],[])).
% 22.90/23.12 tff(7640,plain,
% 22.90/23.12 ((mult(a, mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c))) = mult(a, mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a))) <=> (mult(a, mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a)) = mult(a, mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c))))),
% 22.90/23.12 inference(symmetry,[status(thm)],[7639])).
% 22.90/23.12 tff(7641,plain,
% 22.90/23.12 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))),
% 22.90/23.12 inference(monotonicity,[status(thm)],[6893])).
% 22.90/23.12 tff(7642,plain,
% 22.90/23.12 (mult(a, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))))),
% 22.90/23.12 inference(monotonicity,[status(thm)],[7641])).
% 22.90/23.12 tff(7643,plain,
% 22.90/23.12 (mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c)))),
% 22.90/23.12 inference(symmetry,[status(thm)],[7642])).
% 22.90/23.12 tff(7644,plain,
% 22.90/23.12 (mult(mult(rd(mult(b, c), mult(a, c)), c), a) = mult(b, c)),
% 22.90/23.12 inference(transitivity,[status(thm)],[83, 4360, 4340, 1377, 5500, 1370])).
% 22.90/23.12 tff(7645,plain,
% 22.90/23.12 (mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c) = mult(mult(b, c), c)),
% 22.90/23.12 inference(monotonicity,[status(thm)],[7644])).
% 22.90/23.12 tff(7646,plain,
% 22.90/23.12 (mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))) = mult(mult(b, c), c)),
% 22.90/23.12 inference(transitivity,[status(thm)],[6088, 6087, 4855, 7645])).
% 22.90/23.12 tff(7647,plain,
% 22.90/23.12 (mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))) = mult(a, mult(mult(b, c), c))),
% 22.90/23.12 inference(monotonicity,[status(thm)],[7646])).
% 22.90/23.12 tff(7648,plain,
% 22.90/23.12 (mult(a, mult(mult(b, c), c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))))),
% 22.90/23.12 inference(symmetry,[status(thm)],[7647])).
% 22.90/23.12 tff(7649,assumption,(~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), c), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c))), introduced(assumption)).
% 22.90/23.12 tff(7650,plain,
% 22.90/23.12 ((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), c), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(c, a)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c))))),
% 22.90/23.12 inference(unit_resolution,[status(thm)],[3981, 7649])).
% 22.90/23.12 tff(7651,plain,
% 22.90/23.12 (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), c), a) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(c, a)))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)))))),
% 22.90/23.12 inference(unit_resolution,[status(thm)],[3986, 7650])).
% 22.90/23.12 tff(7652,plain,
% 22.90/23.12 (mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c))),
% 22.90/23.12 inference(unit_resolution,[status(thm)],[3988, 7651])).
% 22.90/23.12 tff(7653,plain,
% 22.90/23.12 (mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c)),
% 22.90/23.12 inference(symmetry,[status(thm)],[7652])).
% 22.90/23.12 tff(7654,plain,
% 22.90/23.12 (mult(mult(mult(rd(mult(b, c), mult(a, c)), c), c), a) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(c, a))),
% 22.90/23.13 inference(unit_resolution,[status(thm)],[3992, 7651])).
% 22.90/23.13 tff(7655,plain,
% 22.90/23.13 (mult(mult(mult(rd(mult(b, c), mult(a, c)), c), c), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c)),
% 22.90/23.13 inference(transitivity,[status(thm)],[7654, 3991, 7653])).
% 22.90/23.13 tff(7656,plain,
% 22.90/23.13 ($false),
% 22.90/23.13 inference(unit_resolution,[status(thm)],[7649, 7655])).
% 22.90/23.13 tff(7657,plain,((mult(mult(mult(rd(mult(b, c), mult(a, c)), c), c), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c)) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit)))))), inference(lemma,lemma(discharge,[]))).
% 22.90/23.13 tff(7658,plain,
% 22.90/23.13 (mult(mult(mult(rd(mult(b, c), mult(a, c)), c), c), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c)),
% 22.90/23.13 inference(unit_resolution,[status(thm)],[7657, 3862])).
% 22.90/23.13 tff(7659,plain,
% 22.90/23.13 (mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))),
% 22.90/23.13 inference(unit_resolution,[status(thm)],[5118, 7271])).
% 22.90/23.13 tff(7660,plain,
% 22.90/23.13 (mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))) = mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c))),
% 22.90/23.13 inference(symmetry,[status(thm)],[7659])).
% 22.90/23.13 tff(7661,plain,
% 22.90/23.13 (mult(a, mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), c))),
% 22.90/23.13 inference(transitivity,[status(thm)],[5122, 7660, 5117])).
% 22.90/23.13 tff(7662,plain,
% 22.90/23.13 (ld(a, mult(a, mult(c, rd(mult(b, c), mult(a, c))))) = ld(a, mult(a, mult(rd(mult(b, c), mult(a, c)), c)))),
% 22.90/23.13 inference(monotonicity,[status(thm)],[7661])).
% 22.90/23.13 tff(7663,plain,
% 22.90/23.13 (ld(a, mult(a, mult(rd(mult(b, c), mult(a, c)), c))) = ld(a, mult(a, mult(c, rd(mult(b, c), mult(a, c)))))),
% 22.90/23.13 inference(symmetry,[status(thm)],[7662])).
% 22.90/23.13 tff(7664,plain,
% 22.90/23.13 (mult(rd(mult(b, c), mult(a, c)), c) = mult(c, rd(mult(b, c), mult(a, c)))),
% 22.90/23.13 inference(transitivity,[status(thm)],[5128, 7663, 5114])).
% 22.90/23.13 tff(7665,plain,
% 22.90/23.13 (mult(mult(rd(mult(b, c), mult(a, c)), c), c) = mult(mult(c, rd(mult(b, c), mult(a, c))), c)),
% 22.90/23.13 inference(monotonicity,[status(thm)],[7664])).
% 22.90/23.13 tff(7666,plain,
% 22.90/23.13 (mult(mult(c, rd(mult(b, c), mult(a, c))), c) = mult(mult(rd(mult(b, c), mult(a, c)), c), c)),
% 22.90/23.13 inference(symmetry,[status(thm)],[7665])).
% 22.90/23.13 tff(7667,plain,
% 22.90/23.13 (mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), c), a)),
% 22.90/23.13 inference(monotonicity,[status(thm)],[7666])).
% 22.90/23.13 tff(7668,plain,
% 22.90/23.13 (mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a) = mult(mult(b, c), c)),
% 22.90/23.13 inference(transitivity,[status(thm)],[7667, 7658, 7645])).
% 22.90/23.13 tff(7669,plain,
% 22.90/23.13 (mult(a, mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a)) = mult(a, mult(mult(b, c), c))),
% 22.90/23.13 inference(monotonicity,[status(thm)],[7668])).
% 22.90/23.13 tff(7670,plain,
% 22.90/23.13 (mult(a, mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c)))),
% 22.90/23.13 inference(transitivity,[status(thm)],[7669, 7648, 7643])).
% 22.90/23.13 tff(7671,plain,
% 22.90/23.13 (mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))) = mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 22.90/23.13 inference(monotonicity,[status(thm)],[6893])).
% 22.90/23.13 tff(7672,plain,
% 22.90/23.13 (mult(a, mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))))),
% 22.90/23.13 inference(monotonicity,[status(thm)],[7671])).
% 22.90/23.13 tff(7673,plain,
% 22.90/23.13 (mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))))),
% 22.90/23.13 inference(symmetry,[status(thm)],[7672])).
% 22.90/23.13 tff(7674,plain,
% 22.90/23.13 (mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a)),
% 22.90/23.13 inference(symmetry,[status(thm)],[7638])).
% 22.90/23.13 tff(7675,plain,
% 22.90/23.13 (mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(c, mult(a, c)), b)),
% 22.90/23.13 inference(monotonicity,[status(thm)],[5503])).
% 22.90/23.13 tff(7676,plain,
% 22.90/23.13 (mult(mult(c, mult(a, c)), b) = mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a))),
% 22.90/23.13 inference(symmetry,[status(thm)],[7675])).
% 22.90/23.13 tff(7677,plain,
% 22.90/23.13 (mult(mult(c, a), c) = mult(mult(a, c), c)),
% 22.90/23.13 inference(symmetry,[status(thm)],[6892])).
% 22.90/23.13 tff(7678,plain,
% 22.90/23.13 (mult(c, mult(a, c)) = mult(mult(a, c), c)),
% 22.90/23.13 inference(transitivity,[status(thm)],[3877, 7677])).
% 22.90/23.13 tff(7679,plain,
% 22.90/23.13 (mult(mult(c, mult(a, c)), b) = mult(mult(mult(a, c), c), b)),
% 22.90/23.13 inference(monotonicity,[status(thm)],[7678])).
% 22.90/23.13 tff(7680,plain,
% 22.90/23.13 (mult(mult(mult(a, c), c), b) = mult(mult(c, mult(a, c)), b)),
% 22.90/23.13 inference(symmetry,[status(thm)],[7679])).
% 22.90/23.13 tff(7681,plain,
% 22.90/23.13 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), b)),
% 22.90/23.13 inference(transitivity,[status(thm)],[1799, 5504])).
% 22.90/23.13 tff(7682,plain,
% 22.90/23.13 (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(a, c), b), c)),
% 22.90/23.13 inference(monotonicity,[status(thm)],[7681])).
% 22.90/23.13 tff(7683,plain,
% 22.90/23.13 ((~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))))),
% 22.90/23.13 inference(unit_resolution,[status(thm)],[4486, 753])).
% 22.90/23.13 tff(7684,plain,
% 22.90/23.13 (~((~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)))) | (~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))))),
% 22.90/23.13 inference(unit_resolution,[status(thm)],[4484, 7683])).
% 22.90/23.13 tff(7685,plain,
% 22.90/23.13 (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))),
% 22.90/23.13 inference(unit_resolution,[status(thm)],[121, 7684])).
% 22.90/23.13 tff(7686,plain,
% 22.90/23.13 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c)),
% 22.90/23.13 inference(symmetry,[status(thm)],[7685])).
% 22.90/23.13 tff(7687,plain,
% 22.90/23.13 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))),
% 22.90/23.13 inference(monotonicity,[status(thm)],[3885])).
% 22.90/23.13 tff(7688,plain,
% 22.90/23.13 (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a))),
% 22.90/23.13 inference(unit_resolution,[status(thm)],[123, 7684])).
% 22.90/23.13 tff(7689,plain,
% 22.90/23.13 (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c)),
% 22.90/23.13 inference(transitivity,[status(thm)],[7688, 7687, 7686])).
% 22.90/23.13 tff(7690,plain,
% 22.90/23.13 ($false),
% 22.90/23.13 inference(unit_resolution,[status(thm)],[753, 7689])).
% 22.90/23.13 tff(7691,plain,((mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c)) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit)))))), inference(lemma,lemma(discharge,[]))).
% 22.90/23.13 tff(7692,plain,
% 22.90/23.13 (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c)),
% 22.90/23.13 inference(unit_resolution,[status(thm)],[7691, 3862])).
% 22.90/23.13 tff(7693,plain,
% 22.90/23.13 (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a)),
% 22.90/23.13 inference(transitivity,[status(thm)],[7692, 7682, 4371, 7680, 7676, 7674])).
% 22.90/23.13 tff(7694,plain,
% 22.90/23.13 (rd(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a), a) = rd(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a), a)),
% 22.90/23.13 inference(monotonicity,[status(thm)],[7693])).
% 22.90/23.13 tff(7695,plain,
% 22.90/23.13 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = rd(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a), a)),
% 22.90/23.13 inference(symmetry,[status(thm)],[2227])).
% 22.90/23.13 tff(7696,plain,
% 22.90/23.13 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 22.90/23.13 inference(transitivity,[status(thm)],[7695, 7694, 2786])).
% 22.90/23.13 tff(7697,plain,
% 22.90/23.13 (mult(a, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))))),
% 22.90/23.13 inference(monotonicity,[status(thm)],[7696])).
% 22.90/23.13 tff(7698,plain,
% 22.90/23.13 (mult(a, mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c))) = mult(a, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c))),
% 22.90/23.13 inference(monotonicity,[status(thm)],[3157])).
% 22.90/23.13 tff(7699,plain,
% 22.90/23.13 (mult(a, mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c))) = mult(a, mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))))),
% 22.90/23.13 inference(transitivity,[status(thm)],[7698, 7697, 7673])).
% 22.90/23.13 tff(7700,plain,
% 22.90/23.13 ((mult(a, mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c))) = mult(a, mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a))) <=> (mult(a, mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c))))),
% 22.90/23.13 inference(monotonicity,[status(thm)],[7699, 7670])).
% 22.90/23.13 tff(7701,plain,
% 22.90/23.13 ((mult(a, mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c)))) <=> (mult(a, mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c))) = mult(a, mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a)))),
% 22.90/23.13 inference(symmetry,[status(thm)],[7700])).
% 22.90/23.13 tff(7702,plain,
% 22.90/23.13 ((mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a))) <=> (mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))),
% 22.90/23.13 inference(commutativity,[status(thm)],[])).
% 22.90/23.13 tff(7703,plain,
% 22.90/23.13 (mult(a, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c))) = mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a))),
% 22.90/23.13 inference(transitivity,[status(thm)],[7642, 7647, 4372, 234, 4371, 7680, 7676])).
% 22.90/23.13 tff(7704,plain,
% 22.90/23.13 (mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c))))),
% 22.90/23.13 inference(unit_resolution,[status(thm)],[5253, 7637])).
% 22.90/23.13 tff(7705,plain,
% 22.90/23.13 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(mult(c, mult(a, c)), a))) = mult(mult(c, mult(a, c)), a))),
% 22.90/23.13 inference(quant_inst,[status(thm)],[])).
% 22.90/23.13 tff(7706,plain,
% 22.90/23.13 (ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(mult(c, mult(a, c)), a))) = mult(mult(c, mult(a, c)), a)),
% 22.90/23.13 inference(unit_resolution,[status(thm)],[7705, 7])).
% 22.90/23.13 tff(7707,plain,
% 22.90/23.13 (mult(mult(c, mult(a, c)), a) = mult(mult(mult(a, c), c), a)),
% 22.90/23.13 inference(symmetry,[status(thm)],[6894])).
% 22.90/23.13 tff(7708,plain,
% 22.90/23.13 (mult(mult(c, mult(a, c)), a) = mult(mult(a, mult(c, c)), a)),
% 22.90/23.13 inference(transitivity,[status(thm)],[7707, 4663])).
% 22.90/23.13 tff(7709,plain,
% 22.90/23.13 (mult(rd(mult(b, c), mult(a, c)), mult(mult(c, mult(a, c)), a)) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(c, c)), a))),
% 22.90/23.13 inference(monotonicity,[status(thm)],[7708])).
% 22.90/23.13 tff(7710,plain,
% 22.90/23.13 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(c, c)), a)) = mult(rd(mult(b, c), mult(a, c)), mult(mult(c, mult(a, c)), a))),
% 22.90/23.13 inference(symmetry,[status(thm)],[7709])).
% 22.90/23.13 tff(7711,plain,
% 22.90/23.13 (mult(mult(mult(b, c), unit), c) = mult(mult(b, c), c)),
% 22.90/23.13 inference(monotonicity,[status(thm)],[1255])).
% 22.90/23.13 tff(7712,plain,
% 22.90/23.13 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(b, c), unit), c) = mult(b, mult(mult(c, unit), c)))),
% 22.90/23.13 inference(quant_inst,[status(thm)],[])).
% 22.90/23.13 tff(7713,plain,
% 22.90/23.13 (mult(mult(mult(b, c), unit), c) = mult(b, mult(mult(c, unit), c))),
% 22.90/23.13 inference(unit_resolution,[status(thm)],[7712, 56])).
% 22.90/23.13 tff(7714,plain,
% 22.90/23.13 (mult(b, mult(mult(c, unit), c)) = mult(mult(mult(b, c), unit), c)),
% 22.90/23.13 inference(symmetry,[status(thm)],[7713])).
% 22.90/23.13 tff(7715,plain,
% 22.90/23.13 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)) = mult(b, mult(mult(c, unit), c))),
% 22.90/23.13 inference(monotonicity,[status(thm)],[5503, 2617])).
% 22.90/23.13 tff(7716,plain,
% 22.90/23.13 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)) = mult(mult(b, c), c)),
% 22.90/23.13 inference(transitivity,[status(thm)],[7715, 7714, 7711])).
% 22.90/23.13 tff(7717,plain,
% 22.90/23.13 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)), a) = mult(mult(mult(b, c), c), a)),
% 22.90/23.13 inference(monotonicity,[status(thm)],[7716])).
% 22.90/23.13 tff(7718,plain,
% 22.90/23.13 (mult(mult(mult(b, c), c), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)), a)),
% 22.90/23.13 inference(symmetry,[status(thm)],[7717])).
% 22.90/23.13 tff(7719,plain,
% 22.90/23.13 (mult(mult(mult(b, c), a), c) = mult(mult(mult(b, c), c), a)),
% 22.90/23.13 inference(symmetry,[status(thm)],[6774])).
% 22.90/23.13 tff(7720,plain,
% 22.90/23.13 (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), c) = mult(mult(mult(b, c), a), c)),
% 22.90/23.13 inference(monotonicity,[status(thm)],[7529])).
% 22.90/23.13 tff(7721,plain,
% 22.90/23.13 (mult(mult(rd(mult(b, c), mult(a, c)), c), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), c)),
% 22.90/23.13 inference(transitivity,[status(thm)],[83, 4360, 4340])).
% 22.90/23.13 tff(7722,plain,
% 22.90/23.13 (mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), unit) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), unit)),
% 22.90/23.13 inference(monotonicity,[status(thm)],[7721])).
% 22.90/23.13 tff(7723,plain,
% 22.90/23.13 (mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), unit) = mult(mult(rd(mult(b, c), mult(a, c)), a), c)),
% 22.90/23.13 inference(transitivity,[status(thm)],[7722, 1875, 1871, 4340])).
% 22.90/23.13 tff(7724,plain,
% 22.90/23.13 (mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), unit), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a)),
% 22.90/23.13 inference(monotonicity,[status(thm)],[7723])).
% 22.90/23.13 tff(7725,plain,
% 22.90/23.13 (mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, unit), a)) = mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), unit), a)),
% 22.90/23.13 inference(symmetry,[status(thm)],[2665])).
% 22.90/23.13 tff(7726,plain,
% 22.90/23.13 (mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, a)) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))),
% 22.90/23.13 inference(transitivity,[status(thm)],[2662, 7725, 7724, 1168])).
% 22.90/23.13 tff(7727,plain,
% 22.90/23.13 (mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, a)), c) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), c)),
% 22.90/23.13 inference(monotonicity,[status(thm)],[7726])).
% 22.90/23.13 tff(7728,plain,
% 22.90/23.13 (mult(rd(mult(b, c), mult(a, c)), mult(mult(c, mult(a, a)), c)) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, a)), c)),
% 22.90/23.13 inference(symmetry,[status(thm)],[2661])).
% 22.90/23.13 tff(7729,plain,
% 22.90/23.13 (mult(mult(c, a), unit) = mult(a, c)),
% 22.90/23.13 inference(transitivity,[status(thm)],[5719, 3884, 4263, 3872])).
% 22.90/23.13 tff(7730,plain,
% 22.90/23.13 (mult(mult(mult(c, a), unit), a) = mult(mult(a, c), a)),
% 22.90/23.13 inference(monotonicity,[status(thm)],[7729])).
% 22.90/23.13 tff(7731,plain,
% 22.90/23.13 (mult(c, mult(a, a)) = mult(mult(a, c), a)),
% 22.90/23.13 inference(transitivity,[status(thm)],[2656, 2655, 7730])).
% 22.90/23.13 tff(7732,plain,
% 22.90/23.13 (mult(mult(c, mult(a, a)), c) = mult(mult(mult(a, c), a), c)),
% 22.90/23.13 inference(monotonicity,[status(thm)],[7731])).
% 22.90/23.13 tff(7733,plain,
% 22.90/23.13 (mult(mult(mult(a, c), a), c) = mult(mult(c, mult(a, a)), c)),
% 22.90/23.13 inference(symmetry,[status(thm)],[7732])).
% 22.90/23.13 tff(7734,plain,
% 22.90/23.13 (mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), c)) = mult(rd(mult(b, c), mult(a, c)), mult(mult(c, mult(a, a)), c))),
% 22.90/23.13 inference(monotonicity,[status(thm)],[7733])).
% 22.90/23.13 tff(7735,plain,
% 22.90/23.13 (mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), c)) = mult(rd(mult(b, c), mult(a, c)), mult(mult(c, mult(a, c)), a))),
% 22.90/23.13 inference(transitivity,[status(thm)],[7734, 7728, 7727, 7720, 7719, 7718, 4660, 7710])).
% 22.90/23.13 tff(7736,plain,
% 22.90/23.13 (ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), c))) = ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(mult(c, mult(a, c)), a)))),
% 22.90/23.13 inference(monotonicity,[status(thm)],[7735])).
% 22.90/23.13 tff(7737,plain,
% 22.90/23.13 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), c))) = mult(mult(mult(a, c), a), c))),
% 22.90/23.13 inference(quant_inst,[status(thm)],[])).
% 22.90/23.13 tff(7738,plain,
% 22.90/23.13 (ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), c))) = mult(mult(mult(a, c), a), c)),
% 22.90/23.13 inference(unit_resolution,[status(thm)],[7737, 7])).
% 22.90/23.14 tff(7739,plain,
% 22.90/23.14 (mult(mult(mult(a, c), a), c) = ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), c)))),
% 22.90/23.14 inference(symmetry,[status(thm)],[7738])).
% 22.90/23.14 tff(7740,plain,
% 22.90/23.14 (mult(a, mult(c, mult(a, c))) = mult(mult(c, mult(a, c)), a)),
% 22.90/23.14 inference(transitivity,[status(thm)],[4714, 4724, 7739, 7736, 7706])).
% 22.90/23.14 tff(7741,plain,
% 22.90/23.14 (mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c)))),
% 22.90/23.14 inference(monotonicity,[status(thm)],[7740])).
% 22.90/23.14 tff(7742,plain,
% 22.90/23.14 ((mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(unit, mult(mult(a, c), c)), unit)) = mult(mult(a, mult(mult(unit, mult(mult(a, c), c)), unit)), rd(mult(b, c), mult(a, c)))) <=> (mult(mult(a, mult(mult(unit, mult(mult(a, c), c)), unit)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(unit, mult(mult(a, c), c)), unit)))),
% 22.90/23.14 inference(commutativity,[status(thm)],[])).
% 22.90/23.14 tff(7743,plain,
% 22.90/23.14 (mult(unit, mult(mult(a, c), c)) = mult(unit, mult(c, mult(a, c)))),
% 22.90/23.14 inference(monotonicity,[status(thm)],[6893])).
% 22.90/23.14 tff(7744,plain,
% 22.90/23.14 (mult(unit, mult(mult(a, c), c)) = mult(c, mult(a, c))),
% 22.90/23.14 inference(transitivity,[status(thm)],[7743, 4366, 4365, 4362, 2690])).
% 22.90/23.14 tff(7745,plain,
% 22.90/23.14 (mult(mult(unit, mult(mult(a, c), c)), unit) = mult(mult(c, mult(a, c)), unit)),
% 22.90/23.14 inference(monotonicity,[status(thm)],[7744])).
% 22.90/23.14 tff(7746,plain,
% 22.90/23.14 (mult(mult(unit, mult(mult(a, c), c)), unit) = mult(c, mult(a, c))),
% 22.90/23.14 inference(transitivity,[status(thm)],[7745, 6010])).
% 22.90/23.14 tff(7747,plain,
% 22.90/23.14 (mult(a, mult(mult(unit, mult(mult(a, c), c)), unit)) = mult(a, mult(c, mult(a, c)))),
% 22.90/23.14 inference(monotonicity,[status(thm)],[7746])).
% 22.90/23.14 tff(7748,plain,
% 22.90/23.14 (mult(mult(a, mult(mult(unit, mult(mult(a, c), c)), unit)), rd(mult(b, c), mult(a, c))) = mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c)))),
% 22.90/23.14 inference(monotonicity,[status(thm)],[7747])).
% 22.90/23.14 tff(7749,plain,
% 22.90/23.14 (mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(a, mult(mult(unit, mult(mult(a, c), c)), unit)), rd(mult(b, c), mult(a, c)))),
% 22.90/23.14 inference(symmetry,[status(thm)],[7748])).
% 22.90/23.14 tff(7750,plain,
% 22.90/23.14 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(unit, mult(mult(a, c), c)), unit)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c)))),
% 22.90/23.14 inference(monotonicity,[status(thm)],[7746])).
% 22.90/23.14 tff(7751,plain,
% 22.90/23.14 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(unit, mult(mult(a, c), c)), unit))),
% 22.90/23.14 inference(symmetry,[status(thm)],[7750])).
% 22.90/23.14 tff(7752,plain,
% 22.90/23.14 ((mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c)))) <=> (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(unit, mult(mult(a, c), c)), unit)) = mult(mult(a, mult(mult(unit, mult(mult(a, c), c)), unit)), rd(mult(b, c), mult(a, c))))),
% 22.90/23.14 inference(monotonicity,[status(thm)],[7751, 7749])).
% 22.90/23.14 tff(7753,plain,
% 22.90/23.14 ((mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c)))) <=> (mult(mult(a, mult(mult(unit, mult(mult(a, c), c)), unit)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(unit, mult(mult(a, c), c)), unit)))),
% 22.90/23.14 inference(transitivity,[status(thm)],[7752, 7742])).
% 22.90/23.14 tff(7754,plain,
% 22.90/23.14 ((mult(mult(a, mult(mult(unit, mult(mult(a, c), c)), unit)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(unit, mult(mult(a, c), c)), unit))) <=> (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))))),
% 22.90/23.14 inference(symmetry,[status(thm)],[7753])).
% 22.90/23.14 tff(7755,plain,
% 22.90/23.14 (mult(mult(a, rd(mult(b, c), mult(a, c))), c) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))),
% 22.90/23.14 inference(transitivity,[status(thm)],[2189, 7272, 2172, 2178, 2177, 2162])).
% 22.90/23.14 tff(7756,plain,
% 22.90/23.14 (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)),
% 22.90/23.14 inference(monotonicity,[status(thm)],[7755])).
% 22.90/23.14 tff(7757,plain,
% 22.90/23.14 (mult(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), a), c) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c)),
% 22.90/23.14 inference(monotonicity,[status(thm)],[7756])).
% 22.90/23.14 tff(7758,plain,
% 22.90/23.14 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(unit, mult(mult(a, c), c)), unit)) = mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a))),
% 22.90/23.14 inference(transitivity,[status(thm)],[7750, 7565, 5952, 7757, 7682, 4371, 7680, 7676])).
% 22.90/23.14 tff(7759,plain,
% 22.90/23.14 (mult(mult(a, mult(mult(unit, mult(mult(a, c), c)), unit)), rd(mult(b, c), mult(a, c))) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c))))),
% 22.90/23.14 inference(transitivity,[status(thm)],[7748, 7741, 7704])).
% 22.90/23.14 tff(7760,plain,
% 22.90/23.14 ((mult(mult(a, mult(mult(unit, mult(mult(a, c), c)), unit)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(unit, mult(mult(a, c), c)), unit))) <=> (mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)))),
% 22.90/23.14 inference(monotonicity,[status(thm)],[7759, 7758])).
% 22.90/23.14 tff(7761,plain,
% 22.90/23.14 ((mult(mult(a, mult(mult(unit, mult(mult(a, c), c)), unit)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(unit, mult(mult(a, c), c)), unit))) <=> (mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))),
% 22.90/23.14 inference(transitivity,[status(thm)],[7760, 7702])).
% 22.90/23.14 tff(7762,plain,
% 22.90/23.14 ((mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c))))) <=> (mult(mult(a, mult(mult(unit, mult(mult(a, c), c)), unit)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(unit, mult(mult(a, c), c)), unit)))),
% 22.90/23.14 inference(symmetry,[status(thm)],[7761])).
% 22.90/23.14 tff(7763,plain,
% 22.90/23.14 ((mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c))))) <=> (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))))),
% 22.90/23.14 inference(transitivity,[status(thm)],[7762, 7754])).
% 22.90/23.14 tff(7764,plain,
% 22.90/23.14 ((~(mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))) <=> (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c)))))),
% 22.90/23.14 inference(monotonicity,[status(thm)],[7763])).
% 22.90/23.14 tff(7765,plain,
% 22.90/23.14 (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))))),
% 22.90/23.14 inference(modus_ponens,[status(thm)],[7636, 7764])).
% 22.90/23.14 tff(7766,plain,
% 22.90/23.14 (((~(mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))) = mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c)))))) | (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))))),
% 22.90/23.14 inference(tautology,[status(thm)],[])).
% 22.90/23.14 tff(7767,plain,
% 22.90/23.14 ((~(mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))) = mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c)))))),
% 22.90/23.14 inference(unit_resolution,[status(thm)],[7766, 7765])).
% 22.90/23.14 tff(7768,plain,
% 22.90/23.14 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))) = mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))))))) | (~((~(mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))) = mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))))))) | (~((~(mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))))))))),
% 22.90/23.14 inference(rewrite,[status(thm)],[])).
% 22.90/23.14 tff(7769,plain,
% 22.90/23.14 (((~((~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))))) | (~(mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))) = mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))))) | (~(mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))))))))) <=> ((~((~(mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))) = mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))))))) | (~((~(mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))))))))),
% 22.90/23.14 inference(rewrite,[status(thm)],[])).
% 22.90/23.14 tff(7770,plain,
% 22.90/23.14 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))))) | (~(mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))) = mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))))) | (~(mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))) = mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))))))) | (~((~(mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))))))))))),
% 22.90/23.14 inference(monotonicity,[status(thm)],[7769])).
% 22.90/23.14 tff(7771,plain,
% 22.90/23.14 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))))) | (~(mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))) = mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))))) | (~(mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))) = mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))))))) | (~((~(mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))))))))),
% 22.90/23.14 inference(transitivity,[status(thm)],[7770, 7768])).
% 22.90/23.14 tff(7772,plain,
% 22.90/23.14 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))))) | (~(mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))) = mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))))) | (~(mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))))))))),
% 22.90/23.14 inference(quant_inst,[status(thm)],[])).
% 22.90/23.14 tff(7773,plain,
% 22.90/23.14 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))) = mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))))))) | (~((~(mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))))))))),
% 22.90/23.14 inference(modus_ponens,[status(thm)],[7772, 7771])).
% 22.90/23.14 tff(7774,plain,
% 22.90/23.14 ((~((~(mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))) = mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))))))) | (~((~(mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))))))))),
% 22.90/23.15 inference(unit_resolution,[status(thm)],[7773, 27])).
% 22.90/23.15 tff(7775,plain,
% 22.90/23.15 (~((~(mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))))))),
% 22.90/23.15 inference(unit_resolution,[status(thm)],[7774, 7767])).
% 22.90/23.15 tff(7776,plain,
% 22.90/23.15 (((~(mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))))))) | (mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))))),
% 22.90/23.15 inference(tautology,[status(thm)],[])).
% 22.90/23.15 tff(7777,plain,
% 22.90/23.15 (mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))))),
% 22.90/23.15 inference(unit_resolution,[status(thm)],[7776, 7775])).
% 22.90/23.15 tff(7778,plain,
% 22.90/23.15 (mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c)))),
% 22.90/23.15 inference(symmetry,[status(thm)],[7777])).
% 22.90/23.15 tff(7779,plain,
% 22.90/23.15 (mult(a, mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c)))) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c))))),
% 22.90/23.15 inference(transitivity,[status(thm)],[7672, 7778, 7741, 7704])).
% 22.90/23.15 tff(7780,plain,
% 22.90/23.15 ((mult(a, mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c)))) <=> (mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)))),
% 22.90/23.15 inference(monotonicity,[status(thm)],[7779, 7703])).
% 22.90/23.15 tff(7781,plain,
% 22.90/23.15 ((mult(a, mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c)))) <=> (mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))),
% 22.90/23.15 inference(transitivity,[status(thm)],[7780, 7702])).
% 22.90/23.15 tff(7782,plain,
% 22.90/23.15 ((mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c))))) <=> (mult(a, mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c))))),
% 22.90/23.15 inference(symmetry,[status(thm)],[7781])).
% 22.90/23.15 tff(7783,plain,
% 22.90/23.15 ((mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c))))) <=> (mult(a, mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a)) = mult(a, mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c))))),
% 22.90/23.15 inference(transitivity,[status(thm)],[7782, 7701, 7640])).
% 22.90/23.15 tff(7784,plain,
% 22.90/23.15 ((~(mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))) <=> (~(mult(a, mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a)) = mult(a, mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)))))),
% 22.90/23.15 inference(monotonicity,[status(thm)],[7783])).
% 22.90/23.15 tff(7785,plain,
% 22.90/23.15 (~(mult(a, mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a)) = mult(a, mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c))))),
% 22.90/23.15 inference(modus_ponens,[status(thm)],[7636, 7784])).
% 22.90/23.15 tff(7786,plain,
% 22.90/23.15 (((~(mult(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)), a) = mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), c)))) | (~(mult(a, mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a)) = mult(a, mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)))))) | (mult(a, mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a)) = mult(a, mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c))))),
% 22.90/23.15 inference(tautology,[status(thm)],[])).
% 22.90/23.15 tff(7787,plain,
% 22.90/23.15 ((~(mult(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)), a) = mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), c)))) | (~(mult(a, mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a)) = mult(a, mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)))))),
% 22.90/23.15 inference(unit_resolution,[status(thm)],[7786, 7785])).
% 22.90/23.15 tff(7788,plain,
% 22.90/23.15 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)), a) = mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), c)))) | (~(mult(a, mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a)) = mult(a, mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c))))))) | (~((~(mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c))))) | (~(mult(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)), a) = mult(a, mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)), a) = mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), c)))) | (~(mult(a, mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a)) = mult(a, mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c))))))) | (~((~(mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c))))) | (~(mult(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)), a) = mult(a, mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a)))))))),
% 22.90/23.15 inference(rewrite,[status(thm)],[])).
% 22.90/23.15 tff(7789,plain,
% 22.90/23.15 (((~((~(mult(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)), a) = mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), c)))) | (~(mult(a, mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a)) = mult(a, mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c))))))) | (~((~(mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c))))) | (~(mult(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)), a) = mult(a, mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a))))))) <=> ((~((~(mult(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)), a) = mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), c)))) | (~(mult(a, mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a)) = mult(a, mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c))))))) | (~((~(mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c))))) | (~(mult(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)), a) = mult(a, mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a)))))))),
% 22.90/23.15 inference(rewrite,[status(thm)],[])).
% 22.90/23.15 tff(7790,plain,
% 22.90/23.15 ((~((~(mult(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)), a) = mult(a, mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a)))) | (~(mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c))))))) <=> (~((~(mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c))))) | (~(mult(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)), a) = mult(a, mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a))))))),
% 22.90/23.15 inference(rewrite,[status(thm)],[])).
% 22.90/23.15 tff(7791,plain,
% 22.90/23.15 ((~((~(mult(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)), a) = mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), c)))) | (~(mult(a, mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a)) = mult(a, mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c))))))) <=> (~((~(mult(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)), a) = mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), c)))) | (~(mult(a, mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a)) = mult(a, mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)))))))),
% 22.90/23.15 inference(rewrite,[status(thm)],[])).
% 22.90/23.15 tff(7792,plain,
% 22.90/23.15 (((~((~(mult(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)), a) = mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), c)))) | (~(mult(a, mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a)) = mult(a, mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c))))))) | (~((~(mult(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)), a) = mult(a, mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a)))) | (~(mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)))))))) <=> ((~((~(mult(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)), a) = mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), c)))) | (~(mult(a, mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a)) = mult(a, mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c))))))) | (~((~(mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c))))) | (~(mult(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)), a) = mult(a, mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a)))))))),
% 22.90/23.15 inference(monotonicity,[status(thm)],[7791, 7790])).
% 22.90/23.15 tff(7793,plain,
% 22.90/23.15 (((~((~(mult(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)), a) = mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), c)))) | (~(mult(a, mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a)) = mult(a, mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c))))))) | (~((~(mult(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)), a) = mult(a, mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a)))) | (~(mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)))))))) <=> ((~((~(mult(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)), a) = mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), c)))) | (~(mult(a, mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a)) = mult(a, mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c))))))) | (~((~(mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c))))) | (~(mult(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)), a) = mult(a, mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a)))))))),
% 22.90/23.15 inference(transitivity,[status(thm)],[7792, 7789])).
% 22.90/23.15 tff(7794,plain,
% 22.90/23.15 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)), a) = mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), c)))) | (~(mult(a, mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a)) = mult(a, mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c))))))) | (~((~(mult(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)), a) = mult(a, mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a)))) | (~(mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)), a) = mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), c)))) | (~(mult(a, mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a)) = mult(a, mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c))))))) | (~((~(mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c))))) | (~(mult(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)), a) = mult(a, mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a))))))))),
% 22.90/23.16 inference(monotonicity,[status(thm)],[7793])).
% 22.90/23.16 tff(7795,plain,
% 22.90/23.16 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)), a) = mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), c)))) | (~(mult(a, mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a)) = mult(a, mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c))))))) | (~((~(mult(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)), a) = mult(a, mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a)))) | (~(mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)), a) = mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), c)))) | (~(mult(a, mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a)) = mult(a, mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c))))))) | (~((~(mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c))))) | (~(mult(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)), a) = mult(a, mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a)))))))),
% 22.90/23.16 inference(transitivity,[status(thm)],[7794, 7788])).
% 22.90/23.16 tff(7796,plain,
% 22.90/23.16 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)), a) = mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), c)))) | (~(mult(a, mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a)) = mult(a, mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c))))))) | (~((~(mult(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)), a) = mult(a, mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a)))) | (~(mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c))))))))),
% 22.90/23.16 inference(quant_inst,[status(thm)],[])).
% 22.90/23.16 tff(7797,plain,
% 22.90/23.16 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)), a) = mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), c)))) | (~(mult(a, mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a)) = mult(a, mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c))))))) | (~((~(mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c))))) | (~(mult(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)), a) = mult(a, mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a))))))),
% 22.90/23.16 inference(modus_ponens,[status(thm)],[7796, 7795])).
% 22.90/23.16 tff(7798,plain,
% 22.90/23.16 ((~((~(mult(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)), a) = mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), c)))) | (~(mult(a, mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a)) = mult(a, mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c))))))) | (~((~(mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c))))) | (~(mult(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)), a) = mult(a, mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a))))))),
% 22.90/23.16 inference(unit_resolution,[status(thm)],[7797, 27])).
% 22.90/23.16 tff(7799,plain,
% 22.90/23.16 (~((~(mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c))))) | (~(mult(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)), a) = mult(a, mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a)))))),
% 22.90/23.16 inference(unit_resolution,[status(thm)],[7798, 7787])).
% 22.90/23.16 tff(7800,plain,
% 22.90/23.16 (((~(mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c))))) | (~(mult(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)), a) = mult(a, mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a))))) | (mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c))))),
% 22.90/23.16 inference(tautology,[status(thm)],[])).
% 22.90/23.16 tff(7801,plain,
% 22.90/23.16 (mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)))),
% 22.90/23.16 inference(unit_resolution,[status(thm)],[7800, 7799])).
% 22.90/23.16 tff(7802,plain,
% 22.90/23.16 (mult(c, mult(rd(mult(b, c), mult(a, c)), a)) = mult(c, b)),
% 22.90/23.16 inference(monotonicity,[status(thm)],[1380])).
% 22.90/23.16 tff(7803,assumption,(mult(c, mult(rd(mult(b, c), mult(a, c)), a)) = mult(c, mult(a, rd(mult(b, c), mult(a, c))))), introduced(assumption)).
% 22.90/23.16 tff(7804,plain,
% 22.90/23.16 (mult(c, mult(a, rd(mult(b, c), mult(a, c)))) = mult(c, mult(rd(mult(b, c), mult(a, c)), a))),
% 22.90/23.16 inference(symmetry,[status(thm)],[7803])).
% 22.90/23.16 tff(7805,plain,
% 22.90/23.16 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), c), c) = mult(c, mult(a, rd(mult(b, c), mult(a, c)))))),
% 22.90/23.16 inference(quant_inst,[status(thm)],[])).
% 22.90/23.16 tff(7806,plain,
% 22.90/23.16 (rd(mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), c), c) = mult(c, mult(a, rd(mult(b, c), mult(a, c))))),
% 22.90/23.16 inference(unit_resolution,[status(thm)],[7805, 168])).
% 22.90/23.16 tff(7807,plain,
% 22.90/23.16 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(a, mult(a, mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), c))) = mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), c))),
% 22.90/23.16 inference(quant_inst,[status(thm)],[])).
% 22.90/23.16 tff(7808,plain,
% 22.90/23.16 (ld(a, mult(a, mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), c))) = mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), c)),
% 22.90/23.16 inference(unit_resolution,[status(thm)],[7807, 7])).
% 22.90/23.16 tff(7809,plain,
% 22.90/23.16 (mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a)),
% 22.90/23.16 inference(symmetry,[status(thm)],[2731])).
% 22.90/23.16 tff(7810,plain,
% 22.90/23.16 (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(c, c)) = mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c))),
% 22.90/23.16 inference(monotonicity,[status(thm)],[1287])).
% 22.90/23.16 tff(7811,plain,
% 22.90/23.16 (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(mult(c, unit), c)) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(c, c))),
% 22.90/23.16 inference(monotonicity,[status(thm)],[2616])).
% 22.90/23.16 tff(7812,plain,
% 22.90/23.16 (mult(mult(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), unit), c), unit) = mult(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), c), unit)),
% 22.90/23.16 inference(symmetry,[status(thm)],[7580])).
% 22.90/23.16 tff(7813,plain,
% 22.90/23.16 (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(mult(unit, c), unit)) = mult(mult(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), unit), c), unit)),
% 22.90/23.16 inference(symmetry,[status(thm)],[7569])).
% 22.90/23.16 tff(7814,plain,
% 22.90/23.16 (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(mult(unit, c), unit))),
% 22.90/23.16 inference(symmetry,[status(thm)],[7567])).
% 22.90/23.16 tff(7815,plain,
% 22.90/23.16 (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), c)),
% 22.90/23.16 inference(unit_resolution,[status(thm)],[7508, 3865])).
% 22.90/23.16 tff(7816,plain,
% 22.90/23.16 (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), c), unit)),
% 23.00/23.16 inference(transitivity,[status(thm)],[7815, 7814, 7813, 7812])).
% 23.00/23.16 tff(7817,plain,
% 23.00/23.16 (mult(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), a), c) = mult(mult(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), c), unit), c)),
% 23.00/23.16 inference(monotonicity,[status(thm)],[7816])).
% 23.00/23.16 tff(7818,plain,
% 23.00/23.16 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), a)),
% 23.00/23.16 inference(symmetry,[status(thm)],[5948])).
% 23.00/23.16 tff(7819,plain,
% 23.00/23.16 (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), a), c)),
% 23.00/23.16 inference(monotonicity,[status(thm)],[7818])).
% 23.00/23.16 tff(7820,plain,
% 23.00/23.16 (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c)),
% 23.00/23.16 inference(unit_resolution,[status(thm)],[7691, 3865])).
% 23.00/23.16 tff(7821,plain,
% 23.00/23.16 (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a)),
% 23.00/23.16 inference(transitivity,[status(thm)],[7820, 7819, 7817, 7584, 7811, 7810, 6203, 6126, 7809])).
% 23.00/23.16 tff(7822,plain,
% 23.00/23.16 (rd(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a), a) = rd(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a), a)),
% 23.00/23.16 inference(monotonicity,[status(thm)],[7821])).
% 23.00/23.16 tff(7823,plain,
% 23.00/23.16 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 23.00/23.16 inference(transitivity,[status(thm)],[7695, 7822, 2786])).
% 23.00/23.16 tff(7824,plain,
% 23.00/23.16 (mult(a, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))))),
% 23.00/23.16 inference(monotonicity,[status(thm)],[7823])).
% 23.00/23.16 tff(7825,assumption,(mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)))), introduced(assumption)).
% 23.00/23.16 tff(7826,plain,
% 23.00/23.16 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(a, a), c), rd(mult(b, c), mult(a, c))), c) = mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), c)))),
% 23.00/23.16 inference(quant_inst,[status(thm)],[])).
% 23.00/23.16 tff(7827,plain,
% 23.00/23.16 (mult(mult(mult(mult(a, a), c), rd(mult(b, c), mult(a, c))), c) = mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), c))),
% 23.00/23.16 inference(unit_resolution,[status(thm)],[7826, 56])).
% 23.00/23.16 tff(7828,plain,
% 23.00/23.16 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(a, c), a), c), c) = mult(mult(a, c), a))),
% 23.00/23.16 inference(quant_inst,[status(thm)],[])).
% 23.00/23.16 tff(7829,plain,
% 23.00/23.16 (rd(mult(mult(mult(a, c), a), c), c) = mult(mult(a, c), a)),
% 23.00/23.16 inference(unit_resolution,[status(thm)],[7828, 168])).
% 23.00/23.16 tff(7830,plain,
% 23.00/23.16 (mult(c, mult(a, a)) = mult(mult(a, c), a)),
% 23.00/23.16 inference(transitivity,[status(thm)],[2656, 2655, 5721])).
% 23.00/23.16 tff(7831,plain,
% 23.00/23.16 (mult(mult(c, mult(a, a)), c) = mult(mult(mult(a, c), a), c)),
% 23.00/23.16 inference(monotonicity,[status(thm)],[7830])).
% 23.00/23.16 tff(7832,plain,
% 23.00/23.16 (mult(mult(mult(a, c), a), c) = mult(mult(c, mult(a, a)), c)),
% 23.00/23.16 inference(symmetry,[status(thm)],[7831])).
% 23.00/23.16 tff(7833,plain,
% 23.00/23.16 (mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), c)) = mult(rd(mult(b, c), mult(a, c)), mult(mult(c, mult(a, a)), c))),
% 23.00/23.16 inference(monotonicity,[status(thm)],[7832])).
% 23.00/23.16 tff(7834,plain,
% 23.00/23.16 (mult(rd(mult(b, c), mult(a, c)), mult(mult(c, mult(a, a)), c)) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), c))),
% 23.00/23.16 inference(symmetry,[status(thm)],[7833])).
% 23.00/23.16 tff(7835,plain,
% 23.00/23.16 (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), c) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, a)), c)),
% 23.00/23.16 inference(symmetry,[status(thm)],[7727])).
% 23.00/23.16 tff(7836,plain,
% 23.00/23.16 (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), c) = mult(mult(mult(b, c), a), c)),
% 23.00/23.16 inference(monotonicity,[status(thm)],[7491])).
% 23.00/23.16 tff(7837,plain,
% 23.00/23.16 (mult(mult(mult(b, c), a), c) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), c)),
% 23.00/23.16 inference(symmetry,[status(thm)],[7836])).
% 23.00/23.16 tff(7838,plain,
% 23.00/23.16 (mult(mult(mult(b, c), c), a) = mult(mult(mult(b, c), a), c)),
% 23.00/23.16 inference(unit_resolution,[status(thm)],[6773, 3897])).
% 23.00/23.16 tff(7839,plain,
% 23.00/23.16 (mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c) = mult(mult(b, c), c)),
% 23.00/23.16 inference(monotonicity,[status(thm)],[7426])).
% 23.00/23.16 tff(7840,plain,
% 23.00/23.16 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)) = mult(mult(b, c), c)),
% 23.00/23.16 inference(transitivity,[status(thm)],[4656, 4655, 6874, 7839])).
% 23.00/23.16 tff(7841,plain,
% 23.00/23.16 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)), a) = mult(mult(mult(b, c), c), a)),
% 23.00/23.16 inference(monotonicity,[status(thm)],[7840])).
% 23.00/23.16 tff(7842,plain,
% 23.00/23.16 (mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(c, c)), a))),
% 23.00/23.16 inference(monotonicity,[status(thm)],[4663])).
% 23.00/23.16 tff(7843,plain,
% 23.00/23.16 (mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), c))),
% 23.00/23.16 inference(transitivity,[status(thm)],[7842, 4661, 7841, 7838, 7837, 7835, 2661, 7834])).
% 23.00/23.16 tff(7844,plain,
% 23.00/23.16 (ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), c), a))) = ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), c)))),
% 23.00/23.16 inference(monotonicity,[status(thm)],[7843])).
% 23.00/23.16 tff(7845,plain,
% 23.00/23.16 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), c), a))) = mult(mult(mult(a, c), c), a))),
% 23.00/23.16 inference(quant_inst,[status(thm)],[])).
% 23.00/23.16 tff(7846,plain,
% 23.00/23.16 (ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), c), a))) = mult(mult(mult(a, c), c), a)),
% 23.00/23.16 inference(unit_resolution,[status(thm)],[7845, 7])).
% 23.00/23.16 tff(7847,plain,
% 23.00/23.16 (mult(mult(mult(a, c), c), a) = ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), c), a)))),
% 23.00/23.16 inference(symmetry,[status(thm)],[7846])).
% 23.00/23.16 tff(7848,plain,
% 23.00/23.16 (mult(a, mult(mult(a, c), c)) = mult(a, mult(c, mult(a, c)))),
% 23.00/23.16 inference(monotonicity,[status(thm)],[4529])).
% 23.00/23.16 tff(7849,plain,
% 23.00/23.16 (mult(mult(unit, a), mult(mult(a, c), c)) = mult(a, mult(mult(a, c), c))),
% 23.00/23.16 inference(monotonicity,[status(thm)],[244])).
% 23.00/23.16 tff(7850,plain,
% 23.00/23.16 (mult(mult(unit, a), mult(mult(a, c), c)) = mult(a, mult(mult(c, c), a))),
% 23.00/23.16 inference(transitivity,[status(thm)],[7849, 7848, 4713, 4710])).
% 23.00/23.16 tff(7851,plain,
% 23.00/23.16 (mult(mult(unit, mult(mult(a, c), c)), a) = mult(mult(c, mult(a, c)), a)),
% 23.00/23.16 inference(monotonicity,[status(thm)],[6012])).
% 23.00/23.16 tff(7852,plain,
% 23.00/23.16 (mult(mult(unit, mult(mult(a, c), c)), a) = mult(mult(a, mult(c, c)), a)),
% 23.00/23.16 inference(transitivity,[status(thm)],[7851, 4664, 4663])).
% 23.00/23.16 tff(7853,plain,
% 23.00/23.16 ((mult(mult(unit, mult(mult(a, c), c)), a) = mult(mult(unit, a), mult(mult(a, c), c))) <=> (mult(mult(a, mult(c, c)), a) = mult(a, mult(mult(c, c), a)))),
% 23.00/23.16 inference(monotonicity,[status(thm)],[7852, 7850])).
% 23.00/23.16 tff(7854,plain,
% 23.00/23.16 ((mult(mult(a, mult(c, c)), a) = mult(a, mult(mult(c, c), a))) <=> (mult(mult(unit, mult(mult(a, c), c)), a) = mult(mult(unit, a), mult(mult(a, c), c)))),
% 23.00/23.16 inference(symmetry,[status(thm)],[7853])).
% 23.00/23.16 tff(7855,plain,
% 23.00/23.16 (mult(a, mult(mult(c, a), c)) = mult(a, mult(c, mult(a, c)))),
% 23.00/23.16 inference(monotonicity,[status(thm)],[2690])).
% 23.00/23.16 tff(7856,plain,
% 23.00/23.16 (mult(a, mult(c, mult(a, c))) = mult(a, mult(mult(c, a), c))),
% 23.00/23.16 inference(symmetry,[status(thm)],[7855])).
% 23.00/23.16 tff(7857,plain,
% 23.00/23.16 (mult(a, mult(mult(c, c), a)) = mult(mult(mult(a, c), a), c)),
% 23.00/23.16 inference(transitivity,[status(thm)],[4709, 4712, 7856, 4724])).
% 23.00/23.16 tff(7858,plain,
% 23.00/23.16 ((mult(mult(a, mult(c, c)), a) = mult(a, mult(mult(c, c), a))) <=> (mult(mult(mult(a, c), c), a) = mult(mult(mult(a, c), a), c))),
% 23.00/23.16 inference(monotonicity,[status(thm)],[4662, 7857])).
% 23.00/23.16 tff(7859,plain,
% 23.00/23.16 ((mult(mult(mult(a, c), c), a) = mult(mult(mult(a, c), a), c)) <=> (mult(mult(a, mult(c, c)), a) = mult(a, mult(mult(c, c), a)))),
% 23.00/23.16 inference(symmetry,[status(thm)],[7858])).
% 23.00/23.16 tff(7860,plain,
% 23.00/23.16 ((mult(mult(mult(a, c), c), a) = mult(mult(mult(a, c), a), c)) <=> (mult(mult(unit, mult(mult(a, c), c)), a) = mult(mult(unit, a), mult(mult(a, c), c)))),
% 23.00/23.17 inference(transitivity,[status(thm)],[7859, 7854])).
% 23.00/23.17 tff(7861,plain,
% 23.00/23.17 (mult(mult(a, mult(c, c)), a) = mult(a, mult(mult(c, c), a))),
% 23.00/23.17 inference(transitivity,[status(thm)],[4662, 7847, 7844, 7738, 4717, 7855, 4713, 4710])).
% 23.00/23.17 tff(7862,plain,
% 23.00/23.17 (mult(mult(mult(a, c), c), a) = mult(mult(mult(a, c), a), c)),
% 23.00/23.17 inference(modus_ponens,[status(thm)],[7861, 7858])).
% 23.00/23.17 tff(7863,plain,
% 23.00/23.17 (mult(mult(unit, mult(mult(a, c), c)), a) = mult(mult(unit, a), mult(mult(a, c), c))),
% 23.00/23.17 inference(modus_ponens,[status(thm)],[7862, 7860])).
% 23.00/23.17 tff(7864,plain,
% 23.00/23.17 ((mult(mult(a, mult(c, c)), a) = mult(mult(a, a), mult(c, c))) <=> (mult(mult(a, a), mult(c, c)) = mult(mult(a, mult(c, c)), a))),
% 23.00/23.17 inference(commutativity,[status(thm)],[])).
% 23.00/23.17 tff(7865,plain,
% 23.00/23.17 ((mult(mult(a, a), mult(c, c)) = mult(mult(a, mult(c, c)), a)) <=> (mult(mult(a, mult(c, c)), a) = mult(mult(a, a), mult(c, c)))),
% 23.00/23.17 inference(symmetry,[status(thm)],[7864])).
% 23.00/23.17 tff(7866,plain,
% 23.00/23.17 ((~![A: $i] : (mult(unit, A) = A)) | (mult(unit, mult(mult(a, c), c)) = mult(mult(a, c), c))),
% 23.00/23.17 inference(quant_inst,[status(thm)],[])).
% 23.00/23.17 tff(7867,plain,
% 23.00/23.17 (mult(unit, mult(mult(a, c), c)) = mult(mult(a, c), c)),
% 23.00/23.17 inference(unit_resolution,[status(thm)],[7866, 71])).
% 23.00/23.17 tff(7868,plain,
% 23.00/23.17 (mult(mult(unit, mult(mult(a, c), c)), a) = mult(mult(mult(a, c), c), a)),
% 23.00/23.17 inference(monotonicity,[status(thm)],[7867])).
% 23.00/23.17 tff(7869,plain,
% 23.00/23.17 (mult(mult(mult(a, c), c), a) = mult(mult(unit, mult(mult(a, c), c)), a)),
% 23.00/23.17 inference(symmetry,[status(thm)],[7868])).
% 23.00/23.17 tff(7870,plain,
% 23.00/23.17 (mult(mult(a, mult(c, c)), a) = mult(mult(unit, mult(mult(a, c), c)), a)),
% 23.00/23.17 inference(transitivity,[status(thm)],[4662, 7869])).
% 23.00/23.17 tff(7871,plain,
% 23.00/23.17 (mult(a, mult(mult(a, c), c)) = mult(mult(unit, a), mult(mult(a, c), c))),
% 23.00/23.17 inference(symmetry,[status(thm)],[7849])).
% 23.00/23.17 tff(7872,plain,
% 23.00/23.17 (mult(a, mult(a, mult(c, c))) = mult(a, mult(mult(a, c), c))),
% 23.00/23.17 inference(monotonicity,[status(thm)],[2619])).
% 23.00/23.17 tff(7873,assumption,(~(mult(mult(a, mult(c, c)), a) = mult(mult(a, a), mult(c, c)))), introduced(assumption)).
% 23.00/23.17 tff(7874,plain,
% 23.00/23.17 (((~(mult(mult(a, mult(c, c)), a) = mult(mult(a, a), mult(c, c)))) | (~(mult(a, mult(mult(c, c), a)) = mult(a, mult(a, mult(c, c)))))) | (mult(mult(a, mult(c, c)), a) = mult(mult(a, a), mult(c, c)))),
% 23.00/23.17 inference(tautology,[status(thm)],[])).
% 23.00/23.17 tff(7875,plain,
% 23.00/23.17 ((~(mult(mult(a, mult(c, c)), a) = mult(mult(a, a), mult(c, c)))) | (~(mult(a, mult(mult(c, c), a)) = mult(a, mult(a, mult(c, c)))))),
% 23.00/23.17 inference(unit_resolution,[status(thm)],[7874, 7873])).
% 23.00/23.17 tff(7876,plain,
% 23.00/23.17 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, a), mult(c, c)) = mult(a, mult(a, mult(c, c))))) | (~(mult(mult(a, mult(c, c)), a) = mult(a, mult(mult(c, c), a)))))) | (~((~(mult(mult(a, mult(c, c)), a) = mult(mult(a, a), mult(c, c)))) | (~(mult(a, mult(mult(c, c), a)) = mult(a, mult(a, mult(c, c))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, a), mult(c, c)) = mult(a, mult(a, mult(c, c))))) | (~(mult(mult(a, mult(c, c)), a) = mult(a, mult(mult(c, c), a)))))) | (~((~(mult(mult(a, mult(c, c)), a) = mult(mult(a, a), mult(c, c)))) | (~(mult(a, mult(mult(c, c), a)) = mult(a, mult(a, mult(c, c))))))))),
% 23.00/23.17 inference(rewrite,[status(thm)],[])).
% 23.00/23.17 tff(7877,plain,
% 23.00/23.17 (((~((~(mult(mult(a, mult(c, c)), a) = mult(mult(a, a), mult(c, c)))) | (~(mult(a, mult(mult(c, c), a)) = mult(a, mult(a, mult(c, c))))))) | (~((~(mult(mult(a, a), mult(c, c)) = mult(a, mult(a, mult(c, c))))) | (~(mult(mult(a, mult(c, c)), a) = mult(a, mult(mult(c, c), a))))))) <=> ((~((~(mult(mult(a, a), mult(c, c)) = mult(a, mult(a, mult(c, c))))) | (~(mult(mult(a, mult(c, c)), a) = mult(a, mult(mult(c, c), a)))))) | (~((~(mult(mult(a, mult(c, c)), a) = mult(mult(a, a), mult(c, c)))) | (~(mult(a, mult(mult(c, c), a)) = mult(a, mult(a, mult(c, c))))))))),
% 23.00/23.17 inference(rewrite,[status(thm)],[])).
% 23.00/23.17 tff(7878,plain,
% 23.00/23.17 ((~((~(mult(mult(a, mult(c, c)), a) = mult(a, mult(mult(c, c), a)))) | (~(mult(mult(a, a), mult(c, c)) = mult(a, mult(a, mult(c, c))))))) <=> (~((~(mult(mult(a, a), mult(c, c)) = mult(a, mult(a, mult(c, c))))) | (~(mult(mult(a, mult(c, c)), a) = mult(a, mult(mult(c, c), a))))))),
% 23.00/23.17 inference(rewrite,[status(thm)],[])).
% 23.00/23.17 tff(7879,plain,
% 23.00/23.17 ((~((~(mult(mult(a, mult(c, c)), a) = mult(mult(a, a), mult(c, c)))) | (~(mult(a, mult(mult(c, c), a)) = mult(a, mult(a, mult(c, c))))))) <=> (~((~(mult(mult(a, mult(c, c)), a) = mult(mult(a, a), mult(c, c)))) | (~(mult(a, mult(mult(c, c), a)) = mult(a, mult(a, mult(c, c)))))))),
% 23.00/23.17 inference(rewrite,[status(thm)],[])).
% 23.00/23.17 tff(7880,plain,
% 23.00/23.17 (((~((~(mult(mult(a, mult(c, c)), a) = mult(mult(a, a), mult(c, c)))) | (~(mult(a, mult(mult(c, c), a)) = mult(a, mult(a, mult(c, c))))))) | (~((~(mult(mult(a, mult(c, c)), a) = mult(a, mult(mult(c, c), a)))) | (~(mult(mult(a, a), mult(c, c)) = mult(a, mult(a, mult(c, c)))))))) <=> ((~((~(mult(mult(a, mult(c, c)), a) = mult(mult(a, a), mult(c, c)))) | (~(mult(a, mult(mult(c, c), a)) = mult(a, mult(a, mult(c, c))))))) | (~((~(mult(mult(a, a), mult(c, c)) = mult(a, mult(a, mult(c, c))))) | (~(mult(mult(a, mult(c, c)), a) = mult(a, mult(mult(c, c), a)))))))),
% 23.00/23.17 inference(monotonicity,[status(thm)],[7879, 7878])).
% 23.00/23.17 tff(7881,plain,
% 23.00/23.17 (((~((~(mult(mult(a, mult(c, c)), a) = mult(mult(a, a), mult(c, c)))) | (~(mult(a, mult(mult(c, c), a)) = mult(a, mult(a, mult(c, c))))))) | (~((~(mult(mult(a, mult(c, c)), a) = mult(a, mult(mult(c, c), a)))) | (~(mult(mult(a, a), mult(c, c)) = mult(a, mult(a, mult(c, c)))))))) <=> ((~((~(mult(mult(a, a), mult(c, c)) = mult(a, mult(a, mult(c, c))))) | (~(mult(mult(a, mult(c, c)), a) = mult(a, mult(mult(c, c), a)))))) | (~((~(mult(mult(a, mult(c, c)), a) = mult(mult(a, a), mult(c, c)))) | (~(mult(a, mult(mult(c, c), a)) = mult(a, mult(a, mult(c, c))))))))),
% 23.00/23.17 inference(transitivity,[status(thm)],[7880, 7877])).
% 23.00/23.17 tff(7882,plain,
% 23.00/23.17 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, mult(c, c)), a) = mult(mult(a, a), mult(c, c)))) | (~(mult(a, mult(mult(c, c), a)) = mult(a, mult(a, mult(c, c))))))) | (~((~(mult(mult(a, mult(c, c)), a) = mult(a, mult(mult(c, c), a)))) | (~(mult(mult(a, a), mult(c, c)) = mult(a, mult(a, mult(c, c))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, a), mult(c, c)) = mult(a, mult(a, mult(c, c))))) | (~(mult(mult(a, mult(c, c)), a) = mult(a, mult(mult(c, c), a)))))) | (~((~(mult(mult(a, mult(c, c)), a) = mult(mult(a, a), mult(c, c)))) | (~(mult(a, mult(mult(c, c), a)) = mult(a, mult(a, mult(c, c)))))))))),
% 23.00/23.17 inference(monotonicity,[status(thm)],[7881])).
% 23.00/23.17 tff(7883,plain,
% 23.00/23.17 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, mult(c, c)), a) = mult(mult(a, a), mult(c, c)))) | (~(mult(a, mult(mult(c, c), a)) = mult(a, mult(a, mult(c, c))))))) | (~((~(mult(mult(a, mult(c, c)), a) = mult(a, mult(mult(c, c), a)))) | (~(mult(mult(a, a), mult(c, c)) = mult(a, mult(a, mult(c, c))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, a), mult(c, c)) = mult(a, mult(a, mult(c, c))))) | (~(mult(mult(a, mult(c, c)), a) = mult(a, mult(mult(c, c), a)))))) | (~((~(mult(mult(a, mult(c, c)), a) = mult(mult(a, a), mult(c, c)))) | (~(mult(a, mult(mult(c, c), a)) = mult(a, mult(a, mult(c, c))))))))),
% 23.00/23.17 inference(transitivity,[status(thm)],[7882, 7876])).
% 23.00/23.17 tff(7884,plain,
% 23.00/23.17 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, mult(c, c)), a) = mult(mult(a, a), mult(c, c)))) | (~(mult(a, mult(mult(c, c), a)) = mult(a, mult(a, mult(c, c))))))) | (~((~(mult(mult(a, mult(c, c)), a) = mult(a, mult(mult(c, c), a)))) | (~(mult(mult(a, a), mult(c, c)) = mult(a, mult(a, mult(c, c))))))))),
% 23.00/23.17 inference(quant_inst,[status(thm)],[])).
% 23.00/23.17 tff(7885,plain,
% 23.00/23.17 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, a), mult(c, c)) = mult(a, mult(a, mult(c, c))))) | (~(mult(mult(a, mult(c, c)), a) = mult(a, mult(mult(c, c), a)))))) | (~((~(mult(mult(a, mult(c, c)), a) = mult(mult(a, a), mult(c, c)))) | (~(mult(a, mult(mult(c, c), a)) = mult(a, mult(a, mult(c, c)))))))),
% 23.00/23.17 inference(modus_ponens,[status(thm)],[7884, 7883])).
% 23.00/23.17 tff(7886,plain,
% 23.00/23.17 ((~((~(mult(mult(a, a), mult(c, c)) = mult(a, mult(a, mult(c, c))))) | (~(mult(mult(a, mult(c, c)), a) = mult(a, mult(mult(c, c), a)))))) | (~((~(mult(mult(a, mult(c, c)), a) = mult(mult(a, a), mult(c, c)))) | (~(mult(a, mult(mult(c, c), a)) = mult(a, mult(a, mult(c, c)))))))),
% 23.00/23.17 inference(unit_resolution,[status(thm)],[7885, 27])).
% 23.00/23.17 tff(7887,plain,
% 23.00/23.17 (~((~(mult(mult(a, a), mult(c, c)) = mult(a, mult(a, mult(c, c))))) | (~(mult(mult(a, mult(c, c)), a) = mult(a, mult(mult(c, c), a)))))),
% 23.00/23.17 inference(unit_resolution,[status(thm)],[7886, 7875])).
% 23.00/23.17 tff(7888,plain,
% 23.00/23.17 (((~(mult(mult(a, a), mult(c, c)) = mult(a, mult(a, mult(c, c))))) | (~(mult(mult(a, mult(c, c)), a) = mult(a, mult(mult(c, c), a))))) | (mult(mult(a, a), mult(c, c)) = mult(a, mult(a, mult(c, c))))),
% 23.00/23.17 inference(tautology,[status(thm)],[])).
% 23.00/23.17 tff(7889,plain,
% 23.00/23.17 (mult(mult(a, a), mult(c, c)) = mult(a, mult(a, mult(c, c)))),
% 23.00/23.17 inference(unit_resolution,[status(thm)],[7888, 7887])).
% 23.00/23.17 tff(7890,plain,
% 23.00/23.17 (mult(mult(a, a), mult(c, c)) = mult(mult(unit, a), mult(mult(a, c), c))),
% 23.00/23.17 inference(transitivity,[status(thm)],[7889, 7872, 7871])).
% 23.00/23.17 tff(7891,plain,
% 23.00/23.17 ((mult(mult(a, a), mult(c, c)) = mult(mult(a, mult(c, c)), a)) <=> (mult(mult(unit, a), mult(mult(a, c), c)) = mult(mult(unit, mult(mult(a, c), c)), a))),
% 23.00/23.17 inference(monotonicity,[status(thm)],[7890, 7870])).
% 23.00/23.17 tff(7892,plain,
% 23.00/23.17 ((mult(mult(unit, a), mult(mult(a, c), c)) = mult(mult(unit, mult(mult(a, c), c)), a)) <=> (mult(mult(a, a), mult(c, c)) = mult(mult(a, mult(c, c)), a))),
% 23.00/23.17 inference(symmetry,[status(thm)],[7891])).
% 23.00/23.17 tff(7893,plain,
% 23.00/23.17 ((mult(mult(unit, mult(mult(a, c), c)), a) = mult(mult(unit, a), mult(mult(a, c), c))) <=> (mult(mult(unit, a), mult(mult(a, c), c)) = mult(mult(unit, mult(mult(a, c), c)), a))),
% 23.00/23.17 inference(commutativity,[status(thm)],[])).
% 23.00/23.17 tff(7894,plain,
% 23.00/23.17 ((mult(mult(unit, mult(mult(a, c), c)), a) = mult(mult(unit, a), mult(mult(a, c), c))) <=> (mult(mult(a, mult(c, c)), a) = mult(mult(a, a), mult(c, c)))),
% 23.00/23.17 inference(transitivity,[status(thm)],[7893, 7892, 7865])).
% 23.00/23.17 tff(7895,assumption,(mult(mult(unit, mult(mult(a, c), c)), a) = mult(mult(unit, a), mult(mult(a, c), c))), introduced(assumption)).
% 23.00/23.17 tff(7896,plain,
% 23.00/23.17 (mult(mult(a, mult(c, c)), a) = mult(mult(a, a), mult(c, c))),
% 23.00/23.17 inference(modus_ponens,[status(thm)],[7895, 7894])).
% 23.00/23.17 tff(7897,plain,
% 23.00/23.17 ($false),
% 23.00/23.17 inference(unit_resolution,[status(thm)],[7873, 7896])).
% 23.00/23.17 tff(7898,plain,((~(mult(mult(unit, mult(mult(a, c), c)), a) = mult(mult(unit, a), mult(mult(a, c), c)))) | (mult(mult(a, mult(c, c)), a) = mult(mult(a, a), mult(c, c)))), inference(lemma,lemma(discharge,[]))).
% 23.00/23.17 tff(7899,plain,
% 23.00/23.17 (mult(mult(a, mult(c, c)), a) = mult(mult(a, a), mult(c, c))),
% 23.00/23.17 inference(unit_resolution,[status(thm)],[7898, 7863])).
% 23.00/23.17 tff(7900,plain,
% 23.00/23.17 (mult(mult(a, a), mult(c, c)) = mult(mult(a, mult(c, c)), a)),
% 23.00/23.17 inference(symmetry,[status(thm)],[7899])).
% 23.00/23.17 tff(7901,plain,
% 23.00/23.17 (mult(mult(a, a), mult(mult(c, unit), c)) = mult(mult(a, a), mult(c, c))),
% 23.00/23.17 inference(monotonicity,[status(thm)],[2616])).
% 23.00/23.17 tff(7902,plain,
% 23.00/23.17 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(a, a), c), unit), c) = mult(mult(a, a), mult(mult(c, unit), c)))),
% 23.00/23.17 inference(quant_inst,[status(thm)],[])).
% 23.00/23.17 tff(7903,plain,
% 23.00/23.17 (mult(mult(mult(mult(a, a), c), unit), c) = mult(mult(a, a), mult(mult(c, unit), c))),
% 23.00/23.17 inference(unit_resolution,[status(thm)],[7902, 56])).
% 23.00/23.17 tff(7904,plain,
% 23.00/23.17 (mult(mult(mult(mult(a, a), c), unit), c) = mult(mult(mult(a, c), a), c)),
% 23.00/23.17 inference(transitivity,[status(thm)],[7903, 7901, 7900, 4662, 7847, 7844, 7738])).
% 23.00/23.17 tff(7905,plain,
% 23.00/23.17 (rd(mult(mult(mult(mult(a, a), c), unit), c), c) = rd(mult(mult(mult(a, c), a), c), c)),
% 23.00/23.17 inference(monotonicity,[status(thm)],[7904])).
% 23.00/23.17 tff(7906,plain,
% 23.00/23.17 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(mult(a, a), c), unit), c), c) = mult(mult(mult(a, a), c), unit))),
% 23.00/23.17 inference(quant_inst,[status(thm)],[])).
% 23.00/23.17 tff(7907,plain,
% 23.00/23.17 (rd(mult(mult(mult(mult(a, a), c), unit), c), c) = mult(mult(mult(a, a), c), unit)),
% 23.00/23.17 inference(unit_resolution,[status(thm)],[7906, 168])).
% 23.00/23.17 tff(7908,plain,
% 23.00/23.17 (mult(mult(mult(a, a), c), unit) = rd(mult(mult(mult(mult(a, a), c), unit), c), c)),
% 23.00/23.17 inference(symmetry,[status(thm)],[7907])).
% 23.00/23.17 tff(7909,plain,
% 23.00/23.17 ((~![A: $i] : (mult(A, unit) = A)) | (mult(mult(mult(a, a), c), unit) = mult(mult(a, a), c))),
% 23.00/23.17 inference(quant_inst,[status(thm)],[])).
% 23.00/23.17 tff(7910,plain,
% 23.00/23.17 (mult(mult(mult(a, a), c), unit) = mult(mult(a, a), c)),
% 23.00/23.17 inference(unit_resolution,[status(thm)],[7909, 43])).
% 23.00/23.17 tff(7911,plain,
% 23.00/23.17 (mult(mult(a, a), c) = mult(mult(mult(a, a), c), unit)),
% 23.00/23.17 inference(symmetry,[status(thm)],[7910])).
% 23.00/23.17 tff(7912,plain,
% 23.00/23.17 (mult(mult(a, a), c) = mult(mult(a, c), a)),
% 23.00/23.17 inference(transitivity,[status(thm)],[7911, 7908, 7905, 7829])).
% 23.00/23.17 tff(7913,plain,
% 23.00/23.17 (mult(mult(mult(a, a), c), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))),
% 23.00/23.17 inference(monotonicity,[status(thm)],[7912])).
% 23.00/23.17 tff(7914,plain,
% 23.00/23.17 (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, a), c), rd(mult(b, c), mult(a, c)))),
% 23.00/23.17 inference(symmetry,[status(thm)],[7913])).
% 23.00/23.17 tff(7915,plain,
% 23.00/23.17 (mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(mult(a, a), c), rd(mult(b, c), mult(a, c))), c)),
% 23.00/23.17 inference(monotonicity,[status(thm)],[7914])).
% 23.00/23.17 tff(7916,plain,
% 23.00/23.17 (mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), c)),
% 23.00/23.17 inference(monotonicity,[status(thm)],[6663])).
% 23.00/23.17 tff(7917,plain,
% 23.00/23.17 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(a, mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), c)))),
% 23.00/23.17 inference(quant_inst,[status(thm)],[])).
% 23.00/23.17 tff(7918,plain,
% 23.00/23.17 (mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(a, mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), c))),
% 23.00/23.17 inference(unit_resolution,[status(thm)],[7917, 56])).
% 23.00/23.17 tff(7919,plain,
% 23.00/23.17 (mult(a, mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), c)) = mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), c)),
% 23.00/23.17 inference(symmetry,[status(thm)],[7918])).
% 23.00/23.17 tff(7920,plain,
% 23.00/23.17 (mult(a, mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), c)) = mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))))),
% 23.00/23.18 inference(transitivity,[status(thm)],[7919, 7916, 7915, 7827, 7825, 7698, 7824])).
% 23.00/23.18 tff(7921,plain,
% 23.00/23.18 (ld(a, mult(a, mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), c))) = ld(a, mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))))),
% 23.00/23.18 inference(monotonicity,[status(thm)],[7920])).
% 23.00/23.18 tff(7922,plain,
% 23.00/23.18 (ld(a, mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))))) = ld(a, mult(a, mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), c)))),
% 23.00/23.18 inference(symmetry,[status(thm)],[7921])).
% 23.00/23.18 tff(7923,plain,
% 23.00/23.18 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), c)),
% 23.00/23.18 inference(transitivity,[status(thm)],[7695, 7822, 2786, 6733, 7922, 7808])).
% 23.00/23.18 tff(7924,plain,
% 23.00/23.18 (rd(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), c) = rd(mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), c), c)),
% 23.00/23.18 inference(monotonicity,[status(thm)],[7923])).
% 23.00/23.18 tff(7925,plain,
% 23.00/23.18 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), c) = mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 23.00/23.18 inference(quant_inst,[status(thm)],[])).
% 23.00/23.18 tff(7926,plain,
% 23.00/23.18 (rd(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), c) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))),
% 23.00/23.18 inference(unit_resolution,[status(thm)],[7925, 168])).
% 23.00/23.18 tff(7927,plain,
% 23.00/23.18 (mult(mult(a, c), rd(mult(b, c), mult(a, c))) = rd(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), c)),
% 23.00/23.18 inference(symmetry,[status(thm)],[7926])).
% 23.00/23.18 tff(7928,plain,
% 23.00/23.18 (mult(mult(a, c), rd(mult(b, c), mult(a, c))) = mult(b, c)),
% 23.00/23.18 inference(transitivity,[status(thm)],[7927, 7924, 7806, 7804, 7802, 240, 237, 141])).
% 23.00/23.18 tff(7929,plain,
% 23.00/23.18 (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(b, c))),
% 23.00/23.18 inference(monotonicity,[status(thm)],[7928])).
% 23.00/23.18 tff(7930,plain,
% 23.00/23.18 (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))),
% 23.00/23.18 inference(transitivity,[status(thm)],[7929, 289])).
% 23.00/23.18 tff(7931,plain,
% 23.00/23.18 ($false),
% 23.00/23.18 inference(unit_resolution,[status(thm)],[270, 7930])).
% 23.00/23.18 tff(7932,plain,((~(mult(c, mult(rd(mult(b, c), mult(a, c)), a)) = mult(c, mult(a, rd(mult(b, c), mult(a, c)))))) | (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) | (~(mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit))))) | (~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))), inference(lemma,lemma(discharge,[]))).
% 23.00/23.18 tff(7933,plain,
% 23.00/23.18 ((~(mult(c, mult(rd(mult(b, c), mult(a, c)), a)) = mult(c, mult(a, rd(mult(b, c), mult(a, c)))))) | (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) | (~(mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)))) | (~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))),
% 23.00/23.18 inference(unit_resolution,[status(thm)],[7932, 3862])).
% 23.00/23.18 tff(7934,plain,
% 23.00/23.18 (~(mult(c, mult(rd(mult(b, c), mult(a, c)), a)) = mult(c, mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.00/23.18 inference(unit_resolution,[status(thm)],[7933, 7801, 4360, 4331, 7272, 6582, 7638, 7634, 6581, 270])).
% 23.00/23.18 tff(7935,plain,
% 23.00/23.18 (((~(mult(mult(c, rd(mult(b, c), mult(a, c))), a) = mult(mult(c, a), rd(mult(b, c), mult(a, c))))) | (~(mult(c, mult(rd(mult(b, c), mult(a, c)), a)) = mult(c, mult(a, rd(mult(b, c), mult(a, c))))))) | (mult(c, mult(rd(mult(b, c), mult(a, c)), a)) = mult(c, mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.00/23.18 inference(tautology,[status(thm)],[])).
% 23.00/23.18 tff(7936,plain,
% 23.00/23.18 ((~(mult(mult(c, rd(mult(b, c), mult(a, c))), a) = mult(mult(c, a), rd(mult(b, c), mult(a, c))))) | (~(mult(c, mult(rd(mult(b, c), mult(a, c)), a)) = mult(c, mult(a, rd(mult(b, c), mult(a, c))))))),
% 23.00/23.18 inference(unit_resolution,[status(thm)],[7935, 7934])).
% 23.00/23.18 tff(7937,plain,
% 23.00/23.18 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(c, rd(mult(b, c), mult(a, c))), a) = mult(mult(c, a), rd(mult(b, c), mult(a, c))))) | (~(mult(c, mult(rd(mult(b, c), mult(a, c)), a)) = mult(c, mult(a, rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(c, rd(mult(b, c), mult(a, c))), a) = mult(c, mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(c, a), rd(mult(b, c), mult(a, c))) = mult(c, mult(a, rd(mult(b, c), mult(a, c)))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(c, rd(mult(b, c), mult(a, c))), a) = mult(mult(c, a), rd(mult(b, c), mult(a, c))))) | (~(mult(c, mult(rd(mult(b, c), mult(a, c)), a)) = mult(c, mult(a, rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(c, rd(mult(b, c), mult(a, c))), a) = mult(c, mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(c, a), rd(mult(b, c), mult(a, c))) = mult(c, mult(a, rd(mult(b, c), mult(a, c)))))))))),
% 23.00/23.18 inference(rewrite,[status(thm)],[])).
% 23.00/23.18 tff(7938,plain,
% 23.00/23.18 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(c, rd(mult(b, c), mult(a, c))), a) = mult(mult(c, a), rd(mult(b, c), mult(a, c))))) | (~(mult(c, mult(rd(mult(b, c), mult(a, c)), a)) = mult(c, mult(a, rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(c, rd(mult(b, c), mult(a, c))), a) = mult(c, mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(c, a), rd(mult(b, c), mult(a, c))) = mult(c, mult(a, rd(mult(b, c), mult(a, c)))))))))),
% 23.00/23.18 inference(quant_inst,[status(thm)],[])).
% 23.00/23.18 tff(7939,plain,
% 23.00/23.18 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(c, rd(mult(b, c), mult(a, c))), a) = mult(mult(c, a), rd(mult(b, c), mult(a, c))))) | (~(mult(c, mult(rd(mult(b, c), mult(a, c)), a)) = mult(c, mult(a, rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(c, rd(mult(b, c), mult(a, c))), a) = mult(c, mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(c, a), rd(mult(b, c), mult(a, c))) = mult(c, mult(a, rd(mult(b, c), mult(a, c))))))))),
% 23.00/23.18 inference(modus_ponens,[status(thm)],[7938, 7937])).
% 23.00/23.18 tff(7940,plain,
% 23.00/23.18 ((~((~(mult(mult(c, rd(mult(b, c), mult(a, c))), a) = mult(mult(c, a), rd(mult(b, c), mult(a, c))))) | (~(mult(c, mult(rd(mult(b, c), mult(a, c)), a)) = mult(c, mult(a, rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(c, rd(mult(b, c), mult(a, c))), a) = mult(c, mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(c, a), rd(mult(b, c), mult(a, c))) = mult(c, mult(a, rd(mult(b, c), mult(a, c))))))))),
% 23.00/23.18 inference(unit_resolution,[status(thm)],[7939, 27])).
% 23.00/23.18 tff(7941,plain,
% 23.00/23.18 (~((~(mult(mult(c, rd(mult(b, c), mult(a, c))), a) = mult(c, mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(c, a), rd(mult(b, c), mult(a, c))) = mult(c, mult(a, rd(mult(b, c), mult(a, c)))))))),
% 23.00/23.18 inference(unit_resolution,[status(thm)],[7940, 7936])).
% 23.00/23.18 tff(7942,plain,
% 23.00/23.18 (((~(mult(mult(c, rd(mult(b, c), mult(a, c))), a) = mult(c, mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(c, a), rd(mult(b, c), mult(a, c))) = mult(c, mult(a, rd(mult(b, c), mult(a, c))))))) | (mult(mult(c, a), rd(mult(b, c), mult(a, c))) = mult(c, mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.00/23.18 inference(tautology,[status(thm)],[])).
% 23.00/23.18 tff(7943,plain,
% 23.00/23.18 (mult(mult(c, a), rd(mult(b, c), mult(a, c))) = mult(c, mult(a, rd(mult(b, c), mult(a, c))))),
% 23.00/23.18 inference(unit_resolution,[status(thm)],[7942, 7941])).
% 23.00/23.18 tff(7944,assumption,(mult(mult(c, a), rd(mult(b, c), mult(a, c))) = mult(c, mult(a, rd(mult(b, c), mult(a, c))))), introduced(assumption)).
% 23.00/23.18 tff(7945,plain,
% 23.00/23.18 (mult(c, mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(c, a), rd(mult(b, c), mult(a, c)))),
% 23.00/23.18 inference(symmetry,[status(thm)],[7944])).
% 23.00/23.18 tff(7946,plain,
% 23.00/23.18 (mult(c, mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))),
% 23.00/23.18 inference(transitivity,[status(thm)],[7945, 6348])).
% 23.00/23.18 tff(7947,plain,
% 23.00/23.18 (mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 23.00/23.18 inference(monotonicity,[status(thm)],[7946])).
% 23.00/23.18 tff(7948,plain,
% 23.00/23.18 (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.00/23.18 inference(symmetry,[status(thm)],[7947])).
% 23.00/23.18 tff(7949,plain,
% 23.00/23.18 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(b, a), mult(mult(b, a), mult(b, c))) = mult(b, c))),
% 23.00/23.18 inference(quant_inst,[status(thm)],[])).
% 23.00/23.18 tff(7950,plain,
% 23.00/23.18 (ld(mult(b, a), mult(mult(b, a), mult(b, c))) = mult(b, c)),
% 23.00/23.18 inference(unit_resolution,[status(thm)],[7949, 7])).
% 23.00/23.18 tff(7951,plain,
% 23.00/23.18 (mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), mult(a, c))) = mult(mult(b, a), mult(b, c))),
% 23.00/23.18 inference(monotonicity,[status(thm)],[137])).
% 23.00/23.18 tff(7952,plain,
% 23.00/23.18 (mult(a, mult(b, c)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))),
% 23.00/23.18 inference(transitivity,[status(thm)],[289, 4416])).
% 23.00/23.18 tff(7953,plain,
% 23.00/23.18 (mult(b, mult(a, mult(b, c))) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 23.00/23.18 inference(monotonicity,[status(thm)],[7952])).
% 23.00/23.18 tff(7954,assumption,(mult(mult(b, a), mult(b, c)) = mult(b, mult(a, mult(b, c)))), introduced(assumption)).
% 23.00/23.18 tff(7955,plain,
% 23.00/23.18 (mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), mult(a, c))) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 23.00/23.18 inference(transitivity,[status(thm)],[7951, 7954, 7953])).
% 23.00/23.18 tff(7956,plain,
% 23.00/23.18 (mult(mult(b, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a)),
% 23.00/23.18 inference(transitivity,[status(thm)],[7352, 470])).
% 23.00/23.18 tff(7957,plain,
% 23.00/23.18 (rd(mult(mult(b, mult(a, rd(mult(b, c), mult(a, c)))), a), a) = rd(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), a), a)),
% 23.00/23.18 inference(monotonicity,[status(thm)],[7956])).
% 23.00/23.18 tff(7958,plain,
% 23.00/23.18 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(b, mult(a, rd(mult(b, c), mult(a, c)))), a), a) = mult(b, mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.00/23.18 inference(quant_inst,[status(thm)],[])).
% 23.00/23.18 tff(7959,plain,
% 23.00/23.18 (rd(mult(mult(b, mult(a, rd(mult(b, c), mult(a, c)))), a), a) = mult(b, mult(a, rd(mult(b, c), mult(a, c))))),
% 23.00/23.18 inference(unit_resolution,[status(thm)],[7958, 168])).
% 23.00/23.18 tff(7960,plain,
% 23.00/23.18 (mult(b, mult(a, rd(mult(b, c), mult(a, c)))) = rd(mult(mult(b, mult(a, rd(mult(b, c), mult(a, c)))), a), a)),
% 23.00/23.18 inference(symmetry,[status(thm)],[7959])).
% 23.00/23.18 tff(7961,plain,
% 23.00/23.18 (mult(b, mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(b, a), rd(mult(b, c), mult(a, c)))),
% 23.00/23.18 inference(transitivity,[status(thm)],[7960, 7957, 546])).
% 23.00/23.18 tff(7962,plain,
% 23.00/23.18 (mult(mult(b, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(a, c))),
% 23.00/23.18 inference(monotonicity,[status(thm)],[7961])).
% 23.00/23.18 tff(7963,plain,
% 23.00/23.18 (mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(b, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c))),
% 23.00/23.18 inference(symmetry,[status(thm)],[7962])).
% 23.00/23.18 tff(7964,plain,
% 23.00/23.18 ((mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))) <=> (mult(mult(b, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))))),
% 23.00/23.18 inference(monotonicity,[status(thm)],[7963, 7955])).
% 23.00/23.18 tff(7965,plain,
% 23.00/23.18 ((mult(mult(b, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))) <=> (mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))),
% 23.00/23.18 inference(symmetry,[status(thm)],[7964])).
% 23.00/23.18 tff(7966,assumption,(~(mult(mult(b, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(b, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))))), introduced(assumption)).
% 23.00/23.18 tff(7967,plain,
% 23.00/23.18 (((~(mult(mult(b, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(b, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(b, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))))) | (mult(mult(b, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(b, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))))),
% 23.00/23.18 inference(tautology,[status(thm)],[])).
% 23.00/23.18 tff(7968,plain,
% 23.00/23.18 ((~(mult(mult(b, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(b, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(b, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))))),
% 23.00/23.18 inference(unit_resolution,[status(thm)],[7967, 7966])).
% 23.00/23.18 tff(7969,plain,
% 23.00/23.18 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(b, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(b, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c)))) | (~(mult(b, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))))))) | (~((~(mult(mult(b, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(b, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(b, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(b, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(b, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c)))) | (~(mult(b, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))))))) | (~((~(mult(mult(b, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(b, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(b, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))))))))),
% 23.00/23.19 inference(rewrite,[status(thm)],[])).
% 23.00/23.19 tff(7970,plain,
% 23.00/23.19 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(b, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(b, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c)))) | (~(mult(b, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))))))) | (~((~(mult(mult(b, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(b, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(b, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))))))))),
% 23.00/23.19 inference(quant_inst,[status(thm)],[])).
% 23.00/23.19 tff(7971,plain,
% 23.00/23.19 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(b, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(b, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c)))) | (~(mult(b, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))))))) | (~((~(mult(mult(b, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(b, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(b, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))))))),
% 23.00/23.19 inference(modus_ponens,[status(thm)],[7970, 7969])).
% 23.00/23.19 tff(7972,plain,
% 23.00/23.19 ((~((~(mult(mult(b, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(b, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c)))) | (~(mult(b, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))))))) | (~((~(mult(mult(b, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(b, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(b, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))))))),
% 23.00/23.19 inference(unit_resolution,[status(thm)],[7971, 27])).
% 23.00/23.19 tff(7973,plain,
% 23.00/23.19 (~((~(mult(mult(b, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(b, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c)))) | (~(mult(b, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))))))),
% 23.00/23.19 inference(unit_resolution,[status(thm)],[7972, 7968])).
% 23.00/23.19 tff(7974,plain,
% 23.00/23.19 (((~(mult(mult(b, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(b, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c)))) | (~(mult(b, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))))) | (mult(b, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))))),
% 23.00/23.19 inference(tautology,[status(thm)],[])).
% 23.00/23.19 tff(7975,plain,
% 23.00/23.19 (mult(b, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 23.00/23.19 inference(unit_resolution,[status(thm)],[7974, 7973])).
% 23.00/23.19 tff(7976,plain,
% 23.00/23.19 (((~(mult(mult(b, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(b, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c)))) | (~(mult(b, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))))) | (mult(mult(b, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(b, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c)))),
% 23.00/23.19 inference(tautology,[status(thm)],[])).
% 23.00/23.19 tff(7977,plain,
% 23.00/23.19 (mult(mult(b, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(b, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c))),
% 23.00/23.19 inference(unit_resolution,[status(thm)],[7976, 7973])).
% 23.00/23.19 tff(7978,plain,
% 23.00/23.19 ((mult(mult(b, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(b, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))) <=> (mult(mult(b, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))))),
% 23.00/23.19 inference(monotonicity,[status(thm)],[7977, 7975])).
% 23.00/23.19 tff(7979,plain,
% 23.00/23.19 ((mult(mult(b, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(b, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))) <=> (mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))),
% 23.00/23.19 inference(transitivity,[status(thm)],[7978, 7965])).
% 23.00/23.19 tff(7980,plain,
% 23.00/23.19 ((~(mult(mult(b, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(b, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))))) <=> (~(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))),
% 23.00/23.19 inference(monotonicity,[status(thm)],[7979])).
% 23.00/23.19 tff(7981,plain,
% 23.00/23.19 (~(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))),
% 23.00/23.19 inference(modus_ponens,[status(thm)],[7966, 7980])).
% 23.00/23.19 tff(7982,plain,
% 23.00/23.19 (((~(mult(mult(mult(b, a), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(b, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))) | (mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))),
% 23.00/23.19 inference(tautology,[status(thm)],[])).
% 23.00/23.19 tff(7983,plain,
% 23.00/23.19 ((~(mult(mult(mult(b, a), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(b, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))),
% 23.00/23.19 inference(unit_resolution,[status(thm)],[7982, 7981])).
% 23.00/23.19 tff(7984,plain,
% 23.00/23.19 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(b, a), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(b, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))) | (~((~(mult(mult(mult(b, a), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(mult(b, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(b, a), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(b, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))) | (~((~(mult(mult(mult(b, a), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(mult(b, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))))),
% 23.00/23.19 inference(rewrite,[status(thm)],[])).
% 23.00/23.19 tff(7985,plain,
% 23.00/23.19 (((~((~(mult(mult(mult(b, a), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(mult(b, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))) | (~((~(mult(mult(mult(b, a), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(b, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))))) <=> ((~((~(mult(mult(mult(b, a), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(b, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))) | (~((~(mult(mult(mult(b, a), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(mult(b, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))))),
% 23.00/23.19 inference(rewrite,[status(thm)],[])).
% 23.00/23.19 tff(7986,plain,
% 23.00/23.19 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(b, a), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(mult(b, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))) | (~((~(mult(mult(mult(b, a), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(b, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(b, a), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(b, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))) | (~((~(mult(mult(mult(b, a), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(mult(b, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))))))),
% 23.00/23.19 inference(monotonicity,[status(thm)],[7985])).
% 23.00/23.19 tff(7987,plain,
% 23.00/23.19 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(b, a), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(mult(b, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))) | (~((~(mult(mult(mult(b, a), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(b, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(b, a), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(b, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))) | (~((~(mult(mult(mult(b, a), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(mult(b, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))))),
% 23.00/23.19 inference(transitivity,[status(thm)],[7986, 7984])).
% 23.00/23.19 tff(7988,plain,
% 23.00/23.19 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(b, a), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(mult(b, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))) | (~((~(mult(mult(mult(b, a), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(b, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))))),
% 23.00/23.19 inference(quant_inst,[status(thm)],[])).
% 23.00/23.19 tff(7989,plain,
% 23.00/23.19 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(b, a), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(b, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))) | (~((~(mult(mult(mult(b, a), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(mult(b, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))))),
% 23.00/23.19 inference(modus_ponens,[status(thm)],[7988, 7987])).
% 23.00/23.19 tff(7990,plain,
% 23.00/23.19 ((~((~(mult(mult(mult(b, a), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(b, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))) | (~((~(mult(mult(mult(b, a), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(mult(b, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))))),
% 23.00/23.19 inference(unit_resolution,[status(thm)],[7989, 27])).
% 23.00/23.19 tff(7991,plain,
% 23.00/23.19 (~((~(mult(mult(mult(b, a), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(mult(b, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))),
% 23.00/23.19 inference(unit_resolution,[status(thm)],[7990, 7983])).
% 23.00/23.19 tff(7992,plain,
% 23.00/23.19 (((~(mult(mult(mult(b, a), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(b, a), rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(mult(b, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))) | (mult(mult(b, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))),
% 23.00/23.19 inference(tautology,[status(thm)],[])).
% 23.00/23.19 tff(7993,plain,
% 23.00/23.19 (mult(mult(b, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))),
% 23.00/23.19 inference(unit_resolution,[status(thm)],[7992, 7991])).
% 23.00/23.20 tff(7994,plain,
% 23.00/23.20 (mult(mult(b, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(b, a), mult(b, c))),
% 23.00/23.20 inference(transitivity,[status(thm)],[7993, 7951])).
% 23.00/23.20 tff(7995,plain,
% 23.00/23.20 (ld(mult(b, a), mult(mult(b, a), mult(mult(a, c), rd(mult(b, c), mult(a, c))))) = ld(mult(b, a), mult(mult(b, a), mult(b, c)))),
% 23.00/23.20 inference(monotonicity,[status(thm)],[7994])).
% 23.00/23.20 tff(7996,plain,
% 23.00/23.20 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(b, a), mult(mult(b, a), mult(mult(a, c), rd(mult(b, c), mult(a, c))))) = mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 23.00/23.20 inference(quant_inst,[status(thm)],[])).
% 23.00/23.20 tff(7997,plain,
% 23.00/23.20 (ld(mult(b, a), mult(mult(b, a), mult(mult(a, c), rd(mult(b, c), mult(a, c))))) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))),
% 23.00/23.20 inference(unit_resolution,[status(thm)],[7996, 7])).
% 23.00/23.20 tff(7998,plain,
% 23.00/23.20 (mult(mult(a, c), rd(mult(b, c), mult(a, c))) = ld(mult(b, a), mult(mult(b, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 23.00/23.20 inference(symmetry,[status(thm)],[7997])).
% 23.00/23.20 tff(7999,plain,
% 23.00/23.20 (mult(mult(a, c), rd(mult(b, c), mult(a, c))) = mult(b, c)),
% 23.00/23.20 inference(transitivity,[status(thm)],[7998, 7995, 7950])).
% 23.00/23.20 tff(8000,plain,
% 23.00/23.20 (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(b, c))),
% 23.00/23.20 inference(monotonicity,[status(thm)],[7999])).
% 23.00/23.20 tff(8001,plain,
% 23.00/23.20 (mult(a, mult(b, c)) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 23.00/23.20 inference(symmetry,[status(thm)],[8000])).
% 23.00/23.20 tff(8002,plain,
% 23.00/23.20 (mult(b, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))))),
% 23.00/23.20 inference(monotonicity,[status(thm)],[6663])).
% 23.00/23.20 tff(8003,plain,
% 23.00/23.20 (mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))) = mult(b, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.00/23.20 inference(symmetry,[status(thm)],[7975])).
% 23.00/23.20 tff(8004,plain,
% 23.00/23.20 (mult(b, mult(a, mult(b, c))) = mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))))),
% 23.00/23.20 inference(transitivity,[status(thm)],[7953, 8003, 8002])).
% 23.00/23.20 tff(8005,plain,
% 23.00/23.20 (ld(b, mult(b, mult(a, mult(b, c)))) = ld(b, mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))))),
% 23.00/23.20 inference(monotonicity,[status(thm)],[8004])).
% 23.00/23.20 tff(8006,plain,
% 23.00/23.20 (ld(b, mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))))) = ld(b, mult(b, mult(a, mult(b, c))))),
% 23.00/23.20 inference(symmetry,[status(thm)],[8005])).
% 23.00/23.20 tff(8007,plain,
% 23.00/23.20 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(b, mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))))) = mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))))),
% 23.00/23.20 inference(quant_inst,[status(thm)],[])).
% 23.00/23.20 tff(8008,plain,
% 23.00/23.20 (ld(b, mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))))) = mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))),
% 23.00/23.20 inference(unit_resolution,[status(thm)],[8007, 7])).
% 23.00/23.20 tff(8009,plain,
% 23.00/23.20 (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = ld(b, mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))))),
% 23.00/23.20 inference(symmetry,[status(thm)],[8008])).
% 23.00/23.20 tff(8010,plain,
% 23.00/23.20 (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.00/23.20 inference(transitivity,[status(thm)],[6663, 8009, 8006, 7454, 8001, 7948])).
% 23.00/23.20 tff(8011,plain,
% 23.00/23.20 (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))),
% 23.00/23.20 inference(transitivity,[status(thm)],[6663, 8009, 8006, 7454, 289])).
% 23.00/23.20 tff(8012,plain,
% 23.00/23.20 ((mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c)))))) <=> (mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 23.00/23.20 inference(monotonicity,[status(thm)],[8011, 7947])).
% 23.00/23.20 tff(8013,plain,
% 23.00/23.20 ((mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c)))))) <=> (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))),
% 23.00/23.20 inference(transitivity,[status(thm)],[8012, 6658])).
% 23.00/23.20 tff(8014,plain,
% 23.00/23.20 ((mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))) <=> (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c))))))),
% 23.00/23.20 inference(symmetry,[status(thm)],[8013])).
% 23.00/23.20 tff(8015,plain,
% 23.00/23.20 ((~(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) <=> (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c)))))))),
% 23.00/23.20 inference(monotonicity,[status(thm)],[8014])).
% 23.00/23.20 tff(8016,plain,
% 23.00/23.20 (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c))))))),
% 23.00/23.20 inference(modus_ponens,[status(thm)],[270, 8015])).
% 23.00/23.20 tff(8017,plain,
% 23.00/23.20 ($false),
% 23.00/23.20 inference(unit_resolution,[status(thm)],[8016, 8010])).
% 23.00/23.20 tff(8018,plain,((mult(mult(b, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(b, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(c, a), rd(mult(b, c), mult(a, c))) = mult(c, mult(a, rd(mult(b, c), mult(a, c)))))) | (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))) | (~(mult(mult(b, a), mult(b, c)) = mult(b, mult(a, mult(b, c))))) | (~(mult(mult(b, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), a))))), inference(lemma,lemma(discharge,[]))).
% 23.00/23.20 tff(8019,plain,
% 23.00/23.20 (mult(mult(b, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(b, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.00/23.20 inference(unit_resolution,[status(thm)],[8018, 7943, 6582, 270, 7562, 7219])).
% 23.00/23.20 tff(8020,plain,
% 23.00/23.20 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, b), c))),
% 23.00/23.20 inference(quant_inst,[status(thm)],[])).
% 23.00/23.20 tff(8021,plain,
% 23.00/23.20 (rd(mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, b), c)),
% 23.00/23.20 inference(unit_resolution,[status(thm)],[8020, 168])).
% 23.00/23.20 tff(8022,plain,
% 23.00/23.20 (mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, c), b), mult(a, rd(mult(b, c), mult(a, c))))),
% 23.00/23.20 inference(monotonicity,[status(thm)],[227])).
% 23.00/23.20 tff(8023,plain,
% 23.00/23.20 (mult(mult(mult(a, c), b), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c))))),
% 23.00/23.20 inference(symmetry,[status(thm)],[8022])).
% 23.00/23.20 tff(8024,plain,
% 23.00/23.20 (mult(rd(mult(b, c), mult(a, c)), mult(b, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c))),
% 23.00/23.20 inference(transitivity,[status(thm)],[5529, 5528])).
% 23.00/23.20 tff(8025,plain,
% 23.00/23.20 (ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(b, mult(a, c)))) = ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)))),
% 23.00/23.20 inference(monotonicity,[status(thm)],[8024])).
% 23.00/23.20 tff(8026,plain,
% 23.00/23.20 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(b, mult(a, c)))) = mult(b, mult(a, c)))),
% 23.00/23.20 inference(quant_inst,[status(thm)],[])).
% 23.00/23.20 tff(8027,plain,
% 23.00/23.20 (ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(b, mult(a, c)))) = mult(b, mult(a, c))),
% 23.00/23.20 inference(unit_resolution,[status(thm)],[8026, 7])).
% 23.00/23.20 tff(8028,plain,
% 23.00/23.20 (mult(b, mult(a, c)) = ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(b, mult(a, c))))),
% 23.00/23.20 inference(symmetry,[status(thm)],[8027])).
% 23.00/23.20 tff(8029,plain,
% 23.00/23.20 (mult(b, mult(a, c)) = mult(mult(a, c), b)),
% 23.00/23.20 inference(transitivity,[status(thm)],[8028, 8025, 5526, 227])).
% 23.00/23.20 tff(8030,plain,
% 23.00/23.20 (mult(mult(b, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, c), b), mult(a, rd(mult(b, c), mult(a, c))))),
% 23.00/23.20 inference(monotonicity,[status(thm)],[8029])).
% 23.00/23.20 tff(8031,assumption,(mult(mult(b, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(b, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))), introduced(assumption)).
% 23.00/23.20 tff(8032,plain,
% 23.00/23.20 (mult(b, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(b, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c))))),
% 23.00/23.20 inference(symmetry,[status(thm)],[8031])).
% 23.00/23.20 tff(8033,plain,
% 23.00/23.20 (mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))) = mult(b, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.00/23.20 inference(monotonicity,[status(thm)],[2319])).
% 23.00/23.20 tff(8034,assumption,(mult(mult(b, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))))), introduced(assumption)).
% 23.00/23.20 tff(8035,plain,
% 23.00/23.20 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(b, a), c), a) = mult(b, mult(mult(a, c), a)))),
% 23.00/23.20 inference(quant_inst,[status(thm)],[])).
% 23.00/23.20 tff(8036,plain,
% 23.00/23.20 (mult(mult(mult(b, a), c), a) = mult(b, mult(mult(a, c), a))),
% 23.00/23.20 inference(unit_resolution,[status(thm)],[8035, 56])).
% 23.00/23.20 tff(8037,plain,
% 23.00/23.20 (mult(b, a) = mult(mult(rd(mult(b, c), mult(a, c)), a), a)),
% 23.00/23.20 inference(symmetry,[status(thm)],[6426])).
% 23.00/23.20 tff(8038,plain,
% 23.00/23.20 (mult(mult(b, a), c) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c)),
% 23.00/23.20 inference(monotonicity,[status(thm)],[8037])).
% 23.00/23.20 tff(8039,plain,
% 23.00/23.20 (mult(mult(b, a), c) = mult(mult(b, c), a)),
% 23.00/23.20 inference(transitivity,[status(thm)],[8038, 5793, 1168, 1372, 1332])).
% 23.00/23.20 tff(8040,plain,
% 23.00/23.20 (mult(mult(mult(b, a), c), a) = mult(mult(mult(b, c), a), a)),
% 23.00/23.20 inference(monotonicity,[status(thm)],[8039])).
% 23.00/23.20 tff(8041,plain,
% 23.00/23.20 (mult(mult(mult(b, c), a), a) = mult(mult(mult(b, a), c), a)),
% 23.00/23.20 inference(symmetry,[status(thm)],[8040])).
% 23.00/23.20 tff(8042,plain,
% 23.00/23.20 (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a) = mult(mult(mult(b, c), a), a)),
% 23.00/23.20 inference(monotonicity,[status(thm)],[7491])).
% 23.00/23.20 tff(8043,plain,
% 23.00/23.20 (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a) = mult(b, mult(mult(a, c), a))),
% 23.00/23.20 inference(transitivity,[status(thm)],[8042, 8041, 8036])).
% 23.00/23.20 tff(8044,plain,
% 23.00/23.20 (mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c))) = mult(mult(b, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c)))),
% 23.00/23.20 inference(monotonicity,[status(thm)],[8043])).
% 23.00/23.20 tff(8045,plain,
% 23.00/23.20 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c))), a), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c))))),
% 23.00/23.20 inference(quant_inst,[status(thm)],[])).
% 23.00/23.20 tff(8046,plain,
% 23.00/23.20 (rd(mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c))), a), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c)))),
% 23.00/23.20 inference(unit_resolution,[status(thm)],[8045, 168])).
% 23.00/23.20 tff(8047,plain,
% 23.00/23.20 (mult(mult(mult(b, c), a), a) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a)),
% 23.00/23.20 inference(symmetry,[status(thm)],[8042])).
% 23.00/23.20 tff(8048,plain,
% 23.00/23.20 (mult(mult(mult(mult(b, c), a), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c)))),
% 23.00/23.20 inference(monotonicity,[status(thm)],[8047])).
% 23.00/23.20 tff(8049,plain,
% 23.00/23.20 (mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(mult(b, c), a), a), rd(mult(b, c), mult(a, c)))),
% 23.00/23.20 inference(symmetry,[status(thm)],[8048])).
% 23.00/23.20 tff(8050,plain,
% 23.00/23.20 (mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(mult(mult(b, c), a), a), rd(mult(b, c), mult(a, c))), a)),
% 23.00/23.20 inference(monotonicity,[status(thm)],[8049])).
% 23.00/23.20 tff(8051,plain,
% 23.00/23.20 (mult(mult(mult(mult(mult(b, c), a), a), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c))), a)),
% 23.00/23.20 inference(symmetry,[status(thm)],[8050])).
% 23.00/23.20 tff(8052,plain,
% 23.00/23.20 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(mult(b, c), a), a), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(b, c), a), mult(mult(a, rd(mult(b, c), mult(a, c))), a)))),
% 23.00/23.20 inference(quant_inst,[status(thm)],[])).
% 23.00/23.20 tff(8053,plain,
% 23.00/23.20 (mult(mult(mult(mult(mult(b, c), a), a), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(b, c), a), mult(mult(a, rd(mult(b, c), mult(a, c))), a))),
% 23.00/23.20 inference(unit_resolution,[status(thm)],[8052, 56])).
% 23.00/23.20 tff(8054,plain,
% 23.00/23.20 (mult(mult(mult(b, c), a), mult(mult(a, rd(mult(b, c), mult(a, c))), a)) = mult(mult(mult(mult(mult(b, c), a), a), rd(mult(b, c), mult(a, c))), a)),
% 23.00/23.20 inference(symmetry,[status(thm)],[8053])).
% 23.00/23.20 tff(8055,plain,
% 23.00/23.20 (mult(mult(mult(b, c), a), mult(a, b)) = mult(mult(mult(b, c), a), mult(mult(a, rd(mult(b, c), mult(a, c))), a))),
% 23.00/23.20 inference(monotonicity,[status(thm)],[1396])).
% 23.00/23.20 tff(8056,plain,
% 23.00/23.20 (mult(mult(b, c), mult(a, mult(a, b))) = mult(mult(mult(b, c), a), mult(a, b))),
% 23.00/23.20 inference(symmetry,[status(thm)],[2070])).
% 23.00/23.20 tff(8057,plain,
% 23.00/23.20 (mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), a)) = mult(a, mult(a, b))),
% 23.00/23.20 inference(monotonicity,[status(thm)],[7147])).
% 23.00/23.20 tff(8058,plain,
% 23.00/23.20 (mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(a, a), rd(mult(b, c), mult(a, c))), a)),
% 23.00/23.20 inference(monotonicity,[status(thm)],[1971])).
% 23.00/23.20 tff(8059,plain,
% 23.00/23.20 (mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(a, mult(a, b))),
% 23.00/23.20 inference(transitivity,[status(thm)],[8058, 1394, 8057])).
% 23.00/23.20 tff(8060,plain,
% 23.00/23.20 (mult(mult(c, b), mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), a)) = mult(mult(b, c), mult(a, mult(a, b)))),
% 23.00/23.20 inference(monotonicity,[status(thm)],[241, 8059])).
% 23.00/23.20 tff(8061,plain,
% 23.00/23.20 (mult(mult(b, c), mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), a)) = mult(mult(c, b), mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), a))),
% 23.00/23.20 inference(monotonicity,[status(thm)],[1399])).
% 23.00/23.20 tff(8062,plain,
% 23.00/23.20 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(b, c), a), mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(mult(b, c), mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), a)))),
% 23.00/23.20 inference(quant_inst,[status(thm)],[])).
% 23.00/23.20 tff(8063,plain,
% 23.00/23.20 (mult(mult(mult(mult(b, c), a), mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(mult(b, c), mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), a))),
% 23.00/23.20 inference(unit_resolution,[status(thm)],[8062, 56])).
% 23.00/23.20 tff(8064,plain,
% 23.00/23.20 (mult(mult(mult(mult(b, c), a), mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c))), a)),
% 23.00/23.20 inference(transitivity,[status(thm)],[8063, 8061, 8060, 8056, 8055, 8054, 8051])).
% 23.00/23.20 tff(8065,plain,
% 23.00/23.20 (rd(mult(mult(mult(mult(b, c), a), mult(a, rd(mult(b, c), mult(a, c)))), a), a) = rd(mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), rd(mult(b, c), mult(a, c))), a), a)),
% 23.00/23.20 inference(monotonicity,[status(thm)],[8064])).
% 23.00/23.21 tff(8066,plain,
% 23.00/23.21 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(mult(b, c), a), mult(a, rd(mult(b, c), mult(a, c)))), a), a) = mult(mult(mult(b, c), a), mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.00/23.21 inference(quant_inst,[status(thm)],[])).
% 23.00/23.21 tff(8067,plain,
% 23.00/23.21 (rd(mult(mult(mult(mult(b, c), a), mult(a, rd(mult(b, c), mult(a, c)))), a), a) = mult(mult(mult(b, c), a), mult(a, rd(mult(b, c), mult(a, c))))),
% 23.00/23.21 inference(unit_resolution,[status(thm)],[8066, 168])).
% 23.00/23.21 tff(8068,plain,
% 23.00/23.21 (mult(mult(mult(b, c), a), mult(a, rd(mult(b, c), mult(a, c)))) = rd(mult(mult(mult(mult(b, c), a), mult(a, rd(mult(b, c), mult(a, c)))), a), a)),
% 23.00/23.21 inference(symmetry,[status(thm)],[8067])).
% 23.00/23.21 tff(8069,plain,
% 23.00/23.21 (mult(mult(mult(b, c), a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c))))),
% 23.00/23.21 inference(transitivity,[status(thm)],[8068, 8065, 8046, 8044, 8034, 8033, 8032, 8030, 8023])).
% 23.00/23.21 tff(8070,plain,
% 23.00/23.21 (rd(mult(mult(mult(b, c), a), mult(a, rd(mult(b, c), mult(a, c)))), mult(a, rd(mult(b, c), mult(a, c)))) = rd(mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))), mult(a, rd(mult(b, c), mult(a, c))))),
% 23.00/23.21 inference(monotonicity,[status(thm)],[8069])).
% 23.00/23.21 tff(8071,plain,
% 23.00/23.21 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(b, c), a), mult(a, rd(mult(b, c), mult(a, c)))), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(b, c), a))),
% 23.00/23.21 inference(quant_inst,[status(thm)],[])).
% 23.00/23.21 tff(8072,plain,
% 23.00/23.21 (rd(mult(mult(mult(b, c), a), mult(a, rd(mult(b, c), mult(a, c)))), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(b, c), a)),
% 23.00/23.21 inference(unit_resolution,[status(thm)],[8071, 168])).
% 23.00/23.21 tff(8073,plain,
% 23.00/23.21 (mult(mult(b, c), a) = rd(mult(mult(mult(b, c), a), mult(a, rd(mult(b, c), mult(a, c)))), mult(a, rd(mult(b, c), mult(a, c))))),
% 23.00/23.21 inference(symmetry,[status(thm)],[8072])).
% 23.00/23.21 tff(8074,plain,
% 23.00/23.21 (mult(c, mult(b, a)) = mult(c, mult(a, b))),
% 23.00/23.21 inference(transitivity,[status(thm)],[4304, 2298, 8073, 8070, 8021, 227, 6986, 4221])).
% 23.00/23.21 tff(8075,plain,
% 23.00/23.21 ($false),
% 23.00/23.21 inference(unit_resolution,[status(thm)],[2302, 8074])).
% 23.00/23.21 tff(8076,plain,((~(mult(mult(b, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))))) | (mult(c, mult(b, a)) = mult(c, mult(a, b))) | (~(mult(mult(b, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(b, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(b, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), b)))) | (~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a))) | (~(mult(mult(mult(b, c), a), mult(a, b)) = mult(mult(b, c), mult(a, mult(a, b))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), a))))), inference(lemma,lemma(discharge,[]))).
% 23.00/23.21 tff(8077,plain,
% 23.00/23.21 (~(mult(mult(b, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))))),
% 23.00/23.21 inference(unit_resolution,[status(thm)],[8076, 7115, 8019, 7560, 6582, 4331, 7544, 7531, 6581])).
% 23.00/23.21 tff(8078,plain,
% 23.00/23.21 (((~(mult(mult(b, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(b, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))) | (~(mult(mult(b, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))))))) | (mult(mult(b, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))))),
% 23.00/23.21 inference(tautology,[status(thm)],[])).
% 23.00/23.21 tff(8079,plain,
% 23.00/23.21 ((~(mult(mult(b, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(b, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))) | (~(mult(mult(b, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))))))),
% 23.00/23.21 inference(unit_resolution,[status(thm)],[8078, 8077])).
% 23.00/23.21 tff(8080,plain,
% 23.00/23.21 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(b, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(mult(b, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))))) | (~(mult(b, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) = mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(b, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(b, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))) | (~(mult(mult(b, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(b, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(mult(b, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))))) | (~(mult(b, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) = mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(b, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(b, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))) | (~(mult(mult(b, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))))))))),
% 23.00/23.21 inference(rewrite,[status(thm)],[])).
% 23.00/23.21 tff(8081,plain,
% 23.00/23.21 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(b, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(mult(b, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))))) | (~(mult(b, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) = mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(b, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(b, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))) | (~(mult(mult(b, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))))))))),
% 23.00/23.21 inference(quant_inst,[status(thm)],[])).
% 23.00/23.21 tff(8082,plain,
% 23.00/23.21 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(b, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(mult(b, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))))) | (~(mult(b, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) = mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(b, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(b, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))) | (~(mult(mult(b, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))))))))),
% 23.00/23.21 inference(modus_ponens,[status(thm)],[8081, 8080])).
% 23.00/23.21 tff(8083,plain,
% 23.00/23.21 ((~((~(mult(mult(b, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(mult(b, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))))) | (~(mult(b, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) = mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(b, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(b, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))) | (~(mult(mult(b, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))))))))),
% 23.00/23.21 inference(unit_resolution,[status(thm)],[8082, 27])).
% 23.00/23.21 tff(8084,plain,
% 23.00/23.21 (~((~(mult(mult(b, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(mult(b, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))))) | (~(mult(b, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) = mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))))))),
% 23.00/23.21 inference(unit_resolution,[status(thm)],[8083, 8079])).
% 23.00/23.21 tff(8085,plain,
% 23.00/23.21 (((~(mult(mult(b, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(mult(b, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))))) | (~(mult(b, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) = mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))))))) | (mult(b, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) = mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))))),
% 23.00/23.21 inference(tautology,[status(thm)],[])).
% 23.00/23.21 tff(8086,plain,
% 23.00/23.21 (mult(b, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) = mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))))),
% 23.05/23.21 inference(unit_resolution,[status(thm)],[8085, 8084])).
% 23.05/23.21 tff(8087,plain,
% 23.05/23.21 (mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))) = mult(b, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))),
% 23.05/23.21 inference(symmetry,[status(thm)],[8086])).
% 23.05/23.21 tff(8088,plain,
% 23.05/23.21 (mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))) = mult(mult(b, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a))),
% 23.05/23.21 inference(transitivity,[status(thm)],[8087, 7530, 7528, 6961, 7265, 7096])).
% 23.05/23.21 tff(8089,plain,
% 23.05/23.21 ((mult(mult(b, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))))) <=> (mult(mult(b, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(mult(b, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)))),
% 23.05/23.21 inference(monotonicity,[status(thm)],[8088])).
% 23.05/23.21 tff(8090,plain,
% 23.05/23.21 ((mult(mult(b, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))))) <=> (mult(mult(b, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(mult(b, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))))),
% 23.05/23.21 inference(transitivity,[status(thm)],[8089, 7094])).
% 23.05/23.21 tff(8091,plain,
% 23.05/23.21 ((mult(mult(b, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(mult(b, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c)))) <=> (mult(mult(b, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))))),
% 23.05/23.21 inference(symmetry,[status(thm)],[8090])).
% 23.05/23.21 tff(8092,plain,
% 23.05/23.21 (((~(mult(mult(b, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(mult(b, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))))) | (~(mult(b, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) = mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))))))) | (mult(mult(b, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(mult(b, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))))),
% 23.05/23.21 inference(tautology,[status(thm)],[])).
% 23.05/23.21 tff(8093,plain,
% 23.05/23.21 (mult(mult(b, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(mult(b, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c)))),
% 23.05/23.21 inference(unit_resolution,[status(thm)],[8092, 8084])).
% 23.05/23.21 tff(8094,plain,
% 23.05/23.21 (mult(mult(b, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))))),
% 23.05/23.21 inference(modus_ponens,[status(thm)],[8093, 8091])).
% 23.05/23.21 tff(8095,plain,
% 23.05/23.21 ($false),
% 23.05/23.21 inference(unit_resolution,[status(thm)],[8077, 8094])).
% 23.05/23.21 tff(8096,plain,((mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) | (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(c, b), mult(mult(unit, mult(b, a)), unit)) = mult(c, mult(b, mult(mult(unit, mult(b, a)), unit))))) | (mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a))), inference(lemma,lemma(discharge,[]))).
% 23.05/23.21 tff(8097,plain,
% 23.05/23.21 ((mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) | (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)))) | (~(mult(mult(c, b), mult(mult(unit, mult(b, a)), unit)) = mult(c, mult(b, mult(mult(unit, mult(b, a)), unit))))) | (mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a))),
% 23.05/23.21 inference(unit_resolution,[status(thm)],[8096, 5496])).
% 23.05/23.21 tff(8098,plain,
% 23.05/23.21 (~(mult(mult(c, b), mult(mult(unit, mult(b, a)), unit)) = mult(c, mult(b, mult(mult(unit, mult(b, a)), unit))))),
% 23.05/23.21 inference(unit_resolution,[status(thm)],[8097, 6529, 4327, 6534, 6560])).
% 23.05/23.22 tff(8099,plain,
% 23.05/23.22 (((~(mult(mult(c, b), mult(mult(unit, mult(b, a)), unit)) = mult(c, mult(b, mult(mult(unit, mult(b, a)), unit))))) | (~(mult(mult(c, mult(mult(unit, mult(b, a)), unit)), b) = mult(c, mult(mult(mult(unit, mult(b, a)), unit), b))))) | (mult(mult(c, b), mult(mult(unit, mult(b, a)), unit)) = mult(c, mult(b, mult(mult(unit, mult(b, a)), unit))))),
% 23.05/23.22 inference(tautology,[status(thm)],[])).
% 23.05/23.22 tff(8100,plain,
% 23.05/23.22 ((~(mult(mult(c, b), mult(mult(unit, mult(b, a)), unit)) = mult(c, mult(b, mult(mult(unit, mult(b, a)), unit))))) | (~(mult(mult(c, mult(mult(unit, mult(b, a)), unit)), b) = mult(c, mult(mult(mult(unit, mult(b, a)), unit), b))))),
% 23.05/23.22 inference(unit_resolution,[status(thm)],[8099, 8098])).
% 23.05/23.22 tff(8101,plain,
% 23.05/23.22 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(c, b), mult(mult(unit, mult(b, a)), unit)) = mult(mult(c, mult(mult(unit, mult(b, a)), unit)), b))) | (~(mult(c, mult(b, mult(mult(unit, mult(b, a)), unit))) = mult(c, mult(mult(mult(unit, mult(b, a)), unit), b)))))) | (~((~(mult(mult(c, b), mult(mult(unit, mult(b, a)), unit)) = mult(c, mult(b, mult(mult(unit, mult(b, a)), unit))))) | (~(mult(mult(c, mult(mult(unit, mult(b, a)), unit)), b) = mult(c, mult(mult(mult(unit, mult(b, a)), unit), b)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(c, b), mult(mult(unit, mult(b, a)), unit)) = mult(mult(c, mult(mult(unit, mult(b, a)), unit)), b))) | (~(mult(c, mult(b, mult(mult(unit, mult(b, a)), unit))) = mult(c, mult(mult(mult(unit, mult(b, a)), unit), b)))))) | (~((~(mult(mult(c, b), mult(mult(unit, mult(b, a)), unit)) = mult(c, mult(b, mult(mult(unit, mult(b, a)), unit))))) | (~(mult(mult(c, mult(mult(unit, mult(b, a)), unit)), b) = mult(c, mult(mult(mult(unit, mult(b, a)), unit), b)))))))),
% 23.05/23.22 inference(rewrite,[status(thm)],[])).
% 23.05/23.22 tff(8102,plain,
% 23.05/23.22 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(c, b), mult(mult(unit, mult(b, a)), unit)) = mult(mult(c, mult(mult(unit, mult(b, a)), unit)), b))) | (~(mult(c, mult(b, mult(mult(unit, mult(b, a)), unit))) = mult(c, mult(mult(mult(unit, mult(b, a)), unit), b)))))) | (~((~(mult(mult(c, b), mult(mult(unit, mult(b, a)), unit)) = mult(c, mult(b, mult(mult(unit, mult(b, a)), unit))))) | (~(mult(mult(c, mult(mult(unit, mult(b, a)), unit)), b) = mult(c, mult(mult(mult(unit, mult(b, a)), unit), b)))))))),
% 23.05/23.22 inference(quant_inst,[status(thm)],[])).
% 23.05/23.22 tff(8103,plain,
% 23.05/23.22 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(c, b), mult(mult(unit, mult(b, a)), unit)) = mult(mult(c, mult(mult(unit, mult(b, a)), unit)), b))) | (~(mult(c, mult(b, mult(mult(unit, mult(b, a)), unit))) = mult(c, mult(mult(mult(unit, mult(b, a)), unit), b)))))) | (~((~(mult(mult(c, b), mult(mult(unit, mult(b, a)), unit)) = mult(c, mult(b, mult(mult(unit, mult(b, a)), unit))))) | (~(mult(mult(c, mult(mult(unit, mult(b, a)), unit)), b) = mult(c, mult(mult(mult(unit, mult(b, a)), unit), b))))))),
% 23.05/23.22 inference(modus_ponens,[status(thm)],[8102, 8101])).
% 23.05/23.22 tff(8104,plain,
% 23.05/23.22 ((~((~(mult(mult(c, b), mult(mult(unit, mult(b, a)), unit)) = mult(mult(c, mult(mult(unit, mult(b, a)), unit)), b))) | (~(mult(c, mult(b, mult(mult(unit, mult(b, a)), unit))) = mult(c, mult(mult(mult(unit, mult(b, a)), unit), b)))))) | (~((~(mult(mult(c, b), mult(mult(unit, mult(b, a)), unit)) = mult(c, mult(b, mult(mult(unit, mult(b, a)), unit))))) | (~(mult(mult(c, mult(mult(unit, mult(b, a)), unit)), b) = mult(c, mult(mult(mult(unit, mult(b, a)), unit), b))))))),
% 23.05/23.22 inference(unit_resolution,[status(thm)],[8103, 27])).
% 23.05/23.22 tff(8105,plain,
% 23.05/23.22 (~((~(mult(mult(c, b), mult(mult(unit, mult(b, a)), unit)) = mult(mult(c, mult(mult(unit, mult(b, a)), unit)), b))) | (~(mult(c, mult(b, mult(mult(unit, mult(b, a)), unit))) = mult(c, mult(mult(mult(unit, mult(b, a)), unit), b)))))),
% 23.05/23.22 inference(unit_resolution,[status(thm)],[8104, 8100])).
% 23.05/23.22 tff(8106,plain,
% 23.05/23.22 (((~(mult(mult(c, b), mult(mult(unit, mult(b, a)), unit)) = mult(mult(c, mult(mult(unit, mult(b, a)), unit)), b))) | (~(mult(c, mult(b, mult(mult(unit, mult(b, a)), unit))) = mult(c, mult(mult(mult(unit, mult(b, a)), unit), b))))) | (mult(mult(c, b), mult(mult(unit, mult(b, a)), unit)) = mult(mult(c, mult(mult(unit, mult(b, a)), unit)), b))),
% 23.05/23.22 inference(tautology,[status(thm)],[])).
% 23.05/23.22 tff(8107,plain,
% 23.05/23.22 (mult(mult(c, b), mult(mult(unit, mult(b, a)), unit)) = mult(mult(c, mult(mult(unit, mult(b, a)), unit)), b)),
% 23.05/23.22 inference(unit_resolution,[status(thm)],[8106, 8105])).
% 23.05/23.22 tff(8108,plain,
% 23.05/23.22 (mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a)),
% 23.05/23.22 inference(modus_ponens,[status(thm)],[8107, 7093])).
% 23.05/23.22 tff(8109,plain,
% 23.05/23.22 ($false),
% 23.05/23.22 inference(unit_resolution,[status(thm)],[6529, 8108])).
% 23.05/23.22 tff(8110,plain,((mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a)) | (mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))), inference(lemma,lemma(discharge,[]))).
% 23.05/23.22 tff(8111,plain,
% 23.05/23.22 (mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a)),
% 23.05/23.22 inference(unit_resolution,[status(thm)],[8110, 4327])).
% 23.05/23.22 tff(8112,plain,
% 23.05/23.22 (mult(mult(c, b), mult(mult(unit, mult(b, a)), unit)) = mult(mult(c, mult(mult(unit, mult(b, a)), unit)), b)),
% 23.05/23.22 inference(modus_ponens,[status(thm)],[8111, 7091])).
% 23.05/23.22 tff(8113,plain,
% 23.05/23.22 (mult(mult(mult(b, c), a), b) = mult(mult(b, c), mult(a, b))),
% 23.05/23.22 inference(unit_resolution,[status(thm)],[1229, 7086])).
% 23.05/23.22 tff(8114,plain,
% 23.05/23.22 ((~((~(mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a))) | (~(mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a)))))) | (~(mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a))) | (~(mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a))))),
% 23.05/23.22 inference(tautology,[status(thm)],[])).
% 23.05/23.22 tff(8115,plain,
% 23.05/23.22 (~(mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a)))),
% 23.05/23.22 inference(unit_resolution,[status(thm)],[8114, 8111, 7085])).
% 23.05/23.22 tff(8116,plain,
% 23.05/23.22 ((mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a))) <=> (mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a))),
% 23.05/23.22 inference(monotonicity,[status(thm)],[1312, 3107])).
% 23.05/23.22 tff(8117,plain,
% 23.05/23.22 ((mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a)) <=> (mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a)))),
% 23.05/23.22 inference(symmetry,[status(thm)],[8116])).
% 23.05/23.22 tff(8118,plain,
% 23.05/23.22 (mult(mult(mult(b, c), b), a) = mult(mult(c, b), mult(b, a))),
% 23.05/23.22 inference(transitivity,[status(thm)],[3106, 3468])).
% 23.05/23.22 tff(8119,plain,
% 23.05/23.22 ((mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a)) <=> (mult(mult(c, mult(b, a)), b) = mult(mult(c, b), mult(b, a)))),
% 23.05/23.22 inference(monotonicity,[status(thm)],[4307, 8118])).
% 23.05/23.22 tff(8120,plain,
% 23.05/23.22 ((mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a)) <=> (mult(mult(c, b), mult(b, a)) = mult(mult(c, mult(b, a)), b))),
% 23.05/23.22 inference(transitivity,[status(thm)],[8119, 4326])).
% 23.05/23.22 tff(8121,plain,
% 23.05/23.22 ((mult(mult(c, b), mult(b, a)) = mult(mult(c, mult(b, a)), b)) <=> (mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a))),
% 23.05/23.22 inference(symmetry,[status(thm)],[8120])).
% 23.05/23.22 tff(8122,plain,
% 23.05/23.22 ((mult(mult(c, b), mult(mult(unit, mult(b, a)), unit)) = mult(mult(c, mult(mult(unit, mult(b, a)), unit)), b)) <=> (mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a)))),
% 23.05/23.22 inference(transitivity,[status(thm)],[4324, 8121, 8117])).
% 23.05/23.22 tff(8123,assumption,(mult(mult(c, b), mult(mult(unit, mult(b, a)), unit)) = mult(mult(c, mult(mult(unit, mult(b, a)), unit)), b)), introduced(assumption)).
% 23.05/23.22 tff(8124,plain,
% 23.05/23.22 (mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a))),
% 23.05/23.22 inference(modus_ponens,[status(thm)],[8123, 8122])).
% 23.05/23.22 tff(8125,plain,
% 23.05/23.22 ($false),
% 23.05/23.22 inference(unit_resolution,[status(thm)],[3024, 8124])).
% 23.05/23.22 tff(8126,plain,((~(mult(mult(c, b), mult(mult(unit, mult(b, a)), unit)) = mult(mult(c, mult(mult(unit, mult(b, a)), unit)), b))) | (mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a))) | (~(mult(mult(mult(b, c), b), a) = mult(mult(b, c), mult(b, a)))) | (~(mult(mult(mult(b, c), a), b) = mult(mult(b, c), mult(a, b))))), inference(lemma,lemma(discharge,[]))).
% 23.05/23.22 tff(8127,plain,
% 23.05/23.22 (~(mult(mult(c, b), mult(mult(unit, mult(b, a)), unit)) = mult(mult(c, mult(mult(unit, mult(b, a)), unit)), b))),
% 23.05/23.22 inference(unit_resolution,[status(thm)],[8126, 8115, 7087, 8113])).
% 23.05/23.22 tff(8128,plain,
% 23.05/23.22 ($false),
% 23.05/23.22 inference(unit_resolution,[status(thm)],[8127, 8112])).
% 23.05/23.22 tff(8129,plain,(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))), inference(lemma,lemma(discharge,[]))).
% 23.05/23.22 tff(8130,plain,
% 23.05/23.22 (mult(mult(mult(mult(a, c), c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))), a)),
% 23.05/23.22 inference(unit_resolution,[status(thm)],[6741, 4288, 270, 6583, 6582, 316, 4360, 1799, 6581])).
% 23.05/23.22 tff(8131,plain,
% 23.05/23.22 (mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c))))),
% 23.05/23.22 inference(unit_resolution,[status(thm)],[6600, 8130])).
% 23.05/23.22 tff(8132,plain,
% 23.05/23.22 (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)),
% 23.05/23.22 inference(unit_resolution,[status(thm)],[2390, 8131, 1799, 6582])).
% 23.05/23.22 tff(8133,plain,
% 23.05/23.22 (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))),
% 23.05/23.22 inference(unit_resolution,[status(thm)],[2329, 8132])).
% 23.05/23.22 tff(8134,plain,
% 23.05/23.22 ((~(mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))) | (~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)))) | (~(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a))) | (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))),
% 23.05/23.22 inference(unit_resolution,[status(thm)],[4844, 3862, 7692])).
% 23.05/23.22 tff(8135,plain,
% 23.05/23.22 ($false),
% 23.05/23.22 inference(unit_resolution,[status(thm)],[8134, 8133, 8132, 285, 4360, 4495, 4517, 4501, 6697, 279, 4499, 4390, 281])).
% 23.05/23.22 tff(8136,plain,(((~(mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))) | (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))), inference(lemma,lemma(discharge,[]))).
% 23.05/23.22 tff(8137,plain,
% 23.05/23.22 (((~(mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a))) | (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))),
% 23.05/23.22 inference(unit_resolution,[status(thm)],[8136, 5496])).
% 23.05/23.22 tff(8138,plain,
% 23.05/23.22 (((~(mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a))) | (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))),
% 23.05/23.22 inference(unit_resolution,[status(thm)],[8137, 8129])).
% 23.05/23.22 tff(8139,plain,
% 23.05/23.22 ($false),
% 23.05/23.22 inference(unit_resolution,[status(thm)],[8138, 4303, 4298, 4288, 270])).
% 23.05/23.22 tff(8140,plain,((mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) | ((~(mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c))))) | (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))), inference(lemma,lemma(discharge,[]))).
% 23.05/23.22 tff(8141,plain,
% 23.05/23.22 (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))),
% 23.05/23.22 inference(unit_resolution,[status(thm)],[8140, 270, 4288])).
% 23.05/23.22 tff(8142,plain,
% 23.05/23.22 ((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) | (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c))))),
% 23.05/23.22 inference(unit_resolution,[status(thm)],[6653, 5496, 6462])).
% 23.05/23.22 tff(8143,plain,
% 23.05/23.22 (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)))),
% 23.05/23.22 inference(unit_resolution,[status(thm)],[8142, 8141, 4289, 270])).
% 23.05/23.22 tff(8144,plain,
% 23.05/23.22 ((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit)))))),
% 23.05/23.23 inference(unit_resolution,[status(thm)],[4302, 8143])).
% 23.05/23.23 tff(8145,plain,
% 23.05/23.23 (~((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit))))))),
% 23.05/23.23 inference(unit_resolution,[status(thm)],[31, 8144])).
% 23.05/23.23 tff(8146,plain,
% 23.05/23.23 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit)))),
% 23.05/23.23 inference(unit_resolution,[status(thm)],[33, 8145])).
% 23.05/23.23 tff(8147,plain,
% 23.05/23.23 (mult(mult(rd(mult(b, c), mult(a, c)), a), c) = mult(b, c)),
% 23.05/23.23 inference(transitivity,[status(thm)],[76, 8146, 61, 137])).
% 23.05/23.23 tff(8148,plain,
% 23.05/23.23 (rd(mult(mult(rd(mult(b, c), mult(a, c)), a), c), c) = rd(mult(b, c), c)),
% 23.05/23.23 inference(monotonicity,[status(thm)],[8147])).
% 23.05/23.23 tff(8149,plain,
% 23.05/23.23 (mult(rd(mult(b, c), mult(a, c)), a) = b),
% 23.05/23.23 inference(transitivity,[status(thm)],[175, 8148, 170])).
% 23.05/23.23 tff(8150,plain,
% 23.05/23.23 (mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, c), b)),
% 23.05/23.23 inference(monotonicity,[status(thm)],[8149])).
% 23.05/23.23 tff(8151,plain,
% 23.05/23.23 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), b)),
% 23.05/23.23 inference(transitivity,[status(thm)],[5496, 8150])).
% 23.05/23.23 tff(8152,plain,
% 23.05/23.23 (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(a, c), b), c)),
% 23.05/23.23 inference(monotonicity,[status(thm)],[8151])).
% 23.05/23.23 tff(8153,plain,
% 23.05/23.23 (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 23.05/23.23 inference(unit_resolution,[status(thm)],[6559, 8143])).
% 23.05/23.23 tff(8154,plain,
% 23.05/23.23 ((~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))))),
% 23.05/23.23 inference(unit_resolution,[status(thm)],[115, 8153])).
% 23.05/23.23 tff(8155,plain,
% 23.05/23.23 (~((~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)))) | (~(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))))),
% 23.05/23.23 inference(unit_resolution,[status(thm)],[119, 27, 8154])).
% 23.05/23.23 tff(8156,plain,
% 23.05/23.23 (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))),
% 23.05/23.23 inference(unit_resolution,[status(thm)],[121, 8155])).
% 23.05/23.23 tff(8157,plain,
% 23.05/23.23 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c)),
% 23.05/23.23 inference(symmetry,[status(thm)],[8156])).
% 23.05/23.23 tff(8158,plain,
% 23.05/23.23 (mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))),
% 23.05/23.23 inference(symmetry,[status(thm)],[316])).
% 23.05/23.23 tff(8159,plain,
% 23.05/23.23 (mult(mult(a, mult(b, c)), c) = mult(mult(a, c), mult(b, c))),
% 23.05/23.23 inference(symmetry,[status(thm)],[266])).
% 23.05/23.23 tff(8160,plain,
% 23.05/23.23 (mult(mult(a, mult(b, c)), c) = mult(a, mult(mult(b, c), c))),
% 23.05/23.23 inference(transitivity,[status(thm)],[8159, 268, 8158, 8157, 8152, 233, 2414])).
% 23.05/23.23 tff(8161,plain,
% 23.05/23.23 ($false),
% 23.05/23.23 inference(unit_resolution,[status(thm)],[258, 8160])).
% 23.05/23.23 tff(8162,plain,((mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))) | ((~(mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)))))), inference(lemma,lemma(discharge,[]))).
% 23.05/23.23 tff(8163,plain,
% 23.05/23.23 ((~(mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c))))),
% 23.05/23.23 inference(unit_resolution,[status(thm)],[8162, 270])).
% 23.05/23.23 tff(8164,plain,
% 23.05/23.23 (~((~(mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))))),
% 23.05/23.23 inference(unit_resolution,[status(thm)],[2213, 8163])).
% 23.05/23.23 tff(8165,plain,
% 23.05/23.23 (mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))),
% 23.05/23.23 inference(unit_resolution,[status(thm)],[2201, 8164])).
% 23.05/23.23 tff(8166,plain,
% 23.05/23.23 (ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c)))) = ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))),
% 23.05/23.23 inference(monotonicity,[status(thm)],[8129])).
% 23.05/23.23 tff(8167,plain,
% 23.05/23.23 (ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) = ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))))),
% 23.05/23.23 inference(symmetry,[status(thm)],[8166])).
% 23.05/23.23 tff(8168,plain,
% 23.05/23.23 (mult(mult(a, c), a) = mult(a, mult(a, c))),
% 23.05/23.23 inference(transitivity,[status(thm)],[4609, 8167, 4451])).
% 23.05/23.23 tff(8169,plain,
% 23.05/23.23 (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 23.05/23.23 inference(monotonicity,[status(thm)],[8168])).
% 23.05/23.23 tff(8170,plain,
% 23.05/23.23 (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))),
% 23.05/23.23 inference(symmetry,[status(thm)],[5709])).
% 23.05/23.23 tff(8171,plain,
% 23.05/23.23 (mult(mult(unit, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 23.05/23.23 inference(transitivity,[status(thm)],[6664, 8170, 8169, 281])).
% 23.05/23.23 tff(8172,plain,
% 23.05/23.23 ((mult(mult(unit, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(mult(unit, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c))))) <=> (mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 23.05/23.23 inference(monotonicity,[status(thm)],[6674, 8171])).
% 23.05/23.23 tff(8173,plain,
% 23.05/23.23 ((mult(mult(unit, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(mult(unit, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c))))) <=> (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))),
% 23.05/23.23 inference(transitivity,[status(thm)],[8172, 6658])).
% 23.05/23.23 tff(8174,plain,
% 23.05/23.23 ((mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))) <=> (mult(mult(unit, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(mult(unit, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.05/23.23 inference(symmetry,[status(thm)],[8173])).
% 23.05/23.23 tff(8175,plain,
% 23.05/23.23 ((~(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) <=> (~(mult(mult(unit, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(mult(unit, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c))))))),
% 23.05/23.23 inference(monotonicity,[status(thm)],[8174])).
% 23.05/23.23 tff(8176,plain,
% 23.05/23.23 (~(mult(mult(unit, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(mult(unit, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.05/23.23 inference(modus_ponens,[status(thm)],[270, 8175])).
% 23.05/23.23 tff(8177,plain,
% 23.05/23.23 (mult(b, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))))),
% 23.05/23.23 inference(symmetry,[status(thm)],[8033])).
% 23.05/23.23 tff(8178,assumption,(mult(b, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))), introduced(assumption)).
% 23.05/23.23 tff(8179,plain,
% 23.05/23.23 (mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))) = mult(b, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.05/23.23 inference(symmetry,[status(thm)],[8178])).
% 23.05/23.23 tff(8180,plain,
% 23.05/23.23 (mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))) = mult(b, mult(a, mult(b, c)))),
% 23.05/23.23 inference(monotonicity,[status(thm)],[5181])).
% 23.05/23.23 tff(8181,plain,
% 23.05/23.23 (mult(b, mult(a, mult(b, c))) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 23.05/23.23 inference(symmetry,[status(thm)],[8180])).
% 23.05/23.23 tff(8182,plain,
% 23.05/23.23 (mult(b, mult(a, mult(b, c))) = mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))))),
% 23.05/23.23 inference(transitivity,[status(thm)],[8181, 8179, 8177])).
% 23.05/23.23 tff(8183,plain,
% 23.05/23.23 (ld(b, mult(b, mult(a, mult(b, c)))) = ld(b, mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))))),
% 23.05/23.23 inference(monotonicity,[status(thm)],[8182])).
% 23.05/23.23 tff(8184,plain,
% 23.05/23.23 (mult(mult(unit, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(mult(unit, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c))))),
% 23.05/23.23 inference(transitivity,[status(thm)],[6673, 6671, 287, 142, 7455, 8183, 8008, 2319, 6680])).
% 23.05/23.23 tff(8185,plain,
% 23.05/23.23 ($false),
% 23.05/23.23 inference(unit_resolution,[status(thm)],[6686, 8184])).
% 23.05/23.23 tff(8186,plain,((~(mult(b, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))))) | (mult(mult(unit, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(mult(unit, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))))), inference(lemma,lemma(discharge,[]))).
% 23.05/23.23 tff(8187,plain,
% 23.05/23.23 ((~(mult(b, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))))) | (mult(mult(unit, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(mult(unit, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))),
% 23.05/23.23 inference(unit_resolution,[status(thm)],[8186, 5709])).
% 23.05/23.23 tff(8188,plain,
% 23.05/23.23 (~(mult(b, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))))),
% 23.05/23.23 inference(unit_resolution,[status(thm)],[8187, 8176, 279])).
% 23.05/23.23 tff(8189,plain,
% 23.05/23.23 ((~(mult(mult(b, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(b, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c)))) | (~(mult(b, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))))),
% 23.05/23.23 inference(unit_resolution,[status(thm)],[7974, 8188])).
% 23.05/23.23 tff(8190,plain,
% 23.05/23.23 (~((~(mult(mult(b, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(b, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(b, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))))))),
% 23.05/23.23 inference(unit_resolution,[status(thm)],[7971, 27, 8189])).
% 23.05/23.23 tff(8191,plain,
% 23.05/23.23 (mult(mult(b, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(b, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.05/23.23 inference(unit_resolution,[status(thm)],[7967, 8190])).
% 23.05/23.23 tff(8192,plain,
% 23.05/23.23 ((mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, c), c), mult(a, rd(mult(b, c), mult(a, c))))) <=> (mult(mult(mult(a, c), c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a)))),
% 23.05/23.23 inference(commutativity,[status(thm)],[])).
% 23.05/23.23 tff(8193,plain,
% 23.05/23.23 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))),
% 23.05/23.23 inference(symmetry,[status(thm)],[5434])).
% 23.05/23.23 tff(8194,plain,
% 23.05/23.23 (ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c))) = ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))))),
% 23.05/23.24 inference(monotonicity,[status(thm)],[8193])).
% 23.05/23.24 tff(8195,plain,
% 23.05/23.24 (mult(mult(a, c), c) = mult(c, mult(a, c))),
% 23.05/23.24 inference(transitivity,[status(thm)],[2596, 8194, 2590])).
% 23.05/23.24 tff(8196,plain,
% 23.05/23.24 (mult(mult(mult(a, c), c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c))))),
% 23.05/23.24 inference(monotonicity,[status(thm)],[8195])).
% 23.05/23.24 tff(8197,plain,
% 23.05/23.24 (mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, c), c), mult(a, rd(mult(b, c), mult(a, c))))),
% 23.05/23.24 inference(symmetry,[status(thm)],[8196])).
% 23.05/23.24 tff(8198,plain,
% 23.05/23.24 (mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 23.05/23.24 inference(monotonicity,[status(thm)],[5936])).
% 23.05/23.24 tff(8199,plain,
% 23.05/23.24 (mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c)) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))),
% 23.05/23.24 inference(transitivity,[status(thm)],[8198, 4676, 4520, 2319])).
% 23.05/23.24 tff(8200,plain,
% 23.05/23.24 ((mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c)))))) <=> (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c))))))),
% 23.05/23.24 inference(monotonicity,[status(thm)],[8199])).
% 23.05/23.24 tff(8201,assumption,(~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c))))))), introduced(assumption)).
% 23.05/23.24 tff(8202,plain,
% 23.05/23.24 (((~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c))))) | (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c))))))),
% 23.05/23.24 inference(tautology,[status(thm)],[])).
% 23.05/23.24 tff(8203,plain,
% 23.05/23.24 ((~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c))))),
% 23.05/23.24 inference(unit_resolution,[status(thm)],[8202, 8201])).
% 23.05/23.24 tff(8204,plain,
% 23.05/23.24 (~((~(mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))))),
% 23.05/23.24 inference(unit_resolution,[status(thm)],[5826, 8203])).
% 23.05/23.24 tff(8205,plain,
% 23.05/23.24 (mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.05/23.24 inference(unit_resolution,[status(thm)],[5828, 8204])).
% 23.05/23.24 tff(8206,plain,
% 23.05/23.24 (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.05/23.24 inference(modus_ponens,[status(thm)],[8205, 8200])).
% 23.05/23.24 tff(8207,plain,
% 23.05/23.24 ($false),
% 23.05/23.24 inference(unit_resolution,[status(thm)],[8201, 8206])).
% 23.05/23.24 tff(8208,plain,((mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))), inference(lemma,lemma(discharge,[]))).
% 23.05/23.24 tff(8209,plain,
% 23.05/23.24 ((mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))),
% 23.05/23.24 inference(unit_resolution,[status(thm)],[8208, 5709])).
% 23.05/23.24 tff(8210,plain,
% 23.05/23.24 ((mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))),
% 23.05/23.24 inference(unit_resolution,[status(thm)],[8209, 8129])).
% 23.05/23.24 tff(8211,plain,
% 23.05/23.24 (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.05/23.24 inference(unit_resolution,[status(thm)],[8210, 8165, 281])).
% 23.05/23.24 tff(8212,plain,
% 23.05/23.24 (ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))) = ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c)))),
% 23.05/23.24 inference(symmetry,[status(thm)],[8194])).
% 23.05/23.24 tff(8213,plain,
% 23.05/23.24 (mult(mult(c, a), c) = mult(mult(a, c), c)),
% 23.05/23.24 inference(transitivity,[status(thm)],[2690, 4068, 8212, 2595])).
% 23.05/23.24 tff(8214,plain,
% 23.05/23.24 (rd(mult(mult(c, a), c), c) = rd(mult(mult(a, c), c), c)),
% 23.05/23.24 inference(monotonicity,[status(thm)],[8213])).
% 23.05/23.24 tff(8215,plain,
% 23.05/23.24 (mult(c, a) = mult(a, c)),
% 23.05/23.24 inference(transitivity,[status(thm)],[2770, 8214, 2723])).
% 23.05/23.24 tff(8216,plain,
% 23.05/23.24 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, a)) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c))),
% 23.05/23.24 inference(monotonicity,[status(thm)],[8215])).
% 23.05/23.24 tff(8217,assumption,(~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a))), introduced(assumption)).
% 23.05/23.24 tff(8218,plain,
% 23.05/23.24 ((~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))),
% 23.05/23.24 inference(unit_resolution,[status(thm)],[4297, 8217])).
% 23.05/23.24 tff(8219,plain,
% 23.05/23.24 (~((~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))))),
% 23.05/23.24 inference(unit_resolution,[status(thm)],[4295, 8218])).
% 23.05/23.24 tff(8220,plain,
% 23.05/23.24 (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))),
% 23.05/23.24 inference(unit_resolution,[status(thm)],[4290, 8219])).
% 23.05/23.24 tff(8221,plain,
% 23.05/23.24 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a)),
% 23.05/23.24 inference(symmetry,[status(thm)],[8220])).
% 23.05/23.24 tff(8222,plain,
% 23.05/23.24 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a)),
% 23.05/23.24 inference(transitivity,[status(thm)],[1168, 8221])).
% 23.05/23.24 tff(8223,plain,
% 23.05/23.24 ((mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, a))) <=> (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)))),
% 23.05/23.24 inference(monotonicity,[status(thm)],[8222, 8216])).
% 23.05/23.24 tff(8224,plain,
% 23.05/23.24 ((mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, a))) <=> (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a))),
% 23.05/23.24 inference(transitivity,[status(thm)],[8223, 1429])).
% 23.05/23.24 tff(8225,plain,
% 23.05/23.24 ((mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a)) <=> (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, a)))),
% 23.05/23.24 inference(symmetry,[status(thm)],[8224])).
% 23.05/23.24 tff(8226,plain,
% 23.05/23.24 ((~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a))) <=> (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, a))))),
% 23.05/23.24 inference(monotonicity,[status(thm)],[8225])).
% 23.05/23.24 tff(8227,plain,
% 23.05/23.24 (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, a)))),
% 23.05/23.24 inference(modus_ponens,[status(thm)],[8217, 8226])).
% 23.05/23.24 tff(8228,plain,
% 23.05/23.24 ((mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, a)) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a)) <=> (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, a)))),
% 23.05/23.24 inference(commutativity,[status(thm)],[])).
% 23.05/23.24 tff(8229,plain,
% 23.05/23.24 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), a))),
% 23.05/23.24 inference(quant_inst,[status(thm)],[])).
% 23.05/23.24 tff(8230,plain,
% 23.05/23.24 (rd(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), a)),
% 23.05/23.24 inference(unit_resolution,[status(thm)],[8229, 168])).
% 23.05/23.24 tff(8231,assumption,(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c)))))), introduced(assumption)).
% 23.05/23.24 tff(8232,plain,
% 23.05/23.24 (mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))),
% 23.05/23.24 inference(symmetry,[status(thm)],[8231])).
% 23.05/23.24 tff(8233,plain,
% 23.05/23.24 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), a), a) = mult(c, mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.05/23.24 inference(quant_inst,[status(thm)],[])).
% 23.05/23.24 tff(8234,plain,
% 23.05/23.24 (rd(mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), a), a) = mult(c, mult(a, rd(mult(b, c), mult(a, c))))),
% 23.05/23.24 inference(unit_resolution,[status(thm)],[8233, 168])).
% 23.05/23.24 tff(8235,plain,
% 23.05/23.24 (mult(mult(c, a), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))),
% 23.05/23.24 inference(monotonicity,[status(thm)],[8215])).
% 23.05/23.24 tff(8236,plain,
% 23.05/23.24 (mult(mult(mult(c, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)),
% 23.05/23.24 inference(monotonicity,[status(thm)],[8235])).
% 23.05/23.24 tff(8237,plain,
% 23.05/23.24 ((mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))) <=> (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))),
% 23.05/23.24 inference(monotonicity,[status(thm)],[8170, 5497])).
% 23.05/23.24 tff(8238,plain,
% 23.05/23.24 ((mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)) <=> (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))),
% 23.05/23.24 inference(symmetry,[status(thm)],[8237])).
% 23.05/23.24 tff(8239,plain,
% 23.05/23.24 (mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), a)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)),
% 23.05/23.24 inference(transitivity,[status(thm)],[5404, 8236])).
% 23.05/23.24 tff(8240,plain,
% 23.05/23.24 (mult(mult(c, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))),
% 23.05/23.24 inference(monotonicity,[status(thm)],[8215])).
% 23.05/23.24 tff(8241,assumption,(~(mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), a)))), introduced(assumption)).
% 23.05/23.24 tff(8242,plain,
% 23.05/23.24 (((~(mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), a)))) | (~(mult(mult(c, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))) | (mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), a)))),
% 23.05/23.24 inference(tautology,[status(thm)],[])).
% 23.05/23.24 tff(8243,plain,
% 23.05/23.24 ((~(mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), a)))) | (~(mult(mult(c, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))),
% 23.05/23.24 inference(unit_resolution,[status(thm)],[8242, 8241])).
% 23.05/23.24 tff(8244,plain,
% 23.05/23.24 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), a)) = mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(mult(c, a), mult(a, rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), a)))) | (~(mult(mult(c, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), a)) = mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(mult(c, a), mult(a, rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), a)))) | (~(mult(mult(c, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))))))),
% 23.05/23.24 inference(rewrite,[status(thm)],[])).
% 23.05/23.24 tff(8245,plain,
% 23.05/23.24 (((~((~(mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(mult(c, a), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), a)) = mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))))) | (~((~(mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), a)))) | (~(mult(mult(c, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))))) <=> ((~((~(mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), a)) = mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(mult(c, a), mult(a, rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), a)))) | (~(mult(mult(c, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))))))),
% 23.05/23.24 inference(rewrite,[status(thm)],[])).
% 23.05/23.24 tff(8246,plain,
% 23.05/23.24 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(mult(c, a), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), a)) = mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))))) | (~((~(mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), a)))) | (~(mult(mult(c, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), a)) = mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(mult(c, a), mult(a, rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), a)))) | (~(mult(mult(c, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))))))),
% 23.05/23.24 inference(monotonicity,[status(thm)],[8245])).
% 23.05/23.24 tff(8247,plain,
% 23.05/23.25 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(mult(c, a), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), a)) = mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))))) | (~((~(mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), a)))) | (~(mult(mult(c, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), a)) = mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(mult(c, a), mult(a, rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), a)))) | (~(mult(mult(c, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))))))),
% 23.05/23.25 inference(transitivity,[status(thm)],[8246, 8244])).
% 23.05/23.25 tff(8248,plain,
% 23.05/23.25 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(mult(c, a), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), a)) = mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))))) | (~((~(mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), a)))) | (~(mult(mult(c, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))))))),
% 23.05/23.25 inference(quant_inst,[status(thm)],[])).
% 23.05/23.25 tff(8249,plain,
% 23.05/23.25 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), a)) = mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(mult(c, a), mult(a, rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), a)))) | (~(mult(mult(c, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))))),
% 23.05/23.25 inference(modus_ponens,[status(thm)],[8248, 8247])).
% 23.05/23.25 tff(8250,plain,
% 23.05/23.25 ((~((~(mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), a)) = mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(mult(c, a), mult(a, rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), a)))) | (~(mult(mult(c, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))))),
% 23.05/23.25 inference(unit_resolution,[status(thm)],[8249, 27])).
% 23.05/23.25 tff(8251,plain,
% 23.05/23.25 (~((~(mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), a)) = mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(mult(c, a), mult(a, rd(mult(b, c), mult(a, c)))))))),
% 23.05/23.25 inference(unit_resolution,[status(thm)],[8250, 8243])).
% 23.05/23.25 tff(8252,plain,
% 23.05/23.25 (((~(mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), a)) = mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(mult(c, a), mult(a, rd(mult(b, c), mult(a, c))))))) | (mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(mult(c, a), mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.05/23.25 inference(tautology,[status(thm)],[])).
% 23.05/23.25 tff(8253,plain,
% 23.05/23.25 (mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(mult(c, a), mult(a, rd(mult(b, c), mult(a, c))))),
% 23.05/23.25 inference(unit_resolution,[status(thm)],[8252, 8251])).
% 23.05/23.25 tff(8254,plain,
% 23.05/23.25 (mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))),
% 23.05/23.25 inference(transitivity,[status(thm)],[8253, 8240, 8170])).
% 23.05/23.25 tff(8255,plain,
% 23.05/23.25 ((mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), a))) <=> (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))),
% 23.05/23.25 inference(monotonicity,[status(thm)],[8254, 8239])).
% 23.05/23.25 tff(8256,plain,
% 23.05/23.25 ((mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), a))) <=> (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))),
% 23.05/23.25 inference(transitivity,[status(thm)],[8255, 8238])).
% 23.05/23.25 tff(8257,plain,
% 23.05/23.25 ((~(mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), a)))) <=> (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))))),
% 23.05/23.25 inference(monotonicity,[status(thm)],[8256])).
% 23.05/23.25 tff(8258,plain,
% 23.05/23.25 (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))),
% 23.05/23.25 inference(modus_ponens,[status(thm)],[8241, 8257])).
% 23.05/23.25 tff(8259,plain,
% 23.05/23.25 ((mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))) <=> (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))),
% 23.05/23.25 inference(commutativity,[status(thm)],[])).
% 23.05/23.25 tff(8260,plain,
% 23.05/23.25 (mult(mult(c, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))),
% 23.05/23.25 inference(monotonicity,[status(thm)],[5700])).
% 23.05/23.25 tff(8261,plain,
% 23.05/23.25 (mult(mult(c, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))),
% 23.05/23.25 inference(transitivity,[status(thm)],[8260, 8170])).
% 23.05/23.25 tff(8262,plain,
% 23.05/23.25 (mult(a, mult(a, c)) = mult(mult(a, c), a)),
% 23.05/23.25 inference(transitivity,[status(thm)],[4452, 8166, 4447])).
% 23.05/23.25 tff(8263,plain,
% 23.05/23.25 (mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))),
% 23.05/23.25 inference(monotonicity,[status(thm)],[8262])).
% 23.05/23.25 tff(8264,plain,
% 23.05/23.25 (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 23.05/23.25 inference(symmetry,[status(thm)],[8263])).
% 23.05/23.25 tff(8265,plain,
% 23.05/23.25 (mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 23.05/23.25 inference(transitivity,[status(thm)],[8232, 8170, 8264, 299])).
% 23.05/23.25 tff(8266,plain,
% 23.05/23.25 (ld(a, mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c)))))) = ld(a, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 23.05/23.25 inference(monotonicity,[status(thm)],[8265])).
% 23.05/23.25 tff(8267,plain,
% 23.05/23.25 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(a, mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c)))))) = mult(c, mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.05/23.25 inference(quant_inst,[status(thm)],[])).
% 23.05/23.25 tff(8268,plain,
% 23.05/23.25 (ld(a, mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c)))))) = mult(c, mult(a, rd(mult(b, c), mult(a, c))))),
% 23.05/23.25 inference(unit_resolution,[status(thm)],[8267, 7])).
% 23.05/23.25 tff(8269,plain,
% 23.05/23.25 (mult(c, mult(a, rd(mult(b, c), mult(a, c)))) = ld(a, mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c))))))),
% 23.05/23.25 inference(symmetry,[status(thm)],[8268])).
% 23.05/23.25 tff(8270,plain,
% 23.05/23.25 (mult(c, mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))),
% 23.09/23.25 inference(transitivity,[status(thm)],[8269, 8266, 4336])).
% 23.09/23.25 tff(8271,plain,
% 23.09/23.25 (mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)),
% 23.09/23.25 inference(monotonicity,[status(thm)],[8270])).
% 23.09/23.25 tff(8272,plain,
% 23.09/23.25 ((mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(mult(c, a), mult(a, rd(mult(b, c), mult(a, c))))) <=> (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))))),
% 23.09/23.25 inference(monotonicity,[status(thm)],[8271, 8261])).
% 23.09/23.25 tff(8273,plain,
% 23.09/23.25 ((mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(mult(c, a), mult(a, rd(mult(b, c), mult(a, c))))) <=> (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))),
% 23.09/23.25 inference(transitivity,[status(thm)],[8272, 8259])).
% 23.09/23.25 tff(8274,plain,
% 23.09/23.25 ((mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(mult(c, a), mult(a, rd(mult(b, c), mult(a, c))))) <=> (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))),
% 23.09/23.25 inference(transitivity,[status(thm)],[8273, 8238])).
% 23.09/23.25 tff(8275,assumption,(mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(mult(c, a), mult(a, rd(mult(b, c), mult(a, c))))), introduced(assumption)).
% 23.09/23.25 tff(8276,plain,
% 23.09/23.25 (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))),
% 23.09/23.25 inference(modus_ponens,[status(thm)],[8275, 8274])).
% 23.09/23.25 tff(8277,plain,
% 23.09/23.25 ($false),
% 23.09/23.25 inference(unit_resolution,[status(thm)],[330, 8276])).
% 23.09/23.25 tff(8278,plain,((~(mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(mult(c, a), mult(a, rd(mult(b, c), mult(a, c)))))) | (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))) | (~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c)))))))), inference(lemma,lemma(discharge,[]))).
% 23.09/23.25 tff(8279,plain,
% 23.09/23.25 (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))),
% 23.09/23.25 inference(unit_resolution,[status(thm)],[8278, 8253, 299, 8231])).
% 23.09/23.25 tff(8280,plain,
% 23.09/23.25 ($false),
% 23.09/23.25 inference(unit_resolution,[status(thm)],[8279, 8258])).
% 23.09/23.25 tff(8281,plain,((mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), a))) | (~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c)))))))), inference(lemma,lemma(discharge,[]))).
% 23.09/23.25 tff(8282,plain,
% 23.09/23.25 (mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), a))),
% 23.09/23.25 inference(unit_resolution,[status(thm)],[8281, 299, 8231])).
% 23.09/23.25 tff(8283,plain,
% 23.09/23.25 (mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)),
% 23.09/23.25 inference(transitivity,[status(thm)],[8282, 5404, 8236])).
% 23.09/23.25 tff(8284,plain,
% 23.09/23.25 (rd(mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), a), a) = rd(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), a)),
% 23.09/23.25 inference(monotonicity,[status(thm)],[8283])).
% 23.09/23.25 tff(8285,plain,
% 23.09/23.25 (rd(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), a) = rd(mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), a), a)),
% 23.09/23.25 inference(symmetry,[status(thm)],[8284])).
% 23.09/23.25 tff(8286,plain,
% 23.09/23.25 (mult(mult(a, c), rd(mult(b, c), mult(a, c))) = mult(c, mult(a, rd(mult(b, c), mult(a, c))))),
% 23.09/23.25 inference(transitivity,[status(thm)],[6325, 8285, 8234])).
% 23.09/23.25 tff(8287,plain,
% 23.09/23.25 (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.09/23.25 inference(monotonicity,[status(thm)],[8286])).
% 23.09/23.25 tff(8288,plain,
% 23.09/23.25 (mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))),
% 23.09/23.25 inference(transitivity,[status(thm)],[299, 8287, 8232, 8170])).
% 23.09/23.25 tff(8289,plain,
% 23.09/23.25 (rd(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))), rd(mult(b, c), mult(a, c))) = rd(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), rd(mult(b, c), mult(a, c)))),
% 23.09/23.25 inference(monotonicity,[status(thm)],[8288])).
% 23.09/23.25 tff(8290,plain,
% 23.09/23.25 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(a, mult(a, c)))),
% 23.09/23.25 inference(quant_inst,[status(thm)],[])).
% 23.09/23.25 tff(8291,plain,
% 23.09/23.25 (rd(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(a, mult(a, c))),
% 23.09/23.25 inference(unit_resolution,[status(thm)],[8290, 168])).
% 23.09/23.25 tff(8292,plain,
% 23.09/23.25 (mult(a, mult(a, c)) = rd(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))), rd(mult(b, c), mult(a, c)))),
% 23.09/23.25 inference(symmetry,[status(thm)],[8291])).
% 23.09/23.25 tff(8293,plain,
% 23.09/23.25 (mult(a, mult(a, c)) = mult(mult(a, c), a)),
% 23.09/23.25 inference(transitivity,[status(thm)],[8292, 8289, 8230])).
% 23.09/23.25 tff(8294,plain,
% 23.09/23.25 (mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))),
% 23.09/23.25 inference(monotonicity,[status(thm)],[8293])).
% 23.09/23.25 tff(8295,plain,
% 23.09/23.25 (mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a)),
% 23.09/23.25 inference(transitivity,[status(thm)],[8294, 1169])).
% 23.09/23.25 tff(8296,plain,
% 23.09/23.25 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, a))),
% 23.09/23.25 inference(symmetry,[status(thm)],[8216])).
% 23.09/23.25 tff(8297,plain,
% 23.09/23.25 ((mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c)))) <=> (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, a)) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a))),
% 23.09/23.25 inference(monotonicity,[status(thm)],[8296, 8295])).
% 23.09/23.25 tff(8298,plain,
% 23.09/23.25 ((mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c)))) <=> (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, a)))),
% 23.09/23.25 inference(transitivity,[status(thm)],[8297, 8228])).
% 23.09/23.25 tff(8299,plain,
% 23.09/23.25 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c)))),
% 23.09/23.25 inference(unit_resolution,[status(thm)],[4332, 8219])).
% 23.09/23.25 tff(8300,plain,
% 23.09/23.25 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, a))),
% 23.09/23.25 inference(modus_ponens,[status(thm)],[8299, 8298])).
% 23.09/23.25 tff(8301,plain,
% 23.09/23.25 ($false),
% 23.09/23.25 inference(unit_resolution,[status(thm)],[8300, 8227])).
% 23.09/23.25 tff(8302,plain,((mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a)) | (~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c)))))))), inference(lemma,lemma(discharge,[]))).
% 23.09/23.25 tff(8303,plain,
% 23.09/23.25 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a)),
% 23.09/23.25 inference(unit_resolution,[status(thm)],[8302, 8211, 281])).
% 23.09/23.25 tff(8304,plain,
% 23.09/23.25 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))),
% 23.09/23.25 inference(monotonicity,[status(thm)],[8215])).
% 23.09/23.25 tff(8305,plain,
% 23.09/23.25 (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit))),
% 23.09/23.25 inference(unit_resolution,[status(thm)],[6559, 8304])).
% 23.09/23.25 tff(8306,assumption,(mult(c, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))), introduced(assumption)).
% 23.09/23.25 tff(8307,plain,
% 23.09/23.25 (mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))) = mult(c, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.09/23.26 inference(symmetry,[status(thm)],[8306])).
% 23.09/23.26 tff(8308,plain,
% 23.09/23.26 (mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))) = mult(c, mult(a, mult(b, c)))),
% 23.09/23.26 inference(monotonicity,[status(thm)],[5181])).
% 23.09/23.26 tff(8309,plain,
% 23.09/23.26 (mult(c, mult(a, mult(b, c))) = mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 23.09/23.26 inference(symmetry,[status(thm)],[8308])).
% 23.09/23.26 tff(8310,plain,
% 23.09/23.26 (mult(c, mult(a, mult(b, c))) = mult(c, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))))),
% 23.09/23.26 inference(transitivity,[status(thm)],[8309, 8307, 6841])).
% 23.09/23.26 tff(8311,plain,
% 23.09/23.26 (ld(c, mult(c, mult(a, mult(b, c)))) = ld(c, mult(c, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))))),
% 23.09/23.26 inference(monotonicity,[status(thm)],[8310])).
% 23.09/23.26 tff(8312,plain,
% 23.09/23.26 (mult(a, mult(b, c)) = ld(c, mult(c, mult(a, mult(b, c))))),
% 23.09/23.26 inference(symmetry,[status(thm)],[4461])).
% 23.09/23.26 tff(8313,plain,
% 23.09/23.26 (mult(mult(unit, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(mult(unit, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c))))),
% 23.09/23.26 inference(transitivity,[status(thm)],[6673, 6671, 287, 142, 8312, 8311, 4523, 2319, 6680])).
% 23.09/23.26 tff(8314,plain,
% 23.09/23.26 ($false),
% 23.09/23.26 inference(unit_resolution,[status(thm)],[6686, 8313])).
% 23.09/23.26 tff(8315,plain,((~(mult(c, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))))) | (mult(mult(unit, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(mult(unit, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))))), inference(lemma,lemma(discharge,[]))).
% 23.09/23.26 tff(8316,plain,
% 23.09/23.26 ((~(mult(c, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))))) | (mult(mult(unit, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(mult(unit, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))),
% 23.09/23.26 inference(unit_resolution,[status(thm)],[8315, 5709])).
% 23.09/23.26 tff(8317,plain,
% 23.09/23.26 (~(mult(c, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))))),
% 23.09/23.26 inference(unit_resolution,[status(thm)],[8316, 8176, 279])).
% 23.09/23.26 tff(8318,assumption,(~(mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))), introduced(assumption)).
% 23.09/23.26 tff(8319,plain,
% 23.09/23.26 (mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(c, a), c))),
% 23.09/23.26 inference(transitivity,[status(thm)],[2620, 7641, 4860, 4858])).
% 23.09/23.26 tff(8320,plain,
% 23.09/23.26 (mult(mult(rd(mult(b, c), mult(a, c)), mult(c, a)), c) = mult(mult(b, c), c)),
% 23.09/23.26 inference(monotonicity,[status(thm)],[7463])).
% 23.09/23.26 tff(8321,plain,
% 23.09/23.26 (mult(mult(b, c), c) = mult(mult(rd(mult(b, c), mult(a, c)), mult(c, a)), c)),
% 23.09/23.26 inference(symmetry,[status(thm)],[8320])).
% 23.09/23.26 tff(8322,plain,
% 23.09/23.26 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(c, a), mult(mult(c, a), b)) = b)),
% 23.09/23.26 inference(quant_inst,[status(thm)],[])).
% 23.09/23.26 tff(8323,plain,
% 23.09/23.26 (ld(mult(c, a), mult(mult(c, a), b)) = b),
% 23.09/23.26 inference(unit_resolution,[status(thm)],[8322, 7])).
% 23.09/23.26 tff(8324,plain,
% 23.09/23.26 (mult(c, ld(c, mult(a, b))) = mult(b, a)),
% 23.09/23.26 inference(transitivity,[status(thm)],[204, 397, 394, 390])).
% 23.09/23.26 tff(8325,plain,
% 23.09/23.26 (mult(c, mult(c, ld(c, mult(a, b)))) = mult(c, mult(b, a))),
% 23.09/23.26 inference(monotonicity,[status(thm)],[8324])).
% 23.09/23.26 tff(8326,plain,
% 23.09/23.26 (mult(c, mult(b, a)) = mult(c, mult(c, ld(c, mult(a, b))))),
% 23.09/23.26 inference(symmetry,[status(thm)],[8325])).
% 23.09/23.26 tff(8327,plain,
% 23.09/23.26 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(b, c), a)),
% 23.09/23.26 inference(monotonicity,[status(thm)],[5651])).
% 23.09/23.26 tff(8328,plain,
% 23.09/23.26 (mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(c, a), b)),
% 23.09/23.26 inference(transitivity,[status(thm)],[5497, 8327, 3057, 4208, 8326, 1443, 4270])).
% 23.09/23.26 tff(8329,plain,
% 23.09/23.26 (ld(mult(a, c), mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))) = ld(mult(c, a), mult(mult(c, a), b))),
% 23.09/23.26 inference(monotonicity,[status(thm)],[6891, 8328])).
% 23.09/23.26 tff(8330,plain,
% 23.09/23.26 (mult(rd(mult(b, c), mult(a, c)), a) = b),
% 23.09/23.26 inference(transitivity,[status(thm)],[4412, 8329, 8323])).
% 23.09/23.26 tff(8331,plain,
% 23.09/23.26 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)) = mult(b, mult(mult(c, unit), c))),
% 23.09/23.26 inference(monotonicity,[status(thm)],[8330, 2617])).
% 23.09/23.26 tff(8332,plain,
% 23.09/23.26 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(c, a)), c)),
% 23.09/23.26 inference(transitivity,[status(thm)],[8331, 7714, 7711, 8321])).
% 23.09/23.26 tff(8333,plain,
% 23.09/23.26 ((mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, c)))) <=> (mult(mult(rd(mult(b, c), mult(a, c)), mult(c, a)), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(c, a), c)))),
% 23.09/23.26 inference(monotonicity,[status(thm)],[8332, 8319])).
% 23.09/23.26 tff(8334,plain,
% 23.09/23.26 ((mult(mult(rd(mult(b, c), mult(a, c)), mult(c, a)), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(c, a), c))) <=> (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, c))))),
% 23.09/23.26 inference(symmetry,[status(thm)],[8333])).
% 23.09/23.26 tff(8335,plain,
% 23.09/23.26 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c)) = mult(rd(mult(b, c), mult(a, c)), mult(mult(c, a), c))),
% 23.09/23.26 inference(transitivity,[status(thm)],[7641, 4860, 4858])).
% 23.09/23.26 tff(8336,plain,
% 23.09/23.26 (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), c) = mult(mult(rd(mult(b, c), mult(a, c)), mult(c, a)), c)),
% 23.09/23.26 inference(transitivity,[status(thm)],[2588, 8321])).
% 23.09/23.26 tff(8337,plain,
% 23.09/23.26 ((mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c))) <=> (mult(mult(rd(mult(b, c), mult(a, c)), mult(c, a)), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(c, a), c)))),
% 23.09/23.26 inference(monotonicity,[status(thm)],[8336, 8335])).
% 23.09/23.26 tff(8338,plain,
% 23.09/23.26 (mult(c, mult(b, a)) = mult(c, mult(a, b))),
% 23.09/23.26 inference(transitivity,[status(thm)],[8326, 1443])).
% 23.09/23.26 tff(8339,plain,
% 23.09/23.26 ((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) | (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))) | (~(mult(c, mult(b, a)) = mult(c, mult(a, b))))),
% 23.09/23.26 inference(unit_resolution,[status(thm)],[2242, 6462])).
% 23.09/23.26 tff(8340,plain,
% 23.09/23.26 (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))),
% 23.09/23.26 inference(unit_resolution,[status(thm)],[8339, 1371, 8338])).
% 23.09/23.26 tff(8341,plain,
% 23.09/23.26 ((mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))) <=> (mult(a, mult(rd(mult(b, c), mult(a, c)), c)) = mult(a, mult(c, rd(mult(b, c), mult(a, c)))))),
% 23.09/23.26 inference(monotonicity,[status(thm)],[5117, 6696])).
% 23.09/23.26 tff(8342,plain,
% 23.09/23.26 ((mult(a, mult(rd(mult(b, c), mult(a, c)), c)) = mult(a, mult(c, rd(mult(b, c), mult(a, c))))) <=> (mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))),
% 23.09/23.26 inference(symmetry,[status(thm)],[8341])).
% 23.09/23.26 tff(8343,plain,
% 23.09/23.26 ((~(mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))),
% 23.09/23.26 inference(unit_resolution,[status(thm)],[5118, 8318])).
% 23.09/23.26 tff(8344,plain,
% 23.09/23.26 (~((~(mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)))))),
% 23.09/23.26 inference(unit_resolution,[status(thm)],[2213, 8343])).
% 23.09/23.26 tff(8345,plain,
% 23.09/23.26 (mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c))),
% 23.09/23.26 inference(unit_resolution,[status(thm)],[2357, 8344])).
% 23.09/23.26 tff(8346,plain,
% 23.09/23.26 (mult(mult(a, rd(mult(b, c), mult(a, c))), c) = mult(b, c)),
% 23.09/23.26 inference(monotonicity,[status(thm)],[472])).
% 23.09/23.26 tff(8347,plain,
% 23.09/23.26 (mult(b, c) = mult(mult(a, rd(mult(b, c), mult(a, c))), c)),
% 23.09/23.26 inference(symmetry,[status(thm)],[8346])).
% 23.09/23.26 tff(8348,plain,
% 23.09/23.26 (mult(mult(a, c), rd(mult(b, c), mult(a, c))) = mult(a, mult(rd(mult(b, c), mult(a, c)), c))),
% 23.09/23.26 inference(transitivity,[status(thm)],[734, 1490, 141, 8347, 6639, 8345, 5117])).
% 23.09/23.26 tff(8349,plain,
% 23.09/23.26 ((mult(mult(a, c), rd(mult(b, c), mult(a, c))) = mult(a, mult(c, rd(mult(b, c), mult(a, c))))) <=> (mult(a, mult(rd(mult(b, c), mult(a, c)), c)) = mult(a, mult(c, rd(mult(b, c), mult(a, c)))))),
% 23.09/23.26 inference(monotonicity,[status(thm)],[8348])).
% 23.09/23.26 tff(8350,plain,
% 23.09/23.26 ((mult(mult(a, c), rd(mult(b, c), mult(a, c))) = mult(a, mult(c, rd(mult(b, c), mult(a, c))))) <=> (mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))),
% 23.09/23.26 inference(transitivity,[status(thm)],[8349, 8342])).
% 23.09/23.26 tff(8351,plain,
% 23.09/23.26 ((mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))) <=> (mult(mult(a, c), rd(mult(b, c), mult(a, c))) = mult(a, mult(c, rd(mult(b, c), mult(a, c)))))),
% 23.09/23.26 inference(monotonicity,[status(thm)],[6298, 6696])).
% 23.09/23.26 tff(8352,plain,
% 23.09/23.26 (mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))),
% 23.09/23.26 inference(unit_resolution,[status(thm)],[2215, 8344])).
% 23.09/23.26 tff(8353,plain,
% 23.09/23.26 (mult(mult(a, c), rd(mult(b, c), mult(a, c))) = mult(a, mult(c, rd(mult(b, c), mult(a, c))))),
% 23.09/23.26 inference(modus_ponens,[status(thm)],[8352, 8351])).
% 23.09/23.26 tff(8354,plain,
% 23.09/23.26 (mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))),
% 23.09/23.26 inference(modus_ponens,[status(thm)],[8353, 8350])).
% 23.09/23.26 tff(8355,plain,
% 23.09/23.26 ($false),
% 23.09/23.26 inference(unit_resolution,[status(thm)],[8318, 8354])).
% 23.09/23.26 tff(8356,plain,((mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))) | (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit))))) | (~(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))), inference(lemma,lemma(discharge,[]))).
% 23.09/23.26 tff(8357,plain,
% 23.09/23.26 (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit))))),
% 23.09/23.26 inference(unit_resolution,[status(thm)],[8356, 8340, 8318, 1488])).
% 23.09/23.26 tff(8358,plain,
% 23.09/23.26 ((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit)))))),
% 23.09/23.26 inference(unit_resolution,[status(thm)],[33, 8357])).
% 23.09/23.26 tff(8359,plain,
% 23.09/23.26 (~((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit))))))),
% 23.09/23.26 inference(unit_resolution,[status(thm)],[31, 8358])).
% 23.09/23.26 tff(8360,plain,
% 23.09/23.26 (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit))),
% 23.09/23.26 inference(unit_resolution,[status(thm)],[4302, 8359])).
% 23.09/23.26 tff(8361,plain,
% 23.09/23.26 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c)) = mult(rd(mult(b, c), mult(a, c)), mult(mult(c, a), c))),
% 23.09/23.26 inference(monotonicity,[status(thm)],[4066])).
% 23.09/23.26 tff(8362,plain,
% 23.09/23.26 (mult(rd(mult(b, c), mult(a, c)), mult(mult(c, a), c)) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c))),
% 23.09/23.26 inference(symmetry,[status(thm)],[8361])).
% 23.09/23.26 tff(8363,plain,
% 23.09/23.26 (mult(mult(rd(mult(b, c), mult(a, c)), c), a) = mult(b, c)),
% 23.09/23.26 inference(transitivity,[status(thm)],[83, 4360, 4340, 1377, 2181, 1370])).
% 23.09/23.26 tff(8364,plain,
% 23.09/23.26 (mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c) = mult(mult(b, c), c)),
% 23.09/23.26 inference(monotonicity,[status(thm)],[8363])).
% 23.09/23.26 tff(8365,plain,
% 23.09/23.26 (mult(mult(b, c), c) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c)),
% 23.09/23.26 inference(symmetry,[status(thm)],[8364])).
% 23.09/23.26 tff(8366,plain,
% 23.09/23.26 (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c))),
% 23.09/23.26 inference(transitivity,[status(thm)],[2588, 8365, 2627, 8362])).
% 23.09/23.27 tff(8367,assumption,(~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c)))), introduced(assumption)).
% 23.09/23.27 tff(8368,plain,
% 23.09/23.27 ($false),
% 23.09/23.27 inference(unit_resolution,[status(thm)],[8367, 8366])).
% 23.09/23.27 tff(8369,plain,((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) | (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit)))))), inference(lemma,lemma(discharge,[]))).
% 23.09/23.27 tff(8370,plain,
% 23.09/23.27 ((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) | (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit))))),
% 23.09/23.27 inference(unit_resolution,[status(thm)],[8369, 3862])).
% 23.09/23.27 tff(8371,plain,
% 23.09/23.27 (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c))),
% 23.09/23.27 inference(unit_resolution,[status(thm)],[8370, 8360, 1371])).
% 23.09/23.27 tff(8372,plain,
% 23.09/23.27 (mult(mult(rd(mult(b, c), mult(a, c)), mult(c, a)), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(c, a), c))),
% 23.09/23.27 inference(modus_ponens,[status(thm)],[8371, 8337])).
% 23.09/23.27 tff(8373,plain,
% 23.09/23.27 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, c)))),
% 23.09/23.27 inference(modus_ponens,[status(thm)],[8372, 8334])).
% 23.09/23.27 tff(8374,plain,
% 23.09/23.27 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(b, mult(c, c)), mult(c, c)) = b)),
% 23.09/23.27 inference(quant_inst,[status(thm)],[])).
% 23.09/23.27 tff(8375,plain,
% 23.09/23.27 (rd(mult(b, mult(c, c)), mult(c, c)) = b),
% 23.09/23.27 inference(unit_resolution,[status(thm)],[8374, 168])).
% 23.09/23.27 tff(8376,plain,
% 23.09/23.27 (mult(b, mult(c, c)) = mult(b, mult(mult(c, unit), c))),
% 23.09/23.27 inference(monotonicity,[status(thm)],[2617])).
% 23.09/23.27 tff(8377,plain,
% 23.09/23.27 (mult(b, mult(mult(c, unit), c)) = mult(b, mult(c, c))),
% 23.09/23.27 inference(symmetry,[status(thm)],[8376])).
% 23.09/23.27 tff(8378,plain,
% 23.09/23.27 (mult(mult(b, c), c) = mult(mult(mult(b, c), unit), c)),
% 23.09/23.27 inference(symmetry,[status(thm)],[7711])).
% 23.09/23.27 tff(8379,assumption,(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c))), introduced(assumption)).
% 23.09/23.27 tff(8380,plain,
% 23.09/23.27 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), c)),
% 23.09/23.27 inference(symmetry,[status(thm)],[8379])).
% 23.09/23.27 tff(8381,assumption,(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, c)))), introduced(assumption)).
% 23.09/23.27 tff(8382,plain,
% 23.09/23.27 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)) = mult(b, mult(c, c))),
% 23.09/23.27 inference(transitivity,[status(thm)],[8381, 2620, 8380, 2588, 8378, 7713, 8377])).
% 23.09/23.27 tff(8383,plain,
% 23.09/23.27 (rd(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)), mult(c, c)) = rd(mult(b, mult(c, c)), mult(c, c))),
% 23.09/23.27 inference(monotonicity,[status(thm)],[8382])).
% 23.09/23.27 tff(8384,plain,
% 23.09/23.27 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)), mult(c, c)) = mult(rd(mult(b, c), mult(a, c)), a))),
% 23.09/23.27 inference(quant_inst,[status(thm)],[])).
% 23.09/23.27 tff(8385,plain,
% 23.09/23.27 (rd(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)), mult(c, c)) = mult(rd(mult(b, c), mult(a, c)), a)),
% 23.09/23.27 inference(unit_resolution,[status(thm)],[8384, 168])).
% 23.09/23.27 tff(8386,plain,
% 23.09/23.27 (mult(rd(mult(b, c), mult(a, c)), a) = rd(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)), mult(c, c))),
% 23.09/23.27 inference(symmetry,[status(thm)],[8385])).
% 23.09/23.27 tff(8387,plain,
% 23.09/23.27 (mult(rd(mult(b, c), mult(a, c)), a) = b),
% 23.09/23.27 inference(transitivity,[status(thm)],[8386, 8383, 8375])).
% 23.09/23.27 tff(8388,plain,
% 23.09/23.27 (mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, c), b)),
% 23.09/23.27 inference(monotonicity,[status(thm)],[8387])).
% 23.09/23.27 tff(8389,plain,
% 23.09/23.27 (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), b)),
% 23.09/23.27 inference(transitivity,[status(thm)],[359, 8388])).
% 23.09/23.27 tff(8390,plain,
% 23.09/23.27 (ld(mult(a, c), mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = ld(mult(a, c), mult(mult(a, c), b))),
% 23.09/23.27 inference(monotonicity,[status(thm)],[8389])).
% 23.09/23.27 tff(8391,plain,
% 23.09/23.27 (mult(a, rd(mult(b, c), mult(a, c))) = b),
% 23.09/23.27 inference(transitivity,[status(thm)],[471, 8390, 364])).
% 23.09/23.27 tff(8392,plain,
% 23.09/23.27 (mult(mult(a, rd(mult(b, c), mult(a, c))), c) = mult(b, c)),
% 23.09/23.27 inference(monotonicity,[status(thm)],[8391])).
% 23.09/23.27 tff(8393,plain,
% 23.09/23.27 (mult(b, c) = mult(mult(a, rd(mult(b, c), mult(a, c))), c)),
% 23.09/23.27 inference(symmetry,[status(thm)],[8392])).
% 23.09/23.27 tff(8394,plain,
% 23.09/23.27 (mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))),
% 23.09/23.27 inference(symmetry,[status(thm)],[8352])).
% 23.09/23.27 tff(8395,plain,
% 23.09/23.27 (mult(a, mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), c))),
% 23.09/23.27 inference(transitivity,[status(thm)],[2220, 8394, 2172, 2178, 2177, 2162, 734, 1490, 141, 8393, 6639, 8345, 5117])).
% 23.09/23.27 tff(8396,plain,
% 23.09/23.27 ((mult(a, mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), c))) <=> (mult(a, mult(rd(mult(b, c), mult(a, c)), c)) = mult(a, mult(c, rd(mult(b, c), mult(a, c)))))),
% 23.09/23.27 inference(commutativity,[status(thm)],[])).
% 23.09/23.27 tff(8397,plain,
% 23.09/23.27 ((mult(a, mult(rd(mult(b, c), mult(a, c)), c)) = mult(a, mult(c, rd(mult(b, c), mult(a, c))))) <=> (mult(a, mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), c)))),
% 23.09/23.27 inference(symmetry,[status(thm)],[8396])).
% 23.09/23.27 tff(8398,plain,
% 23.09/23.27 ((mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))) <=> (mult(a, mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), c)))),
% 23.09/23.27 inference(transitivity,[status(thm)],[8341, 8397])).
% 23.09/23.27 tff(8399,plain,
% 23.09/23.27 ((~(mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) <=> (~(mult(a, mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), c))))),
% 23.09/23.27 inference(monotonicity,[status(thm)],[8398])).
% 23.09/23.27 tff(8400,plain,
% 23.09/23.27 (~(mult(a, mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), c)))),
% 23.09/23.27 inference(modus_ponens,[status(thm)],[8318, 8399])).
% 23.09/23.27 tff(8401,plain,
% 23.09/23.27 ($false),
% 23.09/23.27 inference(unit_resolution,[status(thm)],[8400, 8395])).
% 23.09/23.27 tff(8402,plain,((mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))) | (~(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c))))), inference(lemma,lemma(discharge,[]))).
% 23.09/23.27 tff(8403,plain,
% 23.09/23.27 (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, c))))),
% 23.09/23.27 inference(unit_resolution,[status(thm)],[8402, 8371, 8318, 1488, 8340])).
% 23.09/23.27 tff(8404,plain,
% 23.09/23.27 ($false),
% 23.09/23.27 inference(unit_resolution,[status(thm)],[8403, 8373])).
% 23.09/23.27 tff(8405,plain,((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) | (~(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (~(mult(b, mult(a, b)) = mult(b, mult(b, a)))) | (mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))), inference(lemma,lemma(discharge,[]))).
% 23.09/23.27 tff(8406,plain,
% 23.09/23.27 (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))),
% 23.09/23.27 inference(unit_resolution,[status(thm)],[8405, 1916, 1488, 8318])).
% 23.09/23.27 tff(8407,plain,
% 23.09/23.27 (mult(mult(unit, mult(a, c)), mult(unit, mult(mult(b, unit), b))) = mult(mult(a, c), mult(unit, mult(mult(b, unit), b)))),
% 23.09/23.27 inference(monotonicity,[status(thm)],[1549])).
% 23.09/23.27 tff(8408,plain,
% 23.09/23.27 (mult(mult(a, c), mult(unit, mult(mult(b, unit), b))) = mult(mult(unit, mult(a, c)), mult(unit, mult(mult(b, unit), b)))),
% 23.09/23.27 inference(symmetry,[status(thm)],[8407])).
% 23.09/23.27 tff(8409,plain,
% 23.09/23.27 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(b, mult(a, c)), mult(a, c)) = b)),
% 23.09/23.27 inference(quant_inst,[status(thm)],[])).
% 23.09/23.27 tff(8410,plain,
% 23.09/23.27 (rd(mult(b, mult(a, c)), mult(a, c)) = b),
% 23.09/23.27 inference(unit_resolution,[status(thm)],[8409, 168])).
% 23.09/23.27 tff(8411,plain,
% 23.09/23.27 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(b, mult(a, c)), b), b) = mult(b, mult(a, c)))),
% 23.09/23.27 inference(quant_inst,[status(thm)],[])).
% 23.09/23.27 tff(8412,plain,
% 23.09/23.27 (rd(mult(mult(b, mult(a, c)), b), b) = mult(b, mult(a, c))),
% 23.09/23.27 inference(unit_resolution,[status(thm)],[8411, 168])).
% 23.09/23.27 tff(8413,plain,
% 23.09/23.27 (mult(b, mult(mult(b, c), a)) = mult(mult(b, mult(b, c)), a)),
% 23.09/23.27 inference(symmetry,[status(thm)],[6977])).
% 23.09/23.27 tff(8414,assumption,(mult(mult(b, mult(a, c)), b) = mult(b, mult(mult(a, c), b))), introduced(assumption)).
% 23.09/23.27 tff(8415,plain,
% 23.09/23.27 (mult(mult(b, mult(a, c)), b) = mult(mult(mult(a, b), c), b)),
% 23.09/23.27 inference(transitivity,[status(thm)],[8414, 5603, 6988, 8413, 6961, 5521, 6949])).
% 23.09/23.27 tff(8416,plain,
% 23.09/23.27 (rd(mult(mult(b, mult(a, c)), b), b) = rd(mult(mult(mult(a, b), c), b), b)),
% 23.09/23.27 inference(monotonicity,[status(thm)],[8415])).
% 23.09/23.27 tff(8417,plain,
% 23.09/23.27 (rd(mult(mult(mult(a, b), c), b), b) = rd(mult(mult(b, mult(a, c)), b), b)),
% 23.09/23.27 inference(symmetry,[status(thm)],[8416])).
% 23.09/23.27 tff(8418,plain,
% 23.09/23.27 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(b, mult(a, c))),
% 23.09/23.27 inference(transitivity,[status(thm)],[4298, 1332, 3892, 4208, 6746, 4225, 4270, 6761, 161, 794, 8417, 8412])).
% 23.09/23.27 tff(8419,plain,
% 23.09/23.27 (rd(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)), mult(a, c)) = rd(mult(b, mult(a, c)), mult(a, c))),
% 23.09/23.27 inference(monotonicity,[status(thm)],[8418])).
% 23.09/23.27 tff(8420,plain,
% 23.09/23.27 (mult(rd(mult(b, c), mult(a, c)), a) = rd(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)), mult(a, c))),
% 23.09/23.27 inference(symmetry,[status(thm)],[6351])).
% 23.09/23.27 tff(8421,plain,
% 23.09/23.27 (mult(rd(mult(b, c), mult(a, c)), a) = b),
% 23.09/23.27 inference(transitivity,[status(thm)],[8420, 8419, 8410])).
% 23.09/23.27 tff(8422,plain,
% 23.09/23.27 (mult(mult(rd(mult(b, c), mult(a, c)), a), c) = mult(b, c)),
% 23.09/23.27 inference(monotonicity,[status(thm)],[8421])).
% 23.09/23.27 tff(8423,plain,
% 23.09/23.27 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a) = mult(mult(b, c), a)),
% 23.09/23.27 inference(monotonicity,[status(thm)],[8422])).
% 23.09/23.27 tff(8424,plain,
% 23.09/23.27 (mult(mult(b, c), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a)),
% 23.09/23.27 inference(symmetry,[status(thm)],[8423])).
% 23.09/23.27 tff(8425,plain,
% 23.09/23.27 (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))),
% 23.09/23.27 inference(transitivity,[status(thm)],[1332, 8424, 1168])).
% 23.09/23.27 tff(8426,plain,
% 23.09/23.27 ($false),
% 23.09/23.27 inference(unit_resolution,[status(thm)],[1364, 8425])).
% 23.09/23.27 tff(8427,plain,((~(mult(mult(b, mult(a, c)), b) = mult(b, mult(mult(a, c), b)))) | (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) | (~(mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a)))) | (~(mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a)))), inference(lemma,lemma(discharge,[]))).
% 23.09/23.27 tff(8428,plain,
% 23.09/23.27 (~(mult(mult(b, mult(a, c)), b) = mult(b, mult(mult(a, c), b)))),
% 23.09/23.27 inference(unit_resolution,[status(thm)],[8427, 6562, 1364, 6563])).
% 23.09/23.27 tff(8429,plain,
% 23.09/23.27 ((~(mult(mult(b, b), mult(a, c)) = mult(b, mult(b, mult(a, c))))) | (~(mult(mult(b, mult(a, c)), b) = mult(b, mult(mult(a, c), b))))),
% 23.09/23.27 inference(unit_resolution,[status(thm)],[5632, 8428])).
% 23.09/23.27 tff(8430,plain,
% 23.09/23.27 (~((~(mult(mult(b, mult(a, c)), b) = mult(mult(b, b), mult(a, c)))) | (~(mult(b, mult(mult(a, c), b)) = mult(b, mult(b, mult(a, c))))))),
% 23.09/23.27 inference(unit_resolution,[status(thm)],[5630, 8429])).
% 23.09/23.27 tff(8431,plain,
% 23.09/23.27 (mult(b, mult(mult(a, c), b)) = mult(b, mult(b, mult(a, c)))),
% 23.09/23.27 inference(unit_resolution,[status(thm)],[5618, 8430])).
% 23.09/23.27 tff(8432,plain,
% 23.09/23.27 (mult(b, mult(b, mult(a, c))) = mult(b, mult(mult(a, c), b))),
% 23.09/23.27 inference(symmetry,[status(thm)],[8431])).
% 23.09/23.27 tff(8433,plain,
% 23.09/23.27 (mult(b, mult(b, mult(a, c))) = mult(b, mult(mult(a, b), c))),
% 23.09/23.27 inference(transitivity,[status(thm)],[8432, 5603, 3388])).
% 23.09/23.27 tff(8434,plain,
% 23.09/23.27 (ld(b, mult(b, mult(b, mult(a, c)))) = ld(b, mult(b, mult(mult(a, b), c)))),
% 23.09/23.27 inference(monotonicity,[status(thm)],[8433])).
% 23.09/23.27 tff(8435,plain,
% 23.09/23.27 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(b, mult(b, mult(b, mult(a, c)))) = mult(b, mult(a, c)))),
% 23.09/23.27 inference(quant_inst,[status(thm)],[])).
% 23.09/23.27 tff(8436,plain,
% 23.09/23.27 (ld(b, mult(b, mult(b, mult(a, c)))) = mult(b, mult(a, c))),
% 23.09/23.27 inference(unit_resolution,[status(thm)],[8435, 7])).
% 23.09/23.27 tff(8437,plain,
% 23.09/23.27 (mult(b, mult(a, c)) = ld(b, mult(b, mult(b, mult(a, c))))),
% 23.09/23.27 inference(symmetry,[status(thm)],[8436])).
% 23.09/23.27 tff(8438,plain,
% 23.09/23.27 (mult(b, mult(a, c)) = mult(mult(a, b), c)),
% 23.09/23.27 inference(transitivity,[status(thm)],[8437, 8434, 5605])).
% 23.09/23.27 tff(8439,plain,
% 23.09/23.27 (mult(mult(b, mult(a, c)), b) = mult(mult(mult(a, b), c), b)),
% 23.09/23.27 inference(monotonicity,[status(thm)],[8438])).
% 23.09/23.27 tff(8440,plain,
% 23.09/23.27 (((~(mult(mult(b, mult(a, c)), b) = mult(mult(b, b), mult(a, c)))) | (~(mult(b, mult(mult(a, c), b)) = mult(b, mult(b, mult(a, c)))))) | (mult(mult(b, mult(a, c)), b) = mult(mult(b, b), mult(a, c)))),
% 23.09/23.27 inference(tautology,[status(thm)],[])).
% 23.09/23.27 tff(8441,plain,
% 23.09/23.27 (mult(mult(b, mult(a, c)), b) = mult(mult(b, b), mult(a, c))),
% 23.09/23.27 inference(unit_resolution,[status(thm)],[8440, 8430])).
% 23.09/23.27 tff(8442,plain,
% 23.09/23.27 (mult(mult(b, b), mult(a, c)) = mult(mult(b, mult(a, c)), b)),
% 23.09/23.27 inference(symmetry,[status(thm)],[8441])).
% 23.09/23.27 tff(8443,plain,
% 23.09/23.27 (mult(mult(unit, mult(mult(b, unit), b)), mult(a, c)) = mult(mult(b, b), mult(a, c))),
% 23.09/23.27 inference(monotonicity,[status(thm)],[1106])).
% 23.09/23.27 tff(8444,plain,
% 23.09/23.27 (mult(unit, mult(unit, mult(mult(b, unit), b))) = mult(unit, mult(mult(b, unit), b))),
% 23.09/23.27 inference(monotonicity,[status(thm)],[429])).
% 23.09/23.27 tff(8445,plain,
% 23.09/23.27 (mult(mult(unit, mult(unit, mult(mult(b, unit), b))), mult(a, c)) = mult(mult(unit, mult(mult(b, unit), b)), mult(a, c))),
% 23.09/23.27 inference(monotonicity,[status(thm)],[8444])).
% 23.09/23.27 tff(8446,plain,
% 23.09/23.27 (mult(mult(unit, mult(unit, mult(mult(b, unit), b))), mult(a, c)) = mult(mult(unit, mult(a, c)), mult(unit, mult(mult(b, unit), b)))),
% 23.09/23.27 inference(transitivity,[status(thm)],[8445, 8443, 8442, 8439, 1709, 868, 1708, 8408])).
% 23.09/23.27 tff(8447,plain,
% 23.09/23.27 (mult(mult(b, c), mult(b, a)) = mult(mult(b, c), mult(a, b))),
% 23.09/23.27 inference(symmetry,[status(thm)],[6562])).
% 23.09/23.27 tff(8448,plain,
% 23.09/23.27 (ld(mult(b, c), mult(mult(b, c), mult(b, a))) = ld(mult(b, c), mult(mult(b, c), mult(a, b)))),
% 23.09/23.27 inference(monotonicity,[status(thm)],[8447])).
% 23.09/23.27 tff(8449,plain,
% 23.09/23.27 (mult(b, a) = mult(c, ld(c, mult(a, b)))),
% 23.09/23.27 inference(transitivity,[status(thm)],[1444, 8448, 1185, 1441])).
% 23.09/23.27 tff(8450,plain,
% 23.09/23.27 (mult(c, mult(b, a)) = mult(c, mult(c, ld(c, mult(a, b))))),
% 23.09/23.27 inference(monotonicity,[status(thm)],[8449])).
% 23.09/23.27 tff(8451,plain,
% 23.09/23.27 (mult(mult(b, c), a) = mult(mult(a, b), c)),
% 23.09/23.27 inference(transitivity,[status(thm)],[3892, 4208, 8450, 4225, 4270, 6761, 161])).
% 23.09/23.27 tff(8452,plain,
% 23.09/23.27 (mult(mult(mult(b, c), a), b) = mult(mult(mult(a, b), c), b)),
% 23.09/23.27 inference(monotonicity,[status(thm)],[8451])).
% 23.09/23.27 tff(8453,plain,
% 23.09/23.27 (mult(mult(mult(b, c), b), a) = mult(mult(mult(b, c), a), b)),
% 23.09/23.27 inference(symmetry,[status(thm)],[6563])).
% 23.09/23.27 tff(8454,plain,
% 23.09/23.27 (mult(mult(b, mult(b, c)), a) = mult(mult(mult(a, b), b), c)),
% 23.09/23.27 inference(transitivity,[status(thm)],[6961, 8453, 8452, 827])).
% 23.09/23.27 tff(8455,plain,
% 23.09/23.27 (mult(b, a) = mult(a, b)),
% 23.09/23.27 inference(transitivity,[status(thm)],[1444, 8448, 1185])).
% 23.09/23.27 tff(8456,plain,
% 23.09/23.27 (mult(mult(b, a), mult(b, c)) = mult(mult(a, b), mult(b, c))),
% 23.09/23.27 inference(monotonicity,[status(thm)],[8455])).
% 23.09/23.27 tff(8457,plain,
% 23.09/23.27 ((mult(mult(b, a), mult(b, c)) = mult(mult(b, mult(b, c)), a)) <=> (mult(mult(a, b), mult(b, c)) = mult(mult(mult(a, b), b), c))),
% 23.09/23.27 inference(monotonicity,[status(thm)],[8456, 8454])).
% 23.09/23.27 tff(8458,plain,
% 23.09/23.27 ((mult(mult(b, a), mult(b, c)) = mult(mult(b, mult(b, c)), a)) <=> (mult(mult(mult(a, b), b), c) = mult(mult(a, b), mult(b, c)))),
% 23.09/23.27 inference(transitivity,[status(thm)],[8457, 6959])).
% 23.09/23.27 tff(8459,plain,
% 23.09/23.27 ((mult(mult(mult(a, b), b), c) = mult(mult(a, b), mult(b, c))) <=> (mult(mult(b, a), mult(b, c)) = mult(mult(b, mult(b, c)), a))),
% 23.09/23.27 inference(symmetry,[status(thm)],[8458])).
% 23.09/23.27 tff(8460,plain,
% 23.09/23.27 ((~(mult(mult(mult(a, b), b), c) = mult(mult(a, b), mult(b, c)))) <=> (~(mult(mult(b, a), mult(b, c)) = mult(mult(b, mult(b, c)), a)))),
% 23.09/23.27 inference(monotonicity,[status(thm)],[8459])).
% 23.09/23.27 tff(8461,plain,
% 23.09/23.27 (~(mult(mult(b, a), mult(b, c)) = mult(mult(b, mult(b, c)), a))),
% 23.09/23.27 inference(modus_ponens,[status(thm)],[1729, 8460])).
% 23.09/23.27 tff(8462,plain,
% 23.09/23.27 ((~(mult(mult(b, a), mult(b, c)) = mult(mult(b, mult(b, c)), a))) | (~(mult(b, mult(a, mult(b, c))) = mult(b, mult(mult(b, c), a))))),
% 23.09/23.27 inference(unit_resolution,[status(thm)],[6969, 8461])).
% 23.09/23.27 tff(8463,plain,
% 23.09/23.27 (~((~(mult(mult(b, a), mult(b, c)) = mult(b, mult(a, mult(b, c))))) | (~(mult(mult(b, mult(b, c)), a) = mult(b, mult(mult(b, c), a)))))),
% 23.09/23.27 inference(unit_resolution,[status(thm)],[6974, 8462])).
% 23.09/23.27 tff(8464,plain,
% 23.09/23.27 (mult(mult(b, mult(b, c)), a) = mult(b, mult(mult(b, c), a))),
% 23.09/23.27 inference(unit_resolution,[status(thm)],[6976, 8463])).
% 23.09/23.27 tff(8465,plain,
% 23.09/23.27 (mult(b, mult(mult(b, c), a)) = mult(mult(b, mult(b, c)), a)),
% 23.09/23.27 inference(symmetry,[status(thm)],[8464])).
% 23.09/23.27 tff(8466,plain,
% 23.09/23.27 (mult(c, mult(c, ld(c, mult(a, b)))) = mult(c, mult(b, a))),
% 23.09/23.27 inference(symmetry,[status(thm)],[8450])).
% 23.09/23.27 tff(8467,plain,
% 23.09/23.27 (mult(mult(a, b), c) = mult(mult(b, c), a)),
% 23.09/23.27 inference(transitivity,[status(thm)],[227, 6986, 4221, 6985, 8466, 4304, 4975])).
% 23.09/23.27 tff(8468,plain,
% 23.09/23.27 (mult(mult(unit, b), mult(mult(a, b), c)) = mult(b, mult(mult(b, c), a))),
% 23.09/23.27 inference(monotonicity,[status(thm)],[184, 8467])).
% 23.09/23.27 tff(8469,plain,
% 23.09/23.27 (mult(b, mult(mult(a, c), b)) = mult(mult(unit, mult(a, c)), mult(unit, mult(mult(b, unit), b)))),
% 23.09/23.27 inference(transitivity,[status(thm)],[5603, 8468, 8465, 6961, 8453, 8452, 1709, 868, 1708, 8408])).
% 23.09/23.27 tff(8470,plain,
% 23.09/23.27 (mult(mult(unit, mult(mult(b, unit), b)), mult(a, c)) = mult(mult(unit, mult(unit, mult(mult(b, unit), b))), mult(a, c))),
% 23.09/23.27 inference(symmetry,[status(thm)],[8445])).
% 23.09/23.27 tff(8471,plain,
% 23.09/23.27 (mult(mult(b, b), mult(a, c)) = mult(mult(unit, mult(mult(b, unit), b)), mult(a, c))),
% 23.09/23.27 inference(symmetry,[status(thm)],[8443])).
% 23.09/23.27 tff(8472,plain,
% 23.09/23.27 (mult(mult(b, mult(a, c)), b) = mult(mult(unit, mult(unit, mult(mult(b, unit), b))), mult(a, c))),
% 23.09/23.27 inference(transitivity,[status(thm)],[8441, 8471, 8470])).
% 23.09/23.27 tff(8473,plain,
% 23.09/23.27 ((mult(mult(b, mult(a, c)), b) = mult(b, mult(mult(a, c), b))) <=> (mult(mult(unit, mult(unit, mult(mult(b, unit), b))), mult(a, c)) = mult(mult(unit, mult(a, c)), mult(unit, mult(mult(b, unit), b))))),
% 23.09/23.28 inference(monotonicity,[status(thm)],[8472, 8469])).
% 23.09/23.28 tff(8474,plain,
% 23.09/23.28 ((~(mult(mult(b, mult(a, c)), b) = mult(b, mult(mult(a, c), b)))) <=> (~(mult(mult(unit, mult(unit, mult(mult(b, unit), b))), mult(a, c)) = mult(mult(unit, mult(a, c)), mult(unit, mult(mult(b, unit), b)))))),
% 23.09/23.28 inference(monotonicity,[status(thm)],[8473])).
% 23.09/23.28 tff(8475,plain,
% 23.09/23.28 (~(mult(mult(unit, mult(unit, mult(mult(b, unit), b))), mult(a, c)) = mult(mult(unit, mult(a, c)), mult(unit, mult(mult(b, unit), b))))),
% 23.09/23.28 inference(modus_ponens,[status(thm)],[8428, 8474])).
% 23.09/23.28 tff(8476,plain,
% 23.09/23.28 ($false),
% 23.09/23.28 inference(unit_resolution,[status(thm)],[8475, 8446])).
% 23.09/23.28 tff(8477,plain,(((~(mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a))) | (~(mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a))))) | (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))), inference(lemma,lemma(discharge,[]))).
% 23.09/23.28 tff(8478,plain,
% 23.09/23.28 ((~(mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a))) | (~(mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a))))),
% 23.09/23.28 inference(unit_resolution,[status(thm)],[8477, 8406])).
% 23.09/23.28 tff(8479,plain,
% 23.09/23.28 (~((~(mult(mult(mult(b, c), a), b) = mult(mult(b, c), mult(a, b)))) | (~(mult(mult(mult(b, c), b), a) = mult(mult(b, c), mult(b, a)))))),
% 23.09/23.28 inference(unit_resolution,[status(thm)],[1205, 8478])).
% 23.09/23.28 tff(8480,plain,
% 23.09/23.28 (mult(mult(mult(b, c), a), b) = mult(mult(b, c), mult(a, b))),
% 23.09/23.28 inference(unit_resolution,[status(thm)],[1229, 8479])).
% 23.09/23.28 tff(8481,plain,
% 23.09/23.28 ((mult(mult(b, b), a) = mult(mult(b, a), b)) <=> (mult(mult(b, a), b) = mult(mult(b, b), a))),
% 23.09/23.28 inference(commutativity,[status(thm)],[])).
% 23.09/23.28 tff(8482,plain,
% 23.09/23.28 (mult(b, mult(b, a)) = mult(mult(b, a), b)),
% 23.09/23.28 inference(transitivity,[status(thm)],[1917, 6524, 6521, 6515])).
% 23.09/23.28 tff(8483,plain,
% 23.09/23.28 ((mult(mult(b, b), a) = mult(b, mult(b, a))) <=> (mult(mult(b, b), a) = mult(mult(b, a), b))),
% 23.09/23.28 inference(monotonicity,[status(thm)],[8482])).
% 23.09/23.28 tff(8484,plain,
% 23.09/23.28 ((mult(mult(b, b), a) = mult(b, mult(b, a))) <=> (mult(mult(b, a), b) = mult(mult(b, b), a))),
% 23.09/23.28 inference(transitivity,[status(thm)],[8483, 8481])).
% 23.09/23.28 tff(8485,plain,
% 23.09/23.28 ((mult(mult(b, a), b) = mult(mult(b, b), a)) <=> (mult(mult(b, b), a) = mult(b, mult(b, a)))),
% 23.09/23.28 inference(symmetry,[status(thm)],[8484])).
% 23.09/23.28 tff(8486,plain,
% 23.09/23.28 (mult(mult(b, b), a) = mult(b, mult(b, a))),
% 23.09/23.28 inference(modus_ponens,[status(thm)],[1937, 8485])).
% 23.09/23.28 tff(8487,plain,
% 23.09/23.28 ($false),
% 23.09/23.28 inference(unit_resolution,[status(thm)],[1526, 8486])).
% 23.09/23.28 tff(8488,plain,((mult(mult(b, b), a) = mult(b, mult(b, a))) | (~(mult(mult(c, b), mult(a, b)) = mult(c, mult(b, mult(a, b))))) | (~(mult(mult(mult(b, c), a), b) = mult(mult(b, c), mult(a, b))))), inference(lemma,lemma(discharge,[]))).
% 23.09/23.28 tff(8489,plain,
% 23.09/23.28 (~(mult(mult(c, b), mult(a, b)) = mult(c, mult(b, mult(a, b))))),
% 23.09/23.28 inference(unit_resolution,[status(thm)],[8488, 8480, 1526])).
% 23.09/23.28 tff(8490,assumption,((~(mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a))) | (~(mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a))))), introduced(assumption)).
% 23.09/23.28 tff(8491,plain,
% 23.09/23.28 (~((~(mult(mult(mult(b, c), a), b) = mult(mult(b, c), mult(a, b)))) | (~(mult(mult(mult(b, c), b), a) = mult(mult(b, c), mult(b, a)))))),
% 23.09/23.28 inference(unit_resolution,[status(thm)],[1205, 8490])).
% 23.09/23.28 tff(8492,plain,
% 23.09/23.28 (mult(mult(mult(b, c), b), a) = mult(mult(b, c), mult(b, a))),
% 23.09/23.28 inference(unit_resolution,[status(thm)],[1207, 8491])).
% 23.09/23.28 tff(8493,plain,
% 23.09/23.28 (mult(mult(b, c), mult(b, a)) = mult(mult(mult(b, c), b), a)),
% 23.09/23.28 inference(symmetry,[status(thm)],[8492])).
% 23.09/23.28 tff(8494,plain,
% 23.09/23.28 (mult(mult(mult(b, c), a), b) = mult(mult(b, c), mult(a, b))),
% 23.09/23.28 inference(unit_resolution,[status(thm)],[1229, 8491])).
% 23.09/23.28 tff(8495,plain,
% 23.09/23.28 (mult(mult(b, c), mult(a, b)) = mult(mult(mult(b, c), a), b)),
% 23.09/23.28 inference(symmetry,[status(thm)],[8494])).
% 23.09/23.28 tff(8496,plain,
% 23.09/23.28 ((mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a))) <=> (mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a))),
% 23.09/23.28 inference(monotonicity,[status(thm)],[8495, 8493])).
% 23.09/23.28 tff(8497,plain,
% 23.09/23.28 ((mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a)) <=> (mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a)))),
% 23.09/23.28 inference(symmetry,[status(thm)],[8496])).
% 23.09/23.28 tff(8498,assumption,(mult(mult(c, mult(a, b)), b) = mult(mult(c, b), mult(a, b))), introduced(assumption)).
% 23.09/23.28 tff(8499,plain,
% 23.09/23.28 (mult(mult(c, b), mult(a, b)) = mult(mult(c, mult(a, b)), b)),
% 23.09/23.28 inference(symmetry,[status(thm)],[8498])).
% 23.09/23.28 tff(8500,plain,
% 23.09/23.28 (mult(mult(mult(b, c), a), b) = mult(mult(unit, a), mult(mult(b, c), b))),
% 23.09/23.28 inference(transitivity,[status(thm)],[8494, 7119, 8499, 7117, 781, 779])).
% 23.09/23.28 tff(8501,plain,
% 23.09/23.28 ((mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a)) <=> (mult(mult(unit, a), mult(mult(b, c), b)) = mult(mult(unit, mult(mult(b, c), b)), a))),
% 23.09/23.28 inference(monotonicity,[status(thm)],[8500, 777])).
% 23.09/23.28 tff(8502,plain,
% 23.09/23.28 ((mult(mult(unit, a), mult(mult(b, c), b)) = mult(mult(unit, mult(mult(b, c), b)), a)) <=> (mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a))),
% 23.09/23.28 inference(symmetry,[status(thm)],[8501])).
% 23.09/23.28 tff(8503,plain,
% 23.09/23.28 ((mult(mult(unit, a), mult(mult(b, b), c)) = mult(mult(unit, mult(mult(b, b), c)), a)) <=> (mult(mult(unit, mult(mult(b, b), c)), a) = mult(mult(unit, a), mult(mult(b, b), c)))),
% 23.09/23.28 inference(commutativity,[status(thm)],[])).
% 23.09/23.28 tff(8504,plain,
% 23.09/23.28 ((~![A: $i] : (mult(unit, A) = A)) | (mult(unit, mult(mult(b, b), c)) = mult(mult(b, b), c))),
% 23.09/23.28 inference(quant_inst,[status(thm)],[])).
% 23.09/23.28 tff(8505,plain,
% 23.09/23.28 (mult(unit, mult(mult(b, b), c)) = mult(mult(b, b), c)),
% 23.09/23.28 inference(unit_resolution,[status(thm)],[8504, 71])).
% 23.09/23.28 tff(8506,plain,
% 23.09/23.28 (mult(unit, mult(mult(b, b), c)) = mult(mult(unit, mult(mult(b, unit), b)), c)),
% 23.09/23.28 inference(transitivity,[status(thm)],[8505, 7098])).
% 23.09/23.28 tff(8507,plain,
% 23.09/23.28 (mult(mult(unit, mult(mult(b, b), c)), a) = mult(mult(mult(unit, mult(mult(b, unit), b)), c), a)),
% 23.09/23.28 inference(monotonicity,[status(thm)],[8506])).
% 23.09/23.28 tff(8508,plain,
% 23.09/23.28 (mult(mult(mult(unit, mult(mult(b, unit), b)), c), a) = mult(mult(unit, mult(mult(b, b), c)), a)),
% 23.09/23.28 inference(symmetry,[status(thm)],[8507])).
% 23.09/23.28 tff(8509,plain,
% 23.09/23.28 (mult(mult(unit, mult(mult(b, unit), b)), c) = mult(mult(b, c), b)),
% 23.09/23.28 inference(transitivity,[status(thm)],[7097, 7104, 7101, 5563])).
% 23.09/23.28 tff(8510,plain,
% 23.09/23.28 (mult(mult(mult(unit, mult(mult(b, unit), b)), c), a) = mult(mult(mult(b, c), b), a)),
% 23.09/23.28 inference(monotonicity,[status(thm)],[8509])).
% 23.09/23.28 tff(8511,plain,
% 23.09/23.28 (mult(mult(mult(b, c), b), a) = mult(mult(mult(unit, mult(mult(b, unit), b)), c), a)),
% 23.09/23.28 inference(symmetry,[status(thm)],[8510])).
% 23.09/23.28 tff(8512,plain,
% 23.09/23.28 (mult(mult(unit, mult(mult(b, c), b)), a) = mult(mult(unit, mult(mult(b, b), c)), a)),
% 23.09/23.28 inference(transitivity,[status(thm)],[776, 8511, 8508])).
% 23.09/23.28 tff(8513,plain,
% 23.09/23.28 (mult(mult(unit, a), mult(mult(b, b), c)) = mult(a, mult(mult(unit, mult(mult(b, unit), b)), c))),
% 23.09/23.28 inference(monotonicity,[status(thm)],[244, 7098])).
% 23.09/23.28 tff(8514,plain,
% 23.09/23.28 (mult(a, mult(mult(unit, mult(mult(b, unit), b)), c)) = mult(mult(unit, a), mult(mult(b, b), c))),
% 23.09/23.28 inference(symmetry,[status(thm)],[8513])).
% 23.09/23.28 tff(8515,plain,
% 23.09/23.28 (mult(mult(unit, a), mult(mult(b, c), b)) = mult(mult(unit, a), mult(mult(b, b), c))),
% 23.09/23.28 inference(transitivity,[status(thm)],[778, 783, 827, 832, 892, 8514])).
% 23.09/23.28 tff(8516,plain,
% 23.09/23.28 ((mult(mult(unit, a), mult(mult(b, c), b)) = mult(mult(unit, mult(mult(b, c), b)), a)) <=> (mult(mult(unit, a), mult(mult(b, b), c)) = mult(mult(unit, mult(mult(b, b), c)), a))),
% 23.09/23.28 inference(monotonicity,[status(thm)],[8515, 8512])).
% 23.09/23.28 tff(8517,plain,
% 23.09/23.28 ((mult(mult(unit, a), mult(mult(b, c), b)) = mult(mult(unit, mult(mult(b, c), b)), a)) <=> (mult(mult(unit, mult(mult(b, b), c)), a) = mult(mult(unit, a), mult(mult(b, b), c)))),
% 23.09/23.28 inference(transitivity,[status(thm)],[8516, 8503])).
% 23.09/23.28 tff(8518,plain,
% 23.09/23.28 ((mult(mult(unit, mult(mult(b, b), c)), a) = mult(mult(unit, a), mult(mult(b, b), c))) <=> (mult(mult(unit, a), mult(mult(b, c), b)) = mult(mult(unit, mult(mult(b, c), b)), a))),
% 23.09/23.28 inference(symmetry,[status(thm)],[8517])).
% 23.09/23.28 tff(8519,plain,
% 23.09/23.28 ((mult(mult(unit, mult(mult(b, b), c)), a) = mult(mult(unit, a), mult(mult(b, b), c))) <=> (mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a)))),
% 23.09/23.28 inference(transitivity,[status(thm)],[8518, 8502, 8497])).
% 23.09/23.28 tff(8520,plain,
% 23.09/23.28 ((mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a)) <=> (mult(mult(unit, mult(mult(b, b), c)), a) = mult(mult(unit, a), mult(mult(b, b), c)))),
% 23.09/23.28 inference(transitivity,[status(thm)],[8501, 8517])).
% 23.09/23.28 tff(8521,plain,
% 23.09/23.28 (mult(mult(mult(b, c), a), b) = mult(mult(mult(a, b), c), b)),
% 23.09/23.28 inference(transitivity,[status(thm)],[1311, 7119, 8499, 7117])).
% 23.09/23.28 tff(8522,plain,
% 23.09/23.28 (rd(mult(mult(mult(b, c), a), b), b) = rd(mult(mult(mult(a, b), c), b), b)),
% 23.09/23.28 inference(monotonicity,[status(thm)],[8521])).
% 23.09/23.28 tff(8523,plain,
% 23.09/23.28 (mult(c, mult(b, a)) = mult(c, mult(a, b))),
% 23.09/23.28 inference(transitivity,[status(thm)],[4304, 2298, 7124, 8522, 793, 227, 6986, 4221])).
% 23.09/23.28 tff(8524,plain,
% 23.09/23.28 (ld(c, mult(c, mult(b, a))) = ld(c, mult(c, mult(a, b)))),
% 23.09/23.28 inference(monotonicity,[status(thm)],[8523])).
% 23.09/23.28 tff(8525,plain,
% 23.09/23.28 (mult(b, a) = mult(a, b)),
% 23.09/23.28 inference(transitivity,[status(thm)],[1473, 8524, 1468])).
% 23.09/23.28 tff(8526,plain,
% 23.09/23.28 (mult(mult(b, c), mult(b, a)) = mult(mult(b, c), mult(a, b))),
% 23.09/23.28 inference(monotonicity,[status(thm)],[8525])).
% 23.09/23.28 tff(8527,plain,
% 23.09/23.28 (mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a))),
% 23.09/23.28 inference(symmetry,[status(thm)],[8526])).
% 23.09/23.28 tff(8528,plain,
% 23.09/23.28 (mult(mult(c, b), mult(a, b)) = mult(mult(b, c), mult(a, b))),
% 23.09/23.28 inference(symmetry,[status(thm)],[7119])).
% 23.09/23.28 tff(8529,plain,
% 23.09/23.28 (mult(mult(unit, a), mult(mult(b, c), b)) = mult(mult(unit, mult(mult(b, c), b)), a)),
% 23.09/23.28 inference(transitivity,[status(thm)],[778, 783, 7446, 8498, 8528, 8527, 3107, 777])).
% 23.09/23.28 tff(8530,plain,
% 23.09/23.28 (mult(mult(unit, a), mult(mult(b, c), b)) = mult(mult(mult(b, c), a), b)),
% 23.09/23.28 inference(transitivity,[status(thm)],[778, 783, 7446, 8498, 8528, 1312])).
% 23.09/23.28 tff(8531,plain,
% 23.09/23.28 ((mult(mult(unit, a), mult(mult(b, c), b)) = mult(mult(unit, mult(mult(b, c), b)), a)) <=> (mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a))),
% 23.09/23.28 inference(monotonicity,[status(thm)],[8530, 776])).
% 23.09/23.28 tff(8532,plain,
% 23.09/23.28 ((mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a)) <=> (mult(mult(unit, a), mult(mult(b, c), b)) = mult(mult(unit, mult(mult(b, c), b)), a))),
% 23.09/23.28 inference(symmetry,[status(thm)],[8531])).
% 23.09/23.28 tff(8533,plain,
% 23.09/23.28 ((~(mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a))) <=> (~(mult(mult(unit, a), mult(mult(b, c), b)) = mult(mult(unit, mult(mult(b, c), b)), a)))),
% 23.09/23.28 inference(monotonicity,[status(thm)],[8532])).
% 23.09/23.28 tff(8534,plain,
% 23.09/23.28 (~(mult(mult(unit, a), mult(mult(b, c), b)) = mult(mult(unit, mult(mult(b, c), b)), a))),
% 23.09/23.28 inference(modus_ponens,[status(thm)],[6529, 8533])).
% 23.09/23.28 tff(8535,plain,
% 23.09/23.28 ($false),
% 23.09/23.28 inference(unit_resolution,[status(thm)],[8534, 8529])).
% 23.09/23.28 tff(8536,plain,((~(mult(mult(c, mult(a, b)), b) = mult(mult(c, b), mult(a, b)))) | (~(mult(mult(mult(b, c), b), a) = mult(mult(b, c), mult(b, a)))) | (~(mult(mult(mult(b, c), a), b) = mult(mult(b, c), mult(a, b)))) | (mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a))), inference(lemma,lemma(discharge,[]))).
% 23.09/23.28 tff(8537,plain,
% 23.09/23.28 (mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a)),
% 23.09/23.28 inference(unit_resolution,[status(thm)],[8536, 8498, 8494, 8492])).
% 23.09/23.28 tff(8538,plain,
% 23.09/23.28 (mult(mult(unit, mult(mult(b, b), c)), a) = mult(mult(unit, a), mult(mult(b, b), c))),
% 23.09/23.28 inference(modus_ponens,[status(thm)],[8537, 8520])).
% 23.09/23.28 tff(8539,plain,
% 23.09/23.28 (mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a))),
% 23.09/23.28 inference(modus_ponens,[status(thm)],[8538, 8519])).
% 23.09/23.28 tff(8540,plain,
% 23.09/23.28 (~(mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a)))),
% 23.09/23.28 inference(unit_resolution,[status(thm)],[8114, 8537, 8490])).
% 23.09/23.28 tff(8541,plain,
% 23.09/23.28 ($false),
% 23.09/23.28 inference(unit_resolution,[status(thm)],[8540, 8539])).
% 23.09/23.28 tff(8542,plain,((~(mult(mult(c, mult(a, b)), b) = mult(mult(c, b), mult(a, b)))) | (~((~(mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a))) | (~(mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a))))))), inference(lemma,lemma(discharge,[]))).
% 23.09/23.28 tff(8543,plain,
% 23.09/23.28 (~(mult(mult(c, mult(a, b)), b) = mult(mult(c, b), mult(a, b)))),
% 23.09/23.28 inference(unit_resolution,[status(thm)],[8542, 8478])).
% 23.09/23.28 tff(8544,plain,
% 23.09/23.28 ((~(mult(mult(c, mult(a, b)), b) = mult(mult(c, b), mult(a, b)))) | (~(mult(c, mult(mult(a, b), b)) = mult(c, mult(b, mult(a, b)))))),
% 23.09/23.28 inference(unit_resolution,[status(thm)],[7279, 8543])).
% 23.09/23.28 tff(8545,plain,
% 23.09/23.28 (~((~(mult(mult(c, b), mult(a, b)) = mult(c, mult(b, mult(a, b))))) | (~(mult(mult(c, mult(a, b)), b) = mult(c, mult(mult(a, b), b)))))),
% 23.09/23.28 inference(unit_resolution,[status(thm)],[7291, 8544])).
% 23.09/23.28 tff(8546,plain,
% 23.09/23.28 ($false),
% 23.09/23.28 inference(unit_resolution,[status(thm)],[7136, 8545, 8489])).
% 23.09/23.28 tff(8547,plain,((mult(mult(b, b), a) = mult(b, mult(b, a))) | (~(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))), inference(lemma,lemma(discharge,[]))).
% 23.09/23.28 tff(8548,plain,
% 23.09/23.28 (~(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))),
% 23.09/23.28 inference(unit_resolution,[status(thm)],[8547, 1526, 8318])).
% 23.09/23.28 tff(8549,plain,
% 23.09/23.28 (~(mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))),
% 23.09/23.28 inference(unit_resolution,[status(thm)],[306, 8548])).
% 23.09/23.28 tff(8550,plain,
% 23.09/23.28 ((~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))),
% 23.09/23.28 inference(unit_resolution,[status(thm)],[308, 8549])).
% 23.09/23.28 tff(8551,plain,
% 23.09/23.28 (~((~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))),
% 23.09/23.28 inference(unit_resolution,[status(thm)],[313, 8550])).
% 23.09/23.28 tff(8552,plain,
% 23.09/23.28 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))),
% 23.09/23.28 inference(unit_resolution,[status(thm)],[315, 8551])).
% 23.09/23.28 tff(8553,plain,
% 23.09/23.28 (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))),
% 23.09/23.28 inference(unit_resolution,[status(thm)],[8140, 8548, 8344])).
% 23.09/23.28 tff(8554,plain,
% 23.09/23.28 (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))),
% 23.09/23.28 inference(unit_resolution,[status(thm)],[8339, 8553, 1936])).
% 23.09/23.28 tff(8555,plain,
% 23.09/23.28 ($false),
% 23.09/23.28 inference(unit_resolution,[status(thm)],[6458, 8554, 8553, 8548, 8552])).
% 23.09/23.28 tff(8556,plain,((mult(mult(b, b), a) = mult(b, mult(b, a))) | (mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))), inference(lemma,lemma(discharge,[]))).
% 23.09/23.28 tff(8557,plain,
% 23.09/23.28 (mult(mult(b, b), a) = mult(b, mult(b, a))),
% 23.09/23.28 inference(unit_resolution,[status(thm)],[8556, 8318])).
% 23.09/23.28 tff(8558,plain,
% 23.09/23.28 (mult(b, mult(b, a)) = mult(mult(b, b), a)),
% 23.09/23.28 inference(symmetry,[status(thm)],[8557])).
% 23.09/23.28 tff(8559,plain,
% 23.09/23.28 (mult(b, mult(c, mult(a, c))) = mult(b, mult(mult(c, a), c))),
% 23.09/23.28 inference(monotonicity,[status(thm)],[3877])).
% 23.09/23.28 tff(8560,plain,
% 23.09/23.28 (mult(b, mult(mult(c, a), c)) = mult(b, mult(c, mult(a, c)))),
% 23.09/23.28 inference(symmetry,[status(thm)],[8559])).
% 23.09/23.28 tff(8561,plain,
% 23.09/23.28 (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))),
% 23.09/23.28 inference(unit_resolution,[status(thm)],[8162, 8344])).
% 23.09/23.28 tff(8562,plain,
% 23.09/23.28 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(b, c), c)),
% 23.09/23.28 inference(monotonicity,[status(thm)],[5651])).
% 23.09/23.28 tff(8563,plain,
% 23.09/23.28 ((mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c)))) <=> (mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c))),
% 23.09/23.29 inference(symmetry,[status(thm)],[5297])).
% 23.09/23.29 tff(8564,plain,
% 23.09/23.29 ((mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))) <=> (mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 23.09/23.29 inference(commutativity,[status(thm)],[])).
% 23.09/23.29 tff(8565,plain,
% 23.09/23.29 (mult(a, c) = mult(c, a)),
% 23.09/23.29 inference(transitivity,[status(thm)],[3873, 6890, 4266])).
% 23.09/23.29 tff(8566,plain,
% 23.09/23.29 (mult(mult(a, c), c) = mult(mult(c, a), c)),
% 23.09/23.29 inference(monotonicity,[status(thm)],[8565])).
% 23.09/23.29 tff(8567,plain,
% 23.09/23.29 (mult(mult(c, a), c) = mult(mult(a, c), c)),
% 23.09/23.29 inference(symmetry,[status(thm)],[8566])).
% 23.09/23.29 tff(8568,plain,
% 23.09/23.29 (mult(c, mult(a, c)) = mult(mult(a, c), c)),
% 23.09/23.29 inference(transitivity,[status(thm)],[3877, 8567])).
% 23.09/23.29 tff(8569,plain,
% 23.09/23.29 (mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c)))),
% 23.09/23.29 inference(monotonicity,[status(thm)],[8568])).
% 23.09/23.29 tff(8570,plain,
% 23.09/23.29 (mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))) = mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 23.09/23.29 inference(symmetry,[status(thm)],[8569])).
% 23.09/23.29 tff(8571,plain,
% 23.09/23.29 (mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(b, c))),
% 23.09/23.29 inference(monotonicity,[status(thm)],[5651])).
% 23.09/23.29 tff(8572,plain,
% 23.09/23.29 (mult(c, mult(b, c)) = mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 23.09/23.29 inference(symmetry,[status(thm)],[8571])).
% 23.09/23.29 tff(8573,plain,
% 23.09/23.29 (mult(mult(b, c), c) = ld(a, mult(a, mult(mult(b, c), c)))),
% 23.09/23.29 inference(symmetry,[status(thm)],[4173])).
% 23.09/23.29 tff(8574,plain,
% 23.09/23.29 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 23.09/23.29 inference(transitivity,[status(thm)],[8562, 8573, 4537, 4178, 8572])).
% 23.09/23.29 tff(8575,plain,
% 23.09/23.29 ((mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c)))) <=> (mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))))),
% 23.09/23.29 inference(monotonicity,[status(thm)],[8574, 8570])).
% 23.09/23.29 tff(8576,plain,
% 23.09/23.29 ((mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c)))) <=> (mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 23.09/23.29 inference(transitivity,[status(thm)],[8575, 8564])).
% 23.09/23.29 tff(8577,plain,
% 23.09/23.29 ((mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c))))) <=> (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))))),
% 23.09/23.29 inference(symmetry,[status(thm)],[8576])).
% 23.09/23.29 tff(8578,plain,
% 23.09/23.29 ((mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c))))) <=> (mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c))),
% 23.09/23.29 inference(transitivity,[status(thm)],[8577, 8563])).
% 23.09/23.29 tff(8579,plain,
% 23.09/23.29 (mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))),
% 23.09/23.29 inference(transitivity,[status(thm)],[8571, 2803])).
% 23.09/23.29 tff(8580,plain,
% 23.09/23.29 (mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c))) = mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 23.09/23.29 inference(symmetry,[status(thm)],[4375])).
% 23.09/23.29 tff(8581,plain,
% 23.09/23.29 (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))),
% 23.09/23.29 inference(unit_resolution,[status(thm)],[4385, 4375])).
% 23.09/23.29 tff(8582,plain,
% 23.09/23.29 (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(b, c))),
% 23.09/23.29 inference(transitivity,[status(thm)],[8581, 142])).
% 23.09/23.29 tff(8583,plain,
% 23.09/23.29 (ld(a, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))) = ld(a, mult(a, mult(b, c)))),
% 23.09/23.29 inference(monotonicity,[status(thm)],[8582])).
% 23.09/23.29 tff(8584,plain,
% 23.09/23.29 (mult(mult(a, c), rd(mult(b, c), mult(a, c))) = mult(b, c)),
% 23.09/23.29 inference(transitivity,[status(thm)],[5650, 8583, 141])).
% 23.09/23.29 tff(8585,plain,
% 23.09/23.29 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(b, c), c)),
% 23.09/23.29 inference(monotonicity,[status(thm)],[8584])).
% 23.09/23.29 tff(8586,assumption,(ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(c, a))) = mult(c, a)), introduced(assumption)).
% 23.09/23.29 tff(8587,plain,
% 23.09/23.29 (mult(a, c) = mult(c, a)),
% 23.09/23.29 inference(transitivity,[status(thm)],[3873, 6890, 8586])).
% 23.09/23.29 tff(8588,plain,
% 23.09/23.29 (mult(mult(a, c), c) = mult(mult(c, a), c)),
% 23.09/23.29 inference(monotonicity,[status(thm)],[8587])).
% 23.09/23.29 tff(8589,plain,
% 23.09/23.29 (mult(mult(c, a), c) = mult(mult(a, c), c)),
% 23.09/23.29 inference(symmetry,[status(thm)],[8588])).
% 23.09/23.29 tff(8590,plain,
% 23.09/23.29 (mult(c, mult(a, c)) = mult(mult(a, c), c)),
% 23.09/23.29 inference(transitivity,[status(thm)],[3877, 8589])).
% 23.09/23.29 tff(8591,plain,
% 23.09/23.29 (mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c)))),
% 23.09/23.29 inference(monotonicity,[status(thm)],[8590])).
% 23.09/23.29 tff(8592,plain,
% 23.09/23.29 (mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))) = mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 23.09/23.29 inference(symmetry,[status(thm)],[8591])).
% 23.09/23.29 tff(8593,plain,
% 23.09/23.29 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 23.09/23.29 inference(transitivity,[status(thm)],[8585, 8573, 4537, 4178, 2803, 8580])).
% 23.09/23.29 tff(8594,plain,
% 23.09/23.29 ((mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c)))) <=> (mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))))),
% 23.09/23.29 inference(monotonicity,[status(thm)],[8593, 8592])).
% 23.09/23.29 tff(8595,plain,
% 23.09/23.29 ((mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c)))) <=> (mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 23.09/23.29 inference(transitivity,[status(thm)],[8594, 8564])).
% 23.09/23.29 tff(8596,plain,
% 23.09/23.29 ((mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c))))) <=> (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))))),
% 23.09/23.29 inference(symmetry,[status(thm)],[8595])).
% 23.09/23.29 tff(8597,plain,
% 23.09/23.29 ((~(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) <=> (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c)))))),
% 23.09/23.29 inference(monotonicity,[status(thm)],[8596])).
% 23.09/23.29 tff(8598,assumption,(~(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))), introduced(assumption)).
% 23.09/23.29 tff(8599,plain,
% 23.09/23.29 (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))))),
% 23.09/23.29 inference(modus_ponens,[status(thm)],[8598, 8597])).
% 23.09/23.29 tff(8600,plain,
% 23.09/23.29 ((~(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c)))))),
% 23.09/23.29 inference(unit_resolution,[status(thm)],[4596, 8599])).
% 23.09/23.29 tff(8601,plain,
% 23.09/23.29 (~((~(mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)))))),
% 23.09/23.29 inference(unit_resolution,[status(thm)],[4594, 8600])).
% 23.09/23.29 tff(8602,plain,
% 23.09/23.29 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c))),
% 23.09/23.29 inference(unit_resolution,[status(thm)],[5311, 8601])).
% 23.09/23.29 tff(8603,plain,
% 23.09/23.29 (mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)),
% 23.09/23.29 inference(symmetry,[status(thm)],[8602])).
% 23.09/23.29 tff(8604,plain,
% 23.09/23.29 (ld(a, mult(a, mult(b, c))) = ld(a, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 23.09/23.29 inference(symmetry,[status(thm)],[8583])).
% 23.09/23.29 tff(8605,plain,
% 23.09/23.29 (mult(c, a) = ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(c, a)))),
% 23.09/23.29 inference(symmetry,[status(thm)],[8586])).
% 23.09/23.29 tff(8606,plain,
% 23.09/23.29 (mult(c, a) = mult(a, c)),
% 23.09/23.29 inference(transitivity,[status(thm)],[8605, 4263, 3872])).
% 23.09/23.29 tff(8607,plain,
% 23.09/23.29 (mult(mult(c, a), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))),
% 23.09/23.29 inference(monotonicity,[status(thm)],[8606])).
% 23.09/23.29 tff(8608,plain,
% 23.09/23.29 (mult(mult(c, a), rd(mult(b, c), mult(a, c))) = mult(b, c)),
% 23.09/23.29 inference(transitivity,[status(thm)],[8607, 5650, 8583, 141])).
% 23.09/23.29 tff(8609,plain,
% 23.09/23.29 (mult(mult(mult(c, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(b, c), a)),
% 23.09/23.29 inference(monotonicity,[status(thm)],[8608])).
% 23.09/23.29 tff(8610,plain,
% 23.09/23.29 (mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), a)) = mult(c, mult(b, a))),
% 23.09/23.29 inference(transitivity,[status(thm)],[5404, 8609, 3057, 4208])).
% 23.09/23.29 tff(8611,plain,
% 23.09/23.29 (ld(c, mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), a))) = ld(c, mult(c, mult(b, a)))),
% 23.09/23.29 inference(monotonicity,[status(thm)],[8610])).
% 23.09/23.29 tff(8612,plain,
% 23.09/23.29 (mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(b, a)),
% 23.09/23.29 inference(transitivity,[status(thm)],[5409, 8611, 1472])).
% 23.09/23.29 tff(8613,plain,
% 23.09/23.29 (rd(mult(mult(a, rd(mult(b, c), mult(a, c))), a), a) = rd(mult(b, a), a)),
% 23.09/23.29 inference(monotonicity,[status(thm)],[8612])).
% 23.09/23.29 tff(8614,plain,
% 23.09/23.29 (mult(a, rd(mult(b, c), mult(a, c))) = b),
% 23.09/23.29 inference(transitivity,[status(thm)],[1456, 8613, 1451])).
% 23.09/23.29 tff(8615,plain,
% 23.09/23.29 (mult(mult(a, rd(mult(b, c), mult(a, c))), c) = mult(b, c)),
% 23.09/23.29 inference(monotonicity,[status(thm)],[8614])).
% 23.09/23.29 tff(8616,plain,
% 23.09/23.29 (mult(a, mult(rd(mult(b, c), mult(a, c)), c)) = mult(a, mult(c, rd(mult(b, c), mult(a, c))))),
% 23.09/23.29 inference(transitivity,[status(thm)],[5116, 6622, 6620, 8615, 843, 8604, 4336, 2167, 4851, 4850, 2171, 2699, 6696])).
% 23.09/23.29 tff(8617,plain,
% 23.09/23.29 (ld(a, mult(a, mult(rd(mult(b, c), mult(a, c)), c))) = ld(a, mult(a, mult(c, rd(mult(b, c), mult(a, c)))))),
% 23.09/23.29 inference(monotonicity,[status(thm)],[8616])).
% 23.09/23.29 tff(8618,plain,
% 23.09/23.29 (ld(a, mult(a, mult(c, rd(mult(b, c), mult(a, c))))) = ld(a, mult(a, mult(rd(mult(b, c), mult(a, c)), c)))),
% 23.09/23.29 inference(symmetry,[status(thm)],[8617])).
% 23.09/23.29 tff(8619,plain,
% 23.09/23.29 (mult(c, rd(mult(b, c), mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), c)),
% 23.09/23.29 inference(transitivity,[status(thm)],[5202, 8618, 5127])).
% 23.09/23.29 tff(8620,plain,
% 23.09/23.29 (mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c))),
% 23.09/23.29 inference(monotonicity,[status(thm)],[8619])).
% 23.09/23.29 tff(8621,plain,
% 23.09/23.29 (mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))),
% 23.09/23.29 inference(unit_resolution,[status(thm)],[4582, 8601])).
% 23.09/23.29 tff(8622,plain,
% 23.09/23.29 (mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 23.09/23.29 inference(transitivity,[status(thm)],[8591, 8621, 8620, 8603, 8585, 8573, 4537, 4178, 2803, 8580])).
% 23.09/23.29 tff(8623,plain,
% 23.09/23.29 ($false),
% 23.09/23.29 inference(unit_resolution,[status(thm)],[8598, 8622])).
% 23.09/23.29 tff(8624,plain,((~(ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(c, a))) = mult(c, a))) | (mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c))))) | (~(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)))) | (~(mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))))), inference(lemma,lemma(discharge,[]))).
% 23.09/23.29 tff(8625,plain,
% 23.09/23.29 (mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 23.09/23.29 inference(unit_resolution,[status(thm)],[8624, 8579, 4266, 6621, 2699])).
% 23.09/23.29 tff(8626,plain,
% 23.09/23.29 (mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)),
% 23.09/23.29 inference(modus_ponens,[status(thm)],[8625, 8578])).
% 23.09/23.29 tff(8627,plain,
% 23.09/23.29 (mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(b, c), c)),
% 23.09/23.29 inference(transitivity,[status(thm)],[2815, 8569, 8626, 8562])).
% 23.09/23.29 tff(8628,plain,
% 23.09/23.29 (mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))) = mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(b, c), c))),
% 23.09/23.29 inference(monotonicity,[status(thm)],[8627])).
% 23.09/23.29 tff(8629,plain,
% 23.09/23.29 (mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(b, c), c)) = mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 23.09/23.29 inference(symmetry,[status(thm)],[8628])).
% 23.09/23.29 tff(8630,plain,
% 23.09/23.29 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(b, c), c), a), a) = mult(mult(b, c), c))),
% 23.09/23.29 inference(quant_inst,[status(thm)],[])).
% 23.09/23.29 tff(8631,plain,
% 23.09/23.29 (rd(mult(mult(mult(b, c), c), a), a) = mult(mult(b, c), c)),
% 23.09/23.29 inference(unit_resolution,[status(thm)],[8630, 168])).
% 23.09/23.29 tff(8632,plain,
% 23.09/23.29 (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(b, c), a), c)),
% 23.09/23.29 inference(monotonicity,[status(thm)],[8327])).
% 23.09/23.29 tff(8633,plain,
% 23.09/23.29 (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(b, c), c), a)),
% 23.09/23.29 inference(monotonicity,[status(thm)],[8562])).
% 23.09/23.29 tff(8634,plain,
% 23.09/23.29 ((mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c)) <=> (mult(mult(mult(b, c), c), a) = mult(mult(mult(b, c), a), c))),
% 23.09/23.29 inference(monotonicity,[status(thm)],[8633, 8632])).
% 23.09/23.29 tff(8635,plain,
% 23.09/23.29 (mult(mult(mult(b, c), c), a) = mult(mult(mult(b, c), a), c)),
% 23.09/23.29 inference(modus_ponens,[status(thm)],[7692, 8634])).
% 23.09/23.29 tff(8636,plain,
% 23.09/23.29 (mult(mult(a, c), b) = mult(mult(c, a), b)),
% 23.09/23.29 inference(symmetry,[status(thm)],[4269])).
% 23.09/23.29 tff(8637,plain,
% 23.09/23.29 (mult(mult(c, a), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))),
% 23.09/23.29 inference(monotonicity,[status(thm)],[4268])).
% 23.09/23.29 tff(8638,plain,
% 23.09/23.29 (mult(mult(c, a), rd(mult(b, c), mult(a, c))) = mult(b, c)),
% 23.09/23.29 inference(transitivity,[status(thm)],[8637, 5650, 1490, 141])).
% 23.09/23.29 tff(8639,plain,
% 23.09/23.29 (mult(mult(mult(c, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(b, c), a)),
% 23.09/23.29 inference(monotonicity,[status(thm)],[8638])).
% 23.09/23.29 tff(8640,plain,
% 23.09/23.29 (mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), a)) = mult(c, mult(b, a))),
% 23.09/23.29 inference(transitivity,[status(thm)],[5404, 8639, 3057, 4208])).
% 23.09/23.29 tff(8641,plain,
% 23.09/23.29 (ld(c, mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), a))) = ld(c, mult(c, mult(b, a)))),
% 23.09/23.29 inference(monotonicity,[status(thm)],[8640])).
% 23.09/23.29 tff(8642,plain,
% 23.09/23.29 (mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(b, a)),
% 23.09/23.29 inference(transitivity,[status(thm)],[5409, 8641, 1472])).
% 23.09/23.29 tff(8643,plain,
% 23.09/23.29 (rd(mult(mult(a, rd(mult(b, c), mult(a, c))), a), a) = rd(mult(b, a), a)),
% 23.09/23.29 inference(monotonicity,[status(thm)],[8642])).
% 23.09/23.29 tff(8644,plain,
% 23.09/23.29 (mult(a, rd(mult(b, c), mult(a, c))) = b),
% 23.09/23.29 inference(transitivity,[status(thm)],[1456, 8643, 1451])).
% 23.09/23.29 tff(8645,plain,
% 23.09/23.29 (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), b)),
% 23.09/23.29 inference(monotonicity,[status(thm)],[8644])).
% 23.09/23.29 tff(8646,plain,
% 23.09/23.29 ((mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))) <=> (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))))),
% 23.09/23.29 inference(symmetry,[status(thm)],[4516])).
% 23.09/23.29 tff(8647,plain,
% 23.09/23.29 ((mult(mult(unit, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(unit, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c))) <=> (mult(mult(unit, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(mult(unit, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.09/23.29 inference(commutativity,[status(thm)],[])).
% 23.09/23.29 tff(8648,plain,
% 23.09/23.29 (mult(mult(mult(unit, mult(a, rd(mult(b, c), mult(a, c)))), unit), mult(a, c)) = mult(mult(unit, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c))),
% 23.09/23.30 inference(symmetry,[status(thm)],[6673])).
% 23.09/23.30 tff(8649,plain,
% 23.09/23.30 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(mult(unit, mult(a, rd(mult(b, c), mult(a, c)))), unit), mult(a, c))),
% 23.09/23.30 inference(symmetry,[status(thm)],[6671])).
% 23.09/23.30 tff(8650,plain,
% 23.09/23.30 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(unit, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c))),
% 23.09/23.30 inference(transitivity,[status(thm)],[8649, 8648])).
% 23.09/23.30 tff(8651,plain,
% 23.09/23.30 (mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(unit, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c))))),
% 23.09/23.30 inference(transitivity,[status(thm)],[8263, 5709, 6680])).
% 23.09/23.30 tff(8652,plain,
% 23.09/23.30 ((mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))) <=> (mult(mult(unit, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(unit, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c)))),
% 23.09/23.30 inference(monotonicity,[status(thm)],[8651, 8650])).
% 23.09/23.30 tff(8653,plain,
% 23.09/23.30 ((mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))) <=> (mult(mult(unit, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(mult(unit, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.09/23.30 inference(transitivity,[status(thm)],[8652, 8647])).
% 23.09/23.30 tff(8654,plain,
% 23.09/23.30 ((mult(mult(unit, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(mult(unit, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c))))) <=> (mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 23.09/23.30 inference(symmetry,[status(thm)],[8653])).
% 23.09/23.30 tff(8655,plain,
% 23.09/23.30 (mult(mult(a, c), b) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))),
% 23.09/23.30 inference(symmetry,[status(thm)],[8645])).
% 23.09/23.30 tff(8656,plain,
% 23.09/23.30 (mult(mult(unit, mult(a, c)), b) = mult(mult(unit, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c))))),
% 23.09/23.30 inference(transitivity,[status(thm)],[5506, 8655, 6680])).
% 23.09/23.30 tff(8657,plain,
% 23.09/23.30 (rd(mult(b, a), a) = rd(mult(mult(a, rd(mult(b, c), mult(a, c))), a), a)),
% 23.09/23.30 inference(symmetry,[status(thm)],[8643])).
% 23.09/23.30 tff(8658,plain,
% 23.09/23.30 (b = rd(mult(b, a), a)),
% 23.09/23.30 inference(symmetry,[status(thm)],[1451])).
% 23.09/23.30 tff(8659,plain,
% 23.09/23.30 (b = mult(a, rd(mult(b, c), mult(a, c)))),
% 23.09/23.30 inference(transitivity,[status(thm)],[8658, 8657, 1455])).
% 23.09/23.30 tff(8660,plain,
% 23.09/23.30 (mult(b, mult(a, c)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))),
% 23.09/23.30 inference(monotonicity,[status(thm)],[8659])).
% 23.09/23.30 tff(8661,plain,
% 23.09/23.30 (mult(mult(unit, b), mult(a, c)) = mult(mult(unit, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c))),
% 23.09/23.30 inference(transitivity,[status(thm)],[5511, 8660, 8649, 8648])).
% 23.09/23.30 tff(8662,plain,
% 23.09/23.30 ((mult(mult(unit, b), mult(a, c)) = mult(mult(unit, mult(a, c)), b)) <=> (mult(mult(unit, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(mult(unit, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.09/23.30 inference(monotonicity,[status(thm)],[8661, 8656])).
% 23.09/23.30 tff(8663,plain,
% 23.09/23.30 ((mult(mult(unit, b), mult(a, c)) = mult(mult(unit, mult(a, c)), b)) <=> (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))))),
% 23.09/23.30 inference(transitivity,[status(thm)],[8662, 8654, 8646])).
% 23.09/23.30 tff(8664,plain,
% 23.09/23.30 ((mult(mult(unit, mult(a, c)), b) = mult(mult(unit, b), mult(a, c))) <=> (mult(mult(unit, b), mult(a, c)) = mult(mult(unit, mult(a, c)), b))),
% 23.09/23.30 inference(commutativity,[status(thm)],[])).
% 23.09/23.30 tff(8665,plain,
% 23.09/23.30 (mult(b, mult(a, c)) = mult(mult(unit, b), mult(a, c))),
% 23.09/23.30 inference(symmetry,[status(thm)],[5511])).
% 23.09/23.30 tff(8666,plain,
% 23.09/23.30 (mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), a)) = mult(c, mult(b, a))),
% 23.09/23.30 inference(transitivity,[status(thm)],[5404, 6349, 8327, 3057, 4208])).
% 23.09/23.30 tff(8667,plain,
% 23.09/23.30 (ld(c, mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), a))) = ld(c, mult(c, mult(b, a)))),
% 23.09/23.30 inference(monotonicity,[status(thm)],[8666])).
% 23.09/23.30 tff(8668,plain,
% 23.09/23.30 (mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(b, a)),
% 23.09/23.30 inference(transitivity,[status(thm)],[5409, 8667, 1472])).
% 23.09/23.30 tff(8669,plain,
% 23.09/23.30 (rd(mult(mult(a, rd(mult(b, c), mult(a, c))), a), a) = rd(mult(b, a), a)),
% 23.09/23.30 inference(monotonicity,[status(thm)],[8668])).
% 23.09/23.30 tff(8670,plain,
% 23.09/23.30 (mult(a, rd(mult(b, c), mult(a, c))) = b),
% 23.09/23.30 inference(transitivity,[status(thm)],[1456, 8669, 1451])).
% 23.09/23.30 tff(8671,plain,
% 23.09/23.30 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(b, mult(a, c))),
% 23.09/23.30 inference(monotonicity,[status(thm)],[8670])).
% 23.09/23.30 tff(8672,plain,
% 23.09/23.30 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(unit, b), mult(a, c))),
% 23.09/23.30 inference(transitivity,[status(thm)],[8671, 8665])).
% 23.09/23.30 tff(8673,plain,
% 23.09/23.30 (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), b)),
% 23.09/23.30 inference(monotonicity,[status(thm)],[8670])).
% 23.09/23.30 tff(8674,plain,
% 23.09/23.30 (mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(unit, mult(a, c)), b)),
% 23.09/23.30 inference(transitivity,[status(thm)],[8263, 5709, 8673, 5517])).
% 23.09/23.30 tff(8675,plain,
% 23.09/23.30 ((mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))) <=> (mult(mult(unit, mult(a, c)), b) = mult(mult(unit, b), mult(a, c)))),
% 23.09/23.30 inference(monotonicity,[status(thm)],[8674, 8672])).
% 23.09/23.30 tff(8676,plain,
% 23.09/23.30 ((mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))) <=> (mult(mult(unit, b), mult(a, c)) = mult(mult(unit, mult(a, c)), b))),
% 23.09/23.30 inference(transitivity,[status(thm)],[8675, 8664])).
% 23.09/23.30 tff(8677,plain,
% 23.09/23.30 ((mult(mult(unit, b), mult(a, c)) = mult(mult(unit, mult(a, c)), b)) <=> (mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 23.09/23.30 inference(symmetry,[status(thm)],[8676])).
% 23.09/23.30 tff(8678,plain,
% 23.09/23.30 ((~(mult(mult(unit, b), mult(a, c)) = mult(mult(unit, mult(a, c)), b))) <=> (~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))))),
% 23.09/23.30 inference(monotonicity,[status(thm)],[8677])).
% 23.09/23.30 tff(8679,plain,
% 23.09/23.30 (~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 23.09/23.30 inference(modus_ponens,[status(thm)],[5524, 8678])).
% 23.09/23.30 tff(8680,plain,
% 23.09/23.30 ((~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))),
% 23.09/23.30 inference(unit_resolution,[status(thm)],[6389, 8679])).
% 23.09/23.30 tff(8681,plain,
% 23.09/23.30 (mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, b), c)),
% 23.09/23.30 inference(transitivity,[status(thm)],[8263, 5709, 8673, 161])).
% 23.09/23.30 tff(8682,plain,
% 23.09/23.30 ((mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))) <=> (mult(mult(a, b), c) = mult(a, mult(b, c)))),
% 23.09/23.30 inference(monotonicity,[status(thm)],[8681, 1489])).
% 23.09/23.30 tff(8683,plain,
% 23.09/23.30 ((mult(mult(a, b), c) = mult(a, mult(b, c))) <=> (mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 23.09/23.30 inference(symmetry,[status(thm)],[8682])).
% 23.09/23.30 tff(8684,plain,
% 23.09/23.30 ((~(mult(mult(a, b), c) = mult(a, mult(b, c)))) <=> (~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))),
% 23.09/23.30 inference(monotonicity,[status(thm)],[8683])).
% 23.09/23.30 tff(8685,plain,
% 23.09/23.30 (~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 23.09/23.30 inference(modus_ponens,[status(thm)],[146, 8684])).
% 23.09/23.30 tff(8686,plain,
% 23.09/23.30 ((~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))),
% 23.09/23.30 inference(unit_resolution,[status(thm)],[280, 8685])).
% 23.09/23.30 tff(8687,plain,
% 23.09/23.30 ($false),
% 23.09/23.30 inference(unit_resolution,[status(thm)],[276, 8686, 8680])).
% 23.09/23.30 tff(8688,plain,((~(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (mult(mult(unit, b), mult(a, c)) = mult(mult(unit, mult(a, c)), b))), inference(lemma,lemma(discharge,[]))).
% 23.09/23.30 tff(8689,plain,
% 23.09/23.30 (mult(mult(unit, b), mult(a, c)) = mult(mult(unit, mult(a, c)), b)),
% 23.09/23.30 inference(unit_resolution,[status(thm)],[8688, 1488])).
% 23.09/23.30 tff(8690,plain,
% 23.09/23.30 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 23.09/23.30 inference(modus_ponens,[status(thm)],[8689, 8663])).
% 23.09/23.30 tff(8691,plain,
% 23.09/23.30 (mult(b, mult(a, c)) = mult(b, mult(c, a))),
% 23.09/23.30 inference(monotonicity,[status(thm)],[6891])).
% 23.09/23.30 tff(8692,plain,
% 23.09/23.30 (mult(b, mult(c, a)) = mult(b, mult(a, c))),
% 23.09/23.30 inference(symmetry,[status(thm)],[8691])).
% 23.09/23.30 tff(8693,plain,
% 23.09/23.30 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(b, mult(a, c))),
% 23.09/23.30 inference(transitivity,[status(thm)],[4298, 1332, 2283, 8692])).
% 23.09/23.30 tff(8694,plain,
% 23.09/23.30 (rd(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)), mult(a, c)) = rd(mult(b, mult(a, c)), mult(a, c))),
% 23.09/23.30 inference(monotonicity,[status(thm)],[8693])).
% 23.09/23.30 tff(8695,plain,
% 23.09/23.30 (mult(rd(mult(b, c), mult(a, c)), a) = b),
% 23.09/23.30 inference(transitivity,[status(thm)],[8420, 8694, 8410])).
% 23.09/23.30 tff(8696,plain,
% 23.09/23.30 (mult(mult(rd(mult(b, c), mult(a, c)), a), c) = mult(b, c)),
% 23.09/23.30 inference(monotonicity,[status(thm)],[8695])).
% 23.09/23.30 tff(8697,plain,
% 23.09/23.30 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a) = mult(mult(b, c), a)),
% 23.09/23.30 inference(monotonicity,[status(thm)],[8696])).
% 23.09/23.30 tff(8698,plain,
% 23.09/23.30 (mult(mult(b, c), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a)),
% 23.09/23.30 inference(symmetry,[status(thm)],[8697])).
% 23.09/23.30 tff(8699,plain,
% 23.09/23.30 (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))),
% 23.09/23.30 inference(transitivity,[status(thm)],[1332, 8698, 1168])).
% 23.09/23.30 tff(8700,plain,
% 23.09/23.30 ($false),
% 23.09/23.30 inference(unit_resolution,[status(thm)],[1364, 8699])).
% 23.09/23.30 tff(8701,plain,((~(mult(mult(b, c), a) = mult(b, mult(c, a)))) | (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))), inference(lemma,lemma(discharge,[]))).
% 23.09/23.30 tff(8702,plain,
% 23.09/23.30 (~(mult(mult(b, c), a) = mult(b, mult(c, a)))),
% 23.09/23.30 inference(unit_resolution,[status(thm)],[8701, 1364])).
% 23.09/23.30 tff(8703,plain,
% 23.09/23.30 ((~(mult(mult(b, a), c) = mult(b, mult(a, c)))) | (~(mult(mult(b, c), a) = mult(b, mult(c, a))))),
% 23.09/23.30 inference(unit_resolution,[status(thm)],[2277, 8702])).
% 23.09/23.30 tff(8704,plain,
% 23.09/23.30 (~((~(mult(mult(b, a), c) = mult(mult(b, c), a))) | (~(mult(b, mult(a, c)) = mult(b, mult(c, a)))))),
% 23.09/23.30 inference(unit_resolution,[status(thm)],[2275, 8703])).
% 23.09/23.30 tff(8705,plain,
% 23.09/23.30 (mult(b, mult(a, c)) = mult(b, mult(c, a))),
% 23.09/23.30 inference(unit_resolution,[status(thm)],[2270, 8704])).
% 23.09/23.30 tff(8706,plain,
% 23.09/23.30 (mult(b, mult(c, a)) = mult(b, mult(a, c))),
% 23.09/23.30 inference(symmetry,[status(thm)],[8705])).
% 23.09/23.30 tff(8707,plain,
% 23.09/23.30 (mult(b, mult(c, a)) = mult(c, mult(a, b))),
% 23.09/23.30 inference(transitivity,[status(thm)],[8706, 8660, 8690, 8263, 5709, 8645, 8636, 4221])).
% 23.09/23.30 tff(8708,plain,
% 23.09/23.30 (mult(mult(b, c), a) = mult(c, mult(b, a))),
% 23.09/23.30 inference(transitivity,[status(thm)],[3057, 4208])).
% 23.09/23.30 tff(8709,plain,
% 23.09/23.30 ((mult(mult(b, c), a) = mult(b, mult(c, a))) <=> (mult(c, mult(b, a)) = mult(c, mult(a, b)))),
% 23.09/23.30 inference(monotonicity,[status(thm)],[8708, 8707])).
% 23.09/23.30 tff(8710,plain,
% 23.09/23.30 ((~(mult(mult(b, c), a) = mult(b, mult(c, a)))) <=> (~(mult(c, mult(b, a)) = mult(c, mult(a, b))))),
% 23.09/23.30 inference(monotonicity,[status(thm)],[8709])).
% 23.09/23.30 tff(8711,plain,
% 23.09/23.30 (~(mult(c, mult(b, a)) = mult(c, mult(a, b)))),
% 23.09/23.30 inference(modus_ponens,[status(thm)],[8702, 8710])).
% 23.09/23.30 tff(8712,plain,
% 23.09/23.30 (mult(b, mult(c, a)) = mult(mult(a, c), b)),
% 23.09/23.30 inference(transitivity,[status(thm)],[2262, 8660, 8690, 8263, 5709, 8645])).
% 23.09/23.30 tff(8713,plain,
% 23.09/23.30 (mult(c, mult(b, mult(c, a))) = mult(c, mult(mult(a, c), b))),
% 23.09/23.30 inference(monotonicity,[status(thm)],[8712])).
% 23.09/23.30 tff(8714,plain,
% 23.09/23.30 (mult(c, mult(b, mult(a, c))) = mult(c, mult(b, mult(c, a)))),
% 23.09/23.30 inference(monotonicity,[status(thm)],[2261])).
% 23.09/23.30 tff(8715,plain,
% 23.09/23.30 (mult(c, mult(b, mult(c, a))) = mult(c, mult(b, mult(a, c)))),
% 23.09/23.30 inference(symmetry,[status(thm)],[8714])).
% 23.09/23.30 tff(8716,plain,
% 23.09/23.30 (mult(mult(b, c), mult(a, c)) = mult(mult(c, b), mult(a, c))),
% 23.09/23.30 inference(monotonicity,[status(thm)],[1399])).
% 23.09/23.30 tff(8717,plain,
% 23.09/23.30 (mult(mult(b, c), mult(c, a)) = mult(mult(b, c), mult(a, c))),
% 23.09/23.30 inference(monotonicity,[status(thm)],[4268])).
% 23.09/23.30 tff(8718,plain,
% 23.09/23.30 (mult(mult(c, b), mult(c, a)) = mult(mult(c, b), mult(a, c))),
% 23.09/23.30 inference(transitivity,[status(thm)],[2231, 8717, 8716])).
% 23.09/23.30 tff(8719,plain,
% 23.09/23.30 ((mult(mult(c, b), mult(c, a)) = mult(c, mult(b, mult(c, a)))) <=> (mult(mult(c, b), mult(a, c)) = mult(c, mult(b, mult(a, c))))),
% 23.09/23.30 inference(monotonicity,[status(thm)],[8718, 8715])).
% 23.09/23.30 tff(8720,plain,
% 23.09/23.30 (mult(mult(c, b), mult(a, c)) = mult(c, mult(b, mult(a, c)))),
% 23.09/23.30 inference(modus_ponens,[status(thm)],[6922, 8719])).
% 23.09/23.30 tff(8721,plain,
% 23.09/23.30 (mult(mult(c, a), mult(a, c)) = mult(mult(a, c), mult(a, c))),
% 23.09/23.30 inference(monotonicity,[status(thm)],[4268])).
% 23.09/23.30 tff(8722,plain,
% 23.09/23.30 (mult(mult(a, c), mult(c, a)) = mult(mult(a, c), mult(a, c))),
% 23.09/23.30 inference(monotonicity,[status(thm)],[4268])).
% 23.09/23.30 tff(8723,plain,
% 23.09/23.30 (mult(mult(a, c), mult(a, c)) = mult(mult(a, c), mult(c, a))),
% 23.09/23.30 inference(symmetry,[status(thm)],[8722])).
% 23.09/23.30 tff(8724,plain,
% 23.09/23.30 (mult(mult(c, a), mult(a, c)) = mult(mult(a, c), mult(c, a))),
% 23.09/23.30 inference(transitivity,[status(thm)],[8721, 8723])).
% 23.09/23.30 tff(8725,plain,
% 23.09/23.30 (mult(mult(a, c), c) = mult(c, mult(a, c))),
% 23.09/23.30 inference(transitivity,[status(thm)],[8566, 2690])).
% 23.09/23.30 tff(8726,plain,
% 23.09/23.30 (mult(mult(mult(a, c), c), a) = mult(mult(c, mult(a, c)), a)),
% 23.09/23.30 inference(monotonicity,[status(thm)],[8725])).
% 23.09/23.30 tff(8727,plain,
% 23.09/23.30 (mult(mult(c, mult(a, c)), a) = mult(mult(mult(a, c), c), a)),
% 23.09/23.30 inference(symmetry,[status(thm)],[8726])).
% 23.09/23.30 tff(8728,plain,
% 23.09/23.30 ((mult(mult(c, mult(a, c)), a) = mult(mult(c, a), mult(a, c))) <=> (mult(mult(mult(a, c), c), a) = mult(mult(a, c), mult(c, a)))),
% 23.09/23.30 inference(monotonicity,[status(thm)],[8727, 8724])).
% 23.09/23.30 tff(8729,plain,
% 23.09/23.30 ((mult(mult(mult(a, c), c), a) = mult(mult(a, c), mult(c, a))) <=> (mult(mult(c, mult(a, c)), a) = mult(mult(c, a), mult(a, c)))),
% 23.09/23.30 inference(symmetry,[status(thm)],[8728])).
% 23.09/23.30 tff(8730,plain,
% 23.09/23.30 (mult(mult(mult(a, c), c), a) = mult(mult(a, c), mult(c, a))),
% 23.09/23.30 inference(unit_resolution,[status(thm)],[6752, 8129])).
% 23.09/23.30 tff(8731,plain,
% 23.09/23.30 (mult(mult(c, mult(a, c)), a) = mult(mult(c, a), mult(a, c))),
% 23.09/23.30 inference(modus_ponens,[status(thm)],[8730, 8729])).
% 23.09/23.30 tff(8732,plain,
% 23.09/23.30 (mult(mult(a, mult(c, c)), a) = mult(mult(mult(a, c), unit), mult(a, c))),
% 23.09/23.30 inference(transitivity,[status(thm)],[4662, 8726, 8731, 8721, 2504])).
% 23.09/23.30 tff(8733,plain,
% 23.09/23.30 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(c, c)), a)) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), unit), mult(a, c)))),
% 23.09/23.30 inference(monotonicity,[status(thm)],[8732])).
% 23.09/23.30 tff(8734,plain,
% 23.09/23.30 (mult(mult(a, rd(mult(b, c), mult(a, c))), c) = mult(b, c)),
% 23.09/23.30 inference(monotonicity,[status(thm)],[8644])).
% 23.09/23.30 tff(8735,plain,
% 23.09/23.30 (mult(b, c) = mult(mult(a, rd(mult(b, c), mult(a, c))), c)),
% 23.09/23.30 inference(symmetry,[status(thm)],[8734])).
% 23.09/23.30 tff(8736,plain,
% 23.09/23.30 (mult(a, mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), c))),
% 23.09/23.30 inference(transitivity,[status(thm)],[2220, 2700, 2172, 2178, 2177, 2162, 5650, 1490, 141, 8735, 6639, 6621, 5117])).
% 23.09/23.30 tff(8737,plain,
% 23.09/23.30 (ld(a, mult(a, mult(c, rd(mult(b, c), mult(a, c))))) = ld(a, mult(a, mult(rd(mult(b, c), mult(a, c)), c)))),
% 23.09/23.30 inference(monotonicity,[status(thm)],[8736])).
% 23.09/23.30 tff(8738,plain,
% 23.09/23.30 (mult(c, rd(mult(b, c), mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), c)),
% 23.09/23.30 inference(transitivity,[status(thm)],[5202, 8737, 5127])).
% 23.09/23.30 tff(8739,plain,
% 23.09/23.30 (mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a))),
% 23.09/23.30 inference(monotonicity,[status(thm)],[8738])).
% 23.09/23.30 tff(8740,plain,
% 23.09/23.30 (mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c)))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))),
% 23.09/23.30 inference(monotonicity,[status(thm)],[8129])).
% 23.09/23.30 tff(8741,plain,
% 23.09/23.30 (mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, mult(a, c))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a))),
% 23.09/23.30 inference(monotonicity,[status(thm)],[8262])).
% 23.09/23.30 tff(8742,plain,
% 23.09/23.30 ((mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, mult(a, c))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))))) <=> (mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))),
% 23.09/23.30 inference(monotonicity,[status(thm)],[8741, 8740])).
% 23.09/23.30 tff(8743,plain,
% 23.09/23.30 ((mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) <=> (mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, mult(a, c))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c)))))),
% 23.09/23.30 inference(symmetry,[status(thm)],[8742])).
% 23.09/23.30 tff(8744,plain,
% 23.09/23.30 ((mult(c, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) <=> (mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) = mult(c, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))))),
% 23.09/23.30 inference(commutativity,[status(thm)],[])).
% 23.09/23.30 tff(8745,plain,
% 23.09/23.30 (mult(c, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))) = mult(c, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.09/23.30 inference(monotonicity,[status(thm)],[5709])).
% 23.09/23.30 tff(8746,plain,
% 23.09/23.30 (mult(c, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))))),
% 23.09/23.30 inference(symmetry,[status(thm)],[8745])).
% 23.09/23.30 tff(8747,plain,
% 23.09/23.30 (mult(c, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(mult(a, c), b))),
% 23.09/23.30 inference(monotonicity,[status(thm)],[8645])).
% 23.09/23.30 tff(8748,plain,
% 23.09/23.30 (mult(c, mult(mult(a, c), b)) = mult(c, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.09/23.30 inference(symmetry,[status(thm)],[8747])).
% 23.09/23.30 tff(8749,plain,
% 23.09/23.30 (mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(c, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))))),
% 23.09/23.30 inference(transitivity,[status(thm)],[8739, 2632, 6871, 6877, 4660, 8733, 2502, 2499, 8716, 8720, 8714, 8713, 8748, 8746])).
% 23.09/23.30 tff(8750,plain,
% 23.09/23.30 ((mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) <=> (mult(c, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))),
% 23.09/23.30 inference(monotonicity,[status(thm)],[8749])).
% 23.09/23.30 tff(8751,plain,
% 23.09/23.30 ((mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) <=> (mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) = mult(c, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))))),
% 23.09/23.30 inference(transitivity,[status(thm)],[8750, 8744])).
% 23.09/23.30 tff(8752,plain,
% 23.09/23.30 ((mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) = mult(c, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))))) <=> (mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))),
% 23.09/23.30 inference(symmetry,[status(thm)],[8751])).
% 23.09/23.30 tff(8753,plain,
% 23.09/23.30 ((mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) = mult(c, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))))) <=> (mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, mult(a, c))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c)))))),
% 23.09/23.30 inference(transitivity,[status(thm)],[8752, 8743])).
% 23.09/23.30 tff(8754,assumption,(~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))), introduced(assumption)).
% 23.09/23.30 tff(8755,plain,
% 23.09/23.30 (((~(mult(mult(c, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))))) | (mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))),
% 23.09/23.31 inference(tautology,[status(thm)],[])).
% 23.09/23.31 tff(8756,plain,
% 23.09/23.31 ((~(mult(mult(c, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))))),
% 23.09/23.31 inference(unit_resolution,[status(thm)],[8755, 8754])).
% 23.09/23.31 tff(8757,plain,
% 23.09/23.31 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) = mult(c, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(mult(c, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))))))) | (~((~(mult(mult(c, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) = mult(c, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(mult(c, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))))))) | (~((~(mult(mult(c, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))))))),
% 23.09/23.31 inference(rewrite,[status(thm)],[])).
% 23.09/23.31 tff(8758,plain,
% 23.09/23.31 (((~((~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(mult(c, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))))) | (~(mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) = mult(c, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))) | (~(mult(mult(c, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))))))))) <=> ((~((~(mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) = mult(c, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(mult(c, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))))))) | (~((~(mult(mult(c, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))))))),
% 23.09/23.31 inference(rewrite,[status(thm)],[])).
% 23.09/23.31 tff(8759,plain,
% 23.09/23.31 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(mult(c, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))))) | (~(mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) = mult(c, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))) | (~(mult(mult(c, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) = mult(c, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(mult(c, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))))))) | (~((~(mult(mult(c, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))))))))),
% 23.09/23.31 inference(monotonicity,[status(thm)],[8758])).
% 23.09/23.31 tff(8760,plain,
% 23.09/23.31 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(mult(c, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))))) | (~(mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) = mult(c, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))) | (~(mult(mult(c, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) = mult(c, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(mult(c, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))))))) | (~((~(mult(mult(c, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))))))),
% 23.09/23.31 inference(transitivity,[status(thm)],[8759, 8757])).
% 23.09/23.31 tff(8761,plain,
% 23.09/23.31 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(mult(c, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))))) | (~(mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) = mult(c, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))) | (~(mult(mult(c, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))))))))),
% 23.09/23.31 inference(quant_inst,[status(thm)],[])).
% 23.09/23.31 tff(8762,plain,
% 23.09/23.31 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) = mult(c, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(mult(c, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))))))) | (~((~(mult(mult(c, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))))))),
% 23.09/23.31 inference(modus_ponens,[status(thm)],[8761, 8760])).
% 23.09/23.31 tff(8763,plain,
% 23.09/23.31 ((~((~(mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) = mult(c, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(mult(c, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))))))) | (~((~(mult(mult(c, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))))))),
% 23.09/23.31 inference(unit_resolution,[status(thm)],[8762, 27])).
% 23.09/23.31 tff(8764,plain,
% 23.09/23.31 (~((~(mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) = mult(c, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(mult(c, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))))))),
% 23.09/23.31 inference(unit_resolution,[status(thm)],[8763, 8756])).
% 23.09/23.31 tff(8765,plain,
% 23.09/23.31 (((~(mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) = mult(c, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(mult(c, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c)))))) | (mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) = mult(c, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))))),
% 23.09/23.31 inference(tautology,[status(thm)],[])).
% 23.09/23.31 tff(8766,plain,
% 23.09/23.31 (mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) = mult(c, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))))),
% 23.09/23.31 inference(unit_resolution,[status(thm)],[8765, 8764])).
% 23.09/23.31 tff(8767,plain,
% 23.09/23.31 (mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, mult(a, c))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))))),
% 23.09/23.31 inference(modus_ponens,[status(thm)],[8766, 8753])).
% 23.09/23.31 tff(8768,assumption,(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, mult(a, c))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))))), introduced(assumption)).
% 23.09/23.31 tff(8769,plain,
% 23.09/23.31 (mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))),
% 23.09/23.31 inference(modus_ponens,[status(thm)],[8768, 8742])).
% 23.09/23.31 tff(8770,plain,
% 23.09/23.31 ($false),
% 23.09/23.31 inference(unit_resolution,[status(thm)],[8754, 8769])).
% 23.09/23.31 tff(8771,plain,((mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, mult(a, c))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))))))), inference(lemma,lemma(discharge,[]))).
% 23.09/23.31 tff(8772,plain,
% 23.09/23.31 (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, mult(a, c))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c)))))),
% 23.09/23.31 inference(unit_resolution,[status(thm)],[8771, 8754])).
% 23.09/23.31 tff(8773,plain,
% 23.09/23.31 ($false),
% 23.09/23.31 inference(unit_resolution,[status(thm)],[8772, 8767])).
% 23.09/23.31 tff(8774,plain,((mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) | (~(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (~(mult(b, mult(a, c)) = mult(b, mult(c, a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)))) | (~(mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))))), inference(lemma,lemma(discharge,[]))).
% 23.09/23.31 tff(8775,plain,
% 23.09/23.31 (mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))),
% 23.09/23.31 inference(unit_resolution,[status(thm)],[8774, 2261, 1488, 4360, 6621, 2699])).
% 23.09/23.31 tff(8776,plain,
% 23.09/23.31 (mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a))),
% 23.09/23.31 inference(symmetry,[status(thm)],[8775])).
% 23.09/23.31 tff(8777,plain,
% 23.09/23.31 (mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) = mult(c, mult(mult(a, b), c))),
% 23.09/23.31 inference(transitivity,[status(thm)],[8776, 8739, 2632, 6871, 6877, 4660, 8733, 2502, 2499, 8716, 8720, 8714, 8713, 5654])).
% 23.09/23.31 tff(8778,plain,
% 23.09/23.31 (ld(c, mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) = ld(c, mult(c, mult(mult(a, b), c)))),
% 23.09/23.31 inference(monotonicity,[status(thm)],[8777])).
% 23.09/23.31 tff(8779,plain,
% 23.09/23.31 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(a, c), mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), a), c))) = mult(mult(rd(mult(b, c), mult(a, c)), a), c))),
% 23.09/23.31 inference(quant_inst,[status(thm)],[])).
% 23.09/23.31 tff(8780,plain,
% 23.09/23.31 (ld(mult(a, c), mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), a), c))) = mult(mult(rd(mult(b, c), mult(a, c)), a), c)),
% 23.09/23.31 inference(unit_resolution,[status(thm)],[8779, 7])).
% 23.09/23.31 tff(8781,plain,
% 23.09/23.31 (mult(a, mult(rd(mult(b, c), mult(a, c)), c)) = mult(b, c)),
% 23.09/23.31 inference(transitivity,[status(thm)],[5116, 6622, 6620, 8734])).
% 23.09/23.31 tff(8782,plain,
% 23.09/23.31 (mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))) = mult(mult(a, c), mult(b, c))),
% 23.09/23.31 inference(monotonicity,[status(thm)],[8781])).
% 23.09/23.31 tff(8783,assumption,(mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c)))), introduced(assumption)).
% 23.09/23.31 tff(8784,plain,
% 23.09/23.31 (mult(mult(unit, mult(a, c)), mult(mult(rd(mult(b, c), mult(a, c)), a), c)) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a))),
% 23.09/23.31 inference(monotonicity,[status(thm)],[1549, 7606])).
% 23.09/23.31 tff(8785,plain,
% 23.09/23.31 (mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), a), c)) = mult(mult(unit, mult(a, c)), mult(mult(rd(mult(b, c), mult(a, c)), a), c))),
% 23.09/23.32 inference(monotonicity,[status(thm)],[1551])).
% 23.09/23.32 tff(8786,plain,
% 23.09/23.32 (mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), a), c)) = mult(mult(a, c), mult(b, c))),
% 23.09/23.32 inference(transitivity,[status(thm)],[8785, 8784, 8783, 8782])).
% 23.09/23.32 tff(8787,plain,
% 23.09/23.32 (ld(mult(a, c), mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), a), c))) = ld(mult(a, c), mult(mult(a, c), mult(b, c)))),
% 23.09/23.32 inference(monotonicity,[status(thm)],[8786])).
% 23.09/23.32 tff(8788,plain,
% 23.09/23.32 (ld(mult(a, c), mult(mult(a, c), mult(b, c))) = ld(mult(a, c), mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), a), c)))),
% 23.09/23.32 inference(symmetry,[status(thm)],[8787])).
% 23.09/23.32 tff(8789,plain,
% 23.09/23.32 (mult(b, c) = mult(mult(rd(mult(b, c), mult(a, c)), a), c)),
% 23.09/23.32 inference(transitivity,[status(thm)],[740, 8788, 8780])).
% 23.09/23.32 tff(8790,plain,
% 23.09/23.32 (mult(mult(b, c), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a)),
% 23.09/23.32 inference(monotonicity,[status(thm)],[8789])).
% 23.09/23.32 tff(8791,plain,
% 23.09/23.32 (mult(c, mult(b, a)) = mult(c, mult(a, b))),
% 23.09/23.32 inference(transitivity,[status(thm)],[4304, 2298, 8790, 1168, 6930, 8778, 4031, 227, 8636, 4221])).
% 23.09/23.32 tff(8792,plain,
% 23.09/23.32 ($false),
% 23.09/23.32 inference(unit_resolution,[status(thm)],[2302, 8791])).
% 23.09/23.32 tff(8793,plain,((~(mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))) | (mult(c, mult(b, a)) = mult(c, mult(a, b))) | (~(mult(b, mult(a, c)) = mult(b, mult(c, a)))) | (~(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)))) | (~(mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))))), inference(lemma,lemma(discharge,[]))).
% 23.09/23.32 tff(8794,plain,
% 23.09/23.32 (~(mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))),
% 23.09/23.32 inference(unit_resolution,[status(thm)],[8793, 8711, 8705, 1488, 4303, 6621, 2699])).
% 23.09/23.32 tff(8795,plain,
% 23.09/23.32 (((~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)))) | (~(mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c)))))) | (mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))),
% 23.09/23.32 inference(tautology,[status(thm)],[])).
% 23.09/23.32 tff(8796,plain,
% 23.09/23.32 ((~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)))) | (~(mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c)))))),
% 23.09/23.32 inference(unit_resolution,[status(thm)],[8795, 8794])).
% 23.09/23.32 tff(8797,plain,
% 23.09/23.32 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))) | (~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)))))) | (~((~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)))) | (~(mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))) | (~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)))))) | (~((~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)))) | (~(mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))))))),
% 23.09/23.32 inference(rewrite,[status(thm)],[])).
% 23.09/23.32 tff(8798,plain,
% 23.09/23.32 (((~((~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)))) | (~(mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))))) | (~((~(mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))) | (~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a))))))) <=> ((~((~(mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))) | (~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)))))) | (~((~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)))) | (~(mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))))))),
% 23.09/23.32 inference(rewrite,[status(thm)],[])).
% 23.09/23.32 tff(8799,plain,
% 23.09/23.32 ((~((~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)))) | (~(mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))))) <=> (~((~(mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))) | (~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a))))))),
% 23.09/23.32 inference(rewrite,[status(thm)],[])).
% 23.09/23.32 tff(8800,plain,
% 23.09/23.32 ((~((~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)))) | (~(mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))))) <=> (~((~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)))) | (~(mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c)))))))),
% 23.09/23.32 inference(rewrite,[status(thm)],[])).
% 23.09/23.32 tff(8801,plain,
% 23.09/23.32 (((~((~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)))) | (~(mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))))) | (~((~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)))) | (~(mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c)))))))) <=> ((~((~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)))) | (~(mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))))) | (~((~(mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))) | (~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)))))))),
% 23.09/23.32 inference(monotonicity,[status(thm)],[8800, 8799])).
% 23.09/23.32 tff(8802,plain,
% 23.09/23.32 (((~((~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)))) | (~(mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))))) | (~((~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)))) | (~(mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c)))))))) <=> ((~((~(mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))) | (~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)))))) | (~((~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)))) | (~(mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))))))),
% 23.09/23.32 inference(transitivity,[status(thm)],[8801, 8798])).
% 23.09/23.32 tff(8803,plain,
% 23.09/23.32 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)))) | (~(mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))))) | (~((~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)))) | (~(mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))) | (~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)))))) | (~((~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)))) | (~(mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c)))))))))),
% 23.09/23.32 inference(monotonicity,[status(thm)],[8802])).
% 23.09/23.32 tff(8804,plain,
% 23.09/23.32 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)))) | (~(mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))))) | (~((~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)))) | (~(mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))) | (~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)))))) | (~((~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)))) | (~(mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))))))),
% 23.09/23.32 inference(transitivity,[status(thm)],[8803, 8797])).
% 23.09/23.32 tff(8805,plain,
% 23.09/23.32 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)))) | (~(mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))))) | (~((~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)))) | (~(mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))))))),
% 23.09/23.32 inference(quant_inst,[status(thm)],[])).
% 23.09/23.32 tff(8806,plain,
% 23.09/23.32 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))) | (~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)))))) | (~((~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)))) | (~(mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c)))))))),
% 23.09/23.33 inference(modus_ponens,[status(thm)],[8805, 8804])).
% 23.09/23.33 tff(8807,plain,
% 23.09/23.33 ((~((~(mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))) | (~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)))))) | (~((~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)))) | (~(mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c)))))))),
% 23.09/23.33 inference(unit_resolution,[status(thm)],[8806, 27])).
% 23.09/23.33 tff(8808,plain,
% 23.09/23.33 (~((~(mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))) | (~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)))))),
% 23.09/23.33 inference(unit_resolution,[status(thm)],[8807, 8796])).
% 23.09/23.33 tff(8809,plain,
% 23.09/23.33 (mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c)))),
% 23.09/23.33 inference(unit_resolution,[status(thm)],[5352, 8808])).
% 23.09/23.33 tff(8810,plain,
% 23.09/23.33 (mult(mult(unit, mult(a, c)), a) = mult(mult(a, c), a)),
% 23.09/23.33 inference(monotonicity,[status(thm)],[1549])).
% 23.09/23.33 tff(8811,plain,
% 23.09/23.33 (mult(mult(a, c), a) = mult(mult(unit, mult(a, c)), a)),
% 23.09/23.33 inference(symmetry,[status(thm)],[8810])).
% 23.09/23.33 tff(8812,plain,
% 23.09/23.33 (mult(mult(unit, a), mult(a, c)) = mult(a, mult(a, c))),
% 23.09/23.33 inference(monotonicity,[status(thm)],[244])).
% 23.09/23.33 tff(8813,plain,
% 23.09/23.33 (mult(mult(unit, a), mult(a, c)) = mult(mult(unit, mult(a, c)), a)),
% 23.09/23.33 inference(transitivity,[status(thm)],[8812, 4452, 8166, 4447, 8811])).
% 23.09/23.33 tff(8814,plain,
% 23.09/23.33 ((mult(mult(unit, mult(a, c)), a) = mult(mult(unit, a), mult(a, c))) <=> (mult(mult(unit, a), mult(a, c)) = mult(mult(unit, mult(a, c)), a))),
% 23.09/23.33 inference(commutativity,[status(thm)],[])).
% 23.09/23.33 tff(8815,plain,
% 23.09/23.33 (mult(a, mult(a, c)) = mult(mult(unit, a), mult(a, c))),
% 23.09/23.33 inference(symmetry,[status(thm)],[8812])).
% 23.09/23.33 tff(8816,assumption,(~(mult(mult(a, a), c) = mult(a, mult(a, c)))), introduced(assumption)).
% 23.09/23.33 tff(8817,plain,
% 23.09/23.33 (((~(mult(mult(a, a), c) = mult(a, mult(a, c)))) | (~(mult(mult(a, c), a) = mult(a, mult(c, a))))) | (mult(mult(a, a), c) = mult(a, mult(a, c)))),
% 23.09/23.33 inference(tautology,[status(thm)],[])).
% 23.09/23.33 tff(8818,plain,
% 23.09/23.33 ((~(mult(mult(a, a), c) = mult(a, mult(a, c)))) | (~(mult(mult(a, c), a) = mult(a, mult(c, a))))),
% 23.09/23.33 inference(unit_resolution,[status(thm)],[8817, 8816])).
% 23.09/23.33 tff(8819,plain,
% 23.09/23.33 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, a), c) = mult(mult(a, c), a))) | (~(mult(a, mult(a, c)) = mult(a, mult(c, a)))))) | (~((~(mult(mult(a, a), c) = mult(a, mult(a, c)))) | (~(mult(mult(a, c), a) = mult(a, mult(c, a)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, a), c) = mult(mult(a, c), a))) | (~(mult(a, mult(a, c)) = mult(a, mult(c, a)))))) | (~((~(mult(mult(a, a), c) = mult(a, mult(a, c)))) | (~(mult(mult(a, c), a) = mult(a, mult(c, a)))))))),
% 23.09/23.33 inference(rewrite,[status(thm)],[])).
% 23.09/23.33 tff(8820,plain,
% 23.09/23.33 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, a), c) = mult(mult(a, c), a))) | (~(mult(a, mult(a, c)) = mult(a, mult(c, a)))))) | (~((~(mult(mult(a, a), c) = mult(a, mult(a, c)))) | (~(mult(mult(a, c), a) = mult(a, mult(c, a)))))))),
% 23.09/23.33 inference(quant_inst,[status(thm)],[])).
% 23.09/23.33 tff(8821,plain,
% 23.09/23.33 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, a), c) = mult(mult(a, c), a))) | (~(mult(a, mult(a, c)) = mult(a, mult(c, a)))))) | (~((~(mult(mult(a, a), c) = mult(a, mult(a, c)))) | (~(mult(mult(a, c), a) = mult(a, mult(c, a))))))),
% 23.09/23.33 inference(modus_ponens,[status(thm)],[8820, 8819])).
% 23.09/23.33 tff(8822,plain,
% 23.09/23.33 ((~((~(mult(mult(a, a), c) = mult(mult(a, c), a))) | (~(mult(a, mult(a, c)) = mult(a, mult(c, a)))))) | (~((~(mult(mult(a, a), c) = mult(a, mult(a, c)))) | (~(mult(mult(a, c), a) = mult(a, mult(c, a))))))),
% 23.09/23.33 inference(unit_resolution,[status(thm)],[8821, 27])).
% 23.09/23.33 tff(8823,plain,
% 23.09/23.33 (~((~(mult(mult(a, a), c) = mult(mult(a, c), a))) | (~(mult(a, mult(a, c)) = mult(a, mult(c, a)))))),
% 23.09/23.33 inference(unit_resolution,[status(thm)],[8822, 8818])).
% 23.09/23.33 tff(8824,plain,
% 23.09/23.33 (((~(mult(mult(a, a), c) = mult(mult(a, c), a))) | (~(mult(a, mult(a, c)) = mult(a, mult(c, a))))) | (mult(mult(a, a), c) = mult(mult(a, c), a))),
% 23.09/23.33 inference(tautology,[status(thm)],[])).
% 23.09/23.33 tff(8825,plain,
% 23.09/23.33 (mult(mult(a, a), c) = mult(mult(a, c), a)),
% 23.09/23.33 inference(unit_resolution,[status(thm)],[8824, 8823])).
% 23.09/23.33 tff(8826,plain,
% 23.09/23.33 (mult(mult(a, a), c) = mult(mult(unit, mult(a, c)), a)),
% 23.09/23.33 inference(transitivity,[status(thm)],[8825, 8811])).
% 23.09/23.33 tff(8827,plain,
% 23.09/23.33 ((mult(mult(a, a), c) = mult(a, mult(a, c))) <=> (mult(mult(unit, mult(a, c)), a) = mult(mult(unit, a), mult(a, c)))),
% 23.09/23.33 inference(monotonicity,[status(thm)],[8826, 8815])).
% 23.09/23.33 tff(8828,plain,
% 23.09/23.33 ((mult(mult(a, a), c) = mult(a, mult(a, c))) <=> (mult(mult(unit, a), mult(a, c)) = mult(mult(unit, mult(a, c)), a))),
% 23.09/23.33 inference(transitivity,[status(thm)],[8827, 8814])).
% 23.09/23.33 tff(8829,plain,
% 23.09/23.33 ((mult(mult(unit, a), mult(a, c)) = mult(mult(unit, mult(a, c)), a)) <=> (mult(mult(a, a), c) = mult(a, mult(a, c)))),
% 23.09/23.33 inference(symmetry,[status(thm)],[8828])).
% 23.09/23.33 tff(8830,assumption,(mult(mult(unit, a), mult(a, c)) = mult(mult(unit, mult(a, c)), a)), introduced(assumption)).
% 23.09/23.33 tff(8831,plain,
% 23.09/23.33 (mult(mult(a, a), c) = mult(a, mult(a, c))),
% 23.09/23.33 inference(modus_ponens,[status(thm)],[8830, 8829])).
% 23.09/23.33 tff(8832,plain,
% 23.09/23.33 ($false),
% 23.09/23.33 inference(unit_resolution,[status(thm)],[8816, 8831])).
% 23.09/23.33 tff(8833,plain,((mult(mult(a, a), c) = mult(a, mult(a, c))) | (~(mult(mult(unit, a), mult(a, c)) = mult(mult(unit, mult(a, c)), a)))), inference(lemma,lemma(discharge,[]))).
% 23.09/23.33 tff(8834,plain,
% 23.09/23.33 (mult(mult(a, a), c) = mult(a, mult(a, c))),
% 23.09/23.33 inference(unit_resolution,[status(thm)],[8833, 8813])).
% 23.09/23.33 tff(8835,plain,
% 23.09/23.33 (mult(mult(a, a), c) = mult(mult(a, c), a)),
% 23.09/23.33 inference(transitivity,[status(thm)],[8834, 4452, 8166, 4447])).
% 23.09/23.33 tff(8836,plain,
% 23.09/23.33 (mult(mult(mult(a, a), c), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))),
% 23.09/23.33 inference(monotonicity,[status(thm)],[8835])).
% 23.09/23.33 tff(8837,plain,
% 23.09/23.33 (mult(mult(mult(a, a), c), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), b)),
% 23.09/23.33 inference(transitivity,[status(thm)],[8836, 5709, 8645])).
% 23.09/23.33 tff(8838,plain,
% 23.09/23.33 (mult(mult(mult(mult(a, a), c), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, c), b), c)),
% 23.09/23.33 inference(monotonicity,[status(thm)],[8837])).
% 23.09/23.33 tff(8839,plain,
% 23.09/23.33 (mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), c)) = mult(mult(mult(mult(a, a), c), rd(mult(b, c), mult(a, c))), c)),
% 23.09/23.33 inference(symmetry,[status(thm)],[7827])).
% 23.09/23.33 tff(8840,plain,
% 23.09/23.33 (mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), c)) = mult(mult(unit, a), mult(mult(b, c), c))),
% 23.09/23.33 inference(transitivity,[status(thm)],[8839, 8838, 233, 2414, 3136])).
% 23.09/23.33 tff(8841,plain,
% 23.09/23.33 (mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)) = mult(mult(b, c), c)),
% 23.09/23.33 inference(transitivity,[status(thm)],[3157, 8562])).
% 23.09/23.33 tff(8842,plain,
% 23.09/23.33 (mult(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)), a) = mult(mult(mult(b, c), c), a)),
% 23.09/23.33 inference(monotonicity,[status(thm)],[8841])).
% 23.09/23.33 tff(8843,plain,
% 23.09/23.33 (mult(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)), a) = mult(mult(unit, mult(mult(b, c), c)), a)),
% 23.09/23.33 inference(transitivity,[status(thm)],[8842, 3150])).
% 23.09/23.33 tff(8844,plain,
% 23.09/23.33 ((mult(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)), a) = mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), c))) <=> (mult(mult(unit, mult(mult(b, c), c)), a) = mult(mult(unit, a), mult(mult(b, c), c)))),
% 23.09/23.33 inference(monotonicity,[status(thm)],[8843, 8840])).
% 23.09/23.33 tff(8845,plain,
% 23.09/23.33 ((mult(mult(unit, mult(mult(b, c), c)), a) = mult(mult(unit, a), mult(mult(b, c), c))) <=> (mult(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)), a) = mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), c)))),
% 23.09/23.33 inference(symmetry,[status(thm)],[8844])).
% 23.09/23.33 tff(8846,plain,
% 23.09/23.33 ((~(mult(mult(unit, mult(mult(b, c), c)), a) = mult(mult(unit, a), mult(mult(b, c), c)))) <=> (~(mult(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)), a) = mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), c))))),
% 23.09/23.33 inference(monotonicity,[status(thm)],[8845])).
% 23.09/23.33 tff(8847,plain,
% 23.09/23.33 (mult(mult(c, mult(a, c)), b) = mult(mult(mult(a, c), c), b)),
% 23.09/23.33 inference(monotonicity,[status(thm)],[8568])).
% 23.09/23.33 tff(8848,plain,
% 23.09/23.33 (mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(c, mult(a, c)), b)),
% 23.09/23.33 inference(monotonicity,[status(thm)],[8644])).
% 23.09/23.33 tff(8849,plain,
% 23.09/23.33 (mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(unit, a), mult(mult(b, c), c))),
% 23.09/23.33 inference(transitivity,[status(thm)],[8848, 8847, 2759, 233, 2414, 3136])).
% 23.09/23.33 tff(8850,plain,
% 23.09/23.33 (mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(b, c), c)),
% 23.09/23.33 inference(transitivity,[status(thm)],[8569, 8626, 8562])).
% 23.09/23.33 tff(8851,plain,
% 23.09/23.33 (mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(b, c), c), a)),
% 23.09/23.33 inference(monotonicity,[status(thm)],[8850])).
% 23.09/23.33 tff(8852,plain,
% 23.09/23.33 ((mult(mult(unit, b), mult(a, c)) = mult(mult(unit, mult(a, c)), b)) <=> (mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 23.09/23.33 inference(transitivity,[status(thm)],[8662, 8654])).
% 23.09/23.33 tff(8853,plain,
% 23.09/23.33 (mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))),
% 23.09/23.33 inference(modus_ponens,[status(thm)],[8689, 8852])).
% 23.09/23.33 tff(8854,plain,
% 23.09/23.33 (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))),
% 23.09/23.33 inference(unit_resolution,[status(thm)],[6387, 8853, 1364, 1488])).
% 23.09/23.33 tff(8855,plain,
% 23.09/23.33 (~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))),
% 23.09/23.33 inference(unit_resolution,[status(thm)],[2329, 8854])).
% 23.09/23.33 tff(8856,plain,
% 23.09/23.33 ((~(mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))) | (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))),
% 23.09/23.33 inference(unit_resolution,[status(thm)],[2390, 5496, 5709])).
% 23.09/23.33 tff(8857,plain,
% 23.09/23.33 (~(mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.09/23.33 inference(unit_resolution,[status(thm)],[8856, 8855])).
% 23.09/23.33 tff(8858,plain,
% 23.09/23.33 (~((~(mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)))))),
% 23.09/23.33 inference(unit_resolution,[status(thm)],[2406, 8857])).
% 23.09/23.33 tff(8859,plain,
% 23.09/23.33 (mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a))),
% 23.09/23.33 inference(unit_resolution,[status(thm)],[2408, 8858])).
% 23.09/23.33 tff(8860,plain,
% 23.09/23.33 (mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a)),
% 23.09/23.33 inference(symmetry,[status(thm)],[8859])).
% 23.09/23.33 tff(8861,plain,
% 23.09/23.33 (mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(unit, mult(mult(b, c), c)), a)),
% 23.09/23.33 inference(transitivity,[status(thm)],[8860, 8851, 3150])).
% 23.09/23.33 tff(8862,plain,
% 23.09/23.33 ((mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c))))) <=> (mult(mult(unit, mult(mult(b, c), c)), a) = mult(mult(unit, a), mult(mult(b, c), c)))),
% 23.09/23.33 inference(monotonicity,[status(thm)],[8861, 8849])).
% 23.09/23.33 tff(8863,plain,
% 23.09/23.33 ((~(mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))) <=> (~(mult(mult(unit, mult(mult(b, c), c)), a) = mult(mult(unit, a), mult(mult(b, c), c))))),
% 23.09/23.33 inference(monotonicity,[status(thm)],[8862])).
% 23.09/23.33 tff(8864,plain,
% 23.09/23.33 (~(mult(mult(unit, mult(mult(b, c), c)), a) = mult(mult(unit, a), mult(mult(b, c), c)))),
% 23.09/23.33 inference(modus_ponens,[status(thm)],[8857, 8863])).
% 23.09/23.33 tff(8865,plain,
% 23.09/23.33 (~(mult(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)), a) = mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), c)))),
% 23.09/23.33 inference(modus_ponens,[status(thm)],[8864, 8846])).
% 23.09/23.33 tff(8866,plain,
% 23.09/23.33 (((~(mult(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)), a) = mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), c)))) | (~(mult(a, mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a)) = mult(a, mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)))))) | (mult(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)), a) = mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), c)))),
% 23.09/23.33 inference(tautology,[status(thm)],[])).
% 23.09/23.33 tff(8867,plain,
% 23.09/23.33 ((~(mult(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)), a) = mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), c)))) | (~(mult(a, mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a)) = mult(a, mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)))))),
% 23.09/23.33 inference(unit_resolution,[status(thm)],[8866, 8865])).
% 23.09/23.33 tff(8868,plain,
% 23.09/23.33 (~((~(mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c))))) | (~(mult(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)), a) = mult(a, mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a)))))),
% 23.09/23.33 inference(unit_resolution,[status(thm)],[7798, 8867])).
% 23.09/23.33 tff(8869,plain,
% 23.09/23.33 (((~(mult(mult(a, a), mult(mult(c, rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c))))) | (~(mult(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)), a) = mult(a, mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a))))) | (mult(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)), a) = mult(a, mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a)))),
% 23.09/23.33 inference(tautology,[status(thm)],[])).
% 23.09/23.33 tff(8870,plain,
% 23.09/23.33 (mult(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)), a) = mult(a, mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a))),
% 23.09/23.33 inference(unit_resolution,[status(thm)],[8869, 8868])).
% 23.09/23.33 tff(8871,plain,
% 23.09/23.33 ((mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c))))) <=> (mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)))),
% 23.09/23.33 inference(commutativity,[status(thm)],[])).
% 23.09/23.33 tff(8872,plain,
% 23.09/23.33 ((mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c))) <=> (mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))))),
% 23.09/23.34 inference(symmetry,[status(thm)],[8871])).
% 23.09/23.34 tff(8873,plain,
% 23.09/23.34 (mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(c, a)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a))),
% 23.09/23.34 inference(monotonicity,[status(thm)],[2701])).
% 23.09/23.34 tff(8874,plain,
% 23.09/23.34 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(c, a))),
% 23.09/23.34 inference(symmetry,[status(thm)],[8873])).
% 23.09/23.34 tff(8875,plain,
% 23.09/23.34 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(b, c), mult(c, a))),
% 23.09/23.34 inference(monotonicity,[status(thm)],[5651])).
% 23.09/23.34 tff(8876,plain,
% 23.09/23.34 (mult(mult(b, c), mult(c, a)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a))),
% 23.09/23.34 inference(symmetry,[status(thm)],[8875])).
% 23.09/23.34 tff(8877,plain,
% 23.09/23.34 (mult(mult(b, c), mult(a, c)) = mult(mult(b, c), mult(c, a))),
% 23.09/23.34 inference(symmetry,[status(thm)],[8717])).
% 23.09/23.34 tff(8878,plain,
% 23.09/23.34 (mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(c, a))),
% 23.09/23.34 inference(transitivity,[status(thm)],[4549, 5652, 8877, 8876, 8874])).
% 23.09/23.34 tff(8879,plain,
% 23.09/23.34 (mult(a, mult(c, a)) = mult(a, mult(a, c))),
% 23.09/23.34 inference(monotonicity,[status(thm)],[4268])).
% 23.09/23.34 tff(8880,plain,
% 23.09/23.34 (mult(mult(a, mult(c, a)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c))))),
% 23.09/23.34 inference(monotonicity,[status(thm)],[8879])).
% 23.09/23.34 tff(8881,plain,
% 23.09/23.34 (mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(c, a)), mult(c, rd(mult(b, c), mult(a, c))))),
% 23.09/23.34 inference(symmetry,[status(thm)],[8880])).
% 23.09/23.34 tff(8882,plain,
% 23.09/23.34 ((mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c))) <=> (mult(mult(a, mult(c, a)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(c, a)))),
% 23.09/23.34 inference(monotonicity,[status(thm)],[8881, 8878])).
% 23.09/23.34 tff(8883,plain,
% 23.09/23.34 ((mult(mult(a, mult(c, a)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(c, a))) <=> (mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)))),
% 23.09/23.34 inference(symmetry,[status(thm)],[8882])).
% 23.09/23.34 tff(8884,plain,
% 23.09/23.34 ((mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), c)) <=> (mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)))),
% 23.09/23.34 inference(commutativity,[status(thm)],[])).
% 23.09/23.34 tff(8885,plain,
% 23.09/23.34 (mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), c)),
% 23.09/23.34 inference(monotonicity,[status(thm)],[5709])).
% 23.09/23.34 tff(8886,plain,
% 23.09/23.34 (mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), c)),
% 23.09/23.34 inference(symmetry,[status(thm)],[8885])).
% 23.09/23.34 tff(8887,plain,
% 23.09/23.34 (mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(mult(a, c), b), c)),
% 23.09/23.34 inference(monotonicity,[status(thm)],[8645])).
% 23.09/23.34 tff(8888,plain,
% 23.09/23.34 (mult(mult(mult(a, c), b), c) = mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), c)),
% 23.09/23.34 inference(symmetry,[status(thm)],[8887])).
% 23.09/23.34 tff(8889,plain,
% 23.09/23.34 (mult(b, mult(c, a)) = mult(mult(a, c), b)),
% 23.09/23.34 inference(transitivity,[status(thm)],[8706, 8660, 8690, 8263, 5709, 8645])).
% 23.09/23.34 tff(8890,plain,
% 23.09/23.34 (mult(c, mult(b, mult(c, a))) = mult(c, mult(mult(a, c), b))),
% 23.09/23.34 inference(monotonicity,[status(thm)],[8889])).
% 23.09/23.34 tff(8891,plain,
% 23.09/23.34 (mult(c, mult(b, mult(a, c))) = mult(c, mult(b, mult(c, a)))),
% 23.09/23.34 inference(monotonicity,[status(thm)],[8705])).
% 23.09/23.34 tff(8892,plain,
% 23.09/23.34 (mult(c, mult(b, mult(c, a))) = mult(c, mult(b, mult(a, c)))),
% 23.09/23.34 inference(symmetry,[status(thm)],[8891])).
% 23.09/23.34 tff(8893,plain,
% 23.09/23.34 ((mult(mult(c, b), mult(c, a)) = mult(c, mult(b, mult(c, a)))) <=> (mult(mult(c, b), mult(a, c)) = mult(c, mult(b, mult(a, c))))),
% 23.09/23.34 inference(monotonicity,[status(thm)],[8718, 8892])).
% 23.09/23.34 tff(8894,plain,
% 23.09/23.34 (mult(mult(c, b), mult(a, c)) = mult(c, mult(b, mult(a, c)))),
% 23.09/23.34 inference(modus_ponens,[status(thm)],[6922, 8893])).
% 23.09/23.34 tff(8895,plain,
% 23.09/23.34 (mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(c, a)) = mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), c)),
% 23.09/23.34 inference(transitivity,[status(thm)],[8873, 8875, 8717, 8716, 8894, 8891, 8890, 3190, 3188, 4284, 8888, 8886])).
% 23.09/23.34 tff(8896,plain,
% 23.09/23.34 (mult(mult(mult(a, c), a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c))),
% 23.09/23.34 inference(monotonicity,[status(thm)],[8738])).
% 23.09/23.34 tff(8897,plain,
% 23.09/23.34 (mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, c), a), mult(c, rd(mult(b, c), mult(a, c))))),
% 23.09/23.34 inference(monotonicity,[status(thm)],[8262])).
% 23.09/23.34 tff(8898,plain,
% 23.09/23.34 (mult(mult(a, mult(c, a)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c))),
% 23.09/23.34 inference(transitivity,[status(thm)],[8880, 8897, 8896])).
% 23.09/23.34 tff(8899,plain,
% 23.09/23.34 ((mult(mult(a, mult(c, a)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(c, a))) <=> (mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), c))),
% 23.09/23.34 inference(monotonicity,[status(thm)],[8898, 8895])).
% 23.09/23.34 tff(8900,plain,
% 23.09/23.34 ((mult(mult(a, mult(c, a)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(c, a))) <=> (mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)))),
% 23.09/23.34 inference(transitivity,[status(thm)],[8899, 8884])).
% 23.09/23.34 tff(8901,plain,
% 23.09/23.34 ((mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c))) <=> (mult(mult(a, mult(c, a)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(c, a)))),
% 23.09/23.34 inference(symmetry,[status(thm)],[8900])).
% 23.09/23.34 tff(8902,plain,
% 23.09/23.34 (mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, mult(b, c)), c)),
% 23.09/23.34 inference(transitivity,[status(thm)],[8809, 8782, 266])).
% 23.09/23.34 tff(8903,plain,
% 23.09/23.34 (mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), c) = mult(a, mult(mult(b, c), c))),
% 23.09/23.34 inference(transitivity,[status(thm)],[8885, 8887, 233, 2414])).
% 23.09/23.34 tff(8904,plain,
% 23.09/23.34 ((mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c))) <=> (mult(a, mult(mult(b, c), c)) = mult(mult(a, mult(b, c)), c))),
% 23.09/23.34 inference(monotonicity,[status(thm)],[8903, 8902])).
% 23.09/23.34 tff(8905,plain,
% 23.09/23.34 ((mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c))) <=> (mult(mult(a, mult(b, c)), c) = mult(a, mult(mult(b, c), c)))),
% 23.09/23.34 inference(transitivity,[status(thm)],[8904, 2412])).
% 23.09/23.34 tff(8906,plain,
% 23.09/23.34 ((mult(mult(a, mult(b, c)), c) = mult(a, mult(mult(b, c), c))) <=> (mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)))),
% 23.09/23.34 inference(symmetry,[status(thm)],[8905])).
% 23.09/23.34 tff(8907,plain,
% 23.09/23.34 ((mult(mult(a, mult(b, c)), c) = mult(a, mult(mult(b, c), c))) <=> (mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))))),
% 23.09/23.34 inference(transitivity,[status(thm)],[8906, 8901, 8883, 8872])).
% 23.09/23.34 tff(8908,plain,
% 23.09/23.34 ((~(mult(mult(a, mult(b, c)), c) = mult(a, mult(mult(b, c), c)))) <=> (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c))))))),
% 23.09/23.34 inference(monotonicity,[status(thm)],[8907])).
% 23.09/23.34 tff(8909,plain,
% 23.09/23.34 (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))))),
% 23.09/23.34 inference(modus_ponens,[status(thm)],[258, 8908])).
% 23.09/23.34 tff(8910,plain,
% 23.09/23.34 (((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))) = mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))))) | (mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))))),
% 23.09/23.34 inference(tautology,[status(thm)],[])).
% 23.09/23.34 tff(8911,plain,
% 23.09/23.34 ((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))) = mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))))),
% 23.09/23.34 inference(unit_resolution,[status(thm)],[8910, 8909])).
% 23.09/23.34 tff(8912,plain,
% 23.09/23.34 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))))) | (~((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))) = mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))))) | (~((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))) = mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))))))))),
% 23.09/23.34 inference(rewrite,[status(thm)],[])).
% 23.09/23.34 tff(8913,plain,
% 23.09/23.34 (((~((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))) = mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))))))) | (~((~(mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))))))) <=> ((~((~(mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))))) | (~((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))) = mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))))))))),
% 23.09/23.34 inference(rewrite,[status(thm)],[])).
% 23.09/23.34 tff(8914,plain,
% 23.09/23.34 ((~((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))) | (~(mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))))))) <=> (~((~(mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))))))),
% 23.09/23.34 inference(rewrite,[status(thm)],[])).
% 23.09/23.34 tff(8915,plain,
% 23.09/23.34 ((~((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))) = mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))))))) <=> (~((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))) = mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))))))),
% 23.09/23.34 inference(rewrite,[status(thm)],[])).
% 23.09/23.34 tff(8916,plain,
% 23.09/23.34 (((~((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))) = mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))))))) | (~((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))) | (~(mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))))))) <=> ((~((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))) = mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))))))) | (~((~(mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))))))),
% 23.09/23.34 inference(monotonicity,[status(thm)],[8915, 8914])).
% 23.09/23.34 tff(8917,plain,
% 23.09/23.34 (((~((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))) = mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))))))) | (~((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))) | (~(mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))))))) <=> ((~((~(mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))))) | (~((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))) = mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))))))))),
% 23.09/23.34 inference(transitivity,[status(thm)],[8916, 8913])).
% 23.09/23.34 tff(8918,plain,
% 23.09/23.34 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))) = mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))))))) | (~((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))) | (~(mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))))) | (~((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))) = mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))))))))),
% 23.09/23.35 inference(monotonicity,[status(thm)],[8917])).
% 23.09/23.35 tff(8919,plain,
% 23.09/23.35 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))) = mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))))))) | (~((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))) | (~(mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))))) | (~((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))) = mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))))))))),
% 23.09/23.35 inference(transitivity,[status(thm)],[8918, 8912])).
% 23.09/23.35 tff(8920,plain,
% 23.09/23.35 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))) = mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))))))) | (~((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))) | (~(mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))))))))),
% 23.09/23.35 inference(quant_inst,[status(thm)],[])).
% 23.09/23.35 tff(8921,plain,
% 23.09/23.35 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))))) | (~((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))) = mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))))))),
% 23.19/23.35 inference(modus_ponens,[status(thm)],[8920, 8919])).
% 23.19/23.35 tff(8922,plain,
% 23.19/23.35 ((~((~(mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))))) | (~((~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))))) | (~(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))) = mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))))))),
% 23.19/23.35 inference(unit_resolution,[status(thm)],[8921, 27])).
% 23.19/23.35 tff(8923,plain,
% 23.19/23.35 (~((~(mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))))),
% 23.19/23.35 inference(unit_resolution,[status(thm)],[8922, 8911])).
% 23.19/23.35 tff(8924,plain,
% 23.19/23.35 (((~(mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))))) | (mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))))),
% 23.19/23.35 inference(tautology,[status(thm)],[])).
% 23.19/23.35 tff(8925,plain,
% 23.19/23.35 (mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))),
% 23.19/23.35 inference(unit_resolution,[status(thm)],[8924, 8923])).
% 23.19/23.35 tff(8926,plain,
% 23.19/23.35 (ld(a, mult(a, mult(rd(mult(b, c), mult(a, c)), c))) = ld(a, mult(a, mult(c, rd(mult(b, c), mult(a, c)))))),
% 23.19/23.35 inference(symmetry,[status(thm)],[8737])).
% 23.19/23.35 tff(8927,plain,
% 23.19/23.35 (mult(rd(mult(b, c), mult(a, c)), c) = mult(c, rd(mult(b, c), mult(a, c)))),
% 23.19/23.35 inference(transitivity,[status(thm)],[5128, 8926, 5114])).
% 23.19/23.35 tff(8928,plain,
% 23.19/23.35 (mult(mult(rd(mult(b, c), mult(a, c)), c), c) = mult(mult(c, rd(mult(b, c), mult(a, c))), c)),
% 23.19/23.35 inference(monotonicity,[status(thm)],[8927])).
% 23.19/23.35 tff(8929,plain,
% 23.19/23.35 (mult(mult(c, rd(mult(b, c), mult(a, c))), c) = mult(mult(rd(mult(b, c), mult(a, c)), c), c)),
% 23.19/23.35 inference(symmetry,[status(thm)],[8928])).
% 23.19/23.35 tff(8930,plain,
% 23.19/23.35 (mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), c), a)),
% 23.19/23.35 inference(monotonicity,[status(thm)],[8929])).
% 23.19/23.35 tff(8931,plain,
% 23.19/23.35 (mult(mult(mult(rd(mult(b, c), mult(a, c)), c), c), a) = mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a)),
% 23.19/23.35 inference(symmetry,[status(thm)],[8930])).
% 23.19/23.35 tff(8932,plain,
% 23.19/23.35 (mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), c), a)),
% 23.19/23.35 inference(symmetry,[status(thm)],[7658])).
% 23.19/23.35 tff(8933,plain,
% 23.19/23.35 (mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))) = mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a)),
% 23.19/23.35 inference(transitivity,[status(thm)],[4860, 4858, 4855, 8932, 8931])).
% 23.19/23.35 tff(8934,plain,
% 23.19/23.35 (mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))) = mult(a, mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a))),
% 23.19/23.35 inference(monotonicity,[status(thm)],[8933])).
% 23.19/23.35 tff(8935,plain,
% 23.19/23.35 (mult(a, mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))))),
% 23.19/23.35 inference(symmetry,[status(thm)],[8934])).
% 23.19/23.35 tff(8936,assumption,(mult(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)), a) = mult(a, mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a))), introduced(assumption)).
% 23.19/23.35 tff(8937,plain,
% 23.19/23.35 (mult(mult(mult(b, c), c), a) = mult(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)), a)),
% 23.19/23.35 inference(symmetry,[status(thm)],[8842])).
% 23.19/23.35 tff(8938,plain,
% 23.19/23.35 (mult(mult(mult(b, c), a), c) = mult(mult(mult(b, c), c), a)),
% 23.19/23.35 inference(symmetry,[status(thm)],[8635])).
% 23.19/23.35 tff(8939,plain,
% 23.19/23.35 (mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(b, c), a)),
% 23.19/23.35 inference(transitivity,[status(thm)],[5497, 8327])).
% 23.19/23.35 tff(8940,plain,
% 23.19/23.35 (mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c) = mult(mult(mult(b, c), a), c)),
% 23.19/23.35 inference(monotonicity,[status(thm)],[8939])).
% 23.19/23.35 tff(8941,plain,
% 23.19/23.35 (mult(a, mult(mult(c, mult(rd(mult(b, c), mult(a, c)), a)), c)) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c)),
% 23.19/23.35 inference(symmetry,[status(thm)],[6220])).
% 23.19/23.35 tff(8942,plain,
% 23.19/23.35 (mult(a, mult(mult(c, mult(rd(mult(b, c), mult(a, c)), a)), c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))))),
% 23.19/23.35 inference(transitivity,[status(thm)],[8941, 8940, 8938, 8937, 8936, 8935])).
% 23.19/23.35 tff(8943,plain,
% 23.19/23.35 (ld(a, mult(a, mult(mult(c, mult(rd(mult(b, c), mult(a, c)), a)), c))) = ld(a, mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))))),
% 23.19/23.35 inference(monotonicity,[status(thm)],[8942])).
% 23.19/23.35 tff(8944,plain,
% 23.19/23.35 (mult(mult(mult(b, c), a), c) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c)),
% 23.19/23.35 inference(symmetry,[status(thm)],[8940])).
% 23.19/23.35 tff(8945,plain,
% 23.19/23.35 (mult(a, mult(b, c)) = mult(mult(b, c), a)),
% 23.19/23.35 inference(transitivity,[status(thm)],[7455, 7452, 7450])).
% 23.19/23.35 tff(8946,plain,
% 23.19/23.35 (mult(mult(a, mult(b, c)), c) = mult(mult(mult(b, c), a), c)),
% 23.19/23.35 inference(monotonicity,[status(thm)],[8945])).
% 23.19/23.35 tff(8947,assumption,(mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c)))), introduced(assumption)).
% 23.19/23.35 tff(8948,assumption,(mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))), introduced(assumption)).
% 23.19/23.35 tff(8949,plain,
% 23.19/23.35 (mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c))))),
% 23.19/23.35 inference(symmetry,[status(thm)],[8948])).
% 23.19/23.35 tff(8950,plain,
% 23.19/23.35 (mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(c, mult(rd(mult(b, c), mult(a, c)), a)), c))),
% 23.19/23.35 inference(transitivity,[status(thm)],[8949, 8897, 8896, 8947, 8782, 266, 8946, 8944, 6220])).
% 23.19/23.35 tff(8951,plain,
% 23.19/23.35 (ld(a, mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))) = ld(a, mult(a, mult(mult(c, mult(rd(mult(b, c), mult(a, c)), a)), c)))),
% 23.19/23.35 inference(monotonicity,[status(thm)],[8950])).
% 23.19/23.35 tff(8952,plain,
% 23.19/23.35 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(a, mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))) = mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))),
% 23.19/23.35 inference(quant_inst,[status(thm)],[])).
% 23.19/23.35 tff(8953,plain,
% 23.19/23.35 (ld(a, mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))) = mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))),
% 23.19/23.35 inference(unit_resolution,[status(thm)],[8952, 7])).
% 23.19/23.35 tff(8954,plain,
% 23.19/23.35 (mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))) = ld(a, mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))))),
% 23.19/23.35 inference(symmetry,[status(thm)],[8953])).
% 23.19/23.35 tff(8955,plain,
% 23.19/23.35 (mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))),
% 23.19/23.35 inference(transitivity,[status(thm)],[8954, 8951, 8943, 7610])).
% 23.19/23.35 tff(8956,plain,
% 23.19/23.35 (mult(mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))), a)),
% 23.19/23.35 inference(monotonicity,[status(thm)],[8955])).
% 23.19/23.35 tff(8957,plain,
% 23.19/23.35 (mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))),
% 23.19/23.35 inference(monotonicity,[status(thm)],[8927])).
% 23.19/23.35 tff(8958,plain,
% 23.19/23.35 (mult(mult(c, a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c))),
% 23.19/23.35 inference(monotonicity,[status(thm)],[4268])).
% 23.19/23.35 tff(8959,plain,
% 23.19/23.35 (mult(mult(c, a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))),
% 23.19/23.35 inference(transitivity,[status(thm)],[8958, 8957])).
% 23.19/23.35 tff(8960,plain,
% 23.19/23.35 (mult(mult(mult(c, a), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))), a)),
% 23.19/23.36 inference(monotonicity,[status(thm)],[8959])).
% 23.19/23.36 tff(8961,plain,
% 23.19/23.36 (mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(b, c), a)),
% 23.19/23.36 inference(monotonicity,[status(thm)],[8781])).
% 23.19/23.36 tff(8962,plain,
% 23.19/23.36 (mult(mult(b, c), a) = mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a)),
% 23.19/23.36 inference(symmetry,[status(thm)],[8961])).
% 23.19/23.36 tff(8963,plain,
% 23.19/23.36 (mult(c, mult(mult(b, c), a)) = mult(c, mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a))),
% 23.19/23.36 inference(monotonicity,[status(thm)],[8962])).
% 23.19/23.36 tff(8964,plain,
% 23.19/23.36 (mult(c, mult(mult(b, c), a)) = mult(c, mult(mult(a, b), c))),
% 23.19/23.36 inference(transitivity,[status(thm)],[8963, 5324, 8960, 8956, 6877, 4660, 8733, 2502, 2499, 8716, 8720, 8714, 8713, 5654])).
% 23.19/23.36 tff(8965,plain,
% 23.19/23.36 (ld(c, mult(c, mult(mult(b, c), a))) = ld(c, mult(c, mult(mult(a, b), c)))),
% 23.19/23.36 inference(monotonicity,[status(thm)],[8964])).
% 23.19/23.36 tff(8966,plain,
% 23.19/23.36 (mult(c, mult(b, a)) = mult(c, mult(a, b))),
% 23.19/23.36 inference(transitivity,[status(thm)],[4304, 2298, 2297, 8965, 4031, 227, 8636, 4221])).
% 23.19/23.36 tff(8967,plain,
% 23.19/23.36 ($false),
% 23.19/23.36 inference(unit_resolution,[status(thm)],[2302, 8966])).
% 23.19/23.36 tff(8968,plain,((~(mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))) | (mult(c, mult(b, a)) = mult(c, mult(a, b))) | (~(mult(b, mult(a, c)) = mult(b, mult(c, a)))) | (~(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)))) | (~(mult(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)), a) = mult(a, mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a)))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)))) | (~(mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(b, mult(a, mult(b, c))) = mult(b, mult(mult(b, c), a))))), inference(lemma,lemma(discharge,[]))).
% 23.19/23.36 tff(8969,plain,
% 23.19/23.36 (~(mult(b, mult(a, mult(b, c))) = mult(b, mult(mult(b, c), a)))),
% 23.19/23.36 inference(unit_resolution,[status(thm)],[8968, 8925, 8705, 1488, 4303, 8870, 6621, 2699, 8809, 8711])).
% 23.19/23.36 tff(8970,plain,
% 23.19/23.36 ((~(mult(mult(b, a), mult(b, c)) = mult(mult(b, mult(b, c)), a))) | (~(mult(b, mult(a, mult(b, c))) = mult(b, mult(mult(b, c), a))))),
% 23.19/23.36 inference(unit_resolution,[status(thm)],[7524, 8969])).
% 23.19/23.36 tff(8971,plain,
% 23.19/23.36 (~((~(mult(mult(b, a), mult(b, c)) = mult(b, mult(a, mult(b, c))))) | (~(mult(mult(b, mult(b, c)), a) = mult(b, mult(mult(b, c), a)))))),
% 23.19/23.36 inference(unit_resolution,[status(thm)],[6974, 8970])).
% 23.19/23.36 tff(8972,plain,
% 23.19/23.36 (mult(mult(b, mult(b, c)), a) = mult(b, mult(mult(b, c), a))),
% 23.19/23.36 inference(unit_resolution,[status(thm)],[6976, 8971])).
% 23.19/23.36 tff(8973,plain,
% 23.19/23.36 (mult(mult(b, a), mult(b, c)) = mult(b, mult(a, mult(b, c)))),
% 23.19/23.36 inference(unit_resolution,[status(thm)],[7561, 8971])).
% 23.19/23.36 tff(8974,plain,
% 23.19/23.36 (mult(b, mult(mult(b, c), a)) = mult(mult(b, mult(b, c)), a)),
% 23.19/23.36 inference(symmetry,[status(thm)],[8972])).
% 23.19/23.36 tff(8975,plain,
% 23.19/23.36 (mult(b, mult(a, mult(b, c))) = mult(mult(b, a), mult(b, c))),
% 23.19/23.36 inference(symmetry,[status(thm)],[8973])).
% 23.19/23.36 tff(8976,plain,
% 23.19/23.36 ((mult(b, mult(a, mult(b, c))) = mult(b, mult(mult(b, c), a))) <=> (mult(mult(b, a), mult(b, c)) = mult(mult(b, mult(b, c)), a))),
% 23.19/23.36 inference(monotonicity,[status(thm)],[8975, 8974])).
% 23.19/23.36 tff(8977,plain,
% 23.19/23.36 ((~(mult(b, mult(a, mult(b, c))) = mult(b, mult(mult(b, c), a)))) <=> (~(mult(mult(b, a), mult(b, c)) = mult(mult(b, mult(b, c)), a)))),
% 23.19/23.36 inference(monotonicity,[status(thm)],[8976])).
% 23.19/23.36 tff(8978,plain,
% 23.19/23.36 (~(mult(mult(b, a), mult(b, c)) = mult(mult(b, mult(b, c)), a))),
% 23.19/23.36 inference(modus_ponens,[status(thm)],[8969, 8977])).
% 23.19/23.36 tff(8979,assumption,(mult(mult(mult(b, c), c), a) = mult(mult(mult(b, c), a), c)), introduced(assumption)).
% 23.19/23.36 tff(8980,assumption,(mult(mult(c, mult(b, c)), a) = mult(mult(c, a), mult(b, c))), introduced(assumption)).
% 23.19/23.36 tff(8981,plain,
% 23.19/23.36 (mult(mult(c, a), mult(b, c)) = mult(mult(c, mult(b, c)), a)),
% 23.19/23.36 inference(symmetry,[status(thm)],[8980])).
% 23.19/23.36 tff(8982,plain,
% 23.19/23.36 (mult(mult(a, c), mult(b, c)) = mult(mult(c, a), mult(b, c))),
% 23.19/23.36 inference(monotonicity,[status(thm)],[8565])).
% 23.19/23.36 tff(8983,plain,
% 23.19/23.36 (mult(mult(a, mult(b, c)), c) = mult(mult(mult(b, c), a), c)),
% 23.19/23.36 inference(transitivity,[status(thm)],[8159, 8982, 8981, 4181, 8979])).
% 23.19/23.36 tff(8984,plain,
% 23.19/23.36 (rd(mult(mult(a, mult(b, c)), c), c) = rd(mult(mult(mult(b, c), a), c), c)),
% 23.19/23.36 inference(monotonicity,[status(thm)],[8983])).
% 23.19/23.36 tff(8985,plain,
% 23.19/23.36 (mult(a, mult(b, c)) = rd(mult(mult(a, mult(b, c)), c), c)),
% 23.19/23.36 inference(symmetry,[status(thm)],[180])).
% 23.19/23.36 tff(8986,plain,
% 23.19/23.36 (mult(a, mult(b, c)) = mult(mult(b, c), a)),
% 23.19/23.36 inference(transitivity,[status(thm)],[8985, 8984, 2676])).
% 23.19/23.36 tff(8987,plain,
% 23.19/23.36 (mult(b, mult(a, mult(b, c))) = mult(b, mult(mult(b, c), a))),
% 23.19/23.36 inference(monotonicity,[status(thm)],[8986])).
% 23.19/23.36 tff(8988,plain,
% 23.19/23.36 (mult(mult(b, a), mult(b, c)) = mult(mult(b, mult(b, c)), a)),
% 23.19/23.36 inference(transitivity,[status(thm)],[7954, 8987, 7550])).
% 23.19/23.36 tff(8989,assumption,(~(mult(mult(b, a), mult(b, c)) = mult(mult(b, mult(b, c)), a))), introduced(assumption)).
% 23.19/23.36 tff(8990,plain,
% 23.19/23.36 ($false),
% 23.19/23.36 inference(unit_resolution,[status(thm)],[8989, 8988])).
% 23.19/23.36 tff(8991,plain,((~(mult(mult(c, mult(b, c)), a) = mult(mult(c, a), mult(b, c)))) | (mult(mult(b, a), mult(b, c)) = mult(mult(b, mult(b, c)), a)) | (~(mult(mult(b, a), mult(b, c)) = mult(b, mult(a, mult(b, c))))) | (~(mult(mult(b, mult(b, c)), a) = mult(b, mult(mult(b, c), a)))) | (~(mult(mult(mult(b, c), c), a) = mult(mult(mult(b, c), a), c)))), inference(lemma,lemma(discharge,[]))).
% 23.19/23.36 tff(8992,plain,
% 23.19/23.36 (~(mult(mult(c, mult(b, c)), a) = mult(mult(c, a), mult(b, c)))),
% 23.19/23.36 inference(unit_resolution,[status(thm)],[8991, 8978, 8973, 8972, 8635])).
% 23.19/23.36 tff(8993,plain,
% 23.19/23.36 ((~(mult(mult(c, mult(b, c)), a) = mult(mult(c, a), mult(b, c)))) | (~(mult(c, mult(mult(b, c), a)) = mult(c, mult(a, mult(b, c)))))),
% 23.19/23.36 inference(unit_resolution,[status(thm)],[4194, 8992])).
% 23.19/23.36 tff(8994,plain,
% 23.19/23.36 (~((~(mult(mult(c, mult(b, c)), a) = mult(c, mult(mult(b, c), a)))) | (~(mult(mult(c, a), mult(b, c)) = mult(c, mult(a, mult(b, c))))))),
% 23.19/23.36 inference(unit_resolution,[status(thm)],[4199, 8993])).
% 23.19/23.36 tff(8995,plain,
% 23.19/23.36 (mult(mult(c, mult(b, c)), a) = mult(c, mult(mult(b, c), a))),
% 23.19/23.36 inference(unit_resolution,[status(thm)],[4201, 8994])).
% 23.19/23.36 tff(8996,plain,
% 23.19/23.36 (mult(c, mult(mult(b, c), a)) = mult(mult(c, mult(b, c)), a)),
% 23.19/23.36 inference(symmetry,[status(thm)],[8995])).
% 23.19/23.36 tff(8997,plain,
% 23.19/23.36 (mult(c, mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a)) = mult(c, mult(mult(b, c), a))),
% 23.19/23.36 inference(monotonicity,[status(thm)],[8961])).
% 23.19/23.36 tff(8998,plain,
% 23.19/23.36 (mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(c, a), mult(rd(mult(b, c), mult(a, c)), c))),
% 23.19/23.36 inference(symmetry,[status(thm)],[8958])).
% 23.19/23.36 tff(8999,plain,
% 23.19/23.36 (mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c))),
% 23.19/23.36 inference(symmetry,[status(thm)],[8957])).
% 23.19/23.36 tff(9000,plain,
% 23.19/23.36 (mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(c, a), mult(rd(mult(b, c), mult(a, c)), c))),
% 23.19/23.36 inference(transitivity,[status(thm)],[8999, 8998])).
% 23.19/23.36 tff(9001,plain,
% 23.19/23.36 (mult(mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(c, a), mult(rd(mult(b, c), mult(a, c)), c)), a)),
% 23.19/23.36 inference(monotonicity,[status(thm)],[9000])).
% 23.19/23.36 tff(9002,plain,
% 23.19/23.36 (mult(mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(b, c), c), a)),
% 23.19/23.36 inference(transitivity,[status(thm)],[9001, 5195, 8997, 8996, 4181])).
% 23.19/23.36 tff(9003,plain,
% 23.19/23.36 (rd(mult(mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))), a), a) = rd(mult(mult(mult(b, c), c), a), a)),
% 23.19/23.36 inference(monotonicity,[status(thm)],[9002])).
% 23.19/23.36 tff(9004,plain,
% 23.19/23.36 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))), a), a) = mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))),
% 23.19/23.36 inference(quant_inst,[status(thm)],[])).
% 23.19/23.36 tff(9005,plain,
% 23.19/23.36 (rd(mult(mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))), a), a) = mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))),
% 23.19/23.36 inference(unit_resolution,[status(thm)],[9004, 168])).
% 23.19/23.36 tff(9006,plain,
% 23.19/23.36 (mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))) = rd(mult(mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))), a), a)),
% 23.19/23.36 inference(symmetry,[status(thm)],[9005])).
% 23.19/23.36 tff(9007,plain,
% 23.19/23.36 (mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(b, c), c)),
% 23.19/23.36 inference(transitivity,[status(thm)],[9006, 9003, 8631])).
% 23.19/23.36 tff(9008,plain,
% 23.19/23.36 (mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(b, c), c))),
% 23.19/23.36 inference(monotonicity,[status(thm)],[9007])).
% 23.19/23.36 tff(9009,plain,
% 23.19/23.36 (mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 23.19/23.36 inference(transitivity,[status(thm)],[9008, 8629])).
% 23.19/23.36 tff(9010,plain,
% 23.19/23.36 (mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c))) = mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 23.19/23.36 inference(transitivity,[status(thm)],[2802, 8572])).
% 23.19/23.36 tff(9011,plain,
% 23.19/23.36 ((mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))) <=> (mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 23.19/23.36 inference(monotonicity,[status(thm)],[2815, 9010])).
% 23.19/23.36 tff(9012,plain,
% 23.19/23.36 ((mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c))))) <=> (mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))),
% 23.19/23.36 inference(symmetry,[status(thm)],[9011])).
% 23.19/23.36 tff(9013,plain,
% 23.19/23.36 (mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))),
% 23.19/23.36 inference(modus_ponens,[status(thm)],[8625, 9012])).
% 23.19/23.36 tff(9014,plain,
% 23.19/23.36 ((mult(mult(a, mult(b, c)), c) = mult(a, mult(mult(b, c), c))) <=> (mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)))),
% 23.19/23.36 inference(transitivity,[status(thm)],[8906, 8901, 8883])).
% 23.19/23.36 tff(9015,plain,
% 23.19/23.36 ((~(mult(mult(a, mult(b, c)), c) = mult(a, mult(mult(b, c), c)))) <=> (~(mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c))))),
% 23.19/23.36 inference(monotonicity,[status(thm)],[9014])).
% 23.19/23.36 tff(9016,plain,
% 23.19/23.36 (~(mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)))),
% 23.19/23.36 inference(modus_ponens,[status(thm)],[258, 9015])).
% 23.19/23.36 tff(9017,assumption,(~(mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)))), introduced(assumption)).
% 23.19/23.36 tff(9018,plain,
% 23.19/23.36 ((~(mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)))) | (~(mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))))),
% 23.19/23.36 inference(unit_resolution,[status(thm)],[4606, 9017])).
% 23.19/23.36 tff(9019,plain,
% 23.19/23.36 (~((~(mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))))),
% 23.19/23.36 inference(unit_resolution,[status(thm)],[4565, 9018])).
% 23.19/23.36 tff(9020,plain,
% 23.19/23.36 (mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 23.19/23.36 inference(unit_resolution,[status(thm)],[4560, 9019])).
% 23.19/23.36 tff(9021,plain,
% 23.19/23.36 (mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c))),
% 23.19/23.36 inference(symmetry,[status(thm)],[9020])).
% 23.19/23.36 tff(9022,plain,
% 23.19/23.36 (mult(a, mult(mult(b, c), c)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 23.19/23.36 inference(symmetry,[status(thm)],[4539])).
% 23.19/23.36 tff(9023,plain,
% 23.19/23.36 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(b, c), c))) = mult(mult(b, c), c))),
% 23.19/23.36 inference(quant_inst,[status(thm)],[])).
% 23.19/23.36 tff(9024,plain,
% 23.19/23.36 (ld(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(b, c), c))) = mult(mult(b, c), c)),
% 23.19/23.36 inference(unit_resolution,[status(thm)],[9023, 7])).
% 23.19/23.36 tff(9025,plain,
% 23.19/23.36 (mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))) = mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(b, c), c))),
% 23.19/23.36 inference(monotonicity,[status(thm)],[4538])).
% 23.19/23.36 tff(9026,assumption,(mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))), introduced(assumption)).
% 23.19/23.36 tff(9027,plain,
% 23.19/23.36 (mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(b, c), c))),
% 23.19/23.36 inference(transitivity,[status(thm)],[9026, 9025])).
% 23.19/23.36 tff(9028,plain,
% 23.19/23.36 (ld(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))) = ld(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(b, c), c)))),
% 23.19/23.36 inference(monotonicity,[status(thm)],[9027])).
% 23.19/23.36 tff(9029,plain,
% 23.19/23.36 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))) = mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))),
% 23.19/23.36 inference(quant_inst,[status(thm)],[])).
% 23.19/23.36 tff(9030,plain,
% 23.19/23.36 (ld(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))) = mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))),
% 23.19/23.36 inference(unit_resolution,[status(thm)],[9029, 7])).
% 23.19/23.36 tff(9031,plain,
% 23.19/23.36 (mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))) = ld(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))))),
% 23.19/23.36 inference(symmetry,[status(thm)],[9030])).
% 23.19/23.36 tff(9032,plain,
% 23.19/23.36 (mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(b, c), c)),
% 23.19/23.36 inference(transitivity,[status(thm)],[9031, 9028, 9024])).
% 23.19/23.36 tff(9033,plain,
% 23.19/23.36 (mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(b, c), c))),
% 23.19/23.36 inference(monotonicity,[status(thm)],[9032])).
% 23.19/23.36 tff(9034,plain,
% 23.19/23.36 (mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))),
% 23.19/23.36 inference(unit_resolution,[status(thm)],[8924, 9019])).
% 23.19/23.36 tff(9035,plain,
% 23.19/23.36 (mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c))),
% 23.19/23.36 inference(transitivity,[status(thm)],[9034, 9033, 9022, 9021])).
% 23.19/23.36 tff(9036,plain,
% 23.19/23.36 ($false),
% 23.19/23.36 inference(unit_resolution,[status(thm)],[9017, 9035])).
% 23.19/23.36 tff(9037,plain,((~(mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))) | (mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))), inference(lemma,lemma(discharge,[]))).
% 23.19/23.37 tff(9038,plain,
% 23.19/23.37 (~(mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))),
% 23.19/23.37 inference(unit_resolution,[status(thm)],[9037, 9016, 9013])).
% 23.19/23.37 tff(9039,plain,
% 23.19/23.37 ($false),
% 23.19/23.37 inference(unit_resolution,[status(thm)],[9038, 9009])).
% 23.19/23.37 tff(9040,plain,((mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) | (~(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)))) | (~(mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))))), inference(lemma,lemma(discharge,[]))).
% 23.19/23.37 tff(9041,plain,
% 23.19/23.37 (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))),
% 23.19/23.37 inference(unit_resolution,[status(thm)],[9040, 8561, 8345, 8352])).
% 23.19/23.37 tff(9042,plain,
% 23.19/23.37 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a)),
% 23.19/23.37 inference(symmetry,[status(thm)],[9041])).
% 23.19/23.37 tff(9043,plain,
% 23.19/23.37 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a) = mult(mult(b, c), a)),
% 23.19/23.37 inference(transitivity,[status(thm)],[1168, 9042, 1332])).
% 23.19/23.37 tff(9044,plain,
% 23.19/23.37 (rd(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a), a) = rd(mult(mult(b, c), a), a)),
% 23.19/23.37 inference(monotonicity,[status(thm)],[9043])).
% 23.19/23.37 tff(9045,plain,
% 23.19/23.37 (mult(mult(rd(mult(b, c), mult(a, c)), a), c) = mult(b, c)),
% 23.19/23.37 inference(transitivity,[status(thm)],[1377, 9044, 1370])).
% 23.19/23.37 tff(9046,plain,
% 23.19/23.37 (rd(mult(mult(rd(mult(b, c), mult(a, c)), a), c), c) = rd(mult(b, c), c)),
% 23.19/23.37 inference(monotonicity,[status(thm)],[9045])).
% 23.19/23.37 tff(9047,plain,
% 23.19/23.37 (mult(rd(mult(b, c), mult(a, c)), a) = b),
% 23.19/23.37 inference(transitivity,[status(thm)],[175, 9046, 170])).
% 23.19/23.37 tff(9048,plain,
% 23.19/23.37 (mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, c), b)),
% 23.19/23.37 inference(monotonicity,[status(thm)],[9047])).
% 23.19/23.37 tff(9049,plain,
% 23.19/23.37 (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(b, c))),
% 23.19/23.37 inference(transitivity,[status(thm)],[8561, 142])).
% 23.19/23.37 tff(9050,plain,
% 23.19/23.37 (ld(a, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))) = ld(a, mult(a, mult(b, c)))),
% 23.19/23.37 inference(monotonicity,[status(thm)],[9049])).
% 23.19/23.37 tff(9051,plain,
% 23.19/23.37 (ld(a, mult(a, mult(b, c))) = ld(a, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 23.19/23.37 inference(symmetry,[status(thm)],[9050])).
% 23.19/23.37 tff(9052,plain,
% 23.19/23.37 (mult(b, c) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))),
% 23.19/23.37 inference(transitivity,[status(thm)],[843, 9051, 4336])).
% 23.19/23.37 tff(9053,plain,
% 23.19/23.37 (mult(mult(b, c), a) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)),
% 23.19/23.37 inference(monotonicity,[status(thm)],[9052])).
% 23.19/23.37 tff(9054,plain,
% 23.19/23.37 (mult(mult(b, c), a) = mult(mult(a, c), b)),
% 23.19/23.37 inference(transitivity,[status(thm)],[9053, 5496, 9048])).
% 23.19/23.37 tff(9055,plain,
% 23.19/23.37 (mult(mult(mult(b, c), a), c) = mult(mult(mult(a, c), b), c)),
% 23.19/23.37 inference(monotonicity,[status(thm)],[9054])).
% 23.19/23.37 tff(9056,plain,
% 23.19/23.37 (mult(mult(mult(a, c), b), c) = mult(mult(mult(b, c), a), c)),
% 23.19/23.37 inference(symmetry,[status(thm)],[9055])).
% 23.19/23.37 tff(9057,plain,
% 23.19/23.37 (mult(mult(unit, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))),
% 23.19/23.37 inference(monotonicity,[status(thm)],[1549])).
% 23.19/23.37 tff(9058,plain,
% 23.19/23.37 (mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(unit, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a))),
% 23.19/23.37 inference(symmetry,[status(thm)],[9057])).
% 23.19/23.37 tff(9059,plain,
% 23.19/23.37 (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(mult(unit, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a))),
% 23.19/23.37 inference(transitivity,[status(thm)],[1332, 9053, 5496, 9058])).
% 23.19/23.37 tff(9060,plain,
% 23.19/23.37 ((~![A: $i] : (mult(A, unit) = A)) | (mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit) = mult(unit, mult(rd(mult(b, c), mult(a, c)), a)))),
% 23.19/23.37 inference(quant_inst,[status(thm)],[])).
% 23.19/23.37 tff(9061,plain,
% 23.19/23.37 (mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit) = mult(unit, mult(rd(mult(b, c), mult(a, c)), a))),
% 23.19/23.37 inference(unit_resolution,[status(thm)],[9060, 43])).
% 23.19/23.37 tff(9062,plain,
% 23.19/23.37 (mult(unit, mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit)),
% 23.19/23.37 inference(symmetry,[status(thm)],[9061])).
% 23.19/23.37 tff(9063,plain,
% 23.19/23.37 (mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), mult(a, c)) = mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit), mult(a, c))),
% 23.19/23.37 inference(monotonicity,[status(thm)],[9062])).
% 23.19/23.37 tff(9064,plain,
% 23.19/23.37 (mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit), mult(a, c)) = mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), mult(a, c))),
% 23.19/23.37 inference(symmetry,[status(thm)],[9063])).
% 23.19/23.37 tff(9065,plain,
% 23.19/23.37 (mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit) = mult(rd(mult(b, c), mult(a, c)), a)),
% 23.19/23.37 inference(transitivity,[status(thm)],[9061, 6238])).
% 23.19/23.37 tff(9066,plain,
% 23.19/23.37 (mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c))),
% 23.19/23.37 inference(monotonicity,[status(thm)],[9065])).
% 23.19/23.37 tff(9067,plain,
% 23.19/23.37 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit), mult(a, c))),
% 23.19/23.37 inference(symmetry,[status(thm)],[9066])).
% 23.19/23.37 tff(9068,plain,
% 23.19/23.37 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), mult(a, c))),
% 23.19/23.37 inference(transitivity,[status(thm)],[9067, 9064])).
% 23.19/23.37 tff(9069,plain,
% 23.19/23.37 ((mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a)) <=> (mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), mult(a, c)) = mult(mult(unit, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)))),
% 23.19/23.37 inference(monotonicity,[status(thm)],[9068, 9059])).
% 23.19/23.37 tff(9070,plain,
% 23.19/23.37 ((mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), mult(a, c)) = mult(mult(unit, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a))) <=> (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a))),
% 23.19/23.37 inference(symmetry,[status(thm)],[9069])).
% 23.19/23.37 tff(9071,plain,
% 23.19/23.37 (mult(mult(a, c), b) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))),
% 23.19/23.37 inference(symmetry,[status(thm)],[9048])).
% 23.19/23.37 tff(9072,plain,
% 23.19/23.37 (mult(mult(unit, mult(a, c)), b) = mult(mult(unit, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a))),
% 23.19/23.37 inference(transitivity,[status(thm)],[5506, 9071, 9058])).
% 23.19/23.37 tff(9073,plain,
% 23.19/23.37 (rd(mult(b, c), c) = rd(mult(mult(rd(mult(b, c), mult(a, c)), a), c), c)),
% 23.19/23.37 inference(symmetry,[status(thm)],[9046])).
% 23.19/23.37 tff(9074,plain,
% 23.19/23.37 (b = mult(rd(mult(b, c), mult(a, c)), a)),
% 23.19/23.37 inference(transitivity,[status(thm)],[2727, 9073, 174])).
% 23.19/23.37 tff(9075,plain,
% 23.19/23.37 (mult(b, mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c))),
% 23.19/23.37 inference(monotonicity,[status(thm)],[9074])).
% 23.19/23.37 tff(9076,plain,
% 23.19/23.37 (mult(mult(unit, b), mult(a, c)) = mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), mult(a, c))),
% 23.19/23.37 inference(transitivity,[status(thm)],[5511, 9075, 9067, 9064])).
% 23.19/23.37 tff(9077,plain,
% 23.19/23.37 ((mult(mult(unit, b), mult(a, c)) = mult(mult(unit, mult(a, c)), b)) <=> (mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), mult(a, c)) = mult(mult(unit, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)))),
% 23.19/23.37 inference(monotonicity,[status(thm)],[9076, 9072])).
% 23.19/23.37 tff(9078,plain,
% 23.19/23.37 ((mult(mult(unit, b), mult(a, c)) = mult(mult(unit, mult(a, c)), b)) <=> (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a))),
% 23.19/23.37 inference(transitivity,[status(thm)],[9077, 9070])).
% 23.19/23.37 tff(9079,plain,
% 23.19/23.37 (mult(mult(unit, b), mult(a, c)) = mult(mult(unit, mult(a, c)), b)),
% 23.19/23.37 inference(unit_resolution,[status(thm)],[8688, 8561])).
% 23.19/23.37 tff(9080,plain,
% 23.19/23.37 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a)),
% 23.19/23.37 inference(modus_ponens,[status(thm)],[9079, 9078])).
% 23.19/23.37 tff(9081,plain,
% 23.19/23.37 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(a, c), b)),
% 23.19/23.37 inference(transitivity,[status(thm)],[9080, 1332, 9053, 5496, 9048])).
% 23.19/23.37 tff(9082,plain,
% 23.19/23.37 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)), c) = mult(mult(mult(a, c), b), c)),
% 23.19/23.37 inference(monotonicity,[status(thm)],[9081])).
% 23.19/23.37 tff(9083,plain,
% 23.19/23.37 (mult(mult(b, mult(a, c)), c) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)), c)),
% 23.19/23.37 inference(monotonicity,[status(thm)],[9075])).
% 23.19/23.37 tff(9084,plain,
% 23.19/23.37 (mult(mult(b, mult(a, c)), c) = mult(mult(mult(b, c), a), c)),
% 23.19/23.37 inference(transitivity,[status(thm)],[9083, 9082, 9056])).
% 23.19/23.37 tff(9085,plain,
% 23.19/23.37 ((mult(mult(b, mult(a, c)), c) = mult(mult(b, c), mult(a, c))) <=> (mult(mult(mult(b, c), a), c) = mult(mult(b, c), mult(a, c)))),
% 23.19/23.37 inference(monotonicity,[status(thm)],[9084])).
% 23.19/23.37 tff(9086,plain,
% 23.19/23.37 (mult(mult(mult(b, c), a), c) = mult(mult(b, c), mult(a, c))),
% 23.19/23.37 inference(modus_ponens,[status(thm)],[5435, 9085])).
% 23.19/23.37 tff(9087,plain,
% 23.19/23.37 (mult(b, mult(c, mult(a, c))) = mult(b, mult(mult(a, c), c))),
% 23.19/23.37 inference(monotonicity,[status(thm)],[4122])).
% 23.19/23.37 tff(9088,plain,
% 23.19/23.37 (mult(b, mult(mult(a, c), c)) = mult(b, mult(c, mult(a, c)))),
% 23.19/23.37 inference(symmetry,[status(thm)],[9087])).
% 23.19/23.37 tff(9089,plain,
% 23.19/23.37 (ld(b, mult(b, mult(c, a))) = ld(b, mult(b, mult(a, c)))),
% 23.19/23.37 inference(monotonicity,[status(thm)],[368])).
% 23.19/23.37 tff(9090,plain,
% 23.19/23.37 (mult(c, a) = mult(a, c)),
% 23.19/23.37 inference(transitivity,[status(thm)],[373, 9089, 2260])).
% 23.19/23.37 tff(9091,plain,
% 23.19/23.37 (mult(mult(b, c), mult(c, a)) = mult(mult(b, c), mult(a, c))),
% 23.19/23.37 inference(monotonicity,[status(thm)],[9090])).
% 23.19/23.37 tff(9092,plain,
% 23.19/23.37 (mult(b, mult(mult(c, a), c)) = mult(mult(b, c), mult(a, c))),
% 23.19/23.37 inference(transitivity,[status(thm)],[4150, 2512])).
% 23.19/23.37 tff(9093,plain,
% 23.19/23.37 (mult(b, mult(a, c)) = mult(b, mult(c, a))),
% 23.19/23.37 inference(symmetry,[status(thm)],[368])).
% 23.19/23.37 tff(9094,plain,
% 23.19/23.37 (mult(mult(b, mult(a, c)), c) = mult(mult(b, mult(c, a)), c)),
% 23.19/23.37 inference(monotonicity,[status(thm)],[9093])).
% 23.19/23.37 tff(9095,plain,
% 23.19/23.37 (mult(mult(b, mult(c, a)), c) = mult(mult(b, mult(a, c)), c)),
% 23.19/23.37 inference(symmetry,[status(thm)],[9094])).
% 23.19/23.37 tff(9096,plain,
% 23.19/23.37 ((mult(mult(b, mult(c, a)), c) = mult(b, mult(mult(c, a), c))) <=> (mult(mult(b, mult(a, c)), c) = mult(mult(b, c), mult(a, c)))),
% 23.19/23.37 inference(monotonicity,[status(thm)],[9095, 9092])).
% 23.19/23.37 tff(9097,plain,
% 23.19/23.37 ((mult(mult(b, mult(a, c)), c) = mult(mult(b, c), mult(a, c))) <=> (mult(mult(b, mult(c, a)), c) = mult(b, mult(mult(c, a), c)))),
% 23.19/23.37 inference(symmetry,[status(thm)],[9096])).
% 23.19/23.37 tff(9098,plain,
% 23.19/23.37 ((~(mult(mult(b, mult(a, c)), c) = mult(mult(b, c), mult(a, c)))) <=> (~(mult(mult(b, mult(c, a)), c) = mult(b, mult(mult(c, a), c))))),
% 23.19/23.37 inference(monotonicity,[status(thm)],[9097])).
% 23.19/23.37 tff(9099,plain,
% 23.19/23.37 (~(mult(mult(b, mult(c, a)), c) = mult(b, mult(mult(c, a), c)))),
% 23.19/23.37 inference(modus_ponens,[status(thm)],[2507, 9098])).
% 23.19/23.37 tff(9100,plain,
% 23.19/23.37 (((~(mult(mult(b, c), mult(c, a)) = mult(b, mult(c, mult(c, a))))) | (~(mult(mult(b, mult(c, a)), c) = mult(b, mult(mult(c, a), c))))) | (mult(mult(b, mult(c, a)), c) = mult(b, mult(mult(c, a), c)))),
% 23.19/23.37 inference(tautology,[status(thm)],[])).
% 23.19/23.37 tff(9101,plain,
% 23.19/23.37 ((~(mult(mult(b, c), mult(c, a)) = mult(b, mult(c, mult(c, a))))) | (~(mult(mult(b, mult(c, a)), c) = mult(b, mult(mult(c, a), c))))),
% 23.19/23.37 inference(unit_resolution,[status(thm)],[9100, 9099])).
% 23.19/23.37 tff(9102,plain,
% 23.19/23.37 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(b, c), mult(c, a)) = mult(b, mult(c, mult(c, a))))) | (~(mult(mult(b, mult(c, a)), c) = mult(b, mult(mult(c, a), c)))))) | (~((~(mult(mult(b, c), mult(c, a)) = mult(mult(b, mult(c, a)), c))) | (~(mult(b, mult(c, mult(c, a))) = mult(b, mult(mult(c, a), c)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(b, c), mult(c, a)) = mult(b, mult(c, mult(c, a))))) | (~(mult(mult(b, mult(c, a)), c) = mult(b, mult(mult(c, a), c)))))) | (~((~(mult(mult(b, c), mult(c, a)) = mult(mult(b, mult(c, a)), c))) | (~(mult(b, mult(c, mult(c, a))) = mult(b, mult(mult(c, a), c)))))))),
% 23.19/23.37 inference(rewrite,[status(thm)],[])).
% 23.19/23.37 tff(9103,plain,
% 23.19/23.37 (((~((~(mult(mult(b, c), mult(c, a)) = mult(mult(b, mult(c, a)), c))) | (~(mult(b, mult(c, mult(c, a))) = mult(b, mult(mult(c, a), c)))))) | (~((~(mult(mult(b, c), mult(c, a)) = mult(b, mult(c, mult(c, a))))) | (~(mult(mult(b, mult(c, a)), c) = mult(b, mult(mult(c, a), c))))))) <=> ((~((~(mult(mult(b, c), mult(c, a)) = mult(b, mult(c, mult(c, a))))) | (~(mult(mult(b, mult(c, a)), c) = mult(b, mult(mult(c, a), c)))))) | (~((~(mult(mult(b, c), mult(c, a)) = mult(mult(b, mult(c, a)), c))) | (~(mult(b, mult(c, mult(c, a))) = mult(b, mult(mult(c, a), c)))))))),
% 23.19/23.37 inference(rewrite,[status(thm)],[])).
% 23.19/23.37 tff(9104,plain,
% 23.19/23.37 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(b, c), mult(c, a)) = mult(mult(b, mult(c, a)), c))) | (~(mult(b, mult(c, mult(c, a))) = mult(b, mult(mult(c, a), c)))))) | (~((~(mult(mult(b, c), mult(c, a)) = mult(b, mult(c, mult(c, a))))) | (~(mult(mult(b, mult(c, a)), c) = mult(b, mult(mult(c, a), c)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(b, c), mult(c, a)) = mult(b, mult(c, mult(c, a))))) | (~(mult(mult(b, mult(c, a)), c) = mult(b, mult(mult(c, a), c)))))) | (~((~(mult(mult(b, c), mult(c, a)) = mult(mult(b, mult(c, a)), c))) | (~(mult(b, mult(c, mult(c, a))) = mult(b, mult(mult(c, a), c))))))))),
% 23.19/23.37 inference(monotonicity,[status(thm)],[9103])).
% 23.19/23.37 tff(9105,plain,
% 23.19/23.37 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(b, c), mult(c, a)) = mult(mult(b, mult(c, a)), c))) | (~(mult(b, mult(c, mult(c, a))) = mult(b, mult(mult(c, a), c)))))) | (~((~(mult(mult(b, c), mult(c, a)) = mult(b, mult(c, mult(c, a))))) | (~(mult(mult(b, mult(c, a)), c) = mult(b, mult(mult(c, a), c)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(b, c), mult(c, a)) = mult(b, mult(c, mult(c, a))))) | (~(mult(mult(b, mult(c, a)), c) = mult(b, mult(mult(c, a), c)))))) | (~((~(mult(mult(b, c), mult(c, a)) = mult(mult(b, mult(c, a)), c))) | (~(mult(b, mult(c, mult(c, a))) = mult(b, mult(mult(c, a), c)))))))),
% 23.19/23.37 inference(transitivity,[status(thm)],[9104, 9102])).
% 23.19/23.37 tff(9106,plain,
% 23.19/23.37 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(b, c), mult(c, a)) = mult(mult(b, mult(c, a)), c))) | (~(mult(b, mult(c, mult(c, a))) = mult(b, mult(mult(c, a), c)))))) | (~((~(mult(mult(b, c), mult(c, a)) = mult(b, mult(c, mult(c, a))))) | (~(mult(mult(b, mult(c, a)), c) = mult(b, mult(mult(c, a), c)))))))),
% 23.19/23.37 inference(quant_inst,[status(thm)],[])).
% 23.19/23.37 tff(9107,plain,
% 23.19/23.37 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(b, c), mult(c, a)) = mult(b, mult(c, mult(c, a))))) | (~(mult(mult(b, mult(c, a)), c) = mult(b, mult(mult(c, a), c)))))) | (~((~(mult(mult(b, c), mult(c, a)) = mult(mult(b, mult(c, a)), c))) | (~(mult(b, mult(c, mult(c, a))) = mult(b, mult(mult(c, a), c))))))),
% 23.19/23.37 inference(modus_ponens,[status(thm)],[9106, 9105])).
% 23.19/23.37 tff(9108,plain,
% 23.19/23.37 ((~((~(mult(mult(b, c), mult(c, a)) = mult(b, mult(c, mult(c, a))))) | (~(mult(mult(b, mult(c, a)), c) = mult(b, mult(mult(c, a), c)))))) | (~((~(mult(mult(b, c), mult(c, a)) = mult(mult(b, mult(c, a)), c))) | (~(mult(b, mult(c, mult(c, a))) = mult(b, mult(mult(c, a), c))))))),
% 23.19/23.37 inference(unit_resolution,[status(thm)],[9107, 27])).
% 23.19/23.37 tff(9109,plain,
% 23.19/23.37 (~((~(mult(mult(b, c), mult(c, a)) = mult(mult(b, mult(c, a)), c))) | (~(mult(b, mult(c, mult(c, a))) = mult(b, mult(mult(c, a), c)))))),
% 23.19/23.37 inference(unit_resolution,[status(thm)],[9108, 9101])).
% 23.19/23.37 tff(9110,plain,
% 23.19/23.37 (((~(mult(mult(b, c), mult(c, a)) = mult(mult(b, mult(c, a)), c))) | (~(mult(b, mult(c, mult(c, a))) = mult(b, mult(mult(c, a), c))))) | (mult(mult(b, c), mult(c, a)) = mult(mult(b, mult(c, a)), c))),
% 23.19/23.37 inference(tautology,[status(thm)],[])).
% 23.19/23.37 tff(9111,plain,
% 23.19/23.37 (mult(mult(b, c), mult(c, a)) = mult(mult(b, mult(c, a)), c)),
% 23.19/23.37 inference(unit_resolution,[status(thm)],[9110, 9109])).
% 23.19/23.37 tff(9112,plain,
% 23.19/23.37 (mult(mult(b, mult(c, a)), c) = mult(mult(b, c), mult(c, a))),
% 23.19/23.37 inference(symmetry,[status(thm)],[9111])).
% 23.19/23.37 tff(9113,plain,
% 23.19/23.37 (mult(mult(b, mult(a, c)), c) = mult(mult(b, c), mult(a, c))),
% 23.19/23.37 inference(transitivity,[status(thm)],[9094, 9112, 9091])).
% 23.19/23.37 tff(9114,plain,
% 23.19/23.37 ($false),
% 23.19/23.37 inference(unit_resolution,[status(thm)],[2507, 9113])).
% 23.19/23.37 tff(9115,plain,((~(mult(b, mult(c, a)) = mult(b, mult(a, c)))) | (mult(mult(b, mult(a, c)), c) = mult(mult(b, c), mult(a, c))) | (~(mult(mult(c, a), c) = mult(c, mult(a, c))))), inference(lemma,lemma(discharge,[]))).
% 23.19/23.37 tff(9116,plain,
% 23.19/23.37 (mult(mult(b, mult(a, c)), c) = mult(mult(b, c), mult(a, c))),
% 23.19/23.37 inference(unit_resolution,[status(thm)],[9115, 4896, 2690])).
% 23.19/23.37 tff(9117,plain,
% 23.19/23.37 ((mult(mult(b, mult(a, c)), c) = mult(b, mult(mult(a, c), c))) <=> (mult(mult(b, c), mult(a, c)) = mult(b, mult(c, mult(a, c))))),
% 23.19/23.37 inference(monotonicity,[status(thm)],[9116, 9088])).
% 23.19/23.37 tff(9118,plain,
% 23.19/23.37 ((mult(mult(b, c), mult(a, c)) = mult(b, mult(c, mult(a, c)))) <=> (mult(mult(b, mult(a, c)), c) = mult(b, mult(mult(a, c), c)))),
% 23.19/23.37 inference(symmetry,[status(thm)],[9117])).
% 23.19/23.37 tff(9119,plain,
% 23.19/23.37 (mult(mult(c, a), c) = mult(c, mult(a, c))),
% 23.19/23.37 inference(transitivity,[status(thm)],[4065, 2596, 2593, 2590])).
% 23.19/23.37 tff(9120,plain,
% 23.19/23.37 (mult(b, mult(mult(c, a), c)) = mult(b, mult(c, mult(a, c)))),
% 23.19/23.37 inference(monotonicity,[status(thm)],[9119])).
% 23.19/23.37 tff(9121,plain,
% 23.19/23.37 (mult(mult(mult(b, c), a), c) = mult(b, mult(c, mult(a, c)))),
% 23.19/23.37 inference(transitivity,[status(thm)],[2570, 9120])).
% 23.19/23.37 tff(9122,plain,
% 23.19/23.37 ((mult(mult(mult(b, c), a), c) = mult(mult(b, c), mult(a, c))) <=> (mult(b, mult(c, mult(a, c))) = mult(mult(b, c), mult(a, c)))),
% 23.19/23.37 inference(monotonicity,[status(thm)],[9121])).
% 23.19/23.37 tff(9123,plain,
% 23.19/23.37 ((mult(mult(mult(b, c), a), c) = mult(mult(b, c), mult(a, c))) <=> (mult(mult(b, c), mult(a, c)) = mult(b, mult(c, mult(a, c))))),
% 23.19/23.37 inference(transitivity,[status(thm)],[9122, 6765])).
% 23.19/23.37 tff(9124,plain,
% 23.19/23.37 ((mult(mult(mult(b, c), a), c) = mult(mult(b, c), mult(a, c))) <=> (mult(mult(b, mult(a, c)), c) = mult(b, mult(mult(a, c), c)))),
% 23.19/23.37 inference(transitivity,[status(thm)],[9123, 9118])).
% 23.19/23.37 tff(9125,assumption,(mult(mult(mult(b, c), a), c) = mult(mult(b, c), mult(a, c))), introduced(assumption)).
% 23.19/23.38 tff(9126,plain,
% 23.19/23.38 (mult(mult(b, mult(a, c)), c) = mult(b, mult(mult(a, c), c))),
% 23.19/23.38 inference(modus_ponens,[status(thm)],[9125, 9124])).
% 23.19/23.38 tff(9127,assumption,(~(mult(mult(b, mult(a, c)), c) = mult(b, mult(mult(a, c), c)))), introduced(assumption)).
% 23.19/23.38 tff(9128,plain,
% 23.19/23.38 ($false),
% 23.19/23.38 inference(unit_resolution,[status(thm)],[9127, 9126])).
% 23.19/23.38 tff(9129,plain,((~(mult(mult(mult(b, c), a), c) = mult(mult(b, c), mult(a, c)))) | (mult(mult(b, mult(a, c)), c) = mult(b, mult(mult(a, c), c))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c)))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit)))))), inference(lemma,lemma(discharge,[]))).
% 23.19/23.38 tff(9130,plain,
% 23.19/23.38 ((~(mult(mult(mult(b, c), a), c) = mult(mult(b, c), mult(a, c)))) | (mult(mult(b, mult(a, c)), c) = mult(b, mult(mult(a, c), c)))),
% 23.19/23.38 inference(unit_resolution,[status(thm)],[9129, 3862, 5434])).
% 23.19/23.38 tff(9131,plain,
% 23.19/23.38 (mult(mult(b, mult(a, c)), c) = mult(b, mult(mult(a, c), c))),
% 23.19/23.38 inference(unit_resolution,[status(thm)],[9130, 9086])).
% 23.19/23.38 tff(9132,plain,
% 23.19/23.38 (mult(b, mult(mult(a, c), c)) = mult(mult(b, mult(a, c)), c)),
% 23.19/23.38 inference(symmetry,[status(thm)],[9131])).
% 23.19/23.38 tff(9133,plain,
% 23.19/23.38 (mult(b, mult(mult(a, c), c)) = mult(b, mult(c, mult(a, c)))),
% 23.19/23.38 inference(transitivity,[status(thm)],[9132, 9083, 9082, 9056, 2570, 8560])).
% 23.19/23.38 tff(9134,plain,
% 23.19/23.38 (ld(b, mult(b, mult(mult(a, c), c))) = ld(b, mult(b, mult(c, mult(a, c))))),
% 23.19/23.38 inference(monotonicity,[status(thm)],[9133])).
% 23.19/23.38 tff(9135,plain,
% 23.19/23.38 (ld(b, mult(b, mult(c, mult(a, c)))) = ld(b, mult(b, mult(mult(a, c), c)))),
% 23.19/23.38 inference(symmetry,[status(thm)],[9134])).
% 23.19/23.38 tff(9136,plain,
% 23.19/23.38 (mult(c, mult(a, c)) = ld(b, mult(b, mult(c, mult(a, c))))),
% 23.19/23.38 inference(symmetry,[status(thm)],[2445])).
% 23.19/23.38 tff(9137,plain,
% 23.19/23.38 (mult(mult(c, a), c) = mult(mult(a, c), c)),
% 23.19/23.38 inference(transitivity,[status(thm)],[2690, 9136, 9135, 2449])).
% 23.19/23.38 tff(9138,plain,
% 23.19/23.38 (rd(mult(mult(c, a), c), c) = rd(mult(mult(a, c), c), c)),
% 23.19/23.38 inference(monotonicity,[status(thm)],[9137])).
% 23.19/23.38 tff(9139,plain,
% 23.19/23.38 (mult(c, a) = mult(a, c)),
% 23.19/23.38 inference(transitivity,[status(thm)],[2770, 9138, 2723])).
% 23.19/23.38 tff(9140,plain,
% 23.19/23.38 (mult(mult(c, a), b) = mult(mult(a, c), b)),
% 23.19/23.38 inference(monotonicity,[status(thm)],[9139])).
% 23.19/23.38 tff(9141,plain,
% 23.19/23.38 (mult(mult(a, c), b) = mult(mult(c, a), b)),
% 23.19/23.38 inference(symmetry,[status(thm)],[9140])).
% 23.19/23.38 tff(9142,plain,
% 23.19/23.38 (mult(c, mult(b, a)) = mult(c, mult(a, b))),
% 23.19/23.38 inference(transitivity,[status(thm)],[4304, 2298, 9053, 5496, 9048, 9141, 4221])).
% 23.19/23.38 tff(9143,plain,
% 23.19/23.38 (ld(c, mult(c, mult(b, a))) = ld(c, mult(c, mult(a, b)))),
% 23.19/23.38 inference(monotonicity,[status(thm)],[9142])).
% 23.19/23.38 tff(9144,plain,
% 23.19/23.38 (mult(b, a) = mult(a, b)),
% 23.19/23.38 inference(transitivity,[status(thm)],[1473, 9143, 1468])).
% 23.19/23.38 tff(9145,plain,
% 23.19/23.38 (mult(b, mult(b, a)) = mult(b, mult(a, b))),
% 23.19/23.38 inference(monotonicity,[status(thm)],[9144])).
% 23.19/23.38 tff(9146,plain,
% 23.19/23.38 (mult(b, mult(a, b)) = mult(b, mult(b, a))),
% 23.19/23.38 inference(symmetry,[status(thm)],[9145])).
% 23.19/23.38 tff(9147,plain,
% 23.19/23.38 (~(mult(b, mult(a, b)) = mult(b, mult(b, a)))),
% 23.19/23.38 inference(unit_resolution,[status(thm)],[8405, 9041, 8561, 8318])).
% 23.19/23.38 tff(9148,plain,
% 23.19/23.38 ((~(mult(mult(b, a), b) = mult(mult(b, b), a))) | (~(mult(b, mult(a, b)) = mult(b, mult(b, a))))),
% 23.19/23.38 inference(unit_resolution,[status(thm)],[413, 9147])).
% 23.19/23.38 tff(9149,plain,
% 23.19/23.38 (~((~(mult(mult(b, a), b) = mult(b, mult(a, b)))) | (~(mult(mult(b, b), a) = mult(b, mult(b, a)))))),
% 23.19/23.38 inference(unit_resolution,[status(thm)],[418, 9148])).
% 23.19/23.38 tff(9150,plain,
% 23.19/23.38 (mult(mult(b, a), b) = mult(b, mult(a, b))),
% 23.19/23.38 inference(unit_resolution,[status(thm)],[420, 9149])).
% 23.19/23.38 tff(9151,plain,
% 23.19/23.38 (mult(mult(b, a), b) = mult(mult(b, b), a)),
% 23.19/23.38 inference(transitivity,[status(thm)],[9150, 9146, 8558])).
% 23.19/23.38 tff(9152,plain,
% 23.19/23.38 (mult(b, mult(a, b)) = mult(mult(b, a), b)),
% 23.19/23.38 inference(symmetry,[status(thm)],[9150])).
% 23.19/23.38 tff(9153,plain,
% 23.19/23.38 ((mult(b, mult(a, b)) = mult(b, mult(b, a))) <=> (mult(mult(b, a), b) = mult(mult(b, b), a))),
% 23.19/23.38 inference(monotonicity,[status(thm)],[9152, 8558])).
% 23.19/23.38 tff(9154,plain,
% 23.19/23.38 ((~(mult(b, mult(a, b)) = mult(b, mult(b, a)))) <=> (~(mult(mult(b, a), b) = mult(mult(b, b), a)))),
% 23.19/23.38 inference(monotonicity,[status(thm)],[9153])).
% 23.19/23.38 tff(9155,plain,
% 23.19/23.38 (~(mult(mult(b, a), b) = mult(mult(b, b), a))),
% 23.19/23.38 inference(modus_ponens,[status(thm)],[9147, 9154])).
% 23.19/23.38 tff(9156,plain,
% 23.19/23.38 ($false),
% 23.19/23.38 inference(unit_resolution,[status(thm)],[9155, 9151])).
% 23.19/23.38 tff(9157,plain,(mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))), inference(lemma,lemma(discharge,[]))).
% 23.19/23.38 tff(9158,plain,
% 23.19/23.38 (mult(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), a), c) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c)),
% 23.19/23.38 inference(symmetry,[status(thm)],[7819])).
% 23.19/23.38 tff(9159,plain,
% 23.19/23.38 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(c, a), c)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c)))),
% 23.19/23.38 inference(monotonicity,[status(thm)],[2690])).
% 23.19/23.38 tff(9160,plain,
% 23.19/23.38 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(c, a), c))),
% 23.19/23.38 inference(symmetry,[status(thm)],[9159])).
% 23.19/23.38 tff(9161,plain,
% 23.19/23.38 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c))),
% 23.19/23.38 inference(transitivity,[status(thm)],[287, 142, 7455, 7452, 7450, 1431, 4502])).
% 23.19/23.38 tff(9162,plain,
% 23.19/23.38 (rd(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)), mult(a, c)) = rd(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)), mult(a, c))),
% 23.19/23.38 inference(monotonicity,[status(thm)],[9161])).
% 23.19/23.38 tff(9163,plain,
% 23.19/23.38 (mult(a, rd(mult(b, c), mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), a)),
% 23.19/23.38 inference(transitivity,[status(thm)],[6360, 9162, 6351])).
% 23.19/23.38 tff(9164,plain,
% 23.19/23.38 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, mult(a, c)))),
% 23.19/23.38 inference(monotonicity,[status(thm)],[9163])).
% 23.19/23.38 tff(9165,plain,
% 23.19/23.38 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c)))),
% 23.19/23.38 inference(symmetry,[status(thm)],[9164])).
% 23.19/23.38 tff(9166,plain,
% 23.19/23.38 (mult(mult(a, mult(a, c)), c) = mult(mult(mult(a, c), a), c)),
% 23.19/23.38 inference(monotonicity,[status(thm)],[8262])).
% 23.19/23.38 tff(9167,plain,
% 23.19/23.38 (mult(mult(mult(a, c), a), c) = mult(mult(a, mult(a, c)), c)),
% 23.19/23.38 inference(symmetry,[status(thm)],[9166])).
% 23.19/23.38 tff(9168,plain,
% 23.19/23.38 (mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), c)) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(a, c)), c))),
% 23.19/23.38 inference(monotonicity,[status(thm)],[9167])).
% 23.19/23.38 tff(9169,plain,
% 23.19/23.38 (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))), c) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), c)),
% 23.19/23.38 inference(monotonicity,[status(thm)],[8129])).
% 23.19/23.38 tff(9170,plain,
% 23.19/23.38 (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), c) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))), c)),
% 23.19/23.38 inference(symmetry,[status(thm)],[9169])).
% 23.19/23.38 tff(9171,plain,
% 23.19/23.38 ((mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), c))) <=> (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(a, c)), c)))),
% 23.19/23.38 inference(monotonicity,[status(thm)],[9170, 9168])).
% 23.19/23.38 tff(9172,plain,
% 23.19/23.38 ((mult(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(a, c)), c))) <=> (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), c)))),
% 23.19/23.38 inference(symmetry,[status(thm)],[9171])).
% 23.19/23.38 tff(9173,plain,
% 23.19/23.38 ((mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(c, a))) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, a))), c)) <=> (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, a))), c) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(c, a))))),
% 23.19/23.38 inference(commutativity,[status(thm)],[])).
% 23.19/23.38 tff(9174,plain,
% 23.19/23.38 (mult(a, mult(c, a)) = mult(a, mult(a, c))),
% 23.19/23.38 inference(monotonicity,[status(thm)],[3885])).
% 23.19/23.38 tff(9175,plain,
% 23.19/23.38 (mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, a))) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c)))),
% 23.19/23.38 inference(monotonicity,[status(thm)],[9174])).
% 23.19/23.38 tff(9176,plain,
% 23.19/23.38 (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, a))), c) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))), c)),
% 23.19/23.38 inference(monotonicity,[status(thm)],[9175])).
% 23.19/23.38 tff(9177,plain,
% 23.19/23.38 (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))), c) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, a))), c)),
% 23.19/23.38 inference(symmetry,[status(thm)],[9176])).
% 23.19/23.38 tff(9178,plain,
% 23.19/23.38 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a) = mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), unit), a)),
% 23.19/23.38 inference(symmetry,[status(thm)],[7724])).
% 23.19/23.38 tff(9179,plain,
% 23.19/23.38 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a)),
% 23.19/23.38 inference(symmetry,[status(thm)],[2179])).
% 23.19/23.38 tff(9180,plain,
% 23.19/23.38 (mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, a))),
% 23.19/23.38 inference(transitivity,[status(thm)],[4517, 9179, 9178, 2665, 2663])).
% 23.19/23.38 tff(9181,plain,
% 23.19/23.38 (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))), c) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, a)), c)),
% 23.19/23.38 inference(monotonicity,[status(thm)],[9180])).
% 23.19/23.38 tff(9182,plain,
% 23.19/23.38 (mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, a)), c) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))), c)),
% 23.19/23.38 inference(symmetry,[status(thm)],[9181])).
% 23.19/23.38 tff(9183,plain,
% 23.19/23.38 (mult(c, mult(a, a)) = mult(a, mult(a, c))),
% 23.19/23.38 inference(transitivity,[status(thm)],[2656, 2655, 5721, 4609, 4719, 4451])).
% 23.19/23.38 tff(9184,plain,
% 23.19/23.38 (mult(mult(c, mult(a, a)), c) = mult(mult(a, mult(a, c)), c)),
% 23.19/23.38 inference(monotonicity,[status(thm)],[9183])).
% 23.19/23.38 tff(9185,plain,
% 23.19/23.38 (mult(rd(mult(b, c), mult(a, c)), mult(mult(c, mult(a, a)), c)) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(a, c)), c))),
% 23.19/23.38 inference(monotonicity,[status(thm)],[9184])).
% 23.19/23.38 tff(9186,plain,
% 23.19/23.38 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(a, c)), c)) = mult(rd(mult(b, c), mult(a, c)), mult(mult(c, mult(a, a)), c))),
% 23.19/23.38 inference(symmetry,[status(thm)],[9185])).
% 23.19/23.38 tff(9187,plain,
% 23.19/23.38 (mult(mult(a, mult(a, c)), c) = mult(a, mult(c, mult(a, c)))),
% 23.19/23.38 inference(transitivity,[status(thm)],[4722, 4717, 4715])).
% 23.19/23.38 tff(9188,plain,
% 23.19/23.38 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(a, c)), c)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, mult(a, c))))),
% 23.19/23.38 inference(monotonicity,[status(thm)],[9187])).
% 23.19/23.38 tff(9189,plain,
% 23.19/23.38 (mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, mult(a, c)))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(a, c)), c))),
% 23.19/23.38 inference(symmetry,[status(thm)],[9188])).
% 23.19/23.38 tff(9190,plain,
% 23.19/23.38 (mult(a, mult(c, mult(a, c))) = mult(mult(mult(a, c), unit), mult(a, c))),
% 23.19/23.38 inference(transitivity,[status(thm)],[4714, 4724, 4721, 4752, 2504])).
% 23.19/23.38 tff(9191,plain,
% 23.19/23.38 (mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, mult(a, c)))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), unit), mult(a, c)))),
% 23.19/23.38 inference(monotonicity,[status(thm)],[9190])).
% 23.19/23.38 tff(9192,plain,
% 23.19/23.38 (mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), unit), mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, mult(a, c))))),
% 23.19/23.38 inference(symmetry,[status(thm)],[9191])).
% 23.19/23.38 tff(9193,plain,
% 23.19/23.38 (mult(mult(c, mult(a, c)), a) = mult(mult(mult(a, c), unit), mult(a, c))),
% 23.19/23.38 inference(transitivity,[status(thm)],[4664, 4782, 4754, 2504])).
% 23.19/23.38 tff(9194,plain,
% 23.19/23.38 (mult(rd(mult(b, c), mult(a, c)), mult(mult(c, mult(a, c)), a)) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), unit), mult(a, c)))),
% 23.19/23.38 inference(monotonicity,[status(thm)],[9193])).
% 23.19/23.38 tff(9195,plain,
% 23.19/23.38 (ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c)))) = ld(rd(mult(b, c), mult(a, c)), mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))),
% 23.19/23.38 inference(symmetry,[status(thm)],[4719])).
% 23.19/23.38 tff(9196,plain,
% 23.19/23.38 (mult(a, mult(a, c)) = mult(mult(a, c), a)),
% 23.19/23.38 inference(transitivity,[status(thm)],[4452, 9195, 4447])).
% 23.19/23.38 tff(9197,plain,
% 23.19/23.38 (mult(c, mult(a, mult(a, c))) = mult(c, mult(mult(a, c), a))),
% 23.19/23.38 inference(monotonicity,[status(thm)],[9196])).
% 23.19/23.38 tff(9198,plain,
% 23.19/23.38 (mult(c, mult(a, mult(a, c))) = mult(mult(c, mult(a, c)), a)),
% 23.19/23.38 inference(transitivity,[status(thm)],[9197, 2562, 6842])).
% 23.19/23.38 tff(9199,plain,
% 23.19/23.38 (mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, mult(a, c)))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(c, mult(a, c)), a))),
% 23.19/23.38 inference(monotonicity,[status(thm)],[9198])).
% 23.19/23.38 tff(9200,plain,
% 23.19/23.38 (mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, mult(a, c)))) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, a))), c)),
% 23.19/23.38 inference(transitivity,[status(thm)],[9199, 9194, 9192, 9189, 9186, 7728, 9182, 9177])).
% 23.19/23.38 tff(9201,plain,
% 23.19/23.38 (mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(c, a))) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c)))),
% 23.19/23.38 inference(monotonicity,[status(thm)],[9174])).
% 23.19/23.38 tff(9202,plain,
% 23.19/23.38 (mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(c, a)))),
% 23.19/23.38 inference(symmetry,[status(thm)],[9201])).
% 23.19/23.38 tff(9203,plain,
% 23.19/23.38 ((mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, mult(a, c))))) <=> (mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(c, a))) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, a))), c))),
% 23.19/23.38 inference(monotonicity,[status(thm)],[9202, 9200])).
% 23.19/23.38 tff(9204,plain,
% 23.19/23.38 ((mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, mult(a, c))))) <=> (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, a))), c) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(c, a))))),
% 23.19/23.38 inference(transitivity,[status(thm)],[9203, 9173])).
% 23.19/23.38 tff(9205,plain,
% 23.19/23.38 ((mult(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, a))), c) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(c, a)))) <=> (mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, mult(a, c)))))),
% 23.19/23.38 inference(symmetry,[status(thm)],[9204])).
% 23.19/23.38 tff(9206,plain,
% 23.19/23.38 (mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a))),
% 23.19/23.38 inference(monotonicity,[status(thm)],[9196])).
% 23.19/23.38 tff(9207,plain,
% 23.19/23.38 (mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c)))),
% 23.19/23.38 inference(symmetry,[status(thm)],[9206])).
% 23.19/23.38 tff(9208,plain,
% 23.19/23.38 (mult(mult(a, mult(c, c)), a) = mult(mult(mult(a, c), unit), mult(a, c))),
% 23.19/23.38 inference(transitivity,[status(thm)],[4662, 4782, 4754, 2504])).
% 23.19/23.38 tff(9209,plain,
% 23.19/23.38 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(c, c)), a)) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), unit), mult(a, c)))),
% 23.19/23.38 inference(monotonicity,[status(thm)],[9208])).
% 23.19/23.38 tff(9210,plain,
% 23.19/23.38 (mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), unit), mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(c, c)), a))),
% 23.19/23.38 inference(symmetry,[status(thm)],[9209])).
% 23.19/23.38 tff(9211,plain,
% 23.19/23.38 (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, a))), c) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(c, a)))),
% 23.19/23.38 inference(transitivity,[status(thm)],[9176, 9181, 2661, 9185, 9188, 9191, 9210, 4661, 6878, 6872, 2631, 9207, 9202])).
% 23.19/23.38 tff(9212,plain,
% 23.19/23.38 (mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, mult(a, c))))),
% 23.19/23.38 inference(modus_ponens,[status(thm)],[9211, 9205])).
% 23.19/23.38 tff(9213,assumption,(~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, mult(a, c)))))), introduced(assumption)).
% 23.19/23.38 tff(9214,plain,
% 23.19/23.38 ($false),
% 23.19/23.38 inference(unit_resolution,[status(thm)],[9213, 9212])).
% 23.19/23.38 tff(9215,plain,((mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, mult(a, c))))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit))))), inference(lemma,lemma(discharge,[]))).
% 23.19/23.39 tff(9216,plain,
% 23.19/23.39 ((mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, mult(a, c))))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit))))),
% 23.19/23.39 inference(unit_resolution,[status(thm)],[9215, 3862])).
% 23.19/23.39 tff(9217,plain,
% 23.19/23.39 ((mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, mult(a, c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit))))),
% 23.19/23.39 inference(unit_resolution,[status(thm)],[9216, 8129])).
% 23.19/23.39 tff(9218,plain,
% 23.19/23.39 (mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, mult(a, c))))),
% 23.19/23.39 inference(unit_resolution,[status(thm)],[9217, 4360])).
% 23.19/23.39 tff(9219,assumption,(~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(a, c)), c)))), introduced(assumption)).
% 23.19/23.39 tff(9220,plain,
% 23.19/23.39 (((~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, mult(a, c)))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(a, c)), c))))) | (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(a, c)), c)))),
% 23.19/23.39 inference(tautology,[status(thm)],[])).
% 23.19/23.39 tff(9221,plain,
% 23.19/23.39 ((~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, mult(a, c)))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(a, c)), c))))),
% 23.19/23.39 inference(unit_resolution,[status(thm)],[9220, 9219])).
% 23.19/23.39 tff(9222,plain,
% 23.19/23.39 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))), c))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, mult(a, c)))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(a, c)), c)))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, mult(a, c)))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(a, c)), c)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))), c))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, mult(a, c)))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(a, c)), c)))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, mult(a, c)))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(a, c)), c)))))))),
% 23.19/23.39 inference(rewrite,[status(thm)],[])).
% 23.19/23.39 tff(9223,plain,
% 23.19/23.39 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))), c))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, mult(a, c)))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(a, c)), c)))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, mult(a, c)))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(a, c)), c)))))))),
% 23.19/23.39 inference(quant_inst,[status(thm)],[])).
% 23.19/23.39 tff(9224,plain,
% 23.19/23.39 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))), c))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, mult(a, c)))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(a, c)), c)))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, mult(a, c)))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(a, c)), c))))))),
% 23.19/23.39 inference(modus_ponens,[status(thm)],[9223, 9222])).
% 23.19/23.39 tff(9225,plain,
% 23.19/23.39 ((~((~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))), c))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, mult(a, c)))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(a, c)), c)))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, mult(a, c)))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(a, c)), c))))))),
% 23.19/23.39 inference(unit_resolution,[status(thm)],[9224, 27])).
% 23.19/23.39 tff(9226,plain,
% 23.19/23.39 (~((~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))), c))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, mult(a, c)))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(a, c)), c)))))),
% 23.19/23.39 inference(unit_resolution,[status(thm)],[9225, 9221])).
% 23.19/23.39 tff(9227,plain,
% 23.19/23.39 (((~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))), c))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, mult(a, c)))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(a, c)), c))))) | (mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, mult(a, c)))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(a, c)), c)))),
% 23.19/23.39 inference(tautology,[status(thm)],[])).
% 23.19/23.39 tff(9228,plain,
% 23.19/23.39 (mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, mult(a, c)))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(a, c)), c))),
% 23.19/23.39 inference(unit_resolution,[status(thm)],[9227, 9226])).
% 23.19/23.39 tff(9229,plain,
% 23.19/23.39 (((~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))), c))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, mult(a, c)))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(a, c)), c))))) | (mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))), c))),
% 23.19/23.39 inference(tautology,[status(thm)],[])).
% 23.19/23.39 tff(9230,plain,
% 23.19/23.39 (mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))), c)),
% 23.19/23.39 inference(unit_resolution,[status(thm)],[9229, 9226])).
% 23.19/23.39 tff(9231,plain,
% 23.19/23.39 ((mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, mult(a, c))))) <=> (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(a, c)), c)))),
% 23.19/23.39 inference(monotonicity,[status(thm)],[9230, 9228])).
% 23.19/23.39 tff(9232,plain,
% 23.19/23.39 ((mult(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(a, c)), c))) <=> (mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, mult(a, c)))))),
% 23.19/23.39 inference(symmetry,[status(thm)],[9231])).
% 23.19/23.39 tff(9233,plain,
% 23.19/23.39 ((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(a, c)), c)))) <=> (~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, mult(a, c))))))),
% 23.19/23.39 inference(monotonicity,[status(thm)],[9232])).
% 23.19/23.39 tff(9234,plain,
% 23.19/23.39 (~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, mult(a, c)))))),
% 23.19/23.39 inference(modus_ponens,[status(thm)],[9219, 9233])).
% 23.19/23.39 tff(9235,assumption,(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, mult(a, c))))), introduced(assumption)).
% 23.19/23.39 tff(9236,plain,
% 23.19/23.39 ($false),
% 23.19/23.39 inference(unit_resolution,[status(thm)],[9235, 9234])).
% 23.19/23.39 tff(9237,plain,((mult(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(a, c)), c))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, mult(a, c))))))), inference(lemma,lemma(discharge,[]))).
% 23.19/23.39 tff(9238,plain,
% 23.19/23.39 (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(a, c)), c))),
% 23.19/23.39 inference(unit_resolution,[status(thm)],[9237, 9218])).
% 23.19/23.39 tff(9239,plain,
% 23.19/23.39 (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), c))),
% 23.19/23.39 inference(modus_ponens,[status(thm)],[9238, 9172])).
% 23.19/23.39 tff(9240,plain,
% 23.19/23.39 (mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), c)),
% 23.19/23.39 inference(symmetry,[status(thm)],[9239])).
% 23.19/23.39 tff(9241,plain,
% 23.19/23.39 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(a, c)), c)) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), c))),
% 23.19/23.39 inference(symmetry,[status(thm)],[9168])).
% 23.19/23.39 tff(9242,plain,
% 23.19/23.39 (mult(a, mult(mult(a, c), c)) = mult(a, mult(c, mult(a, c)))),
% 23.19/23.39 inference(monotonicity,[status(thm)],[6893])).
% 23.19/23.39 tff(9243,plain,
% 23.19/23.39 (mult(a, mult(c, mult(a, c))) = mult(a, mult(mult(a, c), c))),
% 23.19/23.39 inference(symmetry,[status(thm)],[9242])).
% 23.19/23.39 tff(9244,plain,
% 23.19/23.39 (mult(mult(a, mult(a, c)), c) = mult(a, mult(mult(a, c), c))),
% 23.19/23.39 inference(transitivity,[status(thm)],[9166, 4717, 4715, 9243])).
% 23.19/23.39 tff(9245,plain,
% 23.19/23.39 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(a, c)), c)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(a, c), c)))),
% 23.19/23.39 inference(monotonicity,[status(thm)],[9244])).
% 23.19/23.39 tff(9246,plain,
% 23.19/23.39 (mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(a, c), c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(a, c)), c))),
% 23.19/23.39 inference(symmetry,[status(thm)],[9245])).
% 23.19/23.39 tff(9247,plain,
% 23.19/23.39 (mult(mult(c, a), mult(a, c)) = mult(mult(a, c), mult(a, c))),
% 23.19/23.39 inference(monotonicity,[status(thm)],[5700])).
% 23.19/23.39 tff(9248,plain,
% 23.19/23.39 (mult(mult(a, c), mult(c, a)) = mult(mult(a, c), mult(a, c))),
% 23.19/23.39 inference(monotonicity,[status(thm)],[5700])).
% 23.19/23.39 tff(9249,plain,
% 23.19/23.39 (mult(mult(a, c), mult(a, c)) = mult(mult(a, c), mult(c, a))),
% 23.19/23.39 inference(symmetry,[status(thm)],[9248])).
% 23.19/23.39 tff(9250,plain,
% 23.19/23.39 (mult(mult(c, a), mult(a, c)) = mult(mult(a, c), mult(c, a))),
% 23.19/23.39 inference(transitivity,[status(thm)],[9247, 9249])).
% 23.19/23.39 tff(9251,plain,
% 23.19/23.39 ((mult(mult(c, mult(a, c)), a) = mult(mult(c, a), mult(a, c))) <=> (mult(mult(mult(a, c), c), a) = mult(mult(a, c), mult(c, a)))),
% 23.19/23.39 inference(monotonicity,[status(thm)],[7707, 9250])).
% 23.19/23.39 tff(9252,plain,
% 23.19/23.39 ((mult(mult(mult(a, c), c), a) = mult(mult(a, c), mult(c, a))) <=> (mult(mult(c, mult(a, c)), a) = mult(mult(c, a), mult(a, c)))),
% 23.19/23.39 inference(symmetry,[status(thm)],[9251])).
% 23.19/23.39 tff(9253,plain,
% 23.19/23.39 (mult(mult(c, mult(a, c)), a) = mult(mult(c, a), mult(a, c))),
% 23.19/23.39 inference(modus_ponens,[status(thm)],[8730, 9252])).
% 23.19/23.39 tff(9254,plain,
% 23.19/23.39 ((mult(mult(a, a), mult(c, c)) = mult(mult(a, mult(c, c)), a)) <=> (mult(mult(a, mult(c, c)), a) = mult(mult(a, a), mult(c, c)))),
% 23.19/23.39 inference(commutativity,[status(thm)],[])).
% 23.19/23.39 tff(9255,plain,
% 23.19/23.39 ((mult(mult(a, mult(c, c)), a) = mult(mult(a, a), mult(c, c))) <=> (mult(mult(a, a), mult(c, c)) = mult(mult(a, mult(c, c)), a))),
% 23.19/23.39 inference(symmetry,[status(thm)],[9254])).
% 23.19/23.39 tff(9256,plain,
% 23.19/23.39 (mult(c, mult(c, a)) = mult(c, mult(a, c))),
% 23.19/23.39 inference(monotonicity,[status(thm)],[5700])).
% 23.19/23.39 tff(9257,plain,
% 23.19/23.39 (mult(mult(c, c), a) = mult(a, mult(c, c))),
% 23.19/23.39 inference(transitivity,[status(thm)],[3911, 9256, 3877, 7677, 2622, 2614, 2621])).
% 23.19/23.39 tff(9258,plain,
% 23.19/23.39 (mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(c, c), a)) = mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(a, mult(c, c)))),
% 23.19/23.39 inference(monotonicity,[status(thm)],[9257])).
% 23.19/23.39 tff(9259,plain,
% 23.19/23.39 (mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(a, mult(c, c))) = mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(c, c), a))),
% 23.19/23.39 inference(symmetry,[status(thm)],[9258])).
% 23.19/23.39 tff(9260,plain,
% 23.19/23.39 (mult(a, mult(c, mult(c, a))) = mult(a, mult(c, mult(a, c)))),
% 23.19/23.39 inference(monotonicity,[status(thm)],[9256])).
% 23.19/23.39 tff(9261,plain,
% 23.19/23.39 ((mult(mult(a, c), mult(c, a)) = mult(a, mult(c, mult(c, a)))) <=> (mult(mult(a, c), mult(a, c)) = mult(a, mult(c, mult(a, c))))),
% 23.19/23.39 inference(monotonicity,[status(thm)],[9248, 9260])).
% 23.19/23.39 tff(9262,plain,
% 23.19/23.39 ((mult(mult(a, c), mult(a, c)) = mult(a, mult(c, mult(a, c)))) <=> (mult(mult(a, c), mult(c, a)) = mult(a, mult(c, mult(c, a))))),
% 23.19/23.39 inference(symmetry,[status(thm)],[9261])).
% 23.19/23.39 tff(9263,plain,
% 23.19/23.39 ((mult(mult(a, c), mult(a, c)) = mult(a, mult(c, mult(a, c)))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))),
% 23.19/23.39 inference(unit_resolution,[status(thm)],[4750, 3862, 5434])).
% 23.19/23.39 tff(9264,plain,
% 23.19/23.39 (mult(mult(a, c), mult(a, c)) = mult(a, mult(c, mult(a, c)))),
% 23.19/23.39 inference(unit_resolution,[status(thm)],[9263, 8129])).
% 23.19/23.39 tff(9265,plain,
% 23.19/23.39 (mult(mult(a, c), mult(c, a)) = mult(a, mult(c, mult(c, a)))),
% 23.19/23.39 inference(modus_ponens,[status(thm)],[9264, 9262])).
% 23.19/23.39 tff(9266,plain,
% 23.19/23.39 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(a, c), c))) = mult(mult(a, c), c))),
% 23.19/23.39 inference(quant_inst,[status(thm)],[])).
% 23.19/23.39 tff(9267,plain,
% 23.19/23.39 (ld(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(a, c), c))) = mult(mult(a, c), c)),
% 23.19/23.39 inference(unit_resolution,[status(thm)],[9266, 7])).
% 23.19/23.39 tff(9268,plain,
% 23.19/23.39 (mult(c, mult(c, a)) = mult(mult(c, c), a)),
% 23.19/23.39 inference(symmetry,[status(thm)],[3911])).
% 23.19/23.39 tff(9269,plain,
% 23.19/23.39 (mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(c, mult(c, a))) = mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(c, c), a))),
% 23.19/23.39 inference(monotonicity,[status(thm)],[9268])).
% 23.19/23.39 tff(9270,plain,
% 23.19/23.39 (mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(c, c), a)) = mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(c, mult(c, a)))),
% 23.19/23.39 inference(symmetry,[status(thm)],[9269])).
% 23.19/23.39 tff(9271,assumption,(mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(a, mult(c, c))) = mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(c, c), a))), introduced(assumption)).
% 23.19/23.39 tff(9272,plain,
% 23.19/23.39 (mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(a, mult(c, c))) = mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(a, c), c))),
% 23.24/23.40 inference(monotonicity,[status(thm)],[2619])).
% 23.24/23.40 tff(9273,plain,
% 23.24/23.40 (mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(a, c), c)) = mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(a, mult(c, c)))),
% 23.24/23.40 inference(symmetry,[status(thm)],[9272])).
% 23.24/23.40 tff(9274,plain,
% 23.24/23.40 (mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(a, c), c)) = mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(c, mult(c, a)))),
% 23.24/23.40 inference(transitivity,[status(thm)],[9273, 9271, 9270])).
% 23.24/23.40 tff(9275,plain,
% 23.24/23.40 (ld(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(a, c), c))) = ld(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(c, mult(c, a))))),
% 23.24/23.40 inference(monotonicity,[status(thm)],[9274])).
% 23.24/23.40 tff(9276,plain,
% 23.24/23.40 (ld(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(c, mult(c, a)))) = ld(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(a, c), c)))),
% 23.24/23.40 inference(symmetry,[status(thm)],[9275])).
% 23.24/23.40 tff(9277,plain,
% 23.24/23.40 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(c, mult(c, a)))) = mult(c, mult(c, a)))),
% 23.24/23.40 inference(quant_inst,[status(thm)],[])).
% 23.24/23.40 tff(9278,plain,
% 23.24/23.40 (ld(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(c, mult(c, a)))) = mult(c, mult(c, a))),
% 23.24/23.40 inference(unit_resolution,[status(thm)],[9277, 7])).
% 23.24/23.40 tff(9279,plain,
% 23.24/23.40 (mult(c, mult(c, a)) = ld(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(c, mult(c, a))))),
% 23.24/23.40 inference(symmetry,[status(thm)],[9278])).
% 23.24/23.40 tff(9280,plain,
% 23.24/23.40 (mult(c, mult(c, a)) = mult(mult(a, c), c)),
% 23.24/23.40 inference(transitivity,[status(thm)],[9279, 9276, 9267])).
% 23.24/23.40 tff(9281,plain,
% 23.24/23.40 (mult(a, mult(c, mult(c, a))) = mult(a, mult(mult(a, c), c))),
% 23.24/23.40 inference(monotonicity,[status(thm)],[9280])).
% 23.24/23.40 tff(9282,assumption,(mult(mult(a, c), mult(c, a)) = mult(a, mult(c, mult(c, a)))), introduced(assumption)).
% 23.24/23.40 tff(9283,plain,
% 23.24/23.40 (mult(mult(unit, mult(mult(a, c), c)), a) = mult(mult(unit, a), mult(mult(a, c), c))),
% 23.24/23.40 inference(transitivity,[status(thm)],[7868, 4790, 9282, 9281, 7871])).
% 23.24/23.40 tff(9284,assumption,(~(mult(mult(unit, mult(mult(a, c), c)), a) = mult(mult(unit, a), mult(mult(a, c), c)))), introduced(assumption)).
% 23.24/23.40 tff(9285,plain,
% 23.24/23.40 ($false),
% 23.24/23.40 inference(unit_resolution,[status(thm)],[9284, 9283])).
% 23.24/23.40 tff(9286,plain,((~(mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(a, mult(c, c))) = mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(c, c), a)))) | (mult(mult(unit, mult(mult(a, c), c)), a) = mult(mult(unit, a), mult(mult(a, c), c))) | (~(mult(mult(mult(a, c), c), a) = mult(mult(a, c), mult(c, a)))) | (~(mult(mult(a, c), mult(c, a)) = mult(a, mult(c, mult(c, a)))))), inference(lemma,lemma(discharge,[]))).
% 23.24/23.40 tff(9287,plain,
% 23.24/23.40 ((~(mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(a, mult(c, c))) = mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(c, c), a)))) | (mult(mult(unit, mult(mult(a, c), c)), a) = mult(mult(unit, a), mult(mult(a, c), c))) | (~(mult(mult(a, c), mult(c, a)) = mult(a, mult(c, mult(c, a)))))),
% 23.24/23.40 inference(unit_resolution,[status(thm)],[9286, 8730])).
% 23.24/23.40 tff(9288,plain,
% 23.24/23.40 (mult(mult(unit, mult(mult(a, c), c)), a) = mult(mult(unit, a), mult(mult(a, c), c))),
% 23.24/23.40 inference(unit_resolution,[status(thm)],[9287, 9265, 9259])).
% 23.24/23.40 tff(9289,plain,
% 23.24/23.40 (mult(mult(a, mult(c, c)), a) = mult(mult(a, a), mult(c, c))),
% 23.24/23.40 inference(unit_resolution,[status(thm)],[7898, 9288])).
% 23.24/23.40 tff(9290,plain,
% 23.24/23.40 (mult(mult(a, a), mult(c, c)) = mult(mult(a, mult(c, c)), a)),
% 23.24/23.40 inference(modus_ponens,[status(thm)],[9289, 9255])).
% 23.24/23.40 tff(9291,plain,
% 23.24/23.40 (mult(mult(mult(a, a), c), unit) = mult(mult(mult(a, c), a), unit)),
% 23.24/23.40 inference(monotonicity,[status(thm)],[8835])).
% 23.24/23.40 tff(9292,plain,
% 23.24/23.40 (mult(mult(mult(a, c), a), unit) = mult(mult(mult(a, a), c), unit)),
% 23.24/23.40 inference(symmetry,[status(thm)],[9291])).
% 23.24/23.40 tff(9293,plain,
% 23.24/23.40 (mult(mult(mult(a, c), unit), a) = mult(mult(a, c), a)),
% 23.24/23.40 inference(monotonicity,[status(thm)],[45])).
% 23.24/23.40 tff(9294,plain,
% 23.24/23.40 (mult(mult(a, c), a) = mult(mult(mult(a, c), unit), a)),
% 23.24/23.40 inference(symmetry,[status(thm)],[9293])).
% 23.24/23.40 tff(9295,plain,
% 23.24/23.40 (mult(mult(mult(a, c), a), unit) = mult(mult(mult(mult(a, c), unit), a), unit)),
% 23.24/23.40 inference(monotonicity,[status(thm)],[9294])).
% 23.24/23.40 tff(9296,plain,
% 23.24/23.40 (mult(mult(mult(mult(a, c), unit), a), unit) = mult(mult(mult(a, c), a), unit)),
% 23.24/23.40 inference(symmetry,[status(thm)],[9295])).
% 23.24/23.40 tff(9297,plain,
% 23.24/23.40 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(a, c), unit), a), unit) = mult(mult(a, c), mult(mult(unit, a), unit)))),
% 23.24/23.40 inference(quant_inst,[status(thm)],[])).
% 23.24/23.40 tff(9298,plain,
% 23.24/23.40 (mult(mult(mult(mult(a, c), unit), a), unit) = mult(mult(a, c), mult(mult(unit, a), unit))),
% 23.24/23.40 inference(unit_resolution,[status(thm)],[9297, 56])).
% 23.24/23.40 tff(9299,plain,
% 23.24/23.40 (mult(mult(a, c), mult(mult(unit, a), unit)) = mult(mult(mult(mult(a, c), unit), a), unit)),
% 23.24/23.40 inference(symmetry,[status(thm)],[9298])).
% 23.24/23.40 tff(9300,plain,
% 23.24/23.40 (mult(mult(a, c), mult(mult(unit, a), unit)) = mult(mult(a, c), a)),
% 23.24/23.40 inference(monotonicity,[status(thm)],[507])).
% 23.24/23.40 tff(9301,plain,
% 23.24/23.40 (mult(mult(a, c), a) = mult(mult(a, c), mult(mult(unit, a), unit))),
% 23.24/23.40 inference(symmetry,[status(thm)],[9300])).
% 23.24/23.40 tff(9302,plain,
% 23.24/23.40 (mult(mult(a, c), a) = mult(mult(mult(a, a), c), unit)),
% 23.24/23.40 inference(transitivity,[status(thm)],[9301, 9299, 9296, 9292])).
% 23.24/23.40 tff(9303,plain,
% 23.24/23.40 (mult(mult(mult(a, c), a), c) = mult(mult(mult(mult(a, a), c), unit), c)),
% 23.24/23.40 inference(monotonicity,[status(thm)],[9302])).
% 23.24/23.40 tff(9304,plain,
% 23.24/23.40 (mult(a, mult(mult(a, c), c)) = mult(mult(mult(a, c), unit), mult(a, c))),
% 23.24/23.40 inference(transitivity,[status(thm)],[9242, 4714, 4724, 9303, 7903, 7901, 9290, 4662, 6894, 9253, 9247, 2504])).
% 23.24/23.40 tff(9305,plain,
% 23.24/23.40 (mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(a, c), c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), unit), mult(a, c)))),
% 23.24/23.40 inference(monotonicity,[status(thm)],[9304])).
% 23.24/23.40 tff(9306,plain,
% 23.24/23.40 (mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), unit), mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(a, c), c)))),
% 23.24/23.40 inference(symmetry,[status(thm)],[9305])).
% 23.24/23.40 tff(9307,plain,
% 23.24/23.40 (mult(mult(b, mult(a, c)), c) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c)),
% 23.24/23.40 inference(transitivity,[status(thm)],[5435, 5386, 2501, 9306, 9246, 9241, 9240, 5926, 5141, 5924, 9165, 9160, 5952, 9158])).
% 23.24/23.40 tff(9308,plain,
% 23.24/23.40 (rd(mult(mult(b, mult(a, c)), c), c) = rd(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c), c)),
% 23.24/23.40 inference(monotonicity,[status(thm)],[9307])).
% 23.24/23.40 tff(9309,plain,
% 23.24/23.40 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), unit) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), unit)),
% 23.24/23.40 inference(symmetry,[status(thm)],[5937])).
% 23.24/23.40 tff(9310,plain,
% 23.24/23.40 (mult(mult(a, c), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), unit)),
% 23.24/23.40 inference(transitivity,[status(thm)],[2167, 4851, 9309])).
% 23.24/23.40 tff(9311,plain,
% 23.24/23.40 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), unit), c)),
% 23.24/23.40 inference(monotonicity,[status(thm)],[9310])).
% 23.24/23.40 tff(9312,plain,
% 23.24/23.40 (mult(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), unit), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)),
% 23.24/23.40 inference(symmetry,[status(thm)],[9311])).
% 23.24/23.40 tff(9313,plain,
% 23.24/23.40 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(c, unit), c)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c))),
% 23.24/23.40 inference(monotonicity,[status(thm)],[2616])).
% 23.24/23.40 tff(9314,plain,
% 23.24/23.40 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(c, unit), c))),
% 23.24/23.40 inference(symmetry,[status(thm)],[9313])).
% 23.24/23.40 tff(9315,plain,
% 23.24/23.40 (mult(mult(a, mult(c, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c)))),
% 23.24/23.40 inference(monotonicity,[status(thm)],[2619])).
% 23.24/23.40 tff(9316,plain,
% 23.24/23.40 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)),
% 23.24/23.40 inference(transitivity,[status(thm)],[9314, 5942, 9312])).
% 23.24/23.40 tff(9317,plain,
% 23.24/23.40 ((mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)) = mult(mult(a, mult(c, c)), rd(mult(b, c), mult(a, c)))) <=> (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))))),
% 23.24/23.40 inference(monotonicity,[status(thm)],[9316, 9315])).
% 23.24/23.40 tff(9318,plain,
% 23.24/23.40 ((mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c)))) <=> (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)) = mult(mult(a, mult(c, c)), rd(mult(b, c), mult(a, c))))),
% 23.24/23.40 inference(symmetry,[status(thm)],[9317])).
% 23.24/23.40 tff(9319,plain,
% 23.24/23.40 ((mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c)))) | (~(mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))))),
% 23.24/23.40 inference(unit_resolution,[status(thm)],[5315, 3862])).
% 23.24/23.40 tff(9320,plain,
% 23.24/23.40 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c)))),
% 23.24/23.40 inference(unit_resolution,[status(thm)],[9319, 5159])).
% 23.24/23.40 tff(9321,plain,
% 23.24/23.40 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)) = mult(mult(a, mult(c, c)), rd(mult(b, c), mult(a, c)))),
% 23.24/23.40 inference(modus_ponens,[status(thm)],[9320, 9318])).
% 23.24/23.40 tff(9322,plain,
% 23.24/23.40 (mult(mult(a, mult(c, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c))),
% 23.24/23.40 inference(symmetry,[status(thm)],[9321])).
% 23.24/23.40 tff(9323,plain,
% 23.24/23.40 (mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))) = mult(mult(a, mult(c, c)), rd(mult(b, c), mult(a, c)))),
% 23.24/23.40 inference(symmetry,[status(thm)],[9315])).
% 23.24/23.40 tff(9324,plain,
% 23.24/23.40 (mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c)))),
% 23.24/23.40 inference(symmetry,[status(thm)],[7671])).
% 23.24/23.40 tff(9325,plain,
% 23.24/23.40 (mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c))),
% 23.24/23.40 inference(transitivity,[status(thm)],[9324, 9323, 9322, 9314, 5942, 9312, 3152])).
% 23.24/23.40 tff(9326,plain,
% 23.24/23.40 (mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)), a)),
% 23.24/23.40 inference(monotonicity,[status(thm)],[9325])).
% 23.24/23.40 tff(9327,plain,
% 23.24/23.40 ((mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c)))) <=> (mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))))),
% 23.24/23.40 inference(commutativity,[status(thm)],[])).
% 23.24/23.40 tff(9328,plain,
% 23.24/23.40 (mult(a, mult(c, mult(a, c))) = mult(mult(a, c), mult(a, c))),
% 23.24/23.40 inference(transitivity,[status(thm)],[4714, 4724, 9303, 7903, 7901, 9290, 4662, 6894, 9253, 9247])).
% 23.24/23.40 tff(9329,plain,
% 23.24/23.40 (mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 23.24/23.40 inference(monotonicity,[status(thm)],[9328])).
% 23.24/23.40 tff(9330,plain,
% 23.24/23.40 (mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c)))),
% 23.24/23.40 inference(symmetry,[status(thm)],[9329])).
% 23.24/23.40 tff(9331,plain,
% 23.24/23.40 (mult(mult(c, a), mult(a, c)) = mult(mult(c, mult(a, c)), a)),
% 23.24/23.40 inference(symmetry,[status(thm)],[9253])).
% 23.24/23.40 tff(9332,plain,
% 23.24/23.40 (mult(mult(a, c), mult(a, c)) = mult(mult(c, a), mult(a, c))),
% 23.24/23.40 inference(symmetry,[status(thm)],[9247])).
% 23.24/23.40 tff(9333,plain,
% 23.24/23.40 (mult(mult(a, c), mult(a, c)) = mult(mult(c, mult(a, c)), a)),
% 23.24/23.40 inference(transitivity,[status(thm)],[9332, 9331])).
% 23.24/23.40 tff(9334,plain,
% 23.24/23.40 (mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c)))),
% 23.24/23.40 inference(monotonicity,[status(thm)],[9333])).
% 23.24/23.40 tff(9335,plain,
% 23.24/23.40 (mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 23.24/23.40 inference(symmetry,[status(thm)],[9334])).
% 23.24/23.40 tff(9336,plain,
% 23.24/23.40 (mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c)))),
% 23.24/23.40 inference(transitivity,[status(thm)],[9335, 9330])).
% 23.24/23.40 tff(9337,plain,
% 23.24/23.40 (mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c)))),
% 23.24/23.40 inference(transitivity,[status(thm)],[9326, 3158, 7692, 7819, 5951, 9159])).
% 23.24/23.40 tff(9338,plain,
% 23.24/23.40 ((mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c)))) <=> (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))))),
% 23.24/23.40 inference(monotonicity,[status(thm)],[9337, 9336])).
% 23.24/23.40 tff(9339,plain,
% 23.24/23.40 ((mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c)))) <=> (mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))))),
% 23.24/23.40 inference(transitivity,[status(thm)],[9338, 9327])).
% 23.24/23.40 tff(9340,plain,
% 23.24/23.40 ((mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c)))) <=> (mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))))),
% 23.24/23.40 inference(symmetry,[status(thm)],[9339])).
% 23.24/23.40 tff(9341,plain,
% 23.24/23.40 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(mult(a, c), mult(a, c)))),
% 23.24/23.40 inference(transitivity,[status(thm)],[9164, 5923, 6008, 5925, 9239, 9168, 9245, 9305, 5385])).
% 23.24/23.40 tff(9342,plain,
% 23.24/23.40 (mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(unit, mult(mult(a, c), mult(a, c))), rd(mult(b, c), mult(a, c)))),
% 23.24/23.40 inference(symmetry,[status(thm)],[5379])).
% 23.24/23.40 tff(9343,plain,
% 23.24/23.40 (mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(unit, mult(mult(a, c), mult(a, c))), rd(mult(b, c), mult(a, c)))),
% 23.24/23.40 inference(transitivity,[status(thm)],[9329, 9342])).
% 23.24/23.40 tff(9344,plain,
% 23.24/23.40 ((mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c)))) <=> (mult(mult(unit, mult(mult(a, c), mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(mult(a, c), mult(a, c))))),
% 23.24/23.40 inference(monotonicity,[status(thm)],[9343, 9341])).
% 23.24/23.40 tff(9345,plain,
% 23.24/23.40 ((mult(mult(unit, mult(mult(a, c), mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(mult(a, c), mult(a, c)))) <=> (mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))))),
% 23.24/23.40 inference(symmetry,[status(thm)],[9344])).
% 23.24/23.40 tff(9346,plain,
% 23.24/23.40 (mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c)),
% 23.24/23.40 inference(monotonicity,[status(thm)],[5497])).
% 23.24/23.40 tff(9347,plain,
% 23.24/23.40 (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.24/23.40 inference(unit_resolution,[status(thm)],[8210, 299, 2187])).
% 23.24/23.40 tff(9348,plain,
% 23.24/23.40 (mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))),
% 23.24/23.40 inference(symmetry,[status(thm)],[9347])).
% 23.24/23.40 tff(9349,plain,
% 23.24/23.40 (mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 23.24/23.40 inference(transitivity,[status(thm)],[9348, 8170, 8264, 299])).
% 23.24/23.40 tff(9350,plain,
% 23.24/23.40 (ld(a, mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c)))))) = ld(a, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 23.24/23.40 inference(monotonicity,[status(thm)],[9349])).
% 23.24/23.40 tff(9351,plain,
% 23.24/23.41 (rd(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)), mult(a, c)) = rd(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)), mult(a, c))),
% 23.24/23.41 inference(symmetry,[status(thm)],[9162])).
% 23.24/23.41 tff(9352,plain,
% 23.24/23.41 (mult(rd(mult(b, c), mult(a, c)), a) = mult(a, rd(mult(b, c), mult(a, c)))),
% 23.24/23.41 inference(transitivity,[status(thm)],[8420, 9351, 6359])).
% 23.24/23.41 tff(9353,plain,
% 23.24/23.41 (mult(c, mult(rd(mult(b, c), mult(a, c)), a)) = mult(c, mult(a, rd(mult(b, c), mult(a, c))))),
% 23.24/23.41 inference(monotonicity,[status(thm)],[9352])).
% 23.24/23.41 tff(9354,plain,
% 23.24/23.41 (mult(c, mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))),
% 23.24/23.41 inference(transitivity,[status(thm)],[9353, 8269, 9350, 4336])).
% 23.24/23.41 tff(9355,plain,
% 23.24/23.41 (mult(mult(c, mult(rd(mult(b, c), mult(a, c)), a)), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)),
% 23.24/23.41 inference(monotonicity,[status(thm)],[9354])).
% 23.24/23.41 tff(9356,plain,
% 23.24/23.41 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(c, mult(rd(mult(b, c), mult(a, c)), a)), c)),
% 23.24/23.41 inference(symmetry,[status(thm)],[9355])).
% 23.24/23.41 tff(9357,plain,
% 23.24/23.41 (mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(c, mult(rd(mult(b, c), mult(a, c)), a)), c)),
% 23.24/23.41 inference(transitivity,[status(thm)],[9324, 9323, 9322, 9314, 5942, 9312, 9356])).
% 23.24/23.41 tff(9358,plain,
% 23.24/23.41 (mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(c, mult(rd(mult(b, c), mult(a, c)), a)), c))),
% 23.24/23.41 inference(monotonicity,[status(thm)],[9357])).
% 23.24/23.41 tff(9359,plain,
% 23.24/23.41 (mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))) = mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(mult(a, c), mult(a, c)))),
% 23.24/23.41 inference(transitivity,[status(thm)],[9358, 8941, 9346, 7819, 5951, 9159, 9164, 5923, 6008, 5925, 9239, 9168, 9245, 9305, 5385])).
% 23.24/23.41 tff(9360,plain,
% 23.24/23.41 ((mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))))) <=> (mult(mult(unit, mult(mult(a, c), mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(mult(a, c), mult(a, c))))),
% 23.24/23.41 inference(monotonicity,[status(thm)],[9343, 9359])).
% 23.24/23.41 tff(9361,plain,
% 23.24/23.41 ((mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))))) <=> (mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))))),
% 23.24/23.41 inference(transitivity,[status(thm)],[9360, 9345, 9340])).
% 23.24/23.41 tff(9362,plain,
% 23.24/23.41 ((mult(mult(unit, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))), a) = mult(mult(unit, a), mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))))) <=> (mult(mult(unit, a), mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))) = mult(mult(unit, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))), a))),
% 23.24/23.41 inference(commutativity,[status(thm)],[])).
% 23.24/23.41 tff(9363,plain,
% 23.24/23.41 (mult(mult(unit, a), mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))))),
% 23.24/23.41 inference(monotonicity,[status(thm)],[244])).
% 23.24/23.41 tff(9364,plain,
% 23.24/23.41 (mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))) = mult(mult(unit, a), mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))))),
% 23.24/23.41 inference(symmetry,[status(thm)],[9363])).
% 23.24/23.41 tff(9365,assumption,(~(mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))))), introduced(assumption)).
% 23.24/23.41 tff(9366,plain,
% 23.24/23.41 ((~(mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))))))),
% 23.24/23.41 inference(unit_resolution,[status(thm)],[7776, 9365])).
% 23.24/23.41 tff(9367,plain,
% 23.24/23.41 (~((~(mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))) = mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))))))),
% 23.24/23.41 inference(unit_resolution,[status(thm)],[7774, 9366])).
% 23.24/23.41 tff(9368,plain,
% 23.24/23.41 (((~(mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))) = mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c)))))) | (mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))) = mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))))),
% 23.24/23.41 inference(tautology,[status(thm)],[])).
% 23.24/23.41 tff(9369,plain,
% 23.24/23.41 (mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))) = mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))))),
% 23.24/23.41 inference(unit_resolution,[status(thm)],[9368, 9367])).
% 23.24/23.41 tff(9370,plain,
% 23.24/23.41 (mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), unit), c), unit) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), unit)),
% 23.24/23.41 inference(symmetry,[status(thm)],[1875])).
% 23.24/23.41 tff(9371,plain,
% 23.24/23.41 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)) = mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), unit), c), unit)),
% 23.24/23.41 inference(symmetry,[status(thm)],[1871])).
% 23.24/23.41 tff(9372,plain,
% 23.24/23.41 (mult(mult(rd(mult(b, c), mult(a, c)), c), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), unit)),
% 23.24/23.41 inference(transitivity,[status(thm)],[83, 4360, 9371, 9370])).
% 23.24/23.41 tff(9373,plain,
% 23.24/23.41 (mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c) = mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), unit), c)),
% 23.24/23.41 inference(monotonicity,[status(thm)],[9372])).
% 23.24/23.41 tff(9374,plain,
% 23.24/23.41 (mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), unit), c) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c)),
% 23.24/23.41 inference(symmetry,[status(thm)],[9373])).
% 23.24/23.41 tff(9375,plain,
% 23.24/23.41 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))),
% 23.24/23.41 inference(transitivity,[status(thm)],[4656, 4655, 9374, 2627, 6170, 6169])).
% 23.24/23.41 tff(9376,plain,
% 23.24/23.41 (mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))))),
% 23.24/23.41 inference(monotonicity,[status(thm)],[9375])).
% 23.24/23.41 tff(9377,plain,
% 23.24/23.41 (mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit), mult(c, c)) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))),
% 23.24/23.41 inference(monotonicity,[status(thm)],[9065])).
% 23.24/23.41 tff(9378,plain,
% 23.24/23.41 (mult(a, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit), mult(c, c))) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)))),
% 23.24/23.41 inference(monotonicity,[status(thm)],[9377])).
% 23.24/23.41 tff(9379,plain,
% 23.24/23.41 (mult(a, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit), mult(c, c))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))))),
% 23.24/23.41 inference(transitivity,[status(thm)],[9378, 9376])).
% 23.24/23.41 tff(9380,plain,
% 23.24/23.41 (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), a), c)),
% 23.24/23.41 inference(symmetry,[status(thm)],[5949])).
% 23.24/23.41 tff(9381,plain,
% 23.24/23.41 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c))),
% 23.24/23.41 inference(transitivity,[status(thm)],[9314, 5942, 9312, 3152])).
% 23.24/23.41 tff(9382,plain,
% 23.24/23.41 (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)), a) = mult(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)), a)),
% 23.24/23.41 inference(monotonicity,[status(thm)],[9381])).
% 23.24/23.41 tff(9383,plain,
% 23.24/23.41 ((mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(c, c)) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)), a)) <=> (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)), a) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(c, c)))),
% 23.24/23.41 inference(commutativity,[status(thm)],[])).
% 23.24/23.41 tff(9384,plain,
% 23.24/23.41 (mult(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)), a) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)), a)),
% 23.24/23.41 inference(symmetry,[status(thm)],[9382])).
% 23.24/23.41 tff(9385,plain,
% 23.24/23.41 (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a)),
% 23.24/23.41 inference(symmetry,[status(thm)],[7692])).
% 23.24/23.41 tff(9386,plain,
% 23.24/23.41 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(c, c))) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)), a)),
% 23.24/23.41 inference(transitivity,[status(thm)],[5919, 7563, 7565, 5952, 5949, 9385, 3159, 9384])).
% 23.24/23.41 tff(9387,plain,
% 23.24/23.41 ((mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(c, c)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(c, c)))) <=> (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(c, c)) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)), a))),
% 23.24/23.41 inference(monotonicity,[status(thm)],[9386])).
% 23.24/23.41 tff(9388,plain,
% 23.24/23.41 ((mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(c, c)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(c, c)))) <=> (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)), a) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(c, c)))),
% 23.24/23.41 inference(transitivity,[status(thm)],[9387, 9383])).
% 23.24/23.41 tff(9389,plain,
% 23.24/23.41 ((mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(c, c)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(c, c)))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))),
% 23.24/23.41 inference(unit_resolution,[status(thm)],[5970, 3862, 7692])).
% 23.24/23.41 tff(9390,plain,
% 23.24/23.41 (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(c, c)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(c, c)))),
% 23.24/23.41 inference(unit_resolution,[status(thm)],[9389, 2187])).
% 23.24/23.41 tff(9391,plain,
% 23.24/23.41 (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)), a) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(c, c))),
% 23.24/23.41 inference(modus_ponens,[status(thm)],[9390, 9388])).
% 23.24/23.41 tff(9392,plain,
% 23.24/23.41 (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(c, c)) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)), a)),
% 23.24/23.41 inference(symmetry,[status(thm)],[9391])).
% 23.24/23.41 tff(9393,plain,
% 23.24/23.41 (mult(a, mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, rd(mult(b, c), mult(a, c))), a)),
% 23.24/23.41 inference(symmetry,[status(thm)],[6462])).
% 23.24/23.41 tff(9394,plain,
% 23.24/23.41 (mult(mult(a, unit), mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(rd(mult(b, c), mult(a, c)), a))),
% 23.24/23.41 inference(monotonicity,[status(thm)],[47])).
% 23.24/23.41 tff(9395,plain,
% 23.24/23.41 (mult(mult(a, unit), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, rd(mult(b, c), mult(a, c))), a)),
% 23.24/23.41 inference(transitivity,[status(thm)],[9394, 9393])).
% 23.24/23.41 tff(9396,plain,
% 23.24/23.41 (mult(mult(mult(a, unit), mult(rd(mult(b, c), mult(a, c)), a)), unit) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), unit)),
% 23.24/23.41 inference(monotonicity,[status(thm)],[9395])).
% 23.24/23.41 tff(9397,plain,
% 23.24/23.41 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(a, unit), mult(rd(mult(b, c), mult(a, c)), a)), unit) = mult(a, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit)))),
% 23.24/23.41 inference(quant_inst,[status(thm)],[])).
% 23.24/23.41 tff(9398,plain,
% 23.24/23.41 (mult(mult(mult(a, unit), mult(rd(mult(b, c), mult(a, c)), a)), unit) = mult(a, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit))),
% 23.24/23.41 inference(unit_resolution,[status(thm)],[9397, 56])).
% 23.24/23.41 tff(9399,plain,
% 23.24/23.41 (mult(a, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit)) = mult(mult(mult(a, unit), mult(rd(mult(b, c), mult(a, c)), a)), unit)),
% 23.24/23.41 inference(symmetry,[status(thm)],[9398])).
% 23.24/23.41 tff(9400,plain,
% 23.24/23.41 (mult(a, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit)) = mult(mult(a, rd(mult(b, c), mult(a, c))), a)),
% 23.24/23.41 inference(transitivity,[status(thm)],[9399, 9396, 7576, 7572, 7570])).
% 23.24/23.41 tff(9401,plain,
% 23.24/23.41 (mult(mult(a, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit)), mult(c, c)) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(c, c))),
% 23.24/23.41 inference(monotonicity,[status(thm)],[9400])).
% 23.24/23.41 tff(9402,plain,
% 23.24/23.41 (mult(mult(a, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit)), mult(c, c)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c)))),
% 23.24/23.41 inference(transitivity,[status(thm)],[9401, 9392, 9382, 3158, 7692, 9380, 5951, 7566])).
% 23.24/23.41 tff(9403,plain,
% 23.24/23.41 ((mult(mult(a, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit)), mult(c, c)) = mult(a, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit), mult(c, c)))) <=> (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))))),
% 23.24/23.41 inference(monotonicity,[status(thm)],[9402, 9379])).
% 23.24/23.41 tff(9404,plain,
% 23.24/23.41 ((mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))))) <=> (mult(mult(a, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit)), mult(c, c)) = mult(a, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit), mult(c, c))))),
% 23.24/23.41 inference(symmetry,[status(thm)],[9403])).
% 23.24/23.41 tff(9405,plain,
% 23.24/23.41 ((mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c)))) <=> (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))))),
% 23.24/23.41 inference(commutativity,[status(thm)],[])).
% 23.24/23.41 tff(9406,assumption,(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)) = mult(mult(a, mult(c, c)), rd(mult(b, c), mult(a, c)))), introduced(assumption)).
% 23.24/23.41 tff(9407,plain,
% 23.24/23.41 (mult(mult(a, mult(c, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c))),
% 23.24/23.41 inference(symmetry,[status(thm)],[9406])).
% 23.24/23.41 tff(9408,plain,
% 23.24/23.41 (mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c))),
% 23.24/23.41 inference(transitivity,[status(thm)],[9324, 9323, 9407, 9314, 5942, 9312, 3152])).
% 23.24/23.41 tff(9409,plain,
% 23.24/23.41 (mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)), a)),
% 23.24/23.41 inference(monotonicity,[status(thm)],[9408])).
% 23.24/23.41 tff(9410,plain,
% 23.24/23.41 (mult(mult(unit, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, rd(mult(b, c), mult(a, c))))),
% 23.24/23.41 inference(monotonicity,[status(thm)],[73])).
% 23.24/23.41 tff(9411,plain,
% 23.24/23.41 (mult(mult(unit, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))),
% 23.24/23.41 inference(transitivity,[status(thm)],[9410, 8269, 9350, 4336])).
% 23.24/23.41 tff(9412,plain,
% 23.24/23.41 (mult(mult(mult(unit, c), mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)),
% 23.24/23.41 inference(monotonicity,[status(thm)],[9411])).
% 23.24/23.41 tff(9413,plain,
% 23.24/23.41 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(unit, c), mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(unit, mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), c)))),
% 23.24/23.41 inference(quant_inst,[status(thm)],[])).
% 23.24/23.41 tff(9414,plain,
% 23.24/23.41 (mult(mult(mult(unit, c), mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(unit, mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), c))),
% 23.24/23.41 inference(unit_resolution,[status(thm)],[9413, 56])).
% 23.24/23.41 tff(9415,plain,
% 23.24/23.41 (mult(unit, mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), c)) = mult(mult(mult(unit, c), mult(a, rd(mult(b, c), mult(a, c)))), c)),
% 23.24/23.41 inference(symmetry,[status(thm)],[9414])).
% 23.24/23.41 tff(9416,plain,
% 23.24/23.41 (mult(c, mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))),
% 23.24/23.41 inference(transitivity,[status(thm)],[8269, 9350, 4336])).
% 23.24/23.41 tff(9417,plain,
% 23.24/23.41 (mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)),
% 23.24/23.41 inference(monotonicity,[status(thm)],[9416])).
% 23.24/23.41 tff(9418,plain,
% 23.24/23.41 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), c)),
% 23.24/23.41 inference(symmetry,[status(thm)],[9417])).
% 23.24/23.41 tff(9419,plain,
% 23.24/23.41 (mult(unit, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)) = mult(unit, mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), c))),
% 23.24/23.41 inference(monotonicity,[status(thm)],[9418])).
% 23.24/23.41 tff(9420,plain,
% 23.24/23.41 (mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)),
% 23.24/23.42 inference(transitivity,[status(thm)],[9324, 9323, 9407, 9314, 5942, 9312])).
% 23.24/23.42 tff(9421,plain,
% 23.24/23.42 (mult(unit, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))) = mult(unit, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c))),
% 23.24/23.42 inference(monotonicity,[status(thm)],[9420])).
% 23.24/23.42 tff(9422,plain,
% 23.24/23.42 (mult(unit, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))) = mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 23.24/23.42 inference(transitivity,[status(thm)],[9421, 9419, 9415, 9412, 9311, 5941, 9313, 9406, 9315, 7671])).
% 23.24/23.42 tff(9423,plain,
% 23.24/23.42 (mult(mult(unit, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a)),
% 23.24/23.42 inference(monotonicity,[status(thm)],[9422])).
% 23.24/23.42 tff(9424,plain,
% 23.24/23.42 (mult(mult(unit, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))), a) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c)))),
% 23.24/23.42 inference(transitivity,[status(thm)],[9423, 9409, 3158, 7692, 9380, 5951, 7566])).
% 23.24/23.42 tff(9425,plain,
% 23.24/23.42 (mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))))),
% 23.24/23.42 inference(symmetry,[status(thm)],[9369])).
% 23.24/23.42 tff(9426,plain,
% 23.24/23.42 (mult(mult(unit, a), mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))))),
% 23.24/23.42 inference(transitivity,[status(thm)],[9363, 9425])).
% 23.24/23.42 tff(9427,plain,
% 23.24/23.42 ((mult(mult(unit, a), mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))) = mult(mult(unit, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))), a)) <=> (mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))))),
% 23.24/23.42 inference(monotonicity,[status(thm)],[9426, 9424])).
% 23.24/23.42 tff(9428,plain,
% 23.24/23.42 ((mult(mult(unit, a), mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))) = mult(mult(unit, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))), a)) <=> (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))))),
% 23.24/23.42 inference(transitivity,[status(thm)],[9427, 9405])).
% 23.24/23.42 tff(9429,plain,
% 23.24/23.42 ((mult(mult(unit, a), mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))) = mult(mult(unit, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))), a)) <=> (mult(mult(a, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit)), mult(c, c)) = mult(a, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit), mult(c, c))))),
% 23.24/23.42 inference(transitivity,[status(thm)],[9428, 9404])).
% 23.24/23.42 tff(9430,plain,
% 23.24/23.42 ((~(mult(mult(unit, a), mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))) = mult(mult(unit, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))), a))) <=> (~(mult(mult(a, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit)), mult(c, c)) = mult(a, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit), mult(c, c)))))),
% 23.24/23.42 inference(monotonicity,[status(thm)],[9429])).
% 23.24/23.42 tff(9431,plain,
% 23.24/23.42 (mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(unit, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))), a)),
% 23.24/23.42 inference(symmetry,[status(thm)],[9423])).
% 23.24/23.42 tff(9432,plain,
% 23.24/23.42 (mult(mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)), a) = mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a)),
% 23.24/23.42 inference(symmetry,[status(thm)],[9409])).
% 23.24/23.42 tff(9433,plain,
% 23.24/23.42 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c)))),
% 23.24/23.42 inference(unit_resolution,[status(thm)],[7766, 9367])).
% 23.24/23.42 tff(9434,plain,
% 23.24/23.42 (mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c)))),
% 23.24/23.42 inference(symmetry,[status(thm)],[9433])).
% 23.24/23.42 tff(9435,plain,
% 23.24/23.42 (mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(unit, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))), a)),
% 23.24/23.42 inference(transitivity,[status(thm)],[9434, 7565, 5952, 5949, 9385, 3159, 9432, 9431])).
% 23.24/23.42 tff(9436,plain,
% 23.24/23.42 ((mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))))) <=> (mult(mult(unit, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))), a) = mult(mult(unit, a), mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))))),
% 23.24/23.42 inference(monotonicity,[status(thm)],[9435, 9364])).
% 23.24/23.42 tff(9437,plain,
% 23.24/23.42 ((mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))))) <=> (mult(mult(unit, a), mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))) = mult(mult(unit, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))), a))),
% 23.24/23.42 inference(transitivity,[status(thm)],[9436, 9362])).
% 23.24/23.42 tff(9438,plain,
% 23.24/23.42 ((~(mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))))) <=> (~(mult(mult(unit, a), mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))) = mult(mult(unit, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))), a)))),
% 23.24/23.42 inference(monotonicity,[status(thm)],[9437])).
% 23.24/23.42 tff(9439,plain,
% 23.24/23.42 (~(mult(mult(unit, a), mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))) = mult(mult(unit, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))), a))),
% 23.24/23.42 inference(modus_ponens,[status(thm)],[9365, 9438])).
% 23.24/23.42 tff(9440,plain,
% 23.24/23.42 (~(mult(mult(a, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit)), mult(c, c)) = mult(a, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit), mult(c, c))))),
% 23.24/23.42 inference(modus_ponens,[status(thm)],[9439, 9430])).
% 23.24/23.42 tff(9441,plain,
% 23.24/23.42 (((~(mult(mult(a, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit)) = mult(a, mult(mult(c, c), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit))))) | (~(mult(mult(a, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit)), mult(c, c)) = mult(a, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit), mult(c, c)))))) | (mult(mult(a, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit)), mult(c, c)) = mult(a, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit), mult(c, c))))),
% 23.24/23.42 inference(tautology,[status(thm)],[])).
% 23.24/23.42 tff(9442,plain,
% 23.24/23.42 ((~(mult(mult(a, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit)) = mult(a, mult(mult(c, c), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit))))) | (~(mult(mult(a, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit)), mult(c, c)) = mult(a, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit), mult(c, c)))))),
% 23.24/23.42 inference(unit_resolution,[status(thm)],[9441, 9440])).
% 23.24/23.42 tff(9443,plain,
% 23.24/23.42 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit)) = mult(mult(a, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit)), mult(c, c)))) | (~(mult(a, mult(mult(c, c), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit))) = mult(a, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit), mult(c, c))))))) | (~((~(mult(mult(a, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit)) = mult(a, mult(mult(c, c), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit))))) | (~(mult(mult(a, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit)), mult(c, c)) = mult(a, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit), mult(c, c))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit)) = mult(mult(a, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit)), mult(c, c)))) | (~(mult(a, mult(mult(c, c), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit))) = mult(a, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit), mult(c, c))))))) | (~((~(mult(mult(a, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit)) = mult(a, mult(mult(c, c), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit))))) | (~(mult(mult(a, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit)), mult(c, c)) = mult(a, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit), mult(c, c))))))))),
% 23.24/23.42 inference(rewrite,[status(thm)],[])).
% 23.24/23.42 tff(9444,plain,
% 23.24/23.42 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit)) = mult(mult(a, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit)), mult(c, c)))) | (~(mult(a, mult(mult(c, c), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit))) = mult(a, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit), mult(c, c))))))) | (~((~(mult(mult(a, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit)) = mult(a, mult(mult(c, c), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit))))) | (~(mult(mult(a, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit)), mult(c, c)) = mult(a, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit), mult(c, c))))))))),
% 23.24/23.42 inference(quant_inst,[status(thm)],[])).
% 23.24/23.42 tff(9445,plain,
% 23.24/23.42 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit)) = mult(mult(a, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit)), mult(c, c)))) | (~(mult(a, mult(mult(c, c), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit))) = mult(a, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit), mult(c, c))))))) | (~((~(mult(mult(a, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit)) = mult(a, mult(mult(c, c), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit))))) | (~(mult(mult(a, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit)), mult(c, c)) = mult(a, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit), mult(c, c)))))))),
% 23.24/23.42 inference(modus_ponens,[status(thm)],[9444, 9443])).
% 23.24/23.42 tff(9446,plain,
% 23.24/23.42 ((~((~(mult(mult(a, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit)) = mult(mult(a, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit)), mult(c, c)))) | (~(mult(a, mult(mult(c, c), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit))) = mult(a, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit), mult(c, c))))))) | (~((~(mult(mult(a, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit)) = mult(a, mult(mult(c, c), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit))))) | (~(mult(mult(a, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit)), mult(c, c)) = mult(a, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit), mult(c, c)))))))),
% 23.24/23.42 inference(unit_resolution,[status(thm)],[9445, 27])).
% 23.24/23.42 tff(9447,plain,
% 23.24/23.42 (~((~(mult(mult(a, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit)) = mult(mult(a, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit)), mult(c, c)))) | (~(mult(a, mult(mult(c, c), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit))) = mult(a, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit), mult(c, c))))))),
% 23.24/23.42 inference(unit_resolution,[status(thm)],[9446, 9442])).
% 23.24/23.42 tff(9448,plain,
% 23.24/23.42 (((~(mult(mult(a, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit)) = mult(mult(a, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit)), mult(c, c)))) | (~(mult(a, mult(mult(c, c), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit))) = mult(a, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit), mult(c, c)))))) | (mult(a, mult(mult(c, c), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit))) = mult(a, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit), mult(c, c))))),
% 23.24/23.42 inference(tautology,[status(thm)],[])).
% 23.24/23.42 tff(9449,plain,
% 23.24/23.42 (mult(a, mult(mult(c, c), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit))) = mult(a, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit), mult(c, c)))),
% 23.24/23.42 inference(unit_resolution,[status(thm)],[9448, 9447])).
% 23.24/23.42 tff(9450,plain,
% 23.24/23.42 (mult(mult(c, c), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit)) = mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))),
% 23.24/23.42 inference(monotonicity,[status(thm)],[9065])).
% 23.24/23.42 tff(9451,plain,
% 23.24/23.42 (mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(c, c), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit))),
% 23.24/23.42 inference(symmetry,[status(thm)],[9450])).
% 23.24/23.42 tff(9452,plain,
% 23.24/23.42 (mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))) = mult(a, mult(mult(c, c), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit)))),
% 23.24/23.42 inference(monotonicity,[status(thm)],[9451])).
% 23.24/23.42 tff(9453,plain,
% 23.24/23.42 (mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))) = mult(mult(unit, a), mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))))),
% 23.24/23.42 inference(transitivity,[status(thm)],[9452, 9449, 9378, 9376, 9369, 9364])).
% 23.24/23.42 tff(9454,plain,
% 23.24/23.42 (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c)),
% 23.24/23.42 inference(symmetry,[status(thm)],[9346])).
% 23.24/23.42 tff(9455,plain,
% 23.24/23.42 (mult(mult(a, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit)), mult(c, c)) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c)),
% 23.24/23.42 inference(transitivity,[status(thm)],[9401, 9392, 9382, 3158, 7692, 9454])).
% 23.24/23.42 tff(9456,plain,
% 23.24/23.42 (mult(mult(a, c), c) = mult(a, mult(c, c))),
% 23.24/23.42 inference(transitivity,[status(thm)],[2622, 2614, 2621])).
% 23.24/23.42 tff(9457,plain,
% 23.24/23.42 (mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a))),
% 23.24/23.42 inference(monotonicity,[status(thm)],[9456])).
% 23.24/23.42 tff(9458,plain,
% 23.24/23.42 (mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a))),
% 23.24/23.42 inference(symmetry,[status(thm)],[9457])).
% 23.24/23.42 tff(9459,plain,
% 23.24/23.42 (mult(a, mult(c, c)) = mult(c, mult(a, c))),
% 23.24/23.42 inference(transitivity,[status(thm)],[2618, 2615, 2612, 6892, 2690])).
% 23.24/23.42 tff(9460,plain,
% 23.24/23.42 (mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a))),
% 23.24/23.42 inference(monotonicity,[status(thm)],[9459])).
% 23.24/23.42 tff(9461,plain,
% 23.24/23.42 (mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a))),
% 23.24/23.42 inference(symmetry,[status(thm)],[9460])).
% 23.24/23.42 tff(9462,plain,
% 23.24/23.42 (mult(rd(mult(b, c), mult(a, c)), a) = mult(unit, mult(rd(mult(b, c), mult(a, c)), a))),
% 23.24/23.42 inference(symmetry,[status(thm)],[6238])).
% 23.24/23.42 tff(9463,plain,
% 23.24/23.42 (mult(rd(mult(b, c), mult(a, c)), a) = mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit)),
% 23.24/23.42 inference(transitivity,[status(thm)],[9462, 9062])).
% 23.24/23.42 tff(9464,plain,
% 23.24/23.42 (mult(c, mult(a, c)) = mult(a, mult(c, c))),
% 23.24/23.42 inference(transitivity,[status(thm)],[3877, 7677, 2622, 2614, 2621])).
% 23.24/23.42 tff(9465,plain,
% 23.24/23.42 (mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit))),
% 23.24/23.42 inference(monotonicity,[status(thm)],[9464, 9463])).
% 23.24/23.42 tff(9466,plain,
% 23.24/23.42 (mult(mult(a, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit)) = mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a))),
% 23.24/23.43 inference(symmetry,[status(thm)],[9465])).
% 23.24/23.43 tff(9467,plain,
% 23.24/23.43 (mult(mult(a, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit)) = mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a))),
% 23.24/23.43 inference(transitivity,[status(thm)],[9466, 9461, 9458])).
% 23.24/23.43 tff(9468,plain,
% 23.24/23.43 ((mult(mult(a, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit)) = mult(mult(a, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit)), mult(c, c))) <=> (mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c))),
% 23.24/23.43 inference(monotonicity,[status(thm)],[9467, 9455])).
% 23.24/23.43 tff(9469,plain,
% 23.24/23.43 ((mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c)) <=> (mult(mult(a, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit)) = mult(mult(a, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit)), mult(c, c)))),
% 23.24/23.43 inference(symmetry,[status(thm)],[9468])).
% 23.24/23.43 tff(9470,plain,
% 23.24/23.43 (mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(c, c))),
% 23.24/23.43 inference(monotonicity,[status(thm)],[9393])).
% 23.24/23.43 tff(9471,plain,
% 23.24/23.43 (mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c)),
% 23.24/23.43 inference(transitivity,[status(thm)],[9470, 9392, 9382, 3158, 7692, 9454])).
% 23.24/23.43 tff(9472,plain,
% 23.24/23.43 ((mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a))) <=> (mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c) = mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a)))),
% 23.24/23.43 inference(monotonicity,[status(thm)],[9471, 9458])).
% 23.24/23.43 tff(9473,plain,
% 23.24/23.43 ((mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a))) <=> (mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c))),
% 23.24/23.43 inference(transitivity,[status(thm)],[9472, 7588])).
% 23.24/23.43 tff(9474,plain,
% 23.24/23.43 ((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), mult(c, c)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(c, c))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)))) | (mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)))),
% 23.24/23.43 inference(unit_resolution,[status(thm)],[7632, 5496, 6462])).
% 23.24/23.43 tff(9475,plain,
% 23.24/23.43 (mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a))),
% 23.24/23.43 inference(unit_resolution,[status(thm)],[9474, 9390, 4360, 2187])).
% 23.24/23.43 tff(9476,plain,
% 23.24/23.43 (mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c)),
% 23.24/23.43 inference(modus_ponens,[status(thm)],[9475, 9473])).
% 23.24/23.43 tff(9477,plain,
% 23.24/23.43 (mult(mult(a, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit)) = mult(mult(a, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit)), mult(c, c))),
% 23.24/23.43 inference(modus_ponens,[status(thm)],[9476, 9469])).
% 23.24/23.43 tff(9478,plain,
% 23.24/23.43 (mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(unit, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))), a)),
% 23.24/23.43 inference(transitivity,[status(thm)],[9460, 9465, 9477, 9401, 9392, 9382, 9432, 9431])).
% 23.24/23.43 tff(9479,plain,
% 23.24/23.43 ((mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a)))) <=> (mult(mult(unit, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))), a) = mult(mult(unit, a), mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))))),
% 23.24/23.43 inference(monotonicity,[status(thm)],[9478, 9453])).
% 23.24/23.43 tff(9480,plain,
% 23.24/23.43 ((mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a)))) <=> (mult(mult(unit, a), mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))) = mult(mult(unit, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))), a))),
% 23.24/23.43 inference(transitivity,[status(thm)],[9479, 9362])).
% 23.24/23.43 tff(9481,plain,
% 23.24/23.43 ((mult(mult(unit, a), mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))) = mult(mult(unit, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))), a)) <=> (mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))))),
% 23.24/23.43 inference(symmetry,[status(thm)],[9480])).
% 23.24/23.43 tff(9482,plain,
% 23.24/23.43 ((~(mult(mult(unit, a), mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))) = mult(mult(unit, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))), a))) <=> (~(mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a)))))),
% 23.24/23.43 inference(monotonicity,[status(thm)],[9481])).
% 23.24/23.43 tff(9483,plain,
% 23.24/23.43 (~(mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))))),
% 23.24/23.43 inference(modus_ponens,[status(thm)],[9439, 9482])).
% 23.24/23.43 tff(9484,plain,
% 23.24/23.43 (mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.24/23.43 inference(transitivity,[status(thm)],[8198, 4676, 8263, 5709, 9347])).
% 23.24/23.43 tff(9485,plain,
% 23.24/23.43 (mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c)) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))),
% 23.24/23.43 inference(transitivity,[status(thm)],[8198, 4676, 8263, 5709])).
% 23.24/23.43 tff(9486,plain,
% 23.24/23.43 ((mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c))) <=> (mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.24/23.43 inference(monotonicity,[status(thm)],[9485])).
% 23.24/23.43 tff(9487,plain,
% 23.24/23.43 (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 23.24/23.43 inference(monotonicity,[status(thm)],[4610])).
% 23.24/23.43 tff(9488,plain,
% 23.24/23.43 (mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))),
% 23.24/23.43 inference(symmetry,[status(thm)],[9487])).
% 23.24/23.43 tff(9489,plain,
% 23.24/23.43 (mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c)) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))),
% 23.24/23.43 inference(transitivity,[status(thm)],[8198, 4676, 9488, 2319])).
% 23.24/23.43 tff(9490,plain,
% 23.24/23.43 ((mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c))) <=> (mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.24/23.43 inference(monotonicity,[status(thm)],[9489])).
% 23.24/23.43 tff(9491,plain,
% 23.24/23.43 ((mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) <=> (mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c)))),
% 23.24/23.43 inference(symmetry,[status(thm)],[9490])).
% 23.24/23.43 tff(9492,assumption,(~(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c)))), introduced(assumption)).
% 23.24/23.43 tff(9493,plain,
% 23.24/23.43 ((~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c))))),
% 23.24/23.43 inference(unit_resolution,[status(thm)],[5814, 9492])).
% 23.24/23.43 tff(9494,plain,
% 23.24/23.43 (~((~(mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))))),
% 23.24/23.43 inference(unit_resolution,[status(thm)],[5826, 9493])).
% 23.24/23.43 tff(9495,plain,
% 23.24/23.43 (mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))),
% 23.24/23.43 inference(unit_resolution,[status(thm)],[6151, 9494])).
% 23.24/23.43 tff(9496,plain,
% 23.24/23.43 (mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c))),
% 23.24/23.43 inference(modus_ponens,[status(thm)],[9495, 9491])).
% 23.24/23.43 tff(9497,plain,
% 23.24/23.43 ($false),
% 23.24/23.43 inference(unit_resolution,[status(thm)],[9492, 9496])).
% 23.24/23.43 tff(9498,plain,((mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c))) | (~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))), inference(lemma,lemma(discharge,[]))).
% 23.24/23.43 tff(9499,plain,
% 23.24/23.43 ((mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c))) | (~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))),
% 23.24/23.43 inference(unit_resolution,[status(thm)],[9498, 5709])).
% 23.24/23.43 tff(9500,plain,
% 23.24/23.43 ((mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c))) | (~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))),
% 23.24/23.43 inference(unit_resolution,[status(thm)],[9499, 8129])).
% 23.24/23.43 tff(9501,plain,
% 23.24/23.43 (mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c))),
% 23.24/23.43 inference(unit_resolution,[status(thm)],[9500, 299, 2187])).
% 23.24/23.43 tff(9502,plain,
% 23.24/23.43 (mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))),
% 23.24/23.43 inference(modus_ponens,[status(thm)],[9501, 9486])).
% 23.24/23.43 tff(9503,plain,
% 23.24/23.43 ((~((~(mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))))) | (~(mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))))),
% 23.24/23.43 inference(tautology,[status(thm)],[])).
% 23.24/23.43 tff(9504,plain,
% 23.24/23.43 (~((~(mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))))),
% 23.24/23.43 inference(unit_resolution,[status(thm)],[9503, 9502, 9484])).
% 23.24/23.43 tff(9505,plain,
% 23.24/23.43 (mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c))),
% 23.24/23.43 inference(unit_resolution,[status(thm)],[6187, 9475])).
% 23.24/23.43 tff(9506,plain,
% 23.24/23.43 (mult(mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a)),
% 23.24/23.43 inference(monotonicity,[status(thm)],[7671])).
% 23.24/23.43 tff(9507,plain,
% 23.24/23.43 (mult(mult(mult(mult(a, c), c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c)))),
% 23.24/23.43 inference(monotonicity,[status(thm)],[6894])).
% 23.24/23.43 tff(9508,plain,
% 23.24/23.43 ((mult(mult(mult(mult(a, c), c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))), a)) <=> (mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a))),
% 23.24/23.44 inference(monotonicity,[status(thm)],[9507, 9506])).
% 23.24/23.44 tff(9509,plain,
% 23.24/23.44 ((mult(mult(mult(mult(a, c), c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))), a)) <=> (mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))))),
% 23.24/23.44 inference(transitivity,[status(thm)],[9508, 6585])).
% 23.24/23.44 tff(9510,plain,
% 23.24/23.44 ((mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c)))) <=> (mult(mult(mult(mult(a, c), c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))), a))),
% 23.24/23.44 inference(symmetry,[status(thm)],[9509])).
% 23.24/23.44 tff(9511,plain,
% 23.24/23.44 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a)),
% 23.24/23.44 inference(transitivity,[status(thm)],[7565, 5952, 5949, 9385, 3159, 9432])).
% 23.24/23.44 tff(9512,plain,
% 23.24/23.44 (mult(mult(c, mult(a, c)), a) = mult(mult(a, c), mult(a, c))),
% 23.24/23.44 inference(transitivity,[status(thm)],[9253, 9247])).
% 23.24/23.44 tff(9513,plain,
% 23.24/23.44 (mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 23.24/23.44 inference(monotonicity,[status(thm)],[9512])).
% 23.24/23.44 tff(9514,plain,
% 23.24/23.44 (mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c)))),
% 23.24/23.44 inference(symmetry,[status(thm)],[9513])).
% 23.24/23.44 tff(9515,plain,
% 23.24/23.44 (mult(mult(mult(mult(a, a), c), unit), c) = mult(mult(mult(a, c), a), c)),
% 23.24/23.44 inference(symmetry,[status(thm)],[9303])).
% 23.24/23.44 tff(9516,plain,
% 23.24/23.44 (mult(mult(a, a), mult(mult(c, unit), c)) = mult(mult(mult(mult(a, a), c), unit), c)),
% 23.24/23.44 inference(symmetry,[status(thm)],[7903])).
% 23.24/23.44 tff(9517,plain,
% 23.24/23.44 (mult(mult(a, a), mult(c, c)) = mult(mult(a, a), mult(mult(c, unit), c))),
% 23.24/23.44 inference(symmetry,[status(thm)],[7901])).
% 23.24/23.44 tff(9518,plain,
% 23.24/23.44 (mult(mult(a, mult(c, c)), a) = mult(mult(a, a), mult(c, c))),
% 23.24/23.44 inference(symmetry,[status(thm)],[9290])).
% 23.24/23.44 tff(9519,plain,
% 23.24/23.44 (mult(mult(a, c), mult(a, c)) = mult(a, mult(c, mult(a, c)))),
% 23.24/23.44 inference(transitivity,[status(thm)],[9332, 9331, 7707, 4663, 9518, 9517, 9516, 9515, 4717, 4715])).
% 23.24/23.44 tff(9520,plain,
% 23.24/23.44 (mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c)))),
% 23.24/23.44 inference(monotonicity,[status(thm)],[9519])).
% 23.24/23.44 tff(9521,plain,
% 23.24/23.44 (mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 23.24/23.44 inference(symmetry,[status(thm)],[9520])).
% 23.24/23.44 tff(9522,plain,
% 23.24/23.44 (mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c)))),
% 23.24/23.44 inference(transitivity,[status(thm)],[9521, 9514])).
% 23.24/23.44 tff(9523,plain,
% 23.24/23.44 ((mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c)))) <=> (mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a))),
% 23.24/23.44 inference(monotonicity,[status(thm)],[9522, 9511])).
% 23.24/23.44 tff(9524,plain,
% 23.24/23.44 ((mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c)))) <=> (mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))))),
% 23.24/23.44 inference(transitivity,[status(thm)],[9523, 6585])).
% 23.24/23.44 tff(9525,plain,
% 23.24/23.44 ((mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c)))) <=> (mult(mult(mult(mult(a, c), c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))), a))),
% 23.24/23.44 inference(transitivity,[status(thm)],[9327, 9524, 9510])).
% 23.24/23.44 tff(9526,plain,
% 23.24/23.44 (mult(mult(mult(mult(a, c), c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))), a)),
% 23.24/23.44 inference(modus_ponens,[status(thm)],[9433, 9525])).
% 23.24/23.44 tff(9527,plain,
% 23.24/23.44 (mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c))))),
% 23.24/23.44 inference(unit_resolution,[status(thm)],[6600, 9526])).
% 23.24/23.44 tff(9528,plain,
% 23.24/23.44 (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)),
% 23.24/23.44 inference(unit_resolution,[status(thm)],[8856, 9527])).
% 23.24/23.44 tff(9529,plain,
% 23.24/23.44 (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))),
% 23.24/23.44 inference(unit_resolution,[status(thm)],[2329, 9528])).
% 23.24/23.44 tff(9530,plain,
% 23.24/23.44 (mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c)))),
% 23.24/23.44 inference(transitivity,[status(thm)],[9470, 9392, 9382, 3158, 7692, 9380, 5951, 7566])).
% 23.24/23.44 tff(9531,plain,
% 23.24/23.44 ((mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)))) <=> (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))))),
% 23.24/23.44 inference(monotonicity,[status(thm)],[9530, 9376])).
% 23.24/23.44 tff(9532,plain,
% 23.24/23.44 ((mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))))) <=> (mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))))),
% 23.24/23.44 inference(symmetry,[status(thm)],[9531])).
% 23.24/23.44 tff(9533,plain,
% 23.24/23.44 ((mult(mult(unit, a), mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))) = mult(mult(unit, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))), a)) <=> (mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))))),
% 23.24/23.44 inference(transitivity,[status(thm)],[9428, 9532])).
% 23.24/23.44 tff(9534,plain,
% 23.24/23.44 ((~(mult(mult(unit, a), mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))) = mult(mult(unit, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))), a))) <=> (~(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)))))),
% 23.24/23.44 inference(monotonicity,[status(thm)],[9533])).
% 23.24/23.44 tff(9535,plain,
% 23.24/23.44 (~(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))))),
% 23.24/23.44 inference(modus_ponens,[status(thm)],[9439, 9534])).
% 23.24/23.44 tff(9536,plain,
% 23.24/23.44 ((~(mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))))) | (~(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)))))),
% 23.24/23.44 inference(unit_resolution,[status(thm)],[6062, 9535])).
% 23.24/23.44 tff(9537,plain,
% 23.24/23.44 (~((~(mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)))) | (~(mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))))))),
% 23.24/23.44 inference(unit_resolution,[status(thm)],[6198, 9536])).
% 23.24/23.44 tff(9538,plain,
% 23.24/23.44 (mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)))),
% 23.24/23.44 inference(unit_resolution,[status(thm)],[6200, 9537])).
% 23.24/23.44 tff(9539,plain,
% 23.24/23.44 (((~(mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))))) | (mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))))) | (~(mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)))) | (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))),
% 23.28/23.44 inference(unit_resolution,[status(thm)],[6246, 3862])).
% 23.28/23.44 tff(9540,plain,
% 23.28/23.44 (mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a)))),
% 23.28/23.44 inference(unit_resolution,[status(thm)],[9539, 9538, 9529, 2187, 9505, 9504])).
% 23.28/23.44 tff(9541,plain,
% 23.28/23.44 ($false),
% 23.28/23.44 inference(unit_resolution,[status(thm)],[9540, 9483])).
% 23.28/23.44 tff(9542,plain,((mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)) = mult(mult(a, mult(c, c)), rd(mult(b, c), mult(a, c))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))) | (~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))), inference(lemma,lemma(discharge,[]))).
% 23.28/23.44 tff(9543,plain,
% 23.28/23.44 (mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))))),
% 23.28/23.44 inference(unit_resolution,[status(thm)],[9542, 9321, 4360, 2187, 299])).
% 23.28/23.44 tff(9544,plain,
% 23.28/23.44 (mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c)))),
% 23.28/23.44 inference(modus_ponens,[status(thm)],[9543, 9361])).
% 23.28/23.44 tff(9545,plain,
% 23.28/23.44 (mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a)),
% 23.28/23.44 inference(symmetry,[status(thm)],[9544])).
% 23.28/23.44 tff(9546,plain,
% 23.28/23.44 (mult(mult(rd(mult(b, c), mult(a, c)), a), c) = mult(mult(a, rd(mult(b, c), mult(a, c))), c)),
% 23.28/23.44 inference(monotonicity,[status(thm)],[9352])).
% 23.28/23.44 tff(9547,plain,
% 23.28/23.44 (mult(mult(rd(mult(b, c), mult(a, c)), c), a) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))),
% 23.28/23.44 inference(transitivity,[status(thm)],[83, 4360, 4340, 9546, 2189, 2187, 2172, 2178, 2177, 2162])).
% 23.28/23.44 tff(9548,plain,
% 23.28/23.44 (mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)) = mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 23.28/23.44 inference(monotonicity,[status(thm)],[9547])).
% 23.28/23.44 tff(9549,plain,
% 23.28/23.44 ((mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c)) <=> (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 23.28/23.44 inference(commutativity,[status(thm)],[])).
% 23.28/23.44 tff(9550,plain,
% 23.28/23.44 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), c)) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c)),
% 23.28/23.44 inference(transitivity,[status(thm)],[7563, 9160, 5952, 9158])).
% 23.28/23.44 tff(9551,plain,
% 23.28/23.44 (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))),
% 23.28/23.44 inference(transitivity,[status(thm)],[5182, 8159, 139, 5387])).
% 23.28/23.44 tff(9552,plain,
% 23.28/23.44 ((mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)), c) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), c))) <=> (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c))),
% 23.28/23.44 inference(monotonicity,[status(thm)],[9551, 9550])).
% 23.28/23.44 tff(9553,plain,
% 23.28/23.44 ((mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)), c) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), c))) <=> (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 23.28/23.44 inference(transitivity,[status(thm)],[9552, 9549])).
% 23.28/23.44 tff(9554,plain,
% 23.28/23.44 ((mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))) <=> (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)), c) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), c)))),
% 23.28/23.44 inference(symmetry,[status(thm)],[9553])).
% 23.28/23.44 tff(9555,plain,
% 23.28/23.44 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(b, mult(c, mult(a, c)))),
% 23.28/23.44 inference(transitivity,[status(thm)],[1039, 138, 266, 8946, 2570, 4396])).
% 23.28/23.44 tff(9556,plain,
% 23.28/23.44 (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(b, c), mult(a, c))),
% 23.28/23.44 inference(transitivity,[status(thm)],[7819, 5951, 9159, 9164, 5923, 6008, 5925, 9239, 9168, 9245, 9305, 2502, 2499])).
% 23.28/23.44 tff(9557,plain,
% 23.28/23.44 ((mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))) <=> (mult(mult(b, c), mult(a, c)) = mult(b, mult(c, mult(a, c))))),
% 23.28/23.44 inference(monotonicity,[status(thm)],[9556, 9555])).
% 23.28/23.44 tff(9558,plain,
% 23.28/23.44 ((mult(mult(b, c), mult(a, c)) = mult(b, mult(c, mult(a, c)))) <=> (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 23.28/23.44 inference(symmetry,[status(thm)],[9557])).
% 23.28/23.44 tff(9559,plain,
% 23.28/23.44 (mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))),
% 23.28/23.44 inference(monotonicity,[status(thm)],[9416])).
% 23.28/23.44 tff(9560,assumption,(~(mult(c, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))))), introduced(assumption)).
% 23.28/23.44 tff(9561,plain,
% 23.28/23.44 ((~(mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c)))) | (~(mult(c, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))))),
% 23.28/23.44 inference(unit_resolution,[status(thm)],[6803, 9560])).
% 23.28/23.44 tff(9562,plain,
% 23.28/23.44 (~((~(mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(c, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))))))),
% 23.28/23.44 inference(unit_resolution,[status(thm)],[6808, 9561])).
% 23.28/23.44 tff(9563,plain,
% 23.28/23.44 (((~(mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(c, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))))) | (mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))))),
% 23.28/23.44 inference(tautology,[status(thm)],[])).
% 23.28/23.44 tff(9564,plain,
% 23.28/23.44 (mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 23.28/23.44 inference(unit_resolution,[status(thm)],[9563, 9562])).
% 23.28/23.44 tff(9565,plain,
% 23.28/23.44 (mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))) = mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c))),
% 23.28/23.44 inference(symmetry,[status(thm)],[9564])).
% 23.28/23.44 tff(9566,plain,
% 23.28/23.44 (mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))) = mult(b, mult(c, mult(a, c)))),
% 23.28/23.44 inference(transitivity,[status(thm)],[9565, 9559, 1039, 138, 266, 8946, 2570, 4396])).
% 23.28/23.44 tff(9567,plain,
% 23.28/23.44 (rd(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c), c) = rd(mult(mult(b, mult(a, c)), c), c)),
% 23.28/23.44 inference(symmetry,[status(thm)],[9308])).
% 23.28/23.44 tff(9568,plain,
% 23.28/23.44 (mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))),
% 23.28/23.44 inference(monotonicity,[status(thm)],[9352])).
% 23.28/23.44 tff(9569,plain,
% 23.28/23.44 (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))),
% 23.28/23.44 inference(symmetry,[status(thm)],[9568])).
% 23.28/23.45 tff(9570,plain,
% 23.28/23.45 (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(b, mult(a, c))),
% 23.28/23.45 inference(transitivity,[status(thm)],[5709, 9569, 5497, 322, 9567, 2680])).
% 23.28/23.45 tff(9571,plain,
% 23.28/23.45 (mult(c, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))) = mult(c, mult(b, mult(a, c)))),
% 23.28/23.45 inference(monotonicity,[status(thm)],[9570])).
% 23.28/23.45 tff(9572,plain,
% 23.28/23.45 (mult(c, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))))),
% 23.28/23.45 inference(monotonicity,[status(thm)],[8170])).
% 23.28/23.45 tff(9573,plain,
% 23.28/23.45 (mult(c, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(b, c), mult(a, c))),
% 23.28/23.45 inference(transitivity,[status(thm)],[9572, 9571, 6924, 2429])).
% 23.28/23.45 tff(9574,plain,
% 23.28/23.45 ((mult(c, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))) <=> (mult(mult(b, c), mult(a, c)) = mult(b, mult(c, mult(a, c))))),
% 23.28/23.45 inference(monotonicity,[status(thm)],[9573, 9566])).
% 23.28/23.45 tff(9575,plain,
% 23.28/23.45 ((mult(c, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))) <=> (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)), c) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), c)))),
% 23.28/23.45 inference(transitivity,[status(thm)],[9574, 9558, 9554])).
% 23.28/23.45 tff(9576,plain,
% 23.28/23.45 ((~(mult(c, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))))) <=> (~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)), c) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), c))))),
% 23.28/23.45 inference(monotonicity,[status(thm)],[9575])).
% 23.28/23.45 tff(9577,plain,
% 23.28/23.45 (~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)), c) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), c)))),
% 23.28/23.45 inference(modus_ponens,[status(thm)],[9560, 9576])).
% 23.28/23.45 tff(9578,plain,
% 23.28/23.45 (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)),
% 23.28/23.45 inference(transitivity,[status(thm)],[5709, 9569, 5497])).
% 23.28/23.45 tff(9579,plain,
% 23.28/23.45 (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))),
% 23.28/23.45 inference(unit_resolution,[status(thm)],[2329, 9578])).
% 23.28/23.45 tff(9580,plain,
% 23.28/23.45 (((~(mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a))) | (~(mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a))))) | (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)), c) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), c))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))) | (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a)))),
% 23.28/23.45 inference(unit_resolution,[status(thm)],[5215, 3862, 6922, 7692])).
% 23.28/23.45 tff(9581,plain,
% 23.28/23.45 (((~(mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a))) | (~(mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a))))) | (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)), c) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), c))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))) | (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a)))),
% 23.28/23.45 inference(unit_resolution,[status(thm)],[9580, 8129])).
% 23.28/23.45 tff(9582,plain,
% 23.28/23.45 ((~(mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a))) | (~(mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a))))),
% 23.28/23.45 inference(unit_resolution,[status(thm)],[9581, 9579, 1039, 2187, 4360, 9577, 5159, 287, 4535, 4501])).
% 23.28/23.45 tff(9583,plain,
% 23.28/23.45 (~((~(mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))) | (~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)))))),
% 23.28/23.45 inference(unit_resolution,[status(thm)],[5220, 9582])).
% 23.28/23.45 tff(9584,plain,
% 23.28/23.45 (mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a))),
% 23.28/23.45 inference(unit_resolution,[status(thm)],[5222, 9583])).
% 23.28/23.45 tff(9585,plain,
% 23.28/23.45 (mult(mult(c, a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c))),
% 23.28/23.45 inference(monotonicity,[status(thm)],[5700])).
% 23.28/23.45 tff(9586,plain,
% 23.28/23.45 (mult(mult(mult(c, a), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a)),
% 23.28/23.45 inference(monotonicity,[status(thm)],[9585])).
% 23.28/23.45 tff(9587,plain,
% 23.28/23.45 (mult(c, mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a)) = mult(c, mult(b, mult(a, c)))),
% 23.28/23.45 inference(transitivity,[status(thm)],[5324, 9586, 9584, 9548, 5322, 9334, 9545, 9326, 3158, 7692, 7819, 5951, 9159, 9164, 5923, 6008, 5925, 9239, 9168, 9245, 9305, 2502, 2499, 2742, 6923])).
% 23.28/23.45 tff(9588,plain,
% 23.28/23.45 (ld(c, mult(c, mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a))) = ld(c, mult(c, mult(b, mult(a, c))))),
% 23.28/23.45 inference(monotonicity,[status(thm)],[9587])).
% 23.28/23.45 tff(9589,plain,
% 23.28/23.45 (mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)),
% 23.28/23.45 inference(transitivity,[status(thm)],[5329, 9588, 5658, 2681, 9308, 321])).
% 23.28/23.45 tff(9590,plain,
% 23.28/23.45 (rd(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a), a) = rd(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), a)),
% 23.28/23.45 inference(monotonicity,[status(thm)],[9589])).
% 23.28/23.45 tff(9591,plain,
% 23.28/23.45 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), c)))),
% 23.28/23.45 inference(quant_inst,[status(thm)],[])).
% 23.28/23.45 tff(9592,plain,
% 23.28/23.45 (rd(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a), a) = mult(a, mult(rd(mult(b, c), mult(a, c)), c))),
% 23.28/23.45 inference(unit_resolution,[status(thm)],[9591, 168])).
% 23.28/23.45 tff(9593,plain,
% 23.28/23.45 (mult(a, mult(rd(mult(b, c), mult(a, c)), c)) = rd(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a), a)),
% 23.28/23.45 inference(symmetry,[status(thm)],[9592])).
% 23.28/23.45 tff(9594,plain,
% 23.28/23.45 (mult(a, mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))),
% 23.28/23.45 inference(transitivity,[status(thm)],[2220, 5160, 2356, 9593, 9590, 4441])).
% 23.28/23.45 tff(9595,plain,
% 23.28/23.45 (mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))),
% 23.28/23.45 inference(monotonicity,[status(thm)],[9594])).
% 23.28/23.45 tff(9596,plain,
% 23.28/23.45 (mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(b, mult(c, mult(a, c)))),
% 23.28/23.45 inference(transitivity,[status(thm)],[9595, 1039, 138, 266, 8946, 2570, 4396])).
% 23.28/23.45 tff(9597,plain,
% 23.28/23.45 (mult(a, mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))),
% 23.28/23.45 inference(transitivity,[status(thm)],[9593, 9590, 4441])).
% 23.28/23.45 tff(9598,plain,
% 23.28/23.45 (mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))) = mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 23.28/23.45 inference(monotonicity,[status(thm)],[9597])).
% 23.28/23.45 tff(9599,plain,
% 23.28/23.45 (mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c)))),
% 23.28/23.45 inference(unit_resolution,[status(thm)],[5352, 9583])).
% 23.28/23.45 tff(9600,plain,
% 23.28/23.45 (mult(a, mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), c))),
% 23.28/23.45 inference(transitivity,[status(thm)],[2220, 5160, 2356])).
% 23.28/23.45 tff(9601,plain,
% 23.28/23.45 (ld(a, mult(a, mult(c, rd(mult(b, c), mult(a, c))))) = ld(a, mult(a, mult(rd(mult(b, c), mult(a, c)), c)))),
% 23.28/23.45 inference(monotonicity,[status(thm)],[9600])).
% 23.28/23.45 tff(9602,plain,
% 23.28/23.45 (mult(c, rd(mult(b, c), mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), c)),
% 23.28/23.45 inference(transitivity,[status(thm)],[5202, 9601, 5127])).
% 23.28/23.45 tff(9603,plain,
% 23.28/23.45 (mult(mult(mult(a, c), a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c))),
% 23.28/23.45 inference(monotonicity,[status(thm)],[9602])).
% 23.28/23.45 tff(9604,plain,
% 23.28/23.45 (mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(b, c), mult(a, c))),
% 23.28/23.45 inference(transitivity,[status(thm)],[8897, 9603, 9599, 9598, 5322, 9334, 9545, 9326, 3158, 7692, 7819, 5951, 9159, 9164, 5923, 6008, 5925, 9239, 9168, 9245, 9305, 2502, 2499])).
% 23.28/23.45 tff(9605,plain,
% 23.28/23.45 ((mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c))) <=> (mult(mult(b, c), mult(a, c)) = mult(b, mult(c, mult(a, c))))),
% 23.28/23.45 inference(monotonicity,[status(thm)],[9604, 9596])).
% 23.28/23.45 tff(9606,plain,
% 23.28/23.45 ((mult(mult(b, c), mult(a, c)) = mult(b, mult(c, mult(a, c)))) <=> (mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)))),
% 23.28/23.45 inference(symmetry,[status(thm)],[9605])).
% 23.28/23.45 tff(9607,plain,
% 23.28/23.45 ((~(mult(mult(b, c), mult(a, c)) = mult(b, mult(c, mult(a, c))))) <=> (~(mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c))))),
% 23.28/23.45 inference(monotonicity,[status(thm)],[9606])).
% 23.28/23.45 tff(9608,plain,
% 23.28/23.45 ((~(mult(c, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))))) <=> (~(mult(mult(b, c), mult(a, c)) = mult(b, mult(c, mult(a, c)))))),
% 23.28/23.45 inference(monotonicity,[status(thm)],[9574])).
% 23.28/23.45 tff(9609,plain,
% 23.28/23.45 (~(mult(mult(b, c), mult(a, c)) = mult(b, mult(c, mult(a, c))))),
% 23.28/23.45 inference(modus_ponens,[status(thm)],[9560, 9608])).
% 23.28/23.45 tff(9610,plain,
% 23.28/23.45 (~(mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)))),
% 23.28/23.45 inference(modus_ponens,[status(thm)],[9609, 9607])).
% 23.28/23.45 tff(9611,plain,
% 23.28/23.45 ((~(mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)))) | (~(mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))))),
% 23.28/23.46 inference(unit_resolution,[status(thm)],[4606, 9610])).
% 23.28/23.46 tff(9612,plain,
% 23.28/23.46 (mult(mult(unit, mult(mult(a, c), c)), b) = mult(mult(c, mult(a, c)), b)),
% 23.28/23.46 inference(monotonicity,[status(thm)],[7744])).
% 23.28/23.46 tff(9613,plain,
% 23.28/23.46 (mult(mult(c, mult(a, c)), b) = mult(mult(unit, mult(mult(a, c), c)), b)),
% 23.28/23.46 inference(symmetry,[status(thm)],[9612])).
% 23.28/23.46 tff(9614,plain,
% 23.28/23.46 (mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))) = mult(mult(unit, mult(mult(a, c), c)), b)),
% 23.28/23.46 inference(transitivity,[status(thm)],[4539, 4372, 234, 4371, 7680, 9613])).
% 23.28/23.46 tff(9615,plain,
% 23.28/23.46 (mult(mult(unit, b), mult(mult(a, c), c)) = mult(b, mult(mult(a, c), c))),
% 23.28/23.46 inference(monotonicity,[status(thm)],[184])).
% 23.28/23.46 tff(9616,plain,
% 23.28/23.46 (mult(b, mult(mult(a, c), c)) = mult(mult(unit, b), mult(mult(a, c), c))),
% 23.28/23.46 inference(symmetry,[status(thm)],[9615])).
% 23.28/23.46 tff(9617,plain,
% 23.28/23.46 (mult(b, mult(c, mult(a, c))) = mult(b, mult(mult(a, c), c))),
% 23.28/23.46 inference(monotonicity,[status(thm)],[7678])).
% 23.28/23.46 tff(9618,plain,
% 23.28/23.46 (mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(mult(unit, b), mult(mult(a, c), c))),
% 23.28/23.46 inference(transitivity,[status(thm)],[9595, 1039, 138, 266, 8946, 2570, 4396, 9617, 9616])).
% 23.28/23.46 tff(9619,plain,
% 23.28/23.46 ((mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))) <=> (mult(mult(unit, b), mult(mult(a, c), c)) = mult(mult(unit, mult(mult(a, c), c)), b))),
% 23.28/23.46 inference(monotonicity,[status(thm)],[9618, 9614])).
% 23.28/23.46 tff(9620,plain,
% 23.28/23.46 ((mult(mult(unit, b), mult(mult(a, c), c)) = mult(mult(unit, mult(mult(a, c), c)), b)) <=> (mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))),
% 23.28/23.46 inference(symmetry,[status(thm)],[9619])).
% 23.28/23.46 tff(9621,plain,
% 23.28/23.46 ((~(mult(mult(unit, b), mult(mult(a, c), c)) = mult(mult(unit, mult(mult(a, c), c)), b))) <=> (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))))),
% 23.28/23.46 inference(monotonicity,[status(thm)],[9620])).
% 23.28/23.46 tff(9622,plain,
% 23.28/23.46 (mult(a, mult(mult(b, c), c)) = mult(mult(unit, mult(mult(a, c), c)), b)),
% 23.28/23.46 inference(transitivity,[status(thm)],[4372, 234, 4371, 7680, 9613])).
% 23.28/23.46 tff(9623,plain,
% 23.28/23.46 (mult(mult(a, mult(b, c)), c) = mult(mult(unit, b), mult(mult(a, c), c))),
% 23.28/23.46 inference(transitivity,[status(thm)],[8946, 2570, 4396, 9617, 9616])).
% 23.28/23.46 tff(9624,plain,
% 23.28/23.46 ((mult(mult(a, mult(b, c)), c) = mult(a, mult(mult(b, c), c))) <=> (mult(mult(unit, b), mult(mult(a, c), c)) = mult(mult(unit, mult(mult(a, c), c)), b))),
% 23.28/23.46 inference(monotonicity,[status(thm)],[9623, 9622])).
% 23.28/23.46 tff(9625,plain,
% 23.28/23.46 ((~(mult(mult(a, mult(b, c)), c) = mult(a, mult(mult(b, c), c)))) <=> (~(mult(mult(unit, b), mult(mult(a, c), c)) = mult(mult(unit, mult(mult(a, c), c)), b)))),
% 23.28/23.46 inference(monotonicity,[status(thm)],[9624])).
% 23.28/23.46 tff(9626,plain,
% 23.28/23.46 (~(mult(mult(unit, b), mult(mult(a, c), c)) = mult(mult(unit, mult(mult(a, c), c)), b))),
% 23.28/23.46 inference(modus_ponens,[status(thm)],[258, 9625])).
% 23.28/23.46 tff(9627,plain,
% 23.28/23.46 (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))),
% 23.28/23.46 inference(modus_ponens,[status(thm)],[9626, 9621])).
% 23.28/23.46 tff(9628,plain,
% 23.28/23.46 ((~(mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))))),
% 23.28/23.46 inference(unit_resolution,[status(thm)],[4560, 9627])).
% 23.28/23.46 tff(9629,plain,
% 23.28/23.46 ($false),
% 23.28/23.46 inference(unit_resolution,[status(thm)],[4565, 9628, 9611])).
% 23.28/23.46 tff(9630,plain,((~(mult(b, mult(a, mult(b, c))) = mult(b, mult(mult(b, c), a)))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (~(mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))) | (~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)))) | (mult(c, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))), inference(lemma,lemma(discharge,[]))).
% 23.28/23.46 tff(9631,plain,
% 23.28/23.46 ((~(mult(b, mult(a, mult(b, c))) = mult(b, mult(mult(b, c), a)))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))) | (~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)))) | (mult(c, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))),
% 23.28/23.46 inference(unit_resolution,[status(thm)],[9630, 9157])).
% 23.28/23.46 tff(9632,plain,
% 23.28/23.46 (~(mult(b, mult(a, mult(b, c))) = mult(b, mult(mult(b, c), a)))),
% 23.28/23.46 inference(unit_resolution,[status(thm)],[9631, 8317, 316, 279, 8303, 8165, 6583, 8305, 4390, 281])).
% 23.28/23.46 tff(9633,plain,
% 23.28/23.46 (mult(a, mult(b, c)) = mult(mult(b, c), a)),
% 23.28/23.46 inference(transitivity,[status(thm)],[7060, 288, 7066, 4501, 1332])).
% 23.28/23.46 tff(9634,plain,
% 23.28/23.46 (mult(b, mult(a, mult(b, c))) = mult(b, mult(mult(b, c), a))),
% 23.28/23.46 inference(monotonicity,[status(thm)],[9633])).
% 23.28/23.46 tff(9635,assumption,(~(mult(b, mult(a, mult(b, c))) = mult(b, mult(mult(b, c), a)))), introduced(assumption)).
% 23.28/23.46 tff(9636,plain,
% 23.28/23.46 ($false),
% 23.28/23.46 inference(unit_resolution,[status(thm)],[9635, 9634])).
% 23.28/23.46 tff(9637,plain,((~(mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))) | (mult(b, mult(a, mult(b, c))) = mult(b, mult(mult(b, c), a))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a)))), inference(lemma,lemma(discharge,[]))).
% 23.28/23.46 tff(9638,plain,
% 23.28/23.46 (~(mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.28/23.46 inference(unit_resolution,[status(thm)],[9637, 9632, 279, 8303])).
% 23.28/23.46 tff(9639,plain,
% 23.28/23.46 (~((~(mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)))))),
% 23.28/23.46 inference(unit_resolution,[status(thm)],[2406, 9638])).
% 23.28/23.46 tff(9640,plain,
% 23.28/23.46 (mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c))))),
% 23.28/23.46 inference(unit_resolution,[status(thm)],[5253, 9639])).
% 23.28/23.46 tff(9641,plain,
% 23.28/23.46 (mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), c), mult(a, rd(mult(b, c), mult(a, c))))),
% 23.28/23.46 inference(transitivity,[status(thm)],[9640, 8197])).
% 23.28/23.46 tff(9642,plain,
% 23.28/23.46 (mult(a, mult(c, c)) = mult(c, mult(a, c))),
% 23.28/23.46 inference(transitivity,[status(thm)],[2618, 2615, 2612, 2596, 8194, 2590])).
% 23.28/23.46 tff(9643,plain,
% 23.28/23.46 (mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a))),
% 23.28/23.46 inference(monotonicity,[status(thm)],[9642])).
% 23.28/23.46 tff(9644,plain,
% 23.28/23.46 (mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a))),
% 23.28/23.46 inference(symmetry,[status(thm)],[9643])).
% 23.28/23.46 tff(9645,plain,
% 23.28/23.46 (mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a))),
% 23.28/23.46 inference(unit_resolution,[status(thm)],[2408, 9639])).
% 23.28/23.46 tff(9646,plain,
% 23.28/23.46 (mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a))),
% 23.28/23.46 inference(transitivity,[status(thm)],[9645, 9644, 9458])).
% 23.28/23.46 tff(9647,plain,
% 23.28/23.46 ((mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c)))) <=> (mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, c), c), mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.28/23.46 inference(monotonicity,[status(thm)],[9646, 9641])).
% 23.28/23.46 tff(9648,plain,
% 23.28/23.46 ((mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c)))) <=> (mult(mult(mult(a, c), c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a)))),
% 23.28/23.46 inference(transitivity,[status(thm)],[9647, 8192])).
% 23.28/23.46 tff(9649,plain,
% 23.28/23.46 ((mult(mult(mult(a, c), c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a))) <=> (mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))))),
% 23.28/23.46 inference(symmetry,[status(thm)],[9648])).
% 23.28/23.46 tff(9650,plain,
% 23.28/23.46 ((~(mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c)))) | (~(mult(c, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))))),
% 23.28/23.46 inference(unit_resolution,[status(thm)],[6803, 8317])).
% 23.28/23.46 tff(9651,plain,
% 23.28/23.46 (~((~(mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(c, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))))))),
% 23.28/23.46 inference(unit_resolution,[status(thm)],[6808, 9650])).
% 23.28/23.46 tff(9652,plain,
% 23.28/23.46 (mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(c, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.28/23.46 inference(unit_resolution,[status(thm)],[6810, 9651])).
% 23.28/23.46 tff(9653,plain,
% 23.28/23.46 (mult(c, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c))))),
% 23.28/23.46 inference(symmetry,[status(thm)],[9652])).
% 23.28/23.46 tff(9654,plain,
% 23.28/23.46 (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 23.28/23.46 inference(transitivity,[status(thm)],[8170, 8169, 281])).
% 23.28/23.46 tff(9655,plain,
% 23.28/23.46 (mult(c, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 23.28/23.46 inference(monotonicity,[status(thm)],[9654])).
% 23.28/23.46 tff(9656,plain,
% 23.28/23.46 (mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))) = mult(c, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.28/23.46 inference(symmetry,[status(thm)],[9655])).
% 23.28/23.46 tff(9657,plain,
% 23.28/23.46 (~(mult(mult(mult(mult(a, c), c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))), a))),
% 23.28/23.46 inference(unit_resolution,[status(thm)],[6600, 9638])).
% 23.28/23.46 tff(9658,plain,
% 23.28/23.46 ((~(mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (mult(mult(mult(mult(a, c), c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))), a)) | (~(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c))))))),
% 23.28/23.46 inference(unit_resolution,[status(thm)],[6754, 8730])).
% 23.28/23.46 tff(9659,plain,
% 23.28/23.46 (~(mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 23.28/23.46 inference(unit_resolution,[status(thm)],[9658, 9657, 4495, 6583])).
% 23.28/23.46 tff(9660,plain,
% 23.28/23.46 ((~(mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(c, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))))),
% 23.28/23.46 inference(unit_resolution,[status(thm)],[4699, 9659])).
% 23.28/23.46 tff(9661,plain,
% 23.28/23.46 (~((~(mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(c, mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)))))),
% 23.28/23.46 inference(unit_resolution,[status(thm)],[4697, 9660])).
% 23.28/23.46 tff(9662,plain,
% 23.28/23.46 (mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 23.28/23.46 inference(unit_resolution,[status(thm)],[4685, 9661])).
% 23.28/23.46 tff(9663,plain,
% 23.28/23.46 (mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, c), c), mult(a, rd(mult(b, c), mult(a, c))))),
% 23.28/23.46 inference(transitivity,[status(thm)],[9662, 9656, 9653, 8197])).
% 23.28/23.46 tff(9664,plain,
% 23.28/23.46 (mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a)),
% 23.28/23.46 inference(monotonicity,[status(thm)],[4496])).
% 23.28/23.46 tff(9665,plain,
% 23.28/23.46 (mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a))),
% 23.28/23.46 inference(transitivity,[status(thm)],[9664, 9645, 9644, 9458])).
% 23.28/23.46 tff(9666,plain,
% 23.28/23.46 ((mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c))))) <=> (mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, c), c), mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.28/23.46 inference(monotonicity,[status(thm)],[9665, 9663])).
% 23.28/23.46 tff(9667,plain,
% 23.28/23.46 ((mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c))))) <=> (mult(mult(mult(a, c), c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a)))),
% 23.28/23.46 inference(transitivity,[status(thm)],[9666, 8192])).
% 23.28/23.46 tff(9668,plain,
% 23.28/23.46 ((mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c))))) <=> (mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))))),
% 23.28/23.46 inference(transitivity,[status(thm)],[9667, 9649])).
% 23.28/23.46 tff(9669,plain,
% 23.28/23.46 ((~(mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) <=> (~(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c)))))),
% 23.28/23.46 inference(monotonicity,[status(thm)],[9668])).
% 23.28/23.46 tff(9670,plain,
% 23.28/23.46 (~(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))))),
% 23.28/23.47 inference(modus_ponens,[status(thm)],[9659, 9669])).
% 23.28/23.47 tff(9671,plain,
% 23.28/23.47 ((mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c)))) | (~(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c))))))),
% 23.28/23.47 inference(unit_resolution,[status(thm)],[7080, 8129])).
% 23.28/23.47 tff(9672,plain,
% 23.28/23.47 (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))),
% 23.28/23.47 inference(unit_resolution,[status(thm)],[9671, 9670, 4495, 6583])).
% 23.28/23.47 tff(9673,plain,
% 23.28/23.47 (~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))),
% 23.28/23.47 inference(unit_resolution,[status(thm)],[2329, 9672])).
% 23.28/23.47 tff(9674,plain,
% 23.28/23.47 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(mult(b, c), a), mult(mult(mult(b, c), a), mult(a, rd(mult(b, c), mult(a, c))))) = mult(a, rd(mult(b, c), mult(a, c))))),
% 23.28/23.47 inference(quant_inst,[status(thm)],[])).
% 23.28/23.47 tff(9675,plain,
% 23.28/23.47 (ld(mult(mult(b, c), a), mult(mult(mult(b, c), a), mult(a, rd(mult(b, c), mult(a, c))))) = mult(a, rd(mult(b, c), mult(a, c)))),
% 23.28/23.47 inference(unit_resolution,[status(thm)],[9674, 7])).
% 23.28/23.47 tff(9676,assumption,(mult(mult(mult(b, c), a), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(b, c), a), mult(a, rd(mult(b, c), mult(a, c))))), introduced(assumption)).
% 23.28/23.47 tff(9677,plain,
% 23.28/23.47 (ld(mult(mult(b, c), a), mult(mult(mult(b, c), a), mult(rd(mult(b, c), mult(a, c)), a))) = ld(mult(mult(b, c), a), mult(mult(mult(b, c), a), mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.28/23.47 inference(monotonicity,[status(thm)],[9676])).
% 23.28/23.47 tff(9678,plain,
% 23.28/23.47 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(mult(b, c), a), mult(mult(mult(b, c), a), mult(rd(mult(b, c), mult(a, c)), a))) = mult(rd(mult(b, c), mult(a, c)), a))),
% 23.28/23.47 inference(quant_inst,[status(thm)],[])).
% 23.28/23.47 tff(9679,plain,
% 23.28/23.47 (ld(mult(mult(b, c), a), mult(mult(mult(b, c), a), mult(rd(mult(b, c), mult(a, c)), a))) = mult(rd(mult(b, c), mult(a, c)), a)),
% 23.28/23.47 inference(unit_resolution,[status(thm)],[9678, 7])).
% 23.28/23.47 tff(9680,plain,
% 23.28/23.47 (mult(rd(mult(b, c), mult(a, c)), a) = ld(mult(mult(b, c), a), mult(mult(mult(b, c), a), mult(rd(mult(b, c), mult(a, c)), a)))),
% 23.28/23.47 inference(symmetry,[status(thm)],[9679])).
% 23.28/23.47 tff(9681,plain,
% 23.28/23.47 (mult(rd(mult(b, c), mult(a, c)), a) = mult(a, rd(mult(b, c), mult(a, c)))),
% 23.28/23.47 inference(transitivity,[status(thm)],[9680, 9677, 9675])).
% 23.28/23.47 tff(9682,plain,
% 23.28/23.47 (mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))),
% 23.28/23.47 inference(monotonicity,[status(thm)],[9681])).
% 23.28/23.47 tff(9683,plain,
% 23.28/23.47 (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))),
% 23.28/23.47 inference(symmetry,[status(thm)],[9682])).
% 23.28/23.47 tff(9684,plain,
% 23.28/23.47 (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)),
% 23.28/23.47 inference(transitivity,[status(thm)],[5709, 9683, 5497])).
% 23.28/23.47 tff(9685,plain,
% 23.28/23.47 ($false),
% 23.28/23.47 inference(unit_resolution,[status(thm)],[2331, 9684])).
% 23.28/23.47 tff(9686,plain,((~(mult(mult(mult(b, c), a), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(b, c), a), mult(a, rd(mult(b, c), mult(a, c)))))) | (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))), inference(lemma,lemma(discharge,[]))).
% 23.28/23.47 tff(9687,plain,
% 23.28/23.47 (~(mult(mult(mult(b, c), a), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(b, c), a), mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.28/23.47 inference(unit_resolution,[status(thm)],[9686, 9673])).
% 23.28/23.47 tff(9688,plain,
% 23.28/23.47 (((~(mult(mult(mult(mult(b, c), a), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(mult(b, c), a), a), rd(mult(b, c), mult(a, c))))) | (~(mult(mult(mult(b, c), a), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(b, c), a), mult(a, rd(mult(b, c), mult(a, c))))))) | (mult(mult(mult(b, c), a), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(b, c), a), mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.28/23.47 inference(tautology,[status(thm)],[])).
% 23.28/23.47 tff(9689,plain,
% 23.28/23.47 ((~(mult(mult(mult(mult(b, c), a), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(mult(b, c), a), a), rd(mult(b, c), mult(a, c))))) | (~(mult(mult(mult(b, c), a), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(b, c), a), mult(a, rd(mult(b, c), mult(a, c))))))),
% 23.28/23.47 inference(unit_resolution,[status(thm)],[9688, 9687])).
% 23.28/23.47 tff(9690,plain,
% 23.28/23.47 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(mult(b, c), a), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(mult(b, c), a), a), rd(mult(b, c), mult(a, c))))) | (~(mult(mult(mult(b, c), a), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(b, c), a), mult(a, rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(mult(mult(b, c), a), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(b, c), a), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(mult(mult(b, c), a), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(b, c), a), mult(a, rd(mult(b, c), mult(a, c)))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(mult(b, c), a), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(mult(b, c), a), a), rd(mult(b, c), mult(a, c))))) | (~(mult(mult(mult(b, c), a), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(b, c), a), mult(a, rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(mult(mult(b, c), a), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(b, c), a), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(mult(mult(b, c), a), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(b, c), a), mult(a, rd(mult(b, c), mult(a, c)))))))))),
% 23.28/23.47 inference(rewrite,[status(thm)],[])).
% 23.28/23.47 tff(9691,plain,
% 23.28/23.47 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(mult(b, c), a), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(mult(b, c), a), a), rd(mult(b, c), mult(a, c))))) | (~(mult(mult(mult(b, c), a), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(b, c), a), mult(a, rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(mult(mult(b, c), a), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(b, c), a), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(mult(mult(b, c), a), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(b, c), a), mult(a, rd(mult(b, c), mult(a, c)))))))))),
% 23.28/23.47 inference(quant_inst,[status(thm)],[])).
% 23.28/23.47 tff(9692,plain,
% 23.28/23.47 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(mult(b, c), a), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(mult(b, c), a), a), rd(mult(b, c), mult(a, c))))) | (~(mult(mult(mult(b, c), a), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(b, c), a), mult(a, rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(mult(mult(b, c), a), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(b, c), a), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(mult(mult(b, c), a), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(b, c), a), mult(a, rd(mult(b, c), mult(a, c))))))))),
% 23.28/23.47 inference(modus_ponens,[status(thm)],[9691, 9690])).
% 23.28/23.47 tff(9693,plain,
% 23.28/23.47 (~((~(mult(mult(mult(mult(b, c), a), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(b, c), a), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(mult(mult(b, c), a), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(b, c), a), mult(a, rd(mult(b, c), mult(a, c)))))))),
% 23.28/23.47 inference(unit_resolution,[status(thm)],[9692, 27, 9689])).
% 23.28/23.47 tff(9694,plain,
% 23.28/23.47 (((~(mult(mult(mult(mult(b, c), a), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(b, c), a), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(mult(mult(b, c), a), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(b, c), a), mult(a, rd(mult(b, c), mult(a, c))))))) | (mult(mult(mult(mult(b, c), a), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(b, c), a), mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.28/23.47 inference(tautology,[status(thm)],[])).
% 23.28/23.47 tff(9695,plain,
% 23.28/23.47 (mult(mult(mult(mult(b, c), a), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(b, c), a), mult(a, rd(mult(b, c), mult(a, c))))),
% 23.28/23.47 inference(unit_resolution,[status(thm)],[9694, 9693])).
% 23.28/23.47 tff(9696,plain,
% 23.28/23.47 ((~(mult(mult(b, a), mult(b, c)) = mult(mult(b, mult(b, c)), a))) | (~(mult(b, mult(a, mult(b, c))) = mult(b, mult(mult(b, c), a))))),
% 23.28/23.47 inference(unit_resolution,[status(thm)],[7524, 9632])).
% 23.28/23.47 tff(9697,plain,
% 23.28/23.47 (~((~(mult(mult(b, a), mult(b, c)) = mult(b, mult(a, mult(b, c))))) | (~(mult(mult(b, mult(b, c)), a) = mult(b, mult(mult(b, c), a)))))),
% 23.28/23.47 inference(unit_resolution,[status(thm)],[6974, 9696])).
% 23.28/23.47 tff(9698,plain,
% 23.28/23.47 (mult(mult(b, mult(b, c)), a) = mult(b, mult(mult(b, c), a))),
% 23.28/23.47 inference(unit_resolution,[status(thm)],[6976, 9697])).
% 23.28/23.47 tff(9699,plain,
% 23.28/23.47 ((mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, mult(a, c))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))))) | (~(mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(c, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))),
% 23.28/23.47 inference(unit_resolution,[status(thm)],[6860, 5709])).
% 23.28/23.47 tff(9700,plain,
% 23.28/23.47 ((mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, mult(a, c))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))))) | (~(mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(c, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))),
% 23.28/23.47 inference(unit_resolution,[status(thm)],[9699, 8129])).
% 23.28/23.47 tff(9701,plain,
% 23.28/23.47 (mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, mult(a, c))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))))),
% 23.28/23.47 inference(unit_resolution,[status(thm)],[9700, 9640, 9652, 281])).
% 23.28/23.47 tff(9702,plain,
% 23.28/23.47 (mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))),
% 23.28/23.47 inference(unit_resolution,[status(thm)],[8771, 9701])).
% 23.28/23.47 tff(9703,assumption,(~(ld(mult(mult(a, b), c), mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c))))) = mult(a, rd(mult(b, c), mult(a, c))))), introduced(assumption)).
% 23.28/23.47 tff(9704,plain,
% 23.28/23.47 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(mult(a, b), c), mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c))))) = mult(a, rd(mult(b, c), mult(a, c))))),
% 23.28/23.47 inference(quant_inst,[status(thm)],[])).
% 23.28/23.47 tff(9705,plain,
% 23.28/23.47 ($false),
% 23.28/23.47 inference(unit_resolution,[status(thm)],[9704, 7, 9703])).
% 23.28/23.47 tff(9706,plain,(ld(mult(mult(a, b), c), mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c))))) = mult(a, rd(mult(b, c), mult(a, c)))), inference(lemma,lemma(discharge,[]))).
% 23.28/23.48 tff(9707,assumption,(ld(mult(mult(a, b), c), mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c))))) = mult(a, rd(mult(b, c), mult(a, c)))), introduced(assumption)).
% 23.28/23.48 tff(9708,assumption,(mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c))))), introduced(assumption)).
% 23.28/23.48 tff(9709,plain,
% 23.28/23.48 (ld(mult(mult(a, b), c), mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a))) = ld(mult(mult(a, b), c), mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.28/23.48 inference(monotonicity,[status(thm)],[9708])).
% 23.28/23.48 tff(9710,plain,
% 23.28/23.48 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(mult(a, b), c), mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a))) = mult(rd(mult(b, c), mult(a, c)), a))),
% 23.28/23.48 inference(quant_inst,[status(thm)],[])).
% 23.28/23.48 tff(9711,plain,
% 23.28/23.48 (ld(mult(mult(a, b), c), mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a))) = mult(rd(mult(b, c), mult(a, c)), a)),
% 23.28/23.48 inference(unit_resolution,[status(thm)],[9710, 7])).
% 23.28/23.48 tff(9712,plain,
% 23.28/23.48 (mult(rd(mult(b, c), mult(a, c)), a) = ld(mult(mult(a, b), c), mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a)))),
% 23.28/23.48 inference(symmetry,[status(thm)],[9711])).
% 23.28/23.48 tff(9713,plain,
% 23.28/23.48 (mult(rd(mult(b, c), mult(a, c)), a) = mult(a, rd(mult(b, c), mult(a, c)))),
% 23.28/23.48 inference(transitivity,[status(thm)],[9712, 9709, 9707])).
% 23.28/23.48 tff(9714,plain,
% 23.28/23.48 (mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))),
% 23.28/23.48 inference(monotonicity,[status(thm)],[9713])).
% 23.28/23.48 tff(9715,plain,
% 23.28/23.48 (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))),
% 23.28/23.48 inference(symmetry,[status(thm)],[9714])).
% 23.28/23.48 tff(9716,plain,
% 23.28/23.48 (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)),
% 23.28/23.48 inference(transitivity,[status(thm)],[5709, 9715, 5497])).
% 23.28/23.48 tff(9717,plain,
% 23.28/23.48 ($false),
% 23.28/23.48 inference(unit_resolution,[status(thm)],[2331, 9716])).
% 23.28/23.48 tff(9718,plain,((~(ld(mult(mult(a, b), c), mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c))))) = mult(a, rd(mult(b, c), mult(a, c))))) | (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)) | (~(mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c))))))), inference(lemma,lemma(discharge,[]))).
% 23.28/23.48 tff(9719,plain,
% 23.28/23.48 ((mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)) | (~(mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c))))))),
% 23.28/23.48 inference(unit_resolution,[status(thm)],[9718, 9706])).
% 23.28/23.48 tff(9720,plain,
% 23.28/23.48 (~(mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.28/23.48 inference(unit_resolution,[status(thm)],[9719, 9673])).
% 23.28/23.48 tff(9721,plain,
% 23.28/23.48 (((~(mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(mult(a, b), c), a), rd(mult(b, c), mult(a, c)))))) | (mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.28/23.48 inference(tautology,[status(thm)],[])).
% 23.28/23.48 tff(9722,plain,
% 23.28/23.48 ((~(mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(mult(a, b), c), a), rd(mult(b, c), mult(a, c)))))),
% 23.28/23.48 inference(unit_resolution,[status(thm)],[9721, 9720])).
% 23.28/23.48 tff(9723,assumption,(~(mult(mult(mult(mult(a, b), c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))))), introduced(assumption)).
% 23.28/23.48 tff(9724,plain,
% 23.28/23.48 (((~(mult(mult(mult(mult(a, b), c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a))))) | (mult(mult(mult(mult(a, b), c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.28/23.48 inference(tautology,[status(thm)],[])).
% 23.28/23.48 tff(9725,plain,
% 23.28/23.48 ((~(mult(mult(mult(mult(a, b), c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a))))),
% 23.28/23.48 inference(unit_resolution,[status(thm)],[9724, 9723])).
% 23.28/23.48 tff(9726,assumption,((~(mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(mult(a, b), c), a), rd(mult(b, c), mult(a, c)))))), introduced(assumption)).
% 23.28/23.48 tff(9727,plain,
% 23.28/23.48 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(mult(a, b), c), a), rd(mult(b, c), mult(a, c))))))) | (~((~(mult(mult(mult(mult(a, b), c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(mult(a, b), c), a), rd(mult(b, c), mult(a, c))))))) | (~((~(mult(mult(mult(mult(a, b), c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a)))))))),
% 23.28/23.48 inference(rewrite,[status(thm)],[])).
% 23.28/23.48 tff(9728,plain,
% 23.28/23.48 (((~((~(mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(mult(a, b), c), a), rd(mult(b, c), mult(a, c))))) | (~(mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(mult(mult(a, b), c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c))))))))) <=> ((~((~(mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(mult(a, b), c), a), rd(mult(b, c), mult(a, c))))))) | (~((~(mult(mult(mult(mult(a, b), c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a)))))))),
% 23.28/23.48 inference(rewrite,[status(thm)],[])).
% 23.28/23.48 tff(9729,plain,
% 23.28/23.48 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(mult(a, b), c), a), rd(mult(b, c), mult(a, c))))) | (~(mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(mult(mult(a, b), c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(mult(a, b), c), a), rd(mult(b, c), mult(a, c))))))) | (~((~(mult(mult(mult(mult(a, b), c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a))))))))),
% 23.28/23.48 inference(monotonicity,[status(thm)],[9728])).
% 23.28/23.48 tff(9730,plain,
% 23.28/23.48 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(mult(a, b), c), a), rd(mult(b, c), mult(a, c))))) | (~(mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(mult(mult(a, b), c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(mult(a, b), c), a), rd(mult(b, c), mult(a, c))))))) | (~((~(mult(mult(mult(mult(a, b), c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a)))))))),
% 23.28/23.48 inference(transitivity,[status(thm)],[9729, 9727])).
% 23.28/23.48 tff(9731,plain,
% 23.28/23.48 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(mult(a, b), c), a), rd(mult(b, c), mult(a, c))))) | (~(mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(mult(mult(a, b), c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))))))))),
% 23.28/23.48 inference(quant_inst,[status(thm)],[])).
% 23.28/23.48 tff(9732,plain,
% 23.28/23.48 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(mult(a, b), c), a), rd(mult(b, c), mult(a, c))))))) | (~((~(mult(mult(mult(mult(a, b), c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a))))))),
% 23.28/23.48 inference(modus_ponens,[status(thm)],[9731, 9730])).
% 23.28/23.48 tff(9733,plain,
% 23.28/23.48 ($false),
% 23.28/23.48 inference(unit_resolution,[status(thm)],[9732, 27, 9726, 9725])).
% 23.28/23.48 tff(9734,plain,((~((~(mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(mult(a, b), c), a), rd(mult(b, c), mult(a, c))))))) | (mult(mult(mult(mult(a, b), c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))))), inference(lemma,lemma(discharge,[]))).
% 23.28/23.48 tff(9735,plain,
% 23.28/23.48 (mult(mult(mult(mult(a, b), c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c))))),
% 23.28/23.48 inference(unit_resolution,[status(thm)],[9734, 9722])).
% 23.28/23.48 tff(9736,plain,
% 23.28/23.48 (mult(mult(c, a), mult(a, c)) = mult(mult(a, c), mult(a, c))),
% 23.28/23.48 inference(monotonicity,[status(thm)],[8215])).
% 23.28/23.48 tff(9737,plain,
% 23.28/23.48 (mult(mult(a, c), mult(c, a)) = mult(mult(a, c), mult(a, c))),
% 23.28/23.48 inference(monotonicity,[status(thm)],[8215])).
% 23.28/23.48 tff(9738,plain,
% 23.28/23.48 (mult(mult(a, c), mult(a, c)) = mult(mult(a, c), mult(c, a))),
% 23.28/23.48 inference(symmetry,[status(thm)],[9737])).
% 23.28/23.48 tff(9739,plain,
% 23.28/23.48 (mult(mult(c, a), mult(a, c)) = mult(mult(a, c), mult(c, a))),
% 23.28/23.48 inference(transitivity,[status(thm)],[9736, 9738])).
% 23.28/23.48 tff(9740,plain,
% 23.28/23.48 (mult(mult(mult(a, c), c), a) = mult(mult(c, mult(a, c)), a)),
% 23.28/23.48 inference(monotonicity,[status(thm)],[8195])).
% 23.28/23.48 tff(9741,plain,
% 23.28/23.48 (mult(mult(c, mult(a, c)), a) = mult(mult(mult(a, c), c), a)),
% 23.28/23.48 inference(symmetry,[status(thm)],[9740])).
% 23.28/23.48 tff(9742,plain,
% 23.28/23.48 ((mult(mult(c, mult(a, c)), a) = mult(mult(c, a), mult(a, c))) <=> (mult(mult(mult(a, c), c), a) = mult(mult(a, c), mult(c, a)))),
% 23.28/23.48 inference(monotonicity,[status(thm)],[9741, 9739])).
% 23.28/23.48 tff(9743,plain,
% 23.28/23.48 ((mult(mult(mult(a, c), c), a) = mult(mult(a, c), mult(c, a))) <=> (mult(mult(c, mult(a, c)), a) = mult(mult(c, a), mult(a, c)))),
% 23.28/23.48 inference(symmetry,[status(thm)],[9742])).
% 23.28/23.48 tff(9744,plain,
% 23.28/23.48 (mult(mult(c, mult(a, c)), a) = mult(mult(c, a), mult(a, c))),
% 23.28/23.48 inference(modus_ponens,[status(thm)],[8730, 9743])).
% 23.28/23.48 tff(9745,plain,
% 23.28/23.48 (mult(mult(a, mult(c, c)), a) = mult(mult(mult(a, c), unit), mult(a, c))),
% 23.28/23.48 inference(transitivity,[status(thm)],[4662, 9740, 9744, 9736, 2504])).
% 23.28/23.48 tff(9746,plain,
% 23.28/23.48 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(c, c)), a)) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), unit), mult(a, c)))),
% 23.28/23.48 inference(monotonicity,[status(thm)],[9745])).
% 23.28/23.48 tff(9747,plain,
% 23.28/23.48 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a)),
% 23.28/23.48 inference(symmetry,[status(thm)],[8305])).
% 23.28/23.48 tff(9748,plain,
% 23.28/23.48 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), unit) = mult(mult(rd(mult(b, c), mult(a, c)), c), a)),
% 23.28/23.48 inference(transitivity,[status(thm)],[1875, 1871, 9747, 4488])).
% 23.28/23.48 tff(9749,plain,
% 23.28/23.48 (mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), unit), c) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c)),
% 23.28/23.48 inference(monotonicity,[status(thm)],[9748])).
% 23.28/23.48 tff(9750,plain,
% 23.28/23.49 (mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c) = mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), unit), c)),
% 23.28/23.49 inference(symmetry,[status(thm)],[9749])).
% 23.28/23.49 tff(9751,plain,
% 23.28/23.49 (mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))),
% 23.28/23.49 inference(transitivity,[status(thm)],[4860, 4858, 4855, 9750, 4654, 5994])).
% 23.28/23.49 tff(9752,plain,
% 23.28/23.49 (mult(mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)), a)),
% 23.28/23.49 inference(monotonicity,[status(thm)],[9751])).
% 23.28/23.49 tff(9753,plain,
% 23.28/23.49 (mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a)),
% 23.28/23.49 inference(symmetry,[status(thm)],[9664])).
% 23.28/23.49 tff(9754,plain,
% 23.28/23.49 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c)))),
% 23.28/23.49 inference(unit_resolution,[status(thm)],[9319, 9157])).
% 23.28/23.49 tff(9755,plain,
% 23.28/23.49 (mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)),
% 23.28/23.49 inference(symmetry,[status(thm)],[9754])).
% 23.28/23.49 tff(9756,plain,
% 23.28/23.49 (mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))) = mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 23.28/23.49 inference(monotonicity,[status(thm)],[8195])).
% 23.28/23.49 tff(9757,plain,
% 23.28/23.49 (mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c)))),
% 23.28/23.49 inference(symmetry,[status(thm)],[9756])).
% 23.28/23.49 tff(9758,plain,
% 23.28/23.49 (mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)),
% 23.28/23.49 inference(transitivity,[status(thm)],[9757, 9755])).
% 23.28/23.49 tff(9759,plain,
% 23.28/23.49 (mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a)),
% 23.28/23.49 inference(monotonicity,[status(thm)],[9758])).
% 23.28/23.49 tff(9760,plain,
% 23.28/23.49 (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a)),
% 23.28/23.49 inference(symmetry,[status(thm)],[9759])).
% 23.28/23.49 tff(9761,plain,
% 23.28/23.49 (mult(mult(a, rd(mult(b, c), mult(a, c))), c) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))),
% 23.28/23.49 inference(transitivity,[status(thm)],[2189, 8165, 2172, 2178, 2177, 2162])).
% 23.28/23.49 tff(9762,plain,
% 23.28/23.49 (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)),
% 23.28/23.49 inference(monotonicity,[status(thm)],[9761])).
% 23.28/23.49 tff(9763,plain,
% 23.28/23.49 (mult(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), a), c) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c)),
% 23.28/23.49 inference(monotonicity,[status(thm)],[9762])).
% 23.28/23.49 tff(9764,plain,
% 23.28/23.49 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a)),
% 23.28/23.49 inference(transitivity,[status(thm)],[7565, 5952, 9763, 9385, 9760, 9753])).
% 23.28/23.49 tff(9765,plain,
% 23.28/23.49 (mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 23.28/23.49 inference(monotonicity,[status(thm)],[8215])).
% 23.28/23.49 tff(9766,plain,
% 23.28/23.49 (mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 23.28/23.49 inference(symmetry,[status(thm)],[9765])).
% 23.28/23.49 tff(9767,plain,
% 23.28/23.49 (mult(c, mult(c, a)) = mult(c, mult(a, c))),
% 23.28/23.49 inference(monotonicity,[status(thm)],[8215])).
% 23.28/23.49 tff(9768,plain,
% 23.28/23.49 (mult(mult(c, c), a) = mult(c, mult(a, c))),
% 23.28/23.49 inference(transitivity,[status(thm)],[3911, 9767])).
% 23.28/23.49 tff(9769,plain,
% 23.28/23.49 (mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(c, c), a)) = mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(c, mult(a, c)))),
% 23.28/23.49 inference(monotonicity,[status(thm)],[9768])).
% 23.28/23.49 tff(9770,plain,
% 23.28/23.49 (mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(c, mult(a, c))) = mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(c, c), a))),
% 23.28/23.49 inference(symmetry,[status(thm)],[9769])).
% 23.28/23.49 tff(9771,plain,
% 23.28/23.49 (mult(c, mult(a, c)) = mult(a, mult(c, c))),
% 23.28/23.49 inference(transitivity,[status(thm)],[4068, 8212, 2595, 2622, 2614, 2621])).
% 23.28/23.49 tff(9772,plain,
% 23.28/23.49 (mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(c, mult(a, c))) = mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(a, mult(c, c)))),
% 23.28/23.49 inference(monotonicity,[status(thm)],[9771])).
% 23.28/23.49 tff(9773,plain,
% 23.28/23.49 (mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(a, mult(c, c))) = mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(c, mult(a, c)))),
% 23.28/23.49 inference(symmetry,[status(thm)],[9772])).
% 23.28/23.49 tff(9774,plain,
% 23.28/23.49 (mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(a, mult(c, c))) = mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(c, c), a))),
% 23.28/23.49 inference(transitivity,[status(thm)],[9773, 9770])).
% 23.28/23.49 tff(9775,plain,
% 23.28/23.49 (mult(a, mult(c, mult(c, a))) = mult(a, mult(c, mult(a, c)))),
% 23.28/23.49 inference(monotonicity,[status(thm)],[9767])).
% 23.28/23.49 tff(9776,plain,
% 23.28/23.49 ((mult(mult(a, c), mult(c, a)) = mult(a, mult(c, mult(c, a)))) <=> (mult(mult(a, c), mult(a, c)) = mult(a, mult(c, mult(a, c))))),
% 23.28/23.49 inference(monotonicity,[status(thm)],[9737, 9775])).
% 23.28/23.49 tff(9777,plain,
% 23.28/23.49 ((mult(mult(a, c), mult(a, c)) = mult(a, mult(c, mult(a, c)))) <=> (mult(mult(a, c), mult(c, a)) = mult(a, mult(c, mult(c, a))))),
% 23.28/23.49 inference(symmetry,[status(thm)],[9776])).
% 23.28/23.49 tff(9778,plain,
% 23.28/23.49 (mult(mult(a, c), mult(c, a)) = mult(a, mult(c, mult(c, a)))),
% 23.28/23.49 inference(modus_ponens,[status(thm)],[9264, 9777])).
% 23.28/23.49 tff(9779,plain,
% 23.28/23.49 (mult(mult(unit, mult(mult(a, c), c)), a) = mult(mult(unit, a), mult(mult(a, c), c))),
% 23.28/23.49 inference(unit_resolution,[status(thm)],[9287, 9778, 9774])).
% 23.28/23.49 tff(9780,plain,
% 23.28/23.49 (mult(mult(a, mult(c, c)), a) = mult(mult(a, a), mult(c, c))),
% 23.28/23.49 inference(unit_resolution,[status(thm)],[7898, 9779])).
% 23.28/23.49 tff(9781,plain,
% 23.28/23.49 (mult(mult(a, a), mult(c, c)) = mult(mult(a, mult(c, c)), a)),
% 23.28/23.49 inference(modus_ponens,[status(thm)],[9780, 9255])).
% 23.28/23.49 tff(9782,plain,
% 23.28/23.49 (mult(mult(a, mult(c, c)), a) = mult(mult(a, a), mult(c, c))),
% 23.28/23.49 inference(symmetry,[status(thm)],[9781])).
% 23.28/23.49 tff(9783,plain,
% 23.28/23.49 (mult(mult(c, a), mult(a, c)) = mult(mult(c, mult(a, c)), a)),
% 23.28/23.49 inference(symmetry,[status(thm)],[9744])).
% 23.28/23.49 tff(9784,plain,
% 23.28/23.49 (mult(mult(a, c), mult(a, c)) = mult(mult(c, a), mult(a, c))),
% 23.28/23.49 inference(symmetry,[status(thm)],[9736])).
% 23.28/23.49 tff(9785,plain,
% 23.28/23.49 (mult(mult(a, c), mult(a, c)) = mult(a, mult(c, mult(a, c)))),
% 23.28/23.49 inference(transitivity,[status(thm)],[9784, 9783, 9741, 4663, 9782, 9517, 9516, 9515, 4717, 4715])).
% 23.28/23.49 tff(9786,plain,
% 23.28/23.49 (mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c)))),
% 23.28/23.49 inference(monotonicity,[status(thm)],[9785])).
% 23.28/23.49 tff(9787,plain,
% 23.28/23.49 (mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 23.28/23.49 inference(symmetry,[status(thm)],[9786])).
% 23.28/23.49 tff(9788,plain,
% 23.28/23.49 (mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 23.28/23.49 inference(transitivity,[status(thm)],[9787, 6583, 9766])).
% 23.28/23.49 tff(9789,plain,
% 23.28/23.49 ((mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c)))) <=> (mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a))),
% 23.28/23.49 inference(monotonicity,[status(thm)],[9788, 9764])).
% 23.28/23.49 tff(9790,plain,
% 23.28/23.49 ((mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c)))) <=> (mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 23.28/23.49 inference(transitivity,[status(thm)],[9789, 4783])).
% 23.28/23.49 tff(9791,plain,
% 23.28/23.49 ((mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c))))) <=> (mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))))),
% 23.28/23.49 inference(symmetry,[status(thm)],[9790])).
% 23.28/23.49 tff(9792,plain,
% 23.28/23.49 ((~(mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) <=> (~(mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c)))))),
% 23.28/23.49 inference(monotonicity,[status(thm)],[9791])).
% 23.28/23.49 tff(9793,plain,
% 23.28/23.49 (~(mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))))),
% 23.28/23.49 inference(modus_ponens,[status(thm)],[9659, 9792])).
% 23.28/23.49 tff(9794,plain,
% 23.28/23.49 (((~(mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))))) | (~(mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))))))) | (mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))))),
% 23.28/23.49 inference(tautology,[status(thm)],[])).
% 23.28/23.49 tff(9795,plain,
% 23.28/23.49 ((~(mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))))) | (~(mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))))))),
% 23.28/23.49 inference(unit_resolution,[status(thm)],[9794, 9793])).
% 23.28/23.49 tff(9796,plain,
% 23.28/23.49 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))))) | (~(mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))))))) | (~((~(mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))))) | (~(mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))))))) | (~((~(mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))))))))),
% 23.28/23.49 inference(rewrite,[status(thm)],[])).
% 23.28/23.49 tff(9797,plain,
% 23.28/23.49 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))))) | (~(mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))))))) | (~((~(mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))))))))),
% 23.28/23.49 inference(quant_inst,[status(thm)],[])).
% 23.28/23.49 tff(9798,plain,
% 23.28/23.49 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))))) | (~(mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))))))) | (~((~(mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))))))))),
% 23.28/23.49 inference(modus_ponens,[status(thm)],[9797, 9796])).
% 23.28/23.49 tff(9799,plain,
% 23.28/23.49 ((~((~(mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))))) | (~(mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))))))) | (~((~(mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))))))))),
% 23.28/23.49 inference(unit_resolution,[status(thm)],[9798, 27])).
% 23.28/23.49 tff(9800,plain,
% 23.28/23.49 (~((~(mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))))))),
% 23.28/23.49 inference(unit_resolution,[status(thm)],[9799, 9795])).
% 23.28/23.49 tff(9801,plain,
% 23.28/23.49 (((~(mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))))))) | (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))))),
% 23.28/23.49 inference(tautology,[status(thm)],[])).
% 23.28/23.49 tff(9802,plain,
% 23.28/23.49 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))))),
% 23.28/23.49 inference(unit_resolution,[status(thm)],[9801, 9800])).
% 23.28/23.49 tff(9803,plain,
% 23.28/23.49 (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), a), c)),
% 23.28/23.49 inference(symmetry,[status(thm)],[9763])).
% 23.28/23.49 tff(9804,plain,
% 23.28/23.49 (mult(a, mult(mult(c, mult(rd(mult(b, c), mult(a, c)), a)), c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))))),
% 23.28/23.49 inference(transitivity,[status(thm)],[8941, 9346, 9803, 5951, 7566, 9802])).
% 23.28/23.49 tff(9805,plain,
% 23.28/23.49 (ld(a, mult(a, mult(mult(c, mult(rd(mult(b, c), mult(a, c)), a)), c))) = ld(a, mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))))),
% 23.28/23.49 inference(monotonicity,[status(thm)],[9804])).
% 23.28/23.49 tff(9806,plain,
% 23.28/23.49 (mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a)),
% 23.28/23.49 inference(symmetry,[status(thm)],[9645])).
% 23.28/23.49 tff(9807,plain,
% 23.28/23.49 (mult(mult(unit, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 23.28/23.49 inference(monotonicity,[status(thm)],[73])).
% 23.28/23.49 tff(9808,plain,
% 23.28/23.49 (mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(unit, c), mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 23.28/23.49 inference(symmetry,[status(thm)],[9807])).
% 23.28/23.49 tff(9809,plain,
% 23.28/23.49 (mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))) = mult(mult(unit, c), mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 23.28/23.49 inference(transitivity,[status(thm)],[9756, 4495, 9808])).
% 23.28/23.49 tff(9810,plain,
% 23.28/23.49 (mult(mult(unit, mult(a, c)), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))),
% 23.28/23.49 inference(monotonicity,[status(thm)],[1549])).
% 23.28/23.49 tff(9811,plain,
% 23.28/23.49 ((mult(mult(unit, mult(a, c)), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(mult(unit, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), mult(a, c))) <=> (mult(mult(unit, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), mult(a, c)) = mult(mult(unit, mult(a, c)), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))),
% 23.28/23.50 inference(commutativity,[status(thm)],[])).
% 23.28/23.50 tff(9812,plain,
% 23.28/23.50 ((mult(mult(unit, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), mult(a, c)) = mult(mult(unit, mult(a, c)), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))) <=> (mult(mult(unit, mult(a, c)), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(mult(unit, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), mult(a, c)))),
% 23.28/23.50 inference(symmetry,[status(thm)],[9811])).
% 23.28/23.50 tff(9813,plain,
% 23.28/23.50 (mult(mult(unit, mult(a, c)), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(mult(unit, mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 23.28/23.50 inference(transitivity,[status(thm)],[9810, 2172, 2178, 2177, 2162, 4931])).
% 23.28/23.50 tff(9814,plain,
% 23.28/23.50 (mult(unit, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(unit, rd(mult(b, c), mult(a, c)))),
% 23.28/23.50 inference(monotonicity,[status(thm)],[1896])).
% 23.28/23.50 tff(9815,plain,
% 23.28/23.50 (mult(unit, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = rd(mult(b, c), mult(a, c))),
% 23.28/23.50 inference(transitivity,[status(thm)],[9814, 1893])).
% 23.28/23.50 tff(9816,plain,
% 23.28/23.50 (mult(mult(unit, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), mult(a, c)) = mult(rd(mult(b, c), mult(a, c)), mult(a, c))),
% 23.28/23.50 inference(monotonicity,[status(thm)],[9815])).
% 23.28/23.50 tff(9817,plain,
% 23.28/23.50 (mult(mult(unit, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), mult(a, c)) = mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(a, c))),
% 23.28/23.50 inference(transitivity,[status(thm)],[9816, 4904, 4902])).
% 23.28/23.50 tff(9818,plain,
% 23.28/23.50 ((mult(mult(unit, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), mult(a, c)) = mult(mult(unit, mult(a, c)), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))) <=> (mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(unit, mult(a, c)), rd(mult(b, c), mult(a, c))))),
% 23.28/23.50 inference(monotonicity,[status(thm)],[9817, 9813])).
% 23.28/23.50 tff(9819,plain,
% 23.28/23.50 ((mult(mult(unit, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), mult(a, c)) = mult(mult(unit, mult(a, c)), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))) <=> (mult(mult(unit, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 23.28/23.50 inference(transitivity,[status(thm)],[9818, 4930])).
% 23.28/23.50 tff(9820,plain,
% 23.28/23.50 ((mult(mult(unit, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(a, c))) <=> (mult(mult(unit, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), mult(a, c)) = mult(mult(unit, mult(a, c)), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))),
% 23.28/23.50 inference(symmetry,[status(thm)],[9819])).
% 23.28/23.50 tff(9821,plain,
% 23.28/23.50 (mult(b, c) = mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(a, c))),
% 23.28/23.50 inference(transitivity,[status(thm)],[267, 4904, 4902])).
% 23.28/23.50 tff(9822,plain,
% 23.28/23.50 ((mult(b, c) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))) <=> (mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(unit, mult(a, c)), rd(mult(b, c), mult(a, c))))),
% 23.28/23.50 inference(monotonicity,[status(thm)],[9821, 4931])).
% 23.28/23.50 tff(9823,plain,
% 23.28/23.50 ((mult(b, c) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))) <=> (mult(mult(unit, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 23.28/23.50 inference(transitivity,[status(thm)],[9822, 4930])).
% 23.28/23.50 tff(9824,plain,
% 23.28/23.50 ((mult(b, c) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))) <=> (mult(mult(unit, mult(a, c)), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(mult(unit, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), mult(a, c)))),
% 23.28/23.50 inference(transitivity,[status(thm)],[9823, 9820, 9812])).
% 23.28/23.50 tff(9825,plain,
% 23.28/23.50 ((~(mult(b, c) = mult(mult(a, c), rd(mult(b, c), mult(a, c))))) <=> (~(mult(mult(unit, mult(a, c)), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(mult(unit, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), mult(a, c))))),
% 23.28/23.50 inference(monotonicity,[status(thm)],[9824])).
% 23.28/23.50 tff(9826,plain,
% 23.28/23.50 ((mult(a, mult(b, c)) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))) <=> (mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 23.28/23.50 inference(monotonicity,[status(thm)],[289])).
% 23.28/23.50 tff(9827,plain,
% 23.28/23.50 ((mult(a, mult(b, c)) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))) <=> (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))),
% 23.28/23.50 inference(transitivity,[status(thm)],[9826, 6658])).
% 23.28/23.50 tff(9828,plain,
% 23.28/23.50 ((mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))) <=> (mult(a, mult(b, c)) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 23.28/23.50 inference(symmetry,[status(thm)],[9827])).
% 23.28/23.50 tff(9829,plain,
% 23.28/23.50 ((~(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) <=> (~(mult(a, mult(b, c)) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))),
% 23.28/23.50 inference(monotonicity,[status(thm)],[9828])).
% 23.28/23.50 tff(9830,plain,
% 23.28/23.50 (~(mult(a, mult(b, c)) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 23.28/23.50 inference(modus_ponens,[status(thm)],[270, 9829])).
% 23.28/23.50 tff(9831,assumption,(~(mult(a, mult(b, c)) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))), introduced(assumption)).
% 23.28/23.50 tff(9832,assumption,(mult(b, c) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))), introduced(assumption)).
% 23.28/23.50 tff(9833,plain,
% 23.28/23.50 (mult(a, mult(b, c)) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 23.28/23.50 inference(monotonicity,[status(thm)],[9832])).
% 23.28/23.50 tff(9834,plain,
% 23.28/23.50 ($false),
% 23.28/23.50 inference(unit_resolution,[status(thm)],[9833, 9831])).
% 23.28/23.50 tff(9835,plain,((~(mult(b, c) = mult(mult(a, c), rd(mult(b, c), mult(a, c))))) | (mult(a, mult(b, c)) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))), inference(lemma,lemma(discharge,[]))).
% 23.28/23.50 tff(9836,plain,
% 23.28/23.50 (~(mult(b, c) = mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 23.28/23.50 inference(unit_resolution,[status(thm)],[9835, 9830])).
% 23.28/23.50 tff(9837,plain,
% 23.28/23.50 (~(mult(mult(unit, mult(a, c)), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(mult(unit, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), mult(a, c)))),
% 23.28/23.50 inference(modus_ponens,[status(thm)],[9836, 9825])).
% 23.28/23.50 tff(9838,plain,
% 23.28/23.50 (((~(mult(mult(unit, mult(a, c)), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(mult(unit, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), mult(a, c)))) | (~(mult(unit, mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))) = mult(unit, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), mult(a, c)))))) | (mult(mult(unit, mult(a, c)), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(mult(unit, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), mult(a, c)))),
% 23.28/23.50 inference(tautology,[status(thm)],[])).
% 23.28/23.50 tff(9839,plain,
% 23.28/23.50 ((~(mult(mult(unit, mult(a, c)), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(mult(unit, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), mult(a, c)))) | (~(mult(unit, mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))) = mult(unit, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), mult(a, c)))))),
% 23.28/23.50 inference(unit_resolution,[status(thm)],[9838, 9837])).
% 23.28/23.50 tff(9840,plain,
% 23.28/23.50 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(unit, mult(a, c)), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(unit, mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(mult(unit, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), mult(a, c)) = mult(unit, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), mult(a, c))))))) | (~((~(mult(mult(unit, mult(a, c)), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(mult(unit, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), mult(a, c)))) | (~(mult(unit, mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))) = mult(unit, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), mult(a, c))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(unit, mult(a, c)), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(unit, mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(mult(unit, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), mult(a, c)) = mult(unit, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), mult(a, c))))))) | (~((~(mult(mult(unit, mult(a, c)), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(mult(unit, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), mult(a, c)))) | (~(mult(unit, mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))) = mult(unit, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), mult(a, c))))))))),
% 23.28/23.50 inference(rewrite,[status(thm)],[])).
% 23.28/23.50 tff(9841,plain,
% 23.28/23.50 (((~((~(mult(mult(unit, mult(a, c)), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(mult(unit, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), mult(a, c)))) | (~(mult(unit, mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))) = mult(unit, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), mult(a, c))))))) | (~((~(mult(mult(unit, mult(a, c)), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(unit, mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(mult(unit, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), mult(a, c)) = mult(unit, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), mult(a, c)))))))) <=> ((~((~(mult(mult(unit, mult(a, c)), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(unit, mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(mult(unit, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), mult(a, c)) = mult(unit, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), mult(a, c))))))) | (~((~(mult(mult(unit, mult(a, c)), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(mult(unit, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), mult(a, c)))) | (~(mult(unit, mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))) = mult(unit, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), mult(a, c))))))))),
% 23.28/23.50 inference(rewrite,[status(thm)],[])).
% 23.28/23.50 tff(9842,plain,
% 23.28/23.50 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(unit, mult(a, c)), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(mult(unit, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), mult(a, c)))) | (~(mult(unit, mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))) = mult(unit, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), mult(a, c))))))) | (~((~(mult(mult(unit, mult(a, c)), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(unit, mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(mult(unit, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), mult(a, c)) = mult(unit, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), mult(a, c))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(unit, mult(a, c)), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(unit, mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(mult(unit, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), mult(a, c)) = mult(unit, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), mult(a, c))))))) | (~((~(mult(mult(unit, mult(a, c)), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(mult(unit, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), mult(a, c)))) | (~(mult(unit, mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))) = mult(unit, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), mult(a, c)))))))))),
% 23.28/23.50 inference(monotonicity,[status(thm)],[9841])).
% 23.28/23.50 tff(9843,plain,
% 23.28/23.50 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(unit, mult(a, c)), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(mult(unit, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), mult(a, c)))) | (~(mult(unit, mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))) = mult(unit, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), mult(a, c))))))) | (~((~(mult(mult(unit, mult(a, c)), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(unit, mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(mult(unit, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), mult(a, c)) = mult(unit, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), mult(a, c))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(unit, mult(a, c)), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(unit, mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(mult(unit, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), mult(a, c)) = mult(unit, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), mult(a, c))))))) | (~((~(mult(mult(unit, mult(a, c)), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(mult(unit, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), mult(a, c)))) | (~(mult(unit, mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))) = mult(unit, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), mult(a, c))))))))),
% 23.28/23.50 inference(transitivity,[status(thm)],[9842, 9840])).
% 23.28/23.50 tff(9844,plain,
% 23.28/23.50 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(unit, mult(a, c)), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(mult(unit, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), mult(a, c)))) | (~(mult(unit, mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))) = mult(unit, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), mult(a, c))))))) | (~((~(mult(mult(unit, mult(a, c)), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(unit, mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(mult(unit, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), mult(a, c)) = mult(unit, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), mult(a, c))))))))),
% 23.28/23.50 inference(quant_inst,[status(thm)],[])).
% 23.28/23.50 tff(9845,plain,
% 23.28/23.50 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(unit, mult(a, c)), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(unit, mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(mult(unit, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), mult(a, c)) = mult(unit, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), mult(a, c))))))) | (~((~(mult(mult(unit, mult(a, c)), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(mult(unit, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), mult(a, c)))) | (~(mult(unit, mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))) = mult(unit, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), mult(a, c)))))))),
% 23.28/23.51 inference(modus_ponens,[status(thm)],[9844, 9843])).
% 23.28/23.51 tff(9846,plain,
% 23.28/23.51 ((~((~(mult(mult(unit, mult(a, c)), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(unit, mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(mult(unit, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), mult(a, c)) = mult(unit, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), mult(a, c))))))) | (~((~(mult(mult(unit, mult(a, c)), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(mult(unit, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), mult(a, c)))) | (~(mult(unit, mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))) = mult(unit, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), mult(a, c)))))))),
% 23.28/23.51 inference(unit_resolution,[status(thm)],[9845, 27])).
% 23.28/23.51 tff(9847,plain,
% 23.28/23.51 (~((~(mult(mult(unit, mult(a, c)), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(unit, mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(mult(unit, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), mult(a, c)) = mult(unit, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), mult(a, c))))))),
% 23.28/23.51 inference(unit_resolution,[status(thm)],[9846, 9839])).
% 23.28/23.51 tff(9848,plain,
% 23.28/23.51 (((~(mult(mult(unit, mult(a, c)), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(unit, mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(mult(unit, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), mult(a, c)) = mult(unit, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), mult(a, c)))))) | (mult(mult(unit, mult(a, c)), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(unit, mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))),
% 23.28/23.51 inference(tautology,[status(thm)],[])).
% 23.28/23.51 tff(9849,plain,
% 23.28/23.51 (mult(mult(unit, mult(a, c)), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(unit, mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))),
% 23.28/23.51 inference(unit_resolution,[status(thm)],[9848, 9847])).
% 23.28/23.51 tff(9850,plain,
% 23.28/23.51 (mult(unit, mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))) = mult(mult(unit, mult(a, c)), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))),
% 23.28/23.51 inference(symmetry,[status(thm)],[9849])).
% 23.28/23.51 tff(9851,plain,
% 23.28/23.51 (mult(mult(a, c), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))),
% 23.28/23.51 inference(transitivity,[status(thm)],[2167, 4851, 4850, 2171])).
% 23.28/23.51 tff(9852,plain,
% 23.28/23.51 (mult(unit, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(unit, mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))),
% 23.28/23.51 inference(monotonicity,[status(thm)],[9851])).
% 23.28/23.51 tff(9853,plain,
% 23.28/23.51 (mult(unit, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))),
% 23.28/23.51 inference(transitivity,[status(thm)],[9852, 9850, 9810, 2172, 2178, 2177, 2162])).
% 23.28/23.51 tff(9854,plain,
% 23.28/23.51 (mult(mult(unit, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)),
% 23.28/23.51 inference(monotonicity,[status(thm)],[9853])).
% 23.28/23.51 tff(9855,plain,
% 23.28/23.51 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(unit, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), c)),
% 23.28/23.51 inference(symmetry,[status(thm)],[9854])).
% 23.28/23.51 tff(9856,plain,
% 23.28/23.51 ((mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c)))) <=> (mult(mult(unit, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), c) = mult(mult(unit, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 23.28/23.51 inference(monotonicity,[status(thm)],[9855, 9809])).
% 23.28/23.51 tff(9857,plain,
% 23.28/23.51 ((mult(mult(unit, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), c) = mult(mult(unit, c), mult(mult(a, c), rd(mult(b, c), mult(a, c))))) <=> (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))))),
% 23.28/23.51 inference(symmetry,[status(thm)],[9856])).
% 23.28/23.51 tff(9858,plain,
% 23.28/23.51 ((mult(mult(unit, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), c) = mult(mult(unit, c), mult(mult(a, c), rd(mult(b, c), mult(a, c))))) <=> (mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c))),
% 23.28/23.51 inference(transitivity,[status(thm)],[9857, 8563])).
% 23.28/23.51 tff(9859,plain,
% 23.28/23.51 (mult(mult(unit, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), c) = mult(mult(unit, c), mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 23.28/23.51 inference(modus_ponens,[status(thm)],[9754, 9856])).
% 23.28/23.51 tff(9860,plain,
% 23.28/23.51 (mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)),
% 23.28/23.51 inference(modus_ponens,[status(thm)],[9859, 9858])).
% 23.28/23.51 tff(9861,plain,
% 23.28/23.51 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c))),
% 23.28/23.51 inference(transitivity,[status(thm)],[4656, 4655, 6874, 2627, 4857, 4859, 6079])).
% 23.28/23.51 tff(9862,plain,
% 23.28/23.51 (mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c)))),
% 23.28/23.51 inference(monotonicity,[status(thm)],[9861])).
% 23.28/23.51 tff(9863,plain,
% 23.28/23.51 (mult(a, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c))) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)))),
% 23.28/23.51 inference(symmetry,[status(thm)],[9862])).
% 23.28/23.51 tff(9864,plain,
% 23.28/23.51 (mult(a, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))))),
% 23.28/23.51 inference(monotonicity,[status(thm)],[6078])).
% 23.28/23.51 tff(9865,plain,
% 23.28/23.51 (mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c)))),
% 23.28/23.51 inference(symmetry,[status(thm)],[9864])).
% 23.28/23.51 tff(9866,assumption,(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))))), introduced(assumption)).
% 23.28/23.51 tff(9867,plain,
% 23.28/23.51 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), c))),
% 23.28/23.51 inference(monotonicity,[status(thm)],[3878])).
% 23.28/23.51 tff(9868,plain,
% 23.28/23.51 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), c)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c)))),
% 23.28/23.51 inference(symmetry,[status(thm)],[9867])).
% 23.28/23.51 tff(9869,plain,
% 23.28/23.51 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(c, a), c)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), c))),
% 23.28/23.51 inference(symmetry,[status(thm)],[5953])).
% 23.28/23.51 tff(9870,assumption,(mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)), introduced(assumption)).
% 23.28/23.51 tff(9871,plain,
% 23.28/23.51 (mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)),
% 23.28/23.51 inference(transitivity,[status(thm)],[6098, 9870])).
% 23.28/23.51 tff(9872,plain,
% 23.28/23.51 (mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a)),
% 23.28/23.51 inference(monotonicity,[status(thm)],[9871])).
% 23.28/23.51 tff(9873,plain,
% 23.28/23.51 (mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)))),
% 23.28/23.51 inference(transitivity,[status(thm)],[6126, 7809, 9872, 7820, 9380, 5951, 9869, 9868, 9866, 9865, 9863])).
% 23.28/23.51 tff(9874,plain,
% 23.28/23.51 ((mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a)))) <=> (mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))))),
% 23.28/23.51 inference(monotonicity,[status(thm)],[9873])).
% 23.28/23.51 tff(9875,plain,
% 23.28/23.51 ((mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a)))) <=> (mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))))),
% 23.28/23.51 inference(transitivity,[status(thm)],[9874, 6258])).
% 23.28/23.51 tff(9876,plain,
% 23.28/23.51 ((mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)))) <=> (mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))))),
% 23.28/23.51 inference(symmetry,[status(thm)],[9875])).
% 23.28/23.51 tff(9877,plain,
% 23.28/23.51 ((~(mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))))) | (~(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)))))),
% 23.28/23.51 inference(unit_resolution,[status(thm)],[6269, 6244])).
% 23.28/23.51 tff(9878,plain,
% 23.28/23.51 (~((~(mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)))) | (~(mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))))))),
% 23.28/23.51 inference(unit_resolution,[status(thm)],[6198, 9877])).
% 23.28/23.51 tff(9879,plain,
% 23.28/23.51 (mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)))),
% 23.28/23.51 inference(unit_resolution,[status(thm)],[6200, 9878])).
% 23.28/23.51 tff(9880,plain,
% 23.28/23.51 (mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a)))),
% 23.28/23.51 inference(modus_ponens,[status(thm)],[9879, 9876])).
% 23.28/23.51 tff(9881,plain,
% 23.28/23.51 ($false),
% 23.28/23.51 inference(unit_resolution,[status(thm)],[6244, 9880])).
% 23.28/23.51 tff(9882,plain,((mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))))) | (~(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit))))), inference(lemma,lemma(discharge,[]))).
% 23.28/23.51 tff(9883,plain,
% 23.28/23.51 ((mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))))) | (~(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit))))),
% 23.28/23.51 inference(unit_resolution,[status(thm)],[9882, 3862])).
% 23.28/23.51 tff(9884,plain,
% 23.28/23.51 (mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a)))),
% 23.28/23.51 inference(unit_resolution,[status(thm)],[9883, 9802, 8165, 8305, 9645, 9860])).
% 23.28/23.51 tff(9885,plain,
% 23.28/23.51 (mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))) = mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a))),
% 23.28/23.51 inference(symmetry,[status(thm)],[9884])).
% 23.28/23.51 tff(9886,plain,
% 23.28/23.51 (mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a))) = mult(a, mult(mult(c, mult(rd(mult(b, c), mult(a, c)), a)), c))),
% 23.28/23.51 inference(transitivity,[status(thm)],[9885, 9643, 9806, 9759, 7692, 9454, 6220])).
% 23.28/23.51 tff(9887,plain,
% 23.28/23.51 (ld(a, mult(a, mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a)))) = ld(a, mult(a, mult(mult(c, mult(rd(mult(b, c), mult(a, c)), a)), c)))),
% 23.28/23.51 inference(monotonicity,[status(thm)],[9886])).
% 23.28/23.51 tff(9888,plain,
% 23.28/23.51 (mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))),
% 23.28/23.51 inference(transitivity,[status(thm)],[6281, 9887, 9805, 7610])).
% 23.28/23.51 tff(9889,plain,
% 23.28/23.51 (mult(mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a)), a) = mult(mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))), a)),
% 23.28/23.51 inference(monotonicity,[status(thm)],[9888])).
% 23.28/23.51 tff(9890,plain,
% 23.28/23.51 (mult(rd(mult(b, c), mult(a, c)), mult(a, a)) = mult(mult(rd(mult(b, c), mult(a, c)), a), a)),
% 23.28/23.51 inference(transitivity,[status(thm)],[541, 540, 6364])).
% 23.28/23.51 tff(9891,plain,
% 23.28/23.51 (mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), mult(a, a))) = mult(mult(c, c), mult(mult(rd(mult(b, c), mult(a, c)), a), a))),
% 23.28/23.51 inference(monotonicity,[status(thm)],[9890])).
% 23.28/23.51 tff(9892,plain,
% 23.28/23.51 (mult(mult(c, c), mult(mult(rd(mult(b, c), mult(a, c)), a), a)) = mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), mult(a, a)))),
% 23.28/23.51 inference(symmetry,[status(thm)],[9891])).
% 23.28/23.51 tff(9893,plain,
% 23.28/23.51 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(a, mult(a, mult(mult(rd(mult(b, c), mult(a, c)), c), c))) = mult(mult(rd(mult(b, c), mult(a, c)), c), c))),
% 23.28/23.51 inference(quant_inst,[status(thm)],[])).
% 23.28/23.51 tff(9894,plain,
% 23.28/23.51 (ld(a, mult(a, mult(mult(rd(mult(b, c), mult(a, c)), c), c))) = mult(mult(rd(mult(b, c), mult(a, c)), c), c)),
% 23.28/23.51 inference(unit_resolution,[status(thm)],[9893, 7])).
% 23.28/23.51 tff(9895,plain,
% 23.28/23.51 (mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))) = mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c))),
% 23.28/23.51 inference(symmetry,[status(thm)],[9157])).
% 23.28/23.51 tff(9896,plain,
% 23.28/23.51 (mult(a, mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), c))),
% 23.28/23.51 inference(transitivity,[status(thm)],[2220, 9895, 2356])).
% 23.28/23.51 tff(9897,plain,
% 23.28/23.51 (ld(a, mult(a, mult(c, rd(mult(b, c), mult(a, c))))) = ld(a, mult(a, mult(rd(mult(b, c), mult(a, c)), c)))),
% 23.28/23.51 inference(monotonicity,[status(thm)],[9896])).
% 23.28/23.51 tff(9898,plain,
% 23.28/23.51 (mult(c, rd(mult(b, c), mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), c)),
% 23.28/23.51 inference(transitivity,[status(thm)],[5202, 9897, 5127])).
% 23.28/23.51 tff(9899,plain,
% 23.28/23.51 (mult(mult(c, rd(mult(b, c), mult(a, c))), c) = mult(mult(rd(mult(b, c), mult(a, c)), c), c)),
% 23.28/23.51 inference(monotonicity,[status(thm)],[9898])).
% 23.28/23.51 tff(9900,plain,
% 23.28/23.51 (mult(mult(rd(mult(b, c), mult(a, c)), c), c) = mult(mult(c, rd(mult(b, c), mult(a, c))), c)),
% 23.28/23.51 inference(symmetry,[status(thm)],[9899])).
% 23.28/23.51 tff(9901,plain,
% 23.28/23.51 (mult(a, mult(mult(rd(mult(b, c), mult(a, c)), c), c)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c))),
% 23.28/23.51 inference(monotonicity,[status(thm)],[9900])).
% 23.28/23.51 tff(9902,plain,
% 23.28/23.51 (mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), c), c))),
% 23.28/23.51 inference(symmetry,[status(thm)],[9901])).
% 23.28/23.51 tff(9903,plain,
% 23.28/23.51 (mult(mult(rd(mult(b, c), mult(a, c)), c), unit) = mult(rd(mult(b, c), mult(a, c)), c)),
% 23.28/23.51 inference(transitivity,[status(thm)],[3961, 3964, 81])).
% 23.28/23.51 tff(9904,plain,
% 23.28/23.51 (mult(mult(mult(rd(mult(b, c), mult(a, c)), c), unit), c) = mult(mult(rd(mult(b, c), mult(a, c)), c), c)),
% 23.28/23.51 inference(monotonicity,[status(thm)],[9903])).
% 23.28/23.51 tff(9905,plain,
% 23.28/23.51 (mult(rd(mult(b, c), mult(a, c)), mult(c, c)) = mult(mult(rd(mult(b, c), mult(a, c)), c), c)),
% 23.28/23.51 inference(transitivity,[status(thm)],[3972, 3971, 9904])).
% 23.28/23.51 tff(9906,plain,
% 23.28/23.51 (mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, c))) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), c), c))),
% 23.28/23.51 inference(monotonicity,[status(thm)],[9905])).
% 23.28/23.52 tff(9907,plain,
% 23.28/23.52 (mult(a, mult(mult(rd(mult(b, c), mult(a, c)), c), c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, c)))),
% 23.28/23.52 inference(symmetry,[status(thm)],[9906])).
% 23.28/23.52 tff(9908,plain,
% 23.28/23.52 (mult(mult(a, mult(c, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, c)))),
% 23.28/23.52 inference(transitivity,[status(thm)],[9315, 9755, 3152, 9902, 9907])).
% 23.28/23.52 tff(9909,plain,
% 23.28/23.52 ((mult(mult(a, mult(c, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(c, c), rd(mult(b, c), mult(a, c))))) <=> (mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, c))) = mult(a, mult(mult(c, c), rd(mult(b, c), mult(a, c)))))),
% 23.28/23.52 inference(monotonicity,[status(thm)],[9908])).
% 23.28/23.52 tff(9910,plain,
% 23.28/23.52 ((mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, c))) = mult(a, mult(mult(c, c), rd(mult(b, c), mult(a, c))))) <=> (mult(mult(a, mult(c, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(c, c), rd(mult(b, c), mult(a, c)))))),
% 23.28/23.52 inference(symmetry,[status(thm)],[9909])).
% 23.28/23.52 tff(9911,plain,
% 23.28/23.52 (ld(a, mult(a, mult(rd(mult(b, c), mult(a, c)), c))) = ld(a, mult(a, mult(c, rd(mult(b, c), mult(a, c)))))),
% 23.28/23.52 inference(symmetry,[status(thm)],[5201])).
% 23.28/23.52 tff(9912,plain,
% 23.28/23.52 (mult(rd(mult(b, c), mult(a, c)), c) = mult(c, rd(mult(b, c), mult(a, c)))),
% 23.28/23.52 inference(transitivity,[status(thm)],[5128, 9911, 5114])).
% 23.28/23.52 tff(9913,plain,
% 23.28/23.52 (mult(mult(rd(mult(b, c), mult(a, c)), c), c) = mult(mult(c, rd(mult(b, c), mult(a, c))), c)),
% 23.28/23.52 inference(monotonicity,[status(thm)],[9912])).
% 23.28/23.52 tff(9914,plain,
% 23.28/23.52 (mult(rd(mult(b, c), mult(a, c)), mult(c, c)) = mult(mult(c, rd(mult(b, c), mult(a, c))), c)),
% 23.28/23.52 inference(transitivity,[status(thm)],[3972, 3971, 9904, 9913])).
% 23.28/23.52 tff(9915,plain,
% 23.28/23.52 (mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, c))) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c))),
% 23.28/23.52 inference(monotonicity,[status(thm)],[9914])).
% 23.28/23.52 tff(9916,plain,
% 23.28/23.52 (mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, c)))),
% 23.28/23.52 inference(symmetry,[status(thm)],[9915])).
% 23.28/23.52 tff(9917,plain,
% 23.28/23.52 (mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)),
% 23.28/23.52 inference(symmetry,[status(thm)],[9320])).
% 23.28/23.52 tff(9918,plain,
% 23.28/23.52 (mult(mult(a, mult(c, c)), rd(mult(b, c), mult(a, c))) = mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 23.28/23.52 inference(monotonicity,[status(thm)],[9459])).
% 23.28/23.52 tff(9919,plain,
% 23.28/23.52 (mult(mult(a, mult(c, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, c)))),
% 23.28/23.52 inference(transitivity,[status(thm)],[9918, 9324, 9917, 3152, 9916])).
% 23.28/23.52 tff(9920,plain,
% 23.28/23.52 ((mult(mult(a, mult(c, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(c, c), rd(mult(b, c), mult(a, c))))) <=> (mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, c))) = mult(a, mult(mult(c, c), rd(mult(b, c), mult(a, c)))))),
% 23.28/23.52 inference(monotonicity,[status(thm)],[9919])).
% 23.28/23.52 tff(9921,assumption,(~(mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, c))) = mult(a, mult(mult(c, c), rd(mult(b, c), mult(a, c)))))), introduced(assumption)).
% 23.28/23.52 tff(9922,plain,
% 23.28/23.52 (((~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)) = mult(mult(a, mult(c, c)), rd(mult(b, c), mult(a, c))))) | (~(mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, c))) = mult(a, mult(mult(c, c), rd(mult(b, c), mult(a, c))))))) | (mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, c))) = mult(a, mult(mult(c, c), rd(mult(b, c), mult(a, c)))))),
% 23.28/23.52 inference(tautology,[status(thm)],[])).
% 23.28/23.52 tff(9923,plain,
% 23.28/23.52 ((~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)) = mult(mult(a, mult(c, c)), rd(mult(b, c), mult(a, c))))) | (~(mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, c))) = mult(a, mult(mult(c, c), rd(mult(b, c), mult(a, c))))))),
% 23.28/23.52 inference(unit_resolution,[status(thm)],[9922, 9921])).
% 23.28/23.52 tff(9924,plain,
% 23.28/23.52 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, mult(c, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(c, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, c))))))) | (~((~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)) = mult(mult(a, mult(c, c)), rd(mult(b, c), mult(a, c))))) | (~(mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, c))) = mult(a, mult(mult(c, c), rd(mult(b, c), mult(a, c)))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, mult(c, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(c, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, c))))))) | (~((~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)) = mult(mult(a, mult(c, c)), rd(mult(b, c), mult(a, c))))) | (~(mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, c))) = mult(a, mult(mult(c, c), rd(mult(b, c), mult(a, c)))))))))),
% 23.28/23.52 inference(rewrite,[status(thm)],[])).
% 23.28/23.52 tff(9925,plain,
% 23.28/23.52 (((~((~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)) = mult(mult(a, mult(c, c)), rd(mult(b, c), mult(a, c))))) | (~(mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, c))) = mult(a, mult(mult(c, c), rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(a, mult(c, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(c, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, c)))))))) <=> ((~((~(mult(mult(a, mult(c, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(c, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, c))))))) | (~((~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)) = mult(mult(a, mult(c, c)), rd(mult(b, c), mult(a, c))))) | (~(mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, c))) = mult(a, mult(mult(c, c), rd(mult(b, c), mult(a, c)))))))))),
% 23.28/23.52 inference(rewrite,[status(thm)],[])).
% 23.28/23.52 tff(9926,plain,
% 23.28/23.52 ((~((~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, c))))) | (~(mult(mult(a, mult(c, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(c, c), rd(mult(b, c), mult(a, c)))))))) <=> (~((~(mult(mult(a, mult(c, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(c, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, c)))))))),
% 23.28/23.52 inference(rewrite,[status(thm)],[])).
% 23.28/23.52 tff(9927,plain,
% 23.28/23.52 ((~((~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)) = mult(mult(a, mult(c, c)), rd(mult(b, c), mult(a, c))))) | (~(mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, c))) = mult(a, mult(mult(c, c), rd(mult(b, c), mult(a, c)))))))) <=> (~((~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)) = mult(mult(a, mult(c, c)), rd(mult(b, c), mult(a, c))))) | (~(mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, c))) = mult(a, mult(mult(c, c), rd(mult(b, c), mult(a, c))))))))),
% 23.28/23.52 inference(rewrite,[status(thm)],[])).
% 23.28/23.52 tff(9928,plain,
% 23.28/23.52 (((~((~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)) = mult(mult(a, mult(c, c)), rd(mult(b, c), mult(a, c))))) | (~(mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, c))) = mult(a, mult(mult(c, c), rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, c))))) | (~(mult(mult(a, mult(c, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(c, c), rd(mult(b, c), mult(a, c))))))))) <=> ((~((~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)) = mult(mult(a, mult(c, c)), rd(mult(b, c), mult(a, c))))) | (~(mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, c))) = mult(a, mult(mult(c, c), rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(a, mult(c, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(c, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, c))))))))),
% 23.28/23.52 inference(monotonicity,[status(thm)],[9927, 9926])).
% 23.28/23.52 tff(9929,plain,
% 23.28/23.52 (((~((~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)) = mult(mult(a, mult(c, c)), rd(mult(b, c), mult(a, c))))) | (~(mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, c))) = mult(a, mult(mult(c, c), rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, c))))) | (~(mult(mult(a, mult(c, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(c, c), rd(mult(b, c), mult(a, c))))))))) <=> ((~((~(mult(mult(a, mult(c, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(c, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, c))))))) | (~((~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)) = mult(mult(a, mult(c, c)), rd(mult(b, c), mult(a, c))))) | (~(mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, c))) = mult(a, mult(mult(c, c), rd(mult(b, c), mult(a, c)))))))))),
% 23.28/23.52 inference(transitivity,[status(thm)],[9928, 9925])).
% 23.28/23.52 tff(9930,plain,
% 23.28/23.52 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)) = mult(mult(a, mult(c, c)), rd(mult(b, c), mult(a, c))))) | (~(mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, c))) = mult(a, mult(mult(c, c), rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, c))))) | (~(mult(mult(a, mult(c, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(c, c), rd(mult(b, c), mult(a, c)))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, mult(c, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(c, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, c))))))) | (~((~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)) = mult(mult(a, mult(c, c)), rd(mult(b, c), mult(a, c))))) | (~(mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, c))) = mult(a, mult(mult(c, c), rd(mult(b, c), mult(a, c))))))))))),
% 23.28/23.52 inference(monotonicity,[status(thm)],[9929])).
% 23.28/23.52 tff(9931,plain,
% 23.28/23.52 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)) = mult(mult(a, mult(c, c)), rd(mult(b, c), mult(a, c))))) | (~(mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, c))) = mult(a, mult(mult(c, c), rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, c))))) | (~(mult(mult(a, mult(c, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(c, c), rd(mult(b, c), mult(a, c)))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, mult(c, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(c, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, c))))))) | (~((~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)) = mult(mult(a, mult(c, c)), rd(mult(b, c), mult(a, c))))) | (~(mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, c))) = mult(a, mult(mult(c, c), rd(mult(b, c), mult(a, c)))))))))),
% 23.28/23.53 inference(transitivity,[status(thm)],[9930, 9924])).
% 23.28/23.53 tff(9932,plain,
% 23.28/23.53 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)) = mult(mult(a, mult(c, c)), rd(mult(b, c), mult(a, c))))) | (~(mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, c))) = mult(a, mult(mult(c, c), rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, c))))) | (~(mult(mult(a, mult(c, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(c, c), rd(mult(b, c), mult(a, c)))))))))),
% 23.28/23.53 inference(quant_inst,[status(thm)],[])).
% 23.28/23.53 tff(9933,plain,
% 23.28/23.53 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, mult(c, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(c, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, c))))))) | (~((~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)) = mult(mult(a, mult(c, c)), rd(mult(b, c), mult(a, c))))) | (~(mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, c))) = mult(a, mult(mult(c, c), rd(mult(b, c), mult(a, c))))))))),
% 23.28/23.53 inference(modus_ponens,[status(thm)],[9932, 9931])).
% 23.28/23.53 tff(9934,plain,
% 23.28/23.53 ((~((~(mult(mult(a, mult(c, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(c, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, c))))))) | (~((~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)) = mult(mult(a, mult(c, c)), rd(mult(b, c), mult(a, c))))) | (~(mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, c))) = mult(a, mult(mult(c, c), rd(mult(b, c), mult(a, c))))))))),
% 23.28/23.53 inference(unit_resolution,[status(thm)],[9933, 27])).
% 23.28/23.53 tff(9935,plain,
% 23.28/23.53 (~((~(mult(mult(a, mult(c, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(c, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, c))))))),
% 23.28/23.53 inference(unit_resolution,[status(thm)],[9934, 9923])).
% 23.28/23.53 tff(9936,plain,
% 23.28/23.53 (((~(mult(mult(a, mult(c, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(c, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, c)))))) | (mult(mult(a, mult(c, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(c, c), rd(mult(b, c), mult(a, c)))))),
% 23.28/23.53 inference(tautology,[status(thm)],[])).
% 23.28/23.53 tff(9937,plain,
% 23.28/23.53 (mult(mult(a, mult(c, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(c, c), rd(mult(b, c), mult(a, c))))),
% 23.28/23.53 inference(unit_resolution,[status(thm)],[9936, 9935])).
% 23.28/23.53 tff(9938,plain,
% 23.28/23.53 (mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, c))) = mult(a, mult(mult(c, c), rd(mult(b, c), mult(a, c))))),
% 23.28/23.53 inference(modus_ponens,[status(thm)],[9937, 9920])).
% 23.28/23.53 tff(9939,plain,
% 23.28/23.53 ($false),
% 23.28/23.53 inference(unit_resolution,[status(thm)],[9921, 9938])).
% 23.28/23.53 tff(9940,plain,((mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, c))) = mult(a, mult(mult(c, c), rd(mult(b, c), mult(a, c))))) | (~(mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))))), inference(lemma,lemma(discharge,[]))).
% 23.28/23.53 tff(9941,plain,
% 23.28/23.53 (mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, c))) = mult(a, mult(mult(c, c), rd(mult(b, c), mult(a, c))))),
% 23.28/23.53 inference(unit_resolution,[status(thm)],[9940, 9157])).
% 23.28/23.53 tff(9942,plain,
% 23.28/23.53 (mult(mult(a, mult(c, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(c, c), rd(mult(b, c), mult(a, c))))),
% 23.28/23.53 inference(modus_ponens,[status(thm)],[9941, 9910])).
% 23.28/23.53 tff(9943,plain,
% 23.28/23.53 (mult(a, mult(mult(c, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(c, c)), rd(mult(b, c), mult(a, c)))),
% 23.28/23.53 inference(symmetry,[status(thm)],[9942])).
% 23.28/23.53 tff(9944,plain,
% 23.28/23.53 (mult(a, mult(mult(c, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), c), c))),
% 23.28/23.53 inference(transitivity,[status(thm)],[9943, 9315, 9755, 3152, 9902])).
% 23.28/23.53 tff(9945,plain,
% 23.28/23.53 (ld(a, mult(a, mult(mult(c, c), rd(mult(b, c), mult(a, c))))) = ld(a, mult(a, mult(mult(rd(mult(b, c), mult(a, c)), c), c)))),
% 23.28/23.53 inference(monotonicity,[status(thm)],[9944])).
% 23.28/23.53 tff(9946,plain,
% 23.28/23.53 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(a, mult(a, mult(mult(c, c), rd(mult(b, c), mult(a, c))))) = mult(mult(c, c), rd(mult(b, c), mult(a, c))))),
% 23.28/23.53 inference(quant_inst,[status(thm)],[])).
% 23.28/23.53 tff(9947,plain,
% 23.28/23.53 (ld(a, mult(a, mult(mult(c, c), rd(mult(b, c), mult(a, c))))) = mult(mult(c, c), rd(mult(b, c), mult(a, c)))),
% 23.28/23.53 inference(unit_resolution,[status(thm)],[9946, 7])).
% 23.28/23.53 tff(9948,plain,
% 23.28/23.53 (mult(mult(c, c), rd(mult(b, c), mult(a, c))) = ld(a, mult(a, mult(mult(c, c), rd(mult(b, c), mult(a, c)))))),
% 23.28/23.53 inference(symmetry,[status(thm)],[9947])).
% 23.28/23.53 tff(9949,plain,
% 23.28/23.53 (mult(mult(c, c), rd(mult(b, c), mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), c), c)),
% 23.28/23.53 inference(transitivity,[status(thm)],[9948, 9945, 9894])).
% 23.28/23.53 tff(9950,plain,
% 23.28/23.53 (mult(mult(mult(c, c), rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), c), mult(a, a))),
% 23.28/23.53 inference(monotonicity,[status(thm)],[9949])).
% 23.28/23.53 tff(9951,plain,
% 23.28/23.53 (mult(mult(mult(rd(mult(b, c), mult(a, c)), c), c), mult(a, a)) = mult(mult(mult(c, c), rd(mult(b, c), mult(a, c))), mult(a, a))),
% 23.28/23.53 inference(symmetry,[status(thm)],[9950])).
% 23.28/23.53 tff(9952,plain,
% 23.28/23.53 (mult(mult(mult(rd(mult(b, c), mult(a, c)), c), c), mult(a, a)) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), c), mult(mult(a, unit), a))),
% 23.28/23.53 inference(monotonicity,[status(thm)],[520])).
% 23.28/23.53 tff(9953,plain,
% 23.28/23.53 (mult(mult(mult(rd(mult(b, c), mult(a, c)), c), c), mult(mult(a, unit), a)) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), c), mult(a, a))),
% 23.28/23.53 inference(symmetry,[status(thm)],[9952])).
% 23.28/23.53 tff(9954,plain,
% 23.28/23.53 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), c), a), unit), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), c), mult(mult(a, unit), a)))),
% 23.28/23.53 inference(quant_inst,[status(thm)],[])).
% 23.28/23.53 tff(9955,plain,
% 23.28/23.53 (mult(mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), c), a), unit), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), c), mult(mult(a, unit), a))),
% 23.28/23.53 inference(unit_resolution,[status(thm)],[9954, 56])).
% 23.28/23.53 tff(9956,plain,
% 23.28/23.53 (mult(mult(unit, mult(c, mult(a, c))), unit) = mult(mult(c, mult(a, c)), unit)),
% 23.28/23.53 inference(monotonicity,[status(thm)],[4367])).
% 23.28/23.53 tff(9957,plain,
% 23.28/23.53 (mult(mult(unit, mult(c, mult(a, c))), unit) = mult(c, mult(a, c))),
% 23.28/23.53 inference(transitivity,[status(thm)],[9956, 6010])).
% 23.28/23.53 tff(9958,plain,
% 23.28/23.53 (mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, mult(c, mult(a, c))), unit)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))),
% 23.28/23.53 inference(monotonicity,[status(thm)],[9957])).
% 23.28/23.53 tff(9959,plain,
% 23.28/23.53 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(rd(mult(b, c), mult(a, c)), unit), mult(c, mult(a, c))), unit) = mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, mult(c, mult(a, c))), unit)))),
% 23.28/23.53 inference(quant_inst,[status(thm)],[])).
% 23.28/23.53 tff(9960,plain,
% 23.28/23.53 (mult(mult(mult(rd(mult(b, c), mult(a, c)), unit), mult(c, mult(a, c))), unit) = mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, mult(c, mult(a, c))), unit))),
% 23.28/23.53 inference(unit_resolution,[status(thm)],[9959, 56])).
% 23.28/23.53 tff(9961,plain,
% 23.28/23.53 (mult(mult(rd(mult(b, c), mult(a, c)), unit), mult(c, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))),
% 23.28/23.53 inference(monotonicity,[status(thm)],[532])).
% 23.28/23.53 tff(9962,plain,
% 23.28/23.53 (mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), unit), mult(c, mult(a, c)))),
% 23.28/23.53 inference(symmetry,[status(thm)],[9961])).
% 23.28/23.53 tff(9963,plain,
% 23.28/23.53 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c)) = mult(mult(rd(mult(b, c), mult(a, c)), unit), mult(c, mult(a, c)))),
% 23.28/23.53 inference(transitivity,[status(thm)],[8193, 9962])).
% 23.28/23.53 tff(9964,plain,
% 23.28/23.53 (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c)), unit) = mult(mult(mult(rd(mult(b, c), mult(a, c)), unit), mult(c, mult(a, c))), unit)),
% 23.28/23.53 inference(monotonicity,[status(thm)],[9963])).
% 23.28/23.53 tff(9965,plain,
% 23.28/23.53 (mult(mult(c, rd(mult(b, c), mult(a, c))), a) = mult(mult(rd(mult(b, c), mult(a, c)), c), a)),
% 23.28/23.53 inference(monotonicity,[status(thm)],[9898])).
% 23.28/23.53 tff(9966,plain,
% 23.28/23.53 (mult(mult(mult(c, rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c)),
% 23.28/23.53 inference(monotonicity,[status(thm)],[9965])).
% 23.28/23.53 tff(9967,plain,
% 23.28/23.53 (mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c) = mult(mult(mult(c, rd(mult(b, c), mult(a, c))), a), c)),
% 23.28/23.53 inference(symmetry,[status(thm)],[9966])).
% 23.28/23.53 tff(9968,plain,
% 23.28/23.53 (mult(mult(mult(rd(mult(b, c), mult(a, c)), c), c), a) = mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a)),
% 23.28/23.53 inference(monotonicity,[status(thm)],[9900])).
% 23.28/23.53 tff(9969,plain,
% 23.28/23.53 ((mult(mult(mult(rd(mult(b, c), mult(a, c)), c), c), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c)) <=> (mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(c, rd(mult(b, c), mult(a, c))), a), c))),
% 23.28/23.53 inference(monotonicity,[status(thm)],[9968, 9967])).
% 23.28/23.53 tff(9970,plain,
% 23.28/23.53 (mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(c, rd(mult(b, c), mult(a, c))), a), c)),
% 23.28/23.53 inference(modus_ponens,[status(thm)],[7658, 9969])).
% 23.28/23.53 tff(9971,plain,
% 23.28/23.53 (mult(mult(mult(rd(mult(b, c), mult(a, c)), c), c), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c))),
% 23.28/23.53 inference(transitivity,[status(thm)],[9968, 9970, 9966, 2627, 4857, 4859, 5434])).
% 23.28/23.53 tff(9972,plain,
% 23.28/23.53 (mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), c), a), unit) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), c)), unit)),
% 23.28/23.53 inference(monotonicity,[status(thm)],[9971])).
% 23.28/23.53 tff(9973,plain,
% 23.28/23.53 (mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), c), a), unit) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))),
% 23.28/23.53 inference(transitivity,[status(thm)],[9972, 9964, 9960, 9958])).
% 23.28/23.53 tff(9974,plain,
% 23.28/23.53 (mult(mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), c), a), unit), a) = mult(mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))), a)),
% 23.28/23.53 inference(monotonicity,[status(thm)],[9973])).
% 23.28/23.53 tff(9975,plain,
% 23.28/23.53 (mult(mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))), a) = mult(mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), c), a), unit), a)),
% 23.28/23.53 inference(symmetry,[status(thm)],[9974])).
% 23.28/23.53 tff(9976,plain,
% 23.28/23.53 (mult(mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a)), a) = mult(mult(mult(c, c), rd(mult(b, c), mult(a, c))), mult(a, a))),
% 23.28/23.53 inference(transitivity,[status(thm)],[9889, 9975, 9955, 9953, 9951])).
% 23.28/23.53 tff(9977,plain,
% 23.28/23.53 ((mult(mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a)), a) = mult(mult(c, c), mult(mult(rd(mult(b, c), mult(a, c)), a), a))) <=> (mult(mult(mult(c, c), rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), mult(a, a))))),
% 23.28/23.53 inference(monotonicity,[status(thm)],[9976, 9892])).
% 23.28/23.53 tff(9978,plain,
% 23.28/23.53 ((mult(mult(mult(c, c), rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), mult(a, a)))) <=> (mult(mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a)), a) = mult(mult(c, c), mult(mult(rd(mult(b, c), mult(a, c)), a), a)))),
% 23.28/23.53 inference(symmetry,[status(thm)],[9977])).
% 23.28/23.53 tff(9979,plain,
% 23.28/23.53 (mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a))),
% 23.28/23.53 inference(transitivity,[status(thm)],[9644, 9458])).
% 23.28/23.53 tff(9980,plain,
% 23.28/23.53 (mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c)),
% 23.28/23.53 inference(transitivity,[status(thm)],[9759, 7692, 9454])).
% 23.28/23.53 tff(9981,plain,
% 23.28/23.53 ((mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a))) <=> (mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c) = mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a)))),
% 23.28/23.53 inference(monotonicity,[status(thm)],[9980, 9979])).
% 23.28/23.53 tff(9982,plain,
% 23.28/23.53 ((mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a))) <=> (mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c))),
% 23.28/23.53 inference(transitivity,[status(thm)],[9981, 7588])).
% 23.28/23.53 tff(9983,plain,
% 23.28/23.53 (mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c)),
% 23.28/23.53 inference(modus_ponens,[status(thm)],[9645, 9982])).
% 23.28/23.53 tff(9984,plain,
% 23.28/23.53 (mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))),
% 23.28/23.53 inference(symmetry,[status(thm)],[8211])).
% 23.28/23.53 tff(9985,plain,
% 23.28/23.53 (mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 23.28/23.53 inference(transitivity,[status(thm)],[9984, 8170, 8169, 281])).
% 23.28/23.53 tff(9986,plain,
% 23.28/23.53 (ld(a, mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c)))))) = ld(a, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 23.28/23.53 inference(monotonicity,[status(thm)],[9985])).
% 23.28/23.53 tff(9987,plain,
% 23.28/23.53 (ld(a, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))) = ld(a, mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c))))))),
% 23.28/23.53 inference(symmetry,[status(thm)],[9986])).
% 23.28/23.53 tff(9988,plain,
% 23.28/23.53 (mult(mult(c, a), rd(mult(b, c), mult(a, c))) = mult(c, mult(a, rd(mult(b, c), mult(a, c))))),
% 23.28/23.53 inference(transitivity,[status(thm)],[8235, 5650, 9987, 8268])).
% 23.28/23.53 tff(9989,assumption,(~(mult(mult(c, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))), introduced(assumption)).
% 23.28/23.53 tff(9990,plain,
% 23.28/23.53 (((~(mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), a)))) | (~(mult(mult(c, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))) | (mult(mult(c, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))),
% 23.28/23.53 inference(tautology,[status(thm)],[])).
% 23.28/23.53 tff(9991,plain,
% 23.28/23.53 ((~(mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), a)))) | (~(mult(mult(c, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))),
% 23.28/23.53 inference(unit_resolution,[status(thm)],[9990, 9989])).
% 23.28/23.53 tff(9992,plain,
% 23.28/23.53 (~((~(mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), a)) = mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(mult(c, a), mult(a, rd(mult(b, c), mult(a, c)))))))),
% 23.28/23.53 inference(unit_resolution,[status(thm)],[8250, 9991])).
% 23.28/23.53 tff(9993,plain,
% 23.28/23.53 (((~(mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), a)) = mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(mult(c, a), mult(a, rd(mult(b, c), mult(a, c))))))) | (mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), a)) = mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))),
% 23.28/23.53 inference(tautology,[status(thm)],[])).
% 23.28/23.53 tff(9994,plain,
% 23.28/23.53 (mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), a)) = mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.28/23.53 inference(unit_resolution,[status(thm)],[9993, 9992])).
% 23.28/23.53 tff(9995,plain,
% 23.28/23.54 (mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), a))),
% 23.28/23.54 inference(symmetry,[status(thm)],[9994])).
% 23.28/23.54 tff(9996,plain,
% 23.28/23.54 (mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)),
% 23.28/23.54 inference(transitivity,[status(thm)],[9995, 5404, 8236])).
% 23.28/23.54 tff(9997,plain,
% 23.28/23.54 (mult(mult(c, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))),
% 23.28/23.54 inference(transitivity,[status(thm)],[8240, 8170])).
% 23.28/23.54 tff(9998,plain,
% 23.28/23.54 ((mult(mult(c, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))) <=> (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))),
% 23.28/23.54 inference(monotonicity,[status(thm)],[9997, 9996])).
% 23.28/23.54 tff(9999,plain,
% 23.28/23.54 ((mult(mult(c, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))) <=> (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))),
% 23.28/23.54 inference(transitivity,[status(thm)],[9998, 8238])).
% 23.28/23.54 tff(10000,plain,
% 23.28/23.54 ((~(mult(mult(c, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) <=> (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))))),
% 23.28/23.54 inference(monotonicity,[status(thm)],[9999])).
% 23.28/23.54 tff(10001,plain,
% 23.28/23.54 (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))),
% 23.28/23.54 inference(modus_ponens,[status(thm)],[9989, 10000])).
% 23.28/23.54 tff(10002,plain,
% 23.28/23.54 (mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(mult(c, a), mult(a, rd(mult(b, c), mult(a, c))))),
% 23.28/23.54 inference(unit_resolution,[status(thm)],[8252, 9992])).
% 23.28/23.54 tff(10003,plain,
% 23.28/23.54 (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))),
% 23.28/23.54 inference(unit_resolution,[status(thm)],[8278, 10002, 299, 8231])).
% 23.28/23.54 tff(10004,plain,
% 23.28/23.54 ($false),
% 23.28/23.54 inference(unit_resolution,[status(thm)],[10003, 10001])).
% 23.28/23.54 tff(10005,plain,((mult(mult(c, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c)))))))), inference(lemma,lemma(discharge,[]))).
% 23.28/23.54 tff(10006,plain,
% 23.28/23.54 (mult(mult(c, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.28/23.54 inference(unit_resolution,[status(thm)],[10005, 8211, 281])).
% 23.28/23.54 tff(10007,plain,
% 23.28/23.54 (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), unit) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), unit)),
% 23.28/23.54 inference(monotonicity,[status(thm)],[9761])).
% 23.28/23.54 tff(10008,plain,
% 23.28/23.54 (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), unit) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))),
% 23.28/23.54 inference(transitivity,[status(thm)],[10007, 2177, 2162])).
% 23.28/23.54 tff(10009,plain,
% 23.28/23.54 (mult(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), unit), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)),
% 23.28/23.54 inference(monotonicity,[status(thm)],[10008])).
% 23.28/23.54 tff(10010,plain,
% 23.28/23.54 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)) = mult(mult(a, mult(c, c)), rd(mult(b, c), mult(a, c)))),
% 23.28/23.54 inference(transitivity,[status(thm)],[5943, 5942, 10009, 9754, 9323])).
% 23.28/23.54 tff(10011,plain,
% 23.28/23.54 (mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))))),
% 23.28/23.54 inference(unit_resolution,[status(thm)],[9542, 10010, 8165, 8305, 281])).
% 23.28/23.54 tff(10012,plain,
% 23.28/23.54 (mult(mult(a, a), rd(mult(b, c), mult(a, c))) = mult(a, mult(a, rd(mult(b, c), mult(a, c))))),
% 23.28/23.54 inference(unit_resolution,[status(thm)],[1360, 6462])).
% 23.28/23.54 tff(10013,plain,
% 23.28/23.54 ((mult(c, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))) = mult(mult(c, c), mult(a, mult(a, rd(mult(b, c), mult(a, c)))))) <=> (mult(mult(c, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))),
% 23.28/23.54 inference(commutativity,[status(thm)],[])).
% 23.28/23.54 tff(10014,plain,
% 23.28/23.54 (mult(mult(c, c), mult(mult(a, a), rd(mult(b, c), mult(a, c)))) = mult(mult(c, c), mult(a, mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.28/23.54 inference(monotonicity,[status(thm)],[1391])).
% 23.28/23.54 tff(10015,assumption,(~(mult(mult(mult(c, c), rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), mult(a, a))))), introduced(assumption)).
% 23.28/23.54 tff(10016,plain,
% 23.28/23.54 (((~(mult(mult(mult(c, c), rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), mult(a, a))))) | (~(mult(mult(mult(c, c), mult(a, a)), rd(mult(b, c), mult(a, c))) = mult(mult(c, c), mult(mult(a, a), rd(mult(b, c), mult(a, c))))))) | (mult(mult(mult(c, c), rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), mult(a, a))))),
% 23.28/23.54 inference(tautology,[status(thm)],[])).
% 23.28/23.54 tff(10017,plain,
% 23.28/23.54 ((~(mult(mult(mult(c, c), rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), mult(a, a))))) | (~(mult(mult(mult(c, c), mult(a, a)), rd(mult(b, c), mult(a, c))) = mult(mult(c, c), mult(mult(a, a), rd(mult(b, c), mult(a, c))))))),
% 23.28/23.54 inference(unit_resolution,[status(thm)],[10016, 10015])).
% 23.28/23.54 tff(10018,plain,
% 23.28/23.54 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(c, c), rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(mult(mult(c, c), mult(a, a)), rd(mult(b, c), mult(a, c))))) | (~(mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), mult(a, a))) = mult(mult(c, c), mult(mult(a, a), rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(mult(c, c), rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), mult(a, a))))) | (~(mult(mult(mult(c, c), mult(a, a)), rd(mult(b, c), mult(a, c))) = mult(mult(c, c), mult(mult(a, a), rd(mult(b, c), mult(a, c)))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(c, c), rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(mult(mult(c, c), mult(a, a)), rd(mult(b, c), mult(a, c))))) | (~(mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), mult(a, a))) = mult(mult(c, c), mult(mult(a, a), rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(mult(c, c), rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), mult(a, a))))) | (~(mult(mult(mult(c, c), mult(a, a)), rd(mult(b, c), mult(a, c))) = mult(mult(c, c), mult(mult(a, a), rd(mult(b, c), mult(a, c)))))))))),
% 23.28/23.54 inference(rewrite,[status(thm)],[])).
% 23.28/23.54 tff(10019,plain,
% 23.28/23.54 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(c, c), rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(mult(mult(c, c), mult(a, a)), rd(mult(b, c), mult(a, c))))) | (~(mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), mult(a, a))) = mult(mult(c, c), mult(mult(a, a), rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(mult(c, c), rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), mult(a, a))))) | (~(mult(mult(mult(c, c), mult(a, a)), rd(mult(b, c), mult(a, c))) = mult(mult(c, c), mult(mult(a, a), rd(mult(b, c), mult(a, c)))))))))),
% 23.28/23.54 inference(quant_inst,[status(thm)],[])).
% 23.28/23.54 tff(10020,plain,
% 23.28/23.54 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(c, c), rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(mult(mult(c, c), mult(a, a)), rd(mult(b, c), mult(a, c))))) | (~(mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), mult(a, a))) = mult(mult(c, c), mult(mult(a, a), rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(mult(c, c), rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), mult(a, a))))) | (~(mult(mult(mult(c, c), mult(a, a)), rd(mult(b, c), mult(a, c))) = mult(mult(c, c), mult(mult(a, a), rd(mult(b, c), mult(a, c))))))))),
% 23.28/23.54 inference(modus_ponens,[status(thm)],[10019, 10018])).
% 23.28/23.54 tff(10021,plain,
% 23.28/23.54 ((~((~(mult(mult(mult(c, c), rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(mult(mult(c, c), mult(a, a)), rd(mult(b, c), mult(a, c))))) | (~(mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), mult(a, a))) = mult(mult(c, c), mult(mult(a, a), rd(mult(b, c), mult(a, c)))))))) | (~((~(mult(mult(mult(c, c), rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), mult(a, a))))) | (~(mult(mult(mult(c, c), mult(a, a)), rd(mult(b, c), mult(a, c))) = mult(mult(c, c), mult(mult(a, a), rd(mult(b, c), mult(a, c))))))))),
% 23.28/23.54 inference(unit_resolution,[status(thm)],[10020, 27])).
% 23.28/23.54 tff(10022,plain,
% 23.28/23.54 (~((~(mult(mult(mult(c, c), rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(mult(mult(c, c), mult(a, a)), rd(mult(b, c), mult(a, c))))) | (~(mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), mult(a, a))) = mult(mult(c, c), mult(mult(a, a), rd(mult(b, c), mult(a, c)))))))),
% 23.28/23.54 inference(unit_resolution,[status(thm)],[10021, 10017])).
% 23.28/23.54 tff(10023,plain,
% 23.28/23.54 (((~(mult(mult(mult(c, c), rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(mult(mult(c, c), mult(a, a)), rd(mult(b, c), mult(a, c))))) | (~(mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), mult(a, a))) = mult(mult(c, c), mult(mult(a, a), rd(mult(b, c), mult(a, c))))))) | (mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), mult(a, a))) = mult(mult(c, c), mult(mult(a, a), rd(mult(b, c), mult(a, c)))))),
% 23.28/23.54 inference(tautology,[status(thm)],[])).
% 23.28/23.54 tff(10024,plain,
% 23.28/23.54 (mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), mult(a, a))) = mult(mult(c, c), mult(mult(a, a), rd(mult(b, c), mult(a, c))))),
% 23.28/23.54 inference(unit_resolution,[status(thm)],[10023, 10022])).
% 23.28/23.54 tff(10025,plain,
% 23.28/23.54 (mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), mult(a, a))) = mult(mult(c, c), mult(a, mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.28/23.54 inference(transitivity,[status(thm)],[10024, 10014])).
% 23.28/23.54 tff(10026,plain,
% 23.28/23.54 (mult(mult(c, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))),
% 23.28/23.54 inference(monotonicity,[status(thm)],[3885])).
% 23.28/23.54 tff(10027,assumption,(mult(mult(c, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))), introduced(assumption)).
% 23.28/23.54 tff(10028,plain,
% 23.28/23.54 (mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(c, a), mult(a, rd(mult(b, c), mult(a, c))))),
% 23.28/23.54 inference(symmetry,[status(thm)],[10027])).
% 23.28/23.54 tff(10029,plain,
% 23.28/23.54 (mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))),
% 23.28/23.54 inference(transitivity,[status(thm)],[10028, 10026, 6796])).
% 23.28/23.54 tff(10030,plain,
% 23.28/23.54 (mult(c, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))) = mult(c, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))))),
% 23.28/23.54 inference(monotonicity,[status(thm)],[10029])).
% 23.28/23.54 tff(10031,plain,
% 23.28/23.54 (mult(c, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))) = mult(c, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))),
% 23.28/23.54 inference(symmetry,[status(thm)],[10030])).
% 23.28/23.54 tff(10032,plain,
% 23.28/23.54 (mult(mult(c, c), mult(mult(unit, a), unit)) = mult(mult(c, c), a)),
% 23.28/23.54 inference(monotonicity,[status(thm)],[507])).
% 23.28/23.54 tff(10033,plain,
% 23.28/23.54 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(c, c), unit), a), unit) = mult(mult(c, c), mult(mult(unit, a), unit)))),
% 23.38/23.54 inference(quant_inst,[status(thm)],[])).
% 23.38/23.54 tff(10034,plain,
% 23.38/23.54 (mult(mult(mult(mult(c, c), unit), a), unit) = mult(mult(c, c), mult(mult(unit, a), unit))),
% 23.38/23.54 inference(unit_resolution,[status(thm)],[10033, 56])).
% 23.38/23.54 tff(10035,plain,
% 23.38/23.54 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(c, unit), c), unit) = mult(c, mult(mult(unit, c), unit)))),
% 23.38/23.54 inference(quant_inst,[status(thm)],[])).
% 23.38/23.54 tff(10036,plain,
% 23.38/23.54 (mult(mult(mult(c, unit), c), unit) = mult(c, mult(mult(unit, c), unit))),
% 23.38/23.54 inference(unit_resolution,[status(thm)],[10035, 56])).
% 23.38/23.54 tff(10037,plain,
% 23.38/23.54 (mult(mult(c, c), unit) = mult(mult(mult(c, unit), c), unit)),
% 23.38/23.54 inference(monotonicity,[status(thm)],[2617])).
% 23.38/23.54 tff(10038,plain,
% 23.38/23.54 (mult(mult(c, c), unit) = mult(c, c)),
% 23.38/23.54 inference(transitivity,[status(thm)],[10037, 10036, 3181])).
% 23.38/23.54 tff(10039,plain,
% 23.38/23.54 (mult(mult(mult(c, c), unit), a) = mult(mult(c, c), a)),
% 23.38/23.54 inference(monotonicity,[status(thm)],[10038])).
% 23.38/23.54 tff(10040,plain,
% 23.38/23.54 (mult(mult(c, c), a) = mult(mult(mult(c, c), unit), a)),
% 23.38/23.54 inference(symmetry,[status(thm)],[10039])).
% 23.38/23.54 tff(10041,plain,
% 23.38/23.54 (mult(c, mult(c, a)) = mult(mult(mult(c, c), unit), a)),
% 23.38/23.54 inference(transitivity,[status(thm)],[9268, 10040])).
% 23.38/23.54 tff(10042,plain,
% 23.38/23.54 (mult(mult(c, mult(c, a)), unit) = mult(mult(mult(mult(c, c), unit), a), unit)),
% 23.38/23.54 inference(monotonicity,[status(thm)],[10041])).
% 23.38/23.54 tff(10043,plain,
% 23.38/23.54 (mult(mult(mult(c, c), a), unit) = mult(mult(c, mult(c, a)), unit)),
% 23.38/23.54 inference(monotonicity,[status(thm)],[3911])).
% 23.38/23.54 tff(10044,plain,
% 23.38/23.54 (mult(mult(mult(c, c), a), unit) = mult(c, mult(a, c))),
% 23.38/23.54 inference(transitivity,[status(thm)],[10043, 10042, 10034, 10032, 3911, 4711])).
% 23.38/23.54 tff(10045,plain,
% 23.38/23.54 (mult(mult(mult(mult(c, c), a), unit), a) = mult(mult(c, mult(a, c)), a)),
% 23.38/23.54 inference(monotonicity,[status(thm)],[10044])).
% 23.38/23.54 tff(10046,plain,
% 23.38/23.54 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(c, c), a), unit), a) = mult(mult(c, c), mult(mult(a, unit), a)))),
% 23.38/23.54 inference(quant_inst,[status(thm)],[])).
% 23.38/23.54 tff(10047,plain,
% 23.38/23.54 (mult(mult(mult(mult(c, c), a), unit), a) = mult(mult(c, c), mult(mult(a, unit), a))),
% 23.38/23.54 inference(unit_resolution,[status(thm)],[10046, 56])).
% 23.38/23.54 tff(10048,plain,
% 23.38/23.54 (mult(mult(c, c), mult(mult(a, unit), a)) = mult(mult(mult(mult(c, c), a), unit), a)),
% 23.38/23.54 inference(symmetry,[status(thm)],[10047])).
% 23.38/23.54 tff(10049,plain,
% 23.38/23.54 (mult(mult(c, c), mult(a, a)) = mult(mult(c, c), mult(mult(a, unit), a))),
% 23.38/23.54 inference(monotonicity,[status(thm)],[520])).
% 23.38/23.54 tff(10050,plain,
% 23.38/23.54 (mult(mult(c, c), mult(a, a)) = mult(mult(mult(a, c), c), a)),
% 23.38/23.54 inference(transitivity,[status(thm)],[10049, 10048, 10045, 4868])).
% 23.38/23.54 tff(10051,plain,
% 23.38/23.54 (mult(mult(mult(c, c), mult(a, a)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(mult(a, c), c), a), rd(mult(b, c), mult(a, c)))),
% 23.38/23.54 inference(monotonicity,[status(thm)],[10050])).
% 23.38/23.54 tff(10052,plain,
% 23.38/23.54 (((~(mult(mult(mult(c, c), rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(mult(mult(c, c), mult(a, a)), rd(mult(b, c), mult(a, c))))) | (~(mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), mult(a, a))) = mult(mult(c, c), mult(mult(a, a), rd(mult(b, c), mult(a, c))))))) | (mult(mult(mult(c, c), rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(mult(mult(c, c), mult(a, a)), rd(mult(b, c), mult(a, c))))),
% 23.38/23.54 inference(tautology,[status(thm)],[])).
% 23.38/23.54 tff(10053,plain,
% 23.38/23.54 (mult(mult(mult(c, c), rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(mult(mult(c, c), mult(a, a)), rd(mult(b, c), mult(a, c)))),
% 23.38/23.54 inference(unit_resolution,[status(thm)],[10052, 10022])).
% 23.38/23.54 tff(10054,plain,
% 23.38/23.54 (mult(mult(mult(c, c), rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(c, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))),
% 23.38/23.54 inference(transitivity,[status(thm)],[10053, 10051, 5231, 6819, 6820, 6797, 10031])).
% 23.38/23.54 tff(10055,plain,
% 23.38/23.54 ((mult(mult(mult(c, c), rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), mult(a, a)))) <=> (mult(c, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))) = mult(mult(c, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))))),
% 23.38/23.55 inference(monotonicity,[status(thm)],[10054, 10025])).
% 23.38/23.55 tff(10056,plain,
% 23.38/23.55 ((mult(mult(mult(c, c), rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), mult(a, a)))) <=> (mult(mult(c, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))),
% 23.38/23.55 inference(transitivity,[status(thm)],[10055, 10013])).
% 23.38/23.55 tff(10057,plain,
% 23.38/23.55 ((~(mult(mult(mult(c, c), rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), mult(a, a))))) <=> (~(mult(mult(c, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))))),
% 23.38/23.55 inference(monotonicity,[status(thm)],[10056])).
% 23.38/23.55 tff(10058,plain,
% 23.38/23.55 (~(mult(mult(c, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))),
% 23.38/23.55 inference(modus_ponens,[status(thm)],[10015, 10057])).
% 23.38/23.55 tff(10059,plain,
% 23.38/23.55 (((~(mult(mult(c, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))) | (~(mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c))))) | (mult(mult(c, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))),
% 23.38/23.55 inference(tautology,[status(thm)],[])).
% 23.38/23.55 tff(10060,plain,
% 23.38/23.55 ((~(mult(mult(c, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))) | (~(mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c))))),
% 23.38/23.55 inference(unit_resolution,[status(thm)],[10059, 10058])).
% 23.38/23.55 tff(10061,plain,
% 23.38/23.55 (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 23.38/23.55 inference(transitivity,[status(thm)],[4521, 299])).
% 23.38/23.55 tff(10062,plain,
% 23.38/23.55 (mult(c, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 23.38/23.55 inference(monotonicity,[status(thm)],[10061])).
% 23.38/23.55 tff(10063,plain,
% 23.38/23.55 (mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))) = mult(c, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))))),
% 23.38/23.55 inference(symmetry,[status(thm)],[10062])).
% 23.38/23.55 tff(10064,plain,
% 23.38/23.55 (mult(mult(unit, mult(mult(a, c), c)), a) = mult(mult(a, mult(c, c)), a)),
% 23.38/23.55 inference(transitivity,[status(thm)],[7851, 4868, 4663])).
% 23.38/23.55 tff(10065,plain,
% 23.38/23.55 ((mult(mult(unit, mult(mult(a, c), c)), a) = mult(mult(unit, a), mult(mult(a, c), c))) <=> (mult(mult(a, mult(c, c)), a) = mult(a, mult(mult(c, c), a)))),
% 23.38/23.55 inference(monotonicity,[status(thm)],[10064, 7850])).
% 23.38/23.55 tff(10066,plain,
% 23.38/23.55 ((mult(mult(a, mult(c, c)), a) = mult(a, mult(mult(c, c), a))) <=> (mult(mult(unit, mult(mult(a, c), c)), a) = mult(mult(unit, a), mult(mult(a, c), c)))),
% 23.38/23.55 inference(symmetry,[status(thm)],[10065])).
% 23.38/23.55 tff(10067,plain,
% 23.38/23.55 (mult(a, mult(mult(c, c), a)) = mult(a, mult(c, mult(a, c)))),
% 23.38/23.55 inference(transitivity,[status(thm)],[4709, 4712])).
% 23.38/23.55 tff(10068,plain,
% 23.38/23.55 (mult(mult(a, mult(c, c)), a) = mult(mult(a, c), mult(a, c))),
% 23.38/23.55 inference(transitivity,[status(thm)],[4662, 4867, 4871, 2561, 5056, 5233, 4880])).
% 23.38/23.55 tff(10069,plain,
% 23.38/23.55 ((mult(mult(a, mult(c, c)), a) = mult(a, mult(mult(c, c), a))) <=> (mult(mult(a, c), mult(a, c)) = mult(a, mult(c, mult(a, c))))),
% 23.38/23.55 inference(monotonicity,[status(thm)],[10068, 10067])).
% 23.38/23.55 tff(10070,plain,
% 23.38/23.55 ((mult(mult(a, c), mult(a, c)) = mult(a, mult(c, mult(a, c)))) <=> (mult(mult(a, mult(c, c)), a) = mult(a, mult(mult(c, c), a)))),
% 23.38/23.55 inference(symmetry,[status(thm)],[10069])).
% 23.38/23.55 tff(10071,plain,
% 23.38/23.55 ((mult(mult(a, c), mult(a, c)) = mult(a, mult(c, mult(a, c)))) <=> (mult(mult(unit, mult(mult(a, c), c)), a) = mult(mult(unit, a), mult(mult(a, c), c)))),
% 23.38/23.55 inference(transitivity,[status(thm)],[10070, 10066])).
% 23.38/23.55 tff(10072,plain,
% 23.38/23.55 (mult(mult(unit, mult(mult(a, c), c)), a) = mult(mult(unit, a), mult(mult(a, c), c))),
% 23.38/23.55 inference(modus_ponens,[status(thm)],[4751, 10071])).
% 23.38/23.55 tff(10073,plain,
% 23.38/23.55 (mult(mult(a, mult(c, c)), a) = mult(mult(a, a), mult(c, c))),
% 23.38/23.55 inference(unit_resolution,[status(thm)],[7898, 10072])).
% 23.38/23.55 tff(10074,plain,
% 23.38/23.55 (mult(mult(a, a), mult(c, c)) = mult(mult(a, mult(c, c)), a)),
% 23.38/23.55 inference(symmetry,[status(thm)],[10073])).
% 23.38/23.55 tff(10075,plain,
% 23.38/23.55 (mult(mult(unit, a), mult(a, c)) = mult(mult(unit, mult(a, c)), a)),
% 23.38/23.55 inference(transitivity,[status(thm)],[8812, 4452, 4518, 4447, 8811])).
% 23.38/23.55 tff(10076,plain,
% 23.38/23.55 (mult(mult(a, a), c) = mult(a, mult(a, c))),
% 23.38/23.55 inference(unit_resolution,[status(thm)],[8833, 10075])).
% 23.38/23.55 tff(10077,plain,
% 23.38/23.55 (mult(mult(a, a), c) = mult(mult(a, c), a)),
% 23.38/23.55 inference(transitivity,[status(thm)],[10076, 4452, 4518, 4447])).
% 23.38/23.55 tff(10078,plain,
% 23.38/23.55 (mult(mult(mult(a, a), c), unit) = mult(mult(mult(a, c), a), unit)),
% 23.38/23.55 inference(monotonicity,[status(thm)],[10077])).
% 23.38/23.55 tff(10079,plain,
% 23.38/23.55 (mult(mult(mult(a, c), a), unit) = mult(mult(mult(a, a), c), unit)),
% 23.38/23.55 inference(symmetry,[status(thm)],[10078])).
% 23.38/23.55 tff(10080,plain,
% 23.38/23.55 (mult(mult(a, c), a) = mult(mult(mult(a, a), c), unit)),
% 23.38/23.55 inference(transitivity,[status(thm)],[9301, 9299, 9296, 10079])).
% 23.38/23.55 tff(10081,plain,
% 23.38/23.55 (mult(mult(mult(a, c), a), c) = mult(mult(mult(mult(a, a), c), unit), c)),
% 23.38/23.55 inference(monotonicity,[status(thm)],[10080])).
% 23.38/23.55 tff(10082,plain,
% 23.38/23.55 (mult(a, mult(c, mult(a, c))) = mult(mult(a, c), mult(a, c))),
% 23.38/23.55 inference(transitivity,[status(thm)],[4714, 4724, 10081, 7903, 7901, 10074, 4662, 4867, 4871, 2561, 5056, 5233, 4880])).
% 23.38/23.55 tff(10083,plain,
% 23.38/23.55 (mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 23.38/23.55 inference(monotonicity,[status(thm)],[10082])).
% 23.38/23.55 tff(10084,assumption,(mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))))), introduced(assumption)).
% 23.38/23.55 tff(10085,plain,
% 23.38/23.55 (mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c)))),
% 23.38/23.55 inference(symmetry,[status(thm)],[10084])).
% 23.38/23.55 tff(10086,plain,
% 23.38/23.55 (mult(c, mult(a, c)) = mult(a, mult(c, c))),
% 23.38/23.55 inference(transitivity,[status(thm)],[3877, 3876, 2622, 2614, 2621])).
% 23.38/23.55 tff(10087,plain,
% 23.38/23.55 (mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a))),
% 23.38/23.55 inference(monotonicity,[status(thm)],[10086])).
% 23.38/23.55 tff(10088,plain,
% 23.38/23.55 (mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a))),
% 23.38/23.55 inference(symmetry,[status(thm)],[10087])).
% 23.38/23.55 tff(10089,plain,
% 23.38/23.55 (mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a))),
% 23.38/23.55 inference(monotonicity,[status(thm)],[2619])).
% 23.38/23.55 tff(10090,plain,
% 23.38/23.55 (mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, mult(c, c)), mult(rd(mult(b, c), mult(a, c)), a))),
% 23.38/23.55 inference(symmetry,[status(thm)],[10089])).
% 23.38/23.55 tff(10091,assumption,(mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c)), introduced(assumption)).
% 23.38/23.55 tff(10092,plain,
% 23.38/23.55 (mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c) = mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a))),
% 23.38/23.55 inference(symmetry,[status(thm)],[10091])).
% 23.38/23.55 tff(10093,plain,
% 23.38/23.55 (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a)),
% 23.38/23.55 inference(transitivity,[status(thm)],[7820, 7592, 10092, 10090, 10088, 7809])).
% 23.38/23.55 tff(10094,plain,
% 23.38/23.55 (rd(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a), a) = rd(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a), a)),
% 23.38/23.55 inference(monotonicity,[status(thm)],[10093])).
% 23.38/23.55 tff(10095,plain,
% 23.38/23.55 (mult(c, mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))),
% 23.38/23.55 inference(transitivity,[status(thm)],[7945, 5710])).
% 23.38/23.55 tff(10096,plain,
% 23.38/23.55 (mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)),
% 23.38/23.55 inference(monotonicity,[status(thm)],[10095])).
% 23.38/23.55 tff(10097,plain,
% 23.38/23.55 (mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 23.38/23.55 inference(transitivity,[status(thm)],[10096, 7695, 10094, 2786])).
% 23.38/23.55 tff(10098,plain,
% 23.38/23.55 (mult(a, mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), c)) = mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))))),
% 23.38/23.55 inference(monotonicity,[status(thm)],[10097])).
% 23.38/23.55 tff(10099,plain,
% 23.38/23.55 (mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), c)),
% 23.38/23.55 inference(monotonicity,[status(thm)],[6582])).
% 23.38/23.55 tff(10100,plain,
% 23.38/23.55 (mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), c)),
% 23.38/23.55 inference(monotonicity,[status(thm)],[10029])).
% 23.38/23.55 tff(10101,plain,
% 23.38/23.55 (mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(c, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))),
% 23.38/23.55 inference(transitivity,[status(thm)],[10100, 10099, 7918, 10098, 10085, 10083, 4789, 4788, 6879, 10063, 10031])).
% 23.38/23.55 tff(10102,plain,
% 23.38/23.55 ((mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(mult(c, c), mult(a, mult(a, rd(mult(b, c), mult(a, c)))))) <=> (mult(c, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))) = mult(mult(c, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))))),
% 23.38/23.55 inference(monotonicity,[status(thm)],[10101])).
% 23.38/23.55 tff(10103,plain,
% 23.38/23.55 ((mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(mult(c, c), mult(a, mult(a, rd(mult(b, c), mult(a, c)))))) <=> (mult(mult(c, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))),
% 23.38/23.55 inference(transitivity,[status(thm)],[10102, 10013])).
% 23.38/23.55 tff(10104,plain,
% 23.38/23.55 ((mult(mult(c, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) <=> (mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(mult(c, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))))),
% 23.38/23.55 inference(symmetry,[status(thm)],[10103])).
% 23.38/23.55 tff(10105,plain,
% 23.38/23.55 ((mult(mult(mult(c, c), rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), mult(a, a)))) <=> (mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(mult(c, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))))),
% 23.38/23.55 inference(transitivity,[status(thm)],[10056, 10104])).
% 23.38/23.55 tff(10106,plain,
% 23.38/23.55 ((~(mult(mult(mult(c, c), rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), mult(a, a))))) <=> (~(mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(mult(c, c), mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))),
% 23.38/23.55 inference(monotonicity,[status(thm)],[10105])).
% 23.38/23.55 tff(10107,plain,
% 23.38/23.55 (~(mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(mult(c, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))))),
% 23.38/23.55 inference(modus_ponens,[status(thm)],[10015, 10106])).
% 23.38/23.55 tff(10108,plain,
% 23.38/23.55 (((~(mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)) = mult(c, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))) | (~(mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(mult(c, c), mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))) | (mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(mult(c, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))))),
% 23.38/23.55 inference(tautology,[status(thm)],[])).
% 23.38/23.55 tff(10109,plain,
% 23.38/23.55 ((~(mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)) = mult(c, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))) | (~(mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(mult(c, c), mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))),
% 23.38/23.55 inference(unit_resolution,[status(thm)],[10108, 10107])).
% 23.38/23.55 tff(10110,plain,
% 23.38/23.55 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(c, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))) | (~(mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)))))) | (~((~(mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)) = mult(c, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))) | (~(mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(mult(c, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(c, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))) | (~(mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)))))) | (~((~(mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)) = mult(c, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))) | (~(mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(mult(c, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))))))))),
% 23.38/23.55 inference(rewrite,[status(thm)],[])).
% 23.38/23.55 tff(10111,plain,
% 23.38/23.55 (((~((~(mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)) = mult(c, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))) | (~(mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(mult(c, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))))))) | (~((~(mult(mult(c, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))) | (~(mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c))))))) <=> ((~((~(mult(mult(c, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))) | (~(mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)))))) | (~((~(mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)) = mult(c, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))) | (~(mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(mult(c, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))))))))),
% 23.38/23.55 inference(rewrite,[status(thm)],[])).
% 23.38/23.55 tff(10112,plain,
% 23.38/23.55 ((~((~(mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)))) | (~(mult(mult(c, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))))) <=> (~((~(mult(mult(c, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))) | (~(mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c))))))),
% 23.38/23.55 inference(rewrite,[status(thm)],[])).
% 23.38/23.55 tff(10113,plain,
% 23.38/23.55 ((~((~(mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(mult(c, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)) = mult(c, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))))) <=> (~((~(mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)) = mult(c, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))) | (~(mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(mult(c, c), mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))))),
% 23.38/23.55 inference(rewrite,[status(thm)],[])).
% 23.38/23.56 tff(10114,plain,
% 23.38/23.56 (((~((~(mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(mult(c, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)) = mult(c, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))))) | (~((~(mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)))) | (~(mult(mult(c, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))))))) <=> ((~((~(mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)) = mult(c, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))) | (~(mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(mult(c, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))))))) | (~((~(mult(mult(c, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))) | (~(mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)))))))),
% 23.38/23.56 inference(monotonicity,[status(thm)],[10113, 10112])).
% 23.38/23.56 tff(10115,plain,
% 23.38/23.56 (((~((~(mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(mult(c, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)) = mult(c, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))))) | (~((~(mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)))) | (~(mult(mult(c, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))))))) <=> ((~((~(mult(mult(c, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))) | (~(mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)))))) | (~((~(mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)) = mult(c, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))) | (~(mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(mult(c, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))))))))),
% 23.38/23.56 inference(transitivity,[status(thm)],[10114, 10111])).
% 23.38/23.56 tff(10116,plain,
% 23.38/23.56 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(mult(c, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)) = mult(c, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))))) | (~((~(mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)))) | (~(mult(mult(c, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(c, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))) | (~(mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)))))) | (~((~(mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)) = mult(c, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))) | (~(mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(mult(c, c), mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))))))),
% 23.38/23.56 inference(monotonicity,[status(thm)],[10115])).
% 23.38/23.56 tff(10117,plain,
% 23.38/23.56 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(mult(c, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)) = mult(c, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))))) | (~((~(mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)))) | (~(mult(mult(c, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(c, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))) | (~(mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)))))) | (~((~(mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)) = mult(c, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))) | (~(mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(mult(c, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))))))))),
% 23.38/23.56 inference(transitivity,[status(thm)],[10116, 10110])).
% 23.38/23.56 tff(10118,plain,
% 23.38/23.56 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(mult(c, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)) = mult(c, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))))) | (~((~(mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)))) | (~(mult(mult(c, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))))))),
% 23.38/23.56 inference(quant_inst,[status(thm)],[])).
% 23.38/23.56 tff(10119,plain,
% 23.38/23.56 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(c, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))) | (~(mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)))))) | (~((~(mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)) = mult(c, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))) | (~(mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(mult(c, c), mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))))),
% 23.38/23.56 inference(modus_ponens,[status(thm)],[10118, 10117])).
% 23.38/23.56 tff(10120,plain,
% 23.38/23.56 ((~((~(mult(mult(c, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))) | (~(mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)))))) | (~((~(mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)) = mult(c, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))) | (~(mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(mult(c, c), mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))))),
% 23.38/23.56 inference(unit_resolution,[status(thm)],[10119, 27])).
% 23.38/23.56 tff(10121,plain,
% 23.38/23.56 ($false),
% 23.38/23.56 inference(unit_resolution,[status(thm)],[10120, 10109, 10060])).
% 23.38/23.56 tff(10122,plain,((mult(mult(mult(c, c), rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), mult(a, a)))) | (~(mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) | (~(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(c, a), rd(mult(b, c), mult(a, c))) = mult(c, mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(unit, c), unit), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, c), unit))))) | (~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(c, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, a), rd(mult(b, c), mult(a, c))) = mult(a, mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(c, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))))), inference(lemma,lemma(discharge,[]))).
% 23.38/23.56 tff(10123,plain,
% 23.38/23.56 ((mult(mult(mult(c, c), rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), mult(a, a)))) | (~(mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) | (~(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(c, a), rd(mult(b, c), mult(a, c))) = mult(c, mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(c, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, a), rd(mult(b, c), mult(a, c))) = mult(a, mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(c, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))))),
% 23.38/23.56 inference(unit_resolution,[status(thm)],[10122, 3862])).
% 23.38/23.56 tff(10124,plain,
% 23.38/23.56 ((mult(mult(mult(c, c), rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), mult(a, a)))) | (~(mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) | (~(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c))) | (~(mult(mult(c, a), rd(mult(b, c), mult(a, c))) = mult(c, mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(c, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(c, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))))),
% 23.38/23.57 inference(unit_resolution,[status(thm)],[10123, 5496, 10012])).
% 23.38/23.57 tff(10125,plain,
% 23.38/23.57 ((mult(mult(mult(c, c), rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), mult(a, a)))) | (~(mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(mult(a, c), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c))) | (~(mult(mult(c, a), rd(mult(b, c), mult(a, c))) = mult(c, mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(c, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(c, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))))),
% 23.38/23.57 inference(unit_resolution,[status(thm)],[10124, 8129])).
% 23.38/23.57 tff(10126,plain,
% 23.38/23.57 (mult(mult(mult(c, c), rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), mult(a, a)))),
% 23.38/23.57 inference(unit_resolution,[status(thm)],[10125, 10011, 6583, 10006, 9645, 9662, 9988, 281, 9983, 9652, 9640])).
% 23.38/23.57 tff(10127,plain,
% 23.38/23.57 (mult(mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a)), a) = mult(mult(c, c), mult(mult(rd(mult(b, c), mult(a, c)), a), a))),
% 23.38/23.57 inference(modus_ponens,[status(thm)],[10126, 9978])).
% 23.38/23.57 tff(10128,plain,
% 23.38/23.57 (mult(mult(c, c), mult(mult(rd(mult(b, c), mult(a, c)), a), a)) = mult(mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a)), a)),
% 23.38/23.57 inference(symmetry,[status(thm)],[10127])).
% 23.38/23.57 tff(10129,plain,
% 23.38/23.57 (mult(mult(c, c), mult(mult(rd(mult(b, c), mult(a, c)), a), a)) = mult(mult(b, c), mult(a, c))),
% 23.38/23.57 inference(transitivity,[status(thm)],[10128, 9889, 9752, 4660, 9746, 2502, 2499])).
% 23.38/23.57 tff(10130,plain,
% 23.38/23.57 (mult(unit, mult(mult(c, c), mult(mult(rd(mult(b, c), mult(a, c)), a), a))) = mult(unit, mult(mult(b, c), mult(a, c)))),
% 23.38/23.57 inference(monotonicity,[status(thm)],[10129])).
% 23.38/23.57 tff(10131,plain,
% 23.38/23.57 (mult(unit, mult(mult(b, c), mult(a, c))) = mult(unit, mult(mult(c, c), mult(mult(rd(mult(b, c), mult(a, c)), a), a)))),
% 23.38/23.57 inference(symmetry,[status(thm)],[10130])).
% 23.38/23.57 tff(10132,plain,
% 23.38/23.57 (mult(c, mult(a, mult(a, c))) = mult(c, mult(mult(a, c), a))),
% 23.38/23.57 inference(monotonicity,[status(thm)],[8262])).
% 23.38/23.57 tff(10133,plain,
% 23.38/23.57 (mult(c, mult(a, mult(a, c))) = mult(mult(mult(a, c), unit), mult(a, c))),
% 23.38/23.57 inference(transitivity,[status(thm)],[10132, 2562, 6842, 9744, 9736, 2504])).
% 23.38/23.57 tff(10134,plain,
% 23.38/23.57 (mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, mult(a, c)))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), unit), mult(a, c)))),
% 23.38/23.57 inference(monotonicity,[status(thm)],[10133])).
% 23.38/23.57 tff(10135,plain,
% 23.38/23.57 (mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, mult(a, c)))) = mult(mult(b, c), mult(a, c))),
% 23.38/23.57 inference(transitivity,[status(thm)],[10134, 2502, 2499])).
% 23.38/23.57 tff(10136,plain,
% 23.38/23.57 (mult(unit, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, mult(a, c))))) = mult(unit, mult(mult(b, c), mult(a, c)))),
% 23.38/23.57 inference(monotonicity,[status(thm)],[10135])).
% 23.38/23.57 tff(10137,plain,
% 23.38/23.57 (mult(mult(unit, mult(b, c)), mult(a, c)) = mult(mult(b, c), mult(a, c))),
% 23.38/23.57 inference(monotonicity,[status(thm)],[1054])).
% 23.38/23.57 tff(10138,plain,
% 23.38/23.57 (mult(mult(b, c), mult(a, c)) = mult(mult(unit, mult(b, c)), mult(a, c))),
% 23.38/23.57 inference(symmetry,[status(thm)],[10137])).
% 23.38/23.57 tff(10139,plain,
% 23.38/23.57 (mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(c, mult(a, mult(a, c)))) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, mult(a, c))))),
% 23.38/23.57 inference(monotonicity,[status(thm)],[1893])).
% 23.38/23.57 tff(10140,plain,
% 23.38/23.57 (mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(c, mult(a, mult(a, c)))) = mult(mult(unit, mult(b, c)), mult(a, c))),
% 23.38/23.57 inference(transitivity,[status(thm)],[10139, 10134, 2502, 2499, 10138])).
% 23.38/23.57 tff(10141,plain,
% 23.38/23.57 ((mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(c, mult(a, mult(a, c)))) = mult(unit, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, mult(a, c)))))) <=> (mult(mult(unit, mult(b, c)), mult(a, c)) = mult(unit, mult(mult(b, c), mult(a, c))))),
% 23.38/23.57 inference(monotonicity,[status(thm)],[10140, 10136])).
% 23.38/23.57 tff(10142,plain,
% 23.38/23.57 ((~![A: $i] : (mult(unit, A) = A)) | (mult(unit, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, mult(a, c))))) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, mult(a, c)))))),
% 23.38/23.57 inference(quant_inst,[status(thm)],[])).
% 23.38/23.57 tff(10143,plain,
% 23.38/23.57 (mult(unit, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, mult(a, c))))) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, mult(a, c))))),
% 23.38/23.57 inference(unit_resolution,[status(thm)],[10142, 71])).
% 23.38/23.57 tff(10144,plain,
% 23.38/23.57 (mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, mult(a, c)))) = mult(unit, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, mult(a, c)))))),
% 23.38/23.57 inference(symmetry,[status(thm)],[10143])).
% 23.38/23.57 tff(10145,plain,
% 23.38/23.57 (mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(c, mult(a, mult(a, c)))) = mult(unit, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, mult(a, c)))))),
% 23.38/23.57 inference(transitivity,[status(thm)],[10139, 10144])).
% 23.38/23.57 tff(10146,assumption,(~(mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(c, mult(a, mult(a, c)))) = mult(unit, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, mult(a, c))))))), introduced(assumption)).
% 23.38/23.57 tff(10147,plain,
% 23.38/23.57 ($false),
% 23.38/23.57 inference(unit_resolution,[status(thm)],[10146, 10145])).
% 23.38/23.57 tff(10148,plain,(mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(c, mult(a, mult(a, c)))) = mult(unit, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, mult(a, c)))))), inference(lemma,lemma(discharge,[]))).
% 23.38/23.57 tff(10149,plain,
% 23.38/23.57 (mult(mult(unit, mult(b, c)), mult(a, c)) = mult(unit, mult(mult(b, c), mult(a, c)))),
% 23.38/23.57 inference(modus_ponens,[status(thm)],[10148, 10141])).
% 23.38/23.57 tff(10150,plain,
% 23.38/23.57 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)), a) = mult(unit, mult(mult(c, c), mult(mult(rd(mult(b, c), mult(a, c)), a), a)))),
% 23.38/23.57 inference(transitivity,[status(thm)],[4660, 9746, 2502, 2499, 10138, 10149, 10131])).
% 23.38/23.57 tff(10151,plain,
% 23.38/23.57 (mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), a)),
% 23.38/23.57 inference(monotonicity,[status(thm)],[6238])).
% 23.38/23.57 tff(10152,plain,
% 23.38/23.57 (mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), mult(c, c)) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), mult(c, c))),
% 23.38/23.57 inference(monotonicity,[status(thm)],[10151])).
% 23.38/23.57 tff(10153,plain,
% 23.38/23.57 (mult(unit, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), mult(c, c))) = mult(unit, mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), mult(c, c)))),
% 23.38/23.57 inference(monotonicity,[status(thm)],[10152])).
% 23.38/23.57 tff(10154,plain,
% 23.38/23.57 (mult(unit, mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), mult(c, c))) = mult(unit, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), mult(c, c)))),
% 23.38/23.57 inference(symmetry,[status(thm)],[10153])).
% 23.38/23.57 tff(10155,plain,
% 23.38/23.57 (mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a) = mult(rd(mult(b, c), mult(a, c)), mult(a, a))),
% 23.38/23.57 inference(transitivity,[status(thm)],[10151, 6368, 539, 6367])).
% 23.38/23.57 tff(10156,plain,
% 23.38/23.57 (mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)) = mult(unit, mult(rd(mult(b, c), mult(a, c)), mult(a, a)))),
% 23.38/23.57 inference(monotonicity,[status(thm)],[10155])).
% 23.38/23.57 tff(10157,plain,
% 23.38/23.57 (mult(unit, mult(rd(mult(b, c), mult(a, c)), mult(a, a))) = mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a))),
% 23.38/23.57 inference(symmetry,[status(thm)],[10156])).
% 23.38/23.57 tff(10158,plain,
% 23.38/23.57 (mult(unit, mult(rd(mult(b, c), mult(a, c)), mult(a, a))) = mult(unit, mult(mult(rd(mult(b, c), mult(a, c)), a), a))),
% 23.38/23.57 inference(monotonicity,[status(thm)],[9890])).
% 23.38/23.57 tff(10159,plain,
% 23.38/23.57 (mult(unit, mult(mult(rd(mult(b, c), mult(a, c)), a), a)) = mult(unit, mult(rd(mult(b, c), mult(a, c)), mult(a, a)))),
% 23.38/23.57 inference(symmetry,[status(thm)],[10158])).
% 23.38/23.57 tff(10160,plain,
% 23.38/23.57 (mult(unit, mult(mult(rd(mult(b, c), mult(a, c)), a), a)) = mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a))),
% 23.38/23.57 inference(transitivity,[status(thm)],[10159, 10157])).
% 23.38/23.57 tff(10161,plain,
% 23.38/23.57 (mult(mult(unit, mult(mult(rd(mult(b, c), mult(a, c)), a), a)), mult(c, c)) = mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c))),
% 23.38/23.57 inference(monotonicity,[status(thm)],[10160])).
% 23.38/23.57 tff(10162,plain,
% 23.38/23.57 ((mult(mult(unit, mult(mult(rd(mult(b, c), mult(a, c)), a), a)), mult(c, c)) = mult(unit, mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), mult(c, c)))) <=> (mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c)) = mult(unit, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), mult(c, c))))),
% 23.38/23.57 inference(monotonicity,[status(thm)],[10161, 10154])).
% 23.38/23.57 tff(10163,plain,
% 23.38/23.57 ((mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c)) = mult(unit, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), mult(c, c)))) <=> (mult(mult(unit, mult(mult(rd(mult(b, c), mult(a, c)), a), a)), mult(c, c)) = mult(unit, mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), mult(c, c))))),
% 23.38/23.57 inference(symmetry,[status(thm)],[10162])).
% 23.38/23.57 tff(10164,assumption,(~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(mult(a, c), a))))), introduced(assumption)).
% 23.38/23.57 tff(10165,plain,
% 23.38/23.57 (mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), a))),
% 23.38/23.57 inference(unit_resolution,[status(thm)],[8281, 8211, 281])).
% 23.38/23.57 tff(10166,plain,
% 23.38/23.57 (mult(c, mult(a, c)) = mult(mult(a, c), c)),
% 23.38/23.57 inference(transitivity,[status(thm)],[4068, 8212, 2595])).
% 23.38/23.57 tff(10167,plain,
% 23.38/23.57 (mult(mult(c, mult(a, c)), a) = mult(mult(mult(a, c), c), a)),
% 23.38/23.57 inference(monotonicity,[status(thm)],[10166])).
% 23.38/23.57 tff(10168,plain,
% 23.38/23.57 (mult(c, mult(mult(a, c), a)) = mult(mult(mult(a, c), c), a)),
% 23.38/23.57 inference(transitivity,[status(thm)],[2562, 6842, 10167])).
% 23.38/23.57 tff(10169,plain,
% 23.38/23.57 (mult(rd(mult(b, c), mult(a, c)), mult(c, mult(mult(a, c), a))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), c), a))),
% 23.38/23.57 inference(monotonicity,[status(thm)],[10168])).
% 23.38/23.57 tff(10170,plain,
% 23.38/23.57 (mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(mult(a, c), a)))),
% 23.38/23.57 inference(symmetry,[status(thm)],[10169])).
% 23.38/23.57 tff(10171,assumption,(mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), a))), introduced(assumption)).
% 23.38/23.57 tff(10172,plain,
% 23.38/23.57 (mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)),
% 23.38/23.57 inference(transitivity,[status(thm)],[10171, 5404, 8236])).
% 23.38/23.57 tff(10173,plain,
% 23.38/23.57 (rd(mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), a), a) = rd(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), a)),
% 23.38/23.57 inference(monotonicity,[status(thm)],[10172])).
% 23.38/23.57 tff(10174,plain,
% 23.38/23.57 (rd(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), a) = rd(mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), a), a)),
% 23.38/23.57 inference(symmetry,[status(thm)],[10173])).
% 23.38/23.57 tff(10175,plain,
% 23.38/23.57 (mult(mult(a, c), rd(mult(b, c), mult(a, c))) = mult(c, mult(a, rd(mult(b, c), mult(a, c))))),
% 23.38/23.57 inference(transitivity,[status(thm)],[6325, 10174, 8234])).
% 23.38/23.57 tff(10176,plain,
% 23.38/23.57 (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.38/23.57 inference(monotonicity,[status(thm)],[10175])).
% 23.38/23.57 tff(10177,plain,
% 23.38/23.57 (mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))),
% 23.38/23.57 inference(transitivity,[status(thm)],[299, 10176, 8232, 8170])).
% 23.38/23.57 tff(10178,plain,
% 23.38/23.57 (rd(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))), rd(mult(b, c), mult(a, c))) = rd(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), rd(mult(b, c), mult(a, c)))),
% 23.38/23.57 inference(monotonicity,[status(thm)],[10177])).
% 23.38/23.57 tff(10179,plain,
% 23.38/23.57 (mult(a, mult(a, c)) = mult(mult(a, c), a)),
% 23.38/23.57 inference(transitivity,[status(thm)],[8292, 10178, 8230])).
% 23.38/23.57 tff(10180,plain,
% 23.38/23.57 (mult(c, mult(a, mult(a, c))) = mult(c, mult(mult(a, c), a))),
% 23.38/23.57 inference(monotonicity,[status(thm)],[10179])).
% 23.38/23.57 tff(10181,plain,
% 23.38/23.57 (mult(c, mult(a, mult(a, c))) = mult(mult(mult(a, c), c), a)),
% 23.38/23.57 inference(transitivity,[status(thm)],[10180, 2562, 6842, 10167])).
% 23.38/23.57 tff(10182,plain,
% 23.38/23.57 (mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, mult(a, c)))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), c), a))),
% 23.38/23.57 inference(monotonicity,[status(thm)],[10181])).
% 23.38/23.57 tff(10183,plain,
% 23.38/23.57 (mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, mult(a, c)))) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(mult(a, c), a)))),
% 23.38/23.57 inference(transitivity,[status(thm)],[10182, 10170])).
% 23.38/23.57 tff(10184,plain,
% 23.38/23.57 (mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a))),
% 23.38/23.57 inference(monotonicity,[status(thm)],[10179])).
% 23.38/23.57 tff(10185,plain,
% 23.38/23.57 ((mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, mult(a, c))))) <=> (mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(mult(a, c), a))))),
% 23.38/23.57 inference(monotonicity,[status(thm)],[10184, 10183])).
% 23.38/23.57 tff(10186,plain,
% 23.38/23.57 ((mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(mult(a, c), a)))) <=> (mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, mult(a, c)))))),
% 23.38/23.57 inference(symmetry,[status(thm)],[10185])).
% 23.38/23.57 tff(10187,plain,
% 23.38/23.57 ((~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(mult(a, c), a))))) <=> (~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, mult(a, c))))))),
% 23.38/23.57 inference(monotonicity,[status(thm)],[10186])).
% 23.38/23.57 tff(10188,plain,
% 23.38/23.57 (~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, mult(a, c)))))),
% 23.38/23.57 inference(modus_ponens,[status(thm)],[10164, 10187])).
% 23.38/23.57 tff(10189,plain,
% 23.38/23.57 (mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, mult(a, c))))),
% 23.38/23.57 inference(unit_resolution,[status(thm)],[9217, 8305])).
% 23.38/23.57 tff(10190,plain,
% 23.38/23.58 ($false),
% 23.38/23.58 inference(unit_resolution,[status(thm)],[10189, 10188])).
% 23.38/23.58 tff(10191,plain,((~(mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), a)))) | (mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(mult(a, c), a)))) | (~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c)))))))), inference(lemma,lemma(discharge,[]))).
% 23.38/23.58 tff(10192,plain,
% 23.38/23.58 ($false),
% 23.38/23.58 inference(unit_resolution,[status(thm)],[10191, 10165, 8211, 10164, 281])).
% 23.38/23.58 tff(10193,plain,((mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))) | (mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(mult(a, c), a))))), inference(lemma,lemma(discharge,[]))).
% 23.38/23.58 tff(10194,plain,
% 23.38/23.58 (mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(mult(a, c), a)))),
% 23.38/23.58 inference(unit_resolution,[status(thm)],[10193, 270])).
% 23.38/23.58 tff(10195,assumption,(~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a))), introduced(assumption)).
% 23.38/23.58 tff(10196,plain,
% 23.38/23.58 ((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, a))))),
% 23.38/23.58 inference(unit_resolution,[status(thm)],[6330, 10195])).
% 23.38/23.58 tff(10197,plain,
% 23.38/23.58 (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, a)))))),
% 23.38/23.58 inference(unit_resolution,[status(thm)],[6335, 10196])).
% 23.38/23.58 tff(10198,plain,
% 23.38/23.58 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, a))),
% 23.38/23.58 inference(unit_resolution,[status(thm)],[6337, 10197])).
% 23.38/23.58 tff(10199,plain,
% 23.38/23.58 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, a)) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a)),
% 23.38/23.58 inference(symmetry,[status(thm)],[10198])).
% 23.38/23.58 tff(10200,plain,
% 23.38/23.58 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a)),
% 23.38/23.58 inference(transitivity,[status(thm)],[8296, 10199])).
% 23.38/23.58 tff(10201,plain,
% 23.38/23.58 ((mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c))) <=> (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a))),
% 23.38/23.58 inference(monotonicity,[status(thm)],[10200])).
% 23.38/23.58 tff(10202,plain,
% 23.38/23.58 ((mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a)) <=> (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)))),
% 23.38/23.58 inference(symmetry,[status(thm)],[10201])).
% 23.38/23.58 tff(10203,plain,
% 23.38/23.58 ((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a))) <=> (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c))))),
% 23.38/23.58 inference(monotonicity,[status(thm)],[10202])).
% 23.38/23.58 tff(10204,plain,
% 23.38/23.58 (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)))),
% 23.38/23.58 inference(modus_ponens,[status(thm)],[10195, 10203])).
% 23.38/23.58 tff(10205,plain,
% 23.38/23.58 (((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, a))))) | (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)))),
% 23.38/23.58 inference(tautology,[status(thm)],[])).
% 23.38/23.58 tff(10206,plain,
% 23.38/23.58 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c))),
% 23.38/23.58 inference(unit_resolution,[status(thm)],[10205, 10197])).
% 23.38/23.58 tff(10207,plain,
% 23.38/23.58 ($false),
% 23.38/23.58 inference(unit_resolution,[status(thm)],[10206, 10204])).
% 23.38/23.58 tff(10208,plain,(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a)), inference(lemma,lemma(discharge,[]))).
% 23.38/23.58 tff(10209,plain,
% 23.38/23.58 ((mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), mult(a, a))) = mult(mult(mult(c, c), rd(mult(b, c), mult(a, c))), mult(a, a))) <=> (mult(mult(mult(c, c), rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), mult(a, a))))),
% 23.38/23.58 inference(commutativity,[status(thm)],[])).
% 23.38/23.58 tff(10210,plain,
% 23.38/23.58 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)), a) = mult(mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))), a)),
% 23.38/23.58 inference(symmetry,[status(thm)],[9752])).
% 23.38/23.58 tff(10211,plain,
% 23.38/23.58 (mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), unit), mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(c, c)), a))),
% 23.38/23.58 inference(symmetry,[status(thm)],[9746])).
% 23.38/23.58 tff(10212,plain,
% 23.38/23.58 ((~![A: $i] : (mult(unit, A) = A)) | (mult(unit, mult(mult(b, c), mult(a, c))) = mult(mult(b, c), mult(a, c)))),
% 23.38/23.58 inference(quant_inst,[status(thm)],[])).
% 23.38/23.58 tff(10213,plain,
% 23.38/23.58 (mult(unit, mult(mult(b, c), mult(a, c))) = mult(mult(b, c), mult(a, c))),
% 23.38/23.58 inference(unit_resolution,[status(thm)],[10212, 71])).
% 23.38/23.58 tff(10214,plain,
% 23.38/23.58 (mult(b, mult(mult(unit, mult(a, c)), unit)) = mult(b, mult(a, c))),
% 23.38/23.58 inference(monotonicity,[status(thm)],[5372])).
% 23.38/23.58 tff(10215,plain,
% 23.38/23.58 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(b, unit), mult(a, c)), unit) = mult(b, mult(mult(unit, mult(a, c)), unit)))),
% 23.38/23.58 inference(quant_inst,[status(thm)],[])).
% 23.38/23.58 tff(10216,plain,
% 23.38/23.58 (mult(mult(mult(b, unit), mult(a, c)), unit) = mult(b, mult(mult(unit, mult(a, c)), unit))),
% 23.38/23.58 inference(unit_resolution,[status(thm)],[10215, 56])).
% 23.38/23.58 tff(10217,plain,
% 23.38/23.58 (mult(mult(b, unit), mult(a, c)) = mult(b, mult(a, c))),
% 23.38/23.58 inference(monotonicity,[status(thm)],[182])).
% 23.38/23.58 tff(10218,plain,
% 23.38/23.58 (mult(b, mult(a, c)) = mult(mult(b, unit), mult(a, c))),
% 23.38/23.58 inference(symmetry,[status(thm)],[10217])).
% 23.38/23.58 tff(10219,plain,
% 23.38/23.58 (mult(mult(b, mult(a, c)), unit) = mult(mult(mult(b, unit), mult(a, c)), unit)),
% 23.38/23.58 inference(monotonicity,[status(thm)],[10218])).
% 23.38/23.58 tff(10220,plain,
% 23.38/23.58 (mult(b, mult(c, a)) = mult(b, mult(a, c))),
% 23.38/23.58 inference(monotonicity,[status(thm)],[8215])).
% 23.38/23.58 tff(10221,plain,
% 23.38/23.58 (mult(c, mult(b, mult(c, a))) = mult(c, mult(b, mult(a, c)))),
% 23.38/23.58 inference(monotonicity,[status(thm)],[10220])).
% 23.38/23.58 tff(10222,plain,
% 23.38/23.58 (mult(mult(b, c), mult(c, a)) = mult(mult(b, c), mult(a, c))),
% 23.38/23.58 inference(monotonicity,[status(thm)],[8215])).
% 23.38/23.58 tff(10223,plain,
% 23.38/23.58 (mult(mult(c, b), mult(c, a)) = mult(mult(c, b), mult(a, c))),
% 23.38/23.58 inference(transitivity,[status(thm)],[2231, 10222, 2742])).
% 23.38/23.58 tff(10224,plain,
% 23.38/23.58 ((mult(mult(c, b), mult(c, a)) = mult(c, mult(b, mult(c, a)))) <=> (mult(mult(c, b), mult(a, c)) = mult(c, mult(b, mult(a, c))))),
% 23.38/23.58 inference(monotonicity,[status(thm)],[10223, 10221])).
% 23.38/23.58 tff(10225,plain,
% 23.38/23.58 (mult(mult(c, b), mult(a, c)) = mult(c, mult(b, mult(a, c)))),
% 23.38/23.58 inference(modus_ponens,[status(thm)],[6922, 10224])).
% 23.38/23.58 tff(10226,plain,
% 23.38/23.58 (mult(c, mult(mult(a, c), a)) = mult(mult(mult(a, c), unit), mult(a, c))),
% 23.38/23.58 inference(transitivity,[status(thm)],[2562, 6842, 9744, 9736, 2504])).
% 23.38/23.58 tff(10227,plain,
% 23.38/23.58 (mult(rd(mult(b, c), mult(a, c)), mult(c, mult(mult(a, c), a))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), unit), mult(a, c)))),
% 23.38/23.58 inference(monotonicity,[status(thm)],[10226])).
% 23.38/23.58 tff(10228,assumption,(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(mult(a, c), a)))), introduced(assumption)).
% 23.38/23.58 tff(10229,plain,
% 23.38/23.58 (mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a))),
% 23.38/23.58 inference(monotonicity,[status(thm)],[9898])).
% 23.38/23.58 tff(10230,assumption,(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))), introduced(assumption)).
% 23.38/23.58 tff(10231,plain,
% 23.38/23.58 (mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a))),
% 23.38/23.58 inference(symmetry,[status(thm)],[10230])).
% 23.38/23.58 tff(10232,plain,
% 23.38/23.58 (mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) = mult(c, mult(b, mult(a, c)))),
% 23.38/23.58 inference(transitivity,[status(thm)],[10231, 10229, 10228, 10227, 2502, 2499, 2742, 10225])).
% 23.38/23.58 tff(10233,plain,
% 23.38/23.58 (ld(c, mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) = ld(c, mult(c, mult(b, mult(a, c))))),
% 23.38/23.58 inference(monotonicity,[status(thm)],[10232])).
% 23.38/23.58 tff(10234,plain,
% 23.38/23.58 (mult(mult(rd(mult(b, c), mult(a, c)), a), a) = mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)),
% 23.38/23.58 inference(monotonicity,[status(thm)],[9462])).
% 23.38/23.58 tff(10235,plain,
% 23.38/23.58 (mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), a)),
% 23.38/23.58 inference(symmetry,[status(thm)],[10234])).
% 23.38/23.58 tff(10236,plain,
% 23.38/23.58 (mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), c) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c)),
% 23.38/23.58 inference(monotonicity,[status(thm)],[10235])).
% 23.38/23.58 tff(10237,plain,
% 23.38/23.58 (mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), c) = mult(b, mult(a, c))),
% 23.38/23.58 inference(transitivity,[status(thm)],[10236, 5793, 1168, 6930, 10233, 5658])).
% 23.38/23.58 tff(10238,plain,
% 23.38/23.58 (mult(mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), c), unit) = mult(mult(b, mult(a, c)), unit)),
% 23.38/23.58 inference(monotonicity,[status(thm)],[10237])).
% 23.38/23.58 tff(10239,plain,
% 23.38/23.58 (mult(mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), c), unit) = mult(b, mult(a, c))),
% 23.38/23.58 inference(transitivity,[status(thm)],[10238, 10219, 10216, 10214])).
% 23.38/23.58 tff(10240,plain,
% 23.38/23.58 (mult(mult(mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), c), unit), c) = mult(mult(b, mult(a, c)), c)),
% 23.38/23.58 inference(monotonicity,[status(thm)],[10239])).
% 23.38/23.58 tff(10241,plain,
% 23.38/23.58 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), c), unit), c) = mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), mult(mult(c, unit), c)))),
% 23.38/23.58 inference(quant_inst,[status(thm)],[])).
% 23.38/23.58 tff(10242,plain,
% 23.38/23.58 (mult(mult(mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), c), unit), c) = mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), mult(mult(c, unit), c))),
% 23.38/23.58 inference(unit_resolution,[status(thm)],[10241, 56])).
% 23.38/23.58 tff(10243,plain,
% 23.38/23.58 (mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), mult(mult(c, unit), c)) = mult(mult(mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), c), unit), c)),
% 23.38/23.58 inference(symmetry,[status(thm)],[10242])).
% 23.38/23.58 tff(10244,plain,
% 23.38/23.58 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), mult(c, c)) = mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), mult(mult(c, unit), c))),
% 23.38/23.58 inference(monotonicity,[status(thm)],[10234, 2617])).
% 23.38/23.58 tff(10245,plain,
% 23.38/23.58 (mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), mult(c, c)) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), mult(c, c))),
% 23.38/23.58 inference(monotonicity,[status(thm)],[10235])).
% 23.38/23.58 tff(10246,plain,
% 23.38/23.58 (mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), mult(c, c)) = mult(mult(b, c), mult(a, c))),
% 23.38/23.58 inference(transitivity,[status(thm)],[10245, 10244, 10243, 10240, 5435])).
% 23.38/23.58 tff(10247,plain,
% 23.38/23.58 (mult(unit, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), mult(c, c))) = mult(unit, mult(mult(b, c), mult(a, c)))),
% 23.38/23.58 inference(monotonicity,[status(thm)],[10246])).
% 23.38/23.58 tff(10248,plain,
% 23.38/23.58 (mult(unit, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), mult(c, c))) = mult(mult(mult(c, c), rd(mult(b, c), mult(a, c))), mult(a, a))),
% 23.38/23.58 inference(transitivity,[status(thm)],[10247, 10213, 5386, 2501, 10211, 4661, 10210, 9975, 9955, 9953, 9951])).
% 23.38/23.58 tff(10249,plain,
% 23.38/23.58 (mult(mult(mult(unit, c), unit), c) = mult(c, c)),
% 23.38/23.58 inference(monotonicity,[status(thm)],[78])).
% 23.38/23.58 tff(10250,plain,
% 23.38/23.58 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(unit, c), unit), c) = mult(unit, mult(mult(c, unit), c)))),
% 23.38/23.58 inference(quant_inst,[status(thm)],[])).
% 23.38/23.58 tff(10251,plain,
% 23.38/23.58 (mult(mult(mult(unit, c), unit), c) = mult(unit, mult(mult(c, unit), c))),
% 23.38/23.58 inference(unit_resolution,[status(thm)],[10250, 56])).
% 23.38/23.58 tff(10252,plain,
% 23.38/23.58 (mult(unit, mult(mult(c, unit), c)) = mult(mult(mult(unit, c), unit), c)),
% 23.38/23.58 inference(symmetry,[status(thm)],[10251])).
% 23.38/23.58 tff(10253,plain,
% 23.38/23.58 (mult(unit, mult(c, c)) = mult(unit, mult(mult(c, unit), c))),
% 23.38/23.58 inference(monotonicity,[status(thm)],[2617])).
% 23.38/23.58 tff(10254,plain,
% 23.38/23.58 (mult(unit, mult(c, c)) = mult(c, c)),
% 23.38/23.58 inference(transitivity,[status(thm)],[10253, 10252, 10249])).
% 23.38/23.58 tff(10255,plain,
% 23.38/23.58 (mult(mult(unit, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)) = mult(mult(c, c), mult(mult(rd(mult(b, c), mult(a, c)), a), a))),
% 23.38/23.58 inference(monotonicity,[status(thm)],[10254, 10235])).
% 23.38/23.58 tff(10256,assumption,(~(mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c)) = mult(unit, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), mult(c, c))))), introduced(assumption)).
% 23.38/23.58 tff(10257,plain,
% 23.38/23.58 (((~(mult(mult(unit, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)) = mult(unit, mult(mult(c, c), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a))))) | (~(mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c)) = mult(unit, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), mult(c, c)))))) | (mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c)) = mult(unit, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), mult(c, c))))),
% 23.38/23.58 inference(tautology,[status(thm)],[])).
% 23.38/23.58 tff(10258,plain,
% 23.38/23.58 ((~(mult(mult(unit, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)) = mult(unit, mult(mult(c, c), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a))))) | (~(mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c)) = mult(unit, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), mult(c, c)))))),
% 23.38/23.58 inference(unit_resolution,[status(thm)],[10257, 10256])).
% 23.38/23.58 tff(10259,plain,
% 23.38/23.58 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(unit, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)) = mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c)))) | (~(mult(unit, mult(mult(c, c), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a))) = mult(unit, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), mult(c, c))))))) | (~((~(mult(mult(unit, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)) = mult(unit, mult(mult(c, c), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a))))) | (~(mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c)) = mult(unit, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), mult(c, c))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(unit, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)) = mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c)))) | (~(mult(unit, mult(mult(c, c), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a))) = mult(unit, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), mult(c, c))))))) | (~((~(mult(mult(unit, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)) = mult(unit, mult(mult(c, c), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a))))) | (~(mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c)) = mult(unit, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), mult(c, c))))))))),
% 23.38/23.59 inference(rewrite,[status(thm)],[])).
% 23.38/23.59 tff(10260,plain,
% 23.38/23.59 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(unit, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)) = mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c)))) | (~(mult(unit, mult(mult(c, c), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a))) = mult(unit, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), mult(c, c))))))) | (~((~(mult(mult(unit, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)) = mult(unit, mult(mult(c, c), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a))))) | (~(mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c)) = mult(unit, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), mult(c, c))))))))),
% 23.38/23.59 inference(quant_inst,[status(thm)],[])).
% 23.38/23.59 tff(10261,plain,
% 23.38/23.59 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(unit, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)) = mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c)))) | (~(mult(unit, mult(mult(c, c), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a))) = mult(unit, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), mult(c, c))))))) | (~((~(mult(mult(unit, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)) = mult(unit, mult(mult(c, c), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a))))) | (~(mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c)) = mult(unit, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), mult(c, c)))))))),
% 23.38/23.59 inference(modus_ponens,[status(thm)],[10260, 10259])).
% 23.38/23.59 tff(10262,plain,
% 23.38/23.59 ((~((~(mult(mult(unit, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)) = mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c)))) | (~(mult(unit, mult(mult(c, c), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a))) = mult(unit, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), mult(c, c))))))) | (~((~(mult(mult(unit, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)) = mult(unit, mult(mult(c, c), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a))))) | (~(mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c)) = mult(unit, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), mult(c, c)))))))),
% 23.38/23.59 inference(unit_resolution,[status(thm)],[10261, 27])).
% 23.38/23.59 tff(10263,plain,
% 23.38/23.59 (~((~(mult(mult(unit, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)) = mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c)))) | (~(mult(unit, mult(mult(c, c), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a))) = mult(unit, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), mult(c, c))))))),
% 23.38/23.59 inference(unit_resolution,[status(thm)],[10262, 10258])).
% 23.38/23.59 tff(10264,plain,
% 23.38/23.59 (((~(mult(mult(unit, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)) = mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c)))) | (~(mult(unit, mult(mult(c, c), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a))) = mult(unit, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), mult(c, c)))))) | (mult(mult(unit, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)) = mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c)))),
% 23.38/23.59 inference(tautology,[status(thm)],[])).
% 23.38/23.59 tff(10265,plain,
% 23.38/23.59 (mult(mult(unit, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)) = mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c))),
% 23.38/23.59 inference(unit_resolution,[status(thm)],[10264, 10263])).
% 23.38/23.59 tff(10266,plain,
% 23.38/23.59 (mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c)) = mult(mult(unit, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a))),
% 23.38/23.59 inference(symmetry,[status(thm)],[10265])).
% 23.38/23.59 tff(10267,plain,
% 23.38/23.59 (mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c)) = mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), mult(a, a)))),
% 23.38/23.59 inference(transitivity,[status(thm)],[10266, 10255, 9892])).
% 23.38/23.59 tff(10268,plain,
% 23.38/23.59 ((mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c)) = mult(unit, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), mult(c, c)))) <=> (mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), mult(a, a))) = mult(mult(mult(c, c), rd(mult(b, c), mult(a, c))), mult(a, a)))),
% 23.38/23.59 inference(monotonicity,[status(thm)],[10267, 10248])).
% 23.38/23.59 tff(10269,plain,
% 23.38/23.59 ((mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c)) = mult(unit, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), mult(c, c)))) <=> (mult(mult(mult(c, c), rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), mult(a, a))))),
% 23.38/23.59 inference(transitivity,[status(thm)],[10268, 10209])).
% 23.38/23.59 tff(10270,plain,
% 23.38/23.59 ((mult(mult(mult(c, c), rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), mult(a, a)))) <=> (mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c)) = mult(unit, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), mult(c, c))))),
% 23.38/23.59 inference(symmetry,[status(thm)],[10269])).
% 23.38/23.59 tff(10271,assumption,(mult(mult(mult(c, c), rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), mult(a, a)))), introduced(assumption)).
% 23.38/23.59 tff(10272,plain,
% 23.38/23.59 (mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c)) = mult(unit, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), mult(c, c)))),
% 23.38/23.59 inference(modus_ponens,[status(thm)],[10271, 10270])).
% 23.38/23.59 tff(10273,plain,
% 23.38/23.59 ($false),
% 23.38/23.59 inference(unit_resolution,[status(thm)],[10256, 10272])).
% 23.38/23.59 tff(10274,plain,((mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c)) = mult(unit, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), mult(c, c)))) | (~(mult(mult(mult(c, c), rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), mult(a, a))))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(mult(a, c), a)))))), inference(lemma,lemma(discharge,[]))).
% 23.38/23.59 tff(10275,plain,
% 23.38/23.59 (mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c)) = mult(unit, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), mult(c, c)))),
% 23.38/23.59 inference(unit_resolution,[status(thm)],[10274, 10126, 10208, 10194, 9702])).
% 23.38/23.59 tff(10276,plain,
% 23.38/23.59 (mult(mult(unit, mult(mult(rd(mult(b, c), mult(a, c)), a), a)), mult(c, c)) = mult(unit, mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), mult(c, c)))),
% 23.38/23.59 inference(modus_ponens,[status(thm)],[10275, 10163])).
% 23.38/23.59 tff(10277,plain,
% 23.38/23.59 (mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c)) = mult(mult(unit, mult(mult(rd(mult(b, c), mult(a, c)), a), a)), mult(c, c))),
% 23.38/23.59 inference(symmetry,[status(thm)],[10161])).
% 23.38/23.59 tff(10278,plain,
% 23.38/23.59 (mult(mult(rd(mult(b, c), mult(a, c)), a), a) = mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)),
% 23.38/23.59 inference(symmetry,[status(thm)],[10151])).
% 23.38/23.59 tff(10279,plain,
% 23.38/23.59 ((~![A: $i] : (mult(unit, A) = A)) | (mult(unit, mult(mult(rd(mult(b, c), mult(a, c)), a), a)) = mult(mult(rd(mult(b, c), mult(a, c)), a), a))),
% 23.38/23.59 inference(quant_inst,[status(thm)],[])).
% 23.38/23.59 tff(10280,plain,
% 23.38/23.59 (mult(unit, mult(mult(rd(mult(b, c), mult(a, c)), a), a)) = mult(mult(rd(mult(b, c), mult(a, c)), a), a)),
% 23.38/23.59 inference(unit_resolution,[status(thm)],[10279, 71])).
% 23.38/23.59 tff(10281,plain,
% 23.38/23.59 (mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)) = mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)),
% 23.38/23.59 inference(transitivity,[status(thm)],[10156, 10158, 10280, 10278])).
% 23.38/23.59 tff(10282,plain,
% 23.38/23.59 (mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c)) = mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), mult(c, c))),
% 23.38/23.59 inference(monotonicity,[status(thm)],[10281])).
% 23.38/23.59 tff(10283,plain,
% 23.38/23.59 (mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), mult(c, c)) = mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c))),
% 23.38/23.59 inference(symmetry,[status(thm)],[10282])).
% 23.38/23.59 tff(10284,plain,
% 23.38/23.59 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), mult(c, c)) = mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), mult(c, c))),
% 23.38/23.59 inference(symmetry,[status(thm)],[10152])).
% 23.38/23.59 tff(10285,plain,
% 23.38/23.59 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), mult(c, c)) = mult(unit, mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), mult(c, c)))),
% 23.38/23.59 inference(transitivity,[status(thm)],[10284, 10283, 10277, 10276])).
% 23.38/23.59 tff(10286,plain,
% 23.38/23.59 ((mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), mult(c, c)) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)), a)) <=> (mult(unit, mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), mult(c, c))) = mult(unit, mult(mult(c, c), mult(mult(rd(mult(b, c), mult(a, c)), a), a))))),
% 23.38/23.59 inference(monotonicity,[status(thm)],[10285, 10150])).
% 23.38/23.59 tff(10287,plain,
% 23.38/23.59 ((mult(unit, mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), mult(c, c))) = mult(unit, mult(mult(c, c), mult(mult(rd(mult(b, c), mult(a, c)), a), a)))) <=> (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), mult(c, c)) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)), a))),
% 23.38/23.59 inference(symmetry,[status(thm)],[10286])).
% 23.38/23.59 tff(10288,plain,
% 23.38/23.59 (mult(mult(unit, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)) = mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), mult(a, a)))),
% 23.38/23.59 inference(monotonicity,[status(thm)],[10254, 10155])).
% 23.38/23.59 tff(10289,plain,
% 23.38/23.59 (mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), mult(a, a))) = mult(mult(unit, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a))),
% 23.38/23.59 inference(symmetry,[status(thm)],[10288])).
% 23.38/23.59 tff(10290,plain,
% 23.38/23.59 (mult(mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))), a) = mult(mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), a)), a)),
% 23.38/23.59 inference(symmetry,[status(thm)],[9889])).
% 23.38/23.59 tff(10291,plain,
% 23.38/23.59 (mult(unit, mult(mult(b, c), mult(a, c))) = mult(mult(unit, mult(b, c)), mult(a, c))),
% 23.38/23.59 inference(symmetry,[status(thm)],[10149])).
% 23.38/23.59 tff(10292,plain,
% 23.38/23.59 (mult(unit, mult(mult(c, c), mult(mult(rd(mult(b, c), mult(a, c)), a), a))) = mult(mult(unit, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a))),
% 23.38/23.59 inference(transitivity,[status(thm)],[10130, 10291, 10137, 5386, 2501, 10211, 4661, 10210, 10290, 10127, 9892, 10289])).
% 23.38/23.59 tff(10293,plain,
% 23.38/23.59 (mult(unit, mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), mult(c, c))) = mult(mult(unit, mult(mult(rd(mult(b, c), mult(a, c)), a), a)), mult(c, c))),
% 23.38/23.59 inference(symmetry,[status(thm)],[10276])).
% 23.38/23.59 tff(10294,plain,
% 23.38/23.59 (mult(unit, mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), mult(c, c))) = mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c))),
% 23.38/23.59 inference(transitivity,[status(thm)],[10293, 10161])).
% 23.38/23.59 tff(10295,plain,
% 23.38/23.59 ((mult(unit, mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), mult(c, c))) = mult(unit, mult(mult(c, c), mult(mult(rd(mult(b, c), mult(a, c)), a), a)))) <=> (mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c)) = mult(mult(unit, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)))),
% 23.38/23.59 inference(monotonicity,[status(thm)],[10294, 10292])).
% 23.38/23.59 tff(10296,plain,
% 23.38/23.59 ((mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c)) = mult(mult(unit, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a))) <=> (mult(unit, mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), mult(c, c))) = mult(unit, mult(mult(c, c), mult(mult(rd(mult(b, c), mult(a, c)), a), a))))),
% 23.38/23.59 inference(symmetry,[status(thm)],[10295])).
% 23.38/23.59 tff(10297,plain,
% 23.38/23.59 ((mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c)) = mult(mult(unit, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a))) <=> (mult(mult(unit, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)) = mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c)))),
% 23.38/23.59 inference(commutativity,[status(thm)],[])).
% 23.38/23.59 tff(10298,plain,
% 23.38/23.59 ((mult(mult(unit, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)) = mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c))) <=> (mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c)) = mult(mult(unit, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)))),
% 23.38/23.59 inference(symmetry,[status(thm)],[10297])).
% 23.38/23.59 tff(10299,assumption,(~(mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c)) = mult(mult(unit, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)))), introduced(assumption)).
% 23.38/23.59 tff(10300,plain,
% 23.38/23.59 (((~(mult(unit, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), mult(c, c))) = mult(unit, mult(mult(c, c), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a))))) | (~(mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c)) = mult(mult(unit, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a))))) | (mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c)) = mult(mult(unit, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)))),
% 23.38/23.59 inference(tautology,[status(thm)],[])).
% 23.38/23.59 tff(10301,plain,
% 23.38/23.59 ((~(mult(unit, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), mult(c, c))) = mult(unit, mult(mult(c, c), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a))))) | (~(mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c)) = mult(mult(unit, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a))))),
% 23.38/23.59 inference(unit_resolution,[status(thm)],[10300, 10299])).
% 23.38/23.59 tff(10302,plain,
% 23.38/23.59 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(unit, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), mult(c, c))) = mult(unit, mult(mult(c, c), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a))))) | (~(mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c)) = mult(mult(unit, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)))))) | (~((~(mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c)) = mult(unit, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), mult(c, c))))) | (~(mult(mult(unit, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)) = mult(unit, mult(mult(c, c), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(unit, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), mult(c, c))) = mult(unit, mult(mult(c, c), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a))))) | (~(mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c)) = mult(mult(unit, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)))))) | (~((~(mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c)) = mult(unit, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), mult(c, c))))) | (~(mult(mult(unit, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)) = mult(unit, mult(mult(c, c), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a))))))))),
% 23.43/23.60 inference(rewrite,[status(thm)],[])).
% 23.43/23.60 tff(10303,plain,
% 23.43/23.60 (((~((~(mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c)) = mult(mult(unit, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)))) | (~(mult(unit, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), mult(c, c))) = mult(unit, mult(mult(c, c), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a))))))) | (~((~(mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c)) = mult(unit, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), mult(c, c))))) | (~(mult(mult(unit, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)) = mult(unit, mult(mult(c, c), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)))))))) <=> ((~((~(mult(unit, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), mult(c, c))) = mult(unit, mult(mult(c, c), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a))))) | (~(mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c)) = mult(mult(unit, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)))))) | (~((~(mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c)) = mult(unit, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), mult(c, c))))) | (~(mult(mult(unit, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)) = mult(unit, mult(mult(c, c), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a))))))))),
% 23.43/23.60 inference(rewrite,[status(thm)],[])).
% 23.43/23.60 tff(10304,plain,
% 23.43/23.60 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c)) = mult(mult(unit, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)))) | (~(mult(unit, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), mult(c, c))) = mult(unit, mult(mult(c, c), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a))))))) | (~((~(mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c)) = mult(unit, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), mult(c, c))))) | (~(mult(mult(unit, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)) = mult(unit, mult(mult(c, c), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(unit, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), mult(c, c))) = mult(unit, mult(mult(c, c), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a))))) | (~(mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c)) = mult(mult(unit, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)))))) | (~((~(mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c)) = mult(unit, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), mult(c, c))))) | (~(mult(mult(unit, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)) = mult(unit, mult(mult(c, c), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)))))))))),
% 23.43/23.60 inference(monotonicity,[status(thm)],[10303])).
% 23.43/23.60 tff(10305,plain,
% 23.43/23.60 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c)) = mult(mult(unit, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)))) | (~(mult(unit, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), mult(c, c))) = mult(unit, mult(mult(c, c), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a))))))) | (~((~(mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c)) = mult(unit, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), mult(c, c))))) | (~(mult(mult(unit, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)) = mult(unit, mult(mult(c, c), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(unit, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), mult(c, c))) = mult(unit, mult(mult(c, c), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a))))) | (~(mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c)) = mult(mult(unit, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)))))) | (~((~(mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c)) = mult(unit, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), mult(c, c))))) | (~(mult(mult(unit, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)) = mult(unit, mult(mult(c, c), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a))))))))),
% 23.43/23.60 inference(transitivity,[status(thm)],[10304, 10302])).
% 23.43/23.60 tff(10306,plain,
% 23.43/23.60 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c)) = mult(mult(unit, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)))) | (~(mult(unit, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), mult(c, c))) = mult(unit, mult(mult(c, c), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a))))))) | (~((~(mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c)) = mult(unit, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), mult(c, c))))) | (~(mult(mult(unit, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)) = mult(unit, mult(mult(c, c), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a))))))))),
% 23.43/23.60 inference(quant_inst,[status(thm)],[])).
% 23.43/23.60 tff(10307,plain,
% 23.43/23.60 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(unit, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), mult(c, c))) = mult(unit, mult(mult(c, c), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a))))) | (~(mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c)) = mult(mult(unit, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)))))) | (~((~(mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c)) = mult(unit, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), mult(c, c))))) | (~(mult(mult(unit, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)) = mult(unit, mult(mult(c, c), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)))))))),
% 23.43/23.60 inference(modus_ponens,[status(thm)],[10306, 10305])).
% 23.43/23.60 tff(10308,plain,
% 23.43/23.60 ((~((~(mult(unit, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), mult(c, c))) = mult(unit, mult(mult(c, c), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a))))) | (~(mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c)) = mult(mult(unit, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)))))) | (~((~(mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c)) = mult(unit, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), mult(c, c))))) | (~(mult(mult(unit, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)) = mult(unit, mult(mult(c, c), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)))))))),
% 23.43/23.60 inference(unit_resolution,[status(thm)],[10307, 27])).
% 23.43/23.60 tff(10309,plain,
% 23.43/23.60 (~((~(mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c)) = mult(unit, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), mult(c, c))))) | (~(mult(mult(unit, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)) = mult(unit, mult(mult(c, c), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a))))))),
% 23.43/23.60 inference(unit_resolution,[status(thm)],[10308, 10301])).
% 23.43/23.60 tff(10310,plain,
% 23.43/23.60 (((~(mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c)) = mult(unit, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), mult(c, c))))) | (~(mult(mult(unit, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)) = mult(unit, mult(mult(c, c), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)))))) | (mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c)) = mult(unit, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), mult(c, c))))),
% 23.43/23.60 inference(tautology,[status(thm)],[])).
% 23.43/23.60 tff(10311,plain,
% 23.43/23.60 (mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c)) = mult(unit, mult(mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a), mult(c, c)))),
% 23.43/23.60 inference(unit_resolution,[status(thm)],[10310, 10309])).
% 23.43/23.60 tff(10312,plain,
% 23.43/23.60 (mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c)) = mult(mult(mult(c, c), rd(mult(b, c), mult(a, c))), mult(a, a))),
% 23.43/23.60 inference(transitivity,[status(thm)],[10311, 10247, 10213, 5386, 2501, 10211, 4661, 10210, 9975, 9955, 9953, 9951])).
% 23.43/23.60 tff(10313,plain,
% 23.43/23.60 (mult(mult(unit, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)) = mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), mult(a, a)))),
% 23.43/23.60 inference(transitivity,[status(thm)],[10255, 9892])).
% 23.43/23.60 tff(10314,plain,
% 23.43/23.60 ((mult(mult(unit, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)) = mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c))) <=> (mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), mult(a, a))) = mult(mult(mult(c, c), rd(mult(b, c), mult(a, c))), mult(a, a)))),
% 23.43/23.60 inference(monotonicity,[status(thm)],[10313, 10312])).
% 23.43/23.61 tff(10315,plain,
% 23.43/23.61 ((mult(mult(unit, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)) = mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c))) <=> (mult(mult(mult(c, c), rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), mult(a, a))))),
% 23.43/23.61 inference(transitivity,[status(thm)],[10314, 10209])).
% 23.43/23.61 tff(10316,plain,
% 23.43/23.61 ((mult(mult(mult(c, c), rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), mult(a, a)))) <=> (mult(mult(unit, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)) = mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c)))),
% 23.43/23.61 inference(symmetry,[status(thm)],[10315])).
% 23.43/23.61 tff(10317,plain,
% 23.43/23.61 ((mult(mult(mult(c, c), rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), mult(a, a)))) <=> (mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c)) = mult(mult(unit, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)))),
% 23.43/23.61 inference(transitivity,[status(thm)],[10316, 10298])).
% 23.43/23.61 tff(10318,plain,
% 23.43/23.61 (mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c)) = mult(mult(unit, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a))),
% 23.43/23.61 inference(modus_ponens,[status(thm)],[10271, 10317])).
% 23.43/23.61 tff(10319,plain,
% 23.43/23.61 ($false),
% 23.43/23.61 inference(unit_resolution,[status(thm)],[10299, 10318])).
% 23.43/23.61 tff(10320,plain,((mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c)) = mult(mult(unit, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a))) | (~(mult(mult(mult(c, c), rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(mult(c, c), mult(rd(mult(b, c), mult(a, c)), mult(a, a))))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(mult(a, c), a)))))), inference(lemma,lemma(discharge,[]))).
% 23.43/23.61 tff(10321,plain,
% 23.43/23.61 (mult(mult(unit, mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a)), mult(c, c)) = mult(mult(unit, mult(c, c)), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), a))),
% 23.43/23.61 inference(unit_resolution,[status(thm)],[10320, 10126, 10208, 10194, 9702])).
% 23.43/23.61 tff(10322,plain,
% 23.43/23.61 (mult(unit, mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), mult(c, c))) = mult(unit, mult(mult(c, c), mult(mult(rd(mult(b, c), mult(a, c)), a), a)))),
% 23.43/23.61 inference(modus_ponens,[status(thm)],[10321, 10296])).
% 23.43/23.61 tff(10323,plain,
% 23.43/23.61 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), mult(c, c)) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)), a)),
% 23.43/23.61 inference(modus_ponens,[status(thm)],[10322, 10287])).
% 23.43/23.61 tff(10324,plain,
% 23.43/23.61 ((~(mult(b, c) = mult(mult(a, c), rd(mult(b, c), mult(a, c))))) <=> (~(mult(mult(unit, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(a, c))))),
% 23.43/23.61 inference(monotonicity,[status(thm)],[9823])).
% 23.43/23.61 tff(10325,plain,
% 23.43/23.61 (~(mult(mult(unit, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 23.43/23.61 inference(modus_ponens,[status(thm)],[9836, 10324])).
% 23.43/23.61 tff(10326,plain,
% 23.43/23.61 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(b, mult(mult(a, c), a)), mult(mult(a, c), a)) = b)),
% 23.43/23.61 inference(quant_inst,[status(thm)],[])).
% 23.43/23.61 tff(10327,plain,
% 23.43/23.61 (rd(mult(b, mult(mult(a, c), a)), mult(mult(a, c), a)) = b),
% 23.43/23.61 inference(unit_resolution,[status(thm)],[10326, 168])).
% 23.43/23.61 tff(10328,plain,
% 23.43/23.61 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(b, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(b, mult(mult(a, c), a)))),
% 23.43/23.61 inference(quant_inst,[status(thm)],[])).
% 23.43/23.61 tff(10329,plain,
% 23.43/23.61 (rd(mult(mult(b, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(b, mult(mult(a, c), a))),
% 23.43/23.61 inference(unit_resolution,[status(thm)],[10328, 168])).
% 23.43/23.61 tff(10330,assumption,(mult(mult(mult(mult(a, b), c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c))))), introduced(assumption)).
% 23.43/23.61 tff(10331,plain,
% 23.43/23.61 (mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(mult(a, b), c), a), rd(mult(b, c), mult(a, c)))),
% 23.43/23.61 inference(symmetry,[status(thm)],[10330])).
% 23.43/23.61 tff(10332,plain,
% 23.43/23.61 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(a, b), mult(mult(a, b), mult(mult(a, b), c))) = mult(mult(a, b), c))),
% 23.43/23.61 inference(quant_inst,[status(thm)],[])).
% 23.43/23.61 tff(10333,plain,
% 23.43/23.61 (ld(mult(a, b), mult(mult(a, b), mult(mult(a, b), c))) = mult(mult(a, b), c)),
% 23.43/23.61 inference(unit_resolution,[status(thm)],[10332, 7])).
% 23.43/23.61 tff(10334,plain,
% 23.43/23.61 (mult(mult(a, b), mult(mult(a, c), b)) = mult(mult(a, b), mult(mult(a, b), c))),
% 23.43/23.61 inference(monotonicity,[status(thm)],[161])).
% 23.43/23.61 tff(10335,assumption,(mult(mult(a, b), mult(b, mult(a, c))) = mult(mult(a, b), mult(mult(a, c), b))), introduced(assumption)).
% 23.43/23.61 tff(10336,plain,
% 23.43/23.61 (mult(mult(a, b), mult(b, mult(a, c))) = mult(mult(a, b), mult(mult(a, b), c))),
% 23.43/23.61 inference(transitivity,[status(thm)],[10335, 10334])).
% 23.43/23.61 tff(10337,plain,
% 23.43/23.61 (ld(mult(a, b), mult(mult(a, b), mult(b, mult(a, c)))) = ld(mult(a, b), mult(mult(a, b), mult(mult(a, b), c)))),
% 23.43/23.61 inference(monotonicity,[status(thm)],[10336])).
% 23.43/23.61 tff(10338,plain,
% 23.43/23.61 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(a, b), mult(mult(a, b), mult(b, mult(a, c)))) = mult(b, mult(a, c)))),
% 23.43/23.61 inference(quant_inst,[status(thm)],[])).
% 23.43/23.61 tff(10339,plain,
% 23.43/23.61 (ld(mult(a, b), mult(mult(a, b), mult(b, mult(a, c)))) = mult(b, mult(a, c))),
% 23.43/23.61 inference(unit_resolution,[status(thm)],[10338, 7])).
% 23.43/23.61 tff(10340,plain,
% 23.43/23.61 (mult(b, mult(a, c)) = ld(mult(a, b), mult(mult(a, b), mult(b, mult(a, c))))),
% 23.43/23.61 inference(symmetry,[status(thm)],[10339])).
% 23.43/23.61 tff(10341,plain,
% 23.43/23.61 (mult(b, mult(a, c)) = mult(mult(a, c), b)),
% 23.43/23.61 inference(transitivity,[status(thm)],[10340, 10337, 10333, 227])).
% 23.43/23.61 tff(10342,plain,
% 23.43/23.61 (mult(mult(b, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, c), b), mult(a, rd(mult(b, c), mult(a, c))))),
% 23.43/23.61 inference(monotonicity,[status(thm)],[10341])).
% 23.43/23.61 tff(10343,plain,
% 23.43/23.61 (mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))),
% 23.43/23.61 inference(symmetry,[status(thm)],[8169])).
% 23.43/23.61 tff(10344,plain,
% 23.43/23.61 (mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c))),
% 23.43/23.61 inference(unit_resolution,[status(thm)],[9500, 2187, 299])).
% 23.43/23.61 tff(10345,plain,
% 23.43/23.61 (mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))),
% 23.43/23.61 inference(transitivity,[status(thm)],[10344, 8198, 4676, 10343, 5709])).
% 23.43/23.61 tff(10346,plain,
% 23.43/23.61 (mult(b, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)) = mult(b, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.43/23.61 inference(monotonicity,[status(thm)],[10345])).
% 23.43/23.61 tff(10347,plain,
% 23.43/23.61 (mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c)) = mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)),
% 23.43/23.61 inference(symmetry,[status(thm)],[10344])).
% 23.43/23.61 tff(10348,plain,
% 23.43/23.61 (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c))),
% 23.43/23.61 inference(symmetry,[status(thm)],[8198])).
% 23.43/23.61 tff(10349,plain,
% 23.43/23.61 (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)),
% 23.43/23.61 inference(transitivity,[status(thm)],[8169, 299, 10348, 10347])).
% 23.43/23.61 tff(10350,plain,
% 23.43/23.61 (mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))) = mult(b, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c))),
% 23.43/23.61 inference(monotonicity,[status(thm)],[10349])).
% 23.43/23.61 tff(10351,assumption,(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), mult(c, c)) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)), a)), introduced(assumption)).
% 23.43/23.61 tff(10352,plain,
% 23.43/23.61 (ld(mult(a, b), mult(mult(a, b), mult(mult(a, b), c))) = ld(mult(a, b), mult(mult(a, b), mult(b, mult(a, c))))),
% 23.43/23.61 inference(symmetry,[status(thm)],[10337])).
% 23.43/23.61 tff(10353,plain,
% 23.43/23.61 (mult(mult(a, b), c) = ld(mult(a, b), mult(mult(a, b), mult(mult(a, b), c)))),
% 23.43/23.61 inference(symmetry,[status(thm)],[10333])).
% 23.43/23.61 tff(10354,plain,
% 23.43/23.61 (mult(mult(a, c), b) = mult(b, mult(a, c))),
% 23.43/23.61 inference(transitivity,[status(thm)],[161, 10353, 10352, 10339])).
% 23.43/23.61 tff(10355,plain,
% 23.43/23.61 (mult(mult(mult(a, c), b), c) = mult(mult(b, mult(a, c)), c)),
% 23.43/23.61 inference(monotonicity,[status(thm)],[10354])).
% 23.43/23.61 tff(10356,plain,
% 23.43/23.61 (mult(mult(b, mult(a, c)), c) = mult(mult(mult(a, c), b), c)),
% 23.43/23.61 inference(symmetry,[status(thm)],[10355])).
% 23.43/23.61 tff(10357,plain,
% 23.43/23.61 (mult(mult(b, c), mult(a, c)) = mult(mult(b, mult(a, c)), c)),
% 23.43/23.61 inference(symmetry,[status(thm)],[5435])).
% 23.43/23.61 tff(10358,plain,
% 23.43/23.61 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), mult(c, c)) = mult(mult(a, b), mult(c, c))),
% 23.43/23.61 inference(transitivity,[status(thm)],[10351, 4660, 9746, 2502, 2499, 10357, 10356, 5913, 5909, 5907])).
% 23.43/23.61 tff(10359,plain,
% 23.43/23.61 (rd(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), mult(c, c)), mult(c, c)) = rd(mult(mult(a, b), mult(c, c)), mult(c, c))),
% 23.43/23.61 inference(monotonicity,[status(thm)],[10358])).
% 23.43/23.61 tff(10360,plain,
% 23.43/23.61 (mult(mult(rd(mult(b, c), mult(a, c)), a), a) = mult(a, b)),
% 23.43/23.61 inference(transitivity,[status(thm)],[6177, 10359, 5978])).
% 23.43/23.61 tff(10361,plain,
% 23.43/23.61 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c) = mult(mult(a, b), c)),
% 23.43/23.61 inference(monotonicity,[status(thm)],[10360])).
% 23.43/23.61 tff(10362,plain,
% 23.43/23.61 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c)),
% 23.43/23.61 inference(symmetry,[status(thm)],[10208])).
% 23.43/23.61 tff(10363,plain,
% 23.43/23.61 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)) = mult(mult(a, b), c)),
% 23.43/23.61 inference(transitivity,[status(thm)],[1169, 10362, 10361])).
% 23.43/23.61 tff(10364,plain,
% 23.43/23.61 (mult(b, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) = mult(mult(unit, b), mult(mult(a, b), c))),
% 23.43/23.61 inference(monotonicity,[status(thm)],[3386, 10363])).
% 23.43/23.61 tff(10365,assumption,(mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))) = mult(b, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))), introduced(assumption)).
% 23.43/23.61 tff(10366,plain,
% 23.43/23.61 (mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))),
% 23.43/23.61 inference(transitivity,[status(thm)],[10344, 8198, 4676, 10343])).
% 23.43/23.61 tff(10367,plain,
% 23.43/23.61 (mult(b, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)) = mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))))),
% 23.43/23.61 inference(monotonicity,[status(thm)],[10366])).
% 23.43/23.61 tff(10368,plain,
% 23.43/23.61 (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)),
% 23.43/23.61 inference(transitivity,[status(thm)],[10348, 10347])).
% 23.43/23.61 tff(10369,plain,
% 23.43/23.61 (mult(b, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))) = mult(b, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c))),
% 23.43/23.61 inference(monotonicity,[status(thm)],[10368])).
% 23.43/23.61 tff(10370,plain,
% 23.43/23.61 (mult(b, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))) = mult(b, mult(mult(a, b), c))),
% 23.43/23.61 inference(transitivity,[status(thm)],[10369, 10367, 10365, 10364, 3388])).
% 23.43/23.61 tff(10371,plain,
% 23.43/23.61 (ld(b, mult(b, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) = ld(b, mult(b, mult(mult(a, b), c)))),
% 23.43/23.61 inference(monotonicity,[status(thm)],[10370])).
% 23.43/23.61 tff(10372,plain,
% 23.43/23.61 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(b, mult(b, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 23.43/23.61 inference(quant_inst,[status(thm)],[])).
% 23.43/23.61 tff(10373,plain,
% 23.43/23.61 (ld(b, mult(b, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 23.43/23.61 inference(unit_resolution,[status(thm)],[10372, 7])).
% 23.43/23.61 tff(10374,plain,
% 23.43/23.61 (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = ld(b, mult(b, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))),
% 23.43/23.61 inference(symmetry,[status(thm)],[10373])).
% 23.43/23.61 tff(10375,plain,
% 23.43/23.61 (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), b)),
% 23.43/23.61 inference(transitivity,[status(thm)],[10374, 10371, 5605, 227])).
% 23.43/23.61 tff(10376,plain,
% 23.43/23.61 (mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))) = mult(c, mult(mult(a, c), b))),
% 23.43/23.61 inference(monotonicity,[status(thm)],[10375])).
% 23.43/23.61 tff(10377,plain,
% 23.43/23.61 (rd(mult(mult(a, c), c), c) = rd(mult(mult(c, a), c), c)),
% 23.43/23.61 inference(symmetry,[status(thm)],[8214])).
% 23.43/23.61 tff(10378,plain,
% 23.43/23.61 (mult(a, c) = rd(mult(mult(a, c), c), c)),
% 23.43/23.61 inference(symmetry,[status(thm)],[2723])).
% 23.43/23.61 tff(10379,plain,
% 23.43/23.61 (mult(a, c) = mult(c, a)),
% 23.43/23.61 inference(transitivity,[status(thm)],[10378, 10377, 2769])).
% 23.43/23.61 tff(10380,plain,
% 23.43/23.61 (mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 23.43/23.61 inference(monotonicity,[status(thm)],[10379])).
% 23.43/23.61 tff(10381,plain,
% 23.43/23.61 (mult(a, mult(c, mult(a, c))) = mult(mult(a, c), mult(a, c))),
% 23.43/23.61 inference(transitivity,[status(thm)],[4714, 4724, 9303, 7903, 7901, 9781, 4662, 9740, 9744, 9736])).
% 23.43/23.61 tff(10382,plain,
% 23.43/23.61 (mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 23.43/23.61 inference(monotonicity,[status(thm)],[10381])).
% 23.43/23.61 tff(10383,plain,
% 23.43/23.61 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)) = mult(mult(a, mult(c, c)), rd(mult(b, c), mult(a, c)))),
% 23.43/23.61 inference(transitivity,[status(thm)],[5943, 5942, 5939, 9754, 9323])).
% 23.43/23.61 tff(10384,plain,
% 23.43/23.61 (mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))))),
% 23.43/23.61 inference(unit_resolution,[status(thm)],[9542, 10383, 2187, 8305, 299])).
% 23.43/23.61 tff(10385,plain,
% 23.43/23.61 (mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c)))),
% 23.43/23.61 inference(symmetry,[status(thm)],[10384])).
% 23.43/23.61 tff(10386,plain,
% 23.43/23.61 (mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(b, c), c))),
% 23.43/23.61 inference(transitivity,[status(thm)],[10385, 10382, 4789, 10380, 6879, 10376, 3190, 3188, 4284, 233, 3139])).
% 23.43/23.61 tff(10387,plain,
% 23.43/23.61 (ld(a, mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))))) = ld(a, mult(a, mult(mult(b, c), c)))),
% 23.43/23.61 inference(monotonicity,[status(thm)],[10386])).
% 23.43/23.61 tff(10388,plain,
% 23.43/23.61 (mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))),
% 23.43/23.61 inference(transitivity,[status(thm)],[6733, 10387, 4537, 4178, 2803, 4536])).
% 23.43/23.61 tff(10389,plain,
% 23.43/23.61 ($false),
% 23.43/23.61 inference(unit_resolution,[status(thm)],[2788, 10388])).
% 23.43/23.61 tff(10390,plain,((~(mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))) = mult(b, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))) | (mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), mult(c, c)) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)), a))) | (~(mult(mult(a, b), mult(b, mult(a, c))) = mult(mult(a, b), mult(mult(a, c), b)))) | (~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))), inference(lemma,lemma(discharge,[]))).
% 23.43/23.61 tff(10391,plain,
% 23.43/23.61 (~(mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))) = mult(b, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))),
% 23.43/23.61 inference(unit_resolution,[status(thm)],[10390, 10335, 4535, 4789, 6879, 10351, 2788, 299, 2187])).
% 23.43/23.62 tff(10392,plain,
% 23.43/23.62 (((~(mult(mult(b, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(mult(b, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)))) | (~(mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))) = mult(b, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))))) | (mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))) = mult(b, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))),
% 23.43/23.62 inference(tautology,[status(thm)],[])).
% 23.43/23.62 tff(10393,plain,
% 23.43/23.62 ((~(mult(mult(b, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(mult(b, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)))) | (~(mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))) = mult(b, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))))),
% 23.43/23.62 inference(unit_resolution,[status(thm)],[10392, 10391])).
% 23.43/23.62 tff(10394,plain,
% 23.43/23.62 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(b, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(mult(b, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)))) | (~(mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))) = mult(b, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))))) | (~((~(mult(mult(b, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(b, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(b, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(b, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(mult(b, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)))) | (~(mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))) = mult(b, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))))) | (~((~(mult(mult(b, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(b, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(b, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))))))),
% 23.43/23.62 inference(rewrite,[status(thm)],[])).
% 23.43/23.62 tff(10395,plain,
% 23.43/23.62 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(b, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(mult(b, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)))) | (~(mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))) = mult(b, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))))) | (~((~(mult(mult(b, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(b, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(b, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))))))),
% 23.43/23.62 inference(quant_inst,[status(thm)],[])).
% 23.43/23.62 tff(10396,plain,
% 23.43/23.62 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(b, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(mult(b, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)))) | (~(mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))) = mult(b, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))))) | (~((~(mult(mult(b, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(b, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(b, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))))))),
% 23.43/23.62 inference(modus_ponens,[status(thm)],[10395, 10394])).
% 23.43/23.62 tff(10397,plain,
% 23.43/23.62 ((~((~(mult(mult(b, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(mult(b, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)))) | (~(mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))) = mult(b, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))))) | (~((~(mult(mult(b, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(b, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(b, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))))))),
% 23.43/23.62 inference(unit_resolution,[status(thm)],[10396, 27])).
% 23.43/23.62 tff(10398,plain,
% 23.43/23.62 (~((~(mult(mult(b, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(b, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(b, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))))),
% 23.43/23.62 inference(unit_resolution,[status(thm)],[10397, 10393])).
% 23.43/23.62 tff(10399,plain,
% 23.43/23.62 (((~(mult(mult(b, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(b, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(b, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))))) | (mult(mult(b, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))))),
% 23.43/23.62 inference(tautology,[status(thm)],[])).
% 23.43/23.62 tff(10400,plain,
% 23.43/23.62 (mult(mult(b, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))))),
% 23.43/23.62 inference(unit_resolution,[status(thm)],[10399, 10398])).
% 23.43/23.62 tff(10401,plain,
% 23.43/23.62 (mult(mult(b, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(mult(a, b), c), a), rd(mult(b, c), mult(a, c)))),
% 23.43/23.62 inference(transitivity,[status(thm)],[10400, 10350, 10346, 8032, 10342, 8023, 10331])).
% 23.43/23.62 tff(10402,plain,
% 23.43/23.62 (rd(mult(mult(b, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))), rd(mult(b, c), mult(a, c))) = rd(mult(mult(mult(mult(a, b), c), a), rd(mult(b, c), mult(a, c))), rd(mult(b, c), mult(a, c)))),
% 23.43/23.62 inference(monotonicity,[status(thm)],[10401])).
% 23.43/23.62 tff(10403,plain,
% 23.43/23.62 (rd(mult(mult(mult(mult(a, b), c), a), rd(mult(b, c), mult(a, c))), rd(mult(b, c), mult(a, c))) = rd(mult(mult(b, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))), rd(mult(b, c), mult(a, c)))),
% 23.43/23.62 inference(symmetry,[status(thm)],[10402])).
% 23.43/23.62 tff(10404,plain,
% 23.43/23.62 (mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c), a) = mult(mult(mult(a, b), c), a)),
% 23.43/23.62 inference(monotonicity,[status(thm)],[10361])).
% 23.43/23.62 tff(10405,plain,
% 23.43/23.62 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, c), a)))),
% 23.43/23.62 inference(quant_inst,[status(thm)],[])).
% 23.43/23.62 tff(10406,plain,
% 23.43/23.62 (mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, c), a))),
% 23.43/23.62 inference(unit_resolution,[status(thm)],[10405, 56])).
% 23.43/23.62 tff(10407,plain,
% 23.43/23.62 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, c), a)) = mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c), a)),
% 23.43/23.62 inference(symmetry,[status(thm)],[10406])).
% 23.43/23.62 tff(10408,plain,
% 23.43/23.62 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, c), a)) = mult(b, mult(mult(a, c), a))),
% 23.43/23.62 inference(transitivity,[status(thm)],[10407, 10404, 1148, 10403, 10329])).
% 23.43/23.62 tff(10409,plain,
% 23.43/23.62 (rd(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, c), a)), mult(mult(a, c), a)) = rd(mult(b, mult(mult(a, c), a)), mult(mult(a, c), a))),
% 23.43/23.62 inference(monotonicity,[status(thm)],[10408])).
% 23.43/23.62 tff(10410,plain,
% 23.43/23.62 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, c), a)), mult(mult(a, c), a)) = mult(rd(mult(b, c), mult(a, c)), a))),
% 23.43/23.62 inference(quant_inst,[status(thm)],[])).
% 23.43/23.62 tff(10411,plain,
% 23.43/23.62 (rd(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, c), a)), mult(mult(a, c), a)) = mult(rd(mult(b, c), mult(a, c)), a)),
% 23.43/23.62 inference(unit_resolution,[status(thm)],[10410, 168])).
% 23.43/23.62 tff(10412,plain,
% 23.43/23.62 (mult(rd(mult(b, c), mult(a, c)), a) = rd(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, c), a)), mult(mult(a, c), a))),
% 23.43/23.62 inference(symmetry,[status(thm)],[10411])).
% 23.43/23.62 tff(10413,plain,
% 23.43/23.62 (mult(rd(mult(b, c), mult(a, c)), a) = b),
% 23.43/23.62 inference(transitivity,[status(thm)],[10412, 10409, 10327])).
% 23.43/23.62 tff(10414,plain,
% 23.43/23.62 (mult(mult(rd(mult(b, c), mult(a, c)), a), c) = mult(b, c)),
% 23.43/23.62 inference(monotonicity,[status(thm)],[10413])).
% 23.43/23.62 tff(10415,plain,
% 23.43/23.62 (mult(mult(a, b), c) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c)),
% 23.43/23.62 inference(symmetry,[status(thm)],[10361])).
% 23.43/23.62 tff(10416,plain,
% 23.43/23.62 (mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, c), b)),
% 23.43/23.62 inference(monotonicity,[status(thm)],[10413])).
% 23.43/23.62 tff(10417,plain,
% 23.43/23.62 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a)),
% 23.43/23.62 inference(transitivity,[status(thm)],[5496, 10416, 161, 10415, 10208])).
% 23.43/23.62 tff(10418,plain,
% 23.43/23.62 (rd(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), a) = rd(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a), a)),
% 23.43/23.62 inference(monotonicity,[status(thm)],[10417])).
% 23.43/23.62 tff(10419,plain,
% 23.43/23.62 (mult(mult(unit, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(a, c))),
% 23.43/23.62 inference(transitivity,[status(thm)],[4928, 6325, 10418, 1376, 10414, 267, 4904, 4902])).
% 23.43/23.62 tff(10420,assumption,(~(mult(mult(unit, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(a, c)))), introduced(assumption)).
% 23.43/23.62 tff(10421,plain,
% 23.43/23.62 ($false),
% 23.43/23.62 inference(unit_resolution,[status(thm)],[10420, 10419])).
% 23.43/23.62 tff(10422,plain,((~(mult(mult(a, b), mult(b, mult(a, c))) = mult(mult(a, b), mult(mult(a, c), b)))) | (mult(mult(unit, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(a, c))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), mult(c, c)) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)), a))) | (~(mult(mult(mult(mult(a, b), c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(b, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(b, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))) | (mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))), inference(lemma,lemma(discharge,[]))).
% 23.43/23.62 tff(10423,plain,
% 23.43/23.62 (~(mult(mult(a, b), mult(b, mult(a, c))) = mult(mult(a, b), mult(mult(a, c), b)))),
% 23.43/23.62 inference(unit_resolution,[status(thm)],[10422, 10325, 10323, 9735, 8191, 281, 8165, 4390, 6583, 9662, 4499])).
% 23.43/23.62 tff(10424,plain,
% 23.43/23.62 (((~(mult(mult(a, b), mult(b, mult(a, c))) = mult(mult(a, b), mult(mult(a, c), b)))) | (~(mult(mult(mult(a, b), b), mult(a, c)) = mult(mult(mult(a, b), mult(a, c)), b)))) | (mult(mult(a, b), mult(b, mult(a, c))) = mult(mult(a, b), mult(mult(a, c), b)))),
% 23.43/23.62 inference(tautology,[status(thm)],[])).
% 23.43/23.62 tff(10425,plain,
% 23.43/23.62 ((~(mult(mult(a, b), mult(b, mult(a, c))) = mult(mult(a, b), mult(mult(a, c), b)))) | (~(mult(mult(mult(a, b), b), mult(a, c)) = mult(mult(mult(a, b), mult(a, c)), b)))),
% 23.43/23.62 inference(unit_resolution,[status(thm)],[10424, 10423])).
% 23.43/23.62 tff(10426,plain,
% 23.43/23.62 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, b), mult(b, mult(a, c))) = mult(mult(a, b), mult(mult(a, c), b)))) | (~(mult(mult(mult(a, b), b), mult(a, c)) = mult(mult(mult(a, b), mult(a, c)), b))))) | (~((~(mult(mult(mult(a, b), b), mult(a, c)) = mult(mult(a, b), mult(b, mult(a, c))))) | (~(mult(mult(mult(a, b), mult(a, c)), b) = mult(mult(a, b), mult(mult(a, c), b)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, b), mult(b, mult(a, c))) = mult(mult(a, b), mult(mult(a, c), b)))) | (~(mult(mult(mult(a, b), b), mult(a, c)) = mult(mult(mult(a, b), mult(a, c)), b))))) | (~((~(mult(mult(mult(a, b), b), mult(a, c)) = mult(mult(a, b), mult(b, mult(a, c))))) | (~(mult(mult(mult(a, b), mult(a, c)), b) = mult(mult(a, b), mult(mult(a, c), b)))))))),
% 23.43/23.62 inference(rewrite,[status(thm)],[])).
% 23.43/23.62 tff(10427,plain,
% 23.43/23.62 (((~((~(mult(mult(mult(a, b), b), mult(a, c)) = mult(mult(mult(a, b), mult(a, c)), b))) | (~(mult(mult(a, b), mult(b, mult(a, c))) = mult(mult(a, b), mult(mult(a, c), b)))))) | (~((~(mult(mult(mult(a, b), b), mult(a, c)) = mult(mult(a, b), mult(b, mult(a, c))))) | (~(mult(mult(mult(a, b), mult(a, c)), b) = mult(mult(a, b), mult(mult(a, c), b))))))) <=> ((~((~(mult(mult(a, b), mult(b, mult(a, c))) = mult(mult(a, b), mult(mult(a, c), b)))) | (~(mult(mult(mult(a, b), b), mult(a, c)) = mult(mult(mult(a, b), mult(a, c)), b))))) | (~((~(mult(mult(mult(a, b), b), mult(a, c)) = mult(mult(a, b), mult(b, mult(a, c))))) | (~(mult(mult(mult(a, b), mult(a, c)), b) = mult(mult(a, b), mult(mult(a, c), b)))))))),
% 23.43/23.62 inference(rewrite,[status(thm)],[])).
% 23.43/23.62 tff(10428,plain,
% 23.43/23.62 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, b), b), mult(a, c)) = mult(mult(mult(a, b), mult(a, c)), b))) | (~(mult(mult(a, b), mult(b, mult(a, c))) = mult(mult(a, b), mult(mult(a, c), b)))))) | (~((~(mult(mult(mult(a, b), b), mult(a, c)) = mult(mult(a, b), mult(b, mult(a, c))))) | (~(mult(mult(mult(a, b), mult(a, c)), b) = mult(mult(a, b), mult(mult(a, c), b)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, b), mult(b, mult(a, c))) = mult(mult(a, b), mult(mult(a, c), b)))) | (~(mult(mult(mult(a, b), b), mult(a, c)) = mult(mult(mult(a, b), mult(a, c)), b))))) | (~((~(mult(mult(mult(a, b), b), mult(a, c)) = mult(mult(a, b), mult(b, mult(a, c))))) | (~(mult(mult(mult(a, b), mult(a, c)), b) = mult(mult(a, b), mult(mult(a, c), b))))))))),
% 23.43/23.62 inference(monotonicity,[status(thm)],[10427])).
% 23.43/23.62 tff(10429,plain,
% 23.43/23.62 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, b), b), mult(a, c)) = mult(mult(mult(a, b), mult(a, c)), b))) | (~(mult(mult(a, b), mult(b, mult(a, c))) = mult(mult(a, b), mult(mult(a, c), b)))))) | (~((~(mult(mult(mult(a, b), b), mult(a, c)) = mult(mult(a, b), mult(b, mult(a, c))))) | (~(mult(mult(mult(a, b), mult(a, c)), b) = mult(mult(a, b), mult(mult(a, c), b)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, b), mult(b, mult(a, c))) = mult(mult(a, b), mult(mult(a, c), b)))) | (~(mult(mult(mult(a, b), b), mult(a, c)) = mult(mult(mult(a, b), mult(a, c)), b))))) | (~((~(mult(mult(mult(a, b), b), mult(a, c)) = mult(mult(a, b), mult(b, mult(a, c))))) | (~(mult(mult(mult(a, b), mult(a, c)), b) = mult(mult(a, b), mult(mult(a, c), b)))))))),
% 23.43/23.63 inference(transitivity,[status(thm)],[10428, 10426])).
% 23.43/23.63 tff(10430,plain,
% 23.43/23.63 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, b), b), mult(a, c)) = mult(mult(mult(a, b), mult(a, c)), b))) | (~(mult(mult(a, b), mult(b, mult(a, c))) = mult(mult(a, b), mult(mult(a, c), b)))))) | (~((~(mult(mult(mult(a, b), b), mult(a, c)) = mult(mult(a, b), mult(b, mult(a, c))))) | (~(mult(mult(mult(a, b), mult(a, c)), b) = mult(mult(a, b), mult(mult(a, c), b)))))))),
% 23.43/23.63 inference(quant_inst,[status(thm)],[])).
% 23.43/23.63 tff(10431,plain,
% 23.43/23.63 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, b), mult(b, mult(a, c))) = mult(mult(a, b), mult(mult(a, c), b)))) | (~(mult(mult(mult(a, b), b), mult(a, c)) = mult(mult(mult(a, b), mult(a, c)), b))))) | (~((~(mult(mult(mult(a, b), b), mult(a, c)) = mult(mult(a, b), mult(b, mult(a, c))))) | (~(mult(mult(mult(a, b), mult(a, c)), b) = mult(mult(a, b), mult(mult(a, c), b))))))),
% 23.43/23.63 inference(modus_ponens,[status(thm)],[10430, 10429])).
% 23.43/23.63 tff(10432,plain,
% 23.43/23.63 ((~((~(mult(mult(a, b), mult(b, mult(a, c))) = mult(mult(a, b), mult(mult(a, c), b)))) | (~(mult(mult(mult(a, b), b), mult(a, c)) = mult(mult(mult(a, b), mult(a, c)), b))))) | (~((~(mult(mult(mult(a, b), b), mult(a, c)) = mult(mult(a, b), mult(b, mult(a, c))))) | (~(mult(mult(mult(a, b), mult(a, c)), b) = mult(mult(a, b), mult(mult(a, c), b))))))),
% 23.43/23.63 inference(unit_resolution,[status(thm)],[10431, 27])).
% 23.43/23.63 tff(10433,plain,
% 23.43/23.63 (~((~(mult(mult(mult(a, b), b), mult(a, c)) = mult(mult(a, b), mult(b, mult(a, c))))) | (~(mult(mult(mult(a, b), mult(a, c)), b) = mult(mult(a, b), mult(mult(a, c), b)))))),
% 23.43/23.63 inference(unit_resolution,[status(thm)],[10432, 10425])).
% 23.43/23.63 tff(10434,plain,
% 23.43/23.63 (((~(mult(mult(mult(a, b), b), mult(a, c)) = mult(mult(a, b), mult(b, mult(a, c))))) | (~(mult(mult(mult(a, b), mult(a, c)), b) = mult(mult(a, b), mult(mult(a, c), b))))) | (mult(mult(mult(a, b), mult(a, c)), b) = mult(mult(a, b), mult(mult(a, c), b)))),
% 23.43/23.63 inference(tautology,[status(thm)],[])).
% 23.43/23.63 tff(10435,plain,
% 23.43/23.63 (mult(mult(mult(a, b), mult(a, c)), b) = mult(mult(a, b), mult(mult(a, c), b))),
% 23.43/23.63 inference(unit_resolution,[status(thm)],[10434, 10433])).
% 23.43/23.63 tff(10436,plain,
% 23.43/23.63 (((~(mult(mult(mult(a, b), b), mult(a, c)) = mult(mult(a, b), mult(b, mult(a, c))))) | (~(mult(mult(mult(a, b), mult(a, c)), b) = mult(mult(a, b), mult(mult(a, c), b))))) | (mult(mult(mult(a, b), b), mult(a, c)) = mult(mult(a, b), mult(b, mult(a, c))))),
% 23.43/23.63 inference(tautology,[status(thm)],[])).
% 23.43/23.63 tff(10437,plain,
% 23.43/23.63 (mult(mult(mult(a, b), b), mult(a, c)) = mult(mult(a, b), mult(b, mult(a, c)))),
% 23.43/23.63 inference(unit_resolution,[status(thm)],[10436, 10433])).
% 23.43/23.63 tff(10438,plain,
% 23.43/23.63 ((mult(mult(mult(a, b), b), mult(a, c)) = mult(mult(mult(a, b), mult(a, c)), b)) <=> (mult(mult(a, b), mult(b, mult(a, c))) = mult(mult(a, b), mult(mult(a, c), b)))),
% 23.43/23.63 inference(monotonicity,[status(thm)],[10437, 10435])).
% 23.43/23.63 tff(10439,plain,
% 23.43/23.63 ((mult(mult(a, b), mult(b, mult(a, c))) = mult(mult(a, b), mult(mult(a, c), b))) <=> (mult(mult(mult(a, b), b), mult(a, c)) = mult(mult(mult(a, b), mult(a, c)), b))),
% 23.43/23.63 inference(symmetry,[status(thm)],[10438])).
% 23.43/23.63 tff(10440,plain,
% 23.43/23.63 ((~(mult(mult(a, b), mult(b, mult(a, c))) = mult(mult(a, b), mult(mult(a, c), b)))) <=> (~(mult(mult(mult(a, b), b), mult(a, c)) = mult(mult(mult(a, b), mult(a, c)), b)))),
% 23.43/23.63 inference(monotonicity,[status(thm)],[10439])).
% 23.43/23.63 tff(10441,plain,
% 23.43/23.63 (~(mult(mult(mult(a, b), b), mult(a, c)) = mult(mult(mult(a, b), mult(a, c)), b))),
% 23.43/23.63 inference(modus_ponens,[status(thm)],[10423, 10440])).
% 23.43/23.63 tff(10442,plain,
% 23.43/23.63 ((~(mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a))) | (~(mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a))))),
% 23.43/23.63 inference(unit_resolution,[status(thm)],[7084, 8305, 270])).
% 23.43/23.63 tff(10443,plain,
% 23.43/23.63 (~(mult(mult(c, mult(a, b)), b) = mult(mult(c, b), mult(a, b)))),
% 23.43/23.63 inference(unit_resolution,[status(thm)],[8542, 10442])).
% 23.43/23.63 tff(10444,plain,
% 23.43/23.63 ((~(mult(mult(c, mult(a, b)), b) = mult(mult(c, b), mult(a, b)))) | (~(mult(c, mult(mult(a, b), b)) = mult(c, mult(b, mult(a, b)))))),
% 23.43/23.63 inference(unit_resolution,[status(thm)],[7279, 10443])).
% 23.43/23.63 tff(10445,plain,
% 23.43/23.63 (~((~(mult(mult(c, b), mult(a, b)) = mult(c, mult(b, mult(a, b))))) | (~(mult(mult(c, mult(a, b)), b) = mult(c, mult(mult(a, b), b)))))),
% 23.43/23.63 inference(unit_resolution,[status(thm)],[7291, 10444])).
% 23.43/23.63 tff(10446,plain,
% 23.43/23.63 (mult(mult(c, mult(a, b)), b) = mult(c, mult(mult(a, b), b))),
% 23.43/23.63 inference(unit_resolution,[status(thm)],[7312, 10445])).
% 23.43/23.63 tff(10447,plain,
% 23.43/23.63 (~((~(mult(mult(mult(b, c), a), b) = mult(mult(b, c), mult(a, b)))) | (~(mult(mult(mult(b, c), b), a) = mult(mult(b, c), mult(b, a)))))),
% 23.43/23.63 inference(unit_resolution,[status(thm)],[1205, 10442])).
% 23.43/23.63 tff(10448,plain,
% 23.43/23.63 (mult(mult(mult(b, c), a), b) = mult(mult(b, c), mult(a, b))),
% 23.43/23.63 inference(unit_resolution,[status(thm)],[1229, 10447])).
% 23.43/23.63 tff(10449,plain,
% 23.43/23.63 (mult(mult(c, b), mult(a, b)) = mult(c, mult(b, mult(a, b)))),
% 23.43/23.63 inference(unit_resolution,[status(thm)],[7136, 10445])).
% 23.43/23.63 tff(10450,plain,
% 23.43/23.63 (~(mult(mult(a, c), mult(b, mult(a, b))) = mult(mult(a, c), mult(mult(a, b), b)))),
% 23.43/23.63 inference(unit_resolution,[status(thm)],[7316, 10448, 10443])).
% 23.43/23.63 tff(10451,plain,
% 23.43/23.63 ((~(mult(mult(a, c), mult(b, mult(a, b))) = mult(mult(a, c), mult(mult(a, b), b)))) | (~(mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(mult(a, c), mult(a, b)), b)))),
% 23.43/23.63 inference(unit_resolution,[status(thm)],[576, 10450])).
% 23.43/23.63 tff(10452,plain,
% 23.43/23.63 (~((~(mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(a, c), mult(b, mult(a, b))))) | (~(mult(mult(mult(a, c), mult(a, b)), b) = mult(mult(a, c), mult(mult(a, b), b)))))),
% 23.43/23.63 inference(unit_resolution,[status(thm)],[584, 10451])).
% 23.43/23.63 tff(10453,plain,
% 23.43/23.63 (mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(a, c), mult(b, mult(a, b)))),
% 23.43/23.63 inference(unit_resolution,[status(thm)],[604, 10452])).
% 23.43/23.63 tff(10454,plain,
% 23.43/23.63 (mult(mult(mult(a, c), mult(a, b)), b) = mult(mult(a, c), mult(mult(a, b), b))),
% 23.43/23.63 inference(unit_resolution,[status(thm)],[586, 10452])).
% 23.43/23.63 tff(10455,plain,
% 23.43/23.63 (mult(mult(a, c), mult(mult(a, b), b)) = mult(mult(mult(a, c), mult(a, b)), b)),
% 23.43/23.63 inference(symmetry,[status(thm)],[10454])).
% 23.43/23.63 tff(10456,plain,
% 23.43/23.63 (mult(mult(a, c), mult(b, mult(a, b))) = mult(mult(mult(a, c), b), mult(a, b))),
% 23.43/23.63 inference(symmetry,[status(thm)],[10453])).
% 23.43/23.63 tff(10457,plain,
% 23.43/23.63 ((mult(mult(a, c), mult(b, mult(a, b))) = mult(mult(a, c), mult(mult(a, b), b))) <=> (mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(mult(a, c), mult(a, b)), b))),
% 23.43/23.63 inference(monotonicity,[status(thm)],[10456, 10455])).
% 23.43/23.63 tff(10458,plain,
% 23.43/23.63 ((~(mult(mult(a, c), mult(b, mult(a, b))) = mult(mult(a, c), mult(mult(a, b), b)))) <=> (~(mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(mult(a, c), mult(a, b)), b)))),
% 23.43/23.63 inference(monotonicity,[status(thm)],[10457])).
% 23.43/23.63 tff(10459,plain,
% 23.43/23.63 (~(mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(mult(a, c), mult(a, b)), b))),
% 23.43/23.63 inference(modus_ponens,[status(thm)],[10450, 10458])).
% 23.43/23.63 tff(10460,plain,
% 23.43/23.63 (mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b)))) = mult(mult(a, c), mult(mult(a, b), b))),
% 23.43/23.63 inference(symmetry,[status(thm)],[1621])).
% 23.43/23.63 tff(10461,assumption,(~(mult(mult(mult(a, c), a), mult(unit, mult(mult(b, unit), b))) = mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b)))))), introduced(assumption)).
% 23.43/23.63 tff(10462,plain,
% 23.43/23.63 (((~(mult(mult(mult(a, c), a), mult(unit, mult(mult(b, unit), b))) = mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b)))))) | (~(mult(mult(mult(a, c), mult(unit, mult(mult(b, unit), b))), a) = mult(mult(a, c), mult(mult(unit, mult(mult(b, unit), b)), a))))) | (mult(mult(mult(a, c), a), mult(unit, mult(mult(b, unit), b))) = mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b)))))),
% 23.43/23.63 inference(tautology,[status(thm)],[])).
% 23.43/23.63 tff(10463,plain,
% 23.43/23.63 ((~(mult(mult(mult(a, c), a), mult(unit, mult(mult(b, unit), b))) = mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b)))))) | (~(mult(mult(mult(a, c), mult(unit, mult(mult(b, unit), b))), a) = mult(mult(a, c), mult(mult(unit, mult(mult(b, unit), b)), a))))),
% 23.43/23.63 inference(unit_resolution,[status(thm)],[10462, 10461])).
% 23.43/23.63 tff(10464,plain,
% 23.43/23.63 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, c), a), mult(unit, mult(mult(b, unit), b))) = mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b)))))) | (~(mult(mult(mult(a, c), mult(unit, mult(mult(b, unit), b))), a) = mult(mult(a, c), mult(mult(unit, mult(mult(b, unit), b)), a)))))) | (~((~(mult(mult(mult(a, c), a), mult(unit, mult(mult(b, unit), b))) = mult(mult(mult(a, c), mult(unit, mult(mult(b, unit), b))), a))) | (~(mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b)))) = mult(mult(a, c), mult(mult(unit, mult(mult(b, unit), b)), a)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(a, c), a), mult(unit, mult(mult(b, unit), b))) = mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b)))))) | (~(mult(mult(mult(a, c), mult(unit, mult(mult(b, unit), b))), a) = mult(mult(a, c), mult(mult(unit, mult(mult(b, unit), b)), a)))))) | (~((~(mult(mult(mult(a, c), a), mult(unit, mult(mult(b, unit), b))) = mult(mult(mult(a, c), mult(unit, mult(mult(b, unit), b))), a))) | (~(mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b)))) = mult(mult(a, c), mult(mult(unit, mult(mult(b, unit), b)), a)))))))),
% 23.43/23.63 inference(rewrite,[status(thm)],[])).
% 23.43/23.63 tff(10465,plain,
% 23.43/23.63 (((~((~(mult(mult(mult(a, c), a), mult(unit, mult(mult(b, unit), b))) = mult(mult(mult(a, c), mult(unit, mult(mult(b, unit), b))), a))) | (~(mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b)))) = mult(mult(a, c), mult(mult(unit, mult(mult(b, unit), b)), a)))))) | (~((~(mult(mult(mult(a, c), a), mult(unit, mult(mult(b, unit), b))) = mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b)))))) | (~(mult(mult(mult(a, c), mult(unit, mult(mult(b, unit), b))), a) = mult(mult(a, c), mult(mult(unit, mult(mult(b, unit), b)), a))))))) <=> ((~((~(mult(mult(mult(a, c), a), mult(unit, mult(mult(b, unit), b))) = mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b)))))) | (~(mult(mult(mult(a, c), mult(unit, mult(mult(b, unit), b))), a) = mult(mult(a, c), mult(mult(unit, mult(mult(b, unit), b)), a)))))) | (~((~(mult(mult(mult(a, c), a), mult(unit, mult(mult(b, unit), b))) = mult(mult(mult(a, c), mult(unit, mult(mult(b, unit), b))), a))) | (~(mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b)))) = mult(mult(a, c), mult(mult(unit, mult(mult(b, unit), b)), a)))))))),
% 23.43/23.63 inference(rewrite,[status(thm)],[])).
% 23.43/23.63 tff(10466,plain,
% 23.43/23.63 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, c), a), mult(unit, mult(mult(b, unit), b))) = mult(mult(mult(a, c), mult(unit, mult(mult(b, unit), b))), a))) | (~(mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b)))) = mult(mult(a, c), mult(mult(unit, mult(mult(b, unit), b)), a)))))) | (~((~(mult(mult(mult(a, c), a), mult(unit, mult(mult(b, unit), b))) = mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b)))))) | (~(mult(mult(mult(a, c), mult(unit, mult(mult(b, unit), b))), a) = mult(mult(a, c), mult(mult(unit, mult(mult(b, unit), b)), a)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, c), a), mult(unit, mult(mult(b, unit), b))) = mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b)))))) | (~(mult(mult(mult(a, c), mult(unit, mult(mult(b, unit), b))), a) = mult(mult(a, c), mult(mult(unit, mult(mult(b, unit), b)), a)))))) | (~((~(mult(mult(mult(a, c), a), mult(unit, mult(mult(b, unit), b))) = mult(mult(mult(a, c), mult(unit, mult(mult(b, unit), b))), a))) | (~(mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b)))) = mult(mult(a, c), mult(mult(unit, mult(mult(b, unit), b)), a))))))))),
% 23.43/23.63 inference(monotonicity,[status(thm)],[10465])).
% 23.43/23.63 tff(10467,plain,
% 23.43/23.63 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, c), a), mult(unit, mult(mult(b, unit), b))) = mult(mult(mult(a, c), mult(unit, mult(mult(b, unit), b))), a))) | (~(mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b)))) = mult(mult(a, c), mult(mult(unit, mult(mult(b, unit), b)), a)))))) | (~((~(mult(mult(mult(a, c), a), mult(unit, mult(mult(b, unit), b))) = mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b)))))) | (~(mult(mult(mult(a, c), mult(unit, mult(mult(b, unit), b))), a) = mult(mult(a, c), mult(mult(unit, mult(mult(b, unit), b)), a)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(a, c), a), mult(unit, mult(mult(b, unit), b))) = mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b)))))) | (~(mult(mult(mult(a, c), mult(unit, mult(mult(b, unit), b))), a) = mult(mult(a, c), mult(mult(unit, mult(mult(b, unit), b)), a)))))) | (~((~(mult(mult(mult(a, c), a), mult(unit, mult(mult(b, unit), b))) = mult(mult(mult(a, c), mult(unit, mult(mult(b, unit), b))), a))) | (~(mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b)))) = mult(mult(a, c), mult(mult(unit, mult(mult(b, unit), b)), a)))))))),
% 23.43/23.63 inference(transitivity,[status(thm)],[10466, 10464])).
% 23.43/23.63 tff(10468,plain,
% 23.43/23.63 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, c), a), mult(unit, mult(mult(b, unit), b))) = mult(mult(mult(a, c), mult(unit, mult(mult(b, unit), b))), a))) | (~(mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b)))) = mult(mult(a, c), mult(mult(unit, mult(mult(b, unit), b)), a)))))) | (~((~(mult(mult(mult(a, c), a), mult(unit, mult(mult(b, unit), b))) = mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b)))))) | (~(mult(mult(mult(a, c), mult(unit, mult(mult(b, unit), b))), a) = mult(mult(a, c), mult(mult(unit, mult(mult(b, unit), b)), a)))))))),
% 23.43/23.63 inference(quant_inst,[status(thm)],[])).
% 23.43/23.63 tff(10469,plain,
% 23.43/23.63 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(a, c), a), mult(unit, mult(mult(b, unit), b))) = mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b)))))) | (~(mult(mult(mult(a, c), mult(unit, mult(mult(b, unit), b))), a) = mult(mult(a, c), mult(mult(unit, mult(mult(b, unit), b)), a)))))) | (~((~(mult(mult(mult(a, c), a), mult(unit, mult(mult(b, unit), b))) = mult(mult(mult(a, c), mult(unit, mult(mult(b, unit), b))), a))) | (~(mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b)))) = mult(mult(a, c), mult(mult(unit, mult(mult(b, unit), b)), a))))))),
% 23.43/23.64 inference(modus_ponens,[status(thm)],[10468, 10467])).
% 23.43/23.64 tff(10470,plain,
% 23.43/23.64 ((~((~(mult(mult(mult(a, c), a), mult(unit, mult(mult(b, unit), b))) = mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b)))))) | (~(mult(mult(mult(a, c), mult(unit, mult(mult(b, unit), b))), a) = mult(mult(a, c), mult(mult(unit, mult(mult(b, unit), b)), a)))))) | (~((~(mult(mult(mult(a, c), a), mult(unit, mult(mult(b, unit), b))) = mult(mult(mult(a, c), mult(unit, mult(mult(b, unit), b))), a))) | (~(mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b)))) = mult(mult(a, c), mult(mult(unit, mult(mult(b, unit), b)), a))))))),
% 23.43/23.64 inference(unit_resolution,[status(thm)],[10469, 27])).
% 23.43/23.64 tff(10471,plain,
% 23.43/23.64 (~((~(mult(mult(mult(a, c), a), mult(unit, mult(mult(b, unit), b))) = mult(mult(mult(a, c), mult(unit, mult(mult(b, unit), b))), a))) | (~(mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b)))) = mult(mult(a, c), mult(mult(unit, mult(mult(b, unit), b)), a)))))),
% 23.43/23.64 inference(unit_resolution,[status(thm)],[10470, 10463])).
% 23.43/23.64 tff(10472,plain,
% 23.43/23.64 (((~(mult(mult(mult(a, c), a), mult(unit, mult(mult(b, unit), b))) = mult(mult(mult(a, c), mult(unit, mult(mult(b, unit), b))), a))) | (~(mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b)))) = mult(mult(a, c), mult(mult(unit, mult(mult(b, unit), b)), a))))) | (mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b)))) = mult(mult(a, c), mult(mult(unit, mult(mult(b, unit), b)), a)))),
% 23.43/23.64 inference(tautology,[status(thm)],[])).
% 23.43/23.64 tff(10473,plain,
% 23.43/23.64 (mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b)))) = mult(mult(a, c), mult(mult(unit, mult(mult(b, unit), b)), a))),
% 23.43/23.64 inference(unit_resolution,[status(thm)],[10472, 10471])).
% 23.43/23.64 tff(10474,plain,
% 23.43/23.64 (mult(mult(a, c), mult(mult(unit, mult(mult(b, unit), b)), a)) = mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b))))),
% 23.43/23.64 inference(symmetry,[status(thm)],[10473])).
% 23.43/23.64 tff(10475,plain,
% 23.43/23.64 (mult(mult(a, c), mult(unit, mult(mult(mult(b, unit), b), a))) = mult(mult(a, c), mult(mult(unit, mult(mult(b, unit), b)), a))),
% 23.43/23.64 inference(monotonicity,[status(thm)],[466])).
% 23.43/23.64 tff(10476,plain,
% 23.43/23.64 (mult(mult(b, b), a) = mult(b, mult(b, a))),
% 23.43/23.64 inference(unit_resolution,[status(thm)],[8488, 6518, 1311])).
% 23.43/23.64 tff(10477,plain,
% 23.43/23.64 (mult(b, mult(b, a)) = mult(mult(b, b), a)),
% 23.43/23.64 inference(symmetry,[status(thm)],[10476])).
% 23.43/23.64 tff(10478,plain,
% 23.43/23.64 (mult(b, mult(b, a)) = mult(unit, mult(mult(mult(b, unit), b), a))),
% 23.43/23.64 inference(transitivity,[status(thm)],[10477, 434, 465])).
% 23.43/23.64 tff(10479,plain,
% 23.43/23.64 (mult(mult(a, c), mult(b, mult(b, a))) = mult(mult(a, c), mult(unit, mult(mult(mult(b, unit), b), a)))),
% 23.43/23.64 inference(monotonicity,[status(thm)],[10478])).
% 23.43/23.64 tff(10480,plain,
% 23.43/23.64 (mult(mult(a, c), mult(b, mult(b, a))) = mult(mult(mult(a, c), mult(a, b)), b)),
% 23.43/23.64 inference(transitivity,[status(thm)],[10479, 10475, 10474, 10460, 1091])).
% 23.43/23.64 tff(10481,plain,
% 23.43/23.64 (ld(c, mult(c, mult(mult(b, a), b))) = ld(c, mult(c, mult(b, mult(a, b))))),
% 23.43/23.64 inference(symmetry,[status(thm)],[6521])).
% 23.43/23.64 tff(10482,plain,
% 23.43/23.64 (mult(mult(b, a), b) = mult(b, mult(a, b))),
% 23.43/23.64 inference(transitivity,[status(thm)],[7298, 10481, 6523])).
% 23.43/23.64 tff(10483,plain,
% 23.43/23.64 (mult(mult(a, c), mult(mult(b, a), b)) = mult(mult(a, c), mult(b, mult(a, b)))),
% 23.43/23.64 inference(monotonicity,[status(thm)],[10482])).
% 23.43/23.64 tff(10484,plain,
% 23.43/23.64 (mult(mult(a, c), mult(mult(b, a), b)) = mult(mult(mult(a, c), b), mult(a, b))),
% 23.43/23.64 inference(transitivity,[status(thm)],[10483, 1095])).
% 23.43/23.64 tff(10485,plain,
% 23.43/23.64 ((mult(mult(a, c), mult(mult(b, a), b)) = mult(mult(a, c), mult(b, mult(b, a)))) <=> (mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(mult(a, c), mult(a, b)), b))),
% 23.43/23.64 inference(monotonicity,[status(thm)],[10484, 10480])).
% 23.43/23.64 tff(10486,plain,
% 23.43/23.64 ((mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(mult(a, c), mult(a, b)), b)) <=> (mult(mult(a, c), mult(mult(b, a), b)) = mult(mult(a, c), mult(b, mult(b, a))))),
% 23.43/23.64 inference(symmetry,[status(thm)],[10485])).
% 23.43/23.64 tff(10487,plain,
% 23.43/23.64 ((~(mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(mult(a, c), mult(a, b)), b))) <=> (~(mult(mult(a, c), mult(mult(b, a), b)) = mult(mult(a, c), mult(b, mult(b, a)))))),
% 23.43/23.64 inference(monotonicity,[status(thm)],[10486])).
% 23.43/23.64 tff(10488,plain,
% 23.43/23.64 (~(mult(mult(a, c), mult(mult(b, a), b)) = mult(mult(a, c), mult(b, mult(b, a))))),
% 23.43/23.64 inference(modus_ponens,[status(thm)],[1114, 10487])).
% 23.43/23.64 tff(10489,plain,
% 23.43/23.64 ((~(mult(mult(mult(a, c), mult(b, a)), b) = mult(mult(mult(a, c), b), mult(b, a)))) | (~(mult(mult(a, c), mult(mult(b, a), b)) = mult(mult(a, c), mult(b, mult(b, a)))))),
% 23.43/23.64 inference(unit_resolution,[status(thm)],[617, 10488])).
% 23.43/23.64 tff(10490,plain,
% 23.43/23.64 (~((~(mult(mult(mult(a, c), mult(b, a)), b) = mult(mult(a, c), mult(mult(b, a), b)))) | (~(mult(mult(mult(a, c), b), mult(b, a)) = mult(mult(a, c), mult(b, mult(b, a))))))),
% 23.43/23.64 inference(unit_resolution,[status(thm)],[622, 10489])).
% 23.43/23.64 tff(10491,plain,
% 23.43/23.64 (mult(mult(mult(a, c), b), mult(b, a)) = mult(mult(a, c), mult(b, mult(b, a)))),
% 23.43/23.64 inference(unit_resolution,[status(thm)],[624, 10490])).
% 23.43/23.64 tff(10492,plain,
% 23.43/23.64 (mult(mult(mult(mult(a, b), c), b), a) = mult(mult(mult(a, c), mult(unit, mult(mult(b, unit), b))), a)),
% 23.43/23.64 inference(symmetry,[status(thm)],[1120])).
% 23.43/23.64 tff(10493,assumption,(mult(mult(mult(mult(a, b), c), b), a) = mult(mult(mult(a, b), c), mult(b, a))), introduced(assumption)).
% 23.43/23.64 tff(10494,plain,
% 23.43/23.64 (mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(mult(a, b), c), b), a)),
% 23.43/23.64 inference(symmetry,[status(thm)],[10493])).
% 23.43/23.64 tff(10495,plain,
% 23.43/23.64 (mult(mult(mult(a, c), b), mult(b, a)) = mult(mult(mult(a, b), c), mult(b, a))),
% 23.43/23.64 inference(monotonicity,[status(thm)],[161])).
% 23.43/23.64 tff(10496,assumption,(mult(mult(mult(a, c), b), mult(b, a)) = mult(mult(a, c), mult(b, mult(b, a)))), introduced(assumption)).
% 23.43/23.64 tff(10497,plain,
% 23.43/23.64 (mult(mult(a, c), mult(b, mult(b, a))) = mult(mult(mult(a, c), b), mult(b, a))),
% 23.43/23.64 inference(symmetry,[status(thm)],[10496])).
% 23.43/23.64 tff(10498,plain,
% 23.43/23.64 (mult(unit, mult(mult(mult(b, unit), b), a)) = mult(b, mult(b, a))),
% 23.43/23.64 inference(transitivity,[status(thm)],[466, 435, 591])).
% 23.43/23.64 tff(10499,plain,
% 23.43/23.64 (mult(mult(a, c), mult(unit, mult(mult(mult(b, unit), b), a))) = mult(mult(a, c), mult(b, mult(b, a)))),
% 23.43/23.64 inference(monotonicity,[status(thm)],[10498])).
% 23.43/23.64 tff(10500,plain,
% 23.43/23.64 (mult(mult(a, c), mult(mult(unit, mult(mult(b, unit), b)), a)) = mult(mult(a, c), mult(unit, mult(mult(mult(b, unit), b), a)))),
% 23.43/23.64 inference(monotonicity,[status(thm)],[465])).
% 23.43/23.64 tff(10501,plain,
% 23.43/23.64 (mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b)))) = mult(mult(mult(a, c), mult(unit, mult(mult(b, unit), b))), a)),
% 23.43/23.64 inference(transitivity,[status(thm)],[10473, 10500, 10499, 10497, 10495, 10494, 10492])).
% 23.43/23.64 tff(10502,plain,
% 23.43/23.64 ((mult(mult(mult(a, c), a), mult(unit, mult(mult(b, unit), b))) = mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b))))) <=> (mult(mult(mult(a, c), a), mult(unit, mult(mult(b, unit), b))) = mult(mult(mult(a, c), mult(unit, mult(mult(b, unit), b))), a))),
% 23.43/23.64 inference(monotonicity,[status(thm)],[10501])).
% 23.43/23.64 tff(10503,plain,
% 23.43/23.64 ((mult(mult(mult(a, c), a), mult(unit, mult(mult(b, unit), b))) = mult(mult(mult(a, c), mult(unit, mult(mult(b, unit), b))), a)) <=> (mult(mult(mult(a, c), a), mult(unit, mult(mult(b, unit), b))) = mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b)))))),
% 23.43/23.64 inference(symmetry,[status(thm)],[10502])).
% 23.43/23.64 tff(10504,plain,
% 23.43/23.64 (((~(mult(mult(mult(a, c), a), mult(unit, mult(mult(b, unit), b))) = mult(mult(mult(a, c), mult(unit, mult(mult(b, unit), b))), a))) | (~(mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b)))) = mult(mult(a, c), mult(mult(unit, mult(mult(b, unit), b)), a))))) | (mult(mult(mult(a, c), a), mult(unit, mult(mult(b, unit), b))) = mult(mult(mult(a, c), mult(unit, mult(mult(b, unit), b))), a))),
% 23.43/23.64 inference(tautology,[status(thm)],[])).
% 23.43/23.64 tff(10505,plain,
% 23.43/23.64 (mult(mult(mult(a, c), a), mult(unit, mult(mult(b, unit), b))) = mult(mult(mult(a, c), mult(unit, mult(mult(b, unit), b))), a)),
% 23.43/23.64 inference(unit_resolution,[status(thm)],[10504, 10471])).
% 23.43/23.64 tff(10506,plain,
% 23.43/23.64 (mult(mult(mult(a, c), a), mult(unit, mult(mult(b, unit), b))) = mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b))))),
% 23.43/23.64 inference(modus_ponens,[status(thm)],[10505, 10503])).
% 23.43/23.64 tff(10507,plain,
% 23.43/23.64 ($false),
% 23.43/23.64 inference(unit_resolution,[status(thm)],[10461, 10506])).
% 23.43/23.64 tff(10508,plain,((mult(mult(mult(a, c), a), mult(unit, mult(mult(b, unit), b))) = mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b))))) | (~(mult(mult(mult(a, c), b), mult(b, a)) = mult(mult(a, c), mult(b, mult(b, a))))) | (~(mult(mult(mult(mult(a, b), c), b), a) = mult(mult(mult(a, b), c), mult(b, a)))) | (~(mult(mult(b, b), a) = mult(b, mult(b, a))))), inference(lemma,lemma(discharge,[]))).
% 23.43/23.64 tff(10509,plain,
% 23.43/23.64 (~(mult(mult(mult(mult(a, b), c), b), a) = mult(mult(mult(a, b), c), mult(b, a)))),
% 23.43/23.64 inference(unit_resolution,[status(thm)],[10508, 10491, 10476, 10461])).
% 23.43/23.64 tff(10510,plain,
% 23.43/23.64 ((~(mult(mult(mult(mult(a, b), c), b), a) = mult(mult(mult(a, b), c), mult(b, a)))) | (~(mult(mult(mult(mult(a, b), c), a), b) = mult(mult(mult(a, b), c), mult(a, b))))),
% 23.43/23.64 inference(unit_resolution,[status(thm)],[644, 10509])).
% 23.43/23.64 tff(10511,plain,
% 23.43/23.64 (~((~(mult(mult(mult(mult(a, b), c), b), a) = mult(mult(mult(mult(a, b), c), a), b))) | (~(mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(a, b)))))),
% 23.43/23.64 inference(unit_resolution,[status(thm)],[642, 10510])).
% 23.43/23.64 tff(10512,plain,
% 23.43/23.64 (mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(a, b))),
% 23.43/23.64 inference(unit_resolution,[status(thm)],[637, 10511])).
% 23.43/23.64 tff(10513,plain,
% 23.43/23.64 (mult(mult(mult(a, b), c), mult(a, b)) = mult(mult(mult(a, b), c), mult(b, a))),
% 23.43/23.64 inference(symmetry,[status(thm)],[10512])).
% 23.43/23.64 tff(10514,plain,
% 23.43/23.64 (mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(mult(a, c), mult(a, b)), b)),
% 23.43/23.64 inference(transitivity,[status(thm)],[3298, 10513, 626, 10491, 10479, 10475, 10474, 10460, 1091])).
% 23.43/23.64 tff(10515,plain,
% 23.43/23.64 ($false),
% 23.43/23.64 inference(unit_resolution,[status(thm)],[1114, 10514])).
% 23.43/23.64 tff(10516,plain,((mult(mult(mult(a, c), a), mult(unit, mult(mult(b, unit), b))) = mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b))))) | (mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(mult(a, c), mult(a, b)), b)) | (~(mult(mult(mult(a, c), mult(a, b)), b) = mult(mult(a, c), mult(mult(a, b), b)))) | (~(mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(a, c), mult(b, mult(a, b))))) | (~(mult(mult(c, b), mult(a, b)) = mult(c, mult(b, mult(a, b))))) | (~(mult(mult(mult(b, c), a), b) = mult(mult(b, c), mult(a, b))))), inference(lemma,lemma(discharge,[]))).
% 23.43/23.64 tff(10517,plain,
% 23.43/23.64 (mult(mult(mult(a, c), a), mult(unit, mult(mult(b, unit), b))) = mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b))))),
% 23.43/23.64 inference(unit_resolution,[status(thm)],[10516, 10459, 10454, 10453, 10449, 10448])).
% 23.43/23.64 tff(10518,plain,
% 23.43/23.64 (mult(mult(c, a), b) = mult(mult(a, c), b)),
% 23.43/23.64 inference(monotonicity,[status(thm)],[8215])).
% 23.43/23.64 tff(10519,plain,
% 23.43/23.64 (mult(c, mult(a, b)) = mult(mult(a, b), c)),
% 23.43/23.64 inference(transitivity,[status(thm)],[4270, 10518, 161])).
% 23.43/23.64 tff(10520,plain,
% 23.43/23.64 (mult(mult(c, mult(a, b)), b) = mult(mult(mult(a, b), c), b)),
% 23.43/23.64 inference(monotonicity,[status(thm)],[10519])).
% 23.43/23.64 tff(10521,assumption,(mult(mult(c, mult(a, b)), b) = mult(c, mult(mult(a, b), b))), introduced(assumption)).
% 23.43/23.64 tff(10522,plain,
% 23.43/23.64 (mult(c, mult(mult(a, b), b)) = mult(mult(c, mult(a, b)), b)),
% 23.43/23.64 inference(symmetry,[status(thm)],[10521])).
% 23.43/23.64 tff(10523,plain,
% 23.43/23.64 (mult(c, mult(mult(a, b), b)) = mult(mult(mult(a, b), b), c)),
% 23.43/23.64 inference(transitivity,[status(thm)],[10522, 10520, 827])).
% 23.43/23.64 tff(10524,plain,
% 23.43/23.64 (mult(a, mult(c, mult(mult(a, b), b))) = mult(a, mult(mult(mult(a, b), b), c))),
% 23.43/23.64 inference(monotonicity,[status(thm)],[10523])).
% 23.43/23.64 tff(10525,plain,
% 23.43/23.64 (mult(a, mult(mult(mult(a, b), b), c)) = mult(a, mult(c, mult(mult(a, b), b)))),
% 23.43/23.64 inference(symmetry,[status(thm)],[10524])).
% 23.43/23.64 tff(10526,plain,
% 23.43/23.64 (mult(mult(mult(a, b), b), c) = mult(mult(a, c), mult(unit, mult(mult(b, unit), b)))),
% 23.43/23.64 inference(transitivity,[status(thm)],[828, 1709, 868, 1708])).
% 23.43/23.64 tff(10527,plain,
% 23.43/23.64 (mult(a, mult(mult(mult(a, b), b), c)) = mult(a, mult(mult(a, c), mult(unit, mult(mult(b, unit), b))))),
% 23.43/23.64 inference(monotonicity,[status(thm)],[10526])).
% 23.43/23.64 tff(10528,plain,
% 23.43/23.64 (mult(a, mult(mult(a, c), mult(unit, mult(mult(b, unit), b)))) = mult(a, mult(mult(mult(a, b), b), c))),
% 23.43/23.64 inference(symmetry,[status(thm)],[10527])).
% 23.43/23.64 tff(10529,assumption,(~((~(mult(mult(b, mult(a, c)), b) = mult(mult(b, b), mult(a, c)))) | (~(mult(b, mult(mult(a, c), b)) = mult(b, mult(b, mult(a, c))))))), introduced(assumption)).
% 23.43/23.64 tff(10530,plain,
% 23.43/23.64 (mult(mult(b, mult(a, c)), b) = mult(mult(b, b), mult(a, c))),
% 23.43/23.64 inference(unit_resolution,[status(thm)],[8440, 10529])).
% 23.43/23.64 tff(10531,plain,
% 23.43/23.64 (mult(mult(b, b), mult(a, c)) = mult(mult(b, mult(a, c)), b)),
% 23.43/23.64 inference(symmetry,[status(thm)],[10530])).
% 23.43/23.64 tff(10532,plain,
% 23.43/23.64 (mult(mult(unit, mult(mult(b, unit), b)), mult(c, a)) = mult(mult(unit, mult(mult(b, unit), b)), mult(a, c))),
% 23.43/23.64 inference(monotonicity,[status(thm)],[8215])).
% 23.43/23.64 tff(10533,plain,
% 23.43/23.64 (mult(mult(unit, mult(mult(b, unit), b)), mult(c, a)) = mult(mult(b, mult(a, c)), b)),
% 23.43/23.64 inference(transitivity,[status(thm)],[10532, 8443, 10531])).
% 23.43/23.64 tff(10534,plain,
% 23.43/23.64 (mult(a, mult(mult(unit, mult(mult(b, unit), b)), mult(c, a))) = mult(a, mult(mult(b, mult(a, c)), b))),
% 23.43/23.64 inference(monotonicity,[status(thm)],[10533])).
% 23.43/23.64 tff(10535,plain,
% 23.43/23.64 (mult(mult(unit, mult(mult(b, unit), b)), mult(a, c)) = mult(mult(unit, mult(mult(b, unit), b)), mult(c, a))),
% 23.43/23.64 inference(symmetry,[status(thm)],[10532])).
% 23.43/23.64 tff(10536,plain,
% 23.43/23.64 (mult(a, mult(mult(unit, mult(mult(b, unit), b)), mult(a, c))) = mult(a, mult(mult(unit, mult(mult(b, unit), b)), mult(c, a)))),
% 23.43/23.64 inference(monotonicity,[status(thm)],[10535])).
% 23.43/23.64 tff(10537,plain,
% 23.43/23.64 (mult(a, mult(mult(unit, mult(mult(b, unit), b)), mult(a, c))) = mult(mult(mult(a, b), mult(a, c)), b)),
% 23.43/23.64 inference(transitivity,[status(thm)],[10536, 10534, 1752])).
% 23.43/23.64 tff(10538,plain,
% 23.43/23.64 (mult(mult(a, mult(unit, mult(mult(b, unit), b))), mult(a, c)) = mult(mult(mult(a, b), b), mult(a, c))),
% 23.43/23.64 inference(monotonicity,[status(thm)],[1092])).
% 23.43/23.64 tff(10539,plain,
% 23.43/23.64 ((mult(mult(a, mult(unit, mult(mult(b, unit), b))), mult(a, c)) = mult(a, mult(mult(unit, mult(mult(b, unit), b)), mult(a, c)))) <=> (mult(mult(mult(a, b), b), mult(a, c)) = mult(mult(mult(a, b), mult(a, c)), b))),
% 23.43/23.64 inference(monotonicity,[status(thm)],[10538, 10537])).
% 23.43/23.64 tff(10540,plain,
% 23.43/23.64 ((mult(mult(mult(a, b), b), mult(a, c)) = mult(mult(mult(a, b), mult(a, c)), b)) <=> (mult(mult(a, mult(unit, mult(mult(b, unit), b))), mult(a, c)) = mult(a, mult(mult(unit, mult(mult(b, unit), b)), mult(a, c))))),
% 23.43/23.64 inference(symmetry,[status(thm)],[10539])).
% 23.43/23.64 tff(10541,plain,
% 23.43/23.64 ((~(mult(mult(mult(a, b), b), mult(a, c)) = mult(mult(mult(a, b), mult(a, c)), b))) <=> (~(mult(mult(a, mult(unit, mult(mult(b, unit), b))), mult(a, c)) = mult(a, mult(mult(unit, mult(mult(b, unit), b)), mult(a, c)))))),
% 23.43/23.64 inference(monotonicity,[status(thm)],[10540])).
% 23.43/23.64 tff(10542,assumption,(~(mult(mult(mult(a, b), b), mult(a, c)) = mult(mult(mult(a, b), mult(a, c)), b))), introduced(assumption)).
% 23.43/23.64 tff(10543,plain,
% 23.43/23.64 (~(mult(mult(a, mult(unit, mult(mult(b, unit), b))), mult(a, c)) = mult(a, mult(mult(unit, mult(mult(b, unit), b)), mult(a, c))))),
% 23.43/23.64 inference(modus_ponens,[status(thm)],[10542, 10541])).
% 23.43/23.64 tff(10544,plain,
% 23.43/23.64 (((~(mult(mult(a, mult(unit, mult(mult(b, unit), b))), mult(a, c)) = mult(a, mult(mult(unit, mult(mult(b, unit), b)), mult(a, c))))) | (~(mult(mult(a, mult(a, c)), mult(unit, mult(mult(b, unit), b))) = mult(a, mult(mult(a, c), mult(unit, mult(mult(b, unit), b))))))) | (mult(mult(a, mult(unit, mult(mult(b, unit), b))), mult(a, c)) = mult(a, mult(mult(unit, mult(mult(b, unit), b)), mult(a, c))))),
% 23.43/23.64 inference(tautology,[status(thm)],[])).
% 23.43/23.64 tff(10545,plain,
% 23.43/23.64 ((~(mult(mult(a, mult(unit, mult(mult(b, unit), b))), mult(a, c)) = mult(a, mult(mult(unit, mult(mult(b, unit), b)), mult(a, c))))) | (~(mult(mult(a, mult(a, c)), mult(unit, mult(mult(b, unit), b))) = mult(a, mult(mult(a, c), mult(unit, mult(mult(b, unit), b))))))),
% 23.43/23.64 inference(unit_resolution,[status(thm)],[10544, 10543])).
% 23.43/23.64 tff(10546,plain,
% 23.43/23.64 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, mult(unit, mult(mult(b, unit), b))), mult(a, c)) = mult(mult(a, mult(a, c)), mult(unit, mult(mult(b, unit), b))))) | (~(mult(a, mult(mult(unit, mult(mult(b, unit), b)), mult(a, c))) = mult(a, mult(mult(a, c), mult(unit, mult(mult(b, unit), b)))))))) | (~((~(mult(mult(a, mult(unit, mult(mult(b, unit), b))), mult(a, c)) = mult(a, mult(mult(unit, mult(mult(b, unit), b)), mult(a, c))))) | (~(mult(mult(a, mult(a, c)), mult(unit, mult(mult(b, unit), b))) = mult(a, mult(mult(a, c), mult(unit, mult(mult(b, unit), b)))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, mult(unit, mult(mult(b, unit), b))), mult(a, c)) = mult(mult(a, mult(a, c)), mult(unit, mult(mult(b, unit), b))))) | (~(mult(a, mult(mult(unit, mult(mult(b, unit), b)), mult(a, c))) = mult(a, mult(mult(a, c), mult(unit, mult(mult(b, unit), b)))))))) | (~((~(mult(mult(a, mult(unit, mult(mult(b, unit), b))), mult(a, c)) = mult(a, mult(mult(unit, mult(mult(b, unit), b)), mult(a, c))))) | (~(mult(mult(a, mult(a, c)), mult(unit, mult(mult(b, unit), b))) = mult(a, mult(mult(a, c), mult(unit, mult(mult(b, unit), b)))))))))),
% 23.43/23.64 inference(rewrite,[status(thm)],[])).
% 23.43/23.64 tff(10547,plain,
% 23.43/23.64 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, mult(unit, mult(mult(b, unit), b))), mult(a, c)) = mult(mult(a, mult(a, c)), mult(unit, mult(mult(b, unit), b))))) | (~(mult(a, mult(mult(unit, mult(mult(b, unit), b)), mult(a, c))) = mult(a, mult(mult(a, c), mult(unit, mult(mult(b, unit), b)))))))) | (~((~(mult(mult(a, mult(unit, mult(mult(b, unit), b))), mult(a, c)) = mult(a, mult(mult(unit, mult(mult(b, unit), b)), mult(a, c))))) | (~(mult(mult(a, mult(a, c)), mult(unit, mult(mult(b, unit), b))) = mult(a, mult(mult(a, c), mult(unit, mult(mult(b, unit), b)))))))))),
% 23.43/23.64 inference(quant_inst,[status(thm)],[])).
% 23.43/23.64 tff(10548,plain,
% 23.43/23.64 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, mult(unit, mult(mult(b, unit), b))), mult(a, c)) = mult(mult(a, mult(a, c)), mult(unit, mult(mult(b, unit), b))))) | (~(mult(a, mult(mult(unit, mult(mult(b, unit), b)), mult(a, c))) = mult(a, mult(mult(a, c), mult(unit, mult(mult(b, unit), b)))))))) | (~((~(mult(mult(a, mult(unit, mult(mult(b, unit), b))), mult(a, c)) = mult(a, mult(mult(unit, mult(mult(b, unit), b)), mult(a, c))))) | (~(mult(mult(a, mult(a, c)), mult(unit, mult(mult(b, unit), b))) = mult(a, mult(mult(a, c), mult(unit, mult(mult(b, unit), b))))))))),
% 23.43/23.64 inference(modus_ponens,[status(thm)],[10547, 10546])).
% 23.43/23.64 tff(10549,plain,
% 23.43/23.64 ((~((~(mult(mult(a, mult(unit, mult(mult(b, unit), b))), mult(a, c)) = mult(mult(a, mult(a, c)), mult(unit, mult(mult(b, unit), b))))) | (~(mult(a, mult(mult(unit, mult(mult(b, unit), b)), mult(a, c))) = mult(a, mult(mult(a, c), mult(unit, mult(mult(b, unit), b)))))))) | (~((~(mult(mult(a, mult(unit, mult(mult(b, unit), b))), mult(a, c)) = mult(a, mult(mult(unit, mult(mult(b, unit), b)), mult(a, c))))) | (~(mult(mult(a, mult(a, c)), mult(unit, mult(mult(b, unit), b))) = mult(a, mult(mult(a, c), mult(unit, mult(mult(b, unit), b))))))))),
% 23.43/23.65 inference(unit_resolution,[status(thm)],[10548, 27])).
% 23.43/23.65 tff(10550,plain,
% 23.43/23.65 (~((~(mult(mult(a, mult(unit, mult(mult(b, unit), b))), mult(a, c)) = mult(mult(a, mult(a, c)), mult(unit, mult(mult(b, unit), b))))) | (~(mult(a, mult(mult(unit, mult(mult(b, unit), b)), mult(a, c))) = mult(a, mult(mult(a, c), mult(unit, mult(mult(b, unit), b)))))))),
% 23.43/23.65 inference(unit_resolution,[status(thm)],[10549, 10545])).
% 23.43/23.65 tff(10551,plain,
% 23.43/23.65 (((~(mult(mult(a, mult(unit, mult(mult(b, unit), b))), mult(a, c)) = mult(mult(a, mult(a, c)), mult(unit, mult(mult(b, unit), b))))) | (~(mult(a, mult(mult(unit, mult(mult(b, unit), b)), mult(a, c))) = mult(a, mult(mult(a, c), mult(unit, mult(mult(b, unit), b))))))) | (mult(a, mult(mult(unit, mult(mult(b, unit), b)), mult(a, c))) = mult(a, mult(mult(a, c), mult(unit, mult(mult(b, unit), b)))))),
% 23.43/23.65 inference(tautology,[status(thm)],[])).
% 23.43/23.65 tff(10552,plain,
% 23.43/23.65 (mult(a, mult(mult(unit, mult(mult(b, unit), b)), mult(a, c))) = mult(a, mult(mult(a, c), mult(unit, mult(mult(b, unit), b))))),
% 23.43/23.65 inference(unit_resolution,[status(thm)],[10551, 10550])).
% 23.43/23.65 tff(10553,plain,
% 23.43/23.65 (mult(a, mult(mult(unit, mult(mult(b, unit), b)), mult(c, a))) = mult(a, mult(mult(unit, mult(mult(b, unit), b)), mult(a, c)))),
% 23.43/23.65 inference(symmetry,[status(thm)],[10536])).
% 23.43/23.65 tff(10554,plain,
% 23.43/23.65 (mult(a, mult(mult(b, mult(a, c)), b)) = mult(a, mult(mult(unit, mult(mult(b, unit), b)), mult(c, a)))),
% 23.43/23.65 inference(symmetry,[status(thm)],[10534])).
% 23.43/23.65 tff(10555,assumption,(mult(mult(mult(a, b), mult(a, c)), b) = mult(mult(a, b), mult(mult(a, c), b))), introduced(assumption)).
% 23.43/23.65 tff(10556,plain,
% 23.43/23.65 (mult(mult(a, b), mult(mult(a, c), b)) = mult(mult(mult(a, b), mult(a, c)), b)),
% 23.43/23.65 inference(symmetry,[status(thm)],[10555])).
% 23.43/23.65 tff(10557,plain,
% 23.43/23.65 (mult(mult(a, b), mult(mult(a, b), c)) = mult(mult(a, b), mult(mult(a, c), b))),
% 23.43/23.65 inference(symmetry,[status(thm)],[10334])).
% 23.43/23.65 tff(10558,plain,
% 23.43/23.65 (mult(b, mult(mult(a, c), b)) = mult(b, mult(b, mult(a, c)))),
% 23.43/23.65 inference(unit_resolution,[status(thm)],[5618, 10529])).
% 23.43/23.65 tff(10559,plain,
% 23.43/23.65 (mult(b, mult(b, mult(a, c))) = mult(b, mult(mult(a, c), b))),
% 23.43/23.65 inference(symmetry,[status(thm)],[10558])).
% 23.43/23.65 tff(10560,plain,
% 23.43/23.65 (mult(b, mult(b, mult(a, c))) = mult(b, mult(mult(a, b), c))),
% 23.43/23.65 inference(transitivity,[status(thm)],[10559, 5603, 3388])).
% 23.43/23.65 tff(10561,plain,
% 23.43/23.65 (ld(b, mult(b, mult(b, mult(a, c)))) = ld(b, mult(b, mult(mult(a, b), c)))),
% 23.43/23.65 inference(monotonicity,[status(thm)],[10560])).
% 23.43/23.65 tff(10562,plain,
% 23.43/23.65 (mult(b, mult(a, c)) = mult(mult(a, b), c)),
% 23.43/23.65 inference(transitivity,[status(thm)],[8437, 10561, 5605])).
% 23.43/23.65 tff(10563,plain,
% 23.43/23.65 (mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(b, mult(a, c))) = mult(mult(a, b), mult(mult(a, b), c))),
% 23.43/23.65 inference(monotonicity,[status(thm)],[213, 10562])).
% 23.43/23.65 tff(10564,plain,
% 23.43/23.65 (mult(mult(a, b), mult(b, mult(a, c))) = mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(b, mult(a, c)))),
% 23.43/23.65 inference(monotonicity,[status(thm)],[2899])).
% 23.43/23.65 tff(10565,assumption,(mult(mult(mult(a, b), b), mult(a, c)) = mult(mult(a, b), mult(b, mult(a, c)))), introduced(assumption)).
% 23.43/23.65 tff(10566,plain,
% 23.43/23.65 (((~(mult(mult(a, mult(unit, mult(mult(b, unit), b))), mult(a, c)) = mult(mult(a, mult(a, c)), mult(unit, mult(mult(b, unit), b))))) | (~(mult(a, mult(mult(unit, mult(mult(b, unit), b)), mult(a, c))) = mult(a, mult(mult(a, c), mult(unit, mult(mult(b, unit), b))))))) | (mult(mult(a, mult(unit, mult(mult(b, unit), b))), mult(a, c)) = mult(mult(a, mult(a, c)), mult(unit, mult(mult(b, unit), b))))),
% 23.43/23.65 inference(tautology,[status(thm)],[])).
% 23.43/23.65 tff(10567,plain,
% 23.49/23.65 (mult(mult(a, mult(unit, mult(mult(b, unit), b))), mult(a, c)) = mult(mult(a, mult(a, c)), mult(unit, mult(mult(b, unit), b)))),
% 23.49/23.65 inference(unit_resolution,[status(thm)],[10566, 10550])).
% 23.49/23.65 tff(10568,plain,
% 23.49/23.65 (mult(mult(a, mult(a, c)), mult(unit, mult(mult(b, unit), b))) = mult(mult(a, mult(unit, mult(mult(b, unit), b))), mult(a, c))),
% 23.49/23.65 inference(symmetry,[status(thm)],[10567])).
% 23.49/23.65 tff(10569,plain,
% 23.49/23.65 (mult(mult(mult(a, c), a), mult(unit, mult(mult(b, unit), b))) = mult(mult(a, mult(a, c)), mult(unit, mult(mult(b, unit), b)))),
% 23.49/23.65 inference(monotonicity,[status(thm)],[8168])).
% 23.49/23.65 tff(10570,assumption,(mult(mult(mult(a, c), a), mult(unit, mult(mult(b, unit), b))) = mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b))))), introduced(assumption)).
% 23.49/23.65 tff(10571,plain,
% 23.49/23.65 (mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b)))) = mult(mult(mult(a, c), a), mult(unit, mult(mult(b, unit), b)))),
% 23.49/23.65 inference(symmetry,[status(thm)],[10570])).
% 23.49/23.65 tff(10572,plain,
% 23.49/23.65 (mult(mult(a, c), mult(mult(a, b), b)) = mult(a, mult(c, mult(mult(a, b), b)))),
% 23.49/23.65 inference(transitivity,[status(thm)],[1621, 10571, 10569, 10568, 10538, 10565, 10564, 10563, 10557, 10556, 1751, 10554, 10553, 10552, 10528, 10525])).
% 23.49/23.65 tff(10573,plain,
% 23.49/23.65 (mult(a, mult(mult(a, c), mult(unit, mult(mult(b, unit), b)))) = mult(a, mult(mult(unit, mult(mult(b, unit), b)), mult(a, c)))),
% 23.49/23.65 inference(symmetry,[status(thm)],[10552])).
% 23.49/23.65 tff(10574,plain,
% 23.49/23.65 (mult(a, mult(c, mult(mult(a, b), b))) = mult(mult(mult(a, b), mult(a, c)), b)),
% 23.49/23.65 inference(transitivity,[status(thm)],[10524, 10527, 10573, 10536, 10534, 1752])).
% 23.49/23.65 tff(10575,plain,
% 23.49/23.65 (mult(mult(a, c), mult(mult(a, b), b)) = mult(mult(mult(a, b), b), mult(a, c))),
% 23.49/23.65 inference(transitivity,[status(thm)],[1621, 10571, 10569, 10568, 10538])).
% 23.49/23.65 tff(10576,plain,
% 23.49/23.65 ((mult(mult(a, c), mult(mult(a, b), b)) = mult(a, mult(c, mult(mult(a, b), b)))) <=> (mult(mult(mult(a, b), b), mult(a, c)) = mult(mult(mult(a, b), mult(a, c)), b))),
% 23.49/23.65 inference(monotonicity,[status(thm)],[10575, 10574])).
% 23.49/23.65 tff(10577,plain,
% 23.49/23.65 ((mult(mult(mult(a, b), b), mult(a, c)) = mult(mult(mult(a, b), mult(a, c)), b)) <=> (mult(mult(a, c), mult(mult(a, b), b)) = mult(a, mult(c, mult(mult(a, b), b))))),
% 23.49/23.65 inference(symmetry,[status(thm)],[10576])).
% 23.49/23.65 tff(10578,plain,
% 23.49/23.65 ((~(mult(mult(mult(a, b), b), mult(a, c)) = mult(mult(mult(a, b), mult(a, c)), b))) <=> (~(mult(mult(a, c), mult(mult(a, b), b)) = mult(a, mult(c, mult(mult(a, b), b)))))),
% 23.49/23.65 inference(monotonicity,[status(thm)],[10577])).
% 23.49/23.65 tff(10579,plain,
% 23.49/23.65 (~(mult(mult(a, c), mult(mult(a, b), b)) = mult(a, mult(c, mult(mult(a, b), b))))),
% 23.49/23.65 inference(modus_ponens,[status(thm)],[10542, 10578])).
% 23.49/23.65 tff(10580,plain,
% 23.49/23.65 ($false),
% 23.49/23.65 inference(unit_resolution,[status(thm)],[10579, 10572])).
% 23.49/23.65 tff(10581,plain,(((~(mult(mult(b, mult(a, c)), b) = mult(mult(b, b), mult(a, c)))) | (~(mult(b, mult(mult(a, c), b)) = mult(b, mult(b, mult(a, c)))))) | (~(mult(mult(mult(a, c), a), mult(unit, mult(mult(b, unit), b))) = mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b)))))) | (~(mult(mult(mult(a, b), b), mult(a, c)) = mult(mult(a, b), mult(b, mult(a, c))))) | (~(mult(mult(mult(a, b), mult(a, c)), b) = mult(mult(a, b), mult(mult(a, c), b)))) | (~(mult(mult(c, mult(a, b)), b) = mult(c, mult(mult(a, b), b)))) | (mult(mult(mult(a, b), b), mult(a, c)) = mult(mult(mult(a, b), mult(a, c)), b))), inference(lemma,lemma(discharge,[]))).
% 23.49/23.65 tff(10582,plain,
% 23.49/23.65 ((~(mult(mult(b, mult(a, c)), b) = mult(mult(b, b), mult(a, c)))) | (~(mult(b, mult(mult(a, c), b)) = mult(b, mult(b, mult(a, c)))))),
% 23.49/23.65 inference(unit_resolution,[status(thm)],[10581, 10517, 10437, 10435, 10446, 10441])).
% 23.49/23.65 tff(10583,plain,
% 23.49/23.65 (~((~(mult(mult(b, b), mult(a, c)) = mult(b, mult(b, mult(a, c))))) | (~(mult(mult(b, mult(a, c)), b) = mult(b, mult(mult(a, c), b)))))),
% 23.49/23.65 inference(unit_resolution,[status(thm)],[5630, 10582])).
% 23.49/23.65 tff(10584,plain,
% 23.49/23.65 (mult(mult(b, mult(a, c)), b) = mult(b, mult(mult(a, c), b))),
% 23.49/23.65 inference(unit_resolution,[status(thm)],[5632, 10583])).
% 23.49/23.65 tff(10585,plain,
% 23.49/23.65 (mult(mult(b, a), mult(b, c)) = mult(b, mult(a, mult(b, c)))),
% 23.49/23.65 inference(unit_resolution,[status(thm)],[7561, 9697])).
% 23.49/23.65 tff(10586,plain,
% 23.49/23.65 (mult(mult(c, mult(a, c)), mult(c, a)) = mult(mult(mult(a, c), c), mult(a, c))),
% 23.49/23.65 inference(monotonicity,[status(thm)],[10166, 8215])).
% 23.49/23.65 tff(10587,plain,
% 23.49/23.65 (mult(mult(mult(a, c), c), mult(c, a)) = mult(mult(c, mult(a, c)), mult(c, a))),
% 23.49/23.65 inference(monotonicity,[status(thm)],[8195])).
% 23.49/23.65 tff(10588,plain,
% 23.49/23.65 (mult(mult(mult(a, c), c), mult(c, a)) = mult(mult(mult(a, c), c), mult(a, c))),
% 23.49/23.65 inference(transitivity,[status(thm)],[10587, 10586])).
% 23.49/23.65 tff(10589,plain,
% 23.49/23.65 (mult(mult(mult(b, c), c), a) = mult(mult(mult(b, c), a), c)),
% 23.49/23.65 inference(unit_resolution,[status(thm)],[6773, 10588])).
% 23.49/23.65 tff(10590,plain,
% 23.49/23.65 ((mult(mult(b, a), mult(b, c)) = mult(mult(b, mult(b, c)), a)) <=> (mult(b, mult(a, mult(b, c))) = mult(b, mult(mult(b, c), a)))),
% 23.49/23.65 inference(monotonicity,[status(thm)],[10585, 9698])).
% 23.49/23.65 tff(10591,plain,
% 23.49/23.65 ((mult(b, mult(a, mult(b, c))) = mult(b, mult(mult(b, c), a))) <=> (mult(mult(b, a), mult(b, c)) = mult(mult(b, mult(b, c)), a))),
% 23.49/23.65 inference(symmetry,[status(thm)],[10590])).
% 23.49/23.65 tff(10592,plain,
% 23.49/23.65 ((~(mult(b, mult(a, mult(b, c))) = mult(b, mult(mult(b, c), a)))) <=> (~(mult(mult(b, a), mult(b, c)) = mult(mult(b, mult(b, c)), a)))),
% 23.49/23.65 inference(monotonicity,[status(thm)],[10591])).
% 23.49/23.65 tff(10593,plain,
% 23.49/23.65 (~(mult(mult(b, a), mult(b, c)) = mult(mult(b, mult(b, c)), a))),
% 23.49/23.65 inference(modus_ponens,[status(thm)],[9632, 10592])).
% 23.49/23.65 tff(10594,plain,
% 23.49/23.65 (~(mult(mult(c, mult(b, c)), a) = mult(mult(c, a), mult(b, c)))),
% 23.49/23.65 inference(unit_resolution,[status(thm)],[8991, 10593, 10589, 9698, 10585])).
% 23.49/23.65 tff(10595,plain,
% 23.49/23.65 ((~(mult(mult(c, mult(b, c)), a) = mult(mult(c, a), mult(b, c)))) | (~(mult(c, mult(mult(b, c), a)) = mult(c, mult(a, mult(b, c)))))),
% 23.49/23.65 inference(unit_resolution,[status(thm)],[4194, 10594])).
% 23.49/23.65 tff(10596,plain,
% 23.49/23.65 (~((~(mult(mult(c, mult(b, c)), a) = mult(c, mult(mult(b, c), a)))) | (~(mult(mult(c, a), mult(b, c)) = mult(c, mult(a, mult(b, c))))))),
% 23.49/23.65 inference(unit_resolution,[status(thm)],[4199, 10595])).
% 23.49/23.65 tff(10597,plain,
% 23.49/23.65 (mult(mult(c, mult(b, c)), a) = mult(c, mult(mult(b, c), a))),
% 23.49/23.65 inference(unit_resolution,[status(thm)],[4201, 10596])).
% 23.49/23.65 tff(10598,plain,
% 23.49/23.65 (mult(a, mult(mult(a, c), c)) = mult(a, mult(c, mult(a, c)))),
% 23.49/23.65 inference(monotonicity,[status(thm)],[8195])).
% 23.49/23.65 tff(10599,plain,
% 23.49/23.65 (mult(a, mult(c, mult(a, c))) = mult(a, mult(mult(a, c), c))),
% 23.49/23.65 inference(symmetry,[status(thm)],[10598])).
% 23.49/23.65 tff(10600,plain,
% 23.49/23.65 (mult(unit, mult(mult(a, c), c)) = mult(unit, mult(c, mult(a, c)))),
% 23.49/23.65 inference(monotonicity,[status(thm)],[8195])).
% 23.49/23.65 tff(10601,plain,
% 23.49/23.65 (mult(unit, mult(mult(a, c), c)) = mult(c, mult(a, c))),
% 23.49/23.65 inference(transitivity,[status(thm)],[10600, 4366, 4365, 4362, 2690])).
% 23.49/23.65 tff(10602,plain,
% 23.49/23.65 (mult(mult(unit, mult(mult(a, c), c)), unit) = mult(mult(c, mult(a, c)), unit)),
% 23.49/23.65 inference(monotonicity,[status(thm)],[10601])).
% 23.49/23.65 tff(10603,plain,
% 23.49/23.65 (mult(mult(unit, mult(mult(a, c), c)), unit) = mult(c, mult(a, c))),
% 23.49/23.65 inference(transitivity,[status(thm)],[10602, 6010])).
% 23.49/23.65 tff(10604,plain,
% 23.49/23.65 (mult(a, mult(mult(unit, mult(mult(a, c), c)), unit)) = mult(a, mult(c, mult(a, c)))),
% 23.49/23.65 inference(monotonicity,[status(thm)],[10603])).
% 23.49/23.65 tff(10605,plain,
% 23.49/23.65 (mult(a, mult(mult(unit, mult(mult(a, c), c)), unit)) = mult(a, mult(mult(a, c), c))),
% 23.49/23.65 inference(transitivity,[status(thm)],[10604, 10599])).
% 23.49/23.65 tff(10606,plain,
% 23.49/23.65 (mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, mult(mult(a, c), c)), unit))) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(a, c), c)))),
% 23.49/23.65 inference(monotonicity,[status(thm)],[10605])).
% 23.49/23.65 tff(10607,plain,
% 23.49/23.65 (mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(a, c), c))) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, mult(mult(a, c), c)), unit)))),
% 23.49/23.65 inference(symmetry,[status(thm)],[10606])).
% 23.49/23.65 tff(10608,plain,
% 23.49/23.65 (mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, mult(a, c)))) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(a, c), c)))),
% 23.49/23.65 inference(monotonicity,[status(thm)],[10599])).
% 23.49/23.65 tff(10609,plain,
% 23.49/23.65 (mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, mult(a, c)))) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, mult(mult(a, c), c)), unit)))),
% 23.49/23.65 inference(transitivity,[status(thm)],[10608, 10607])).
% 23.49/23.65 tff(10610,plain,
% 23.49/23.65 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, mult(mult(a, c), c)), unit)) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, mult(a, c)))),
% 23.49/23.65 inference(monotonicity,[status(thm)],[10603])).
% 23.49/23.65 tff(10611,plain,
% 23.49/23.65 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, mult(mult(a, c), c)), unit))),
% 23.49/23.65 inference(symmetry,[status(thm)],[10610])).
% 23.49/23.65 tff(10612,plain,
% 23.49/23.65 ((mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, mult(a, c))))) <=> (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, mult(mult(a, c), c)), unit)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, mult(mult(a, c), c)), unit))))),
% 23.49/23.65 inference(monotonicity,[status(thm)],[10611, 10609])).
% 23.49/23.65 tff(10613,plain,
% 23.49/23.65 ((mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, mult(mult(a, c), c)), unit)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, mult(mult(a, c), c)), unit)))) <=> (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, mult(a, c)))))),
% 23.49/23.65 inference(symmetry,[status(thm)],[10612])).
% 23.49/23.65 tff(10614,plain,
% 23.49/23.65 (mult(mult(a, mult(a, c)), c) = mult(a, mult(mult(a, c), c))),
% 23.49/23.65 inference(transitivity,[status(thm)],[9166, 4717, 4715, 10599])).
% 23.49/23.65 tff(10615,plain,
% 23.49/23.65 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(a, c)), c)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(a, c), c)))),
% 23.49/23.65 inference(monotonicity,[status(thm)],[10614])).
% 23.49/23.65 tff(10616,plain,
% 23.49/23.65 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(a, c)), c)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, mult(mult(a, c), c)), unit)))),
% 23.49/23.65 inference(transitivity,[status(thm)],[10615, 10607])).
% 23.49/23.65 tff(10617,plain,
% 23.49/23.65 (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))), c) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, mult(mult(a, c), c)), unit))),
% 23.49/23.65 inference(transitivity,[status(thm)],[9169, 5142, 5141, 5139, 10611])).
% 23.49/23.65 tff(10618,plain,
% 23.49/23.65 ((mult(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(a, c)), c))) <=> (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, mult(mult(a, c), c)), unit)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, mult(mult(a, c), c)), unit))))),
% 23.49/23.65 inference(monotonicity,[status(thm)],[10617, 10616])).
% 23.49/23.65 tff(10619,plain,
% 23.49/23.65 ((mult(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(a, c)), c))) <=> (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, mult(a, c)))))),
% 23.49/23.65 inference(transitivity,[status(thm)],[10618, 10613])).
% 23.49/23.65 tff(10620,plain,
% 23.49/23.65 (mult(c, mult(mult(a, c), a)) = mult(c, mult(a, mult(a, c)))),
% 23.49/23.65 inference(symmetry,[status(thm)],[10132])).
% 23.49/23.65 tff(10621,plain,
% 23.49/23.65 (mult(rd(mult(b, c), mult(a, c)), mult(c, mult(mult(a, c), a))) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, mult(a, c))))),
% 23.49/23.65 inference(monotonicity,[status(thm)],[10620])).
% 23.49/23.65 tff(10622,plain,
% 23.49/23.65 (mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a))),
% 23.49/23.65 inference(monotonicity,[status(thm)],[8262])).
% 23.49/23.65 tff(10623,plain,
% 23.49/23.65 (mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c)))),
% 23.49/23.65 inference(symmetry,[status(thm)],[10622])).
% 23.49/23.65 tff(10624,plain,
% 23.49/23.65 ((mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(mult(a, c), a)))) <=> (mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, mult(a, c)))))),
% 23.49/23.65 inference(monotonicity,[status(thm)],[10623, 10621])).
% 23.49/23.66 tff(10625,plain,
% 23.49/23.66 (mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, mult(a, c))))),
% 23.49/23.66 inference(modus_ponens,[status(thm)],[10194, 10624])).
% 23.49/23.66 tff(10626,plain,
% 23.49/23.66 (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(a, c)), c))),
% 23.49/23.66 inference(unit_resolution,[status(thm)],[9237, 10625])).
% 23.49/23.66 tff(10627,plain,
% 23.49/23.66 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, mult(a, c))))),
% 23.49/23.66 inference(modus_ponens,[status(thm)],[10626, 10619])).
% 23.49/23.66 tff(10628,plain,
% 23.49/23.66 (mult(mult(mult(b, c), a), mult(a, b)) = mult(mult(b, c), mult(a, mult(a, b)))),
% 23.49/23.66 inference(unit_resolution,[status(thm)],[1320, 10448])).
% 23.49/23.66 tff(10629,plain,
% 23.49/23.66 (mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))) = mult(mult(b, c), mult(a, c))),
% 23.49/23.66 inference(transitivity,[status(thm)],[10622, 2632, 6871, 9752, 4660, 9746, 2502, 2499])).
% 23.49/23.66 tff(10630,plain,
% 23.49/23.66 (ld(a, mult(a, mult(rd(mult(b, c), mult(a, c)), c))) = ld(a, mult(a, mult(c, rd(mult(b, c), mult(a, c)))))),
% 23.49/23.66 inference(symmetry,[status(thm)],[9897])).
% 23.49/23.66 tff(10631,plain,
% 23.49/23.66 (mult(rd(mult(b, c), mult(a, c)), c) = mult(c, rd(mult(b, c), mult(a, c)))),
% 23.49/23.66 inference(transitivity,[status(thm)],[5128, 10630, 5114])).
% 23.49/23.66 tff(10632,plain,
% 23.49/23.66 (mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))),
% 23.49/23.66 inference(monotonicity,[status(thm)],[10631])).
% 23.49/23.66 tff(10633,plain,
% 23.49/23.66 (mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)) = mult(mult(b, c), c)),
% 23.49/23.66 inference(transitivity,[status(thm)],[10632, 4535, 2802, 4179, 4176, 4173])).
% 23.49/23.66 tff(10634,plain,
% 23.49/23.66 (mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)), a) = mult(mult(mult(b, c), c), a)),
% 23.49/23.66 inference(monotonicity,[status(thm)],[10633])).
% 23.49/23.66 tff(10635,assumption,(mult(mult(c, mult(b, c)), a) = mult(c, mult(mult(b, c), a))), introduced(assumption)).
% 23.49/23.66 tff(10636,assumption,(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, mult(a, c))))), introduced(assumption)).
% 23.49/23.66 tff(10637,plain,
% 23.49/23.66 (mult(c, mult(a, b)) = mult(mult(unit, mult(a, c)), b)),
% 23.49/23.66 inference(transitivity,[status(thm)],[4270, 10518, 5517])).
% 23.49/23.66 tff(10638,plain,
% 23.49/23.66 (mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)) = mult(mult(b, c), mult(a, c))),
% 23.49/23.66 inference(transitivity,[status(thm)],[2632, 6871, 9752, 4660, 9746, 2502, 2499])).
% 23.49/23.66 tff(10639,plain,
% 23.49/23.66 (mult(unit, mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a))) = mult(unit, mult(mult(b, c), mult(a, c)))),
% 23.49/23.66 inference(monotonicity,[status(thm)],[10638])).
% 23.49/23.66 tff(10640,plain,
% 23.49/23.66 ((mult(unit, mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a))) = mult(unit, mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)))) <=> (mult(unit, mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c))) = mult(unit, mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a))))),
% 23.49/23.66 inference(commutativity,[status(thm)],[])).
% 23.49/23.66 tff(10641,plain,
% 23.49/23.66 ((mult(unit, mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c))) = mult(unit, mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)))) <=> (mult(unit, mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a))) = mult(unit, mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c))))),
% 23.49/23.66 inference(symmetry,[status(thm)],[10640])).
% 23.49/23.66 tff(10642,plain,
% 23.49/23.66 (mult(unit, mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a))) = mult(mult(b, c), mult(a, c))),
% 23.49/23.66 inference(transitivity,[status(thm)],[10639, 10291, 10137])).
% 23.49/23.66 tff(10643,plain,
% 23.49/23.66 (mult(mult(unit, c), mult(b, a)) = mult(c, mult(b, a))),
% 23.49/23.66 inference(monotonicity,[status(thm)],[73])).
% 23.49/23.66 tff(10644,plain,
% 23.49/23.66 (mult(c, mult(b, a)) = mult(mult(unit, c), mult(b, a))),
% 23.49/23.66 inference(symmetry,[status(thm)],[10643])).
% 23.49/23.66 tff(10645,plain,
% 23.49/23.66 (mult(mult(b, c), a) = mult(mult(unit, c), mult(b, a))),
% 23.49/23.66 inference(transitivity,[status(thm)],[3057, 4208, 10644])).
% 23.49/23.66 tff(10646,plain,
% 23.49/23.66 (mult(mult(mult(b, c), a), c) = mult(mult(mult(unit, c), mult(b, a)), c)),
% 23.49/23.66 inference(monotonicity,[status(thm)],[10645])).
% 23.49/23.66 tff(10647,plain,
% 23.49/23.66 (mult(mult(mult(unit, c), mult(b, a)), c) = mult(mult(mult(b, c), a), c)),
% 23.49/23.66 inference(symmetry,[status(thm)],[10646])).
% 23.49/23.66 tff(10648,plain,
% 23.49/23.66 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(unit, c), mult(b, a)), c) = mult(unit, mult(mult(c, mult(b, a)), c)))),
% 23.49/23.66 inference(quant_inst,[status(thm)],[])).
% 23.49/23.66 tff(10649,plain,
% 23.49/23.66 (mult(mult(mult(unit, c), mult(b, a)), c) = mult(unit, mult(mult(c, mult(b, a)), c))),
% 23.49/23.66 inference(unit_resolution,[status(thm)],[10648, 56])).
% 23.49/23.66 tff(10650,plain,
% 23.49/23.66 (mult(unit, mult(mult(c, mult(b, a)), c)) = mult(mult(mult(unit, c), mult(b, a)), c)),
% 23.49/23.66 inference(symmetry,[status(thm)],[10649])).
% 23.49/23.66 tff(10651,plain,
% 23.49/23.66 (mult(mult(mult(b, c), a), c) = mult(mult(mult(b, c), c), a)),
% 23.49/23.66 inference(symmetry,[status(thm)],[10589])).
% 23.49/23.66 tff(10652,plain,
% 23.49/23.66 (mult(mult(c, mult(b, a)), c) = mult(mult(mult(b, c), a), c)),
% 23.49/23.66 inference(monotonicity,[status(thm)],[4305])).
% 23.49/23.66 tff(10653,plain,
% 23.49/23.66 (mult(mult(c, mult(b, a)), c) = mult(mult(mult(b, c), c), a)),
% 23.49/23.66 inference(transitivity,[status(thm)],[10652, 10651])).
% 23.49/23.66 tff(10654,plain,
% 23.49/23.66 (mult(unit, mult(mult(c, mult(b, a)), c)) = mult(unit, mult(mult(mult(b, c), c), a))),
% 23.49/23.66 inference(monotonicity,[status(thm)],[10653])).
% 23.49/23.66 tff(10655,plain,
% 23.49/23.66 (mult(unit, mult(mult(mult(b, c), c), a)) = mult(unit, mult(mult(c, mult(b, a)), c))),
% 23.49/23.66 inference(symmetry,[status(thm)],[10654])).
% 23.49/23.66 tff(10656,plain,
% 23.49/23.66 (mult(b, mult(mult(a, c), c)) = mult(b, mult(c, mult(a, c)))),
% 23.49/23.66 inference(monotonicity,[status(thm)],[8195])).
% 23.49/23.66 tff(10657,plain,
% 23.49/23.66 (mult(b, mult(c, mult(a, c))) = mult(b, mult(mult(a, c), c))),
% 23.49/23.66 inference(symmetry,[status(thm)],[10656])).
% 23.49/23.66 tff(10658,plain,
% 23.49/23.66 (mult(mult(mult(b, c), c), a) = mult(b, mult(mult(a, c), c))),
% 23.49/23.66 inference(transitivity,[status(thm)],[10589, 2570, 8560, 10657])).
% 23.49/23.66 tff(10659,plain,
% 23.49/23.66 (mult(unit, mult(mult(mult(b, c), c), a)) = mult(unit, mult(b, mult(mult(a, c), c)))),
% 23.49/23.66 inference(monotonicity,[status(thm)],[10658])).
% 23.49/23.66 tff(10660,plain,
% 23.49/23.66 (mult(unit, mult(b, mult(mult(a, c), c))) = mult(unit, mult(mult(mult(b, c), c), a))),
% 23.49/23.66 inference(symmetry,[status(thm)],[10659])).
% 23.49/23.66 tff(10661,plain,
% 23.49/23.66 (mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c))),
% 23.49/23.66 inference(unit_resolution,[status(thm)],[9037, 9026, 4535])).
% 23.49/23.66 tff(10662,plain,
% 23.49/23.66 (mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 23.49/23.66 inference(transitivity,[status(thm)],[9033, 9022])).
% 23.49/23.66 tff(10663,plain,
% 23.49/23.66 ((~((~(mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)))) | (~(mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))))) | (~(mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)))) | (~(mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))))),
% 23.49/23.66 inference(tautology,[status(thm)],[])).
% 23.49/23.66 tff(10664,plain,
% 23.49/23.66 (~((~(mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)))) | (~(mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))))),
% 23.49/23.66 inference(unit_resolution,[status(thm)],[10663, 10662, 10661])).
% 23.49/23.66 tff(10665,plain,
% 23.49/23.66 (mult(mult(mult(b, c), c), a) = mult(mult(c, mult(b, c)), a)),
% 23.49/23.66 inference(symmetry,[status(thm)],[4181])).
% 23.49/23.66 tff(10666,assumption,(~((~(mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)))) | (~(mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))))), introduced(assumption)).
% 23.49/23.66 tff(10667,plain,
% 23.49/23.66 (mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 23.49/23.66 inference(unit_resolution,[status(thm)],[4567, 10666])).
% 23.49/23.66 tff(10668,plain,
% 23.49/23.66 (mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(b, c), c))),
% 23.49/23.66 inference(transitivity,[status(thm)],[10667, 4539])).
% 23.49/23.66 tff(10669,plain,
% 23.49/23.66 (ld(a, mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))) = ld(a, mult(a, mult(mult(b, c), c)))),
% 23.49/23.66 inference(monotonicity,[status(thm)],[10668])).
% 23.49/23.66 tff(10670,plain,
% 23.49/23.66 (mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))),
% 23.49/23.66 inference(monotonicity,[status(thm)],[10631])).
% 23.49/23.66 tff(10671,plain,
% 23.49/23.66 (mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(b, c), c)),
% 23.49/23.66 inference(transitivity,[status(thm)],[10670, 8954, 10669, 4173])).
% 23.49/23.66 tff(10672,plain,
% 23.49/23.66 (mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(b, c), c), a)),
% 23.49/23.66 inference(monotonicity,[status(thm)],[10671])).
% 23.49/23.66 tff(10673,plain,
% 23.49/23.66 (mult(mult(c, a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c))),
% 23.49/23.66 inference(monotonicity,[status(thm)],[8215])).
% 23.49/23.66 tff(10674,plain,
% 23.49/23.66 (mult(mult(mult(c, a), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a)),
% 23.49/23.66 inference(monotonicity,[status(thm)],[10673])).
% 23.49/23.66 tff(10675,plain,
% 23.49/23.66 (mult(c, mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a)) = mult(c, mult(mult(b, c), a))),
% 23.49/23.66 inference(transitivity,[status(thm)],[5324, 10674, 10672, 10665, 10635])).
% 23.49/23.66 tff(10676,plain,
% 23.49/23.66 (ld(c, mult(c, mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a))) = ld(c, mult(c, mult(mult(b, c), a)))),
% 23.49/23.66 inference(monotonicity,[status(thm)],[10675])).
% 23.49/23.66 tff(10677,plain,
% 23.49/23.66 (mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(b, c), a)),
% 23.49/23.66 inference(transitivity,[status(thm)],[5329, 10676, 2296])).
% 23.49/23.66 tff(10678,plain,
% 23.49/23.66 (rd(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a), a) = rd(mult(mult(b, c), a), a)),
% 23.49/23.66 inference(monotonicity,[status(thm)],[10677])).
% 23.49/23.66 tff(10679,plain,
% 23.49/23.66 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), mult(a, c)), mult(a, c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), c)))),
% 23.49/23.66 inference(quant_inst,[status(thm)],[])).
% 23.49/23.66 tff(10680,plain,
% 23.49/23.66 (rd(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), mult(a, c)), mult(a, c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), c))),
% 23.49/23.66 inference(unit_resolution,[status(thm)],[10679, 168])).
% 23.49/23.66 tff(10681,plain,
% 23.49/23.66 (mult(a, mult(rd(mult(b, c), mult(a, c)), c)) = mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c))),
% 23.49/23.66 inference(symmetry,[status(thm)],[2356])).
% 23.49/23.66 tff(10682,plain,
% 23.49/23.66 (mult(a, mult(rd(mult(b, c), mult(a, c)), c)) = mult(a, mult(c, rd(mult(b, c), mult(a, c))))),
% 23.49/23.66 inference(transitivity,[status(thm)],[10681, 9157, 6696])).
% 23.49/23.66 tff(10683,plain,
% 23.49/23.66 (mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), mult(a, c)) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c))),
% 23.49/23.66 inference(monotonicity,[status(thm)],[10682])).
% 23.49/23.66 tff(10684,plain,
% 23.49/23.66 (mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), mult(a, c))),
% 23.49/23.66 inference(symmetry,[status(thm)],[10683])).
% 23.49/23.66 tff(10685,plain,
% 23.49/23.66 (mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c))),
% 23.49/23.66 inference(unit_resolution,[status(thm)],[4606, 10666])).
% 23.49/23.66 tff(10686,plain,
% 23.49/23.66 (mult(mult(a, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c))))),
% 23.49/23.66 inference(monotonicity,[status(thm)],[10631])).
% 23.49/23.66 tff(10687,plain,
% 23.49/23.66 (mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), c))),
% 23.49/23.66 inference(monotonicity,[status(thm)],[8168])).
% 23.49/23.66 tff(10688,plain,
% 23.49/23.66 (mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))) = mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c))),
% 23.49/23.66 inference(symmetry,[status(thm)],[8947])).
% 23.49/23.66 tff(10689,plain,
% 23.49/23.66 (rd(mult(mult(b, c), a), a) = rd(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a), a)),
% 23.49/23.66 inference(symmetry,[status(thm)],[10678])).
% 23.49/23.66 tff(10690,plain,
% 23.49/23.66 (mult(b, c) = rd(mult(mult(b, c), a), a)),
% 23.49/23.66 inference(symmetry,[status(thm)],[1370])).
% 23.49/23.66 tff(10691,plain,
% 23.49/23.66 (mult(b, c) = mult(a, mult(rd(mult(b, c), mult(a, c)), c))),
% 23.49/23.66 inference(transitivity,[status(thm)],[10690, 10689, 9592])).
% 23.49/23.66 tff(10692,plain,
% 23.49/23.66 (mult(mult(a, c), mult(b, c)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c)))),
% 23.49/23.66 inference(monotonicity,[status(thm)],[10691])).
% 23.49/23.66 tff(10693,plain,
% 23.49/23.66 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), mult(a, c))),
% 23.49/23.66 inference(transitivity,[status(thm)],[1039, 138, 10692, 10688, 10687, 10686, 10685, 10684])).
% 23.49/23.66 tff(10694,plain,
% 23.49/23.66 (rd(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)), mult(a, c)) = rd(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), mult(a, c)), mult(a, c))),
% 23.49/23.66 inference(monotonicity,[status(thm)],[10693])).
% 23.49/23.66 tff(10695,plain,
% 23.49/23.66 (mult(mult(unit, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(a, c))),
% 23.49/23.66 inference(transitivity,[status(thm)],[4928, 4423, 10694, 10680, 9593, 10678, 1370, 267, 4904, 4902])).
% 23.49/23.66 tff(10696,plain,
% 23.49/23.66 ($false),
% 23.49/23.66 inference(unit_resolution,[status(thm)],[10420, 10695])).
% 23.49/23.66 tff(10697,plain,(((~(mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)))) | (~(mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))))) | (mult(mult(unit, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(a, c))) | (~(mult(mult(c, mult(b, c)), a) = mult(c, mult(mult(b, c), a)))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (~(mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c)))))), inference(lemma,lemma(discharge,[]))).
% 23.49/23.67 tff(10698,plain,
% 23.49/23.67 (~(mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))),
% 23.49/23.67 inference(unit_resolution,[status(thm)],[10697, 10664, 10635, 4535, 1039, 10420])).
% 23.49/23.67 tff(10699,plain,
% 23.49/23.67 ((~(mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))) | (~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a))))),
% 23.49/23.67 inference(unit_resolution,[status(thm)],[5352, 10698])).
% 23.49/23.67 tff(10700,plain,
% 23.49/23.67 (~((~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)))) | (~(mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))))),
% 23.49/23.67 inference(unit_resolution,[status(thm)],[8807, 10699])).
% 23.49/23.67 tff(10701,plain,
% 23.49/23.67 (((~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)))) | (~(mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c)))))) | (mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)))),
% 23.49/23.67 inference(tautology,[status(thm)],[])).
% 23.49/23.67 tff(10702,plain,
% 23.49/23.67 (mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c))),
% 23.49/23.67 inference(unit_resolution,[status(thm)],[10701, 10700])).
% 23.49/23.67 tff(10703,plain,
% 23.49/23.67 (mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(b, c), c)),
% 23.49/23.67 inference(transitivity,[status(thm)],[10670, 9031, 9028, 9024])).
% 23.49/23.67 tff(10704,plain,
% 23.49/23.67 (mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(b, c), c), a)),
% 23.49/23.67 inference(monotonicity,[status(thm)],[10703])).
% 23.49/23.67 tff(10705,plain,
% 23.49/23.67 (mult(mult(mult(b, c), c), a) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a)),
% 23.49/23.67 inference(symmetry,[status(thm)],[10704])).
% 23.49/23.67 tff(10706,plain,
% 23.49/23.67 (mult(b, mult(mult(a, c), c)) = mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c))),
% 23.49/23.67 inference(transitivity,[status(thm)],[10656, 8559, 4149, 10651, 10705, 10702])).
% 23.49/23.67 tff(10707,plain,
% 23.49/23.67 (mult(unit, mult(b, mult(mult(a, c), c))) = mult(unit, mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)))),
% 23.49/23.67 inference(monotonicity,[status(thm)],[10706])).
% 23.49/23.67 tff(10708,plain,
% 23.49/23.67 (mult(unit, mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c))) = mult(unit, mult(b, mult(mult(a, c), c)))),
% 23.49/23.67 inference(symmetry,[status(thm)],[10707])).
% 23.49/23.67 tff(10709,plain,
% 23.49/23.67 (mult(unit, mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c))) = mult(b, mult(c, mult(a, c)))),
% 23.49/23.67 inference(transitivity,[status(thm)],[10708, 10660, 10655, 10650, 10647, 2570, 8560])).
% 23.49/23.67 tff(10710,plain,
% 23.49/23.67 ((mult(unit, mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c))) = mult(unit, mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)))) <=> (mult(b, mult(c, mult(a, c))) = mult(mult(b, c), mult(a, c)))),
% 23.49/23.67 inference(monotonicity,[status(thm)],[10709, 10642])).
% 23.49/23.67 tff(10711,plain,
% 23.49/23.67 ((mult(unit, mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c))) = mult(unit, mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)))) <=> (mult(mult(b, c), mult(a, c)) = mult(b, mult(c, mult(a, c))))),
% 23.49/23.67 inference(transitivity,[status(thm)],[10710, 6765])).
% 23.49/23.67 tff(10712,plain,
% 23.49/23.67 ((mult(mult(b, c), mult(a, c)) = mult(b, mult(c, mult(a, c)))) <=> (mult(unit, mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c))) = mult(unit, mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a))))),
% 23.49/23.67 inference(symmetry,[status(thm)],[10711])).
% 23.49/23.67 tff(10713,plain,
% 23.49/23.67 ((mult(mult(b, c), mult(a, c)) = mult(b, mult(c, mult(a, c)))) <=> (mult(unit, mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a))) = mult(unit, mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c))))),
% 23.49/23.67 inference(transitivity,[status(thm)],[10712, 10641])).
% 23.49/23.67 tff(10714,plain,
% 23.49/23.67 (ld(a, mult(a, mult(rd(mult(b, c), mult(a, c)), c))) = ld(a, mult(a, mult(c, rd(mult(b, c), mult(a, c)))))),
% 23.49/23.67 inference(symmetry,[status(thm)],[9601])).
% 23.49/23.67 tff(10715,plain,
% 23.49/23.67 (mult(rd(mult(b, c), mult(a, c)), c) = mult(c, rd(mult(b, c), mult(a, c)))),
% 23.49/23.67 inference(transitivity,[status(thm)],[5128, 10714, 5114])).
% 23.49/23.67 tff(10716,plain,
% 23.49/23.67 (mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))),
% 23.49/23.67 inference(monotonicity,[status(thm)],[10715])).
% 23.49/23.67 tff(10717,plain,
% 23.49/23.67 (mult(mult(c, a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(b, c), c)),
% 23.49/23.67 inference(transitivity,[status(thm)],[9585, 10716, 9031, 9028, 9024])).
% 23.49/23.67 tff(10718,plain,
% 23.49/23.67 (mult(mult(mult(c, a), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(b, c), c), a)),
% 23.49/23.67 inference(monotonicity,[status(thm)],[10717])).
% 23.49/23.67 tff(10719,plain,
% 23.49/23.67 (mult(c, mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a)) = mult(c, mult(mult(b, c), a))),
% 23.49/23.67 inference(transitivity,[status(thm)],[5324, 10718, 10665, 10635])).
% 23.49/23.67 tff(10720,plain,
% 23.49/23.67 (ld(c, mult(c, mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a))) = ld(c, mult(c, mult(mult(b, c), a)))),
% 23.49/23.67 inference(monotonicity,[status(thm)],[10719])).
% 23.49/23.67 tff(10721,plain,
% 23.49/23.67 (mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(b, c), a)),
% 23.49/23.67 inference(transitivity,[status(thm)],[5329, 10720, 2296])).
% 23.49/23.67 tff(10722,plain,
% 23.49/23.67 (rd(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a), a) = rd(mult(mult(b, c), a), a)),
% 23.49/23.67 inference(monotonicity,[status(thm)],[10721])).
% 23.49/23.67 tff(10723,plain,
% 23.49/23.67 (mult(a, mult(c, rd(mult(b, c), mult(a, c)))) = mult(b, c)),
% 23.49/23.67 inference(transitivity,[status(thm)],[2220, 5160, 2356, 9593, 10722, 1370])).
% 23.49/23.67 tff(10724,plain,
% 23.49/23.67 (mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(mult(b, c), mult(a, c))),
% 23.49/23.67 inference(monotonicity,[status(thm)],[10723])).
% 23.49/23.67 tff(10725,plain,
% 23.49/23.67 (mult(mult(mult(a, c), a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c))))),
% 23.49/23.67 inference(monotonicity,[status(thm)],[8168])).
% 23.49/23.67 tff(10726,plain,
% 23.49/23.67 (mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(mult(a, c), a), mult(c, rd(mult(b, c), mult(a, c))))),
% 23.49/23.67 inference(monotonicity,[status(thm)],[10715])).
% 23.49/23.67 tff(10727,plain,
% 23.49/23.67 (mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(b, c), c)),
% 23.49/23.67 inference(transitivity,[status(thm)],[10716, 9031, 9028, 9024])).
% 23.49/23.67 tff(10728,plain,
% 23.49/23.67 (mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(b, c), c), a)),
% 23.49/23.67 inference(monotonicity,[status(thm)],[10727])).
% 23.49/23.67 tff(10729,plain,
% 23.49/23.67 (mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(b, mult(c, mult(a, c)))),
% 23.49/23.67 inference(transitivity,[status(thm)],[10728, 6774, 2570, 4396])).
% 23.49/23.67 tff(10730,plain,
% 23.49/23.67 (mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(b, c), mult(a, c))),
% 23.49/23.67 inference(transitivity,[status(thm)],[10726, 10725, 10661, 10724])).
% 23.49/23.67 tff(10731,plain,
% 23.49/23.67 ((mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a)) <=> (mult(mult(b, c), mult(a, c)) = mult(b, mult(c, mult(a, c))))),
% 23.49/23.67 inference(monotonicity,[status(thm)],[10730, 10729])).
% 23.49/23.67 tff(10732,plain,
% 23.49/23.67 ((mult(mult(b, c), mult(a, c)) = mult(b, mult(c, mult(a, c)))) <=> (mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a))),
% 23.49/23.67 inference(symmetry,[status(thm)],[10731])).
% 23.49/23.67 tff(10733,plain,
% 23.49/23.67 ((~(mult(mult(b, c), mult(a, c)) = mult(b, mult(c, mult(a, c))))) <=> (~(mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a)))),
% 23.49/23.67 inference(monotonicity,[status(thm)],[10732])).
% 23.49/23.67 tff(10734,plain,
% 23.49/23.67 (~(mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a))),
% 23.49/23.67 inference(modus_ponens,[status(thm)],[4145, 10733])).
% 23.49/23.67 tff(10735,plain,
% 23.49/23.67 ((~(mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a))) | (~(mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a))))),
% 23.49/23.67 inference(unit_resolution,[status(thm)],[5199, 10734])).
% 23.49/23.67 tff(10736,plain,
% 23.49/23.67 (~((~(mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))) | (~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)))))),
% 23.49/23.67 inference(unit_resolution,[status(thm)],[5220, 10735])).
% 23.49/23.67 tff(10737,plain,
% 23.49/23.67 (mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c)))),
% 23.49/23.67 inference(unit_resolution,[status(thm)],[5352, 10736])).
% 23.49/23.67 tff(10738,plain,
% 23.49/23.67 (mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))) = mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c))),
% 23.49/23.67 inference(symmetry,[status(thm)],[10737])).
% 23.49/23.67 tff(10739,plain,
% 23.49/23.67 (rd(mult(mult(b, c), a), a) = rd(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a), a)),
% 23.49/23.67 inference(symmetry,[status(thm)],[10722])).
% 23.49/23.67 tff(10740,plain,
% 23.49/23.67 (mult(b, c) = mult(a, mult(rd(mult(b, c), mult(a, c)), c))),
% 23.49/23.67 inference(transitivity,[status(thm)],[10690, 10739, 9592])).
% 23.49/23.67 tff(10741,plain,
% 23.49/23.67 (mult(mult(a, c), mult(b, c)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c)))),
% 23.49/23.67 inference(monotonicity,[status(thm)],[10740])).
% 23.49/23.67 tff(10742,plain,
% 23.49/23.67 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(b, c), mult(a, c))),
% 23.49/23.67 inference(transitivity,[status(thm)],[1039, 138, 10741, 10738, 10726, 10725, 10661, 10724])).
% 23.49/23.67 tff(10743,plain,
% 23.49/23.67 (rd(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)), mult(a, c)) = rd(mult(mult(b, c), mult(a, c)), mult(a, c))),
% 23.49/23.67 inference(monotonicity,[status(thm)],[10742])).
% 23.49/23.67 tff(10744,plain,
% 23.49/23.67 (mult(mult(unit, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(a, c))),
% 23.49/23.67 inference(transitivity,[status(thm)],[4928, 4423, 10743, 4402, 267, 4904, 4902])).
% 23.49/23.67 tff(10745,plain,
% 23.49/23.67 ($false),
% 23.49/23.67 inference(unit_resolution,[status(thm)],[10420, 10744])).
% 23.49/23.67 tff(10746,plain,((~(mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))) | (mult(mult(unit, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(a, c))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (~(mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(mult(c, mult(b, c)), a) = mult(c, mult(mult(b, c), a)))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (mult(mult(b, c), mult(a, c)) = mult(b, mult(c, mult(a, c))))), inference(lemma,lemma(discharge,[]))).
% 23.49/23.67 tff(10747,plain,
% 23.49/23.67 ((~(mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))) | (mult(mult(unit, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(a, c))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (~(mult(mult(c, mult(b, c)), a) = mult(c, mult(mult(b, c), a)))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (mult(mult(b, c), mult(a, c)) = mult(b, mult(c, mult(a, c))))),
% 23.49/23.67 inference(unit_resolution,[status(thm)],[10746, 9157])).
% 23.49/23.67 tff(10748,plain,
% 23.49/23.67 (mult(mult(b, c), mult(a, c)) = mult(b, mult(c, mult(a, c)))),
% 23.49/23.67 inference(unit_resolution,[status(thm)],[10747, 9026, 1039, 10420, 4535, 10635])).
% 23.49/23.67 tff(10749,plain,
% 23.49/23.67 (mult(unit, mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a))) = mult(unit, mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)))),
% 23.49/23.67 inference(modus_ponens,[status(thm)],[10748, 10713])).
% 23.49/23.67 tff(10750,plain,
% 23.49/23.67 (mult(unit, mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c))) = mult(unit, mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)))),
% 23.49/23.67 inference(symmetry,[status(thm)],[10749])).
% 23.49/23.67 tff(10751,plain,
% 23.49/23.67 (mult(mult(mult(b, c), a), c) = mult(mult(b, mult(a, c)), c)),
% 23.49/23.67 inference(transitivity,[status(thm)],[10646, 10649, 10654, 10659, 10707, 10750, 10639, 10291, 10137, 10357])).
% 23.49/23.67 tff(10752,plain,
% 23.49/23.67 (rd(mult(mult(mult(b, c), a), c), c) = rd(mult(mult(b, mult(a, c)), c), c)),
% 23.49/23.67 inference(monotonicity,[status(thm)],[10751])).
% 23.49/23.67 tff(10753,plain,
% 23.49/23.67 (mult(mult(b, c), a) = rd(mult(mult(mult(b, c), a), c), c)),
% 23.49/23.67 inference(symmetry,[status(thm)],[2676])).
% 23.49/23.67 tff(10754,plain,
% 23.49/23.67 (mult(c, mult(b, a)) = mult(mult(unit, b), mult(a, c))),
% 23.49/23.67 inference(transitivity,[status(thm)],[4304, 2298, 10753, 10752, 2680, 8665])).
% 23.49/23.67 tff(10755,plain,
% 23.49/23.67 ((mult(c, mult(b, a)) = mult(c, mult(a, b))) <=> (mult(mult(unit, b), mult(a, c)) = mult(mult(unit, mult(a, c)), b))),
% 23.49/23.67 inference(monotonicity,[status(thm)],[10754, 10637])).
% 23.49/23.67 tff(10756,plain,
% 23.49/23.67 ((mult(mult(unit, b), mult(a, c)) = mult(mult(unit, mult(a, c)), b)) <=> (mult(c, mult(b, a)) = mult(c, mult(a, b)))),
% 23.49/23.67 inference(symmetry,[status(thm)],[10755])).
% 23.49/23.67 tff(10757,plain,
% 23.49/23.67 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(b, mult(c, mult(a, c))), mult(c, mult(a, c))) = b)),
% 23.49/23.67 inference(quant_inst,[status(thm)],[])).
% 23.49/23.67 tff(10758,plain,
% 23.49/23.67 (rd(mult(b, mult(c, mult(a, c))), mult(c, mult(a, c))) = b),
% 23.49/23.67 inference(unit_resolution,[status(thm)],[10757, 168])).
% 23.49/23.67 tff(10759,plain,
% 23.49/23.67 (mult(unit, mult(mult(b, c), mult(a, c))) = mult(unit, mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)))),
% 23.49/23.67 inference(symmetry,[status(thm)],[10639])).
% 23.49/23.67 tff(10760,plain,
% 23.49/23.67 (mult(a, mult(mult(a, c), c)) = mult(mult(mult(a, c), unit), mult(a, c))),
% 23.49/23.67 inference(transitivity,[status(thm)],[10598, 4714, 4724, 9303, 7903, 7901, 9781, 4662, 9740, 9744, 9736, 2504])).
% 23.49/23.67 tff(10761,plain,
% 23.49/23.67 (mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(a, c), c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), unit), mult(a, c)))),
% 23.49/23.67 inference(monotonicity,[status(thm)],[10760])).
% 23.49/23.67 tff(10762,plain,
% 23.49/23.67 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, mult(a, c))) = mult(b, mult(c, mult(a, c)))),
% 23.49/23.67 inference(transitivity,[status(thm)],[10636, 10608, 10761, 2502, 2499, 10138, 10149, 10759, 10749, 10708, 10660, 10655, 10650, 10647, 2570, 8560])).
% 23.49/23.67 tff(10763,plain,
% 23.49/23.67 (rd(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, mult(a, c))), mult(c, mult(a, c))) = rd(mult(b, mult(c, mult(a, c))), mult(c, mult(a, c)))),
% 23.49/23.67 inference(monotonicity,[status(thm)],[10762])).
% 23.49/23.67 tff(10764,plain,
% 23.49/23.67 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, mult(a, c))), mult(c, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), a))),
% 23.49/23.67 inference(quant_inst,[status(thm)],[])).
% 23.49/23.67 tff(10765,plain,
% 23.49/23.67 (rd(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, mult(a, c))), mult(c, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), a)),
% 23.49/23.67 inference(unit_resolution,[status(thm)],[10764, 168])).
% 23.49/23.67 tff(10766,plain,
% 23.49/23.67 (mult(rd(mult(b, c), mult(a, c)), a) = rd(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, mult(a, c))), mult(c, mult(a, c)))),
% 23.49/23.67 inference(symmetry,[status(thm)],[10765])).
% 23.49/23.67 tff(10767,plain,
% 23.49/23.67 (mult(rd(mult(b, c), mult(a, c)), a) = b),
% 23.49/23.67 inference(transitivity,[status(thm)],[10766, 10763, 10758])).
% 23.49/23.67 tff(10768,plain,
% 23.49/23.67 (mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, c), b)),
% 23.49/23.67 inference(monotonicity,[status(thm)],[10767])).
% 23.49/23.67 tff(10769,plain,
% 23.49/23.67 (mult(mult(a, c), b) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))),
% 23.49/23.67 inference(symmetry,[status(thm)],[10768])).
% 23.49/23.67 tff(10770,plain,
% 23.49/23.67 (mult(mult(unit, mult(a, c)), b) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)),
% 23.49/23.67 inference(transitivity,[status(thm)],[5506, 10769, 5497])).
% 23.49/23.67 tff(10771,plain,
% 23.49/23.67 (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.49/23.67 inference(unit_resolution,[status(thm)],[8210, 2187, 299])).
% 23.49/23.67 tff(10772,plain,
% 23.49/23.67 (mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))),
% 23.49/23.67 inference(symmetry,[status(thm)],[10771])).
% 23.49/23.67 tff(10773,plain,
% 23.49/23.67 (mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 23.49/23.67 inference(transitivity,[status(thm)],[10772, 8170, 8169, 299])).
% 23.49/23.67 tff(10774,plain,
% 23.49/23.67 (ld(a, mult(a, mult(c, mult(a, rd(mult(b, c), mult(a, c)))))) = ld(a, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 23.49/23.67 inference(monotonicity,[status(thm)],[10773])).
% 23.49/23.67 tff(10775,plain,
% 23.49/23.67 (mult(c, mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))),
% 23.49/23.67 inference(transitivity,[status(thm)],[8269, 10774, 4336])).
% 23.49/23.67 tff(10776,plain,
% 23.49/23.67 (mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)),
% 23.49/23.67 inference(monotonicity,[status(thm)],[10775])).
% 23.49/23.67 tff(10777,plain,
% 23.49/23.67 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), c)),
% 23.49/23.67 inference(symmetry,[status(thm)],[10776])).
% 23.49/23.68 tff(10778,plain,
% 23.49/23.68 (mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), c)),
% 23.49/23.68 inference(transitivity,[status(thm)],[9757, 9755, 10777])).
% 23.49/23.68 tff(10779,plain,
% 23.49/23.68 (mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), c))),
% 23.49/23.68 inference(monotonicity,[status(thm)],[10778])).
% 23.49/23.68 tff(10780,plain,
% 23.49/23.68 (mult(a, mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), c)) = mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))))),
% 23.49/23.68 inference(symmetry,[status(thm)],[10779])).
% 23.49/23.68 tff(10781,plain,
% 23.49/23.68 (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 23.49/23.68 inference(transitivity,[status(thm)],[8170, 8169, 299])).
% 23.49/23.68 tff(10782,plain,
% 23.49/23.68 (mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), c)),
% 23.49/23.68 inference(monotonicity,[status(thm)],[10781])).
% 23.49/23.68 tff(10783,plain,
% 23.49/23.68 (mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), c) = mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), c)),
% 23.49/23.68 inference(symmetry,[status(thm)],[10782])).
% 23.49/23.68 tff(10784,plain,
% 23.49/23.68 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(b, mult(b, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))),
% 23.49/23.68 inference(quant_inst,[status(thm)],[])).
% 23.49/23.68 tff(10785,plain,
% 23.49/23.68 (ld(b, mult(b, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))),
% 23.49/23.68 inference(unit_resolution,[status(thm)],[10784, 7])).
% 23.49/23.68 tff(10786,plain,
% 23.49/23.68 (mult(b, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)) = mult(b, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 23.49/23.68 inference(symmetry,[status(thm)],[10369])).
% 23.49/23.68 tff(10787,plain,
% 23.49/23.68 (mult(b, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) = mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))))),
% 23.49/23.68 inference(symmetry,[status(thm)],[10365])).
% 23.49/23.68 tff(10788,plain,
% 23.49/23.68 (mult(b, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) = mult(b, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 23.49/23.68 inference(transitivity,[status(thm)],[10787, 10350, 10786])).
% 23.49/23.68 tff(10789,plain,
% 23.49/23.68 (ld(b, mult(b, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) = ld(b, mult(b, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))),
% 23.49/23.68 inference(monotonicity,[status(thm)],[10788])).
% 23.49/23.68 tff(10790,plain,
% 23.49/23.68 (ld(b, mult(b, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) = ld(b, mult(b, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))),
% 23.49/23.68 inference(symmetry,[status(thm)],[10789])).
% 23.49/23.68 tff(10791,plain,
% 23.49/23.68 (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))),
% 23.49/23.68 inference(transitivity,[status(thm)],[10374, 10790, 10785])).
% 23.49/23.68 tff(10792,plain,
% 23.49/23.68 (mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), c) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), c)),
% 23.49/23.68 inference(monotonicity,[status(thm)],[10791])).
% 23.49/23.68 tff(10793,plain,
% 23.49/23.68 (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), c) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), c)),
% 23.49/23.68 inference(symmetry,[status(thm)],[10792])).
% 23.49/23.68 tff(10794,plain,
% 23.49/23.68 (mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a), c) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), c)),
% 23.49/23.68 inference(symmetry,[status(thm)],[5142])).
% 23.49/23.68 tff(10795,plain,
% 23.49/23.68 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(c, a), c))),
% 23.49/23.68 inference(symmetry,[status(thm)],[5139])).
% 23.49/23.68 tff(10796,plain,
% 23.49/23.68 (mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, mult(a, c)))) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, mult(a, c)))),
% 23.49/23.68 inference(symmetry,[status(thm)],[10636])).
% 23.49/23.68 tff(10797,plain,
% 23.49/23.68 (mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(a, c), c))) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, mult(a, c))))),
% 23.49/23.68 inference(symmetry,[status(thm)],[10608])).
% 23.49/23.68 tff(10798,plain,
% 23.49/23.68 (mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), unit), mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(a, c), c)))),
% 23.49/23.68 inference(symmetry,[status(thm)],[10761])).
% 23.49/23.68 tff(10799,plain,
% 23.49/23.68 (mult(c, mult(b, mult(a, c))) = mult(mult(c, b), mult(a, c))),
% 23.49/23.68 inference(symmetry,[status(thm)],[10225])).
% 23.49/23.68 tff(10800,plain,
% 23.49/23.68 (mult(c, mult(b, mult(a, c))) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 23.49/23.68 inference(transitivity,[status(thm)],[10799, 2429, 5386, 2501, 10798, 10797, 10796, 10795, 6008, 10794, 10793, 10783, 7918, 10780, 10385, 9787, 4789, 9766, 6879])).
% 23.49/23.68 tff(10801,plain,
% 23.49/23.68 (ld(c, mult(c, mult(b, mult(a, c)))) = ld(c, mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))),
% 23.49/23.68 inference(monotonicity,[status(thm)],[10800])).
% 23.49/23.68 tff(10802,plain,
% 23.49/23.68 (mult(mult(unit, b), mult(a, c)) = mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))),
% 23.49/23.68 inference(transitivity,[status(thm)],[5511, 5659, 10801, 4477, 4676, 10343])).
% 23.49/23.68 tff(10803,plain,
% 23.49/23.68 ((mult(mult(unit, b), mult(a, c)) = mult(mult(unit, mult(a, c)), b)) <=> (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))),
% 23.49/23.68 inference(monotonicity,[status(thm)],[10802, 10770])).
% 23.49/23.68 tff(10804,plain,
% 23.49/23.68 ((mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)) <=> (mult(mult(unit, b), mult(a, c)) = mult(mult(unit, mult(a, c)), b))),
% 23.49/23.68 inference(symmetry,[status(thm)],[10803])).
% 23.49/23.68 tff(10805,plain,
% 23.49/23.68 ((mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)) <=> (mult(c, mult(b, a)) = mult(c, mult(a, b)))),
% 23.49/23.68 inference(transitivity,[status(thm)],[10804, 10756])).
% 23.49/23.68 tff(10806,plain,
% 23.49/23.68 ((~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))) <=> (~(mult(c, mult(b, a)) = mult(c, mult(a, b))))),
% 23.49/23.68 inference(monotonicity,[status(thm)],[10805])).
% 23.49/23.68 tff(10807,plain,
% 23.49/23.68 (~(mult(c, mult(b, a)) = mult(c, mult(a, b)))),
% 23.49/23.68 inference(modus_ponens,[status(thm)],[2331, 10806])).
% 23.49/23.68 tff(10808,plain,
% 23.49/23.68 (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))),
% 23.49/23.68 inference(transitivity,[status(thm)],[1332, 10753, 10752, 2680, 5659, 10801, 4477, 10374, 10790, 10785])).
% 23.49/23.68 tff(10809,plain,
% 23.49/23.68 (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), b) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), b)))),
% 23.49/23.68 inference(unit_resolution,[status(thm)],[7556, 10808, 6990, 10807])).
% 23.49/23.68 tff(10810,plain,
% 23.49/23.68 ((~(mult(mult(rd(mult(b, c), mult(a, c)), b), mult(a, c)) = mult(rd(mult(b, c), mult(a, c)), mult(b, mult(a, c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), b) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), b))))),
% 23.49/23.68 inference(unit_resolution,[status(thm)],[5549, 10809])).
% 23.49/23.68 tff(10811,plain,
% 23.49/23.68 ((~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a))) <=> (~(mult(mult(unit, b), mult(a, c)) = mult(mult(unit, mult(a, c)), b)))),
% 23.49/23.68 inference(monotonicity,[status(thm)],[10804])).
% 23.49/23.68 tff(10812,plain,
% 23.49/23.68 (~(mult(mult(unit, b), mult(a, c)) = mult(mult(unit, mult(a, c)), b))),
% 23.49/23.68 inference(modus_ponens,[status(thm)],[2331, 10811])).
% 23.49/23.68 tff(10813,plain,
% 23.49/23.68 (mult(mult(unit, b), mult(a, c)) = mult(mult(unit, mult(a, c)), b)),
% 23.49/23.68 inference(transitivity,[status(thm)],[5511, 8028, 8025, 5526, 227, 5517])).
% 23.49/23.68 tff(10814,plain,
% 23.49/23.68 ($false),
% 23.49/23.68 inference(unit_resolution,[status(thm)],[5524, 10813])).
% 23.49/23.68 tff(10815,plain,((~(mult(rd(mult(b, c), mult(a, c)), mult(b, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), b)))) | (mult(mult(unit, b), mult(a, c)) = mult(mult(unit, mult(a, c)), b))), inference(lemma,lemma(discharge,[]))).
% 23.49/23.68 tff(10816,plain,
% 23.49/23.68 (~(mult(rd(mult(b, c), mult(a, c)), mult(b, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), b)))),
% 23.49/23.68 inference(unit_resolution,[status(thm)],[10815, 10812])).
% 23.49/23.68 tff(10817,plain,
% 23.49/23.68 ((~(mult(mult(rd(mult(b, c), mult(a, c)), b), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), b))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(b, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), b))))),
% 23.49/23.68 inference(unit_resolution,[status(thm)],[5542, 10816])).
% 23.49/23.68 tff(10818,plain,
% 23.49/23.68 ($false),
% 23.49/23.68 inference(unit_resolution,[status(thm)],[5547, 10817, 10810])).
% 23.49/23.68 tff(10819,plain,((~(mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))) | (~(mult(mult(b, mult(b, c)), a) = mult(b, mult(mult(b, c), a)))) | (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, mult(a, c)))))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))) = mult(b, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))) | (~(mult(mult(c, mult(b, c)), a) = mult(c, mult(mult(b, c), a)))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (mult(mult(unit, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(a, c)))), inference(lemma,lemma(discharge,[]))).
% 23.49/23.68 tff(10820,plain,
% 23.49/23.68 (~(mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))) = mult(b, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))),
% 23.49/23.68 inference(unit_resolution,[status(thm)],[10819, 9026, 2330, 10636, 4535, 299, 6879, 4789, 6990, 2187, 10635, 1039, 10420])).
% 23.49/23.68 tff(10821,plain,
% 23.49/23.68 ((~(mult(mult(b, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(mult(b, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)))) | (~(mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))) = mult(b, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))))),
% 23.49/23.68 inference(unit_resolution,[status(thm)],[10392, 10820])).
% 23.49/23.68 tff(10822,plain,
% 23.49/23.68 (~((~(mult(mult(b, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(b, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(b, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))))),
% 23.49/23.68 inference(unit_resolution,[status(thm)],[10397, 10821])).
% 23.49/23.68 tff(10823,plain,
% 23.49/23.68 (mult(mult(b, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))))),
% 23.49/23.68 inference(unit_resolution,[status(thm)],[10399, 10822])).
% 23.49/23.68 tff(10824,plain,
% 23.49/23.68 (~(mult(c, mult(b, a)) = mult(c, mult(a, b)))),
% 23.49/23.68 inference(unit_resolution,[status(thm)],[8339, 1371, 330])).
% 23.49/23.68 tff(10825,plain,
% 23.49/23.68 ($false),
% 23.49/23.68 inference(unit_resolution,[status(thm)],[7556, 10824, 1371, 6990, 5557])).
% 23.49/23.68 tff(10826,plain,((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) | (~(mult(mult(b, mult(b, c)), a) = mult(b, mult(mult(b, c), a)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), b) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), b)))) | (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))), inference(lemma,lemma(discharge,[]))).
% 23.49/23.68 tff(10827,plain,
% 23.49/23.68 (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), b) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), b)))),
% 23.49/23.68 inference(unit_resolution,[status(thm)],[10826, 1371, 6990, 330])).
% 23.49/23.68 tff(10828,plain,
% 23.49/23.68 ((~(mult(mult(rd(mult(b, c), mult(a, c)), b), mult(a, c)) = mult(rd(mult(b, c), mult(a, c)), mult(b, mult(a, c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), b) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), b))))),
% 23.49/23.68 inference(unit_resolution,[status(thm)],[5549, 10827])).
% 23.49/23.68 tff(10829,plain,
% 23.49/23.68 ((~(mult(mult(b, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))))) | (mult(c, mult(b, a)) = mult(c, mult(a, b))) | (~(mult(mult(b, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(b, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(b, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), b)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a))) | (~(mult(mult(mult(b, c), a), mult(a, b)) = mult(mult(b, c), mult(a, mult(a, b)))))),
% 23.49/23.69 inference(unit_resolution,[status(thm)],[8076, 5709, 6462])).
% 23.49/23.69 tff(10830,plain,
% 23.49/23.69 (~(mult(rd(mult(b, c), mult(a, c)), mult(b, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), b)))),
% 23.49/23.69 inference(unit_resolution,[status(thm)],[10829, 10824, 8031, 1371, 8034, 10208, 2070])).
% 23.49/23.69 tff(10831,plain,
% 23.49/23.69 ((~(mult(mult(rd(mult(b, c), mult(a, c)), b), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), b))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(b, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), b))))),
% 23.49/23.69 inference(unit_resolution,[status(thm)],[5542, 10830])).
% 23.49/23.69 tff(10832,plain,
% 23.49/23.69 ($false),
% 23.49/23.69 inference(unit_resolution,[status(thm)],[5547, 10831, 10828])).
% 23.49/23.69 tff(10833,plain,((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) | (~(mult(mult(b, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(b, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(b, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(b, c), a), mult(a, b)) = mult(mult(b, c), mult(a, mult(a, b))))) | (~(mult(mult(b, mult(b, c)), a) = mult(b, mult(mult(b, c), a)))) | (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)))), inference(lemma,lemma(discharge,[]))).
% 23.49/23.69 tff(10834,plain,
% 23.49/23.69 (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))),
% 23.49/23.69 inference(unit_resolution,[status(thm)],[10833, 10823, 8031, 2070, 6990, 330])).
% 23.49/23.69 tff(10835,plain,
% 23.49/23.69 (mult(a, mult(a, c)) = mult(mult(c, a), a)),
% 23.49/23.69 inference(transitivity,[status(thm)],[4452, 5699, 4447, 6865])).
% 23.49/23.69 tff(10836,plain,
% 23.49/23.69 (mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(c, a), a))),
% 23.49/23.69 inference(monotonicity,[status(thm)],[10835])).
% 23.49/23.69 tff(10837,assumption,(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c)))), introduced(assumption)).
% 23.49/23.69 tff(10838,plain,
% 23.49/23.69 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), mult(a, c)) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, c))),
% 23.49/23.69 inference(monotonicity,[status(thm)],[7606])).
% 23.49/23.69 tff(10839,plain,
% 23.49/23.69 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), mult(a, c)) = mult(mult(b, c), mult(a, c))),
% 23.49/23.69 inference(transitivity,[status(thm)],[10838, 10837, 10836, 6868, 2632, 6871, 6877, 4660, 6896, 2502, 2499])).
% 23.49/23.69 tff(10840,plain,
% 23.49/23.69 (rd(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), mult(a, c)), mult(a, c)) = rd(mult(mult(b, c), mult(a, c)), mult(a, c))),
% 23.49/23.69 inference(monotonicity,[status(thm)],[10839])).
% 23.49/23.69 tff(10841,plain,
% 23.49/23.69 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), mult(a, c)), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), a), c))),
% 23.49/23.69 inference(quant_inst,[status(thm)],[])).
% 23.49/23.69 tff(10842,plain,
% 23.49/23.69 (rd(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), mult(a, c)), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), a), c)),
% 23.49/23.69 inference(unit_resolution,[status(thm)],[10841, 168])).
% 23.49/23.69 tff(10843,plain,
% 23.49/23.69 (mult(mult(rd(mult(b, c), mult(a, c)), a), c) = rd(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), mult(a, c)), mult(a, c))),
% 23.49/23.69 inference(symmetry,[status(thm)],[10842])).
% 23.49/23.69 tff(10844,plain,
% 23.49/23.69 (mult(mult(rd(mult(b, c), mult(a, c)), a), c) = mult(b, c)),
% 23.49/23.69 inference(transitivity,[status(thm)],[10843, 10840, 4402])).
% 23.49/23.69 tff(10845,plain,
% 23.49/23.69 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a) = mult(mult(b, c), a)),
% 23.49/23.69 inference(monotonicity,[status(thm)],[10844])).
% 23.49/23.69 tff(10846,plain,
% 23.49/23.69 (mult(mult(b, c), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a)),
% 23.49/23.69 inference(symmetry,[status(thm)],[10845])).
% 23.49/23.69 tff(10847,plain,
% 23.49/23.69 (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))),
% 23.49/23.69 inference(transitivity,[status(thm)],[1332, 10846, 1168])).
% 23.49/23.69 tff(10848,plain,
% 23.49/23.69 ($false),
% 23.49/23.69 inference(unit_resolution,[status(thm)],[1364, 10847])).
% 23.49/23.69 tff(10849,plain,((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))))) | (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) | (~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(c, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit))))), inference(lemma,lemma(discharge,[]))).
% 23.49/23.69 tff(10850,plain,
% 23.49/23.69 ((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))))) | (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) | (~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(c, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit))))),
% 23.49/23.69 inference(unit_resolution,[status(thm)],[10849, 5709])).
% 23.49/23.69 tff(10851,plain,
% 23.49/23.69 (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))))),
% 23.49/23.69 inference(unit_resolution,[status(thm)],[10850, 10834, 6820, 4789, 6879, 6819, 299, 8305])).
% 23.49/23.69 tff(10852,plain,
% 23.49/23.69 (((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)), a) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a))))) | (mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))))),
% 23.49/23.69 inference(tautology,[status(thm)],[])).
% 23.49/23.69 tff(10853,plain,
% 23.49/23.69 ((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)), a) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a))))),
% 23.49/23.69 inference(unit_resolution,[status(thm)],[10852, 10851])).
% 23.49/23.69 tff(10854,plain,
% 23.49/23.69 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, c)) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)), a))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)))))) | (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)), a) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, c)) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)), a))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)))))) | (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)), a) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)))))))),
% 23.49/23.69 inference(rewrite,[status(thm)],[])).
% 23.49/23.69 tff(10855,plain,
% 23.49/23.69 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, c)) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)), a))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)))))) | (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)), a) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)))))))),
% 23.49/23.69 inference(quant_inst,[status(thm)],[])).
% 23.49/23.69 tff(10856,plain,
% 23.49/23.69 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, c)) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)), a))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)))))) | (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)), a) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a))))))),
% 23.49/23.69 inference(modus_ponens,[status(thm)],[10855, 10854])).
% 23.49/23.69 tff(10857,plain,
% 23.49/23.69 ((~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, c)) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)), a))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)))))) | (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)), a) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a))))))),
% 23.49/23.69 inference(unit_resolution,[status(thm)],[10856, 27])).
% 23.49/23.69 tff(10858,plain,
% 23.49/23.69 (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, c)) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)), a))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)))))),
% 23.49/23.69 inference(unit_resolution,[status(thm)],[10857, 10853])).
% 23.49/23.69 tff(10859,plain,
% 23.49/23.69 (((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, c)) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)), a))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a))))) | (mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, c)) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)), a))),
% 23.49/23.69 inference(tautology,[status(thm)],[])).
% 23.49/23.69 tff(10860,plain,
% 23.49/23.69 (mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, c)) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)), a)),
% 23.49/23.69 inference(unit_resolution,[status(thm)],[10859, 10858])).
% 23.49/23.69 tff(10861,plain,
% 23.49/23.69 (mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, c)) = mult(b, mult(c, mult(a, c)))),
% 23.49/23.69 inference(transitivity,[status(thm)],[10860, 10634, 10589, 2570, 4396])).
% 23.49/23.69 tff(10862,plain,
% 23.49/23.69 ((mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c)))) <=> (mult(b, mult(c, mult(a, c))) = mult(mult(b, c), mult(a, c)))),
% 23.49/23.69 inference(monotonicity,[status(thm)],[10861, 10629])).
% 23.49/23.69 tff(10863,plain,
% 23.49/23.69 ((mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c)))) <=> (mult(mult(b, c), mult(a, c)) = mult(b, mult(c, mult(a, c))))),
% 23.49/23.69 inference(transitivity,[status(thm)],[10862, 6765])).
% 23.49/23.69 tff(10864,plain,
% 23.49/23.69 ((mult(mult(b, c), mult(a, c)) = mult(b, mult(c, mult(a, c)))) <=> (mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))))),
% 23.49/23.69 inference(symmetry,[status(thm)],[10863])).
% 23.49/23.69 tff(10865,plain,
% 23.49/23.69 (mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c)))),
% 23.49/23.69 inference(modus_ponens,[status(thm)],[10748, 10864])).
% 23.49/23.69 tff(10866,plain,
% 23.49/23.69 ($false),
% 23.49/23.69 inference(unit_resolution,[status(thm)],[10851, 10865])).
% 23.49/23.69 tff(10867,plain,((~(mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (~(mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(c, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(c, mult(a, c)), a), rd(mult(b, c), mult(a, c))) = mult(mult(c, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(b, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(b, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(b, c), a), mult(a, b)) = mult(mult(b, c), mult(a, mult(a, b))))) | (~(mult(mult(b, mult(b, c)), a) = mult(b, mult(mult(b, c), a)))) | (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, mult(a, c)))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))) | (~(mult(mult(c, mult(b, c)), a) = mult(c, mult(mult(b, c), a)))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (mult(mult(unit, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(a, c)))), inference(lemma,lemma(discharge,[]))).
% 23.49/23.70 tff(10868,plain,
% 23.49/23.70 (~(mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))),
% 23.49/23.70 inference(unit_resolution,[status(thm)],[10867, 4390, 9652, 6583, 9662, 9640, 281, 8191, 10628, 9698, 9672, 10627, 8165, 10597, 316, 10325])).
% 23.49/23.70 tff(10869,plain,
% 23.49/23.70 (mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(b, c), c)) = mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 23.49/23.70 inference(symmetry,[status(thm)],[9025])).
% 23.49/23.70 tff(10870,plain,
% 23.49/23.70 (mult(c, mult(mult(b, c), a)) = mult(mult(c, mult(b, c)), a)),
% 23.49/23.70 inference(symmetry,[status(thm)],[10635])).
% 23.49/23.70 tff(10871,plain,
% 23.49/23.70 (mult(mult(mult(a, b), b), c) = mult(a, mult(mult(b, c), b))),
% 23.49/23.70 inference(transitivity,[status(thm)],[828, 781])).
% 23.49/23.70 tff(10872,plain,
% 23.49/23.70 (mult(a, mult(mult(mult(a, b), b), c)) = mult(a, mult(a, mult(mult(b, c), b)))),
% 23.49/23.70 inference(monotonicity,[status(thm)],[10871])).
% 23.49/23.70 tff(10873,plain,
% 23.49/23.70 (mult(a, mult(a, mult(mult(b, c), b))) = mult(a, mult(mult(mult(a, b), b), c))),
% 23.49/23.70 inference(symmetry,[status(thm)],[10872])).
% 23.49/23.70 tff(10874,plain,
% 23.49/23.70 (mult(a, mult(mult(mult(a, b), c), b)) = mult(a, mult(a, mult(mult(b, c), b)))),
% 23.49/23.70 inference(monotonicity,[status(thm)],[781])).
% 23.49/23.70 tff(10875,assumption,(mult(a, mult(mult(mult(a, b), c), b)) = mult(a, mult(b, mult(mult(a, b), c)))), introduced(assumption)).
% 23.49/23.70 tff(10876,plain,
% 23.49/23.70 (mult(a, mult(b, mult(mult(a, b), c))) = mult(a, mult(mult(mult(a, b), c), b))),
% 23.49/23.70 inference(symmetry,[status(thm)],[10875])).
% 23.49/23.70 tff(10877,plain,
% 23.49/23.70 (mult(mult(unit, b), mult(mult(a, b), c)) = mult(b, mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), c))),
% 23.49/23.70 inference(monotonicity,[status(thm)],[184, 215])).
% 23.49/23.70 tff(10878,plain,
% 23.49/23.70 (mult(b, mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), c)) = mult(mult(unit, b), mult(mult(a, b), c))),
% 23.49/23.70 inference(symmetry,[status(thm)],[10877])).
% 23.49/23.70 tff(10879,assumption,(~(mult(mult(mult(b, c), c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c))), introduced(assumption)).
% 23.49/23.70 tff(10880,plain,
% 23.49/23.70 (((~(mult(mult(mult(b, c), c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c))) | (~(mult(mult(b, c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(mult(b, c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c))))) | (mult(mult(mult(b, c), c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c))),
% 23.49/23.70 inference(tautology,[status(thm)],[])).
% 23.49/23.70 tff(10881,plain,
% 23.49/23.70 ((~(mult(mult(mult(b, c), c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c))) | (~(mult(mult(b, c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(mult(b, c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c))))),
% 23.49/23.70 inference(unit_resolution,[status(thm)],[10880, 10879])).
% 23.49/23.70 tff(10882,plain,
% 23.49/23.70 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(b, c), c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c))) | (~(mult(mult(b, c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(mult(b, c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)))))) | (~((~(mult(mult(mult(b, c), c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(b, c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))) | (~(mult(mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(b, c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(b, c), c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c))) | (~(mult(mult(b, c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(mult(b, c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)))))) | (~((~(mult(mult(mult(b, c), c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(b, c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))) | (~(mult(mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(b, c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)))))))),
% 23.49/23.70 inference(rewrite,[status(thm)],[])).
% 23.49/23.70 tff(10883,plain,
% 23.49/23.70 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(b, c), c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c))) | (~(mult(mult(b, c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(mult(b, c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)))))) | (~((~(mult(mult(mult(b, c), c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(b, c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))) | (~(mult(mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(b, c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)))))))),
% 23.49/23.70 inference(quant_inst,[status(thm)],[])).
% 23.49/23.70 tff(10884,plain,
% 23.49/23.70 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(b, c), c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c))) | (~(mult(mult(b, c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(mult(b, c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)))))) | (~((~(mult(mult(mult(b, c), c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(b, c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))) | (~(mult(mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(b, c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c))))))),
% 23.49/23.70 inference(modus_ponens,[status(thm)],[10883, 10882])).
% 23.49/23.70 tff(10885,plain,
% 23.49/23.70 ((~((~(mult(mult(mult(b, c), c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c))) | (~(mult(mult(b, c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(mult(b, c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)))))) | (~((~(mult(mult(mult(b, c), c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(b, c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))) | (~(mult(mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(b, c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c))))))),
% 23.49/23.70 inference(unit_resolution,[status(thm)],[10884, 27])).
% 23.49/23.70 tff(10886,plain,
% 23.49/23.70 (~((~(mult(mult(mult(b, c), c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(b, c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))) | (~(mult(mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(b, c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)))))),
% 23.49/23.70 inference(unit_resolution,[status(thm)],[10885, 10881])).
% 23.49/23.70 tff(10887,plain,
% 23.49/23.70 (mult(mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(b, c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c))),
% 23.49/23.70 inference(unit_resolution,[status(thm)],[3419, 10886])).
% 23.49/23.70 tff(10888,plain,
% 23.49/23.70 (mult(mult(b, c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)) = mult(mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c)),
% 23.49/23.70 inference(symmetry,[status(thm)],[10887])).
% 23.49/23.70 tff(10889,plain,
% 23.49/23.70 (mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(unit, c), unit))) = mult(c, mult(mult(mult(unit, c), unit), mult(mult(unit, ld(c, mult(a, b))), unit)))),
% 23.49/23.70 inference(symmetry,[status(thm)],[5428])).
% 23.49/23.70 tff(10890,plain,
% 23.49/23.70 (mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)) = mult(c, mult(a, b))),
% 23.49/23.70 inference(transitivity,[status(thm)],[3290, 10889, 4010, 4225])).
% 23.49/23.70 tff(10891,plain,
% 23.49/23.70 (ld(c, mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), c))) = ld(c, mult(c, mult(a, b)))),
% 23.49/23.70 inference(monotonicity,[status(thm)],[10890])).
% 23.49/23.70 tff(10892,plain,
% 23.49/23.70 (ld(c, mult(c, mult(a, b))) = ld(c, mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)))),
% 23.49/23.70 inference(symmetry,[status(thm)],[10891])).
% 23.49/23.70 tff(10893,plain,
% 23.49/23.70 (mult(a, b) = mult(mult(mult(unit, ld(c, mult(a, b))), unit), c)),
% 23.49/23.70 inference(transitivity,[status(thm)],[2235, 10892, 3294])).
% 23.49/23.70 tff(10894,plain,
% 23.49/23.70 (mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c))),
% 23.49/23.70 inference(monotonicity,[status(thm)],[10893])).
% 23.49/23.70 tff(10895,plain,
% 23.49/23.70 (((~(mult(mult(mult(b, c), c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(b, c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))) | (~(mult(mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(b, c), mult(mult(mult(unit, ld(c, mult(a, b))), unit), c))))) | (mult(mult(mult(b, c), c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(b, c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))))),
% 23.49/23.70 inference(tautology,[status(thm)],[])).
% 23.49/23.70 tff(10896,plain,
% 23.49/23.70 (mult(mult(mult(b, c), c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(b, c), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)))),
% 23.49/23.70 inference(unit_resolution,[status(thm)],[10895, 10886])).
% 23.49/23.70 tff(10897,plain,
% 23.49/23.70 (mult(mult(mult(b, c), c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c)),
% 23.49/23.70 inference(transitivity,[status(thm)],[10896, 3398, 10894, 10888])).
% 23.49/23.70 tff(10898,plain,
% 23.49/23.70 ($false),
% 23.49/23.70 inference(unit_resolution,[status(thm)],[10879, 10897])).
% 23.49/23.70 tff(10899,plain,(mult(mult(mult(b, c), c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c)), inference(lemma,lemma(discharge,[]))).
% 23.49/23.70 tff(10900,plain,
% 23.49/23.70 (mult(mult(mult(b, c), c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(b, mult(mult(a, b), c))),
% 23.49/23.70 inference(transitivity,[status(thm)],[10899, 3391, 10878, 3388])).
% 23.49/23.70 tff(10901,plain,
% 23.49/23.70 (mult(a, mult(mult(mult(b, c), c), mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(a, mult(b, mult(mult(a, b), c)))),
% 23.49/23.70 inference(monotonicity,[status(thm)],[10900])).
% 23.49/23.70 tff(10902,plain,
% 23.49/23.70 (mult(mult(b, c), c) = mult(c, mult(b, c))),
% 23.49/23.70 inference(transitivity,[status(thm)],[8573, 4537, 4178])).
% 23.49/23.70 tff(10903,plain,
% 23.49/23.70 (mult(mult(mult(b, c), c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(c, mult(b, c)), mult(mult(unit, ld(c, mult(a, b))), unit))),
% 23.49/23.70 inference(monotonicity,[status(thm)],[10902])).
% 23.49/23.70 tff(10904,plain,
% 23.49/23.70 (mult(mult(c, mult(b, c)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(mult(b, c), c), mult(mult(unit, ld(c, mult(a, b))), unit))),
% 23.49/23.70 inference(symmetry,[status(thm)],[10903])).
% 23.49/23.70 tff(10905,plain,
% 23.49/23.70 (mult(a, mult(mult(c, mult(b, c)), mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(a, mult(mult(mult(b, c), c), mult(mult(unit, ld(c, mult(a, b))), unit)))),
% 23.49/23.70 inference(monotonicity,[status(thm)],[10904])).
% 23.49/23.70 tff(10906,plain,
% 23.49/23.70 (mult(a, mult(mult(c, mult(b, c)), mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(a, mult(a, mult(mult(unit, mult(mult(b, unit), b)), c)))),
% 23.49/23.70 inference(transitivity,[status(thm)],[10905, 10901, 10876, 10874, 10873, 3815])).
% 23.49/23.70 tff(10907,plain,
% 23.49/23.70 (ld(a, mult(a, mult(mult(c, mult(b, c)), mult(mult(unit, ld(c, mult(a, b))), unit)))) = ld(a, mult(a, mult(a, mult(mult(unit, mult(mult(b, unit), b)), c))))),
% 23.49/23.70 inference(monotonicity,[status(thm)],[10906])).
% 23.49/23.70 tff(10908,plain,
% 23.49/23.70 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(a, mult(a, mult(mult(c, mult(b, c)), mult(mult(unit, ld(c, mult(a, b))), unit)))) = mult(mult(c, mult(b, c)), mult(mult(unit, ld(c, mult(a, b))), unit)))),
% 23.49/23.70 inference(quant_inst,[status(thm)],[])).
% 23.49/23.70 tff(10909,plain,
% 23.49/23.70 (ld(a, mult(a, mult(mult(c, mult(b, c)), mult(mult(unit, ld(c, mult(a, b))), unit)))) = mult(mult(c, mult(b, c)), mult(mult(unit, ld(c, mult(a, b))), unit))),
% 23.49/23.70 inference(unit_resolution,[status(thm)],[10908, 7])).
% 23.49/23.70 tff(10910,plain,
% 23.49/23.70 (mult(mult(c, mult(b, c)), mult(mult(unit, ld(c, mult(a, b))), unit)) = ld(a, mult(a, mult(mult(c, mult(b, c)), mult(mult(unit, ld(c, mult(a, b))), unit))))),
% 23.49/23.70 inference(symmetry,[status(thm)],[10909])).
% 23.49/23.70 tff(10911,plain,
% 23.49/23.70 (mult(mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(mult(b, c), c), mult(mult(unit, ld(c, mult(a, b))), unit))),
% 23.49/23.70 inference(symmetry,[status(thm)],[10899])).
% 23.49/23.70 tff(10912,plain,
% 23.49/23.70 (mult(b, mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), c)) = mult(mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c)),
% 23.49/23.70 inference(symmetry,[status(thm)],[3391])).
% 23.49/23.70 tff(10913,assumption,(~(mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))), introduced(assumption)).
% 23.49/23.70 tff(10914,plain,
% 23.49/23.70 (mult(mult(unit, b), mult(mult(a, b), c)) = mult(b, mult(mult(a, c), b))),
% 23.49/23.70 inference(monotonicity,[status(thm)],[184, 227])).
% 23.49/23.70 tff(10915,plain,
% 23.49/23.70 (mult(b, mult(mult(a, c), b)) = mult(mult(unit, b), mult(mult(a, b), c))),
% 23.49/23.70 inference(symmetry,[status(thm)],[10914])).
% 23.49/23.70 tff(10916,plain,
% 23.49/23.70 (mult(b, mult(b, mult(a, c))) = mult(b, mult(mult(a, b), c))),
% 23.49/23.70 inference(transitivity,[status(thm)],[5607, 10915, 3388])).
% 23.49/23.70 tff(10917,plain,
% 23.49/23.70 (ld(b, mult(b, mult(b, mult(a, c)))) = ld(b, mult(b, mult(mult(a, b), c)))),
% 23.49/23.70 inference(monotonicity,[status(thm)],[10916])).
% 23.49/23.70 tff(10918,plain,
% 23.49/23.70 (ld(b, mult(b, mult(mult(a, b), c))) = ld(b, mult(b, mult(b, mult(a, c))))),
% 23.49/23.70 inference(symmetry,[status(thm)],[10917])).
% 23.49/23.70 tff(10919,plain,
% 23.49/23.70 (mult(mult(a, b), c) = ld(b, mult(b, mult(mult(a, b), c)))),
% 23.49/23.70 inference(symmetry,[status(thm)],[5605])).
% 23.49/23.70 tff(10920,plain,
% 23.49/23.70 (mult(mult(a, c), b) = mult(b, mult(a, c))),
% 23.49/23.70 inference(transitivity,[status(thm)],[161, 10919, 10918, 8436])).
% 23.49/23.70 tff(10921,plain,
% 23.49/23.70 (mult(mult(mult(a, c), b), c) = mult(mult(b, mult(a, c)), c)),
% 23.49/23.70 inference(monotonicity,[status(thm)],[10920])).
% 23.49/23.70 tff(10922,assumption,(mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))), introduced(assumption)).
% 23.49/23.70 tff(10923,plain,
% 23.49/23.70 (mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(b, c), c))),
% 23.49/23.70 inference(transitivity,[status(thm)],[10922, 4539])).
% 23.49/23.70 tff(10924,plain,
% 23.49/23.70 (ld(a, mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))) = ld(a, mult(a, mult(mult(b, c), c)))),
% 23.49/23.70 inference(monotonicity,[status(thm)],[10923])).
% 23.49/23.70 tff(10925,plain,
% 23.49/23.70 (mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(b, c), c)),
% 23.49/23.71 inference(transitivity,[status(thm)],[8954, 10924, 4173])).
% 23.49/23.71 tff(10926,plain,
% 23.49/23.71 (mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(b, c), c))),
% 23.49/23.71 inference(monotonicity,[status(thm)],[10925])).
% 23.49/23.71 tff(10927,plain,
% 23.49/23.71 (mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 23.49/23.71 inference(transitivity,[status(thm)],[10926, 10869])).
% 23.49/23.71 tff(10928,plain,
% 23.49/23.71 ($false),
% 23.49/23.71 inference(unit_resolution,[status(thm)],[10913, 10927])).
% 23.49/23.71 tff(10929,plain,((~(mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))) | (mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))), inference(lemma,lemma(discharge,[]))).
% 23.49/23.71 tff(10930,plain,
% 23.49/23.71 (~(mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))),
% 23.49/23.71 inference(unit_resolution,[status(thm)],[10929, 10913, 4535])).
% 23.49/23.71 tff(10931,plain,
% 23.49/23.71 ((~(mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)))) | (~(mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))))),
% 23.49/23.71 inference(unit_resolution,[status(thm)],[4567, 10930])).
% 23.49/23.71 tff(10932,plain,
% 23.49/23.71 (~((~(mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))))),
% 23.49/23.71 inference(unit_resolution,[status(thm)],[4565, 10931])).
% 23.49/23.71 tff(10933,plain,
% 23.49/23.71 (mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 23.49/23.71 inference(unit_resolution,[status(thm)],[4560, 10932])).
% 23.49/23.71 tff(10934,plain,
% 23.49/23.71 (mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), mult(a, c)) = mult(mult(b, c), mult(a, c))),
% 23.49/23.71 inference(transitivity,[status(thm)],[10683, 10933, 4539, 3138, 234, 10921, 5435])).
% 23.49/23.71 tff(10935,plain,
% 23.49/23.71 (rd(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), mult(a, c)), mult(a, c)) = rd(mult(mult(b, c), mult(a, c)), mult(a, c))),
% 23.49/23.71 inference(monotonicity,[status(thm)],[10934])).
% 23.49/23.71 tff(10936,plain,
% 23.49/23.71 (mult(a, mult(rd(mult(b, c), mult(a, c)), c)) = rd(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), mult(a, c)), mult(a, c))),
% 23.49/23.71 inference(symmetry,[status(thm)],[10680])).
% 23.49/23.71 tff(10937,plain,
% 23.49/23.71 (mult(a, mult(rd(mult(b, c), mult(a, c)), c)) = mult(b, c)),
% 23.49/23.71 inference(transitivity,[status(thm)],[10936, 10935, 4402])).
% 23.49/23.71 tff(10938,plain,
% 23.49/23.71 (mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(b, c), a)),
% 23.49/23.71 inference(monotonicity,[status(thm)],[10937])).
% 23.49/23.71 tff(10939,plain,
% 23.49/23.71 (mult(c, mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a)) = mult(c, mult(mult(b, c), a))),
% 23.49/23.71 inference(monotonicity,[status(thm)],[10938])).
% 23.49/23.71 tff(10940,plain,
% 23.49/23.71 (mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(c, a), mult(rd(mult(b, c), mult(a, c)), c))),
% 23.49/23.71 inference(symmetry,[status(thm)],[10673])).
% 23.49/23.71 tff(10941,plain,
% 23.49/23.71 (mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(c, a), mult(rd(mult(b, c), mult(a, c)), c)), a)),
% 23.49/23.71 inference(monotonicity,[status(thm)],[10940])).
% 23.49/23.71 tff(10942,plain,
% 23.49/23.71 (mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c))),
% 23.49/23.71 inference(symmetry,[status(thm)],[10670])).
% 23.49/23.71 tff(10943,plain,
% 23.49/23.71 (mult(mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a)),
% 23.49/23.71 inference(monotonicity,[status(thm)],[10942])).
% 23.49/23.71 tff(10944,plain,
% 23.49/23.71 (mult(mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(b, c), c), a)),
% 23.49/23.71 inference(transitivity,[status(thm)],[10943, 10941, 5195, 10939, 10870, 4181])).
% 23.49/23.71 tff(10945,plain,
% 23.49/23.71 (rd(mult(mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))), a), a) = rd(mult(mult(mult(b, c), c), a), a)),
% 23.49/23.71 inference(monotonicity,[status(thm)],[10944])).
% 23.49/23.71 tff(10946,plain,
% 23.49/23.71 (mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(b, c), c)),
% 23.49/23.71 inference(transitivity,[status(thm)],[9006, 10945, 8631])).
% 23.49/23.71 tff(10947,plain,
% 23.49/23.71 (mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(b, c), c))),
% 23.49/23.71 inference(monotonicity,[status(thm)],[10946])).
% 23.49/23.71 tff(10948,plain,
% 23.49/23.71 (mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 23.49/23.71 inference(transitivity,[status(thm)],[10947, 10869])).
% 23.49/23.71 tff(10949,plain,
% 23.49/23.71 ($false),
% 23.49/23.71 inference(unit_resolution,[status(thm)],[10913, 10948])).
% 23.49/23.71 tff(10950,plain,((~(mult(b, mult(mult(a, c), b)) = mult(b, mult(b, mult(a, c))))) | (mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (~(mult(mult(c, mult(b, c)), a) = mult(c, mult(mult(b, c), a))))), inference(lemma,lemma(discharge,[]))).
% 23.49/23.71 tff(10951,plain,
% 23.49/23.71 (~(mult(b, mult(mult(a, c), b)) = mult(b, mult(b, mult(a, c))))),
% 23.49/23.71 inference(unit_resolution,[status(thm)],[10950, 10913, 4535, 10635])).
% 23.49/23.71 tff(10952,plain,
% 23.49/23.71 ((~(mult(mult(b, mult(a, c)), b) = mult(mult(b, b), mult(a, c)))) | (~(mult(b, mult(mult(a, c), b)) = mult(b, mult(b, mult(a, c)))))),
% 23.49/23.71 inference(unit_resolution,[status(thm)],[5618, 10951])).
% 23.49/23.71 tff(10953,plain,
% 23.49/23.71 (~((~(mult(mult(b, b), mult(a, c)) = mult(b, mult(b, mult(a, c))))) | (~(mult(mult(b, mult(a, c)), b) = mult(b, mult(mult(a, c), b)))))),
% 23.49/23.71 inference(unit_resolution,[status(thm)],[5630, 10952])).
% 23.49/23.71 tff(10954,plain,
% 23.49/23.71 (mult(mult(b, mult(a, c)), b) = mult(b, mult(mult(a, c), b))),
% 23.49/23.71 inference(unit_resolution,[status(thm)],[5632, 10953])).
% 23.49/23.71 tff(10955,plain,
% 23.49/23.71 (mult(mult(b, mult(a, c)), b) = mult(mult(mult(a, b), c), b)),
% 23.49/23.71 inference(transitivity,[status(thm)],[10954, 5603, 10877, 10912, 10911, 10903, 10910, 10907, 1792, 893, 833, 828])).
% 23.49/23.71 tff(10956,plain,
% 23.49/23.71 (rd(mult(mult(b, mult(a, c)), b), b) = rd(mult(mult(mult(a, b), c), b), b)),
% 23.49/23.71 inference(monotonicity,[status(thm)],[10955])).
% 23.49/23.71 tff(10957,plain,
% 23.49/23.71 (rd(mult(mult(mult(a, b), c), b), b) = rd(mult(mult(b, mult(a, c)), b), b)),
% 23.49/23.71 inference(symmetry,[status(thm)],[10956])).
% 23.49/23.71 tff(10958,plain,
% 23.49/23.71 (mult(mult(a, c), b) = mult(b, mult(a, c))),
% 23.49/23.71 inference(transitivity,[status(thm)],[161, 794, 10957, 8412])).
% 23.49/23.71 tff(10959,plain,
% 23.49/23.71 (mult(mult(mult(a, c), b), c) = mult(mult(b, mult(a, c)), c)),
% 23.49/23.71 inference(monotonicity,[status(thm)],[10958])).
% 23.49/23.71 tff(10960,plain,
% 23.49/23.71 (mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), mult(a, c)) = mult(mult(b, c), mult(a, c))),
% 23.49/23.71 inference(transitivity,[status(thm)],[10683, 10933, 4539, 3138, 234, 10959, 5435])).
% 23.49/23.71 tff(10961,plain,
% 23.49/23.71 (rd(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), mult(a, c)), mult(a, c)) = rd(mult(mult(b, c), mult(a, c)), mult(a, c))),
% 23.49/23.71 inference(monotonicity,[status(thm)],[10960])).
% 23.49/23.71 tff(10962,plain,
% 23.49/23.71 (mult(a, mult(rd(mult(b, c), mult(a, c)), c)) = mult(b, c)),
% 23.49/23.71 inference(transitivity,[status(thm)],[10936, 10961, 4402])).
% 23.49/23.71 tff(10963,plain,
% 23.49/23.71 (mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(b, c), a)),
% 23.49/23.71 inference(monotonicity,[status(thm)],[10962])).
% 23.49/23.71 tff(10964,plain,
% 23.49/23.71 (mult(c, mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a)) = mult(c, mult(mult(b, c), a))),
% 23.49/23.71 inference(monotonicity,[status(thm)],[10963])).
% 23.49/23.71 tff(10965,plain,
% 23.49/23.71 (mult(mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(b, c), c), a)),
% 23.49/23.71 inference(transitivity,[status(thm)],[10943, 10941, 5195, 10964, 10870, 4181])).
% 23.49/23.71 tff(10966,plain,
% 23.49/23.71 (rd(mult(mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))), a), a) = rd(mult(mult(mult(b, c), c), a), a)),
% 23.49/23.71 inference(monotonicity,[status(thm)],[10965])).
% 23.49/23.71 tff(10967,plain,
% 23.49/23.71 (mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(b, c), c)),
% 23.49/23.71 inference(transitivity,[status(thm)],[9006, 10966, 8631])).
% 23.49/23.71 tff(10968,plain,
% 23.49/23.71 (mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(b, c), c))),
% 23.49/23.71 inference(monotonicity,[status(thm)],[10967])).
% 23.49/23.71 tff(10969,plain,
% 23.49/23.71 (mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 23.49/23.71 inference(transitivity,[status(thm)],[10968, 10869])).
% 23.49/23.71 tff(10970,plain,
% 23.49/23.71 ($false),
% 23.49/23.71 inference(unit_resolution,[status(thm)],[10913, 10969])).
% 23.49/23.71 tff(10971,plain,((~(mult(a, mult(mult(mult(a, b), c), b)) = mult(a, mult(b, mult(mult(a, b), c))))) | (mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (~(mult(mult(c, mult(b, c)), a) = mult(c, mult(mult(b, c), a))))), inference(lemma,lemma(discharge,[]))).
% 23.49/23.71 tff(10972,plain,
% 23.49/23.71 (~(mult(a, mult(mult(mult(a, b), c), b)) = mult(a, mult(b, mult(mult(a, b), c))))),
% 23.49/23.71 inference(unit_resolution,[status(thm)],[10971, 10868, 4390, 10597])).
% 23.49/23.71 tff(10973,plain,
% 23.49/23.71 (((~(mult(mult(a, mult(mult(a, b), c)), b) = mult(mult(a, b), mult(mult(a, b), c)))) | (~(mult(a, mult(mult(mult(a, b), c), b)) = mult(a, mult(b, mult(mult(a, b), c)))))) | (mult(a, mult(mult(mult(a, b), c), b)) = mult(a, mult(b, mult(mult(a, b), c))))),
% 23.49/23.71 inference(tautology,[status(thm)],[])).
% 23.49/23.71 tff(10974,plain,
% 23.49/23.71 ((~(mult(mult(a, mult(mult(a, b), c)), b) = mult(mult(a, b), mult(mult(a, b), c)))) | (~(mult(a, mult(mult(mult(a, b), c), b)) = mult(a, mult(b, mult(mult(a, b), c)))))),
% 23.49/23.71 inference(unit_resolution,[status(thm)],[10973, 10972])).
% 23.49/23.71 tff(10975,plain,
% 23.49/23.71 (~((~(mult(mult(a, b), mult(mult(a, b), c)) = mult(a, mult(b, mult(mult(a, b), c))))) | (~(mult(mult(a, mult(mult(a, b), c)), b) = mult(a, mult(mult(mult(a, b), c), b)))))),
% 23.49/23.71 inference(unit_resolution,[status(thm)],[3346, 10974])).
% 23.49/23.71 tff(10976,plain,
% 23.49/23.71 (mult(mult(a, b), mult(mult(a, b), c)) = mult(a, mult(b, mult(mult(a, b), c)))),
% 23.49/23.71 inference(unit_resolution,[status(thm)],[3383, 10975])).
% 23.49/23.71 tff(10977,plain,
% 23.49/23.71 (mult(mult(unit, b), mult(mult(a, b), c)) = mult(b, mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), c))),
% 23.49/23.71 inference(symmetry,[status(thm)],[3389])).
% 23.49/23.71 tff(10978,plain,
% 23.49/23.71 (mult(mult(b, mult(a, c)), b) = mult(mult(mult(b, c), c), mult(mult(unit, ld(c, mult(a, b))), unit))),
% 23.49/23.71 inference(transitivity,[status(thm)],[8414, 10915, 10977, 10912, 10911])).
% 23.49/23.71 tff(10979,plain,
% 23.49/23.71 (mult(a, mult(mult(b, mult(a, c)), b)) = mult(a, mult(mult(mult(b, c), c), mult(mult(unit, ld(c, mult(a, b))), unit)))),
% 23.49/23.71 inference(monotonicity,[status(thm)],[10978])).
% 23.49/23.71 tff(10980,plain,
% 23.49/23.71 (mult(a, mult(mult(mult(b, c), c), mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(a, mult(mult(b, mult(a, c)), b))),
% 23.49/23.71 inference(symmetry,[status(thm)],[10979])).
% 23.49/23.71 tff(10981,plain,
% 23.49/23.71 (mult(mult(mult(b, c), c), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(b, mult(mult(a, b), c))),
% 23.49/23.71 inference(transitivity,[status(thm)],[10899, 3391, 3389, 3388])).
% 23.49/23.71 tff(10982,plain,
% 23.49/23.71 (mult(a, mult(mult(mult(b, c), c), mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(a, mult(b, mult(mult(a, b), c)))),
% 23.49/23.71 inference(monotonicity,[status(thm)],[10981])).
% 23.49/23.71 tff(10983,plain,
% 23.49/23.71 (mult(a, mult(b, mult(mult(a, b), c))) = mult(a, mult(mult(mult(b, c), c), mult(mult(unit, ld(c, mult(a, b))), unit)))),
% 23.49/23.71 inference(symmetry,[status(thm)],[10982])).
% 23.49/23.71 tff(10984,assumption,(mult(mult(a, b), mult(mult(a, b), c)) = mult(a, mult(b, mult(mult(a, b), c)))), introduced(assumption)).
% 23.49/23.71 tff(10985,plain,
% 23.49/23.71 (mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) = mult(c, mult(b, mult(a, c)))),
% 23.49/23.71 inference(transitivity,[status(thm)],[10231, 10229, 2632, 6871, 9752, 4660, 9746, 2502, 2499, 2742, 10225])).
% 23.49/23.71 tff(10986,plain,
% 23.49/23.71 (ld(c, mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) = ld(c, mult(c, mult(b, mult(a, c))))),
% 23.49/23.71 inference(monotonicity,[status(thm)],[10985])).
% 23.49/23.71 tff(10987,plain,
% 23.49/23.71 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)) = mult(mult(a, b), c)),
% 23.49/23.71 inference(transitivity,[status(thm)],[6930, 10986, 5658, 8028, 8025, 5526])).
% 23.49/23.71 tff(10988,plain,
% 23.49/23.71 (mult(mult(a, b), mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) = mult(mult(a, b), mult(mult(a, b), c))),
% 23.49/23.71 inference(monotonicity,[status(thm)],[10987])).
% 23.49/23.71 tff(10989,plain,
% 23.49/23.71 (ld(c, mult(c, mult(b, mult(a, c)))) = ld(c, mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))),
% 23.49/23.71 inference(symmetry,[status(thm)],[10986])).
% 23.49/23.71 tff(10990,plain,
% 23.49/23.71 (mult(b, mult(a, c)) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))),
% 23.49/23.71 inference(transitivity,[status(thm)],[5659, 10989, 6929])).
% 23.49/23.71 tff(10991,plain,
% 23.49/23.71 (mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(b, mult(a, c))) = mult(mult(a, b), mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))),
% 23.49/23.71 inference(monotonicity,[status(thm)],[213, 10990])).
% 23.49/23.71 tff(10992,plain,
% 23.49/23.71 (((~(mult(mult(a, b), mult(b, mult(a, c))) = mult(mult(a, b), mult(mult(a, c), b)))) | (~(mult(mult(mult(a, b), b), mult(a, c)) = mult(mult(mult(a, b), mult(a, c)), b)))) | (mult(mult(mult(a, b), b), mult(a, c)) = mult(mult(mult(a, b), mult(a, c)), b))),
% 23.49/23.71 inference(tautology,[status(thm)],[])).
% 23.49/23.71 tff(10993,plain,
% 23.49/23.71 ((~(mult(mult(a, b), mult(b, mult(a, c))) = mult(mult(a, b), mult(mult(a, c), b)))) | (~(mult(mult(mult(a, b), b), mult(a, c)) = mult(mult(mult(a, b), mult(a, c)), b)))),
% 23.49/23.71 inference(unit_resolution,[status(thm)],[10992, 10542])).
% 23.49/23.71 tff(10994,plain,
% 23.49/23.71 (~((~(mult(mult(mult(a, b), b), mult(a, c)) = mult(mult(a, b), mult(b, mult(a, c))))) | (~(mult(mult(mult(a, b), mult(a, c)), b) = mult(mult(a, b), mult(mult(a, c), b)))))),
% 23.49/23.71 inference(unit_resolution,[status(thm)],[10432, 10993])).
% 23.49/23.71 tff(10995,plain,
% 23.49/23.71 (mult(mult(mult(a, b), b), mult(a, c)) = mult(mult(a, b), mult(b, mult(a, c)))),
% 23.49/23.71 inference(unit_resolution,[status(thm)],[10436, 10994])).
% 23.49/23.71 tff(10996,plain,
% 23.49/23.71 (mult(mult(mult(a, b), b), mult(a, c)) = mult(mult(mult(a, b), mult(a, c)), b)),
% 23.49/23.71 inference(transitivity,[status(thm)],[10995, 10564, 10991, 10988, 10984, 10983, 10980, 1752])).
% 23.49/23.71 tff(10997,plain,
% 23.49/23.71 ($false),
% 23.49/23.71 inference(unit_resolution,[status(thm)],[10542, 10996])).
% 23.49/23.71 tff(10998,plain,((~(mult(rd(mult(b, c), mult(a, c)), mult(b, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), b)))) | (mult(mult(mult(a, b), b), mult(a, c)) = mult(mult(mult(a, b), mult(a, c)), b)) | (~(mult(mult(a, b), mult(mult(a, b), c)) = mult(a, mult(b, mult(mult(a, b), c))))) | (~(mult(mult(b, mult(a, c)), b) = mult(b, mult(mult(a, c), b)))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))))), inference(lemma,lemma(discharge,[]))).
% 23.49/23.71 tff(10999,plain,
% 23.49/23.71 (~(mult(rd(mult(b, c), mult(a, c)), mult(b, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), b)))),
% 23.49/23.71 inference(unit_resolution,[status(thm)],[10998, 10976, 10441, 10584, 9702])).
% 23.49/23.71 tff(11000,plain,
% 23.49/23.71 ((~(mult(mult(rd(mult(b, c), mult(a, c)), b), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), b))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(b, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), b))))),
% 23.49/23.72 inference(unit_resolution,[status(thm)],[5542, 10999])).
% 23.49/23.72 tff(11001,plain,
% 23.49/23.72 (~((~(mult(mult(rd(mult(b, c), mult(a, c)), b), mult(a, c)) = mult(rd(mult(b, c), mult(a, c)), mult(b, mult(a, c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), b) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), b)))))),
% 23.49/23.72 inference(unit_resolution,[status(thm)],[5547, 11000])).
% 23.49/23.72 tff(11002,plain,
% 23.49/23.72 (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), b) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), b))),
% 23.49/23.72 inference(unit_resolution,[status(thm)],[5549, 11001])).
% 23.49/23.72 tff(11003,plain,
% 23.49/23.72 (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))),
% 23.49/23.72 inference(unit_resolution,[status(thm)],[10826, 11002, 9698, 9672])).
% 23.49/23.72 tff(11004,plain,
% 23.49/23.72 (~(mult(mult(b, c), a) = mult(b, mult(c, a)))),
% 23.49/23.72 inference(unit_resolution,[status(thm)],[8701, 11003])).
% 23.49/23.72 tff(11005,plain,
% 23.49/23.72 (mult(b, mult(a, c)) = mult(b, mult(c, a))),
% 23.49/23.72 inference(symmetry,[status(thm)],[10220])).
% 23.49/23.72 tff(11006,plain,
% 23.49/23.72 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(b, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))), mult(a, rd(mult(b, c), mult(a, c)))) = mult(b, mult(a, c)))),
% 23.49/23.72 inference(quant_inst,[status(thm)],[])).
% 23.49/23.72 tff(11007,plain,
% 23.49/23.72 (rd(mult(mult(b, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))), mult(a, rd(mult(b, c), mult(a, c)))) = mult(b, mult(a, c))),
% 23.49/23.72 inference(unit_resolution,[status(thm)],[11006, 168])).
% 23.49/23.72 tff(11008,assumption,(mult(mult(mult(mult(b, c), a), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(b, c), a), mult(a, rd(mult(b, c), mult(a, c))))), introduced(assumption)).
% 23.49/23.72 tff(11009,plain,
% 23.49/23.72 (mult(mult(mult(b, c), a), unit) = mult(mult(b, c), a)),
% 23.49/23.72 inference(transitivity,[status(thm)],[1258, 1261, 1263])).
% 23.49/23.72 tff(11010,plain,
% 23.49/23.72 (mult(mult(mult(mult(b, c), a), unit), a) = mult(mult(mult(b, c), a), a)),
% 23.49/23.72 inference(monotonicity,[status(thm)],[11009])).
% 23.49/23.72 tff(11011,plain,
% 23.49/23.72 (mult(mult(mult(b, c), a), a) = mult(mult(mult(mult(b, c), a), unit), a)),
% 23.49/23.72 inference(symmetry,[status(thm)],[11010])).
% 23.49/23.72 tff(11012,plain,
% 23.49/23.72 (mult(mult(mult(b, c), a), a) = mult(mult(b, c), mult(a, a))),
% 23.49/23.72 inference(transitivity,[status(thm)],[11011, 1254, 1559])).
% 23.49/23.72 tff(11013,plain,
% 23.49/23.72 (mult(mult(mult(mult(b, c), a), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(b, c), mult(a, a)), rd(mult(b, c), mult(a, c)))),
% 23.49/23.72 inference(monotonicity,[status(thm)],[11012])).
% 23.49/23.72 tff(11014,plain,
% 23.49/23.72 (mult(mult(mult(b, c), mult(a, a)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(mult(b, c), a), a), rd(mult(b, c), mult(a, c)))),
% 23.49/23.72 inference(symmetry,[status(thm)],[11013])).
% 23.49/23.72 tff(11015,plain,
% 23.49/23.72 (mult(mult(mult(unit, mult(b, a)), unit), c) = mult(mult(b, a), c)),
% 23.49/23.72 inference(monotonicity,[status(thm)],[4321])).
% 23.49/23.72 tff(11016,plain,
% 23.49/23.72 (mult(mult(b, a), c) = mult(mult(mult(unit, mult(b, a)), unit), c)),
% 23.49/23.72 inference(symmetry,[status(thm)],[11015])).
% 23.49/23.72 tff(11017,plain,
% 23.49/23.72 (mult(mult(mult(b, a), c), a) = mult(mult(mult(mult(unit, mult(b, a)), unit), c), a)),
% 23.49/23.72 inference(monotonicity,[status(thm)],[11016])).
% 23.49/23.72 tff(11018,plain,
% 23.49/23.72 (mult(mult(mult(mult(unit, mult(b, a)), unit), c), a) = mult(mult(mult(b, a), c), a)),
% 23.49/23.72 inference(symmetry,[status(thm)],[11017])).
% 23.49/23.72 tff(11019,assumption,(~(mult(mult(b, c), a) = mult(b, mult(c, a)))), introduced(assumption)).
% 23.49/23.72 tff(11020,plain,
% 23.49/23.72 ((~(mult(mult(b, a), c) = mult(b, mult(a, c)))) | (~(mult(mult(b, c), a) = mult(b, mult(c, a))))),
% 23.49/23.72 inference(unit_resolution,[status(thm)],[2277, 11019])).
% 23.49/23.72 tff(11021,plain,
% 23.49/23.72 (~((~(mult(mult(b, a), c) = mult(mult(b, c), a))) | (~(mult(b, mult(a, c)) = mult(b, mult(c, a)))))),
% 23.49/23.72 inference(unit_resolution,[status(thm)],[2275, 11020])).
% 23.49/23.72 tff(11022,plain,
% 23.49/23.72 (((~(mult(mult(b, a), c) = mult(mult(b, c), a))) | (~(mult(b, mult(a, c)) = mult(b, mult(c, a))))) | (mult(mult(b, a), c) = mult(mult(b, c), a))),
% 23.49/23.72 inference(tautology,[status(thm)],[])).
% 23.49/23.72 tff(11023,plain,
% 23.49/23.72 (mult(mult(b, a), c) = mult(mult(b, c), a)),
% 23.49/23.72 inference(unit_resolution,[status(thm)],[11022, 11021])).
% 23.49/23.72 tff(11024,plain,
% 23.49/23.72 (mult(mult(mult(unit, mult(b, a)), unit), c) = mult(mult(b, c), a)),
% 23.49/23.72 inference(transitivity,[status(thm)],[11015, 11023])).
% 23.49/23.72 tff(11025,plain,
% 23.49/23.72 (mult(mult(mult(mult(unit, mult(b, a)), unit), c), a) = mult(mult(mult(b, c), a), a)),
% 23.49/23.72 inference(monotonicity,[status(thm)],[11024])).
% 23.49/23.72 tff(11026,plain,
% 23.49/23.72 (mult(mult(mult(b, c), a), a) = mult(mult(mult(mult(unit, mult(b, a)), unit), c), a)),
% 23.49/23.72 inference(symmetry,[status(thm)],[11025])).
% 23.49/23.72 tff(11027,plain,
% 23.49/23.72 (mult(mult(b, c), mult(a, a)) = mult(b, mult(mult(a, c), a))),
% 23.49/23.72 inference(transitivity,[status(thm)],[1558, 3507, 11010, 11026, 11018, 8036])).
% 23.49/23.72 tff(11028,plain,
% 23.49/23.72 (mult(mult(mult(b, c), mult(a, a)), rd(mult(b, c), mult(a, c))) = mult(mult(b, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c)))),
% 23.49/23.72 inference(monotonicity,[status(thm)],[11027])).
% 23.49/23.72 tff(11029,plain,
% 23.49/23.72 (mult(mult(b, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(b, c), mult(a, a)), rd(mult(b, c), mult(a, c)))),
% 23.49/23.72 inference(symmetry,[status(thm)],[11028])).
% 23.49/23.72 tff(11030,plain,
% 23.49/23.72 (mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))) = mult(mult(b, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c)))),
% 23.49/23.72 inference(symmetry,[status(thm)],[8034])).
% 23.49/23.72 tff(11031,plain,
% 23.49/23.72 (mult(b, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)) = mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))))),
% 23.49/23.72 inference(symmetry,[status(thm)],[10350])).
% 23.49/23.72 tff(11032,plain,
% 23.49/23.72 (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)),
% 23.49/23.72 inference(transitivity,[status(thm)],[8170, 8169, 299, 10348, 10347])).
% 23.49/23.72 tff(11033,plain,
% 23.49/23.72 (mult(b, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = mult(b, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c))),
% 23.49/23.72 inference(monotonicity,[status(thm)],[11032])).
% 23.49/23.72 tff(11034,plain,
% 23.49/23.72 (mult(mult(b, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(b, c), a), mult(a, rd(mult(b, c), mult(a, c))))),
% 23.49/23.72 inference(transitivity,[status(thm)],[8031, 11033, 11031, 11030, 11029, 11014, 11008])).
% 23.49/23.72 tff(11035,plain,
% 23.49/23.72 (rd(mult(mult(b, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))), mult(a, rd(mult(b, c), mult(a, c)))) = rd(mult(mult(mult(b, c), a), mult(a, rd(mult(b, c), mult(a, c)))), mult(a, rd(mult(b, c), mult(a, c))))),
% 23.49/23.72 inference(monotonicity,[status(thm)],[11034])).
% 23.49/23.72 tff(11036,plain,
% 23.49/23.72 (rd(mult(mult(mult(b, c), a), mult(a, rd(mult(b, c), mult(a, c)))), mult(a, rd(mult(b, c), mult(a, c)))) = rd(mult(mult(b, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))), mult(a, rd(mult(b, c), mult(a, c))))),
% 23.49/23.72 inference(symmetry,[status(thm)],[11035])).
% 23.49/23.72 tff(11037,plain,
% 23.49/23.72 (mult(mult(b, c), a) = mult(b, mult(c, a))),
% 23.49/23.72 inference(transitivity,[status(thm)],[8073, 11036, 11007, 11005])).
% 23.49/23.72 tff(11038,plain,
% 23.49/23.72 ($false),
% 23.49/23.72 inference(unit_resolution,[status(thm)],[11019, 11037])).
% 23.49/23.72 tff(11039,plain,((~(mult(mult(b, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))))) | (mult(mult(b, c), a) = mult(b, mult(c, a))) | (~(mult(mult(mult(mult(b, c), a), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(b, c), a), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(b, mult(a, c)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(b, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))), inference(lemma,lemma(discharge,[]))).
% 23.49/23.72 tff(11040,plain,
% 23.49/23.72 (~(mult(mult(b, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))))),
% 23.49/23.72 inference(unit_resolution,[status(thm)],[11039, 11004, 9695, 8191, 281, 8165])).
% 23.49/23.72 tff(11041,plain,
% 23.49/23.72 ((~(mult(mult(b, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(b, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(b, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))))),
% 23.49/23.72 inference(unit_resolution,[status(thm)],[10399, 11040])).
% 23.49/23.72 tff(11042,plain,
% 23.49/23.72 (~((~(mult(mult(b, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(mult(b, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)))) | (~(mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))) = mult(b, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))))),
% 23.49/23.72 inference(unit_resolution,[status(thm)],[10397, 11041])).
% 23.49/23.72 tff(11043,plain,
% 23.49/23.72 (mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))) = mult(b, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))),
% 23.49/23.72 inference(unit_resolution,[status(thm)],[10392, 11042])).
% 23.49/23.72 tff(11044,plain,
% 23.49/23.72 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))))),
% 23.49/23.72 inference(monotonicity,[status(thm)],[4676])).
% 23.49/23.72 tff(11045,plain,
% 23.49/23.72 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c)))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 23.49/23.72 inference(symmetry,[status(thm)],[11044])).
% 23.49/23.72 tff(11046,plain,
% 23.49/23.72 (ld(c, mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) = ld(c, mult(c, mult(b, mult(a, c))))),
% 23.49/23.72 inference(symmetry,[status(thm)],[10801])).
% 23.49/23.72 tff(11047,plain,
% 23.49/23.72 (mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(b, mult(a, c))),
% 23.49/23.72 inference(transitivity,[status(thm)],[299, 4478, 11046, 5658])).
% 23.49/23.72 tff(11048,plain,
% 23.49/23.72 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c)))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(b, mult(a, c)))),
% 23.49/23.72 inference(monotonicity,[status(thm)],[11047])).
% 23.49/23.72 tff(11049,plain,
% 23.49/23.72 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(b, mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))))),
% 23.49/23.72 inference(symmetry,[status(thm)],[11048])).
% 23.49/23.72 tff(11050,assumption,(~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)), b) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), b)))), introduced(assumption)).
% 23.49/23.72 tff(11051,plain,
% 23.49/23.72 ((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), b), mult(a, c)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(b, mult(a, c))))) | (~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)), b) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), b))))),
% 23.49/23.72 inference(unit_resolution,[status(thm)],[3008, 11050])).
% 23.49/23.72 tff(11052,plain,
% 23.49/23.72 (~((~(mult(mult(mult(a, rd(mult(b, c), mult(a, c))), b), mult(a, c)) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)), b))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(b, mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), b)))))),
% 23.49/23.72 inference(unit_resolution,[status(thm)],[3006, 11051])).
% 23.49/23.72 tff(11053,plain,
% 23.49/23.72 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(b, mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), b))),
% 23.49/23.72 inference(unit_resolution,[status(thm)],[3001, 11052])).
% 23.49/23.72 tff(11054,plain,
% 23.49/23.72 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), b)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(b, mult(a, c)))),
% 23.49/23.72 inference(symmetry,[status(thm)],[11053])).
% 23.49/23.72 tff(11055,plain,
% 23.49/23.72 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), c)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), b))),
% 23.49/23.72 inference(symmetry,[status(thm)],[2966])).
% 23.49/23.72 tff(11056,plain,
% 23.49/23.72 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), c)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 23.49/23.72 inference(transitivity,[status(thm)],[11055, 11054, 11049, 11045])).
% 23.49/23.72 tff(11057,plain,
% 23.49/23.72 (ld(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), c))) = ld(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))),
% 23.49/23.72 inference(monotonicity,[status(thm)],[11056])).
% 23.49/23.72 tff(11058,plain,
% 23.49/23.72 (ld(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) = ld(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), c)))),
% 23.49/23.72 inference(symmetry,[status(thm)],[11057])).
% 23.49/23.72 tff(11059,plain,
% 23.49/23.72 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 23.49/23.72 inference(quant_inst,[status(thm)],[])).
% 23.49/23.72 tff(11060,plain,
% 23.49/23.72 (ld(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 23.49/23.72 inference(unit_resolution,[status(thm)],[11059, 7])).
% 23.49/23.72 tff(11061,plain,
% 23.49/23.72 (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = ld(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))),
% 23.49/23.72 inference(symmetry,[status(thm)],[11060])).
% 23.49/23.72 tff(11062,plain,
% 23.49/23.72 (mult(b, mult(a, c)) = mult(mult(a, c), b)),
% 23.49/23.72 inference(transitivity,[status(thm)],[5659, 10801, 4477, 11061, 11058, 2982, 227])).
% 23.49/23.72 tff(11063,plain,
% 23.49/23.72 (mult(rd(mult(b, c), mult(a, c)), mult(b, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), b))),
% 23.49/23.72 inference(monotonicity,[status(thm)],[11062])).
% 23.49/23.72 tff(11064,assumption,(~(mult(rd(mult(b, c), mult(a, c)), mult(b, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), b)))), introduced(assumption)).
% 23.49/23.72 tff(11065,plain,
% 23.49/23.72 ($false),
% 23.49/23.72 inference(unit_resolution,[status(thm)],[11064, 11063])).
% 23.49/23.72 tff(11066,plain,((mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)), b) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), b))) | (mult(rd(mult(b, c), mult(a, c)), mult(b, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), b))) | (~(mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, mult(a, c)))))) | (~(mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))) = mult(b, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))) | (~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))), inference(lemma,lemma(discharge,[]))).
% 23.49/23.72 tff(11067,plain,
% 23.49/23.72 (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)), b) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), b))),
% 23.49/23.72 inference(unit_resolution,[status(thm)],[11066, 10999, 9662, 6583, 10627, 11043, 8165, 281])).
% 23.49/23.72 tff(11068,plain,
% 23.49/23.72 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, c), b)) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)), b)),
% 23.49/23.72 inference(symmetry,[status(thm)],[11067])).
% 23.49/23.72 tff(11069,plain,
% 23.49/23.72 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), b)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), b)),
% 23.49/23.72 inference(symmetry,[status(thm)],[11002])).
% 23.49/23.72 tff(11070,plain,
% 23.49/23.72 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)) = mult(mult(b, c), b)),
% 23.49/23.72 inference(transitivity,[status(thm)],[5527, 11069, 5522])).
% 23.49/23.72 tff(11071,plain,
% 23.49/23.72 (mult(a, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c))) = mult(mult(unit, a), mult(mult(b, c), b))),
% 23.49/23.72 inference(monotonicity,[status(thm)],[245, 11070])).
% 23.49/23.72 tff(11072,plain,
% 23.49/23.72 (mult(a, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c))) = mult(mult(mult(a, b), b), c)),
% 23.49/23.72 inference(transitivity,[status(thm)],[11071, 778, 783, 827])).
% 23.49/23.72 tff(11073,plain,
% 23.49/23.72 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), c)) = mult(mult(a, b), mult(b, c))),
% 23.49/23.73 inference(transitivity,[status(thm)],[2943, 11068, 4287, 806])).
% 23.49/23.73 tff(11074,plain,
% 23.49/23.73 ((mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)))) <=> (mult(mult(a, b), mult(b, c)) = mult(mult(mult(a, b), b), c))),
% 23.49/23.73 inference(monotonicity,[status(thm)],[11073, 11072])).
% 23.49/23.73 tff(11075,plain,
% 23.49/23.73 ((mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)))) <=> (mult(mult(mult(a, b), b), c) = mult(mult(a, b), mult(b, c)))),
% 23.49/23.73 inference(transitivity,[status(thm)],[11074, 6959])).
% 23.49/23.73 tff(11076,plain,
% 23.49/23.73 ((mult(mult(mult(a, b), b), c) = mult(mult(a, b), mult(b, c))) <=> (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c))))),
% 23.49/23.73 inference(symmetry,[status(thm)],[11075])).
% 23.49/23.73 tff(11077,plain,
% 23.49/23.73 ((~(mult(mult(mult(a, b), b), c) = mult(mult(a, b), mult(b, c)))) <=> (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)))))),
% 23.49/23.73 inference(monotonicity,[status(thm)],[11076])).
% 23.49/23.73 tff(11078,plain,
% 23.49/23.73 (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c))))),
% 23.49/23.73 inference(modus_ponens,[status(thm)],[1729, 11077])).
% 23.49/23.73 tff(11079,plain,
% 23.49/23.73 (((~(mult(mult(a, mult(mult(a, b), c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)))))) | (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c))))),
% 23.49/23.73 inference(tautology,[status(thm)],[])).
% 23.49/23.73 tff(11080,plain,
% 23.49/23.73 ((~(mult(mult(a, mult(mult(a, b), c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)))))),
% 23.49/23.73 inference(unit_resolution,[status(thm)],[11079, 11078])).
% 23.49/23.73 tff(11081,plain,
% 23.49/23.73 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, mult(mult(a, b), c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), c)))) | (~(mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c))))))) | (~((~(mult(mult(a, mult(mult(a, b), c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, mult(mult(a, b), c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), c)))) | (~(mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c))))))) | (~((~(mult(mult(a, mult(mult(a, b), c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c))))))))),
% 23.49/23.73 inference(rewrite,[status(thm)],[])).
% 23.49/23.73 tff(11082,plain,
% 23.49/23.73 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(a, mult(mult(a, b), c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), c)))) | (~(mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c))))))) | (~((~(mult(mult(a, mult(mult(a, b), c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c))))))))),
% 23.49/23.73 inference(quant_inst,[status(thm)],[])).
% 23.49/23.73 tff(11083,plain,
% 23.49/23.73 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(a, mult(mult(a, b), c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), c)))) | (~(mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c))))))) | (~((~(mult(mult(a, mult(mult(a, b), c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)))))))),
% 23.49/23.73 inference(modus_ponens,[status(thm)],[11082, 11081])).
% 23.49/23.73 tff(11084,plain,
% 23.49/23.73 ((~((~(mult(mult(a, mult(mult(a, b), c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), c)))) | (~(mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c))))))) | (~((~(mult(mult(a, mult(mult(a, b), c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)))))))),
% 23.49/23.73 inference(unit_resolution,[status(thm)],[11083, 27])).
% 23.49/23.73 tff(11085,plain,
% 23.49/23.73 (~((~(mult(mult(a, mult(mult(a, b), c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), c)))) | (~(mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c))))))),
% 23.49/23.73 inference(unit_resolution,[status(thm)],[11084, 11080])).
% 23.49/23.73 tff(11086,plain,
% 23.49/23.73 (((~(mult(mult(a, mult(mult(a, b), c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), c)))) | (~(mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)))))) | (mult(mult(a, mult(mult(a, b), c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), c)))),
% 23.49/23.73 inference(tautology,[status(thm)],[])).
% 23.49/23.73 tff(11087,plain,
% 23.49/23.73 (mult(mult(a, mult(mult(a, b), c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), c))),
% 23.49/23.73 inference(unit_resolution,[status(thm)],[11086, 11085])).
% 23.49/23.73 tff(11088,plain,
% 23.49/23.73 (mult(c, mult(c, ld(c, mult(a, b)))) = mult(mult(a, b), c)),
% 23.49/23.73 inference(transitivity,[status(thm)],[4225, 4270, 10518, 161])).
% 23.49/23.73 tff(11089,plain,
% 23.49/23.73 (mult(a, mult(c, mult(c, ld(c, mult(a, b))))) = mult(a, mult(mult(a, b), c))),
% 23.49/23.73 inference(monotonicity,[status(thm)],[11088])).
% 23.49/23.73 tff(11090,plain,
% 23.49/23.73 (mult(mult(a, mult(c, mult(c, ld(c, mult(a, b))))), rd(mult(b, c), mult(a, c))) = mult(mult(a, mult(mult(a, b), c)), rd(mult(b, c), mult(a, c)))),
% 23.49/23.73 inference(monotonicity,[status(thm)],[11089])).
% 23.49/23.73 tff(11091,plain,
% 23.49/23.73 (mult(a, mult(mult(a, b), c)) = mult(a, mult(c, mult(c, ld(c, mult(a, b)))))),
% 23.49/23.73 inference(symmetry,[status(thm)],[11089])).
% 23.49/23.73 tff(11092,plain,
% 23.49/23.73 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(b, mult(b, mult(a, mult(mult(a, b), c)))) = mult(a, mult(mult(a, b), c)))),
% 23.49/23.73 inference(quant_inst,[status(thm)],[])).
% 23.49/23.73 tff(11093,plain,
% 23.49/23.73 (ld(b, mult(b, mult(a, mult(mult(a, b), c)))) = mult(a, mult(mult(a, b), c))),
% 23.49/23.73 inference(unit_resolution,[status(thm)],[11092, 7])).
% 23.49/23.73 tff(11094,plain,
% 23.49/23.73 (mult(mult(b, mult(a, c)), mult(a, b)) = mult(mult(b, mult(c, a)), mult(a, b))),
% 23.49/23.73 inference(monotonicity,[status(thm)],[11005])).
% 23.49/23.73 tff(11095,plain,
% 23.49/23.73 (mult(mult(b, mult(a, b)), mult(c, a)) = mult(mult(b, mult(a, b)), mult(a, c))),
% 23.49/23.73 inference(monotonicity,[status(thm)],[8215])).
% 23.49/23.73 tff(11096,plain,
% 23.49/23.73 (mult(mult(b, mult(a, b)), mult(a, c)) = mult(mult(b, mult(a, b)), mult(c, a))),
% 23.49/23.73 inference(symmetry,[status(thm)],[11095])).
% 23.49/23.73 tff(11097,plain,
% 23.49/23.73 ((mult(mult(b, mult(a, b)), mult(a, c)) = mult(mult(b, mult(a, c)), mult(a, b))) <=> (mult(mult(b, mult(a, b)), mult(c, a)) = mult(mult(b, mult(c, a)), mult(a, b)))),
% 23.49/23.73 inference(monotonicity,[status(thm)],[11096, 11094])).
% 23.49/23.73 tff(11098,plain,
% 23.49/23.73 ((mult(mult(b, mult(a, b)), mult(c, a)) = mult(mult(b, mult(c, a)), mult(a, b))) <=> (mult(mult(b, mult(a, b)), mult(a, c)) = mult(mult(b, mult(a, c)), mult(a, b)))),
% 23.49/23.73 inference(symmetry,[status(thm)],[11097])).
% 23.49/23.73 tff(11099,plain,
% 23.49/23.73 ((mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, c), a)) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)), a)) <=> (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, c), a)))),
% 23.49/23.73 inference(commutativity,[status(thm)],[])).
% 23.49/23.73 tff(11100,plain,
% 23.49/23.73 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(b, c), a)),
% 23.49/23.73 inference(transitivity,[status(thm)],[8303, 1332])).
% 23.49/23.73 tff(11101,plain,
% 23.49/23.73 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)), a) = mult(mult(mult(b, c), a), a)),
% 23.49/23.73 inference(monotonicity,[status(thm)],[11100])).
% 23.49/23.73 tff(11102,plain,
% 23.49/23.73 (mult(mult(mult(b, c), a), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)), a)),
% 23.49/23.73 inference(symmetry,[status(thm)],[11101])).
% 23.49/23.73 tff(11103,plain,
% 23.49/23.73 ((~(mult(mult(b, a), c) = mult(b, mult(a, c)))) | (~(mult(mult(b, c), a) = mult(b, mult(c, a))))),
% 23.49/23.73 inference(unit_resolution,[status(thm)],[2277, 11004])).
% 23.49/23.73 tff(11104,plain,
% 23.49/23.73 (~((~(mult(mult(b, a), c) = mult(mult(b, c), a))) | (~(mult(b, mult(a, c)) = mult(b, mult(c, a)))))),
% 23.49/23.73 inference(unit_resolution,[status(thm)],[2275, 11103])).
% 23.49/23.73 tff(11105,plain,
% 23.49/23.73 (mult(mult(b, a), c) = mult(mult(b, c), a)),
% 23.49/23.73 inference(unit_resolution,[status(thm)],[11022, 11104])).
% 23.49/23.73 tff(11106,plain,
% 23.49/23.73 (mult(mult(mult(unit, mult(b, a)), unit), c) = mult(mult(b, c), a)),
% 23.49/23.73 inference(transitivity,[status(thm)],[11015, 11105])).
% 23.49/23.73 tff(11107,plain,
% 23.49/23.73 (mult(mult(mult(mult(unit, mult(b, a)), unit), c), a) = mult(mult(mult(b, c), a), a)),
% 23.49/23.73 inference(monotonicity,[status(thm)],[11106])).
% 23.49/23.73 tff(11108,plain,
% 23.49/23.73 (mult(b, mult(mult(a, c), a)) = mult(mult(mult(b, a), c), a)),
% 23.49/23.73 inference(symmetry,[status(thm)],[8036])).
% 23.49/23.73 tff(11109,plain,
% 23.49/23.73 (mult(b, mult(mult(a, c), a)) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)), a)),
% 23.49/23.73 inference(transitivity,[status(thm)],[11108, 11017, 11107, 11102])).
% 23.49/23.73 tff(11110,plain,
% 23.49/23.73 ((~(mult(mult(b, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(b, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))) | (~(mult(mult(b, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))))))),
% 23.49/23.73 inference(unit_resolution,[status(thm)],[8078, 11040])).
% 23.49/23.73 tff(11111,plain,
% 23.49/23.73 (~((~(mult(mult(b, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(mult(b, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))))) | (~(mult(b, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) = mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))))))),
% 23.49/23.73 inference(unit_resolution,[status(thm)],[8083, 11110])).
% 23.49/23.73 tff(11112,plain,
% 23.49/23.73 (mult(b, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) = mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))))),
% 23.49/23.73 inference(unit_resolution,[status(thm)],[8085, 11111])).
% 23.49/23.73 tff(11113,plain,
% 23.49/23.73 (mult(b, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))))),
% 23.49/23.73 inference(monotonicity,[status(thm)],[8170])).
% 23.49/23.73 tff(11114,plain,
% 23.49/23.73 (mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))) = mult(b, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.49/23.73 inference(symmetry,[status(thm)],[11113])).
% 23.49/23.73 tff(11115,assumption,(mult(b, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) = mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))))), introduced(assumption)).
% 23.49/23.73 tff(11116,plain,
% 23.49/23.73 (mult(b, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) = mult(b, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.49/23.73 inference(transitivity,[status(thm)],[11115, 11114])).
% 23.49/23.73 tff(11117,plain,
% 23.49/23.73 (ld(b, mult(b, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) = ld(b, mult(b, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))))),
% 23.49/23.73 inference(monotonicity,[status(thm)],[11116])).
% 23.49/23.73 tff(11118,plain,
% 23.49/23.73 (ld(b, mult(b, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))) = ld(b, mult(b, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))),
% 23.49/23.73 inference(symmetry,[status(thm)],[11117])).
% 23.49/23.73 tff(11119,plain,
% 23.49/23.73 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(b, mult(b, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.49/23.73 inference(quant_inst,[status(thm)],[])).
% 23.49/23.73 tff(11120,plain,
% 23.49/23.73 (ld(b, mult(b, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))),
% 23.49/23.73 inference(unit_resolution,[status(thm)],[11119, 7])).
% 23.49/23.73 tff(11121,plain,
% 23.49/23.73 (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = ld(b, mult(b, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))))),
% 23.49/23.73 inference(symmetry,[status(thm)],[11120])).
% 23.49/23.73 tff(11122,plain,
% 23.49/23.73 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), a), a) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.49/23.73 inference(quant_inst,[status(thm)],[])).
% 23.49/23.73 tff(11123,plain,
% 23.49/23.73 (rd(mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), a), a) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))),
% 23.49/23.73 inference(unit_resolution,[status(thm)],[11122, 168])).
% 23.49/23.73 tff(11124,plain,
% 23.49/23.73 (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))),
% 23.49/23.73 inference(transitivity,[status(thm)],[11121, 11118, 10785])).
% 23.49/23.73 tff(11125,plain,
% 23.49/23.73 (mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a)),
% 23.49/23.73 inference(monotonicity,[status(thm)],[11124])).
% 23.49/23.73 tff(11126,plain,
% 23.49/23.73 (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a) = mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), a)),
% 23.49/23.73 inference(symmetry,[status(thm)],[11125])).
% 23.49/23.73 tff(11127,assumption,(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), a))), introduced(assumption)).
% 23.49/23.73 tff(11128,plain,
% 23.49/23.73 (mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), a)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a)),
% 23.49/23.73 inference(symmetry,[status(thm)],[11127])).
% 23.49/23.73 tff(11129,plain,
% 23.49/23.73 (mult(a, mult(c, a)) = mult(a, mult(a, c))),
% 23.49/23.73 inference(monotonicity,[status(thm)],[8215])).
% 23.49/23.73 tff(11130,plain,
% 23.49/23.73 (mult(a, mult(c, a)) = mult(mult(a, c), a)),
% 23.49/23.73 inference(transitivity,[status(thm)],[11129, 4452, 8166, 4447])).
% 23.49/23.73 tff(11131,plain,
% 23.49/23.73 (mult(mult(a, mult(c, a)), a) = mult(mult(mult(a, c), a), a)),
% 23.49/23.73 inference(monotonicity,[status(thm)],[11130])).
% 23.49/23.73 tff(11132,plain,
% 23.49/23.73 (mult(mult(mult(a, c), a), a) = mult(mult(a, mult(c, a)), a)),
% 23.49/23.73 inference(symmetry,[status(thm)],[11131])).
% 23.49/23.73 tff(11133,plain,
% 23.49/23.73 (mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), a)) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(c, a)), a))),
% 23.49/23.73 inference(monotonicity,[status(thm)],[11132])).
% 23.49/23.73 tff(11134,plain,
% 23.49/23.73 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(c, a)), a)) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), a))),
% 23.49/23.74 inference(symmetry,[status(thm)],[11133])).
% 23.49/23.74 tff(11135,plain,
% 23.49/23.74 (mult(mult(a, mult(a, c)), a) = mult(mult(mult(a, c), a), a)),
% 23.49/23.74 inference(monotonicity,[status(thm)],[8262])).
% 23.49/23.74 tff(11136,plain,
% 23.49/23.74 (mult(mult(mult(a, c), a), a) = mult(mult(a, mult(a, c)), a)),
% 23.49/23.74 inference(symmetry,[status(thm)],[11135])).
% 23.49/23.74 tff(11137,plain,
% 23.49/23.74 (mult(mult(a, mult(c, a)), a) = mult(mult(a, mult(a, c)), a)),
% 23.49/23.74 inference(transitivity,[status(thm)],[11131, 11136])).
% 23.49/23.74 tff(11138,plain,
% 23.49/23.74 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(c, a)), a)) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(a, c)), a))),
% 23.49/23.74 inference(monotonicity,[status(thm)],[11137])).
% 23.49/23.74 tff(11139,plain,
% 23.49/23.74 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(a, c)), a)) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(c, a)), a))),
% 23.49/23.74 inference(symmetry,[status(thm)],[11138])).
% 23.49/23.74 tff(11140,plain,
% 23.49/23.74 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(a, c)), a)))),
% 23.49/23.74 inference(quant_inst,[status(thm)],[])).
% 23.49/23.74 tff(11141,plain,
% 23.49/23.74 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(a, c)), a))),
% 23.49/23.74 inference(unit_resolution,[status(thm)],[11140, 56])).
% 23.49/23.74 tff(11142,plain,
% 23.49/23.74 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)) = mult(mult(b, c), a)),
% 23.49/23.74 inference(transitivity,[status(thm)],[4298, 1332])).
% 23.49/23.74 tff(11143,plain,
% 23.49/23.74 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)), a) = mult(mult(mult(b, c), a), a)),
% 23.49/23.74 inference(monotonicity,[status(thm)],[11142])).
% 23.49/23.74 tff(11144,plain,
% 23.49/23.74 (mult(mult(mult(b, c), a), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)), a)),
% 23.49/23.74 inference(symmetry,[status(thm)],[11143])).
% 23.49/23.74 tff(11145,plain,
% 23.49/23.74 (mult(mult(mult(b, c), a), a) = mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), a)),
% 23.49/23.74 inference(transitivity,[status(thm)],[11144, 11141, 11139, 11134, 11128, 11126])).
% 23.49/23.74 tff(11146,plain,
% 23.49/23.74 (rd(mult(mult(mult(b, c), a), a), a) = rd(mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), a), a)),
% 23.49/23.74 inference(monotonicity,[status(thm)],[11145])).
% 23.49/23.74 tff(11147,plain,
% 23.49/23.74 (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))),
% 23.49/23.74 inference(transitivity,[status(thm)],[1332, 1518, 11146, 11123, 11121, 11118, 10785])).
% 23.49/23.74 tff(11148,plain,
% 23.49/23.74 ($false),
% 23.49/23.74 inference(unit_resolution,[status(thm)],[1364, 11147])).
% 23.49/23.74 tff(11149,plain,((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), a)))) | (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) | (~(mult(b, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) = mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))))))), inference(lemma,lemma(discharge,[]))).
% 23.49/23.74 tff(11150,plain,
% 23.49/23.74 (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), a)))),
% 23.49/23.74 inference(unit_resolution,[status(thm)],[11149, 11112, 11003])).
% 23.49/23.74 tff(11151,plain,
% 23.49/23.74 (((~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(a, c), a))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), a))))) | (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), a)))),
% 23.49/23.74 inference(tautology,[status(thm)],[])).
% 23.49/23.74 tff(11152,plain,
% 23.49/23.74 ((~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(a, c), a))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), a))))),
% 23.49/23.74 inference(unit_resolution,[status(thm)],[11151, 11150])).
% 23.49/23.74 tff(11153,plain,
% 23.49/23.74 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, c), a)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(a, c), a))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), a)))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(a, c), a))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), a)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, c), a)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(a, c), a))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), a)))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(a, c), a))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), a)))))))),
% 23.49/23.74 inference(rewrite,[status(thm)],[])).
% 23.49/23.74 tff(11154,plain,
% 23.49/23.74 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, c), a)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(a, c), a))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), a)))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(a, c), a))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), a)))))))),
% 23.49/23.74 inference(quant_inst,[status(thm)],[])).
% 23.49/23.74 tff(11155,plain,
% 23.49/23.74 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, c), a)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(a, c), a))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), a)))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(a, c), a))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), a))))))),
% 23.49/23.74 inference(modus_ponens,[status(thm)],[11154, 11153])).
% 23.49/23.74 tff(11156,plain,
% 23.49/23.74 ((~((~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, c), a)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(a, c), a))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), a)))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(a, c), a))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), a))))))),
% 23.49/23.74 inference(unit_resolution,[status(thm)],[11155, 27])).
% 23.49/23.74 tff(11157,plain,
% 23.49/23.74 (~((~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, c), a)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(a, c), a))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), a)))))),
% 23.49/23.74 inference(unit_resolution,[status(thm)],[11156, 11152])).
% 23.49/23.74 tff(11158,plain,
% 23.49/23.74 (((~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, c), a)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(a, c), a))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), a))))) | (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, c), a)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a))),
% 23.49/23.74 inference(tautology,[status(thm)],[])).
% 23.49/23.74 tff(11159,plain,
% 23.49/23.74 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, c), a)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a)),
% 23.49/23.74 inference(unit_resolution,[status(thm)],[11158, 11157])).
% 23.49/23.74 tff(11160,plain,
% 23.49/23.74 (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, c), a))),
% 23.49/23.74 inference(symmetry,[status(thm)],[11159])).
% 23.49/23.74 tff(11161,plain,
% 23.49/23.74 (mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c))),
% 23.49/23.74 inference(unit_resolution,[status(thm)],[9500, 8165, 281])).
% 23.49/23.74 tff(11162,plain,
% 23.49/23.74 (mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c)) = mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)),
% 23.49/23.74 inference(symmetry,[status(thm)],[11161])).
% 23.49/23.74 tff(11163,plain,
% 23.49/23.74 (mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 23.49/23.74 inference(monotonicity,[status(thm)],[9761])).
% 23.49/23.74 tff(11164,plain,
% 23.49/23.74 (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c))),
% 23.49/23.74 inference(symmetry,[status(thm)],[11163])).
% 23.49/23.74 tff(11165,plain,
% 23.49/23.74 (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)),
% 23.49/23.74 inference(transitivity,[status(thm)],[11164, 11162])).
% 23.49/23.74 tff(11166,plain,
% 23.49/23.74 (mult(b, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))) = mult(b, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c))),
% 23.49/23.74 inference(monotonicity,[status(thm)],[11165])).
% 23.49/23.74 tff(11167,plain,
% 23.49/23.74 (mult(b, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)) = mult(b, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 23.49/23.74 inference(symmetry,[status(thm)],[11166])).
% 23.49/23.74 tff(11168,plain,
% 23.49/23.74 (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)),
% 23.49/23.74 inference(transitivity,[status(thm)],[8169, 281, 11164, 11162])).
% 23.49/23.74 tff(11169,plain,
% 23.49/23.74 (mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))) = mult(b, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c))),
% 23.49/23.74 inference(monotonicity,[status(thm)],[11168])).
% 23.49/23.74 tff(11170,plain,
% 23.49/23.74 (mult(b, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) = mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))))),
% 23.49/23.74 inference(symmetry,[status(thm)],[11043])).
% 23.49/23.74 tff(11171,plain,
% 23.49/23.74 (mult(b, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) = mult(b, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 23.49/23.74 inference(transitivity,[status(thm)],[11170, 11169, 11167])).
% 23.49/23.74 tff(11172,plain,
% 23.49/23.74 (ld(b, mult(b, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) = ld(b, mult(b, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))),
% 23.49/23.74 inference(monotonicity,[status(thm)],[11171])).
% 23.49/23.74 tff(11173,plain,
% 23.49/23.74 (ld(b, mult(b, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) = ld(b, mult(b, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))),
% 23.49/23.74 inference(symmetry,[status(thm)],[11172])).
% 23.49/23.74 tff(11174,plain,
% 23.49/23.74 (mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))),
% 23.49/23.74 inference(transitivity,[status(thm)],[11161, 11163, 10374, 11173, 10785])).
% 23.49/23.75 tff(11175,plain,
% 23.49/23.75 (mult(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c), a) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a)),
% 23.49/23.75 inference(monotonicity,[status(thm)],[11174])).
% 23.49/23.75 tff(11176,plain,
% 23.49/23.75 (mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c)))),
% 23.49/23.75 inference(symmetry,[status(thm)],[10011])).
% 23.49/23.75 tff(11177,plain,
% 23.49/23.75 (mult(c, mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))),
% 23.49/23.75 inference(transitivity,[status(thm)],[8269, 9986, 4336])).
% 23.49/23.75 tff(11178,plain,
% 23.49/23.75 (mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)),
% 23.49/23.75 inference(monotonicity,[status(thm)],[11177])).
% 23.49/23.75 tff(11179,plain,
% 23.49/23.75 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), c)),
% 23.49/23.75 inference(symmetry,[status(thm)],[11178])).
% 23.49/23.75 tff(11180,plain,
% 23.49/23.75 (mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), c)),
% 23.49/23.75 inference(transitivity,[status(thm)],[9757, 9755, 11179])).
% 23.49/23.75 tff(11181,plain,
% 23.49/23.75 (mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), c))),
% 23.49/23.75 inference(monotonicity,[status(thm)],[11180])).
% 23.49/23.75 tff(11182,plain,
% 23.49/23.75 (mult(a, mult(mult(c, mult(a, rd(mult(b, c), mult(a, c)))), c)) = mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))))),
% 23.49/23.75 inference(symmetry,[status(thm)],[11181])).
% 23.49/23.75 tff(11183,plain,
% 23.49/23.75 (mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), c)),
% 23.49/23.75 inference(monotonicity,[status(thm)],[9654])).
% 23.49/23.75 tff(11184,plain,
% 23.49/23.75 (mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), c) = mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), c)),
% 23.49/23.75 inference(symmetry,[status(thm)],[11183])).
% 23.49/23.75 tff(11185,plain,
% 23.49/23.75 (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))),
% 23.49/23.75 inference(transitivity,[status(thm)],[10374, 11173, 10785])).
% 23.49/23.75 tff(11186,plain,
% 23.49/23.75 (mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), c) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), c)),
% 23.49/23.75 inference(monotonicity,[status(thm)],[11185])).
% 23.49/23.75 tff(11187,plain,
% 23.49/23.75 (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), c) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), c)),
% 23.49/23.75 inference(symmetry,[status(thm)],[11186])).
% 23.49/23.75 tff(11188,plain,
% 23.49/23.75 (mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, mult(a, c)))) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, mult(a, c)))),
% 23.49/23.75 inference(symmetry,[status(thm)],[10627])).
% 23.49/23.75 tff(11189,plain,
% 23.49/23.75 (mult(c, mult(b, mult(a, c))) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 23.49/23.75 inference(transitivity,[status(thm)],[10799, 2429, 5386, 2501, 10798, 10797, 11188, 10795, 6008, 10794, 11187, 11184, 7918, 11182, 11176, 9787, 6583, 9766, 9662])).
% 23.49/23.75 tff(11190,plain,
% 23.49/23.75 (ld(c, mult(c, mult(b, mult(a, c)))) = ld(c, mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))),
% 23.49/23.75 inference(monotonicity,[status(thm)],[11189])).
% 23.49/23.75 tff(11191,plain,
% 23.49/23.75 (mult(b, mult(a, c)) = mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)),
% 23.49/23.75 inference(transitivity,[status(thm)],[5659, 11190, 4477, 11164, 11162])).
% 23.49/23.75 tff(11192,plain,
% 23.49/23.75 (mult(mult(b, mult(a, c)), a) = mult(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c), a)),
% 23.49/23.75 inference(monotonicity,[status(thm)],[11191])).
% 23.49/23.75 tff(11193,plain,
% 23.49/23.75 (mult(mult(b, mult(a, c)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, c), a))),
% 23.49/23.75 inference(transitivity,[status(thm)],[11192, 11175, 11160])).
% 23.49/23.75 tff(11194,plain,
% 23.49/23.75 ((mult(mult(b, mult(a, c)), a) = mult(b, mult(mult(a, c), a))) <=> (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, c), a)) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)), a))),
% 23.49/23.75 inference(monotonicity,[status(thm)],[11193, 11109])).
% 23.49/23.75 tff(11195,plain,
% 23.49/23.75 ((mult(mult(b, mult(a, c)), a) = mult(b, mult(mult(a, c), a))) <=> (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, c), a)))),
% 23.49/23.75 inference(transitivity,[status(thm)],[11194, 11099])).
% 23.49/23.75 tff(11196,plain,
% 23.49/23.75 ((mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, c), a))) <=> (mult(mult(b, mult(a, c)), a) = mult(b, mult(mult(a, c), a)))),
% 23.49/23.75 inference(symmetry,[status(thm)],[11195])).
% 23.49/23.75 tff(11197,plain,
% 23.49/23.75 ((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, c), a)))) <=> (~(mult(mult(b, mult(a, c)), a) = mult(b, mult(mult(a, c), a))))),
% 23.49/23.75 inference(monotonicity,[status(thm)],[11196])).
% 23.49/23.75 tff(11198,plain,
% 23.49/23.75 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(a, c)), a)) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)), a)),
% 23.49/23.75 inference(symmetry,[status(thm)],[11141])).
% 23.49/23.75 tff(11199,plain,
% 23.49/23.75 (mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), a)) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(a, c)), a))),
% 23.49/23.75 inference(monotonicity,[status(thm)],[11136])).
% 23.49/23.75 tff(11200,plain,
% 23.49/23.75 (mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), a)) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)), a)),
% 23.49/23.75 inference(transitivity,[status(thm)],[11199, 11198])).
% 23.49/23.75 tff(11201,plain,
% 23.49/23.75 ((mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), a))) <=> (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, c), a)) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)), a))),
% 23.49/23.75 inference(monotonicity,[status(thm)],[11160, 11200])).
% 23.49/23.75 tff(11202,plain,
% 23.49/23.75 ((mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), a))) <=> (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, c), a)))),
% 23.49/23.75 inference(transitivity,[status(thm)],[11201, 11099])).
% 23.49/23.75 tff(11203,plain,
% 23.49/23.75 ((~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), a)))) <=> (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, c), a))))),
% 23.49/23.75 inference(monotonicity,[status(thm)],[11202])).
% 23.49/23.75 tff(11204,plain,
% 23.49/23.75 (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(a, c)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(a, c), a)))),
% 23.49/23.75 inference(modus_ponens,[status(thm)],[11150, 11203])).
% 23.49/23.75 tff(11205,plain,
% 23.49/23.75 (~(mult(mult(b, mult(a, c)), a) = mult(b, mult(mult(a, c), a)))),
% 23.49/23.75 inference(modus_ponens,[status(thm)],[11204, 11197])).
% 23.49/23.75 tff(11206,plain,
% 23.49/23.75 (((~(mult(mult(b, a), mult(a, c)) = mult(b, mult(a, mult(a, c))))) | (~(mult(mult(b, mult(a, c)), a) = mult(b, mult(mult(a, c), a))))) | (mult(mult(b, mult(a, c)), a) = mult(b, mult(mult(a, c), a)))),
% 23.49/23.75 inference(tautology,[status(thm)],[])).
% 23.49/23.75 tff(11207,plain,
% 23.49/23.75 ((~(mult(mult(b, a), mult(a, c)) = mult(b, mult(a, mult(a, c))))) | (~(mult(mult(b, mult(a, c)), a) = mult(b, mult(mult(a, c), a))))),
% 23.49/23.75 inference(unit_resolution,[status(thm)],[11206, 11205])).
% 23.49/23.75 tff(11208,plain,
% 23.49/23.75 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(b, a), mult(a, c)) = mult(mult(b, mult(a, c)), a))) | (~(mult(b, mult(a, mult(a, c))) = mult(b, mult(mult(a, c), a)))))) | (~((~(mult(mult(b, a), mult(a, c)) = mult(b, mult(a, mult(a, c))))) | (~(mult(mult(b, mult(a, c)), a) = mult(b, mult(mult(a, c), a)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(b, a), mult(a, c)) = mult(mult(b, mult(a, c)), a))) | (~(mult(b, mult(a, mult(a, c))) = mult(b, mult(mult(a, c), a)))))) | (~((~(mult(mult(b, a), mult(a, c)) = mult(b, mult(a, mult(a, c))))) | (~(mult(mult(b, mult(a, c)), a) = mult(b, mult(mult(a, c), a)))))))),
% 23.59/23.75 inference(rewrite,[status(thm)],[])).
% 23.59/23.75 tff(11209,plain,
% 23.59/23.75 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(b, a), mult(a, c)) = mult(mult(b, mult(a, c)), a))) | (~(mult(b, mult(a, mult(a, c))) = mult(b, mult(mult(a, c), a)))))) | (~((~(mult(mult(b, a), mult(a, c)) = mult(b, mult(a, mult(a, c))))) | (~(mult(mult(b, mult(a, c)), a) = mult(b, mult(mult(a, c), a)))))))),
% 23.59/23.75 inference(quant_inst,[status(thm)],[])).
% 23.59/23.75 tff(11210,plain,
% 23.59/23.75 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(b, a), mult(a, c)) = mult(mult(b, mult(a, c)), a))) | (~(mult(b, mult(a, mult(a, c))) = mult(b, mult(mult(a, c), a)))))) | (~((~(mult(mult(b, a), mult(a, c)) = mult(b, mult(a, mult(a, c))))) | (~(mult(mult(b, mult(a, c)), a) = mult(b, mult(mult(a, c), a))))))),
% 23.59/23.75 inference(modus_ponens,[status(thm)],[11209, 11208])).
% 23.59/23.75 tff(11211,plain,
% 23.59/23.75 ((~((~(mult(mult(b, a), mult(a, c)) = mult(mult(b, mult(a, c)), a))) | (~(mult(b, mult(a, mult(a, c))) = mult(b, mult(mult(a, c), a)))))) | (~((~(mult(mult(b, a), mult(a, c)) = mult(b, mult(a, mult(a, c))))) | (~(mult(mult(b, mult(a, c)), a) = mult(b, mult(mult(a, c), a))))))),
% 23.59/23.75 inference(unit_resolution,[status(thm)],[11210, 27])).
% 23.59/23.75 tff(11212,plain,
% 23.59/23.75 (~((~(mult(mult(b, a), mult(a, c)) = mult(mult(b, mult(a, c)), a))) | (~(mult(b, mult(a, mult(a, c))) = mult(b, mult(mult(a, c), a)))))),
% 23.59/23.75 inference(unit_resolution,[status(thm)],[11211, 11207])).
% 23.59/23.75 tff(11213,plain,
% 23.59/23.75 (((~(mult(mult(b, a), mult(a, c)) = mult(mult(b, mult(a, c)), a))) | (~(mult(b, mult(a, mult(a, c))) = mult(b, mult(mult(a, c), a))))) | (mult(mult(b, a), mult(a, c)) = mult(mult(b, mult(a, c)), a))),
% 23.59/23.75 inference(tautology,[status(thm)],[])).
% 23.59/23.75 tff(11214,plain,
% 23.59/23.75 (mult(mult(b, a), mult(a, c)) = mult(mult(b, mult(a, c)), a)),
% 23.59/23.75 inference(unit_resolution,[status(thm)],[11213, 11212])).
% 23.59/23.75 tff(11215,plain,
% 23.59/23.75 (mult(mult(b, mult(a, c)), a) = mult(mult(b, a), mult(a, c))),
% 23.59/23.75 inference(symmetry,[status(thm)],[11214])).
% 23.59/23.75 tff(11216,plain,
% 23.59/23.75 (mult(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c), a) = mult(mult(b, mult(a, c)), a)),
% 23.59/23.75 inference(symmetry,[status(thm)],[11192])).
% 23.59/23.75 tff(11217,plain,
% 23.59/23.75 (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a) = mult(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c), a)),
% 23.59/23.75 inference(symmetry,[status(thm)],[11175])).
% 23.59/23.75 tff(11218,plain,
% 23.59/23.75 (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a) = mult(mult(b, a), mult(a, c))),
% 23.59/23.75 inference(transitivity,[status(thm)],[11217, 11216, 11215])).
% 23.59/23.75 tff(11219,plain,
% 23.59/23.75 (mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), b) = mult(mult(mult(b, a), mult(a, c)), b)),
% 23.59/23.75 inference(monotonicity,[status(thm)],[11218])).
% 23.59/23.75 tff(11220,plain,
% 23.59/23.75 (mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c), a)),
% 23.59/23.75 inference(monotonicity,[status(thm)],[11165])).
% 23.59/23.75 tff(11221,plain,
% 23.59/23.75 (mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a)),
% 23.59/23.75 inference(transitivity,[status(thm)],[11220, 11175])).
% 23.59/23.75 tff(11222,plain,
% 23.59/23.75 (mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a), b) = mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), b)),
% 23.59/23.75 inference(monotonicity,[status(thm)],[11221])).
% 23.59/23.75 tff(11223,plain,
% 23.59/23.75 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(mult(b, c), a), mult(mult(mult(b, c), a), mult(a, b))) = mult(a, b))),
% 23.59/23.75 inference(quant_inst,[status(thm)],[])).
% 23.59/23.75 tff(11224,plain,
% 23.59/23.75 (ld(mult(mult(b, c), a), mult(mult(mult(b, c), a), mult(a, b))) = mult(a, b)),
% 23.59/23.75 inference(unit_resolution,[status(thm)],[11223, 7])).
% 23.59/23.75 tff(11225,assumption,(mult(mult(mult(b, c), a), mult(b, a)) = mult(mult(mult(b, c), a), mult(a, b))), introduced(assumption)).
% 23.59/23.75 tff(11226,plain,
% 23.59/23.75 (ld(mult(mult(b, c), a), mult(mult(mult(b, c), a), mult(b, a))) = ld(mult(mult(b, c), a), mult(mult(mult(b, c), a), mult(a, b)))),
% 23.59/23.75 inference(monotonicity,[status(thm)],[11225])).
% 23.59/23.75 tff(11227,plain,
% 23.59/23.75 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(mult(b, c), a), mult(mult(mult(b, c), a), mult(b, a))) = mult(b, a))),
% 23.59/23.75 inference(quant_inst,[status(thm)],[])).
% 23.59/23.75 tff(11228,plain,
% 23.59/23.75 (ld(mult(mult(b, c), a), mult(mult(mult(b, c), a), mult(b, a))) = mult(b, a)),
% 23.59/23.75 inference(unit_resolution,[status(thm)],[11227, 7])).
% 23.59/23.75 tff(11229,plain,
% 23.59/23.75 (mult(b, a) = ld(mult(mult(b, c), a), mult(mult(mult(b, c), a), mult(b, a)))),
% 23.59/23.75 inference(symmetry,[status(thm)],[11228])).
% 23.59/23.75 tff(11230,plain,
% 23.59/23.75 (mult(b, a) = mult(a, b)),
% 23.59/23.75 inference(transitivity,[status(thm)],[11229, 11226, 11224])).
% 23.59/23.75 tff(11231,plain,
% 23.59/23.75 (mult(mult(b, a), b) = mult(mult(a, b), b)),
% 23.59/23.75 inference(monotonicity,[status(thm)],[11230])).
% 23.59/23.75 tff(11232,plain,
% 23.59/23.75 (mult(mult(a, b), b) = mult(mult(b, a), b)),
% 23.59/23.75 inference(symmetry,[status(thm)],[11231])).
% 23.59/23.75 tff(11233,plain,
% 23.59/23.75 (mult(a, mult(unit, mult(mult(b, unit), b))) = mult(mult(b, a), b)),
% 23.59/23.75 inference(transitivity,[status(thm)],[829, 663, 445, 662, 11232])).
% 23.59/23.75 tff(11234,plain,
% 23.59/23.75 (mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b)))) = mult(mult(a, c), mult(mult(b, a), b))),
% 23.59/23.75 inference(monotonicity,[status(thm)],[11233])).
% 23.59/23.75 tff(11235,plain,
% 23.59/23.75 (mult(mult(a, c), mult(mult(b, a), b)) = mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b))))),
% 23.59/23.75 inference(symmetry,[status(thm)],[11234])).
% 23.59/23.75 tff(11236,plain,
% 23.59/23.75 (mult(mult(mult(c, b), a), b) = mult(mult(mult(b, c), a), b)),
% 23.59/23.75 inference(monotonicity,[status(thm)],[4975])).
% 23.59/23.75 tff(11237,plain,
% 23.59/23.75 (mult(mult(mult(b, c), a), b) = mult(mult(mult(c, b), a), b)),
% 23.59/23.75 inference(symmetry,[status(thm)],[11236])).
% 23.59/23.75 tff(11238,plain,
% 23.59/23.75 (mult(c, mult(b, mult(a, b))) = mult(c, mult(mult(b, a), b))),
% 23.59/23.75 inference(transitivity,[status(thm)],[6519, 6496, 1312, 11237, 3429])).
% 23.59/23.75 tff(11239,plain,
% 23.59/23.75 (ld(c, mult(c, mult(b, mult(a, b)))) = ld(c, mult(c, mult(mult(b, a), b)))),
% 23.59/23.75 inference(monotonicity,[status(thm)],[11238])).
% 23.59/23.75 tff(11240,plain,
% 23.59/23.75 (ld(c, mult(c, mult(mult(b, a), b))) = ld(c, mult(c, mult(b, mult(a, b))))),
% 23.59/23.75 inference(symmetry,[status(thm)],[11239])).
% 23.59/23.75 tff(11241,plain,
% 23.59/23.75 (mult(mult(b, a), b) = mult(b, mult(a, b))),
% 23.59/23.75 inference(transitivity,[status(thm)],[7298, 11240, 6523])).
% 23.59/23.75 tff(11242,plain,
% 23.59/23.75 (mult(mult(a, c), mult(mult(b, a), b)) = mult(mult(a, c), mult(b, mult(a, b)))),
% 23.59/23.75 inference(monotonicity,[status(thm)],[11241])).
% 23.59/23.75 tff(11243,plain,
% 23.59/23.75 (mult(mult(a, c), mult(b, mult(a, b))) = mult(mult(a, c), mult(mult(b, a), b))),
% 23.59/23.75 inference(symmetry,[status(thm)],[11242])).
% 23.59/23.75 tff(11244,plain,
% 23.59/23.75 (mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(mult(a, c), mult(a, b)), b)),
% 23.59/23.75 inference(transitivity,[status(thm)],[961, 11243, 11235, 10460, 1091])).
% 23.59/23.75 tff(11245,plain,
% 23.59/23.75 ($false),
% 23.59/23.75 inference(unit_resolution,[status(thm)],[1114, 11244])).
% 23.59/23.75 tff(11246,plain,((~(mult(mult(mult(b, c), a), mult(b, a)) = mult(mult(mult(b, c), a), mult(a, b)))) | (mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(mult(a, c), mult(a, b)), b)) | (~(mult(mult(mult(a, c), mult(a, b)), b) = mult(mult(a, c), mult(mult(a, b), b)))) | (~(mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(a, c), mult(b, mult(a, b))))) | (~(mult(mult(c, b), mult(a, b)) = mult(c, mult(b, mult(a, b))))) | (~(mult(mult(mult(b, c), a), b) = mult(mult(b, c), mult(a, b))))), inference(lemma,lemma(discharge,[]))).
% 23.59/23.75 tff(11247,plain,
% 23.59/23.75 (~(mult(mult(mult(b, c), a), mult(b, a)) = mult(mult(mult(b, c), a), mult(a, b)))),
% 23.59/23.75 inference(unit_resolution,[status(thm)],[11246, 10459, 10454, 10453, 10449, 10448])).
% 23.59/23.76 tff(11248,plain,
% 23.59/23.76 (((~(mult(mult(mult(mult(b, c), a), b), a) = mult(mult(mult(mult(b, c), a), a), b))) | (~(mult(mult(mult(b, c), a), mult(b, a)) = mult(mult(mult(b, c), a), mult(a, b))))) | (mult(mult(mult(b, c), a), mult(b, a)) = mult(mult(mult(b, c), a), mult(a, b)))),
% 23.59/23.76 inference(tautology,[status(thm)],[])).
% 23.59/23.76 tff(11249,plain,
% 23.59/23.76 ((~(mult(mult(mult(mult(b, c), a), b), a) = mult(mult(mult(mult(b, c), a), a), b))) | (~(mult(mult(mult(b, c), a), mult(b, a)) = mult(mult(mult(b, c), a), mult(a, b))))),
% 23.59/23.76 inference(unit_resolution,[status(thm)],[11248, 11247])).
% 23.59/23.76 tff(11250,plain,
% 23.59/23.76 (~((~(mult(mult(mult(mult(b, c), a), b), a) = mult(mult(mult(b, c), a), mult(b, a)))) | (~(mult(mult(mult(mult(b, c), a), a), b) = mult(mult(mult(b, c), a), mult(a, b)))))),
% 23.59/23.76 inference(unit_resolution,[status(thm)],[3115, 11249])).
% 23.59/23.76 tff(11251,plain,
% 23.59/23.76 (mult(mult(mult(mult(b, c), a), b), a) = mult(mult(mult(b, c), a), mult(b, a))),
% 23.59/23.76 inference(unit_resolution,[status(thm)],[3117, 11250])).
% 23.59/23.76 tff(11252,plain,
% 23.59/23.76 (mult(mult(b, c), mult(a, b)) = mult(mult(mult(b, c), a), b)),
% 23.59/23.76 inference(symmetry,[status(thm)],[10448])).
% 23.59/23.76 tff(11253,plain,
% 23.59/23.76 (mult(mult(mult(b, c), mult(a, b)), a) = mult(mult(mult(mult(b, c), a), b), a)),
% 23.59/23.76 inference(monotonicity,[status(thm)],[11252])).
% 23.59/23.76 tff(11254,plain,
% 23.59/23.76 (mult(mult(mult(mult(b, c), a), b), a) = mult(mult(mult(b, c), mult(a, b)), a)),
% 23.59/23.76 inference(symmetry,[status(thm)],[11253])).
% 23.59/23.76 tff(11255,plain,
% 23.59/23.76 (mult(mult(mult(b, c), a), mult(b, a)) = mult(mult(mult(mult(b, c), a), b), a)),
% 23.59/23.76 inference(symmetry,[status(thm)],[11251])).
% 23.59/23.76 tff(11256,plain,
% 23.59/23.76 (mult(mult(mult(b, c), a), mult(b, a)) = mult(mult(mult(b, c), mult(a, b)), a)),
% 23.59/23.76 inference(transitivity,[status(thm)],[11255, 11254])).
% 23.59/23.76 tff(11257,plain,
% 23.59/23.76 ((mult(mult(mult(b, c), a), mult(b, a)) = mult(mult(mult(b, c), a), mult(a, b))) <=> (mult(mult(mult(b, c), mult(a, b)), a) = mult(mult(mult(b, c), a), mult(a, b)))),
% 23.59/23.76 inference(monotonicity,[status(thm)],[11256])).
% 23.59/23.76 tff(11258,plain,
% 23.59/23.76 ((~(mult(mult(mult(b, c), a), mult(b, a)) = mult(mult(mult(b, c), a), mult(a, b)))) <=> (~(mult(mult(mult(b, c), mult(a, b)), a) = mult(mult(mult(b, c), a), mult(a, b))))),
% 23.59/23.76 inference(monotonicity,[status(thm)],[11257])).
% 23.59/23.76 tff(11259,plain,
% 23.59/23.76 (~(mult(mult(mult(b, c), mult(a, b)), a) = mult(mult(mult(b, c), a), mult(a, b)))),
% 23.59/23.76 inference(modus_ponens,[status(thm)],[11247, 11258])).
% 23.59/23.76 tff(11260,plain,
% 23.59/23.76 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(a, b))) = mult(a, b))),
% 23.59/23.76 inference(quant_inst,[status(thm)],[])).
% 23.59/23.76 tff(11261,plain,
% 23.59/23.76 (ld(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(a, b))) = mult(a, b)),
% 23.59/23.76 inference(unit_resolution,[status(thm)],[11260, 7])).
% 23.59/23.76 tff(11262,assumption,(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(a, b))), introduced(assumption)).
% 23.59/23.76 tff(11263,plain,
% 23.59/23.76 (ld(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(b, a))) = ld(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(a, b)))),
% 23.59/23.76 inference(monotonicity,[status(thm)],[11262])).
% 23.59/23.76 tff(11264,plain,
% 23.59/23.76 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(b, a))) = mult(b, a))),
% 23.59/23.76 inference(quant_inst,[status(thm)],[])).
% 23.59/23.76 tff(11265,plain,
% 23.59/23.76 (ld(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(b, a))) = mult(b, a)),
% 23.59/23.76 inference(unit_resolution,[status(thm)],[11264, 7])).
% 23.59/23.76 tff(11266,plain,
% 23.59/23.76 (mult(b, a) = ld(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(b, a)))),
% 23.59/23.76 inference(symmetry,[status(thm)],[11265])).
% 23.59/23.76 tff(11267,plain,
% 23.59/23.76 (mult(b, a) = mult(a, b)),
% 23.59/23.76 inference(transitivity,[status(thm)],[11266, 11263, 11261])).
% 23.59/23.76 tff(11268,plain,
% 23.59/23.76 (mult(mult(mult(b, c), a), mult(b, a)) = mult(mult(mult(b, c), a), mult(a, b))),
% 23.59/23.76 inference(monotonicity,[status(thm)],[11267])).
% 23.59/23.76 tff(11269,assumption,(mult(mult(mult(mult(b, c), a), b), a) = mult(mult(mult(b, c), a), mult(b, a))), introduced(assumption)).
% 23.59/23.76 tff(11270,plain,
% 23.59/23.76 (mult(mult(mult(b, c), mult(a, b)), a) = mult(mult(mult(b, c), a), mult(a, b))),
% 23.59/23.76 inference(transitivity,[status(thm)],[1313, 11269, 11268])).
% 23.59/23.76 tff(11271,assumption,(~(mult(mult(mult(b, c), mult(a, b)), a) = mult(mult(mult(b, c), a), mult(a, b)))), introduced(assumption)).
% 23.59/23.76 tff(11272,plain,
% 23.59/23.76 ($false),
% 23.59/23.76 inference(unit_resolution,[status(thm)],[11271, 11270])).
% 23.59/23.76 tff(11273,plain,((~(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(a, b)))) | (mult(mult(mult(b, c), mult(a, b)), a) = mult(mult(mult(b, c), a), mult(a, b))) | (~(mult(mult(mult(mult(b, c), a), b), a) = mult(mult(mult(b, c), a), mult(b, a)))) | (~(mult(mult(mult(b, c), a), b) = mult(mult(b, c), mult(a, b))))), inference(lemma,lemma(discharge,[]))).
% 23.59/23.76 tff(11274,plain,
% 23.59/23.76 (~(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(a, b)))),
% 23.59/23.76 inference(unit_resolution,[status(thm)],[11273, 11259, 11251, 10448])).
% 23.59/23.76 tff(11275,plain,
% 23.59/23.76 (((~(mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), b), a) = mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a), b))) | (~(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(a, b))))) | (mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(a, b)))),
% 23.59/23.76 inference(tautology,[status(thm)],[])).
% 23.59/23.76 tff(11276,plain,
% 23.59/23.76 ((~(mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), b), a) = mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a), b))) | (~(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(a, b))))),
% 23.59/23.76 inference(unit_resolution,[status(thm)],[11275, 11274])).
% 23.59/23.76 tff(11277,plain,
% 23.59/23.76 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), b), a) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(b, a)))) | (~(mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a), b) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(a, b)))))) | (~((~(mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), b), a) = mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a), b))) | (~(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(a, b)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), b), a) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(b, a)))) | (~(mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a), b) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(a, b)))))) | (~((~(mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), b), a) = mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a), b))) | (~(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(a, b)))))))),
% 23.59/23.76 inference(rewrite,[status(thm)],[])).
% 23.59/23.76 tff(11278,plain,
% 23.59/23.76 (((~((~(mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), b), a) = mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a), b))) | (~(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(a, b)))))) | (~((~(mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), b), a) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(b, a)))) | (~(mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a), b) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(a, b))))))) <=> ((~((~(mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), b), a) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(b, a)))) | (~(mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a), b) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(a, b)))))) | (~((~(mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), b), a) = mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a), b))) | (~(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(a, b)))))))),
% 23.59/23.76 inference(rewrite,[status(thm)],[])).
% 23.59/23.76 tff(11279,plain,
% 23.59/23.76 ((~((~(mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), b), a) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(b, a)))) | (~(mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a), b) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(a, b)))))) <=> (~((~(mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), b), a) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(b, a)))) | (~(mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a), b) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(a, b))))))),
% 23.59/23.76 inference(rewrite,[status(thm)],[])).
% 23.59/23.76 tff(11280,plain,
% 23.59/23.76 ((~((~(mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), b), a) = mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a), b))) | (~(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(a, b)))))) <=> (~((~(mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), b), a) = mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a), b))) | (~(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(a, b))))))),
% 23.59/23.76 inference(rewrite,[status(thm)],[])).
% 23.59/23.76 tff(11281,plain,
% 23.59/23.76 (((~((~(mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), b), a) = mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a), b))) | (~(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(a, b)))))) | (~((~(mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), b), a) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(b, a)))) | (~(mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a), b) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(a, b))))))) <=> ((~((~(mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), b), a) = mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a), b))) | (~(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(a, b)))))) | (~((~(mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), b), a) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(b, a)))) | (~(mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a), b) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(a, b)))))))),
% 23.59/23.76 inference(monotonicity,[status(thm)],[11280, 11279])).
% 23.59/23.76 tff(11282,plain,
% 23.59/23.76 (((~((~(mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), b), a) = mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a), b))) | (~(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(a, b)))))) | (~((~(mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), b), a) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(b, a)))) | (~(mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a), b) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(a, b))))))) <=> ((~((~(mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), b), a) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(b, a)))) | (~(mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a), b) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(a, b)))))) | (~((~(mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), b), a) = mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a), b))) | (~(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(a, b)))))))),
% 23.59/23.76 inference(transitivity,[status(thm)],[11281, 11278])).
% 23.59/23.76 tff(11283,plain,
% 23.59/23.76 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), b), a) = mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a), b))) | (~(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(a, b)))))) | (~((~(mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), b), a) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(b, a)))) | (~(mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a), b) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(a, b)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), b), a) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(b, a)))) | (~(mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a), b) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(a, b)))))) | (~((~(mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), b), a) = mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a), b))) | (~(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(a, b))))))))),
% 23.59/23.76 inference(monotonicity,[status(thm)],[11282])).
% 23.59/23.76 tff(11284,plain,
% 23.59/23.76 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), b), a) = mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a), b))) | (~(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(a, b)))))) | (~((~(mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), b), a) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(b, a)))) | (~(mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a), b) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(a, b)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), b), a) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(b, a)))) | (~(mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a), b) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(a, b)))))) | (~((~(mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), b), a) = mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a), b))) | (~(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(a, b)))))))),
% 23.59/23.77 inference(transitivity,[status(thm)],[11283, 11277])).
% 23.59/23.77 tff(11285,plain,
% 23.59/23.77 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), b), a) = mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a), b))) | (~(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(a, b)))))) | (~((~(mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), b), a) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(b, a)))) | (~(mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a), b) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(a, b)))))))),
% 23.59/23.77 inference(quant_inst,[status(thm)],[])).
% 23.59/23.77 tff(11286,plain,
% 23.59/23.77 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), b), a) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(b, a)))) | (~(mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a), b) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(a, b)))))) | (~((~(mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), b), a) = mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a), b))) | (~(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(a, b))))))),
% 23.59/23.77 inference(modus_ponens,[status(thm)],[11285, 11284])).
% 23.59/23.77 tff(11287,plain,
% 23.59/23.77 ((~((~(mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), b), a) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(b, a)))) | (~(mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a), b) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(a, b)))))) | (~((~(mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), b), a) = mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a), b))) | (~(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(a, b))))))),
% 23.59/23.77 inference(unit_resolution,[status(thm)],[11286, 27])).
% 23.59/23.77 tff(11288,plain,
% 23.59/23.77 (~((~(mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), b), a) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(b, a)))) | (~(mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a), b) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(a, b)))))),
% 23.59/23.77 inference(unit_resolution,[status(thm)],[11287, 11276])).
% 23.59/23.77 tff(11289,plain,
% 23.59/23.77 (((~(mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), b), a) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(b, a)))) | (~(mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a), b) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(a, b))))) | (mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a), b) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(a, b)))),
% 23.59/23.77 inference(tautology,[status(thm)],[])).
% 23.59/23.77 tff(11290,plain,
% 23.59/23.77 (mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a), b) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(a, b))),
% 23.59/23.77 inference(unit_resolution,[status(thm)],[11289, 11288])).
% 23.59/23.77 tff(11291,plain,
% 23.59/23.77 (mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(a, b)) = mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a), b)),
% 23.59/23.77 inference(symmetry,[status(thm)],[11290])).
% 23.59/23.77 tff(11292,plain,
% 23.59/23.77 (mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 23.59/23.77 inference(transitivity,[status(thm)],[11161, 11163])).
% 23.59/23.77 tff(11293,plain,
% 23.59/23.77 (mult(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c), mult(a, b)) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(a, b))),
% 23.59/23.77 inference(monotonicity,[status(thm)],[11292])).
% 23.59/23.77 tff(11294,plain,
% 23.59/23.77 (mult(b, mult(c, a)) = mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)),
% 23.59/23.77 inference(transitivity,[status(thm)],[10220, 5659, 11190, 4477, 11164, 11162])).
% 23.59/23.77 tff(11295,plain,
% 23.59/23.77 (mult(mult(b, mult(c, a)), mult(a, b)) = mult(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c), mult(a, b))),
% 23.59/23.77 inference(monotonicity,[status(thm)],[11294])).
% 23.59/23.77 tff(11296,plain,
% 23.59/23.77 (mult(mult(b, mult(c, a)), mult(a, b)) = mult(mult(mult(b, a), mult(a, c)), b)),
% 23.59/23.77 inference(transitivity,[status(thm)],[11295, 11293, 11291, 11222, 11219])).
% 23.59/23.77 tff(11297,plain,
% 23.59/23.77 (mult(c, mult(b, mult(a, b))) = mult(mult(c, b), mult(a, b))),
% 23.59/23.77 inference(symmetry,[status(thm)],[10449])).
% 23.59/23.77 tff(11298,plain,
% 23.59/23.77 (mult(c, mult(b, mult(a, b))) = mult(c, mult(mult(b, a), b))),
% 23.59/23.77 inference(transitivity,[status(thm)],[11297, 6496, 11252, 6517, 3429])).
% 23.59/23.77 tff(11299,plain,
% 23.59/23.77 (ld(c, mult(c, mult(b, mult(a, b)))) = ld(c, mult(c, mult(mult(b, a), b)))),
% 23.59/23.77 inference(monotonicity,[status(thm)],[11298])).
% 23.59/23.77 tff(11300,plain,
% 23.59/23.77 (mult(b, mult(a, b)) = mult(mult(b, a), b)),
% 23.59/23.77 inference(transitivity,[status(thm)],[6524, 11299, 6515])).
% 23.59/23.77 tff(11301,plain,
% 23.59/23.77 (mult(mult(b, mult(a, b)), mult(a, c)) = mult(mult(mult(b, a), b), mult(a, c))),
% 23.59/23.77 inference(monotonicity,[status(thm)],[11300])).
% 23.59/23.77 tff(11302,plain,
% 23.59/23.77 (mult(mult(b, mult(a, b)), mult(c, a)) = mult(mult(mult(b, a), b), mult(a, c))),
% 23.59/23.77 inference(transitivity,[status(thm)],[11095, 11301])).
% 23.59/23.77 tff(11303,plain,
% 23.59/23.77 ((mult(mult(b, mult(a, b)), mult(c, a)) = mult(mult(b, mult(c, a)), mult(a, b))) <=> (mult(mult(mult(b, a), b), mult(a, c)) = mult(mult(mult(b, a), mult(a, c)), b))),
% 23.59/23.77 inference(monotonicity,[status(thm)],[11302, 11296])).
% 23.59/23.77 tff(11304,plain,
% 23.59/23.77 ((mult(mult(mult(b, a), b), mult(a, c)) = mult(mult(mult(b, a), mult(a, c)), b)) <=> (mult(mult(b, mult(a, b)), mult(c, a)) = mult(mult(b, mult(c, a)), mult(a, b)))),
% 23.59/23.77 inference(symmetry,[status(thm)],[11303])).
% 23.59/23.77 tff(11305,plain,
% 23.59/23.77 ((mult(mult(mult(b, a), b), mult(a, c)) = mult(mult(mult(b, a), mult(a, c)), b)) <=> (mult(mult(b, mult(a, b)), mult(a, c)) = mult(mult(b, mult(a, c)), mult(a, b)))),
% 23.59/23.77 inference(transitivity,[status(thm)],[11304, 11098])).
% 23.59/23.77 tff(11306,plain,
% 23.59/23.77 ((~(mult(mult(mult(b, a), b), mult(a, c)) = mult(mult(mult(b, a), mult(a, c)), b))) <=> (~(mult(mult(b, mult(a, b)), mult(a, c)) = mult(mult(b, mult(a, c)), mult(a, b))))),
% 23.59/23.77 inference(monotonicity,[status(thm)],[11305])).
% 23.59/23.77 tff(11307,plain,
% 23.59/23.77 ((mult(mult(b, a), mult(b, mult(c, a))) = mult(mult(b, a), mult(mult(c, a), b))) <=> (mult(mult(b, a), mult(mult(c, a), b)) = mult(mult(b, a), mult(b, mult(c, a))))),
% 23.59/23.77 inference(commutativity,[status(thm)],[])).
% 23.59/23.77 tff(11308,plain,
% 23.59/23.77 (mult(mult(b, a), mult(mult(c, a), b)) = mult(mult(b, a), mult(c, mult(a, b)))),
% 23.59/23.77 inference(monotonicity,[status(thm)],[4221])).
% 23.59/23.77 tff(11309,plain,
% 23.59/23.77 (mult(mult(b, a), mult(c, mult(a, b))) = mult(mult(b, a), mult(mult(c, a), b))),
% 23.59/23.77 inference(symmetry,[status(thm)],[11308])).
% 23.59/23.77 tff(11310,plain,
% 23.59/23.77 (mult(mult(a, c), b) = mult(mult(c, a), b)),
% 23.59/23.77 inference(symmetry,[status(thm)],[10518])).
% 23.59/23.77 tff(11311,plain,
% 23.59/23.77 (mult(mult(a, b), c) = mult(c, mult(a, b))),
% 23.59/23.77 inference(transitivity,[status(thm)],[227, 11310, 4221])).
% 23.59/23.77 tff(11312,plain,
% 23.59/23.77 (mult(mult(b, a), mult(mult(a, b), c)) = mult(mult(b, a), mult(c, mult(a, b)))),
% 23.59/23.77 inference(monotonicity,[status(thm)],[11311])).
% 23.59/23.77 tff(11313,plain,
% 23.59/23.77 (mult(mult(b, a), mult(mult(a, c), b)) = mult(mult(b, a), mult(mult(a, b), c))),
% 23.59/23.77 inference(monotonicity,[status(thm)],[161])).
% 23.59/23.77 tff(11314,plain,
% 23.59/23.77 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(b, a), mult(mult(b, a), mult(mult(a, b), c))) = mult(mult(a, b), c))),
% 23.59/23.77 inference(quant_inst,[status(thm)],[])).
% 23.59/23.77 tff(11315,plain,
% 23.59/23.77 (ld(mult(b, a), mult(mult(b, a), mult(mult(a, b), c))) = mult(mult(a, b), c)),
% 23.59/23.77 inference(unit_resolution,[status(thm)],[11314, 7])).
% 23.59/23.77 tff(11316,assumption,(mult(mult(b, a), mult(b, mult(a, c))) = mult(mult(b, a), mult(mult(a, c), b))), introduced(assumption)).
% 23.59/23.77 tff(11317,plain,
% 23.59/23.77 (mult(mult(b, a), mult(b, mult(a, c))) = mult(mult(b, a), mult(mult(a, b), c))),
% 23.59/23.77 inference(transitivity,[status(thm)],[11316, 11313])).
% 23.59/23.77 tff(11318,plain,
% 23.59/23.77 (ld(mult(b, a), mult(mult(b, a), mult(b, mult(a, c)))) = ld(mult(b, a), mult(mult(b, a), mult(mult(a, b), c)))),
% 23.59/23.77 inference(monotonicity,[status(thm)],[11317])).
% 23.59/23.77 tff(11319,plain,
% 23.59/23.77 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(b, a), mult(mult(b, a), mult(b, mult(a, c)))) = mult(b, mult(a, c)))),
% 23.59/23.77 inference(quant_inst,[status(thm)],[])).
% 23.59/23.77 tff(11320,plain,
% 23.59/23.77 (ld(mult(b, a), mult(mult(b, a), mult(b, mult(a, c)))) = mult(b, mult(a, c))),
% 23.59/23.77 inference(unit_resolution,[status(thm)],[11319, 7])).
% 23.59/23.77 tff(11321,plain,
% 23.59/23.77 (mult(b, mult(a, c)) = ld(mult(b, a), mult(mult(b, a), mult(b, mult(a, c))))),
% 23.59/23.77 inference(symmetry,[status(thm)],[11320])).
% 23.59/23.77 tff(11322,plain,
% 23.59/23.77 (mult(b, mult(a, c)) = mult(mult(a, c), b)),
% 23.59/23.77 inference(transitivity,[status(thm)],[11321, 11318, 11315, 227])).
% 23.59/23.77 tff(11323,plain,
% 23.59/23.77 (mult(rd(mult(b, c), mult(a, c)), mult(b, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), b))),
% 23.59/23.77 inference(monotonicity,[status(thm)],[11322])).
% 23.59/23.77 tff(11324,plain,
% 23.59/23.77 ($false),
% 23.59/23.77 inference(unit_resolution,[status(thm)],[11064, 11323])).
% 23.59/23.77 tff(11325,plain,((~(mult(mult(b, a), mult(b, mult(a, c))) = mult(mult(b, a), mult(mult(a, c), b)))) | (mult(rd(mult(b, c), mult(a, c)), mult(b, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), b)))), inference(lemma,lemma(discharge,[]))).
% 23.59/23.77 tff(11326,plain,
% 23.59/23.77 (~(mult(mult(b, a), mult(b, mult(a, c))) = mult(mult(b, a), mult(mult(a, c), b)))),
% 23.59/23.77 inference(unit_resolution,[status(thm)],[11325, 10999])).
% 23.59/23.77 tff(11327,plain,
% 23.59/23.77 (((~(mult(mult(mult(b, a), b), mult(a, c)) = mult(mult(mult(b, a), mult(a, c)), b))) | (~(mult(mult(b, a), mult(b, mult(a, c))) = mult(mult(b, a), mult(mult(a, c), b))))) | (mult(mult(b, a), mult(b, mult(a, c))) = mult(mult(b, a), mult(mult(a, c), b)))),
% 23.59/23.77 inference(tautology,[status(thm)],[])).
% 23.59/23.77 tff(11328,plain,
% 23.59/23.77 ((~(mult(mult(mult(b, a), b), mult(a, c)) = mult(mult(mult(b, a), mult(a, c)), b))) | (~(mult(mult(b, a), mult(b, mult(a, c))) = mult(mult(b, a), mult(mult(a, c), b))))),
% 23.59/23.77 inference(unit_resolution,[status(thm)],[11327, 11326])).
% 23.59/23.77 tff(11329,plain,
% 23.59/23.77 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(b, a), b), mult(a, c)) = mult(mult(mult(b, a), mult(a, c)), b))) | (~(mult(mult(b, a), mult(b, mult(a, c))) = mult(mult(b, a), mult(mult(a, c), b)))))) | (~((~(mult(mult(mult(b, a), b), mult(a, c)) = mult(mult(b, a), mult(b, mult(a, c))))) | (~(mult(mult(mult(b, a), mult(a, c)), b) = mult(mult(b, a), mult(mult(a, c), b)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(b, a), b), mult(a, c)) = mult(mult(mult(b, a), mult(a, c)), b))) | (~(mult(mult(b, a), mult(b, mult(a, c))) = mult(mult(b, a), mult(mult(a, c), b)))))) | (~((~(mult(mult(mult(b, a), b), mult(a, c)) = mult(mult(b, a), mult(b, mult(a, c))))) | (~(mult(mult(mult(b, a), mult(a, c)), b) = mult(mult(b, a), mult(mult(a, c), b)))))))),
% 23.59/23.77 inference(rewrite,[status(thm)],[])).
% 23.59/23.77 tff(11330,plain,
% 23.59/23.77 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(b, a), b), mult(a, c)) = mult(mult(mult(b, a), mult(a, c)), b))) | (~(mult(mult(b, a), mult(b, mult(a, c))) = mult(mult(b, a), mult(mult(a, c), b)))))) | (~((~(mult(mult(mult(b, a), b), mult(a, c)) = mult(mult(b, a), mult(b, mult(a, c))))) | (~(mult(mult(mult(b, a), mult(a, c)), b) = mult(mult(b, a), mult(mult(a, c), b)))))))),
% 23.59/23.77 inference(quant_inst,[status(thm)],[])).
% 23.59/23.77 tff(11331,plain,
% 23.59/23.77 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(b, a), b), mult(a, c)) = mult(mult(mult(b, a), mult(a, c)), b))) | (~(mult(mult(b, a), mult(b, mult(a, c))) = mult(mult(b, a), mult(mult(a, c), b)))))) | (~((~(mult(mult(mult(b, a), b), mult(a, c)) = mult(mult(b, a), mult(b, mult(a, c))))) | (~(mult(mult(mult(b, a), mult(a, c)), b) = mult(mult(b, a), mult(mult(a, c), b))))))),
% 23.59/23.77 inference(modus_ponens,[status(thm)],[11330, 11329])).
% 23.59/23.77 tff(11332,plain,
% 23.59/23.77 ((~((~(mult(mult(mult(b, a), b), mult(a, c)) = mult(mult(mult(b, a), mult(a, c)), b))) | (~(mult(mult(b, a), mult(b, mult(a, c))) = mult(mult(b, a), mult(mult(a, c), b)))))) | (~((~(mult(mult(mult(b, a), b), mult(a, c)) = mult(mult(b, a), mult(b, mult(a, c))))) | (~(mult(mult(mult(b, a), mult(a, c)), b) = mult(mult(b, a), mult(mult(a, c), b))))))),
% 23.59/23.77 inference(unit_resolution,[status(thm)],[11331, 27])).
% 23.59/23.77 tff(11333,plain,
% 23.59/23.77 (~((~(mult(mult(mult(b, a), b), mult(a, c)) = mult(mult(b, a), mult(b, mult(a, c))))) | (~(mult(mult(mult(b, a), mult(a, c)), b) = mult(mult(b, a), mult(mult(a, c), b)))))),
% 23.59/23.77 inference(unit_resolution,[status(thm)],[11332, 11328])).
% 23.59/23.77 tff(11334,plain,
% 23.59/23.77 (((~(mult(mult(mult(b, a), b), mult(a, c)) = mult(mult(b, a), mult(b, mult(a, c))))) | (~(mult(mult(mult(b, a), mult(a, c)), b) = mult(mult(b, a), mult(mult(a, c), b))))) | (mult(mult(mult(b, a), mult(a, c)), b) = mult(mult(b, a), mult(mult(a, c), b)))),
% 23.59/23.77 inference(tautology,[status(thm)],[])).
% 23.59/23.77 tff(11335,plain,
% 23.59/23.77 (mult(mult(mult(b, a), mult(a, c)), b) = mult(mult(b, a), mult(mult(a, c), b))),
% 23.59/23.77 inference(unit_resolution,[status(thm)],[11334, 11333])).
% 23.59/23.77 tff(11336,plain,
% 23.59/23.77 (mult(mult(mult(b, a), mult(a, c)), b) = mult(mult(b, a), mult(mult(c, a), b))),
% 23.59/23.77 inference(transitivity,[status(thm)],[11335, 11313, 11312, 11309])).
% 23.59/23.77 tff(11337,plain,
% 23.59/23.77 (mult(mult(b, a), mult(b, mult(c, a))) = mult(mult(b, a), mult(b, mult(a, c)))),
% 23.59/23.77 inference(monotonicity,[status(thm)],[10220])).
% 23.59/23.77 tff(11338,plain,
% 23.59/23.77 (mult(mult(b, a), mult(b, mult(a, c))) = mult(mult(b, a), mult(b, mult(c, a)))),
% 23.59/23.77 inference(symmetry,[status(thm)],[11337])).
% 23.59/23.77 tff(11339,plain,
% 23.59/23.77 (((~(mult(mult(mult(b, a), b), mult(a, c)) = mult(mult(b, a), mult(b, mult(a, c))))) | (~(mult(mult(mult(b, a), mult(a, c)), b) = mult(mult(b, a), mult(mult(a, c), b))))) | (mult(mult(mult(b, a), b), mult(a, c)) = mult(mult(b, a), mult(b, mult(a, c))))),
% 23.59/23.77 inference(tautology,[status(thm)],[])).
% 23.59/23.78 tff(11340,plain,
% 23.59/23.78 (mult(mult(mult(b, a), b), mult(a, c)) = mult(mult(b, a), mult(b, mult(a, c)))),
% 23.59/23.78 inference(unit_resolution,[status(thm)],[11339, 11333])).
% 23.59/23.78 tff(11341,plain,
% 23.59/23.78 (mult(mult(mult(b, a), b), mult(a, c)) = mult(mult(b, a), mult(b, mult(c, a)))),
% 23.59/23.78 inference(transitivity,[status(thm)],[11340, 11338])).
% 23.59/23.78 tff(11342,plain,
% 23.59/23.78 ((mult(mult(mult(b, a), b), mult(a, c)) = mult(mult(mult(b, a), mult(a, c)), b)) <=> (mult(mult(b, a), mult(b, mult(c, a))) = mult(mult(b, a), mult(mult(c, a), b)))),
% 23.59/23.78 inference(monotonicity,[status(thm)],[11341, 11336])).
% 23.59/23.78 tff(11343,plain,
% 23.59/23.78 ((mult(mult(mult(b, a), b), mult(a, c)) = mult(mult(mult(b, a), mult(a, c)), b)) <=> (mult(mult(b, a), mult(mult(c, a), b)) = mult(mult(b, a), mult(b, mult(c, a))))),
% 23.59/23.78 inference(transitivity,[status(thm)],[11342, 11307])).
% 23.59/23.78 tff(11344,plain,
% 23.59/23.78 ((mult(mult(b, a), mult(mult(c, a), b)) = mult(mult(b, a), mult(b, mult(c, a)))) <=> (mult(mult(mult(b, a), b), mult(a, c)) = mult(mult(mult(b, a), mult(a, c)), b))),
% 23.59/23.78 inference(symmetry,[status(thm)],[11343])).
% 23.59/23.78 tff(11345,plain,
% 23.59/23.78 ((~(mult(mult(b, a), mult(mult(c, a), b)) = mult(mult(b, a), mult(b, mult(c, a))))) <=> (~(mult(mult(mult(b, a), b), mult(a, c)) = mult(mult(mult(b, a), mult(a, c)), b)))),
% 23.59/23.78 inference(monotonicity,[status(thm)],[11344])).
% 23.59/23.78 tff(11346,plain,
% 23.59/23.78 (mult(mult(b, a), mult(mult(a, c), b)) = mult(mult(b, a), mult(mult(c, a), b))),
% 23.59/23.78 inference(transitivity,[status(thm)],[11313, 11312, 11309])).
% 23.59/23.78 tff(11347,plain,
% 23.59/23.78 ((mult(mult(b, a), mult(b, mult(a, c))) = mult(mult(b, a), mult(mult(a, c), b))) <=> (mult(mult(b, a), mult(b, mult(c, a))) = mult(mult(b, a), mult(mult(c, a), b)))),
% 23.59/23.78 inference(monotonicity,[status(thm)],[11338, 11346])).
% 23.59/23.78 tff(11348,plain,
% 23.59/23.78 ((mult(mult(b, a), mult(b, mult(a, c))) = mult(mult(b, a), mult(mult(a, c), b))) <=> (mult(mult(b, a), mult(mult(c, a), b)) = mult(mult(b, a), mult(b, mult(c, a))))),
% 23.59/23.78 inference(transitivity,[status(thm)],[11347, 11307])).
% 23.59/23.78 tff(11349,plain,
% 23.59/23.78 ((~(mult(mult(b, a), mult(b, mult(a, c))) = mult(mult(b, a), mult(mult(a, c), b)))) <=> (~(mult(mult(b, a), mult(mult(c, a), b)) = mult(mult(b, a), mult(b, mult(c, a)))))),
% 23.59/23.78 inference(monotonicity,[status(thm)],[11348])).
% 23.59/23.78 tff(11350,plain,
% 23.59/23.78 (~(mult(mult(b, a), mult(mult(c, a), b)) = mult(mult(b, a), mult(b, mult(c, a))))),
% 23.59/23.78 inference(modus_ponens,[status(thm)],[11326, 11349])).
% 23.59/23.78 tff(11351,plain,
% 23.59/23.78 (~(mult(mult(mult(b, a), b), mult(a, c)) = mult(mult(mult(b, a), mult(a, c)), b))),
% 23.59/23.78 inference(modus_ponens,[status(thm)],[11350, 11345])).
% 23.59/23.78 tff(11352,plain,
% 23.59/23.78 (~(mult(mult(b, mult(a, b)), mult(a, c)) = mult(mult(b, mult(a, c)), mult(a, b)))),
% 23.59/23.78 inference(modus_ponens,[status(thm)],[11351, 11306])).
% 23.59/23.78 tff(11353,plain,
% 23.59/23.78 (((~(mult(mult(b, mult(a, b)), mult(a, c)) = mult(mult(b, mult(a, c)), mult(a, b)))) | (~(mult(b, mult(mult(a, b), mult(a, c))) = mult(b, mult(mult(a, c), mult(a, b)))))) | (mult(mult(b, mult(a, b)), mult(a, c)) = mult(mult(b, mult(a, c)), mult(a, b)))),
% 23.59/23.78 inference(tautology,[status(thm)],[])).
% 23.59/23.78 tff(11354,plain,
% 23.59/23.78 ((~(mult(mult(b, mult(a, b)), mult(a, c)) = mult(mult(b, mult(a, c)), mult(a, b)))) | (~(mult(b, mult(mult(a, b), mult(a, c))) = mult(b, mult(mult(a, c), mult(a, b)))))),
% 23.59/23.78 inference(unit_resolution,[status(thm)],[11353, 11352])).
% 23.59/23.78 tff(11355,plain,
% 23.59/23.78 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(b, mult(a, b)), mult(a, c)) = mult(mult(b, mult(a, c)), mult(a, b)))) | (~(mult(b, mult(mult(a, b), mult(a, c))) = mult(b, mult(mult(a, c), mult(a, b))))))) | (~((~(mult(mult(b, mult(a, b)), mult(a, c)) = mult(b, mult(mult(a, b), mult(a, c))))) | (~(mult(mult(b, mult(a, c)), mult(a, b)) = mult(b, mult(mult(a, c), mult(a, b))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(b, mult(a, b)), mult(a, c)) = mult(mult(b, mult(a, c)), mult(a, b)))) | (~(mult(b, mult(mult(a, b), mult(a, c))) = mult(b, mult(mult(a, c), mult(a, b))))))) | (~((~(mult(mult(b, mult(a, b)), mult(a, c)) = mult(b, mult(mult(a, b), mult(a, c))))) | (~(mult(mult(b, mult(a, c)), mult(a, b)) = mult(b, mult(mult(a, c), mult(a, b))))))))),
% 23.59/23.78 inference(rewrite,[status(thm)],[])).
% 23.59/23.78 tff(11356,plain,
% 23.59/23.78 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(b, mult(a, b)), mult(a, c)) = mult(mult(b, mult(a, c)), mult(a, b)))) | (~(mult(b, mult(mult(a, b), mult(a, c))) = mult(b, mult(mult(a, c), mult(a, b))))))) | (~((~(mult(mult(b, mult(a, b)), mult(a, c)) = mult(b, mult(mult(a, b), mult(a, c))))) | (~(mult(mult(b, mult(a, c)), mult(a, b)) = mult(b, mult(mult(a, c), mult(a, b))))))))),
% 23.59/23.78 inference(quant_inst,[status(thm)],[])).
% 23.59/23.78 tff(11357,plain,
% 23.59/23.78 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(b, mult(a, b)), mult(a, c)) = mult(mult(b, mult(a, c)), mult(a, b)))) | (~(mult(b, mult(mult(a, b), mult(a, c))) = mult(b, mult(mult(a, c), mult(a, b))))))) | (~((~(mult(mult(b, mult(a, b)), mult(a, c)) = mult(b, mult(mult(a, b), mult(a, c))))) | (~(mult(mult(b, mult(a, c)), mult(a, b)) = mult(b, mult(mult(a, c), mult(a, b)))))))),
% 23.59/23.78 inference(modus_ponens,[status(thm)],[11356, 11355])).
% 23.59/23.78 tff(11358,plain,
% 23.59/23.78 ((~((~(mult(mult(b, mult(a, b)), mult(a, c)) = mult(mult(b, mult(a, c)), mult(a, b)))) | (~(mult(b, mult(mult(a, b), mult(a, c))) = mult(b, mult(mult(a, c), mult(a, b))))))) | (~((~(mult(mult(b, mult(a, b)), mult(a, c)) = mult(b, mult(mult(a, b), mult(a, c))))) | (~(mult(mult(b, mult(a, c)), mult(a, b)) = mult(b, mult(mult(a, c), mult(a, b)))))))),
% 23.59/23.78 inference(unit_resolution,[status(thm)],[11357, 27])).
% 23.59/23.78 tff(11359,plain,
% 23.59/23.78 (~((~(mult(mult(b, mult(a, b)), mult(a, c)) = mult(b, mult(mult(a, b), mult(a, c))))) | (~(mult(mult(b, mult(a, c)), mult(a, b)) = mult(b, mult(mult(a, c), mult(a, b))))))),
% 23.59/23.78 inference(unit_resolution,[status(thm)],[11358, 11354])).
% 23.59/23.78 tff(11360,plain,
% 23.59/23.78 (((~(mult(mult(b, mult(a, b)), mult(a, c)) = mult(b, mult(mult(a, b), mult(a, c))))) | (~(mult(mult(b, mult(a, c)), mult(a, b)) = mult(b, mult(mult(a, c), mult(a, b)))))) | (mult(mult(b, mult(a, c)), mult(a, b)) = mult(b, mult(mult(a, c), mult(a, b))))),
% 23.59/23.78 inference(tautology,[status(thm)],[])).
% 23.59/23.78 tff(11361,plain,
% 23.59/23.78 (mult(mult(b, mult(a, c)), mult(a, b)) = mult(b, mult(mult(a, c), mult(a, b)))),
% 23.59/23.78 inference(unit_resolution,[status(thm)],[11360, 11359])).
% 23.59/23.78 tff(11362,plain,
% 23.59/23.78 (mult(mult(b, mult(c, a)), mult(a, b)) = mult(mult(b, mult(a, c)), mult(a, b))),
% 23.59/23.78 inference(symmetry,[status(thm)],[11094])).
% 23.59/23.78 tff(11363,plain,
% 23.59/23.78 (mult(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c), mult(a, b)) = mult(mult(b, mult(c, a)), mult(a, b))),
% 23.59/23.78 inference(symmetry,[status(thm)],[11295])).
% 23.59/23.78 tff(11364,plain,
% 23.59/23.78 (mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(a, b)) = mult(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c), mult(a, b))),
% 23.59/23.78 inference(symmetry,[status(thm)],[11293])).
% 23.59/23.78 tff(11365,plain,
% 23.59/23.78 (mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), b) = mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a), b)),
% 23.59/23.78 inference(symmetry,[status(thm)],[11222])).
% 23.59/23.78 tff(11366,plain,
% 23.59/23.78 (mult(mult(mult(b, a), mult(a, c)), b) = mult(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), a), b)),
% 23.59/23.78 inference(symmetry,[status(thm)],[11219])).
% 23.59/23.78 tff(11367,plain,
% 23.59/23.78 (mult(mult(b, a), mult(mult(a, c), b)) = mult(mult(mult(b, a), mult(a, c)), b)),
% 23.59/23.78 inference(symmetry,[status(thm)],[11335])).
% 23.59/23.78 tff(11368,plain,
% 23.59/23.78 (mult(mult(b, a), mult(mult(a, b), c)) = mult(mult(b, a), mult(mult(a, c), b))),
% 23.59/23.78 inference(symmetry,[status(thm)],[11313])).
% 23.59/23.78 tff(11369,plain,
% 23.59/23.78 ((mult(mult(b, mult(mult(a, b), c)), a) = mult(mult(b, a), mult(mult(a, b), c))) <=> (mult(mult(b, a), mult(mult(a, b), c)) = mult(mult(b, mult(mult(a, b), c)), a))),
% 23.59/23.78 inference(commutativity,[status(thm)],[])).
% 23.59/23.78 tff(11370,plain,
% 23.59/23.78 (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)),
% 23.59/23.78 inference(transitivity,[status(thm)],[8170, 8169, 281, 11164, 11162])).
% 23.59/23.78 tff(11371,plain,
% 23.59/23.78 (mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c), mult(a, b))),
% 23.59/23.78 inference(monotonicity,[status(thm)],[11370, 213])).
% 23.59/23.78 tff(11372,plain,
% 23.59/23.78 (mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), mult(a, b)) = mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)))),
% 23.59/23.78 inference(monotonicity,[status(thm)],[2899])).
% 23.59/23.78 tff(11373,plain,
% 23.59/23.78 (mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), mult(a, b)) = mult(mult(b, a), mult(mult(a, b), c))),
% 23.59/23.78 inference(transitivity,[status(thm)],[11372, 11371, 11293, 11291, 11222, 11219, 11335, 11313])).
% 23.59/23.78 tff(11374,plain,
% 23.59/23.78 (mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), b) = mult(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c), b)),
% 23.59/23.78 inference(monotonicity,[status(thm)],[11165])).
% 23.59/23.78 tff(11375,plain,
% 23.59/23.78 (mult(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c), b) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), b)),
% 23.59/23.78 inference(symmetry,[status(thm)],[11374])).
% 23.59/23.78 tff(11376,plain,
% 23.59/23.78 (ld(c, mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) = ld(c, mult(c, mult(b, mult(a, c))))),
% 23.59/23.78 inference(symmetry,[status(thm)],[11190])).
% 23.59/23.78 tff(11377,plain,
% 23.59/23.78 (mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(b, mult(a, c))),
% 23.59/23.78 inference(transitivity,[status(thm)],[11161, 11163, 4478, 11376, 5658])).
% 23.59/23.78 tff(11378,plain,
% 23.59/23.78 (mult(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c), b) = mult(mult(b, mult(a, c)), b)),
% 23.59/23.78 inference(monotonicity,[status(thm)],[11377])).
% 23.59/23.78 tff(11379,plain,
% 23.59/23.78 (mult(mult(b, mult(a, c)), b) = mult(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c), b)),
% 23.59/23.78 inference(symmetry,[status(thm)],[11378])).
% 23.59/23.78 tff(11380,plain,
% 23.59/23.78 (mult(b, mult(mult(a, c), b)) = mult(mult(b, mult(a, c)), b)),
% 23.59/23.78 inference(symmetry,[status(thm)],[10584])).
% 23.59/23.78 tff(11381,plain,
% 23.59/23.78 (mult(mult(unit, b), mult(mult(a, b), c)) = mult(b, mult(mult(a, c), b))),
% 23.59/23.78 inference(symmetry,[status(thm)],[5603])).
% 23.59/23.78 tff(11382,plain,
% 23.59/23.78 (mult(b, mult(mult(a, b), c)) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), b)),
% 23.59/23.78 inference(transitivity,[status(thm)],[3387, 11381, 11380, 11379, 11375])).
% 23.59/23.78 tff(11383,plain,
% 23.59/23.78 (mult(mult(b, mult(mult(a, b), c)), a) = mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), b), a)),
% 23.59/23.78 inference(monotonicity,[status(thm)],[11382])).
% 23.59/23.78 tff(11384,plain,
% 23.59/23.78 (mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), b), a) = mult(mult(b, mult(mult(a, b), c)), a)),
% 23.59/23.78 inference(symmetry,[status(thm)],[11383])).
% 23.59/23.78 tff(11385,plain,
% 23.59/23.78 (((~(mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), b), a) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(b, a)))) | (~(mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a), b) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(a, b))))) | (mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), b), a) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(b, a)))),
% 23.59/23.78 inference(tautology,[status(thm)],[])).
% 23.59/23.78 tff(11386,plain,
% 23.59/23.78 (mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), b), a) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(b, a))),
% 23.59/23.78 inference(unit_resolution,[status(thm)],[11385, 11288])).
% 23.59/23.78 tff(11387,plain,
% 23.59/23.78 (mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), b), a)),
% 23.59/23.78 inference(symmetry,[status(thm)],[11386])).
% 23.59/23.78 tff(11388,plain,
% 23.59/23.78 (mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c), mult(b, a))),
% 23.59/23.78 inference(monotonicity,[status(thm)],[11165])).
% 23.59/23.78 tff(11389,plain,
% 23.59/23.78 (mult(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c), mult(b, a)) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(b, a))),
% 23.59/23.78 inference(symmetry,[status(thm)],[11388])).
% 23.59/23.78 tff(11390,plain,
% 23.59/23.78 (mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c), mult(b, a))),
% 23.59/23.78 inference(monotonicity,[status(thm)],[11370])).
% 23.59/23.78 tff(11391,plain,
% 23.59/23.78 (mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(b, mult(mult(a, b), c)), a)),
% 23.59/23.78 inference(transitivity,[status(thm)],[11390, 11389, 11387, 11384])).
% 23.59/23.78 tff(11392,plain,
% 23.59/23.78 ((mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), mult(a, b))) <=> (mult(mult(b, mult(mult(a, b), c)), a) = mult(mult(b, a), mult(mult(a, b), c)))),
% 23.59/23.78 inference(monotonicity,[status(thm)],[11391, 11373])).
% 23.59/23.78 tff(11393,plain,
% 23.59/23.78 ((mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), mult(a, b))) <=> (mult(mult(b, a), mult(mult(a, b), c)) = mult(mult(b, mult(mult(a, b), c)), a))),
% 23.59/23.78 inference(transitivity,[status(thm)],[11392, 11369])).
% 23.59/23.78 tff(11394,plain,
% 23.59/23.78 ((~(mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), mult(a, b)))) <=> (~(mult(mult(b, a), mult(mult(a, b), c)) = mult(mult(b, mult(mult(a, b), c)), a)))),
% 23.59/23.78 inference(monotonicity,[status(thm)],[11393])).
% 23.59/23.78 tff(11395,plain,
% 23.59/23.78 (mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), mult(a, b))),
% 23.59/23.78 inference(symmetry,[status(thm)],[11372])).
% 23.59/23.78 tff(11396,plain,
% 23.59/23.78 (mult(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c), mult(a, b)) = mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)))),
% 23.59/23.78 inference(symmetry,[status(thm)],[11371])).
% 23.59/23.78 tff(11397,plain,
% 23.59/23.78 (mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(a, b)) = mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), mult(a, b))),
% 23.59/23.78 inference(transitivity,[status(thm)],[11364, 11396, 11395])).
% 23.59/23.78 tff(11398,plain,
% 23.59/23.78 (mult(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c), mult(b, a)) = mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), mult(b, a))),
% 23.59/23.78 inference(symmetry,[status(thm)],[11390])).
% 23.59/23.78 tff(11399,plain,
% 23.59/23.78 (mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), mult(b, a))),
% 23.59/23.78 inference(transitivity,[status(thm)],[11388, 11398])).
% 23.59/23.78 tff(11400,plain,
% 23.59/23.78 ((mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(a, b))) <=> (mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), mult(a, b)))),
% 23.59/23.78 inference(monotonicity,[status(thm)],[11399, 11397])).
% 23.59/23.78 tff(11401,plain,
% 23.59/23.78 ((~(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(a, b)))) <=> (~(mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), mult(a, b))))),
% 23.59/23.78 inference(monotonicity,[status(thm)],[11400])).
% 23.59/23.78 tff(11402,plain,
% 23.59/23.78 (~(mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), mult(a, b)))),
% 23.59/23.79 inference(modus_ponens,[status(thm)],[11274, 11401])).
% 23.59/23.79 tff(11403,plain,
% 23.59/23.79 (~(mult(mult(b, a), mult(mult(a, b), c)) = mult(mult(b, mult(mult(a, b), c)), a))),
% 23.59/23.79 inference(modus_ponens,[status(thm)],[11402, 11394])).
% 23.59/23.79 tff(11404,plain,
% 23.59/23.79 (((~(mult(mult(b, a), mult(mult(a, b), c)) = mult(mult(b, mult(mult(a, b), c)), a))) | (~(mult(b, mult(a, mult(mult(a, b), c))) = mult(b, mult(mult(mult(a, b), c), a))))) | (mult(mult(b, a), mult(mult(a, b), c)) = mult(mult(b, mult(mult(a, b), c)), a))),
% 23.59/23.79 inference(tautology,[status(thm)],[])).
% 23.59/23.79 tff(11405,plain,
% 23.59/23.79 ((~(mult(mult(b, a), mult(mult(a, b), c)) = mult(mult(b, mult(mult(a, b), c)), a))) | (~(mult(b, mult(a, mult(mult(a, b), c))) = mult(b, mult(mult(mult(a, b), c), a))))),
% 23.59/23.79 inference(unit_resolution,[status(thm)],[11404, 11403])).
% 23.59/23.79 tff(11406,plain,
% 23.59/23.79 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(b, a), mult(mult(a, b), c)) = mult(mult(b, mult(mult(a, b), c)), a))) | (~(mult(b, mult(a, mult(mult(a, b), c))) = mult(b, mult(mult(mult(a, b), c), a)))))) | (~((~(mult(mult(b, a), mult(mult(a, b), c)) = mult(b, mult(a, mult(mult(a, b), c))))) | (~(mult(mult(b, mult(mult(a, b), c)), a) = mult(b, mult(mult(mult(a, b), c), a)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(b, a), mult(mult(a, b), c)) = mult(mult(b, mult(mult(a, b), c)), a))) | (~(mult(b, mult(a, mult(mult(a, b), c))) = mult(b, mult(mult(mult(a, b), c), a)))))) | (~((~(mult(mult(b, a), mult(mult(a, b), c)) = mult(b, mult(a, mult(mult(a, b), c))))) | (~(mult(mult(b, mult(mult(a, b), c)), a) = mult(b, mult(mult(mult(a, b), c), a)))))))),
% 23.59/23.79 inference(rewrite,[status(thm)],[])).
% 23.59/23.79 tff(11407,plain,
% 23.59/23.79 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(b, a), mult(mult(a, b), c)) = mult(mult(b, mult(mult(a, b), c)), a))) | (~(mult(b, mult(a, mult(mult(a, b), c))) = mult(b, mult(mult(mult(a, b), c), a)))))) | (~((~(mult(mult(b, a), mult(mult(a, b), c)) = mult(b, mult(a, mult(mult(a, b), c))))) | (~(mult(mult(b, mult(mult(a, b), c)), a) = mult(b, mult(mult(mult(a, b), c), a)))))))),
% 23.59/23.79 inference(quant_inst,[status(thm)],[])).
% 23.59/23.79 tff(11408,plain,
% 23.59/23.79 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(b, a), mult(mult(a, b), c)) = mult(mult(b, mult(mult(a, b), c)), a))) | (~(mult(b, mult(a, mult(mult(a, b), c))) = mult(b, mult(mult(mult(a, b), c), a)))))) | (~((~(mult(mult(b, a), mult(mult(a, b), c)) = mult(b, mult(a, mult(mult(a, b), c))))) | (~(mult(mult(b, mult(mult(a, b), c)), a) = mult(b, mult(mult(mult(a, b), c), a))))))),
% 23.59/23.79 inference(modus_ponens,[status(thm)],[11407, 11406])).
% 23.59/23.79 tff(11409,plain,
% 23.59/23.79 ((~((~(mult(mult(b, a), mult(mult(a, b), c)) = mult(mult(b, mult(mult(a, b), c)), a))) | (~(mult(b, mult(a, mult(mult(a, b), c))) = mult(b, mult(mult(mult(a, b), c), a)))))) | (~((~(mult(mult(b, a), mult(mult(a, b), c)) = mult(b, mult(a, mult(mult(a, b), c))))) | (~(mult(mult(b, mult(mult(a, b), c)), a) = mult(b, mult(mult(mult(a, b), c), a))))))),
% 23.59/23.79 inference(unit_resolution,[status(thm)],[11408, 27])).
% 23.59/23.79 tff(11410,plain,
% 23.59/23.79 (~((~(mult(mult(b, a), mult(mult(a, b), c)) = mult(b, mult(a, mult(mult(a, b), c))))) | (~(mult(mult(b, mult(mult(a, b), c)), a) = mult(b, mult(mult(mult(a, b), c), a)))))),
% 23.59/23.79 inference(unit_resolution,[status(thm)],[11409, 11405])).
% 23.59/23.79 tff(11411,plain,
% 23.59/23.79 (((~(mult(mult(b, a), mult(mult(a, b), c)) = mult(b, mult(a, mult(mult(a, b), c))))) | (~(mult(mult(b, mult(mult(a, b), c)), a) = mult(b, mult(mult(mult(a, b), c), a))))) | (mult(mult(b, a), mult(mult(a, b), c)) = mult(b, mult(a, mult(mult(a, b), c))))),
% 23.59/23.79 inference(tautology,[status(thm)],[])).
% 23.59/23.79 tff(11412,plain,
% 23.59/23.79 (mult(mult(b, a), mult(mult(a, b), c)) = mult(b, mult(a, mult(mult(a, b), c)))),
% 23.59/23.79 inference(unit_resolution,[status(thm)],[11411, 11410])).
% 23.59/23.79 tff(11413,plain,
% 23.59/23.79 (mult(b, mult(a, mult(mult(a, b), c))) = mult(mult(b, a), mult(mult(a, b), c))),
% 23.59/23.79 inference(symmetry,[status(thm)],[11412])).
% 23.59/23.79 tff(11414,plain,
% 23.59/23.79 (mult(b, mult(a, mult(mult(a, b), c))) = mult(b, mult(mult(a, c), mult(a, b)))),
% 23.59/23.79 inference(transitivity,[status(thm)],[11413, 11368, 11367, 11366, 11365, 11290, 11364, 11363, 11362, 11361])).
% 23.59/23.79 tff(11415,plain,
% 23.59/23.79 (ld(b, mult(b, mult(a, mult(mult(a, b), c)))) = ld(b, mult(b, mult(mult(a, c), mult(a, b))))),
% 23.59/23.79 inference(monotonicity,[status(thm)],[11414])).
% 23.59/23.79 tff(11416,plain,
% 23.59/23.79 (ld(b, mult(b, mult(mult(a, c), mult(a, b)))) = ld(b, mult(b, mult(a, mult(mult(a, b), c))))),
% 23.59/23.79 inference(symmetry,[status(thm)],[11415])).
% 23.59/23.79 tff(11417,plain,
% 23.59/23.79 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(b, mult(b, mult(mult(a, c), mult(a, b)))) = mult(mult(a, c), mult(a, b)))),
% 23.59/23.79 inference(quant_inst,[status(thm)],[])).
% 23.59/23.79 tff(11418,plain,
% 23.59/23.79 (ld(b, mult(b, mult(mult(a, c), mult(a, b)))) = mult(mult(a, c), mult(a, b))),
% 23.59/23.79 inference(unit_resolution,[status(thm)],[11417, 7])).
% 23.59/23.79 tff(11419,plain,
% 23.59/23.79 (mult(mult(a, c), mult(a, b)) = ld(b, mult(b, mult(mult(a, c), mult(a, b))))),
% 23.59/23.79 inference(symmetry,[status(thm)],[11418])).
% 23.59/23.79 tff(11420,plain,
% 23.59/23.79 (mult(mult(a, c), mult(a, b)) = mult(a, mult(c, mult(c, ld(c, mult(a, b)))))),
% 23.59/23.79 inference(transitivity,[status(thm)],[11419, 11416, 11093, 11091])).
% 23.59/23.79 tff(11421,plain,
% 23.59/23.79 (mult(mult(mult(a, c), mult(a, b)), rd(mult(b, c), mult(a, c))) = mult(mult(a, mult(c, mult(c, ld(c, mult(a, b))))), rd(mult(b, c), mult(a, c)))),
% 23.59/23.79 inference(monotonicity,[status(thm)],[11420])).
% 23.59/23.79 tff(11422,plain,
% 23.59/23.79 (mult(mult(c, a), mult(a, b)) = mult(mult(a, c), mult(a, b))),
% 23.59/23.79 inference(monotonicity,[status(thm)],[8215])).
% 23.59/23.79 tff(11423,plain,
% 23.59/23.79 (mult(b, mult(mult(c, a), mult(a, b))) = mult(b, mult(mult(a, c), mult(a, b)))),
% 23.59/23.79 inference(monotonicity,[status(thm)],[11422])).
% 23.59/23.79 tff(11424,plain,
% 23.59/23.79 (mult(mult(a, c), mult(a, b)) = mult(mult(c, a), mult(a, b))),
% 23.59/23.79 inference(symmetry,[status(thm)],[11422])).
% 23.59/23.79 tff(11425,plain,
% 23.59/23.79 (mult(mult(mult(a, c), a), mult(mult(b, unit), b)) = mult(mult(mult(a, c), a), mult(unit, mult(mult(b, unit), b)))),
% 23.59/23.79 inference(monotonicity,[status(thm)],[430])).
% 23.59/23.79 tff(11426,plain,
% 23.59/23.79 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(mult(a, c), a), b), unit), b) = mult(mult(mult(a, c), a), mult(mult(b, unit), b)))),
% 23.59/23.79 inference(quant_inst,[status(thm)],[])).
% 23.59/23.79 tff(11427,plain,
% 23.59/23.79 (mult(mult(mult(mult(mult(a, c), a), b), unit), b) = mult(mult(mult(a, c), a), mult(mult(b, unit), b))),
% 23.59/23.79 inference(unit_resolution,[status(thm)],[11426, 56])).
% 23.59/23.79 tff(11428,plain,
% 23.59/23.79 (mult(mult(mult(mult(mult(a, c), a), b), unit), b) = mult(mult(mult(a, c), mult(a, b)), b)),
% 23.59/23.79 inference(transitivity,[status(thm)],[11427, 11425, 10517, 1093, 10455])).
% 23.59/23.79 tff(11429,plain,
% 23.59/23.79 (rd(mult(mult(mult(mult(mult(a, c), a), b), unit), b), b) = rd(mult(mult(mult(a, c), mult(a, b)), b), b)),
% 23.59/23.79 inference(monotonicity,[status(thm)],[11428])).
% 23.59/23.79 tff(11430,plain,
% 23.59/23.79 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(mult(mult(a, c), a), b), unit), b), b) = mult(mult(mult(mult(a, c), a), b), unit))),
% 23.59/23.79 inference(quant_inst,[status(thm)],[])).
% 23.59/23.79 tff(11431,plain,
% 23.59/23.79 (rd(mult(mult(mult(mult(mult(a, c), a), b), unit), b), b) = mult(mult(mult(mult(a, c), a), b), unit)),
% 23.59/23.79 inference(unit_resolution,[status(thm)],[11430, 168])).
% 23.59/23.79 tff(11432,plain,
% 23.59/23.79 (mult(mult(mult(mult(a, c), a), b), unit) = rd(mult(mult(mult(mult(mult(a, c), a), b), unit), b), b)),
% 23.59/23.79 inference(symmetry,[status(thm)],[11431])).
% 23.59/23.79 tff(11433,plain,
% 23.59/23.79 ((~![A: $i] : (mult(A, unit) = A)) | (mult(mult(mult(mult(a, c), a), b), unit) = mult(mult(mult(a, c), a), b))),
% 23.59/23.79 inference(quant_inst,[status(thm)],[])).
% 23.59/23.79 tff(11434,plain,
% 23.59/23.79 (mult(mult(mult(mult(a, c), a), b), unit) = mult(mult(mult(a, c), a), b)),
% 23.59/23.79 inference(unit_resolution,[status(thm)],[11433, 43])).
% 23.59/23.79 tff(11435,plain,
% 23.59/23.79 (mult(mult(mult(a, c), a), b) = mult(mult(mult(mult(a, c), a), b), unit)),
% 23.59/23.79 inference(symmetry,[status(thm)],[11434])).
% 23.59/23.79 tff(11436,plain,
% 23.59/23.79 (mult(mult(mult(a, c), a), b) = mult(mult(c, a), mult(a, b))),
% 23.59/23.79 inference(transitivity,[status(thm)],[11435, 11432, 11429, 1485, 11424])).
% 23.59/23.79 tff(11437,plain,
% 23.59/23.79 (mult(b, mult(mult(mult(a, c), a), b)) = mult(b, mult(mult(c, a), mult(a, b)))),
% 23.59/23.79 inference(monotonicity,[status(thm)],[11436])).
% 23.59/23.79 tff(11438,plain,
% 23.59/23.79 (mult(mult(mult(mult(b, c), a), a), b) = mult(mult(mult(b, c), a), mult(a, b))),
% 23.59/23.79 inference(unit_resolution,[status(thm)],[2110, 11249])).
% 23.59/23.79 tff(11439,plain,
% 23.59/23.79 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(a, b)), mult(a, b)) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 23.59/23.79 inference(quant_inst,[status(thm)],[])).
% 23.59/23.79 tff(11440,plain,
% 23.59/23.79 (rd(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(a, b)), mult(a, b)) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 23.59/23.79 inference(unit_resolution,[status(thm)],[11439, 168])).
% 23.59/23.79 tff(11441,plain,
% 23.59/23.79 (mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 23.59/23.79 inference(transitivity,[status(thm)],[10344, 8198])).
% 23.59/23.79 tff(11442,plain,
% 23.59/23.79 (mult(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c), mult(a, b)) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(a, b))),
% 23.59/23.79 inference(monotonicity,[status(thm)],[11441])).
% 23.59/23.79 tff(11443,plain,
% 23.59/23.79 (mult(b, mult(c, a)) = mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)),
% 23.59/23.79 inference(transitivity,[status(thm)],[10220, 5659, 10801, 4477, 10348, 10347])).
% 23.59/23.79 tff(11444,plain,
% 23.59/23.79 (mult(mult(b, mult(c, a)), mult(a, b)) = mult(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c), mult(a, b))),
% 23.59/23.79 inference(monotonicity,[status(thm)],[11443])).
% 23.59/23.79 tff(11445,assumption,(mult(mult(b, mult(a, c)), mult(a, b)) = mult(b, mult(mult(a, c), mult(a, b)))), introduced(assumption)).
% 23.59/23.79 tff(11446,plain,
% 23.59/23.79 (mult(b, mult(mult(a, c), mult(a, b))) = mult(mult(b, mult(a, c)), mult(a, b))),
% 23.59/23.79 inference(symmetry,[status(thm)],[11445])).
% 23.59/23.79 tff(11447,plain,
% 23.59/23.79 (mult(mult(mult(mult(mult(a, c), a), b), unit), b) = mult(mult(mult(a, c), mult(a, b)), b)),
% 23.59/23.79 inference(transitivity,[status(thm)],[11427, 11425, 10570, 10460, 1091])).
% 23.59/23.79 tff(11448,plain,
% 23.59/23.79 (rd(mult(mult(mult(mult(mult(a, c), a), b), unit), b), b) = rd(mult(mult(mult(a, c), mult(a, b)), b), b)),
% 23.59/23.79 inference(monotonicity,[status(thm)],[11447])).
% 23.59/23.79 tff(11449,plain,
% 23.59/23.79 (mult(mult(mult(a, c), a), b) = mult(mult(c, a), mult(a, b))),
% 23.59/23.79 inference(transitivity,[status(thm)],[11435, 11432, 11448, 1485, 11424])).
% 23.59/23.79 tff(11450,plain,
% 23.59/23.79 (mult(b, mult(mult(mult(a, c), a), b)) = mult(b, mult(mult(c, a), mult(a, b)))),
% 23.59/23.79 inference(monotonicity,[status(thm)],[11449])).
% 23.59/23.79 tff(11451,assumption,(mult(mult(b, mult(mult(a, c), a)), b) = mult(b, mult(mult(mult(a, c), a), b))), introduced(assumption)).
% 23.59/23.79 tff(11452,plain,
% 23.59/23.79 (mult(mult(b, a), c) = mult(mult(b, c), a)),
% 23.59/23.79 inference(unit_resolution,[status(thm)],[11022, 8704])).
% 23.59/23.79 tff(11453,plain,
% 23.59/23.79 (mult(mult(mult(unit, mult(b, a)), unit), c) = mult(mult(b, c), a)),
% 23.59/23.79 inference(transitivity,[status(thm)],[11015, 11452])).
% 23.59/23.79 tff(11454,plain,
% 23.59/23.79 (mult(mult(mult(mult(unit, mult(b, a)), unit), c), a) = mult(mult(mult(b, c), a), a)),
% 23.59/23.79 inference(monotonicity,[status(thm)],[11453])).
% 23.59/23.79 tff(11455,plain,
% 23.59/23.79 (mult(mult(mult(b, c), a), a) = mult(mult(mult(mult(unit, mult(b, a)), unit), c), a)),
% 23.59/23.79 inference(symmetry,[status(thm)],[11454])).
% 23.59/23.79 tff(11456,plain,
% 23.59/23.79 (mult(mult(mult(b, c), a), a) = mult(b, mult(mult(a, c), a))),
% 23.59/23.79 inference(transitivity,[status(thm)],[11455, 11018, 8036])).
% 23.59/23.79 tff(11457,plain,
% 23.59/23.79 (mult(mult(mult(mult(b, c), a), a), b) = mult(mult(b, mult(mult(a, c), a)), b)),
% 23.59/23.79 inference(monotonicity,[status(thm)],[11456])).
% 23.59/23.79 tff(11458,assumption,(mult(mult(mult(mult(b, c), a), a), b) = mult(mult(mult(b, c), a), mult(a, b))), introduced(assumption)).
% 23.59/23.79 tff(11459,plain,
% 23.59/23.79 (mult(mult(mult(b, c), a), mult(a, b)) = mult(mult(mult(mult(b, c), a), a), b)),
% 23.59/23.79 inference(symmetry,[status(thm)],[11458])).
% 23.59/23.79 tff(11460,plain,
% 23.59/23.79 (mult(mult(mult(b, c), a), mult(a, b)) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(a, b))),
% 23.59/23.79 inference(transitivity,[status(thm)],[11459, 11457, 11451, 11450, 11423, 11446, 11094, 11444, 11442])).
% 23.59/23.79 tff(11461,plain,
% 23.59/23.79 (rd(mult(mult(mult(b, c), a), mult(a, b)), mult(a, b)) = rd(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(a, b)), mult(a, b))),
% 23.59/23.79 inference(monotonicity,[status(thm)],[11460])).
% 23.59/23.79 tff(11462,plain,
% 23.59/23.79 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(b, c), a), mult(a, b)), mult(a, b)) = mult(mult(b, c), a))),
% 23.59/23.79 inference(quant_inst,[status(thm)],[])).
% 23.59/23.79 tff(11463,plain,
% 23.59/23.79 (rd(mult(mult(mult(b, c), a), mult(a, b)), mult(a, b)) = mult(mult(b, c), a)),
% 23.59/23.79 inference(unit_resolution,[status(thm)],[11462, 168])).
% 23.59/23.79 tff(11464,plain,
% 23.59/23.79 (mult(mult(b, c), a) = rd(mult(mult(mult(b, c), a), mult(a, b)), mult(a, b))),
% 23.59/23.79 inference(symmetry,[status(thm)],[11463])).
% 23.59/23.79 tff(11465,plain,
% 23.59/23.79 (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))),
% 23.59/23.79 inference(transitivity,[status(thm)],[1332, 11464, 11461, 11440, 10374, 10790, 10785])).
% 23.59/23.79 tff(11466,plain,
% 23.59/23.79 ($false),
% 23.59/23.79 inference(unit_resolution,[status(thm)],[1364, 11465])).
% 23.59/23.79 tff(11467,plain,((~(mult(mult(b, mult(mult(a, c), a)), b) = mult(b, mult(mult(mult(a, c), a), b)))) | (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), a) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) | (~(mult(mult(mult(mult(b, c), a), a), b) = mult(mult(mult(b, c), a), mult(a, b)))) | (~(mult(mult(b, mult(a, c)), mult(a, b)) = mult(b, mult(mult(a, c), mult(a, b))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))) | (~(mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, mult(a, c)))))) | (~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), mult(a, b)), b) = mult(mult(a, c), mult(mult(a, b), b)))) | (~(mult(mult(mult(a, c), a), mult(unit, mult(mult(b, unit), b))) = mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b)))))) | (~(mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))) = mult(b, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))))), inference(lemma,lemma(discharge,[]))).
% 23.59/23.79 tff(11468,plain,
% 23.59/23.79 (~(mult(mult(b, mult(mult(a, c), a)), b) = mult(b, mult(mult(mult(a, c), a), b)))),
% 23.59/23.79 inference(unit_resolution,[status(thm)],[11467, 11003, 11438, 11361, 8165, 9662, 6583, 10627, 281, 10454, 10517, 11043])).
% 23.59/23.79 tff(11469,plain,
% 23.59/23.79 (((~(mult(mult(b, mult(mult(a, c), a)), b) = mult(b, mult(mult(mult(a, c), a), b)))) | (~(mult(mult(b, b), mult(mult(a, c), a)) = mult(b, mult(b, mult(mult(a, c), a)))))) | (mult(mult(b, mult(mult(a, c), a)), b) = mult(b, mult(mult(mult(a, c), a), b)))),
% 23.59/23.79 inference(tautology,[status(thm)],[])).
% 23.59/23.79 tff(11470,plain,
% 23.59/23.79 ((~(mult(mult(b, mult(mult(a, c), a)), b) = mult(b, mult(mult(mult(a, c), a), b)))) | (~(mult(mult(b, b), mult(mult(a, c), a)) = mult(b, mult(b, mult(mult(a, c), a)))))),
% 23.59/23.79 inference(unit_resolution,[status(thm)],[11469, 11468])).
% 23.59/23.79 tff(11471,plain,
% 23.59/23.79 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(b, mult(mult(mult(a, c), a), b)) = mult(b, mult(b, mult(mult(a, c), a))))) | (~(mult(mult(b, mult(mult(a, c), a)), b) = mult(mult(b, b), mult(mult(a, c), a)))))) | (~((~(mult(mult(b, mult(mult(a, c), a)), b) = mult(b, mult(mult(mult(a, c), a), b)))) | (~(mult(mult(b, b), mult(mult(a, c), a)) = mult(b, mult(b, mult(mult(a, c), a))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(b, mult(mult(mult(a, c), a), b)) = mult(b, mult(b, mult(mult(a, c), a))))) | (~(mult(mult(b, mult(mult(a, c), a)), b) = mult(mult(b, b), mult(mult(a, c), a)))))) | (~((~(mult(mult(b, mult(mult(a, c), a)), b) = mult(b, mult(mult(mult(a, c), a), b)))) | (~(mult(mult(b, b), mult(mult(a, c), a)) = mult(b, mult(b, mult(mult(a, c), a))))))))),
% 23.64/23.80 inference(rewrite,[status(thm)],[])).
% 23.64/23.80 tff(11472,plain,
% 23.64/23.80 (((~((~(mult(mult(b, mult(mult(a, c), a)), b) = mult(mult(b, b), mult(mult(a, c), a)))) | (~(mult(b, mult(mult(mult(a, c), a), b)) = mult(b, mult(b, mult(mult(a, c), a))))))) | (~((~(mult(mult(b, mult(mult(a, c), a)), b) = mult(b, mult(mult(mult(a, c), a), b)))) | (~(mult(mult(b, b), mult(mult(a, c), a)) = mult(b, mult(b, mult(mult(a, c), a)))))))) <=> ((~((~(mult(b, mult(mult(mult(a, c), a), b)) = mult(b, mult(b, mult(mult(a, c), a))))) | (~(mult(mult(b, mult(mult(a, c), a)), b) = mult(mult(b, b), mult(mult(a, c), a)))))) | (~((~(mult(mult(b, mult(mult(a, c), a)), b) = mult(b, mult(mult(mult(a, c), a), b)))) | (~(mult(mult(b, b), mult(mult(a, c), a)) = mult(b, mult(b, mult(mult(a, c), a))))))))),
% 23.64/23.80 inference(rewrite,[status(thm)],[])).
% 23.64/23.80 tff(11473,plain,
% 23.64/23.80 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(b, mult(mult(a, c), a)), b) = mult(mult(b, b), mult(mult(a, c), a)))) | (~(mult(b, mult(mult(mult(a, c), a), b)) = mult(b, mult(b, mult(mult(a, c), a))))))) | (~((~(mult(mult(b, mult(mult(a, c), a)), b) = mult(b, mult(mult(mult(a, c), a), b)))) | (~(mult(mult(b, b), mult(mult(a, c), a)) = mult(b, mult(b, mult(mult(a, c), a))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(b, mult(mult(mult(a, c), a), b)) = mult(b, mult(b, mult(mult(a, c), a))))) | (~(mult(mult(b, mult(mult(a, c), a)), b) = mult(mult(b, b), mult(mult(a, c), a)))))) | (~((~(mult(mult(b, mult(mult(a, c), a)), b) = mult(b, mult(mult(mult(a, c), a), b)))) | (~(mult(mult(b, b), mult(mult(a, c), a)) = mult(b, mult(b, mult(mult(a, c), a)))))))))),
% 23.64/23.80 inference(monotonicity,[status(thm)],[11472])).
% 23.64/23.80 tff(11474,plain,
% 23.64/23.80 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(b, mult(mult(a, c), a)), b) = mult(mult(b, b), mult(mult(a, c), a)))) | (~(mult(b, mult(mult(mult(a, c), a), b)) = mult(b, mult(b, mult(mult(a, c), a))))))) | (~((~(mult(mult(b, mult(mult(a, c), a)), b) = mult(b, mult(mult(mult(a, c), a), b)))) | (~(mult(mult(b, b), mult(mult(a, c), a)) = mult(b, mult(b, mult(mult(a, c), a))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(b, mult(mult(mult(a, c), a), b)) = mult(b, mult(b, mult(mult(a, c), a))))) | (~(mult(mult(b, mult(mult(a, c), a)), b) = mult(mult(b, b), mult(mult(a, c), a)))))) | (~((~(mult(mult(b, mult(mult(a, c), a)), b) = mult(b, mult(mult(mult(a, c), a), b)))) | (~(mult(mult(b, b), mult(mult(a, c), a)) = mult(b, mult(b, mult(mult(a, c), a))))))))),
% 23.64/23.80 inference(transitivity,[status(thm)],[11473, 11471])).
% 23.64/23.80 tff(11475,plain,
% 23.64/23.80 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(b, mult(mult(a, c), a)), b) = mult(mult(b, b), mult(mult(a, c), a)))) | (~(mult(b, mult(mult(mult(a, c), a), b)) = mult(b, mult(b, mult(mult(a, c), a))))))) | (~((~(mult(mult(b, mult(mult(a, c), a)), b) = mult(b, mult(mult(mult(a, c), a), b)))) | (~(mult(mult(b, b), mult(mult(a, c), a)) = mult(b, mult(b, mult(mult(a, c), a))))))))),
% 23.64/23.80 inference(quant_inst,[status(thm)],[])).
% 23.64/23.80 tff(11476,plain,
% 23.64/23.80 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(b, mult(mult(mult(a, c), a), b)) = mult(b, mult(b, mult(mult(a, c), a))))) | (~(mult(mult(b, mult(mult(a, c), a)), b) = mult(mult(b, b), mult(mult(a, c), a)))))) | (~((~(mult(mult(b, mult(mult(a, c), a)), b) = mult(b, mult(mult(mult(a, c), a), b)))) | (~(mult(mult(b, b), mult(mult(a, c), a)) = mult(b, mult(b, mult(mult(a, c), a)))))))),
% 23.64/23.80 inference(modus_ponens,[status(thm)],[11475, 11474])).
% 23.64/23.80 tff(11477,plain,
% 23.64/23.80 ((~((~(mult(b, mult(mult(mult(a, c), a), b)) = mult(b, mult(b, mult(mult(a, c), a))))) | (~(mult(mult(b, mult(mult(a, c), a)), b) = mult(mult(b, b), mult(mult(a, c), a)))))) | (~((~(mult(mult(b, mult(mult(a, c), a)), b) = mult(b, mult(mult(mult(a, c), a), b)))) | (~(mult(mult(b, b), mult(mult(a, c), a)) = mult(b, mult(b, mult(mult(a, c), a)))))))),
% 23.64/23.80 inference(unit_resolution,[status(thm)],[11476, 27])).
% 23.64/23.80 tff(11478,plain,
% 23.64/23.80 (~((~(mult(b, mult(mult(mult(a, c), a), b)) = mult(b, mult(b, mult(mult(a, c), a))))) | (~(mult(mult(b, mult(mult(a, c), a)), b) = mult(mult(b, b), mult(mult(a, c), a)))))),
% 23.64/23.80 inference(unit_resolution,[status(thm)],[11477, 11470])).
% 23.64/23.80 tff(11479,plain,
% 23.64/23.80 (((~(mult(b, mult(mult(mult(a, c), a), b)) = mult(b, mult(b, mult(mult(a, c), a))))) | (~(mult(mult(b, mult(mult(a, c), a)), b) = mult(mult(b, b), mult(mult(a, c), a))))) | (mult(b, mult(mult(mult(a, c), a), b)) = mult(b, mult(b, mult(mult(a, c), a))))),
% 23.64/23.80 inference(tautology,[status(thm)],[])).
% 23.64/23.80 tff(11480,plain,
% 23.64/23.80 (mult(b, mult(mult(mult(a, c), a), b)) = mult(b, mult(b, mult(mult(a, c), a)))),
% 23.64/23.80 inference(unit_resolution,[status(thm)],[11479, 11478])).
% 23.64/23.80 tff(11481,plain,
% 23.64/23.80 (mult(b, mult(b, mult(mult(a, c), a))) = mult(b, mult(mult(mult(a, c), a), b))),
% 23.64/23.80 inference(symmetry,[status(thm)],[11480])).
% 23.64/23.80 tff(11482,plain,
% 23.64/23.80 (mult(mult(mult(b, c), a), a) = mult(mult(mult(mult(unit, mult(b, a)), unit), c), a)),
% 23.64/23.80 inference(symmetry,[status(thm)],[11107])).
% 23.64/23.80 tff(11483,plain,
% 23.64/23.80 (mult(mult(mult(b, c), a), a) = mult(b, mult(mult(a, c), a))),
% 23.64/23.80 inference(transitivity,[status(thm)],[11482, 11018, 8036])).
% 23.64/23.80 tff(11484,plain,
% 23.64/23.80 (mult(b, mult(mult(mult(b, c), a), a)) = mult(b, mult(b, mult(mult(a, c), a)))),
% 23.64/23.80 inference(monotonicity,[status(thm)],[11483])).
% 23.64/23.80 tff(11485,plain,
% 23.64/23.80 (mult(b, mult(mult(mult(b, c), a), a)) = mult(b, mult(mult(a, c), mult(a, b)))),
% 23.64/23.80 inference(transitivity,[status(thm)],[11484, 11481, 11437, 11423])).
% 23.64/23.80 tff(11486,plain,
% 23.64/23.80 (ld(b, mult(b, mult(mult(mult(b, c), a), a))) = ld(b, mult(b, mult(mult(a, c), mult(a, b))))),
% 23.64/23.80 inference(monotonicity,[status(thm)],[11485])).
% 23.64/23.80 tff(11487,plain,
% 23.64/23.80 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(b, mult(b, mult(mult(mult(b, c), a), a))) = mult(mult(mult(b, c), a), a))),
% 23.64/23.80 inference(quant_inst,[status(thm)],[])).
% 23.64/23.80 tff(11488,plain,
% 23.64/23.80 (ld(b, mult(b, mult(mult(mult(b, c), a), a))) = mult(mult(mult(b, c), a), a)),
% 23.64/23.80 inference(unit_resolution,[status(thm)],[11487, 7])).
% 23.64/23.80 tff(11489,plain,
% 23.64/23.80 (mult(mult(mult(b, c), a), a) = ld(b, mult(b, mult(mult(mult(b, c), a), a)))),
% 23.64/23.80 inference(symmetry,[status(thm)],[11488])).
% 23.64/23.80 tff(11490,plain,
% 23.64/23.80 (mult(mult(b, c), mult(a, a)) = mult(mult(a, c), mult(a, b))),
% 23.64/23.80 inference(transitivity,[status(thm)],[1558, 3507, 11010, 11489, 11486, 11418])).
% 23.64/23.80 tff(11491,plain,
% 23.64/23.80 (mult(mult(mult(b, c), mult(a, a)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), mult(a, b)), rd(mult(b, c), mult(a, c)))),
% 23.64/23.80 inference(monotonicity,[status(thm)],[11490])).
% 23.64/23.80 tff(11492,plain,
% 23.64/23.80 (mult(mult(mult(b, c), a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(mult(b, c), a), a), rd(mult(b, c), mult(a, c)))),
% 23.64/23.80 inference(symmetry,[status(thm)],[9695])).
% 23.64/23.80 tff(11493,plain,
% 23.64/23.80 (mult(mult(c, mult(b, a)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(b, c), a), mult(a, rd(mult(b, c), mult(a, c))))),
% 23.64/23.80 inference(monotonicity,[status(thm)],[4305])).
% 23.64/23.80 tff(11494,plain,
% 23.64/23.80 (mult(mult(b, a), c) = mult(c, mult(b, a))),
% 23.64/23.80 inference(transitivity,[status(thm)],[11105, 3057, 4208])).
% 23.64/23.80 tff(11495,plain,
% 23.64/23.80 (mult(mult(mult(b, a), c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(c, mult(b, a)), mult(a, rd(mult(b, c), mult(a, c))))),
% 23.64/23.80 inference(monotonicity,[status(thm)],[11494])).
% 23.64/23.80 tff(11496,plain,
% 23.64/23.80 (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, a), c), rd(mult(b, c), mult(a, c)))),
% 23.64/23.80 inference(symmetry,[status(thm)],[8836])).
% 23.64/23.80 tff(11497,plain,
% 23.64/23.80 (mult(mult(mult(a, a), rd(mult(b, c), mult(a, c))), c) = mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)),
% 23.64/23.80 inference(monotonicity,[status(thm)],[10012])).
% 23.64/23.80 tff(11498,plain,
% 23.64/23.80 (mult(mult(mult(a, a), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, a), c), rd(mult(b, c), mult(a, c)))),
% 23.64/23.80 inference(transitivity,[status(thm)],[11497, 11161, 11163, 4455, 10343, 11496])).
% 23.64/23.80 tff(11499,plain,
% 23.64/23.80 (mult(mult(a, c), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), c)),
% 23.64/23.80 inference(transitivity,[status(thm)],[2167, 4851, 4850, 2171, 5046, 4493])).
% 23.64/23.80 tff(11500,plain,
% 23.64/23.80 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), a)),
% 23.64/23.80 inference(monotonicity,[status(thm)],[11499])).
% 23.64/23.80 tff(11501,plain,
% 23.64/23.80 (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)),
% 23.64/23.80 inference(symmetry,[status(thm)],[11500])).
% 23.64/23.80 tff(11502,plain,
% 23.64/23.80 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(b, mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))) = mult(a, mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.64/23.80 inference(quant_inst,[status(thm)],[])).
% 23.64/23.80 tff(11503,plain,
% 23.64/23.80 (ld(b, mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))) = mult(a, mult(a, rd(mult(b, c), mult(a, c))))),
% 23.64/23.80 inference(unit_resolution,[status(thm)],[11502, 7])).
% 23.64/23.80 tff(11504,assumption,(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), a))), introduced(assumption)).
% 23.64/23.80 tff(11505,plain,
% 23.64/23.80 (mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), a)) = mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.64/23.80 inference(symmetry,[status(thm)],[11504])).
% 23.64/23.80 tff(11506,plain,
% 23.64/23.80 (ld(b, mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), a))) = ld(b, mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))),
% 23.64/23.80 inference(monotonicity,[status(thm)],[11505])).
% 23.64/23.80 tff(11507,plain,
% 23.64/23.80 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(b, mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), a))) = mult(mult(a, rd(mult(b, c), mult(a, c))), a))),
% 23.64/23.80 inference(quant_inst,[status(thm)],[])).
% 23.64/23.80 tff(11508,plain,
% 23.64/23.80 (ld(b, mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), a))) = mult(mult(a, rd(mult(b, c), mult(a, c))), a)),
% 23.64/23.80 inference(unit_resolution,[status(thm)],[11507, 7])).
% 23.64/23.80 tff(11509,plain,
% 23.64/23.80 (mult(mult(a, rd(mult(b, c), mult(a, c))), a) = ld(b, mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), a)))),
% 23.64/23.80 inference(symmetry,[status(thm)],[11508])).
% 23.64/23.80 tff(11510,plain,
% 23.64/23.80 (mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(a, mult(a, rd(mult(b, c), mult(a, c))))),
% 23.64/23.80 inference(transitivity,[status(thm)],[11509, 11506, 11503])).
% 23.64/23.80 tff(11511,plain,
% 23.64/23.80 (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), c) = mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)),
% 23.64/23.80 inference(monotonicity,[status(thm)],[11510])).
% 23.64/23.80 tff(11512,plain,
% 23.64/23.80 (mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), c)),
% 23.64/23.80 inference(symmetry,[status(thm)],[11511])).
% 23.64/23.80 tff(11513,plain,
% 23.64/23.80 (mult(a, mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, a), rd(mult(b, c), mult(a, c)))),
% 23.64/23.80 inference(symmetry,[status(thm)],[1391])).
% 23.64/23.80 tff(11514,plain,
% 23.64/23.80 (mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(mult(a, a), rd(mult(b, c), mult(a, c))), c)),
% 23.64/23.80 inference(monotonicity,[status(thm)],[11513])).
% 23.64/23.80 tff(11515,plain,
% 23.64/23.80 (mult(mult(mult(a, a), rd(mult(b, c), mult(a, c))), c) = mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)),
% 23.64/23.80 inference(symmetry,[status(thm)],[11514])).
% 23.64/23.80 tff(11516,assumption,(mult(mult(mult(a, a), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, a), c), rd(mult(b, c), mult(a, c)))), introduced(assumption)).
% 23.64/23.80 tff(11517,plain,
% 23.64/23.80 (mult(mult(mult(a, a), c), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, a), rd(mult(b, c), mult(a, c))), c)),
% 23.64/23.80 inference(symmetry,[status(thm)],[11516])).
% 23.64/23.80 tff(11518,plain,
% 23.64/23.80 (mult(mult(mult(a, a), c), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))),
% 23.64/23.80 inference(monotonicity,[status(thm)],[10077])).
% 23.64/23.80 tff(11519,plain,
% 23.64/23.80 (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, a), c), rd(mult(b, c), mult(a, c)))),
% 23.64/23.80 inference(symmetry,[status(thm)],[11518])).
% 23.64/23.80 tff(11520,plain,
% 23.64/23.80 (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)),
% 23.64/23.80 inference(transitivity,[status(thm)],[11519, 11517, 11515, 11512, 7510, 11501])).
% 23.64/23.80 tff(11521,plain,
% 23.64/23.80 ($false),
% 23.64/23.80 inference(unit_resolution,[status(thm)],[2331, 11520])).
% 23.64/23.80 tff(11522,plain,((~(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), a)))) | (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)) | (~(mult(mult(mult(a, a), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, a), c), rd(mult(b, c), mult(a, c))))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) | (~(mult(mult(a, a), rd(mult(b, c), mult(a, c))) = mult(a, mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))), inference(lemma,lemma(discharge,[]))).
% 23.64/23.80 tff(11523,plain,
% 23.64/23.80 ((~(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), a)))) | (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)) | (~(mult(mult(mult(a, a), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, a), c), rd(mult(b, c), mult(a, c))))) | (~(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))),
% 23.64/23.80 inference(unit_resolution,[status(thm)],[11522, 10012])).
% 23.64/23.80 tff(11524,plain,
% 23.64/23.80 ((~(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), a)))) | (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)) | (~(mult(mult(mult(a, a), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, a), c), rd(mult(b, c), mult(a, c))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))),
% 23.64/23.81 inference(unit_resolution,[status(thm)],[11523, 8129])).
% 23.64/23.81 tff(11525,plain,
% 23.64/23.81 (~(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), a)))),
% 23.64/23.81 inference(unit_resolution,[status(thm)],[11524, 9673, 11498, 8165])).
% 23.64/23.81 tff(11526,plain,
% 23.64/23.81 ((~(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(b, mult(a, rd(mult(b, c), mult(a, c)))), a))) | (~(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), a))))),
% 23.64/23.81 inference(unit_resolution,[status(thm)],[7187, 11525])).
% 23.64/23.81 tff(11527,assumption,((~(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(b, mult(a, rd(mult(b, c), mult(a, c)))), a))) | (~(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), a))))), introduced(assumption)).
% 23.64/23.81 tff(11528,assumption,((~(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(b, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), a))))), introduced(assumption)).
% 23.64/23.81 tff(11529,plain,
% 23.64/23.81 ($false),
% 23.64/23.81 inference(unit_resolution,[status(thm)],[7184, 27, 11527, 11528])).
% 23.64/23.81 tff(11530,plain,((~((~(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(b, mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), a)))))) | (~((~(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(b, mult(a, rd(mult(b, c), mult(a, c)))), a))) | (~(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), a))))))), inference(lemma,lemma(discharge,[]))).
% 23.64/23.81 tff(11531,plain,
% 23.64/23.81 ($false),
% 23.64/23.81 inference(unit_resolution,[status(thm)],[11530, 7181, 11527])).
% 23.64/23.81 tff(11532,plain,((~((~(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(b, mult(a, rd(mult(b, c), mult(a, c)))), a))) | (~(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(b, mult(mult(a, rd(mult(b, c), mult(a, c))), a)))))) | (mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))), inference(lemma,lemma(discharge,[]))).
% 23.64/23.81 tff(11533,plain,
% 23.64/23.81 (mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.64/23.81 inference(unit_resolution,[status(thm)],[11532, 11526])).
% 23.64/23.81 tff(11534,plain,
% 23.64/23.81 ((mult(b, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))) = mult(mult(b, c), mult(a, mult(a, rd(mult(b, c), mult(a, c)))))) <=> (mult(mult(b, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(b, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))),
% 23.64/23.81 inference(commutativity,[status(thm)],[])).
% 23.64/23.81 tff(11535,plain,
% 23.64/23.81 (mult(mult(c, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.64/23.81 inference(unit_resolution,[status(thm)],[10005, 10771, 299])).
% 23.64/23.81 tff(11536,plain,
% 23.64/23.81 (mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(c, a), mult(a, rd(mult(b, c), mult(a, c))))),
% 23.64/23.81 inference(symmetry,[status(thm)],[11535])).
% 23.64/23.81 tff(11537,plain,
% 23.64/23.81 (mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)),
% 23.64/23.81 inference(transitivity,[status(thm)],[11536, 8240, 8170, 8169, 299, 10348, 10347])).
% 23.64/23.81 tff(11538,plain,
% 23.64/23.81 (mult(b, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))) = mult(b, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c))),
% 23.64/23.81 inference(monotonicity,[status(thm)],[11537])).
% 23.64/23.81 tff(11539,plain,
% 23.64/23.81 (mult(b, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)) = mult(b, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))),
% 23.64/23.81 inference(symmetry,[status(thm)],[11538])).
% 23.64/23.81 tff(11540,assumption,(~(mult(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(mult(b, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))))), introduced(assumption)).
% 23.64/23.81 tff(11541,plain,
% 23.64/23.81 (((~(mult(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(mult(b, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(b, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)) = mult(b, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))))) | (mult(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(mult(b, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))))),
% 23.64/23.81 inference(tautology,[status(thm)],[])).
% 23.64/23.81 tff(11542,plain,
% 23.64/23.81 ((~(mult(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(mult(b, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(b, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)) = mult(b, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))))),
% 23.64/23.81 inference(unit_resolution,[status(thm)],[11541, 11540])).
% 23.64/23.81 tff(11543,plain,
% 23.64/23.81 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(b, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(b, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))) | (~(mult(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(b, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)))))) | (~((~(mult(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(mult(b, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(b, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)) = mult(b, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(b, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(b, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))) | (~(mult(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(b, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)))))) | (~((~(mult(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(mult(b, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(b, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)) = mult(b, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))))))),
% 23.64/23.81 inference(rewrite,[status(thm)],[])).
% 23.64/23.81 tff(11544,plain,
% 23.64/23.81 (((~((~(mult(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(mult(b, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(b, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)) = mult(b, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))))) | (~((~(mult(mult(b, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(b, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))) | (~(mult(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(b, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c))))))) <=> ((~((~(mult(mult(b, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(b, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))) | (~(mult(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(b, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)))))) | (~((~(mult(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(mult(b, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(b, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)) = mult(b, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))))))),
% 23.64/23.81 inference(rewrite,[status(thm)],[])).
% 23.64/23.81 tff(11545,plain,
% 23.64/23.81 ((~((~(mult(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(b, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)))) | (~(mult(mult(b, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(b, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))))) <=> (~((~(mult(mult(b, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(b, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))) | (~(mult(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(b, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c))))))),
% 23.64/23.81 inference(rewrite,[status(thm)],[])).
% 23.64/23.81 tff(11546,plain,
% 23.64/23.81 ((~((~(mult(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(mult(b, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(b, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)) = mult(b, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))))) <=> (~((~(mult(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(mult(b, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(b, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)) = mult(b, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))))))),
% 23.64/23.81 inference(rewrite,[status(thm)],[])).
% 23.64/23.81 tff(11547,plain,
% 23.64/23.81 (((~((~(mult(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(mult(b, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(b, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)) = mult(b, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))))) | (~((~(mult(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(b, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)))) | (~(mult(mult(b, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(b, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))))))) <=> ((~((~(mult(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(mult(b, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(b, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)) = mult(b, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))))) | (~((~(mult(mult(b, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(b, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))) | (~(mult(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(b, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)))))))),
% 23.64/23.81 inference(monotonicity,[status(thm)],[11546, 11545])).
% 23.64/23.81 tff(11548,plain,
% 23.64/23.81 (((~((~(mult(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(mult(b, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(b, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)) = mult(b, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))))) | (~((~(mult(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(b, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)))) | (~(mult(mult(b, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(b, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))))))) <=> ((~((~(mult(mult(b, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(b, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))) | (~(mult(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(b, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)))))) | (~((~(mult(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(mult(b, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(b, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)) = mult(b, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))))))),
% 23.64/23.81 inference(transitivity,[status(thm)],[11547, 11544])).
% 23.64/23.81 tff(11549,plain,
% 23.64/23.81 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(mult(b, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(b, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)) = mult(b, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))))) | (~((~(mult(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(b, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)))) | (~(mult(mult(b, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(b, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(b, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(b, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))) | (~(mult(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(b, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)))))) | (~((~(mult(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(mult(b, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(b, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)) = mult(b, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))))))))),
% 23.64/23.82 inference(monotonicity,[status(thm)],[11548])).
% 23.64/23.82 tff(11550,plain,
% 23.64/23.82 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(mult(b, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(b, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)) = mult(b, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))))) | (~((~(mult(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(b, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)))) | (~(mult(mult(b, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(b, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(b, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(b, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))) | (~(mult(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(b, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)))))) | (~((~(mult(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(mult(b, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(b, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)) = mult(b, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))))))),
% 23.64/23.82 inference(transitivity,[status(thm)],[11549, 11543])).
% 23.64/23.82 tff(11551,plain,
% 23.64/23.82 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(mult(b, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(b, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)) = mult(b, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))))) | (~((~(mult(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(b, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)))) | (~(mult(mult(b, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(b, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))))))),
% 23.64/23.82 inference(quant_inst,[status(thm)],[])).
% 23.64/23.82 tff(11552,plain,
% 23.64/23.82 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(b, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(b, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))) | (~(mult(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(b, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)))))) | (~((~(mult(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(mult(b, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(b, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)) = mult(b, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))))))),
% 23.64/23.82 inference(modus_ponens,[status(thm)],[11551, 11550])).
% 23.64/23.82 tff(11553,plain,
% 23.64/23.82 ((~((~(mult(mult(b, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(b, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))) | (~(mult(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(b, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)))))) | (~((~(mult(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(mult(b, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(b, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)) = mult(b, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))))))),
% 23.64/23.82 inference(unit_resolution,[status(thm)],[11552, 27])).
% 23.64/23.82 tff(11554,plain,
% 23.64/23.82 (~((~(mult(mult(b, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(b, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))) | (~(mult(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(b, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)))))),
% 23.64/23.82 inference(unit_resolution,[status(thm)],[11553, 11542])).
% 23.64/23.82 tff(11555,plain,
% 23.64/23.82 (((~(mult(mult(b, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(b, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))) | (~(mult(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(b, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c))))) | (mult(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(b, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)))),
% 23.64/23.82 inference(tautology,[status(thm)],[])).
% 23.64/23.82 tff(11556,plain,
% 23.64/23.82 (mult(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(b, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c))),
% 23.64/23.82 inference(unit_resolution,[status(thm)],[11555, 11554])).
% 23.64/23.82 tff(11557,plain,
% 23.64/23.82 (mult(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(b, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))),
% 23.64/23.82 inference(transitivity,[status(thm)],[11556, 11539])).
% 23.64/23.82 tff(11558,plain,
% 23.64/23.82 ((mult(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(mult(b, c), mult(a, mult(a, rd(mult(b, c), mult(a, c)))))) <=> (mult(b, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))) = mult(mult(b, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))))),
% 23.64/23.82 inference(monotonicity,[status(thm)],[11557])).
% 23.64/23.82 tff(11559,plain,
% 23.64/23.82 ((mult(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(mult(b, c), mult(a, mult(a, rd(mult(b, c), mult(a, c)))))) <=> (mult(mult(b, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(b, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))),
% 23.64/23.82 inference(transitivity,[status(thm)],[11558, 11534])).
% 23.64/23.82 tff(11560,plain,
% 23.64/23.82 ((mult(mult(b, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(b, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) <=> (mult(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(mult(b, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))))),
% 23.64/23.82 inference(symmetry,[status(thm)],[11559])).
% 23.64/23.82 tff(11561,plain,
% 23.64/23.82 (((~(mult(mult(b, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(b, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))) | (~(mult(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(b, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c))))) | (mult(mult(b, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(b, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))),
% 23.64/23.82 inference(tautology,[status(thm)],[])).
% 23.64/23.82 tff(11562,plain,
% 23.64/23.82 (mult(mult(b, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(b, mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))),
% 23.64/23.82 inference(unit_resolution,[status(thm)],[11561, 11554])).
% 23.64/23.82 tff(11563,plain,
% 23.64/23.82 (mult(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(mult(b, c), mult(a, mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.64/23.82 inference(modus_ponens,[status(thm)],[11562, 11560])).
% 23.64/23.82 tff(11564,plain,
% 23.64/23.82 ($false),
% 23.64/23.82 inference(unit_resolution,[status(thm)],[11540, 11563])).
% 23.64/23.82 tff(11565,plain,((mult(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(mult(b, c), mult(a, mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))), inference(lemma,lemma(discharge,[]))).
% 23.64/23.82 tff(11566,plain,
% 23.64/23.82 (mult(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(mult(b, c), mult(a, mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.64/23.82 inference(unit_resolution,[status(thm)],[11565, 299, 2187])).
% 23.64/23.82 tff(11567,plain,
% 23.64/23.82 (mult(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c)),
% 23.64/23.82 inference(monotonicity,[status(thm)],[7212])).
% 23.64/23.82 tff(11568,assumption,(~(mult(mult(mult(b, a), c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))), c))), introduced(assumption)).
% 23.64/23.82 tff(11569,plain,
% 23.64/23.82 (((~(mult(mult(mult(b, a), c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))), c))) | (~(mult(mult(b, a), mult(c, mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(b, a), mult(mult(a, rd(mult(b, c), mult(a, c))), c))))) | (mult(mult(mult(b, a), c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))), c))),
% 23.64/23.82 inference(tautology,[status(thm)],[])).
% 23.64/23.82 tff(11570,plain,
% 23.64/23.82 ((~(mult(mult(mult(b, a), c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))), c))) | (~(mult(mult(b, a), mult(c, mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(b, a), mult(mult(a, rd(mult(b, c), mult(a, c))), c))))),
% 23.64/23.82 inference(unit_resolution,[status(thm)],[11569, 11568])).
% 23.64/23.82 tff(11571,plain,
% 23.64/23.82 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(b, a), c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(b, a), mult(c, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(b, a), mult(mult(a, rd(mult(b, c), mult(a, c))), c)))))) | (~((~(mult(mult(mult(b, a), c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))), c))) | (~(mult(mult(b, a), mult(c, mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(b, a), mult(mult(a, rd(mult(b, c), mult(a, c))), c)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(b, a), c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(b, a), mult(c, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(b, a), mult(mult(a, rd(mult(b, c), mult(a, c))), c)))))) | (~((~(mult(mult(mult(b, a), c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))), c))) | (~(mult(mult(b, a), mult(c, mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(b, a), mult(mult(a, rd(mult(b, c), mult(a, c))), c)))))))),
% 23.64/23.82 inference(rewrite,[status(thm)],[])).
% 23.64/23.82 tff(11572,plain,
% 23.64/23.82 (((~((~(mult(mult(mult(b, a), c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))), c))) | (~(mult(mult(b, a), mult(c, mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(b, a), mult(mult(a, rd(mult(b, c), mult(a, c))), c)))))) | (~((~(mult(mult(mult(b, a), c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(b, a), mult(c, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(b, a), mult(mult(a, rd(mult(b, c), mult(a, c))), c))))))) <=> ((~((~(mult(mult(mult(b, a), c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(b, a), mult(c, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(b, a), mult(mult(a, rd(mult(b, c), mult(a, c))), c)))))) | (~((~(mult(mult(mult(b, a), c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))), c))) | (~(mult(mult(b, a), mult(c, mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(b, a), mult(mult(a, rd(mult(b, c), mult(a, c))), c)))))))),
% 23.64/23.82 inference(rewrite,[status(thm)],[])).
% 23.64/23.82 tff(11573,plain,
% 23.64/23.82 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(b, a), c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))), c))) | (~(mult(mult(b, a), mult(c, mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(b, a), mult(mult(a, rd(mult(b, c), mult(a, c))), c)))))) | (~((~(mult(mult(mult(b, a), c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(b, a), mult(c, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(b, a), mult(mult(a, rd(mult(b, c), mult(a, c))), c)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(b, a), c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(b, a), mult(c, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(b, a), mult(mult(a, rd(mult(b, c), mult(a, c))), c)))))) | (~((~(mult(mult(mult(b, a), c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))), c))) | (~(mult(mult(b, a), mult(c, mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(b, a), mult(mult(a, rd(mult(b, c), mult(a, c))), c))))))))),
% 23.64/23.82 inference(monotonicity,[status(thm)],[11572])).
% 23.64/23.82 tff(11574,plain,
% 23.64/23.82 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(b, a), c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))), c))) | (~(mult(mult(b, a), mult(c, mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(b, a), mult(mult(a, rd(mult(b, c), mult(a, c))), c)))))) | (~((~(mult(mult(mult(b, a), c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(b, a), mult(c, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(b, a), mult(mult(a, rd(mult(b, c), mult(a, c))), c)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(b, a), c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(b, a), mult(c, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(b, a), mult(mult(a, rd(mult(b, c), mult(a, c))), c)))))) | (~((~(mult(mult(mult(b, a), c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))), c))) | (~(mult(mult(b, a), mult(c, mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(b, a), mult(mult(a, rd(mult(b, c), mult(a, c))), c)))))))),
% 23.64/23.83 inference(transitivity,[status(thm)],[11573, 11571])).
% 23.64/23.83 tff(11575,plain,
% 23.64/23.83 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(b, a), c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))), c))) | (~(mult(mult(b, a), mult(c, mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(b, a), mult(mult(a, rd(mult(b, c), mult(a, c))), c)))))) | (~((~(mult(mult(mult(b, a), c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(b, a), mult(c, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(b, a), mult(mult(a, rd(mult(b, c), mult(a, c))), c)))))))),
% 23.64/23.83 inference(quant_inst,[status(thm)],[])).
% 23.64/23.83 tff(11576,plain,
% 23.64/23.83 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(b, a), c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(b, a), mult(c, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(b, a), mult(mult(a, rd(mult(b, c), mult(a, c))), c)))))) | (~((~(mult(mult(mult(b, a), c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))), c))) | (~(mult(mult(b, a), mult(c, mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(b, a), mult(mult(a, rd(mult(b, c), mult(a, c))), c))))))),
% 23.64/23.83 inference(modus_ponens,[status(thm)],[11575, 11574])).
% 23.64/23.83 tff(11577,plain,
% 23.64/23.83 ((~((~(mult(mult(mult(b, a), c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(b, a), mult(c, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(b, a), mult(mult(a, rd(mult(b, c), mult(a, c))), c)))))) | (~((~(mult(mult(mult(b, a), c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))), c))) | (~(mult(mult(b, a), mult(c, mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(b, a), mult(mult(a, rd(mult(b, c), mult(a, c))), c))))))),
% 23.64/23.83 inference(unit_resolution,[status(thm)],[11576, 27])).
% 23.64/23.83 tff(11578,plain,
% 23.64/23.83 (~((~(mult(mult(mult(b, a), c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(b, a), mult(c, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(b, a), mult(mult(a, rd(mult(b, c), mult(a, c))), c)))))),
% 23.64/23.83 inference(unit_resolution,[status(thm)],[11577, 11570])).
% 23.64/23.83 tff(11579,plain,
% 23.64/23.83 (((~(mult(mult(mult(b, a), c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(b, a), mult(c, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(b, a), mult(mult(a, rd(mult(b, c), mult(a, c))), c))))) | (mult(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(b, a), mult(mult(a, rd(mult(b, c), mult(a, c))), c)))),
% 23.64/23.83 inference(tautology,[status(thm)],[])).
% 23.64/23.83 tff(11580,plain,
% 23.64/23.83 (mult(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(b, a), mult(mult(a, rd(mult(b, c), mult(a, c))), c))),
% 23.64/23.83 inference(unit_resolution,[status(thm)],[11579, 11578])).
% 23.64/23.83 tff(11581,plain,
% 23.64/23.83 (mult(mult(b, a), mult(mult(a, rd(mult(b, c), mult(a, c))), c)) = mult(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))), c)),
% 23.64/23.83 inference(symmetry,[status(thm)],[11580])).
% 23.64/23.83 tff(11582,plain,
% 23.64/23.83 (mult(mult(b, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(b, a), mult(mult(a, rd(mult(b, c), mult(a, c))), c))),
% 23.64/23.83 inference(monotonicity,[status(thm)],[11499])).
% 23.64/23.83 tff(11583,plain,
% 23.64/23.83 (mult(mult(b, a), mult(c, mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(b, a), mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 23.64/23.83 inference(monotonicity,[status(thm)],[10775])).
% 23.64/23.83 tff(11584,plain,
% 23.64/23.83 (((~(mult(mult(mult(b, a), c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(b, a), mult(c, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(b, a), mult(mult(a, rd(mult(b, c), mult(a, c))), c))))) | (mult(mult(mult(b, a), c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(b, a), mult(c, mult(a, rd(mult(b, c), mult(a, c))))))),
% 23.64/23.83 inference(tautology,[status(thm)],[])).
% 23.64/23.83 tff(11585,plain,
% 23.64/23.83 (mult(mult(mult(b, a), c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(b, a), mult(c, mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.64/23.83 inference(unit_resolution,[status(thm)],[11584, 11578])).
% 23.64/23.83 tff(11586,assumption,(mult(mult(b, a), c) = mult(mult(b, c), a)), introduced(assumption)).
% 23.64/23.83 tff(11587,plain,
% 23.64/23.83 (mult(mult(b, c), a) = mult(mult(b, a), c)),
% 23.64/23.83 inference(symmetry,[status(thm)],[11586])).
% 23.64/23.83 tff(11588,plain,
% 23.64/23.83 (mult(c, mult(b, a)) = mult(mult(b, a), c)),
% 23.64/23.83 inference(transitivity,[status(thm)],[4304, 2298, 11587])).
% 23.64/23.83 tff(11589,plain,
% 23.64/23.83 (mult(mult(c, mult(b, a)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(b, a), c), mult(a, rd(mult(b, c), mult(a, c))))),
% 23.64/23.83 inference(monotonicity,[status(thm)],[11588])).
% 23.64/23.83 tff(11590,plain,
% 23.64/23.83 (mult(mult(mult(b, c), a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(c, mult(b, a)), mult(a, rd(mult(b, c), mult(a, c))))),
% 23.64/23.83 inference(monotonicity,[status(thm)],[8708])).
% 23.64/23.83 tff(11591,plain,
% 23.64/23.83 (mult(mult(mult(b, c), a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(b, c), mult(a, mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.64/23.83 inference(transitivity,[status(thm)],[11590, 11589, 11585, 11583, 11582, 11581, 11567, 11566])).
% 23.64/23.83 tff(11592,plain,
% 23.64/23.83 (mult(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))), c)),
% 23.64/23.83 inference(symmetry,[status(thm)],[11567])).
% 23.64/23.83 tff(11593,plain,
% 23.64/23.83 (mult(mult(b, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c)),
% 23.64/23.83 inference(symmetry,[status(thm)],[11566])).
% 23.64/23.83 tff(11594,plain,
% 23.64/23.83 (mult(mult(b, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))), c)),
% 23.64/23.83 inference(transitivity,[status(thm)],[11593, 11592])).
% 23.64/23.83 tff(11595,plain,
% 23.64/23.83 (mult(mult(mult(b, c), a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(b, a), c), mult(a, rd(mult(b, c), mult(a, c))))),
% 23.64/23.83 inference(transitivity,[status(thm)],[11590, 11589])).
% 23.64/23.83 tff(11596,plain,
% 23.64/23.83 ((mult(mult(mult(b, c), a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(b, c), mult(a, mult(a, rd(mult(b, c), mult(a, c)))))) <=> (mult(mult(mult(b, a), c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))), c))),
% 23.64/23.83 inference(monotonicity,[status(thm)],[11595, 11594])).
% 23.64/23.83 tff(11597,plain,
% 23.64/23.83 ((mult(mult(mult(b, a), c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))), c)) <=> (mult(mult(mult(b, c), a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(b, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))))),
% 23.64/23.83 inference(symmetry,[status(thm)],[11596])).
% 23.64/23.83 tff(11598,plain,
% 23.64/23.83 ((~(mult(mult(mult(b, a), c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))), c))) <=> (~(mult(mult(mult(b, c), a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(b, c), mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))),
% 23.64/23.83 inference(monotonicity,[status(thm)],[11597])).
% 23.64/23.83 tff(11599,plain,
% 23.64/23.83 (~(mult(mult(mult(b, c), a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(b, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))))),
% 23.64/23.83 inference(modus_ponens,[status(thm)],[11568, 11598])).
% 23.64/23.83 tff(11600,plain,
% 23.64/23.83 ($false),
% 23.64/23.83 inference(unit_resolution,[status(thm)],[11599, 11591])).
% 23.64/23.83 tff(11601,plain,((mult(mult(mult(b, a), c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))), c)) | (~(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))) | (~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(b, a), c) = mult(mult(b, c), a)))), inference(lemma,lemma(discharge,[]))).
% 23.64/23.83 tff(11602,plain,
% 23.64/23.83 (mult(mult(mult(b, a), c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))), c)),
% 23.64/23.83 inference(unit_resolution,[status(thm)],[11601, 11533, 8165, 281, 11105])).
% 23.64/23.83 tff(11603,plain,
% 23.64/23.83 (mult(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(mult(b, a), c), mult(a, rd(mult(b, c), mult(a, c))))),
% 23.64/23.83 inference(symmetry,[status(thm)],[11602])).
% 23.64/23.83 tff(11604,plain,
% 23.64/23.83 (mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c))))),
% 23.64/23.83 inference(symmetry,[status(thm)],[11533])).
% 23.64/23.83 tff(11605,plain,
% 23.64/23.83 (mult(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))), c)),
% 23.64/23.83 inference(monotonicity,[status(thm)],[11604])).
% 23.64/23.83 tff(11606,plain,
% 23.64/23.83 (mult(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(mult(b, c), mult(a, mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.64/23.83 inference(unit_resolution,[status(thm)],[11565, 281, 8165])).
% 23.64/23.83 tff(11607,plain,
% 23.64/23.83 (mult(mult(b, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c)),
% 23.64/23.83 inference(symmetry,[status(thm)],[11606])).
% 23.64/23.83 tff(11608,plain,
% 23.64/23.83 (mult(mult(c, b), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(b, c), mult(a, mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.64/23.83 inference(monotonicity,[status(thm)],[241])).
% 23.64/23.83 tff(11609,plain,
% 23.64/23.83 ((mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, mult(mult(a, c), c)), unit)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, mult(mult(a, c), c)), unit)))) <=> (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(a, c))), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, mult(a, c)), c)))),
% 23.64/23.83 inference(symmetry,[status(thm)],[10618])).
% 23.64/23.83 tff(11610,plain,
% 23.64/23.83 (mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(c, a))) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a))),
% 23.64/23.83 inference(monotonicity,[status(thm)],[11130])).
% 23.64/23.83 tff(11611,plain,
% 23.64/23.83 (mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(c, a)))),
% 23.64/23.83 inference(symmetry,[status(thm)],[11610])).
% 23.64/23.83 tff(11612,plain,
% 23.64/23.83 (mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, mult(mult(a, c), c)), unit))) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(c, a)))),
% 23.64/23.83 inference(transitivity,[status(thm)],[10606, 10761, 10211, 4661, 10210, 6872, 2631, 11611])).
% 23.64/23.83 tff(11613,plain,
% 23.64/23.83 (mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, a))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))),
% 23.64/23.83 inference(monotonicity,[status(thm)],[11130])).
% 23.64/23.83 tff(11614,plain,
% 23.64/23.83 (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, a))), c) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), c)),
% 23.64/23.83 inference(monotonicity,[status(thm)],[11613])).
% 23.64/23.83 tff(11615,plain,
% 23.64/23.83 (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), c) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, a))), c)),
% 23.64/23.83 inference(symmetry,[status(thm)],[11614])).
% 23.64/23.83 tff(11616,plain,
% 23.64/23.83 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, mult(mult(a, c), c)), unit)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, a))), c)),
% 23.64/23.83 inference(transitivity,[status(thm)],[10610, 10795, 6008, 10794, 11615])).
% 23.64/23.83 tff(11617,plain,
% 23.64/23.83 ((mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, mult(mult(a, c), c)), unit)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, mult(mult(a, c), c)), unit)))) <=> (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, a))), c) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(c, a))))),
% 23.64/23.83 inference(monotonicity,[status(thm)],[11616, 11612])).
% 23.64/23.84 tff(11618,plain,
% 23.64/23.84 ((mult(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, a))), c) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(c, a)))) <=> (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, mult(mult(a, c), c)), unit)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, mult(mult(a, c), c)), unit))))),
% 23.64/23.84 inference(symmetry,[status(thm)],[11617])).
% 23.64/23.84 tff(11619,plain,
% 23.64/23.84 ((mult(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, a))), c) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(c, a)))) <=> (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), c)))),
% 23.64/23.84 inference(transitivity,[status(thm)],[11618, 11609, 9172])).
% 23.64/23.84 tff(11620,plain,
% 23.64/23.84 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, mult(mult(a, c), c)), unit)) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(mult(unit, mult(mult(a, c), c)), unit)))),
% 23.64/23.84 inference(modus_ponens,[status(thm)],[10626, 10618])).
% 23.64/23.84 tff(11621,plain,
% 23.64/23.84 (mult(mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, a))), c) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(c, a)))),
% 23.64/23.84 inference(modus_ponens,[status(thm)],[11620, 11617])).
% 23.64/23.84 tff(11622,plain,
% 23.64/23.84 (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), c))),
% 23.64/23.84 inference(modus_ponens,[status(thm)],[11621, 11619])).
% 23.64/23.84 tff(11623,assumption,(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), c))), introduced(assumption)).
% 23.64/23.84 tff(11624,plain,
% 23.64/23.84 (mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c)))),
% 23.64/23.84 inference(monotonicity,[status(thm)],[9602, 8168])).
% 23.64/23.84 tff(11625,plain,
% 23.64/23.84 (mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a))),
% 23.64/23.84 inference(symmetry,[status(thm)],[11624])).
% 23.64/23.84 tff(11626,plain,
% 23.64/23.84 (mult(rd(mult(b, c), mult(a, c)), mult(c, mult(mult(a, c), a))) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a))),
% 23.64/23.84 inference(symmetry,[status(thm)],[10228])).
% 23.64/23.84 tff(11627,plain,
% 23.64/23.84 (mult(c, mult(mult(a, c), a)) = mult(mult(mult(a, c), unit), mult(a, c))),
% 23.64/23.84 inference(transitivity,[status(thm)],[2562, 6842, 9253, 9247, 2504])).
% 23.64/23.84 tff(11628,plain,
% 23.64/23.84 (mult(rd(mult(b, c), mult(a, c)), mult(c, mult(mult(a, c), a))) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), unit), mult(a, c)))),
% 23.64/23.84 inference(monotonicity,[status(thm)],[11627])).
% 23.64/23.84 tff(11629,plain,
% 23.64/23.84 (mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), unit), mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(mult(a, c), a)))),
% 23.64/23.84 inference(symmetry,[status(thm)],[11628])).
% 23.64/23.84 tff(11630,plain,
% 23.64/23.84 (mult(c, mult(b, mult(a, c))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))),
% 23.64/23.84 inference(transitivity,[status(thm)],[6924, 2429, 5386, 2501, 11629, 11626, 10623, 11625, 10230])).
% 23.64/23.84 tff(11631,plain,
% 23.64/23.84 (ld(c, mult(c, mult(b, mult(a, c)))) = ld(c, mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))),
% 23.64/23.84 inference(monotonicity,[status(thm)],[11630])).
% 23.64/23.84 tff(11632,plain,
% 23.64/23.84 (mult(b, mult(mult(a, c), b)) = mult(mult(b, mult(a, c)), b)),
% 23.64/23.84 inference(symmetry,[status(thm)],[8414])).
% 23.64/23.84 tff(11633,assumption,(mult(mult(c, mult(b, c)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(b, c))), introduced(assumption)).
% 23.64/23.84 tff(11634,plain,
% 23.64/23.84 (mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(b, c)) = mult(mult(c, mult(b, c)), mult(mult(unit, ld(c, mult(a, b))), unit))),
% 23.64/23.84 inference(symmetry,[status(thm)],[11633])).
% 23.64/23.84 tff(11635,plain,
% 23.64/23.84 (mult(mult(a, b), mult(b, c)) = mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(b, c))),
% 23.64/23.84 inference(monotonicity,[status(thm)],[2899])).
% 23.64/23.84 tff(11636,plain,
% 23.64/23.84 (mult(mult(a, mult(b, c)), b) = mult(mult(b, mult(a, c)), b)),
% 23.64/23.84 inference(transitivity,[status(thm)],[806, 11635, 11634, 10904, 10899, 3391, 10878, 11381, 11632])).
% 23.64/23.84 tff(11637,plain,
% 23.64/23.84 (rd(mult(mult(a, mult(b, c)), b), b) = rd(mult(mult(b, mult(a, c)), b), b)),
% 23.64/23.84 inference(monotonicity,[status(thm)],[11636])).
% 23.64/23.84 tff(11638,plain,
% 23.64/23.84 (mult(a, mult(b, c)) = rd(mult(mult(a, mult(b, c)), b), b)),
% 23.64/23.84 inference(symmetry,[status(thm)],[787])).
% 23.64/23.84 tff(11639,plain,
% 23.64/23.84 (mult(a, mult(b, c)) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))),
% 23.64/23.84 inference(transitivity,[status(thm)],[11638, 11637, 8412, 5659, 11631, 6929])).
% 23.64/23.84 tff(11640,plain,
% 23.64/23.84 (mult(mult(a, mult(b, c)), c) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), c)),
% 23.64/23.84 inference(monotonicity,[status(thm)],[11639])).
% 23.64/23.84 tff(11641,plain,
% 23.64/23.84 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(b, c), mult(a, c))),
% 23.64/23.84 inference(transitivity,[status(thm)],[1039, 138, 266, 11640, 11623, 9168, 9245, 9305, 2502, 2499])).
% 23.64/23.84 tff(11642,plain,
% 23.64/23.84 (rd(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)), mult(a, c)) = rd(mult(mult(b, c), mult(a, c)), mult(a, c))),
% 23.64/23.84 inference(monotonicity,[status(thm)],[11641])).
% 23.64/23.84 tff(11643,plain,
% 23.64/23.84 (mult(mult(unit, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(a, c))),
% 23.64/23.84 inference(transitivity,[status(thm)],[4928, 4423, 11642, 4402, 267, 4904, 4902])).
% 23.64/23.84 tff(11644,plain,
% 23.64/23.84 ($false),
% 23.64/23.84 inference(unit_resolution,[status(thm)],[10420, 11643])).
% 23.64/23.84 tff(11645,plain,((~(mult(mult(c, mult(b, c)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(b, c)))) | (mult(mult(unit, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(a, c))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), c)))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(mult(a, c), a))))) | (~(mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(mult(b, mult(a, c)), b) = mult(b, mult(mult(a, c), b))))), inference(lemma,lemma(discharge,[]))).
% 23.64/23.84 tff(11646,plain,
% 23.64/23.84 ((~(mult(mult(c, mult(b, c)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(b, c)))) | (mult(mult(unit, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(unit, rd(mult(b, c), mult(a, c))), mult(a, c))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), c) = mult(rd(mult(b, c), mult(a, c)), mult(mult(mult(a, c), a), c)))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(mult(a, c), a))))) | (~(mult(mult(b, mult(a, c)), b) = mult(b, mult(mult(a, c), b))))),
% 23.64/23.84 inference(unit_resolution,[status(thm)],[11645, 9157])).
% 23.64/23.84 tff(11647,plain,
% 23.64/23.84 (~(mult(mult(c, mult(b, c)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(b, c)))),
% 23.64/23.84 inference(unit_resolution,[status(thm)],[11646, 10584, 316, 11622, 9702, 10194, 10325])).
% 23.64/23.84 tff(11648,plain,
% 23.64/23.84 (((~(mult(mult(c, mult(b, c)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(b, c)))) | (~(mult(c, mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(b, c)))))) | (mult(mult(c, mult(b, c)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(b, c)))),
% 23.64/23.84 inference(tautology,[status(thm)],[])).
% 23.64/23.84 tff(11649,plain,
% 23.64/23.84 ((~(mult(mult(c, mult(b, c)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(b, c)))) | (~(mult(c, mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(b, c)))))),
% 23.64/23.84 inference(unit_resolution,[status(thm)],[11648, 11647])).
% 23.64/23.84 tff(11650,plain,
% 23.64/23.84 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(c, mult(b, c)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(b, c)))) | (~(mult(c, mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(b, c))))))) | (~((~(mult(mult(c, mult(b, c)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(c, mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit))))) | (~(mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(b, c)) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(b, c))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(c, mult(b, c)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(b, c)))) | (~(mult(c, mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(b, c))))))) | (~((~(mult(mult(c, mult(b, c)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(c, mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit))))) | (~(mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(b, c)) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(b, c))))))))),
% 23.64/23.84 inference(rewrite,[status(thm)],[])).
% 23.64/23.84 tff(11651,plain,
% 23.64/23.84 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(c, mult(b, c)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(b, c)))) | (~(mult(c, mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(b, c))))))) | (~((~(mult(mult(c, mult(b, c)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(c, mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit))))) | (~(mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(b, c)) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(b, c))))))))),
% 23.64/23.84 inference(quant_inst,[status(thm)],[])).
% 23.64/23.84 tff(11652,plain,
% 23.64/23.84 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(c, mult(b, c)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(b, c)))) | (~(mult(c, mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(b, c))))))) | (~((~(mult(mult(c, mult(b, c)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(c, mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit))))) | (~(mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(b, c)) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(b, c)))))))),
% 23.68/23.84 inference(modus_ponens,[status(thm)],[11651, 11650])).
% 23.68/23.84 tff(11653,plain,
% 23.68/23.84 ((~((~(mult(mult(c, mult(b, c)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(b, c)))) | (~(mult(c, mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(b, c))))))) | (~((~(mult(mult(c, mult(b, c)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(c, mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit))))) | (~(mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(b, c)) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(b, c)))))))),
% 23.68/23.84 inference(unit_resolution,[status(thm)],[11652, 27])).
% 23.68/23.84 tff(11654,plain,
% 23.68/23.84 (~((~(mult(mult(c, mult(b, c)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(c, mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit))))) | (~(mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(b, c)) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(b, c))))))),
% 23.68/23.84 inference(unit_resolution,[status(thm)],[11653, 11649])).
% 23.68/23.84 tff(11655,plain,
% 23.68/23.84 (((~(mult(mult(c, mult(b, c)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(c, mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit))))) | (~(mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), mult(b, c)) = mult(c, mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(b, c)))))) | (mult(mult(c, mult(b, c)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(c, mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit))))),
% 23.68/23.84 inference(tautology,[status(thm)],[])).
% 23.68/23.84 tff(11656,plain,
% 23.68/23.84 (mult(mult(c, mult(b, c)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(c, mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)))),
% 23.68/23.84 inference(unit_resolution,[status(thm)],[11655, 11654])).
% 23.68/23.84 tff(11657,assumption,(~(mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), b) = mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), b)))), introduced(assumption)).
% 23.68/23.84 tff(11658,plain,
% 23.68/23.84 (((~(mult(mult(c, b), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))) | (~(mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), b) = mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), b))))) | (mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), b) = mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), b)))),
% 23.68/23.84 inference(tautology,[status(thm)],[])).
% 23.68/23.84 tff(11659,plain,
% 23.68/23.84 ((~(mult(mult(c, b), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))) | (~(mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), b) = mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), b))))),
% 23.68/23.84 inference(unit_resolution,[status(thm)],[11658, 11657])).
% 23.68/23.84 tff(11660,plain,
% 23.68/23.84 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(c, b), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))) | (~(mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), b) = mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), b)))))) | (~((~(mult(mult(c, b), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), b))) | (~(mult(c, mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))) = mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), b)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(c, b), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))) | (~(mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), b) = mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), b)))))) | (~((~(mult(mult(c, b), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), b))) | (~(mult(c, mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))) = mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), b)))))))),
% 23.68/23.85 inference(rewrite,[status(thm)],[])).
% 23.68/23.85 tff(11661,plain,
% 23.68/23.85 (((~((~(mult(mult(c, b), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), b))) | (~(mult(c, mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))) = mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), b)))))) | (~((~(mult(mult(c, b), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))) | (~(mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), b) = mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), b))))))) <=> ((~((~(mult(mult(c, b), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))) | (~(mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), b) = mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), b)))))) | (~((~(mult(mult(c, b), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), b))) | (~(mult(c, mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))) = mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), b)))))))),
% 23.68/23.85 inference(rewrite,[status(thm)],[])).
% 23.68/23.85 tff(11662,plain,
% 23.68/23.85 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(c, b), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), b))) | (~(mult(c, mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))) = mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), b)))))) | (~((~(mult(mult(c, b), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))) | (~(mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), b) = mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), b)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(c, b), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))) | (~(mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), b) = mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), b)))))) | (~((~(mult(mult(c, b), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), b))) | (~(mult(c, mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))) = mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), b))))))))),
% 23.68/23.85 inference(monotonicity,[status(thm)],[11661])).
% 23.68/23.85 tff(11663,plain,
% 23.68/23.85 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(c, b), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), b))) | (~(mult(c, mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))) = mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), b)))))) | (~((~(mult(mult(c, b), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))) | (~(mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), b) = mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), b)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(c, b), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))) | (~(mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), b) = mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), b)))))) | (~((~(mult(mult(c, b), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), b))) | (~(mult(c, mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))) = mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), b)))))))),
% 23.68/23.85 inference(transitivity,[status(thm)],[11662, 11660])).
% 23.68/23.85 tff(11664,plain,
% 23.68/23.85 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(c, b), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), b))) | (~(mult(c, mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))) = mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), b)))))) | (~((~(mult(mult(c, b), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))) | (~(mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), b) = mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), b)))))))),
% 23.68/23.85 inference(quant_inst,[status(thm)],[])).
% 23.68/23.85 tff(11665,plain,
% 23.68/23.85 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(c, b), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))) | (~(mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), b) = mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), b)))))) | (~((~(mult(mult(c, b), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), b))) | (~(mult(c, mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))) = mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), b))))))),
% 23.68/23.85 inference(modus_ponens,[status(thm)],[11664, 11663])).
% 23.68/23.85 tff(11666,plain,
% 23.68/23.85 ((~((~(mult(mult(c, b), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))) | (~(mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), b) = mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), b)))))) | (~((~(mult(mult(c, b), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), b))) | (~(mult(c, mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))) = mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), b))))))),
% 23.68/23.85 inference(unit_resolution,[status(thm)],[11665, 27])).
% 23.68/23.85 tff(11667,plain,
% 23.68/23.85 (~((~(mult(mult(c, b), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), b))) | (~(mult(c, mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))) = mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), b)))))),
% 23.68/23.85 inference(unit_resolution,[status(thm)],[11666, 11659])).
% 23.68/23.85 tff(11668,plain,
% 23.68/23.85 (((~(mult(mult(c, b), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), b))) | (~(mult(c, mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))) = mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), b))))) | (mult(c, mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))) = mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), b)))),
% 23.68/23.85 inference(tautology,[status(thm)],[])).
% 23.68/23.85 tff(11669,plain,
% 23.68/23.85 (mult(c, mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))) = mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), b))),
% 23.68/23.85 inference(unit_resolution,[status(thm)],[11668, 11667])).
% 23.68/23.85 tff(11670,plain,
% 23.68/23.85 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c), c) = mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)))),
% 23.68/23.85 inference(quant_inst,[status(thm)],[])).
% 23.68/23.85 tff(11671,plain,
% 23.68/23.85 (rd(mult(mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c), c) = mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit))),
% 23.68/23.85 inference(unit_resolution,[status(thm)],[11670, 168])).
% 23.68/23.85 tff(11672,assumption,(mult(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(mult(b, c), mult(a, mult(a, rd(mult(b, c), mult(a, c)))))), introduced(assumption)).
% 23.68/23.85 tff(11673,plain,
% 23.68/23.85 (mult(mult(b, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c)),
% 23.68/23.85 inference(symmetry,[status(thm)],[11672])).
% 23.68/23.85 tff(11674,plain,
% 23.68/23.85 (mult(mult(b, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(c, b), mult(a, mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.68/23.85 inference(monotonicity,[status(thm)],[1399])).
% 23.68/23.85 tff(11675,plain,
% 23.68/23.85 (mult(mult(c, b), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(b, c), mult(a, mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.68/23.85 inference(symmetry,[status(thm)],[11674])).
% 23.68/23.85 tff(11676,plain,
% 23.68/23.85 (((~(mult(mult(c, b), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), b))) | (~(mult(c, mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))) = mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), b))))) | (mult(mult(c, b), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), b))),
% 23.68/23.85 inference(tautology,[status(thm)],[])).
% 23.68/23.85 tff(11677,plain,
% 23.68/23.85 (mult(mult(c, b), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), b)),
% 23.68/23.85 inference(unit_resolution,[status(thm)],[11676, 11667])).
% 23.68/23.85 tff(11678,plain,
% 23.68/23.85 (mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), b) = mult(mult(c, b), mult(a, mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.68/23.85 inference(symmetry,[status(thm)],[11677])).
% 23.68/23.85 tff(11679,plain,
% 23.68/23.85 (mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))),
% 23.68/23.85 inference(transitivity,[status(thm)],[10028, 8240])).
% 23.68/23.85 tff(11680,plain,
% 23.68/23.85 (mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), b) = mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), b)),
% 23.68/23.85 inference(monotonicity,[status(thm)],[11679])).
% 23.68/23.85 tff(11681,plain,
% 23.68/23.85 (mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), b) = mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), b)),
% 23.68/23.85 inference(symmetry,[status(thm)],[11680])).
% 23.68/23.85 tff(11682,plain,
% 23.68/23.85 (mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), b) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), b)),
% 23.68/23.85 inference(monotonicity,[status(thm)],[11124])).
% 23.68/23.85 tff(11683,plain,
% 23.68/23.85 (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), b) = mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), b)),
% 23.68/23.85 inference(symmetry,[status(thm)],[11682])).
% 23.68/23.85 tff(11684,plain,
% 23.68/23.85 (mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a))),
% 23.68/23.85 inference(symmetry,[status(thm)],[10229])).
% 23.68/23.85 tff(11685,plain,
% 23.68/23.85 (mult(c, mult(b, mult(a, c))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))),
% 23.68/23.85 inference(transitivity,[status(thm)],[10799, 2429, 5386, 2501, 10211, 4661, 10210, 6872, 2631, 11684, 10230])).
% 23.68/23.85 tff(11686,plain,
% 23.68/23.85 (ld(c, mult(c, mult(b, mult(a, c)))) = ld(c, mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))),
% 23.68/23.85 inference(monotonicity,[status(thm)],[11685])).
% 23.68/23.85 tff(11687,plain,
% 23.68/23.85 (ld(c, mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) = ld(c, mult(c, mult(b, mult(a, c))))),
% 23.68/23.85 inference(symmetry,[status(thm)],[11686])).
% 23.68/23.85 tff(11688,plain,
% 23.68/23.85 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)) = mult(b, mult(a, c))),
% 23.68/23.85 inference(transitivity,[status(thm)],[6930, 11687, 5658])).
% 23.68/23.85 tff(11689,plain,
% 23.68/23.85 (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), b) = mult(mult(b, mult(a, c)), b)),
% 23.68/23.85 inference(monotonicity,[status(thm)],[11688])).
% 23.68/23.85 tff(11690,plain,
% 23.68/23.85 (mult(mult(b, mult(a, c)), b) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)), b)),
% 23.68/23.85 inference(symmetry,[status(thm)],[11689])).
% 23.68/23.85 tff(11691,plain,
% 23.68/23.85 (mult(mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c) = mult(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c)),
% 23.68/23.85 inference(transitivity,[status(thm)],[3391, 10878, 11381, 11632, 11690, 11683, 11681, 11678, 11675, 11673])).
% 23.68/23.85 tff(11692,plain,
% 23.68/23.85 (rd(mult(mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c), c) = rd(mult(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c), c)),
% 23.68/23.85 inference(monotonicity,[status(thm)],[11691])).
% 23.68/23.85 tff(11693,plain,
% 23.68/23.85 (rd(mult(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c), c) = rd(mult(mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)), c), c)),
% 23.68/23.85 inference(symmetry,[status(thm)],[11692])).
% 23.68/23.85 tff(11694,plain,
% 23.68/23.85 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c), c) = mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))),
% 23.68/23.85 inference(quant_inst,[status(thm)],[])).
% 23.68/23.85 tff(11695,plain,
% 23.68/23.85 (rd(mult(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c), c) = mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.68/23.85 inference(unit_resolution,[status(thm)],[11694, 168])).
% 23.68/23.85 tff(11696,plain,
% 23.68/23.85 (mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = rd(mult(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c), c)),
% 23.68/23.85 inference(symmetry,[status(thm)],[11695])).
% 23.68/23.85 tff(11697,plain,
% 23.68/23.85 (mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit))),
% 23.68/23.85 inference(transitivity,[status(thm)],[11696, 11693, 11671])).
% 23.68/23.85 tff(11698,plain,
% 23.68/23.85 (mult(c, mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))) = mult(c, mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)))),
% 23.68/23.85 inference(monotonicity,[status(thm)],[11697])).
% 23.68/23.85 tff(11699,plain,
% 23.68/23.85 (mult(c, mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit))) = mult(c, mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))),
% 23.68/23.85 inference(symmetry,[status(thm)],[11698])).
% 23.68/23.85 tff(11700,assumption,(mult(mult(c, mult(b, c)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(c, mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit)))), introduced(assumption)).
% 23.68/23.85 tff(11701,plain,
% 23.68/23.85 (mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), b) = mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), b))),
% 23.68/23.85 inference(transitivity,[status(thm)],[11680, 11682, 11689, 8414, 5603, 10877, 10912, 10911, 10903, 11700, 11699, 11669])).
% 23.68/23.85 tff(11702,plain,
% 23.68/23.85 ($false),
% 23.68/23.85 inference(unit_resolution,[status(thm)],[11657, 11701])).
% 23.68/23.85 tff(11703,plain,((mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), b) = mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), b))) | (~(mult(mult(b, mult(a, c)), b) = mult(b, mult(mult(a, c), b)))) | (~(mult(mult(c, mult(b, c)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(c, mult(mult(b, c), mult(mult(unit, ld(c, mult(a, b))), unit))))) | (~(mult(mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), c) = mult(mult(b, c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))) | (~(mult(b, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) = mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(c, a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))), inference(lemma,lemma(discharge,[]))).
% 23.68/23.86 tff(11704,plain,
% 23.68/23.86 (mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), b) = mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), b))),
% 23.68/23.86 inference(unit_resolution,[status(thm)],[11703, 11112, 10006, 11656, 9702, 11606, 10584])).
% 23.68/23.86 tff(11705,assumption,(~(mult(mult(c, b), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))), introduced(assumption)).
% 23.68/23.86 tff(11706,plain,
% 23.68/23.86 (((~(mult(mult(c, b), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))) | (~(mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), b) = mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), b))))) | (mult(mult(c, b), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))),
% 23.68/23.86 inference(tautology,[status(thm)],[])).
% 23.68/23.86 tff(11707,plain,
% 23.68/23.86 ((~(mult(mult(c, b), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))) | (~(mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), b) = mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), b))))),
% 23.68/23.86 inference(unit_resolution,[status(thm)],[11706, 11705])).
% 23.68/23.86 tff(11708,plain,
% 23.68/23.86 (~((~(mult(mult(c, b), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), b))) | (~(mult(c, mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))) = mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), b)))))),
% 23.68/23.86 inference(unit_resolution,[status(thm)],[11666, 11707])).
% 23.68/23.86 tff(11709,plain,
% 23.68/23.86 (mult(c, mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))) = mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), b))),
% 23.68/23.86 inference(unit_resolution,[status(thm)],[11668, 11708])).
% 23.68/23.86 tff(11710,plain,
% 23.68/23.86 (mult(mult(c, b), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), b)),
% 23.68/23.86 inference(unit_resolution,[status(thm)],[11676, 11708])).
% 23.68/23.86 tff(11711,plain,
% 23.68/23.86 ((mult(mult(c, b), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) <=> (mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), b) = mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), b)))),
% 23.68/23.86 inference(monotonicity,[status(thm)],[11710, 11709])).
% 23.68/23.86 tff(11712,plain,
% 23.68/23.86 ((mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), b) = mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), b))) <=> (mult(mult(c, b), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))),
% 23.68/23.86 inference(symmetry,[status(thm)],[11711])).
% 23.68/23.86 tff(11713,assumption,(mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), b) = mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), b))), introduced(assumption)).
% 23.68/23.86 tff(11714,plain,
% 23.68/23.86 (mult(mult(c, b), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))),
% 23.68/23.86 inference(modus_ponens,[status(thm)],[11713, 11712])).
% 23.68/23.86 tff(11715,plain,
% 23.68/23.86 ($false),
% 23.68/23.86 inference(unit_resolution,[status(thm)],[11705, 11714])).
% 23.68/23.86 tff(11716,plain,((mult(mult(c, b), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(c, mult(a, mult(a, rd(mult(b, c), mult(a, c))))), b) = mult(c, mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), b))))), inference(lemma,lemma(discharge,[]))).
% 23.68/23.86 tff(11717,plain,
% 23.68/23.86 (mult(mult(c, b), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(c, mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))),
% 23.68/23.86 inference(unit_resolution,[status(thm)],[11716, 11704])).
% 23.68/23.86 tff(11718,plain,
% 23.68/23.86 (mult(c, mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))) = mult(mult(c, b), mult(a, mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.68/23.86 inference(symmetry,[status(thm)],[11717])).
% 23.68/23.86 tff(11719,plain,
% 23.68/23.86 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(a, c), mult(mult(a, c), mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) = mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))),
% 23.68/23.86 inference(quant_inst,[status(thm)],[])).
% 23.68/23.86 tff(11720,plain,
% 23.68/23.86 (ld(mult(a, c), mult(mult(a, c), mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) = mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.68/23.86 inference(unit_resolution,[status(thm)],[11719, 7])).
% 23.68/23.86 tff(11721,plain,
% 23.68/23.86 (mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b)))) = mult(mult(a, c), mult(mult(unit, a), mult(mult(b, unit), b)))),
% 23.68/23.86 inference(symmetry,[status(thm)],[7303])).
% 23.68/23.86 tff(11722,plain,
% 23.68/23.86 (mult(mult(a, c), mult(mult(a, b), b)) = mult(mult(a, c), mult(a, mult(unit, mult(mult(b, unit), b))))),
% 23.68/23.86 inference(symmetry,[status(thm)],[1093])).
% 23.68/23.86 tff(11723,plain,
% 23.68/23.86 (ld(b, mult(b, mult(mult(a, c), mult(a, b)))) = ld(b, mult(b, mult(mult(mult(b, c), a), a)))),
% 23.68/23.86 inference(symmetry,[status(thm)],[11486])).
% 23.68/23.86 tff(11724,plain,
% 23.68/23.86 (mult(mult(a, c), mult(a, b)) = mult(mult(mult(b, c), a), a)),
% 23.68/23.86 inference(transitivity,[status(thm)],[11419, 11723, 11488])).
% 23.68/23.86 tff(11725,plain,
% 23.68/23.86 (mult(mult(mult(a, c), mult(a, b)), b) = mult(mult(mult(mult(b, c), a), a), b)),
% 23.68/23.86 inference(monotonicity,[status(thm)],[11724])).
% 23.68/23.86 tff(11726,plain,
% 23.68/23.86 (mult(mult(mult(mult(b, c), a), a), b) = mult(mult(mult(a, c), mult(a, b)), b)),
% 23.68/23.86 inference(symmetry,[status(thm)],[11725])).
% 23.68/23.86 tff(11727,plain,
% 23.68/23.86 (mult(mult(mult(mult(b, c), a), a), b) = mult(mult(b, mult(mult(a, c), a)), b)),
% 23.68/23.86 inference(monotonicity,[status(thm)],[11483])).
% 23.68/23.86 tff(11728,plain,
% 23.68/23.86 (mult(mult(b, mult(mult(a, c), a)), b) = mult(mult(mult(mult(b, c), a), a), b)),
% 23.68/23.86 inference(symmetry,[status(thm)],[11727])).
% 23.68/23.86 tff(11729,plain,
% 23.68/23.86 (((~(mult(b, mult(mult(mult(a, c), a), b)) = mult(b, mult(b, mult(mult(a, c), a))))) | (~(mult(mult(b, mult(mult(a, c), a)), b) = mult(mult(b, b), mult(mult(a, c), a))))) | (mult(mult(b, mult(mult(a, c), a)), b) = mult(mult(b, b), mult(mult(a, c), a)))),
% 23.68/23.86 inference(tautology,[status(thm)],[])).
% 23.68/23.86 tff(11730,plain,
% 23.68/23.86 (mult(mult(b, mult(mult(a, c), a)), b) = mult(mult(b, b), mult(mult(a, c), a))),
% 23.68/23.86 inference(unit_resolution,[status(thm)],[11729, 11478])).
% 23.68/23.86 tff(11731,plain,
% 23.68/23.86 (mult(mult(b, b), mult(mult(a, c), a)) = mult(mult(b, mult(mult(a, c), a)), b)),
% 23.68/23.86 inference(symmetry,[status(thm)],[11730])).
% 23.68/23.86 tff(11732,plain,
% 23.68/23.86 (mult(mult(b, b), mult(mult(a, c), a)) = mult(mult(unit, mult(mult(b, unit), b)), mult(mult(a, c), a))),
% 23.68/23.86 inference(monotonicity,[status(thm)],[433])).
% 23.68/23.86 tff(11733,plain,
% 23.68/23.86 (mult(mult(unit, mult(mult(b, unit), b)), mult(mult(a, c), a)) = mult(mult(b, b), mult(mult(a, c), a))),
% 23.68/23.86 inference(symmetry,[status(thm)],[11732])).
% 23.68/23.86 tff(11734,plain,
% 23.68/23.86 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(unit, mult(mult(b, unit), b)), a), c), a) = mult(mult(unit, mult(mult(b, unit), b)), mult(mult(a, c), a)))),
% 23.68/23.86 inference(quant_inst,[status(thm)],[])).
% 23.68/23.86 tff(11735,plain,
% 23.68/23.86 (mult(mult(mult(mult(unit, mult(mult(b, unit), b)), a), c), a) = mult(mult(unit, mult(mult(b, unit), b)), mult(mult(a, c), a))),
% 23.68/23.86 inference(unit_resolution,[status(thm)],[11734, 56])).
% 23.68/23.86 tff(11736,plain,
% 23.68/23.86 (mult(mult(a, mult(unit, mult(mult(b, unit), b))), c) = mult(mult(mult(a, b), b), c)),
% 23.68/23.86 inference(monotonicity,[status(thm)],[1092])).
% 23.68/23.86 tff(11737,plain,
% 23.68/23.86 (mult(a, mult(mult(b, b), c)) = mult(a, mult(mult(b, c), b))),
% 23.68/23.86 inference(transitivity,[status(thm)],[7099, 893, 11736, 828, 781])).
% 23.68/23.86 tff(11738,plain,
% 23.68/23.86 (ld(a, mult(a, mult(mult(b, b), c))) = ld(a, mult(a, mult(mult(b, c), b)))),
% 23.68/23.86 inference(monotonicity,[status(thm)],[11737])).
% 23.68/23.86 tff(11739,plain,
% 23.68/23.86 (mult(mult(unit, mult(mult(b, unit), b)), c) = mult(mult(b, c), b)),
% 23.68/23.86 inference(transitivity,[status(thm)],[7097, 7104, 11738, 5563])).
% 23.68/23.86 tff(11740,plain,
% 23.68/23.86 (mult(mult(mult(unit, mult(mult(b, unit), b)), c), a) = mult(mult(mult(b, c), b), a)),
% 23.68/23.86 inference(monotonicity,[status(thm)],[11739])).
% 23.68/23.86 tff(11741,assumption,(~(mult(mult(mult(unit, mult(mult(b, unit), b)), a), c) = mult(mult(mult(unit, mult(mult(b, unit), b)), c), a))), introduced(assumption)).
% 23.68/23.86 tff(11742,plain,
% 23.68/23.86 (((~(mult(mult(unit, mult(mult(b, unit), b)), mult(a, c)) = mult(mult(unit, mult(mult(b, unit), b)), mult(c, a)))) | (~(mult(mult(mult(unit, mult(mult(b, unit), b)), a), c) = mult(mult(mult(unit, mult(mult(b, unit), b)), c), a)))) | (mult(mult(mult(unit, mult(mult(b, unit), b)), a), c) = mult(mult(mult(unit, mult(mult(b, unit), b)), c), a))),
% 23.68/23.86 inference(tautology,[status(thm)],[])).
% 23.68/23.86 tff(11743,plain,
% 23.68/23.86 ((~(mult(mult(unit, mult(mult(b, unit), b)), mult(a, c)) = mult(mult(unit, mult(mult(b, unit), b)), mult(c, a)))) | (~(mult(mult(mult(unit, mult(mult(b, unit), b)), a), c) = mult(mult(mult(unit, mult(mult(b, unit), b)), c), a)))),
% 23.68/23.86 inference(unit_resolution,[status(thm)],[11742, 11741])).
% 23.68/23.86 tff(11744,plain,
% 23.68/23.86 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(unit, mult(mult(b, unit), b)), mult(a, c)) = mult(mult(unit, mult(mult(b, unit), b)), mult(c, a)))) | (~(mult(mult(mult(unit, mult(mult(b, unit), b)), a), c) = mult(mult(mult(unit, mult(mult(b, unit), b)), c), a))))) | (~((~(mult(mult(mult(unit, mult(mult(b, unit), b)), a), c) = mult(mult(unit, mult(mult(b, unit), b)), mult(a, c)))) | (~(mult(mult(mult(unit, mult(mult(b, unit), b)), c), a) = mult(mult(unit, mult(mult(b, unit), b)), mult(c, a)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(unit, mult(mult(b, unit), b)), mult(a, c)) = mult(mult(unit, mult(mult(b, unit), b)), mult(c, a)))) | (~(mult(mult(mult(unit, mult(mult(b, unit), b)), a), c) = mult(mult(mult(unit, mult(mult(b, unit), b)), c), a))))) | (~((~(mult(mult(mult(unit, mult(mult(b, unit), b)), a), c) = mult(mult(unit, mult(mult(b, unit), b)), mult(a, c)))) | (~(mult(mult(mult(unit, mult(mult(b, unit), b)), c), a) = mult(mult(unit, mult(mult(b, unit), b)), mult(c, a)))))))),
% 23.68/23.86 inference(rewrite,[status(thm)],[])).
% 23.68/23.86 tff(11745,plain,
% 23.68/23.86 (((~((~(mult(mult(mult(unit, mult(mult(b, unit), b)), a), c) = mult(mult(mult(unit, mult(mult(b, unit), b)), c), a))) | (~(mult(mult(unit, mult(mult(b, unit), b)), mult(a, c)) = mult(mult(unit, mult(mult(b, unit), b)), mult(c, a)))))) | (~((~(mult(mult(mult(unit, mult(mult(b, unit), b)), a), c) = mult(mult(unit, mult(mult(b, unit), b)), mult(a, c)))) | (~(mult(mult(mult(unit, mult(mult(b, unit), b)), c), a) = mult(mult(unit, mult(mult(b, unit), b)), mult(c, a))))))) <=> ((~((~(mult(mult(unit, mult(mult(b, unit), b)), mult(a, c)) = mult(mult(unit, mult(mult(b, unit), b)), mult(c, a)))) | (~(mult(mult(mult(unit, mult(mult(b, unit), b)), a), c) = mult(mult(mult(unit, mult(mult(b, unit), b)), c), a))))) | (~((~(mult(mult(mult(unit, mult(mult(b, unit), b)), a), c) = mult(mult(unit, mult(mult(b, unit), b)), mult(a, c)))) | (~(mult(mult(mult(unit, mult(mult(b, unit), b)), c), a) = mult(mult(unit, mult(mult(b, unit), b)), mult(c, a)))))))),
% 23.68/23.86 inference(rewrite,[status(thm)],[])).
% 23.68/23.86 tff(11746,plain,
% 23.68/23.86 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(unit, mult(mult(b, unit), b)), a), c) = mult(mult(mult(unit, mult(mult(b, unit), b)), c), a))) | (~(mult(mult(unit, mult(mult(b, unit), b)), mult(a, c)) = mult(mult(unit, mult(mult(b, unit), b)), mult(c, a)))))) | (~((~(mult(mult(mult(unit, mult(mult(b, unit), b)), a), c) = mult(mult(unit, mult(mult(b, unit), b)), mult(a, c)))) | (~(mult(mult(mult(unit, mult(mult(b, unit), b)), c), a) = mult(mult(unit, mult(mult(b, unit), b)), mult(c, a)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(unit, mult(mult(b, unit), b)), mult(a, c)) = mult(mult(unit, mult(mult(b, unit), b)), mult(c, a)))) | (~(mult(mult(mult(unit, mult(mult(b, unit), b)), a), c) = mult(mult(mult(unit, mult(mult(b, unit), b)), c), a))))) | (~((~(mult(mult(mult(unit, mult(mult(b, unit), b)), a), c) = mult(mult(unit, mult(mult(b, unit), b)), mult(a, c)))) | (~(mult(mult(mult(unit, mult(mult(b, unit), b)), c), a) = mult(mult(unit, mult(mult(b, unit), b)), mult(c, a))))))))),
% 23.68/23.86 inference(monotonicity,[status(thm)],[11745])).
% 23.68/23.86 tff(11747,plain,
% 23.68/23.86 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(unit, mult(mult(b, unit), b)), a), c) = mult(mult(mult(unit, mult(mult(b, unit), b)), c), a))) | (~(mult(mult(unit, mult(mult(b, unit), b)), mult(a, c)) = mult(mult(unit, mult(mult(b, unit), b)), mult(c, a)))))) | (~((~(mult(mult(mult(unit, mult(mult(b, unit), b)), a), c) = mult(mult(unit, mult(mult(b, unit), b)), mult(a, c)))) | (~(mult(mult(mult(unit, mult(mult(b, unit), b)), c), a) = mult(mult(unit, mult(mult(b, unit), b)), mult(c, a)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(unit, mult(mult(b, unit), b)), mult(a, c)) = mult(mult(unit, mult(mult(b, unit), b)), mult(c, a)))) | (~(mult(mult(mult(unit, mult(mult(b, unit), b)), a), c) = mult(mult(mult(unit, mult(mult(b, unit), b)), c), a))))) | (~((~(mult(mult(mult(unit, mult(mult(b, unit), b)), a), c) = mult(mult(unit, mult(mult(b, unit), b)), mult(a, c)))) | (~(mult(mult(mult(unit, mult(mult(b, unit), b)), c), a) = mult(mult(unit, mult(mult(b, unit), b)), mult(c, a)))))))),
% 23.68/23.86 inference(transitivity,[status(thm)],[11746, 11744])).
% 23.68/23.86 tff(11748,plain,
% 23.68/23.86 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(unit, mult(mult(b, unit), b)), a), c) = mult(mult(mult(unit, mult(mult(b, unit), b)), c), a))) | (~(mult(mult(unit, mult(mult(b, unit), b)), mult(a, c)) = mult(mult(unit, mult(mult(b, unit), b)), mult(c, a)))))) | (~((~(mult(mult(mult(unit, mult(mult(b, unit), b)), a), c) = mult(mult(unit, mult(mult(b, unit), b)), mult(a, c)))) | (~(mult(mult(mult(unit, mult(mult(b, unit), b)), c), a) = mult(mult(unit, mult(mult(b, unit), b)), mult(c, a)))))))),
% 23.68/23.86 inference(quant_inst,[status(thm)],[])).
% 23.68/23.86 tff(11749,plain,
% 23.68/23.86 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(unit, mult(mult(b, unit), b)), mult(a, c)) = mult(mult(unit, mult(mult(b, unit), b)), mult(c, a)))) | (~(mult(mult(mult(unit, mult(mult(b, unit), b)), a), c) = mult(mult(mult(unit, mult(mult(b, unit), b)), c), a))))) | (~((~(mult(mult(mult(unit, mult(mult(b, unit), b)), a), c) = mult(mult(unit, mult(mult(b, unit), b)), mult(a, c)))) | (~(mult(mult(mult(unit, mult(mult(b, unit), b)), c), a) = mult(mult(unit, mult(mult(b, unit), b)), mult(c, a))))))),
% 23.68/23.86 inference(modus_ponens,[status(thm)],[11748, 11747])).
% 23.68/23.86 tff(11750,plain,
% 23.68/23.86 ((~((~(mult(mult(unit, mult(mult(b, unit), b)), mult(a, c)) = mult(mult(unit, mult(mult(b, unit), b)), mult(c, a)))) | (~(mult(mult(mult(unit, mult(mult(b, unit), b)), a), c) = mult(mult(mult(unit, mult(mult(b, unit), b)), c), a))))) | (~((~(mult(mult(mult(unit, mult(mult(b, unit), b)), a), c) = mult(mult(unit, mult(mult(b, unit), b)), mult(a, c)))) | (~(mult(mult(mult(unit, mult(mult(b, unit), b)), c), a) = mult(mult(unit, mult(mult(b, unit), b)), mult(c, a))))))),
% 23.68/23.87 inference(unit_resolution,[status(thm)],[11749, 27])).
% 23.68/23.87 tff(11751,plain,
% 23.68/23.87 (~((~(mult(mult(mult(unit, mult(mult(b, unit), b)), a), c) = mult(mult(unit, mult(mult(b, unit), b)), mult(a, c)))) | (~(mult(mult(mult(unit, mult(mult(b, unit), b)), c), a) = mult(mult(unit, mult(mult(b, unit), b)), mult(c, a)))))),
% 23.68/23.87 inference(unit_resolution,[status(thm)],[11750, 11743])).
% 23.68/23.87 tff(11752,plain,
% 23.68/23.87 (((~(mult(mult(mult(unit, mult(mult(b, unit), b)), a), c) = mult(mult(unit, mult(mult(b, unit), b)), mult(a, c)))) | (~(mult(mult(mult(unit, mult(mult(b, unit), b)), c), a) = mult(mult(unit, mult(mult(b, unit), b)), mult(c, a))))) | (mult(mult(mult(unit, mult(mult(b, unit), b)), c), a) = mult(mult(unit, mult(mult(b, unit), b)), mult(c, a)))),
% 23.68/23.87 inference(tautology,[status(thm)],[])).
% 23.68/23.87 tff(11753,plain,
% 23.68/23.87 (mult(mult(mult(unit, mult(mult(b, unit), b)), c), a) = mult(mult(unit, mult(mult(b, unit), b)), mult(c, a))),
% 23.68/23.87 inference(unit_resolution,[status(thm)],[11752, 11751])).
% 23.68/23.87 tff(11754,plain,
% 23.68/23.87 (mult(mult(unit, mult(mult(b, unit), b)), mult(c, a)) = mult(mult(mult(unit, mult(mult(b, unit), b)), c), a)),
% 23.68/23.87 inference(symmetry,[status(thm)],[11753])).
% 23.68/23.87 tff(11755,plain,
% 23.68/23.87 (mult(mult(unit, mult(mult(b, unit), b)), mult(a, c)) = mult(mult(unit, mult(mult(b, unit), b)), mult(c, a))),
% 23.68/23.87 inference(monotonicity,[status(thm)],[6891])).
% 23.68/23.87 tff(11756,plain,
% 23.68/23.87 (((~(mult(mult(mult(unit, mult(mult(b, unit), b)), a), c) = mult(mult(unit, mult(mult(b, unit), b)), mult(a, c)))) | (~(mult(mult(mult(unit, mult(mult(b, unit), b)), c), a) = mult(mult(unit, mult(mult(b, unit), b)), mult(c, a))))) | (mult(mult(mult(unit, mult(mult(b, unit), b)), a), c) = mult(mult(unit, mult(mult(b, unit), b)), mult(a, c)))),
% 23.68/23.87 inference(tautology,[status(thm)],[])).
% 23.68/23.87 tff(11757,plain,
% 23.68/23.87 (mult(mult(mult(unit, mult(mult(b, unit), b)), a), c) = mult(mult(unit, mult(mult(b, unit), b)), mult(a, c))),
% 23.68/23.87 inference(unit_resolution,[status(thm)],[11756, 11751])).
% 23.68/23.87 tff(11758,plain,
% 23.68/23.87 (mult(mult(mult(unit, mult(mult(b, unit), b)), a), c) = mult(mult(mult(unit, mult(mult(b, unit), b)), c), a)),
% 23.68/23.87 inference(transitivity,[status(thm)],[11757, 11755, 11754])).
% 23.68/23.87 tff(11759,plain,
% 23.68/23.87 ($false),
% 23.68/23.87 inference(unit_resolution,[status(thm)],[11741, 11758])).
% 23.68/23.87 tff(11760,plain,(mult(mult(mult(unit, mult(mult(b, unit), b)), a), c) = mult(mult(mult(unit, mult(mult(b, unit), b)), c), a)), inference(lemma,lemma(discharge,[]))).
% 23.68/23.87 tff(11761,plain,
% 23.68/23.87 (mult(mult(mult(unit, mult(mult(b, unit), b)), a), c) = mult(mult(mult(mult(b, c), b), a), unit)),
% 23.68/23.87 inference(transitivity,[status(thm)],[11760, 11740, 3074])).
% 23.68/23.87 tff(11762,plain,
% 23.68/23.87 (mult(mult(mult(mult(unit, mult(mult(b, unit), b)), a), c), a) = mult(mult(mult(mult(mult(b, c), b), a), unit), a)),
% 23.68/23.87 inference(monotonicity,[status(thm)],[11761])).
% 23.68/23.87 tff(11763,plain,
% 23.68/23.87 (mult(mult(mult(mult(mult(b, c), b), a), unit), a) = mult(mult(mult(mult(unit, mult(mult(b, unit), b)), a), c), a)),
% 23.68/23.87 inference(symmetry,[status(thm)],[11762])).
% 23.68/23.87 tff(11764,plain,
% 23.68/23.87 (mult(a, mult(mult(unit, mult(mult(b, unit), b)), c)) = mult(a, mult(mult(b, b), c))),
% 23.68/23.87 inference(symmetry,[status(thm)],[7099])).
% 23.68/23.87 tff(11765,plain,
% 23.68/23.87 (mult(mult(mult(a, b), b), c) = mult(mult(a, mult(unit, mult(mult(b, unit), b))), c)),
% 23.68/23.87 inference(symmetry,[status(thm)],[11736])).
% 23.68/23.87 tff(11766,plain,
% 23.68/23.87 (((~(mult(mult(a, mult(mult(a, b), c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(mult(a, b), c)))) | (~(mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)))))) | (mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c))))),
% 23.68/23.87 inference(tautology,[status(thm)],[])).
% 23.68/23.87 tff(11767,plain,
% 23.68/23.87 (mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)))),
% 23.68/23.87 inference(unit_resolution,[status(thm)],[11766, 11085])).
% 23.68/23.87 tff(11768,plain,
% 23.68/23.87 (mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(b, b), c))),
% 23.68/23.87 inference(transitivity,[status(thm)],[11767, 11071, 778, 783, 827, 11765, 892, 11764])).
% 23.68/23.87 tff(11769,plain,
% 23.68/23.87 (ld(a, mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))))) = ld(a, mult(a, mult(mult(b, b), c)))),
% 23.68/23.87 inference(monotonicity,[status(thm)],[11768])).
% 23.68/23.87 tff(11770,plain,
% 23.68/23.87 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(a, mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))))) = mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))))),
% 23.68/23.87 inference(quant_inst,[status(thm)],[])).
% 23.68/23.87 tff(11771,plain,
% 23.68/23.87 (ld(a, mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))))) = mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))),
% 23.68/23.87 inference(unit_resolution,[status(thm)],[11770, 7])).
% 23.68/23.87 tff(11772,plain,
% 23.68/23.87 (mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))) = ld(a, mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))))),
% 23.68/23.87 inference(symmetry,[status(thm)],[11771])).
% 23.68/23.87 tff(11773,plain,
% 23.68/23.87 (mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))) = mult(mult(b, c), b)),
% 23.68/23.87 inference(transitivity,[status(thm)],[11772, 11769, 11738, 5563])).
% 23.68/23.87 tff(11774,plain,
% 23.68/23.87 (mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(mult(mult(b, c), b), mult(a, a))),
% 23.68/23.87 inference(monotonicity,[status(thm)],[11773])).
% 23.68/23.87 tff(11775,plain,
% 23.68/23.87 (mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), mult(mult(a, unit), a)) = mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), mult(a, a))),
% 23.68/23.87 inference(monotonicity,[status(thm)],[519])).
% 23.68/23.87 tff(11776,plain,
% 23.68/23.87 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a), unit), a) = mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), mult(mult(a, unit), a)))),
% 23.68/23.87 inference(quant_inst,[status(thm)],[])).
% 23.68/23.87 tff(11777,plain,
% 23.68/23.87 (mult(mult(mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a), unit), a) = mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), mult(mult(a, unit), a))),
% 23.68/23.87 inference(unit_resolution,[status(thm)],[11776, 56])).
% 23.68/23.87 tff(11778,plain,
% 23.68/23.87 ((~((~(mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(mult(a, b), c), a), rd(mult(b, c), mult(a, c))))))) | (~((~(mult(mult(mult(mult(a, b), c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a))))))),
% 23.68/23.87 inference(unit_resolution,[status(thm)],[9732, 27])).
% 23.68/23.87 tff(11779,plain,
% 23.68/23.87 (~((~(mult(mult(mult(mult(a, b), c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a)))))),
% 23.68/23.87 inference(unit_resolution,[status(thm)],[11778, 9722])).
% 23.68/23.87 tff(11780,plain,
% 23.68/23.87 (((~(mult(mult(mult(mult(a, b), c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a))))) | (mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a)))),
% 23.68/23.87 inference(tautology,[status(thm)],[])).
% 23.68/23.87 tff(11781,plain,
% 23.68/23.87 (mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a))),
% 23.68/23.87 inference(unit_resolution,[status(thm)],[11780, 11779])).
% 23.68/23.87 tff(11782,plain,
% 23.68/23.87 (mult(mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a), unit) = mult(mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a)), unit)),
% 23.68/23.87 inference(monotonicity,[status(thm)],[11781])).
% 23.68/23.87 tff(11783,plain,
% 23.68/23.87 (mult(mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a)), unit) = mult(mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a), unit)),
% 23.68/23.87 inference(symmetry,[status(thm)],[11782])).
% 23.68/23.87 tff(11784,plain,
% 23.68/23.87 (mult(mult(mult(a, b), c), unit) = mult(mult(a, b), c)),
% 23.68/23.87 inference(transitivity,[status(thm)],[5910, 864, 858, 856, 161])).
% 23.68/23.87 tff(11785,plain,
% 23.68/23.87 (mult(mult(mult(mult(a, b), c), unit), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a))),
% 23.68/23.87 inference(monotonicity,[status(thm)],[11784])).
% 23.68/23.87 tff(11786,plain,
% 23.68/23.87 (mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(mult(a, b), c), unit), mult(rd(mult(b, c), mult(a, c)), a))),
% 23.68/23.87 inference(symmetry,[status(thm)],[11785])).
% 23.68/23.87 tff(11787,plain,
% 23.68/23.87 (mult(mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a)), unit) = mult(mult(mult(mult(mult(a, b), c), unit), mult(rd(mult(b, c), mult(a, c)), a)), unit)),
% 23.68/23.87 inference(monotonicity,[status(thm)],[11786])).
% 23.68/23.87 tff(11788,plain,
% 23.68/23.87 (mult(mult(mult(mult(mult(a, b), c), unit), mult(rd(mult(b, c), mult(a, c)), a)), unit) = mult(mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a)), unit)),
% 23.68/23.87 inference(symmetry,[status(thm)],[11787])).
% 23.68/23.87 tff(11789,plain,
% 23.68/23.87 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(mult(a, b), c), unit), mult(rd(mult(b, c), mult(a, c)), a)), unit) = mult(mult(mult(a, b), c), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit)))),
% 23.68/23.87 inference(quant_inst,[status(thm)],[])).
% 23.68/23.87 tff(11790,plain,
% 23.68/23.87 (mult(mult(mult(mult(mult(a, b), c), unit), mult(rd(mult(b, c), mult(a, c)), a)), unit) = mult(mult(mult(a, b), c), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit))),
% 23.68/23.87 inference(unit_resolution,[status(thm)],[11789, 56])).
% 23.68/23.87 tff(11791,plain,
% 23.68/23.87 (mult(mult(mult(a, b), c), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit)) = mult(mult(mult(mult(mult(a, b), c), unit), mult(rd(mult(b, c), mult(a, c)), a)), unit)),
% 23.68/23.87 inference(symmetry,[status(thm)],[11790])).
% 23.68/23.87 tff(11792,plain,
% 23.68/23.87 (mult(mult(mult(a, b), c), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit)) = mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a))),
% 23.68/23.87 inference(monotonicity,[status(thm)],[9065])).
% 23.68/23.87 tff(11793,plain,
% 23.68/23.87 (mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, b), c), mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), unit))),
% 23.68/23.87 inference(symmetry,[status(thm)],[11792])).
% 23.68/23.87 tff(11794,plain,
% 23.68/23.87 (mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a), unit)),
% 23.68/23.87 inference(transitivity,[status(thm)],[11793, 11791, 11788, 11783])).
% 23.68/23.87 tff(11795,plain,
% 23.68/23.87 (mult(mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a)), a) = mult(mult(mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a), unit), a)),
% 23.68/23.87 inference(monotonicity,[status(thm)],[11794])).
% 23.68/23.87 tff(11796,plain,
% 23.68/23.87 (mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, mult(a, c)))),
% 23.68/23.87 inference(monotonicity,[status(thm)],[6238])).
% 23.68/23.87 tff(11797,plain,
% 23.68/23.87 (mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, mult(a, c))) = mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 23.68/23.87 inference(transitivity,[status(thm)],[11796, 10795, 6008, 10794, 11187, 11184, 7918, 11182, 11176, 9787, 6583, 9766])).
% 23.68/23.87 tff(11798,plain,
% 23.68/23.87 (mult(mult(unit, mult(c, mult(a, c))), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a))),
% 23.68/23.87 inference(monotonicity,[status(thm)],[4367])).
% 23.68/23.87 tff(11799,plain,
% 23.68/23.87 (mult(mult(unit, mult(c, mult(a, c))), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a)),
% 23.68/23.87 inference(transitivity,[status(thm)],[11798, 9806, 9753])).
% 23.68/23.87 tff(11800,plain,
% 23.68/23.87 ((mult(mult(unit, mult(c, mult(a, c))), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, mult(a, c)))) <=> (mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 23.68/23.87 inference(monotonicity,[status(thm)],[11799, 11797])).
% 23.68/23.87 tff(11801,plain,
% 23.68/23.87 ((mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c))))) <=> (mult(mult(unit, mult(c, mult(a, c))), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, mult(a, c))))),
% 23.68/23.87 inference(symmetry,[status(thm)],[11800])).
% 23.68/23.87 tff(11802,plain,
% 23.68/23.87 ((~(mult(mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a) = mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) <=> (~(mult(mult(unit, mult(c, mult(a, c))), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, mult(a, c)))))),
% 23.68/23.87 inference(monotonicity,[status(thm)],[11801])).
% 23.68/23.87 tff(11803,plain,
% 23.68/23.87 (~(mult(mult(unit, mult(c, mult(a, c))), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, mult(a, c))))),
% 23.68/23.87 inference(modus_ponens,[status(thm)],[9659, 11802])).
% 23.68/23.87 tff(11804,plain,
% 23.68/23.87 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, mult(a, c))) = mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, mult(a, c)))),
% 23.68/23.87 inference(symmetry,[status(thm)],[11796])).
% 23.68/23.87 tff(11805,plain,
% 23.68/23.87 (mult(mult(a, mult(a, c)), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)) = mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 23.68/23.87 inference(monotonicity,[status(thm)],[1896])).
% 23.68/23.87 tff(11806,plain,
% 23.68/23.87 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(a, mult(a, c)), unit), rd(mult(b, c), mult(a, c))), unit) = mult(mult(a, mult(a, c)), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))),
% 23.68/23.87 inference(quant_inst,[status(thm)],[])).
% 23.68/23.87 tff(11807,plain,
% 23.68/23.87 (mult(mult(mult(mult(a, mult(a, c)), unit), rd(mult(b, c), mult(a, c))), unit) = mult(mult(a, mult(a, c)), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))),
% 23.68/23.87 inference(unit_resolution,[status(thm)],[11806, 56])).
% 23.68/23.87 tff(11808,plain,
% 23.68/23.87 (mult(mult(a, mult(a, c)), unit) = mult(mult(mult(a, c), a), unit)),
% 23.68/23.87 inference(monotonicity,[status(thm)],[8262])).
% 23.68/23.87 tff(11809,plain,
% 23.68/23.87 (mult(mult(a, mult(a, c)), unit) = mult(mult(a, c), a)),
% 23.68/23.87 inference(transitivity,[status(thm)],[11808, 9295, 9298, 9300])).
% 23.68/23.87 tff(11810,plain,
% 23.68/23.87 (mult(mult(mult(a, mult(a, c)), unit), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))),
% 23.68/23.87 inference(monotonicity,[status(thm)],[11809])).
% 23.68/23.87 tff(11811,plain,
% 23.68/23.87 (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, mult(a, c)), unit), rd(mult(b, c), mult(a, c)))),
% 23.68/23.87 inference(symmetry,[status(thm)],[11810])).
% 23.68/23.87 tff(11812,plain,
% 23.68/23.87 (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, mult(a, c)), unit), rd(mult(b, c), mult(a, c)))),
% 23.68/23.87 inference(transitivity,[status(thm)],[4676, 10343, 11811])).
% 23.68/23.87 tff(11813,plain,
% 23.68/23.87 (mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), unit) = mult(mult(mult(mult(a, mult(a, c)), unit), rd(mult(b, c), mult(a, c))), unit)),
% 23.68/23.87 inference(monotonicity,[status(thm)],[11812])).
% 23.68/23.87 tff(11814,plain,
% 23.68/23.87 (mult(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c), unit) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), unit)),
% 23.68/23.87 inference(monotonicity,[status(thm)],[11441])).
% 23.68/23.87 tff(11815,plain,
% 23.68/23.87 (mult(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c), unit) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 23.68/23.87 inference(transitivity,[status(thm)],[11814, 11813, 11807, 11805, 299])).
% 23.68/23.87 tff(11816,plain,
% 23.68/23.87 (mult(mult(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c), unit), c) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), c)),
% 23.68/23.88 inference(monotonicity,[status(thm)],[11815])).
% 23.68/23.88 tff(11817,plain,
% 23.68/23.88 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c), unit), c) = mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), mult(mult(c, unit), c)))),
% 23.68/23.88 inference(quant_inst,[status(thm)],[])).
% 23.68/23.88 tff(11818,plain,
% 23.68/23.88 (mult(mult(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c), unit), c) = mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), mult(mult(c, unit), c))),
% 23.68/23.88 inference(unit_resolution,[status(thm)],[11817, 56])).
% 23.68/23.88 tff(11819,plain,
% 23.68/23.88 (mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), mult(mult(c, unit), c)) = mult(mult(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c), unit), c)),
% 23.68/23.88 inference(symmetry,[status(thm)],[11818])).
% 23.68/23.88 tff(11820,plain,
% 23.68/23.88 (mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), mult(c, c)) = mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), mult(mult(c, unit), c))),
% 23.68/23.88 inference(monotonicity,[status(thm)],[2617])).
% 23.68/23.88 tff(11821,plain,
% 23.68/23.88 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(mult(a, b), c), mult(mult(mult(a, b), c), mult(a, mult(a, rd(mult(b, c), mult(a, c)))))) = mult(a, mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.68/23.88 inference(quant_inst,[status(thm)],[])).
% 23.68/23.88 tff(11822,plain,
% 23.68/23.88 (ld(mult(mult(a, b), c), mult(mult(mult(a, b), c), mult(a, mult(a, rd(mult(b, c), mult(a, c)))))) = mult(a, mult(a, rd(mult(b, c), mult(a, c))))),
% 23.68/23.88 inference(unit_resolution,[status(thm)],[11821, 7])).
% 23.68/23.88 tff(11823,plain,
% 23.68/23.88 (mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)) = ld(b, mult(b, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))),
% 23.68/23.88 inference(symmetry,[status(thm)],[10785])).
% 23.68/23.88 tff(11824,plain,
% 23.68/23.88 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c) = mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)),
% 23.68/23.88 inference(transitivity,[status(thm)],[10208, 1168, 11823, 10789, 10373, 10348, 10347])).
% 23.68/23.88 tff(11825,plain,
% 23.68/23.88 (rd(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c), c) = rd(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c), c)),
% 23.68/23.88 inference(monotonicity,[status(thm)],[11824])).
% 23.68/23.88 tff(11826,plain,
% 23.68/23.88 (rd(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c), c) = rd(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c), c)),
% 23.68/23.88 inference(symmetry,[status(thm)],[11825])).
% 23.68/23.88 tff(11827,plain,
% 23.68/23.88 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c), c) = mult(a, mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.68/23.88 inference(quant_inst,[status(thm)],[])).
% 23.68/23.88 tff(11828,plain,
% 23.68/23.88 (rd(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c), c) = mult(a, mult(a, rd(mult(b, c), mult(a, c))))),
% 23.68/23.88 inference(unit_resolution,[status(thm)],[11827, 168])).
% 23.68/23.88 tff(11829,plain,
% 23.68/23.88 (mult(a, mult(a, rd(mult(b, c), mult(a, c)))) = rd(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c), c)),
% 23.68/23.88 inference(symmetry,[status(thm)],[11828])).
% 23.68/23.88 tff(11830,plain,
% 23.68/23.88 (mult(a, mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(rd(mult(b, c), mult(a, c)), a), a)),
% 23.68/23.88 inference(transitivity,[status(thm)],[11829, 11826, 5807])).
% 23.68/23.88 tff(11831,plain,
% 23.68/23.88 (mult(mult(mult(a, b), c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(mult(a, b), c), mult(mult(rd(mult(b, c), mult(a, c)), a), a))),
% 23.68/23.88 inference(monotonicity,[status(thm)],[11830])).
% 23.68/23.88 tff(11832,plain,
% 23.68/23.88 (mult(mult(mult(a, b), c), mult(mult(rd(mult(b, c), mult(a, c)), a), a)) = mult(mult(mult(a, b), c), mult(a, mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.68/23.88 inference(symmetry,[status(thm)],[11831])).
% 23.68/23.88 tff(11833,assumption,(mult(mult(mult(a, b), c), mult(a, mult(rd(mult(b, c), mult(a, c)), a))) = mult(mult(mult(a, b), c), mult(mult(rd(mult(b, c), mult(a, c)), a), a))), introduced(assumption)).
% 23.68/23.88 tff(11834,plain,
% 23.68/23.88 (mult(mult(mult(a, b), c), mult(a, mult(rd(mult(b, c), mult(a, c)), a))) = mult(mult(mult(a, b), c), mult(a, mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.68/23.88 inference(transitivity,[status(thm)],[11833, 11832])).
% 23.68/23.88 tff(11835,plain,
% 23.68/23.88 (ld(mult(mult(a, b), c), mult(mult(mult(a, b), c), mult(a, mult(rd(mult(b, c), mult(a, c)), a)))) = ld(mult(mult(a, b), c), mult(mult(mult(a, b), c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))))),
% 23.68/23.88 inference(monotonicity,[status(thm)],[11834])).
% 23.68/23.88 tff(11836,plain,
% 23.68/23.88 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(mult(a, b), c), mult(mult(mult(a, b), c), mult(a, mult(rd(mult(b, c), mult(a, c)), a)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), a)))),
% 23.68/23.88 inference(quant_inst,[status(thm)],[])).
% 23.68/23.88 tff(11837,plain,
% 23.68/23.88 (ld(mult(mult(a, b), c), mult(mult(mult(a, b), c), mult(a, mult(rd(mult(b, c), mult(a, c)), a)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), a))),
% 23.68/23.88 inference(unit_resolution,[status(thm)],[11836, 7])).
% 23.68/23.88 tff(11838,plain,
% 23.68/23.88 (mult(a, mult(rd(mult(b, c), mult(a, c)), a)) = ld(mult(mult(a, b), c), mult(mult(mult(a, b), c), mult(a, mult(rd(mult(b, c), mult(a, c)), a))))),
% 23.68/23.88 inference(symmetry,[status(thm)],[11837])).
% 23.68/23.88 tff(11839,plain,
% 23.68/23.88 (mult(a, mult(rd(mult(b, c), mult(a, c)), a)) = mult(a, mult(a, rd(mult(b, c), mult(a, c))))),
% 23.68/23.88 inference(transitivity,[status(thm)],[11838, 11835, 11822])).
% 23.68/23.88 tff(11840,plain,
% 23.68/23.88 (mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, c)) = mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), mult(c, c))),
% 23.68/23.88 inference(monotonicity,[status(thm)],[11839])).
% 23.68/23.88 tff(11841,plain,
% 23.68/23.88 (mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), c) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), a), c)),
% 23.68/23.88 inference(monotonicity,[status(thm)],[9393])).
% 23.68/23.88 tff(11842,plain,
% 23.68/23.88 (mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), c) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a))),
% 23.68/23.88 inference(transitivity,[status(thm)],[11841, 7510, 5948, 5496])).
% 23.68/23.88 tff(11843,plain,
% 23.68/23.88 (mult(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), c), unit) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), unit)),
% 23.68/23.88 inference(monotonicity,[status(thm)],[11842])).
% 23.68/23.88 tff(11844,plain,
% 23.68/23.88 (mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), unit) = mult(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), c), unit)),
% 23.68/23.88 inference(symmetry,[status(thm)],[11843])).
% 23.68/23.88 tff(11845,plain,
% 23.68/23.88 (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), unit), a) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)),
% 23.68/23.88 inference(monotonicity,[status(thm)],[6023])).
% 23.68/23.88 tff(11846,plain,
% 23.68/23.88 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), unit), a)),
% 23.68/23.88 inference(symmetry,[status(thm)],[11845])).
% 23.68/23.88 tff(11847,plain,
% 23.68/23.88 (mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), unit), a)),
% 23.68/23.88 inference(transitivity,[status(thm)],[5497, 11846])).
% 23.68/23.88 tff(11848,plain,
% 23.68/23.88 (mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), unit) = mult(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), unit), a), unit)),
% 23.68/23.88 inference(monotonicity,[status(thm)],[11847])).
% 23.68/23.88 tff(11849,plain,
% 23.68/23.88 (mult(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), unit), a), unit) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), unit)),
% 23.68/23.88 inference(symmetry,[status(thm)],[11848])).
% 23.68/23.88 tff(11850,plain,
% 23.68/23.88 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), unit), a), unit) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(mult(unit, a), unit)))),
% 23.68/23.88 inference(quant_inst,[status(thm)],[])).
% 23.68/23.88 tff(11851,plain,
% 23.68/23.88 (mult(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), unit), a), unit) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(mult(unit, a), unit))),
% 23.68/23.88 inference(unit_resolution,[status(thm)],[11850, 56])).
% 23.68/23.88 tff(11852,plain,
% 23.68/23.88 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(mult(unit, a), unit)) = mult(mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), unit), a), unit)),
% 23.68/23.88 inference(symmetry,[status(thm)],[11851])).
% 23.68/23.88 tff(11853,plain,
% 23.68/23.88 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(mult(unit, a), unit)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a)),
% 23.68/23.88 inference(monotonicity,[status(thm)],[507])).
% 23.68/23.88 tff(11854,plain,
% 23.68/23.88 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(mult(unit, a), unit))),
% 23.68/23.88 inference(symmetry,[status(thm)],[11853])).
% 23.68/23.88 tff(11855,plain,
% 23.68/23.88 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), c), unit)),
% 23.68/23.88 inference(transitivity,[status(thm)],[11854, 11852, 11849, 11844])).
% 23.68/23.88 tff(11856,plain,
% 23.68/23.88 (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), a)), c), unit), c)),
% 23.68/23.88 inference(monotonicity,[status(thm)],[11855])).
% 23.68/23.88 tff(11857,plain,
% 23.68/23.88 (mult(mult(unit, mult(c, mult(a, c))), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, mult(a, c)))),
% 23.68/23.88 inference(transitivity,[status(thm)],[11798, 7809, 9759, 7692, 11856, 6042, 6044, 11840, 11820, 11819, 11816, 10792, 5142, 5141, 5139, 11804])).
% 23.68/23.88 tff(11858,assumption,(~(mult(mult(unit, mult(c, mult(a, c))), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, mult(a, c))))), introduced(assumption)).
% 23.68/23.88 tff(11859,plain,
% 23.68/23.88 ($false),
% 23.68/23.88 inference(unit_resolution,[status(thm)],[11858, 11857])).
% 23.68/23.88 tff(11860,plain,((~(mult(mult(mult(a, b), c), mult(a, mult(rd(mult(b, c), mult(a, c)), a))) = mult(mult(mult(a, b), c), mult(mult(rd(mult(b, c), mult(a, c)), a), a)))) | (mult(mult(unit, mult(c, mult(a, c))), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(unit, mult(rd(mult(b, c), mult(a, c)), a)), mult(c, mult(a, c)))) | (~(mult(mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))), a) = mult(mult(c, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))) = mult(b, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))) | (~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))), inference(lemma,lemma(discharge,[]))).
% 23.68/23.88 tff(11861,plain,
% 23.68/23.88 (~(mult(mult(mult(a, b), c), mult(a, mult(rd(mult(b, c), mult(a, c)), a))) = mult(mult(mult(a, b), c), mult(mult(rd(mult(b, c), mult(a, c)), a), a)))),
% 23.68/23.88 inference(unit_resolution,[status(thm)],[11860, 11803, 9645, 11043, 8165, 281])).
% 23.68/23.88 tff(11862,plain,
% 23.68/23.88 (((~(mult(mult(mult(mult(a, b), c), a), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a)), a))) | (~(mult(mult(mult(a, b), c), mult(a, mult(rd(mult(b, c), mult(a, c)), a))) = mult(mult(mult(a, b), c), mult(mult(rd(mult(b, c), mult(a, c)), a), a))))) | (mult(mult(mult(a, b), c), mult(a, mult(rd(mult(b, c), mult(a, c)), a))) = mult(mult(mult(a, b), c), mult(mult(rd(mult(b, c), mult(a, c)), a), a)))),
% 23.68/23.88 inference(tautology,[status(thm)],[])).
% 23.68/23.88 tff(11863,plain,
% 23.68/23.88 ((~(mult(mult(mult(mult(a, b), c), a), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a)), a))) | (~(mult(mult(mult(a, b), c), mult(a, mult(rd(mult(b, c), mult(a, c)), a))) = mult(mult(mult(a, b), c), mult(mult(rd(mult(b, c), mult(a, c)), a), a))))),
% 23.68/23.88 inference(unit_resolution,[status(thm)],[11862, 11861])).
% 23.68/23.88 tff(11864,plain,
% 23.68/23.88 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(mult(a, b), c), a), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a)), a))) | (~(mult(mult(mult(a, b), c), mult(a, mult(rd(mult(b, c), mult(a, c)), a))) = mult(mult(mult(a, b), c), mult(mult(rd(mult(b, c), mult(a, c)), a), a)))))) | (~((~(mult(mult(mult(mult(a, b), c), a), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, b), c), mult(a, mult(rd(mult(b, c), mult(a, c)), a))))) | (~(mult(mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a)), a) = mult(mult(mult(a, b), c), mult(mult(rd(mult(b, c), mult(a, c)), a), a)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(mult(a, b), c), a), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a)), a))) | (~(mult(mult(mult(a, b), c), mult(a, mult(rd(mult(b, c), mult(a, c)), a))) = mult(mult(mult(a, b), c), mult(mult(rd(mult(b, c), mult(a, c)), a), a)))))) | (~((~(mult(mult(mult(mult(a, b), c), a), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, b), c), mult(a, mult(rd(mult(b, c), mult(a, c)), a))))) | (~(mult(mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a)), a) = mult(mult(mult(a, b), c), mult(mult(rd(mult(b, c), mult(a, c)), a), a)))))))),
% 23.68/23.89 inference(rewrite,[status(thm)],[])).
% 23.68/23.89 tff(11865,plain,
% 23.68/23.89 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(mult(a, b), c), a), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a)), a))) | (~(mult(mult(mult(a, b), c), mult(a, mult(rd(mult(b, c), mult(a, c)), a))) = mult(mult(mult(a, b), c), mult(mult(rd(mult(b, c), mult(a, c)), a), a)))))) | (~((~(mult(mult(mult(mult(a, b), c), a), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, b), c), mult(a, mult(rd(mult(b, c), mult(a, c)), a))))) | (~(mult(mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a)), a) = mult(mult(mult(a, b), c), mult(mult(rd(mult(b, c), mult(a, c)), a), a)))))))),
% 23.68/23.89 inference(quant_inst,[status(thm)],[])).
% 23.68/23.89 tff(11866,plain,
% 23.68/23.89 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(mult(a, b), c), a), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a)), a))) | (~(mult(mult(mult(a, b), c), mult(a, mult(rd(mult(b, c), mult(a, c)), a))) = mult(mult(mult(a, b), c), mult(mult(rd(mult(b, c), mult(a, c)), a), a)))))) | (~((~(mult(mult(mult(mult(a, b), c), a), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, b), c), mult(a, mult(rd(mult(b, c), mult(a, c)), a))))) | (~(mult(mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a)), a) = mult(mult(mult(a, b), c), mult(mult(rd(mult(b, c), mult(a, c)), a), a))))))),
% 23.68/23.89 inference(modus_ponens,[status(thm)],[11865, 11864])).
% 23.68/23.89 tff(11867,plain,
% 23.68/23.89 (~((~(mult(mult(mult(mult(a, b), c), a), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, b), c), mult(a, mult(rd(mult(b, c), mult(a, c)), a))))) | (~(mult(mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a)), a) = mult(mult(mult(a, b), c), mult(mult(rd(mult(b, c), mult(a, c)), a), a)))))),
% 23.68/23.89 inference(unit_resolution,[status(thm)],[11866, 27, 11863])).
% 23.68/23.89 tff(11868,plain,
% 23.68/23.89 (((~(mult(mult(mult(mult(a, b), c), a), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(a, b), c), mult(a, mult(rd(mult(b, c), mult(a, c)), a))))) | (~(mult(mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a)), a) = mult(mult(mult(a, b), c), mult(mult(rd(mult(b, c), mult(a, c)), a), a))))) | (mult(mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a)), a) = mult(mult(mult(a, b), c), mult(mult(rd(mult(b, c), mult(a, c)), a), a)))),
% 23.68/23.89 inference(tautology,[status(thm)],[])).
% 23.68/23.89 tff(11869,plain,
% 23.68/23.89 (mult(mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a)), a) = mult(mult(mult(a, b), c), mult(mult(rd(mult(b, c), mult(a, c)), a), a))),
% 23.68/23.89 inference(unit_resolution,[status(thm)],[11868, 11867])).
% 23.68/23.89 tff(11870,plain,
% 23.68/23.89 (mult(mult(mult(a, b), c), mult(mult(rd(mult(b, c), mult(a, c)), a), a)) = mult(mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a)), a)),
% 23.68/23.89 inference(symmetry,[status(thm)],[11869])).
% 23.68/23.89 tff(11871,plain,
% 23.68/23.89 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c) = mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c)),
% 23.68/23.89 inference(transitivity,[status(thm)],[10208, 1168, 11823, 11172, 10373, 11164, 11162])).
% 23.68/23.89 tff(11872,plain,
% 23.68/23.89 (rd(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c), c) = rd(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c), c)),
% 23.68/23.89 inference(monotonicity,[status(thm)],[11871])).
% 23.68/23.89 tff(11873,plain,
% 23.68/23.89 (rd(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c), c) = rd(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), a), c), c)),
% 23.68/23.89 inference(symmetry,[status(thm)],[11872])).
% 23.68/23.89 tff(11874,plain,
% 23.68/23.89 (mult(a, mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(rd(mult(b, c), mult(a, c)), a), a)),
% 23.68/23.89 inference(transitivity,[status(thm)],[11829, 11873, 5807])).
% 23.68/23.89 tff(11875,plain,
% 23.68/23.89 (mult(mult(mult(a, b), c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(mult(a, b), c), mult(mult(rd(mult(b, c), mult(a, c)), a), a))),
% 23.68/23.89 inference(monotonicity,[status(thm)],[11874])).
% 23.68/23.89 tff(11876,plain,
% 23.68/23.89 (mult(mult(mult(mult(mult(a, b), c), a), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))), a)),
% 23.68/23.89 inference(monotonicity,[status(thm)],[10330])).
% 23.68/23.89 tff(11877,assumption,(~(mult(mult(mult(mult(a, b), c), a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, b), c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))))), introduced(assumption)).
% 23.68/23.89 tff(11878,plain,
% 23.68/23.89 (((~(mult(mult(mult(mult(a, b), c), a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, b), c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(a, b), c), mult(mult(a, rd(mult(b, c), mult(a, c))), a))))) | (mult(mult(mult(mult(a, b), c), a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, b), c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))))),
% 23.68/23.89 inference(tautology,[status(thm)],[])).
% 23.68/23.89 tff(11879,plain,
% 23.68/23.89 ((~(mult(mult(mult(mult(a, b), c), a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, b), c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(a, b), c), mult(mult(a, rd(mult(b, c), mult(a, c))), a))))),
% 23.68/23.89 inference(unit_resolution,[status(thm)],[11878, 11877])).
% 23.68/23.89 tff(11880,plain,
% 23.68/23.89 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(mult(a, b), c), a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, b), c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(a, b), c), mult(mult(a, rd(mult(b, c), mult(a, c))), a)))))) | (~((~(mult(mult(mult(mult(a, b), c), a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))), a))) | (~(mult(mult(mult(a, b), c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(mult(a, b), c), mult(mult(a, rd(mult(b, c), mult(a, c))), a)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(mult(a, b), c), a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, b), c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(a, b), c), mult(mult(a, rd(mult(b, c), mult(a, c))), a)))))) | (~((~(mult(mult(mult(mult(a, b), c), a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))), a))) | (~(mult(mult(mult(a, b), c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(mult(a, b), c), mult(mult(a, rd(mult(b, c), mult(a, c))), a)))))))),
% 23.68/23.89 inference(rewrite,[status(thm)],[])).
% 23.68/23.89 tff(11881,plain,
% 23.68/23.89 (((~((~(mult(mult(mult(mult(a, b), c), a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))), a))) | (~(mult(mult(mult(a, b), c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(mult(a, b), c), mult(mult(a, rd(mult(b, c), mult(a, c))), a)))))) | (~((~(mult(mult(mult(mult(a, b), c), a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, b), c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(a, b), c), mult(mult(a, rd(mult(b, c), mult(a, c))), a))))))) <=> ((~((~(mult(mult(mult(mult(a, b), c), a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, b), c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(a, b), c), mult(mult(a, rd(mult(b, c), mult(a, c))), a)))))) | (~((~(mult(mult(mult(mult(a, b), c), a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))), a))) | (~(mult(mult(mult(a, b), c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(mult(a, b), c), mult(mult(a, rd(mult(b, c), mult(a, c))), a)))))))),
% 23.68/23.89 inference(rewrite,[status(thm)],[])).
% 23.68/23.89 tff(11882,plain,
% 23.68/23.89 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(mult(a, b), c), a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))), a))) | (~(mult(mult(mult(a, b), c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(mult(a, b), c), mult(mult(a, rd(mult(b, c), mult(a, c))), a)))))) | (~((~(mult(mult(mult(mult(a, b), c), a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, b), c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(a, b), c), mult(mult(a, rd(mult(b, c), mult(a, c))), a)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(mult(a, b), c), a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, b), c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(a, b), c), mult(mult(a, rd(mult(b, c), mult(a, c))), a)))))) | (~((~(mult(mult(mult(mult(a, b), c), a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))), a))) | (~(mult(mult(mult(a, b), c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(mult(a, b), c), mult(mult(a, rd(mult(b, c), mult(a, c))), a))))))))),
% 23.68/23.89 inference(monotonicity,[status(thm)],[11881])).
% 23.68/23.89 tff(11883,plain,
% 23.68/23.89 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(mult(a, b), c), a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))), a))) | (~(mult(mult(mult(a, b), c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(mult(a, b), c), mult(mult(a, rd(mult(b, c), mult(a, c))), a)))))) | (~((~(mult(mult(mult(mult(a, b), c), a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, b), c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(a, b), c), mult(mult(a, rd(mult(b, c), mult(a, c))), a)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(mult(a, b), c), a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, b), c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(a, b), c), mult(mult(a, rd(mult(b, c), mult(a, c))), a)))))) | (~((~(mult(mult(mult(mult(a, b), c), a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))), a))) | (~(mult(mult(mult(a, b), c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(mult(a, b), c), mult(mult(a, rd(mult(b, c), mult(a, c))), a)))))))),
% 23.68/23.89 inference(transitivity,[status(thm)],[11882, 11880])).
% 23.68/23.89 tff(11884,plain,
% 23.68/23.89 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(mult(a, b), c), a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))), a))) | (~(mult(mult(mult(a, b), c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(mult(a, b), c), mult(mult(a, rd(mult(b, c), mult(a, c))), a)))))) | (~((~(mult(mult(mult(mult(a, b), c), a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, b), c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(a, b), c), mult(mult(a, rd(mult(b, c), mult(a, c))), a)))))))),
% 23.68/23.89 inference(quant_inst,[status(thm)],[])).
% 23.68/23.89 tff(11885,plain,
% 23.68/23.89 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(mult(a, b), c), a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, b), c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(a, b), c), mult(mult(a, rd(mult(b, c), mult(a, c))), a)))))) | (~((~(mult(mult(mult(mult(a, b), c), a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))), a))) | (~(mult(mult(mult(a, b), c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(mult(a, b), c), mult(mult(a, rd(mult(b, c), mult(a, c))), a))))))),
% 23.68/23.89 inference(modus_ponens,[status(thm)],[11884, 11883])).
% 23.68/23.89 tff(11886,plain,
% 23.68/23.89 ((~((~(mult(mult(mult(mult(a, b), c), a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, b), c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(a, b), c), mult(mult(a, rd(mult(b, c), mult(a, c))), a)))))) | (~((~(mult(mult(mult(mult(a, b), c), a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))), a))) | (~(mult(mult(mult(a, b), c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(mult(a, b), c), mult(mult(a, rd(mult(b, c), mult(a, c))), a))))))),
% 23.68/23.89 inference(unit_resolution,[status(thm)],[11885, 27])).
% 23.68/23.89 tff(11887,plain,
% 23.68/23.89 (~((~(mult(mult(mult(mult(a, b), c), a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))), a))) | (~(mult(mult(mult(a, b), c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(mult(a, b), c), mult(mult(a, rd(mult(b, c), mult(a, c))), a)))))),
% 23.68/23.90 inference(unit_resolution,[status(thm)],[11886, 11879])).
% 23.68/23.90 tff(11888,plain,
% 23.68/23.90 (((~(mult(mult(mult(mult(a, b), c), a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))), a))) | (~(mult(mult(mult(a, b), c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(mult(a, b), c), mult(mult(a, rd(mult(b, c), mult(a, c))), a))))) | (mult(mult(mult(a, b), c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(mult(a, b), c), mult(mult(a, rd(mult(b, c), mult(a, c))), a)))),
% 23.68/23.90 inference(tautology,[status(thm)],[])).
% 23.68/23.90 tff(11889,plain,
% 23.68/23.90 (mult(mult(mult(a, b), c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(mult(a, b), c), mult(mult(a, rd(mult(b, c), mult(a, c))), a))),
% 23.68/23.90 inference(unit_resolution,[status(thm)],[11888, 11887])).
% 23.68/23.90 tff(11890,plain,
% 23.68/23.90 (mult(mult(mult(a, b), c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))), a)),
% 23.68/23.90 inference(transitivity,[status(thm)],[11889, 7518, 11876])).
% 23.68/23.90 tff(11891,plain,
% 23.68/23.90 ((mult(mult(mult(mult(a, b), c), a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, b), c), mult(a, mult(a, rd(mult(b, c), mult(a, c)))))) <=> (mult(mult(mult(mult(a, b), c), a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))), a))),
% 23.68/23.90 inference(monotonicity,[status(thm)],[11890])).
% 23.68/23.90 tff(11892,plain,
% 23.68/23.90 ((mult(mult(mult(mult(a, b), c), a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))), a)) <=> (mult(mult(mult(mult(a, b), c), a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, b), c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))))),
% 23.68/23.90 inference(symmetry,[status(thm)],[11891])).
% 23.68/23.90 tff(11893,plain,
% 23.68/23.90 (((~(mult(mult(mult(mult(a, b), c), a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))), a))) | (~(mult(mult(mult(a, b), c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(mult(a, b), c), mult(mult(a, rd(mult(b, c), mult(a, c))), a))))) | (mult(mult(mult(mult(a, b), c), a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))), a))),
% 23.68/23.90 inference(tautology,[status(thm)],[])).
% 23.68/23.90 tff(11894,plain,
% 23.68/23.90 (mult(mult(mult(mult(a, b), c), a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c)))), a)),
% 23.68/23.90 inference(unit_resolution,[status(thm)],[11893, 11887])).
% 23.68/23.90 tff(11895,plain,
% 23.68/23.90 (mult(mult(mult(mult(a, b), c), a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, b), c), mult(a, mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.68/23.90 inference(modus_ponens,[status(thm)],[11894, 11892])).
% 23.68/23.90 tff(11896,plain,
% 23.68/23.90 ($false),
% 23.68/23.90 inference(unit_resolution,[status(thm)],[11877, 11895])).
% 23.68/23.90 tff(11897,plain,((mult(mult(mult(mult(a, b), c), a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, b), c), mult(a, mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(mult(a, b), c), a), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, b), c), mult(a, rd(mult(b, c), mult(a, c))))))), inference(lemma,lemma(discharge,[]))).
% 23.68/23.90 tff(11898,plain,
% 23.68/23.90 (mult(mult(mult(mult(a, b), c), a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, b), c), mult(a, mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.68/23.90 inference(unit_resolution,[status(thm)],[11897, 9735])).
% 23.68/23.90 tff(11899,plain,
% 23.68/23.90 (mult(mult(mult(mult(a, c), b), a), b) = mult(mult(mult(mult(a, b), c), a), b)),
% 23.68/23.90 inference(symmetry,[status(thm)],[959])).
% 23.68/23.90 tff(11900,plain,
% 23.68/23.90 (mult(mult(a, c), mult(mult(b, a), b)) = mult(mult(mult(a, b), c), mult(a, b))),
% 23.68/23.90 inference(transitivity,[status(thm)],[10483, 1095, 949])).
% 23.68/23.90 tff(11901,assumption,(~(mult(mult(mult(a, c), mult(b, a)), b) = mult(mult(a, c), mult(mult(b, a), b)))), introduced(assumption)).
% 23.68/23.90 tff(11902,plain,
% 23.68/23.90 (((~(mult(mult(mult(a, c), b), mult(b, a)) = mult(mult(a, c), mult(b, mult(b, a))))) | (~(mult(mult(mult(a, c), mult(b, a)), b) = mult(mult(a, c), mult(mult(b, a), b))))) | (mult(mult(mult(a, c), mult(b, a)), b) = mult(mult(a, c), mult(mult(b, a), b)))),
% 23.68/23.90 inference(tautology,[status(thm)],[])).
% 23.68/23.90 tff(11903,plain,
% 23.68/23.90 ((~(mult(mult(mult(a, c), b), mult(b, a)) = mult(mult(a, c), mult(b, mult(b, a))))) | (~(mult(mult(mult(a, c), mult(b, a)), b) = mult(mult(a, c), mult(mult(b, a), b))))),
% 23.68/23.90 inference(unit_resolution,[status(thm)],[11902, 11901])).
% 23.68/23.90 tff(11904,plain,
% 23.68/23.90 (~((~(mult(mult(mult(a, c), b), mult(b, a)) = mult(mult(mult(a, c), mult(b, a)), b))) | (~(mult(mult(a, c), mult(b, mult(b, a))) = mult(mult(a, c), mult(mult(b, a), b)))))),
% 23.68/23.90 inference(unit_resolution,[status(thm)],[684, 11903])).
% 23.68/23.90 tff(11905,plain,
% 23.68/23.90 (((~(mult(mult(mult(a, c), b), mult(b, a)) = mult(mult(mult(a, c), mult(b, a)), b))) | (~(mult(mult(a, c), mult(b, mult(b, a))) = mult(mult(a, c), mult(mult(b, a), b))))) | (mult(mult(mult(a, c), b), mult(b, a)) = mult(mult(mult(a, c), mult(b, a)), b))),
% 23.68/23.90 inference(tautology,[status(thm)],[])).
% 23.68/23.90 tff(11906,plain,
% 23.68/23.90 (mult(mult(mult(a, c), b), mult(b, a)) = mult(mult(mult(a, c), mult(b, a)), b)),
% 23.68/23.90 inference(unit_resolution,[status(thm)],[11905, 11904])).
% 23.68/23.90 tff(11907,plain,
% 23.68/23.90 (mult(mult(mult(a, c), mult(b, a)), b) = mult(mult(mult(a, c), b), mult(b, a))),
% 23.68/23.90 inference(symmetry,[status(thm)],[11906])).
% 23.68/23.90 tff(11908,plain,
% 23.68/23.90 (mult(mult(mult(a, c), mult(b, a)), b) = mult(mult(mult(a, b), c), mult(b, a))),
% 23.68/23.90 inference(transitivity,[status(thm)],[11907, 10495])).
% 23.68/23.90 tff(11909,plain,
% 23.68/23.90 ((mult(mult(mult(a, c), mult(b, a)), b) = mult(mult(a, c), mult(mult(b, a), b))) <=> (mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(a, b)))),
% 23.68/23.90 inference(monotonicity,[status(thm)],[11908, 11900])).
% 23.68/23.90 tff(11910,plain,
% 23.68/23.90 ((mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(a, b))) <=> (mult(mult(mult(a, c), mult(b, a)), b) = mult(mult(a, c), mult(mult(b, a), b)))),
% 23.68/23.90 inference(symmetry,[status(thm)],[11909])).
% 23.68/23.90 tff(11911,plain,
% 23.68/23.90 (mult(mult(mult(mult(a, b), c), a), b) = mult(mult(mult(a, b), c), mult(a, b))),
% 23.68/23.90 inference(transitivity,[status(thm)],[959, 956, 10483, 1095, 949])).
% 23.68/23.90 tff(11912,plain,
% 23.68/23.90 (((~(mult(mult(mult(a, c), mult(b, a)), b) = mult(mult(a, c), mult(mult(b, a), b)))) | (~(mult(mult(mult(a, c), b), mult(b, a)) = mult(mult(a, c), mult(b, mult(b, a)))))) | (mult(mult(mult(a, c), mult(b, a)), b) = mult(mult(a, c), mult(mult(b, a), b)))),
% 23.68/23.90 inference(tautology,[status(thm)],[])).
% 23.68/23.90 tff(11913,plain,
% 23.68/23.90 ((~(mult(mult(mult(a, c), mult(b, a)), b) = mult(mult(a, c), mult(mult(b, a), b)))) | (~(mult(mult(mult(a, c), b), mult(b, a)) = mult(mult(a, c), mult(b, mult(b, a)))))),
% 23.68/23.90 inference(unit_resolution,[status(thm)],[11912, 11901])).
% 23.68/23.90 tff(11914,plain,
% 23.68/23.90 (~((~(mult(mult(mult(a, c), mult(b, a)), b) = mult(mult(mult(a, c), b), mult(b, a)))) | (~(mult(mult(a, c), mult(mult(b, a), b)) = mult(mult(a, c), mult(b, mult(b, a))))))),
% 23.68/23.90 inference(unit_resolution,[status(thm)],[622, 11913])).
% 23.68/23.90 tff(11915,plain,
% 23.68/23.90 (mult(mult(a, c), mult(mult(b, a), b)) = mult(mult(a, c), mult(b, mult(b, a)))),
% 23.68/23.90 inference(unit_resolution,[status(thm)],[617, 11914])).
% 23.68/23.90 tff(11916,plain,
% 23.68/23.90 (mult(b, mult(a, b)) = mult(b, mult(b, a))),
% 23.68/23.90 inference(unit_resolution,[status(thm)],[974, 11915, 961, 11911])).
% 23.68/23.90 tff(11917,plain,
% 23.68/23.90 (mult(mult(mult(a, b), c), mult(b, a)) = mult(mult(mult(a, b), c), mult(a, b))),
% 23.68/23.90 inference(unit_resolution,[status(thm)],[3458, 11916])).
% 23.68/23.90 tff(11918,plain,
% 23.68/23.90 (mult(mult(mult(a, c), mult(b, a)), b) = mult(mult(a, c), mult(mult(b, a), b))),
% 23.68/23.90 inference(modus_ponens,[status(thm)],[11917, 11910])).
% 23.68/23.90 tff(11919,plain,
% 23.68/23.90 ($false),
% 23.68/23.90 inference(unit_resolution,[status(thm)],[11901, 11918])).
% 23.68/23.90 tff(11920,plain,((mult(mult(mult(a, c), mult(b, a)), b) = mult(mult(a, c), mult(mult(b, a), b))) | (~(mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(a, c), mult(b, mult(a, b))))) | (~(mult(mult(c, b), mult(a, b)) = mult(c, mult(b, mult(a, b))))) | (~(mult(mult(mult(b, c), a), b) = mult(mult(b, c), mult(a, b))))), inference(lemma,lemma(discharge,[]))).
% 23.68/23.90 tff(11921,plain,
% 23.68/23.90 (mult(mult(mult(a, c), mult(b, a)), b) = mult(mult(a, c), mult(mult(b, a), b))),
% 23.68/23.90 inference(unit_resolution,[status(thm)],[11920, 10453, 10448, 10449])).
% 23.68/23.90 tff(11922,plain,
% 23.68/23.90 (mult(mult(mult(a, c), mult(b, a)), b) = mult(mult(mult(mult(a, b), c), a), b)),
% 23.68/23.90 inference(transitivity,[status(thm)],[11921, 964, 11899])).
% 23.68/23.90 tff(11923,plain,
% 23.68/23.90 (rd(mult(mult(mult(a, c), mult(b, a)), b), b) = rd(mult(mult(mult(mult(a, b), c), a), b), b)),
% 23.68/23.90 inference(monotonicity,[status(thm)],[11922])).
% 23.68/23.90 tff(11924,plain,
% 23.68/23.90 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(a, c), mult(b, a)), b), b) = mult(mult(a, c), mult(b, a)))),
% 23.68/23.90 inference(quant_inst,[status(thm)],[])).
% 23.68/23.90 tff(11925,plain,
% 23.68/23.90 (rd(mult(mult(mult(a, c), mult(b, a)), b), b) = mult(mult(a, c), mult(b, a))),
% 23.68/23.90 inference(unit_resolution,[status(thm)],[11924, 168])).
% 23.68/23.90 tff(11926,plain,
% 23.68/23.90 (mult(mult(a, c), mult(b, a)) = rd(mult(mult(mult(a, c), mult(b, a)), b), b)),
% 23.68/23.90 inference(symmetry,[status(thm)],[11925])).
% 23.68/23.90 tff(11927,plain,
% 23.68/23.90 (mult(mult(a, c), mult(b, a)) = mult(mult(mult(a, b), c), a)),
% 23.68/23.90 inference(transitivity,[status(thm)],[11926, 11923, 1478])).
% 23.68/23.90 tff(11928,plain,
% 23.68/23.90 (mult(mult(mult(a, c), mult(b, a)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(mult(a, b), c), a), mult(a, rd(mult(b, c), mult(a, c))))),
% 23.68/23.90 inference(monotonicity,[status(thm)],[11927])).
% 23.68/23.90 tff(11929,assumption,(mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a))), introduced(assumption)).
% 23.68/23.90 tff(11930,assumption,(mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c)))), introduced(assumption)).
% 23.68/23.90 tff(11931,assumption,(mult(mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a)), a) = mult(mult(mult(a, b), c), mult(mult(rd(mult(b, c), mult(a, c)), a), a))), introduced(assumption)).
% 23.68/23.90 tff(11932,assumption,(mult(mult(mult(mult(a, b), c), a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, b), c), mult(a, mult(a, rd(mult(b, c), mult(a, c)))))), introduced(assumption)).
% 23.68/23.90 tff(11933,assumption,(mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(mult(a, c), mult(b, a)), mult(a, rd(mult(b, c), mult(a, c))))), introduced(assumption)).
% 23.68/23.90 tff(11934,plain,
% 23.68/23.90 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(c, mult(b, c)), mult(mult(unit, ld(c, mult(a, b))), unit)), a), a) = mult(mult(c, mult(b, c)), mult(mult(unit, ld(c, mult(a, b))), unit)))),
% 23.68/23.90 inference(quant_inst,[status(thm)],[])).
% 23.68/23.90 tff(11935,plain,
% 23.68/23.90 (rd(mult(mult(mult(c, mult(b, c)), mult(mult(unit, ld(c, mult(a, b))), unit)), a), a) = mult(mult(c, mult(b, c)), mult(mult(unit, ld(c, mult(a, b))), unit))),
% 23.68/23.90 inference(unit_resolution,[status(thm)],[11934, 168])).
% 23.68/23.90 tff(11936,plain,
% 23.68/23.90 (mult(mult(c, mult(b, c)), mult(mult(unit, ld(c, mult(a, b))), unit)) = mult(b, mult(mult(a, b), c))),
% 23.68/23.90 inference(transitivity,[status(thm)],[10904, 10899, 3391, 10878, 3388])).
% 23.68/23.90 tff(11937,plain,
% 23.68/23.90 (mult(mult(mult(c, mult(b, c)), mult(mult(unit, ld(c, mult(a, b))), unit)), a) = mult(mult(b, mult(mult(a, b), c)), a)),
% 23.68/23.90 inference(monotonicity,[status(thm)],[11936])).
% 23.68/23.90 tff(11938,plain,
% 23.68/23.90 (mult(mult(b, mult(mult(a, b), c)), a) = mult(mult(mult(c, mult(b, c)), mult(mult(unit, ld(c, mult(a, b))), unit)), a)),
% 23.68/23.90 inference(symmetry,[status(thm)],[11937])).
% 23.68/23.90 tff(11939,plain,
% 23.68/23.90 (mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), b) = mult(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c), b)),
% 23.68/23.90 inference(monotonicity,[status(thm)],[10368])).
% 23.68/23.90 tff(11940,plain,
% 23.68/23.90 (mult(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c), b) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), b)),
% 23.68/23.90 inference(symmetry,[status(thm)],[11939])).
% 23.68/23.90 tff(11941,plain,
% 23.68/23.90 (mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(b, mult(a, c))),
% 23.68/23.90 inference(transitivity,[status(thm)],[10344, 8198, 4478, 11046, 5658])).
% 23.68/23.90 tff(11942,plain,
% 23.68/23.90 (mult(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c), b) = mult(mult(b, mult(a, c)), b)),
% 23.68/23.90 inference(monotonicity,[status(thm)],[11941])).
% 23.68/23.90 tff(11943,plain,
% 23.68/23.90 (mult(mult(b, mult(a, c)), b) = mult(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c), b)),
% 23.68/23.90 inference(symmetry,[status(thm)],[11942])).
% 23.68/23.90 tff(11944,plain,
% 23.68/23.90 (mult(b, mult(mult(a, b), c)) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), b)),
% 23.68/23.90 inference(transitivity,[status(thm)],[3387, 11381, 11632, 11943, 11940])).
% 23.68/23.90 tff(11945,plain,
% 23.68/23.90 (mult(mult(b, mult(mult(a, b), c)), a) = mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), b), a)),
% 23.68/23.90 inference(monotonicity,[status(thm)],[11944])).
% 23.68/23.90 tff(11946,plain,
% 23.68/23.90 (mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), b), a) = mult(mult(b, mult(mult(a, b), c)), a)),
% 23.68/23.90 inference(symmetry,[status(thm)],[11945])).
% 23.68/23.90 tff(11947,assumption,(mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), b), a) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(b, a))), introduced(assumption)).
% 23.68/23.90 tff(11948,plain,
% 23.68/23.90 (mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), b), a)),
% 23.68/23.90 inference(symmetry,[status(thm)],[11947])).
% 23.68/23.90 tff(11949,plain,
% 23.68/23.90 (mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c), mult(b, a))),
% 23.68/23.90 inference(monotonicity,[status(thm)],[10368])).
% 23.68/23.90 tff(11950,plain,
% 23.68/23.90 (mult(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c), mult(b, a)) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(b, a))),
% 23.68/23.90 inference(symmetry,[status(thm)],[11949])).
% 23.68/23.90 tff(11951,plain,
% 23.68/23.90 (mult(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c), mult(b, a)) = mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), mult(b, a))),
% 23.68/23.90 inference(monotonicity,[status(thm)],[10345])).
% 23.68/23.90 tff(11952,plain,
% 23.68/23.90 (mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c), mult(b, a))),
% 23.68/23.90 inference(symmetry,[status(thm)],[11951])).
% 23.68/23.90 tff(11953,plain,
% 23.68/23.90 (mult(mult(mult(a, c), mult(b, a)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), mult(b, a))),
% 23.68/23.90 inference(symmetry,[status(thm)],[11933])).
% 23.68/23.90 tff(11954,plain,
% 23.68/23.90 (~(mult(mult(a, c), mult(b, mult(a, b))) = mult(mult(a, c), mult(mult(a, b), b)))),
% 23.68/23.90 inference(unit_resolution,[status(thm)],[7316, 1311, 7278])).
% 23.68/23.90 tff(11955,plain,
% 23.68/23.90 ((~(mult(mult(a, c), mult(b, mult(a, b))) = mult(mult(a, c), mult(mult(a, b), b)))) | (~(mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(mult(a, c), mult(a, b)), b)))),
% 23.68/23.90 inference(unit_resolution,[status(thm)],[576, 11954])).
% 23.68/23.90 tff(11956,plain,
% 23.68/23.90 (~((~(mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(a, c), mult(b, mult(a, b))))) | (~(mult(mult(mult(a, c), mult(a, b)), b) = mult(mult(a, c), mult(mult(a, b), b)))))),
% 23.68/23.90 inference(unit_resolution,[status(thm)],[584, 11955])).
% 23.68/23.90 tff(11957,plain,
% 23.68/23.90 (mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(a, c), mult(b, mult(a, b)))),
% 23.68/23.90 inference(unit_resolution,[status(thm)],[604, 11956])).
% 23.68/23.90 tff(11958,plain,
% 23.68/23.90 (mult(mult(mult(a, c), mult(b, a)), b) = mult(mult(a, c), mult(mult(b, a), b))),
% 23.68/23.90 inference(unit_resolution,[status(thm)],[11920, 11957, 1311, 7293])).
% 23.68/23.90 tff(11959,plain,
% 23.68/23.90 (mult(mult(mult(a, c), mult(b, a)), b) = mult(mult(mult(mult(a, b), c), a), b)),
% 23.68/23.90 inference(transitivity,[status(thm)],[11958, 964, 11899])).
% 23.68/23.90 tff(11960,plain,
% 23.68/23.90 (rd(mult(mult(mult(a, c), mult(b, a)), b), b) = rd(mult(mult(mult(mult(a, b), c), a), b), b)),
% 23.68/23.90 inference(monotonicity,[status(thm)],[11959])).
% 23.68/23.90 tff(11961,plain,
% 23.68/23.90 (mult(mult(a, c), mult(b, a)) = mult(mult(mult(a, b), c), a)),
% 23.68/23.90 inference(transitivity,[status(thm)],[11926, 11960, 1478])).
% 23.68/23.90 tff(11962,plain,
% 23.68/23.90 (mult(mult(mult(a, c), mult(b, a)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(mult(a, b), c), a), mult(a, rd(mult(b, c), mult(a, c))))),
% 23.68/23.90 inference(monotonicity,[status(thm)],[11961])).
% 23.68/23.91 tff(11963,plain,
% 23.68/23.91 (mult(mult(mult(mult(a, b), c), a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, c), mult(b, a)), mult(a, rd(mult(b, c), mult(a, c))))),
% 23.68/23.91 inference(symmetry,[status(thm)],[11962])).
% 23.68/23.91 tff(11964,plain,
% 23.68/23.91 (mult(mult(mult(a, b), c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(mult(mult(a, b), c), a), mult(a, rd(mult(b, c), mult(a, c))))),
% 23.68/23.91 inference(symmetry,[status(thm)],[11932])).
% 23.68/23.91 tff(11965,plain,
% 23.68/23.91 (mult(mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a), unit) = mult(mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a)), unit)),
% 23.68/23.91 inference(monotonicity,[status(thm)],[11929])).
% 23.68/23.91 tff(11966,plain,
% 23.68/23.91 (mult(mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a)), unit) = mult(mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a), unit)),
% 23.68/23.91 inference(symmetry,[status(thm)],[11965])).
% 23.68/23.91 tff(11967,plain,
% 23.68/23.91 (mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a), unit)),
% 23.68/23.91 inference(transitivity,[status(thm)],[11793, 11791, 11788, 11966])).
% 23.68/23.91 tff(11968,plain,
% 23.68/23.91 (mult(mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a)), a) = mult(mult(mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a), unit), a)),
% 23.68/23.91 inference(monotonicity,[status(thm)],[11967])).
% 23.68/23.91 tff(11969,plain,
% 23.68/23.91 (mult(mult(mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a), unit), a) = mult(mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a)), a)),
% 23.68/23.91 inference(symmetry,[status(thm)],[11968])).
% 23.68/23.91 tff(11970,plain,
% 23.68/23.91 (mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), mult(mult(a, unit), a)) = mult(mult(mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a), unit), a)),
% 23.68/23.91 inference(symmetry,[status(thm)],[11777])).
% 23.68/23.91 tff(11971,plain,
% 23.68/23.91 (mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), mult(mult(a, unit), a))),
% 23.68/23.91 inference(symmetry,[status(thm)],[11775])).
% 23.68/23.91 tff(11972,plain,
% 23.68/23.91 (mult(a, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c))) = mult(mult(unit, a), mult(mult(b, c), b))),
% 23.68/23.91 inference(monotonicity,[status(thm)],[245, 5559])).
% 23.68/23.91 tff(11973,plain,
% 23.68/23.91 (mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(b, b), c))),
% 23.68/23.91 inference(transitivity,[status(thm)],[11930, 11972, 778, 783, 827, 832, 892, 11764])).
% 23.68/23.91 tff(11974,plain,
% 23.68/23.91 (ld(a, mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))))) = ld(a, mult(a, mult(mult(b, b), c)))),
% 23.68/23.91 inference(monotonicity,[status(thm)],[11973])).
% 23.68/23.91 tff(11975,plain,
% 23.68/23.91 (mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))) = mult(mult(b, c), b)),
% 23.68/23.91 inference(transitivity,[status(thm)],[11772, 11974, 7101, 5563])).
% 23.68/23.91 tff(11976,plain,
% 23.68/23.91 (mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), mult(a, a)) = mult(mult(mult(b, c), b), mult(a, a))),
% 23.68/23.91 inference(monotonicity,[status(thm)],[11975])).
% 23.68/23.91 tff(11977,plain,
% 23.68/23.91 (mult(mult(mult(b, c), b), mult(a, a)) = mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), mult(a, a))),
% 23.68/23.91 inference(symmetry,[status(thm)],[11976])).
% 23.68/23.91 tff(11978,plain,
% 23.68/23.91 (mult(mult(mult(mult(mult(b, c), b), a), unit), a) = mult(mult(mult(c, mult(b, c)), mult(mult(unit, ld(c, mult(a, b))), unit)), a)),
% 23.68/23.91 inference(transitivity,[status(thm)],[3035, 3073, 11977, 11971, 11970, 11969, 11931, 11832, 11964, 11963, 11953, 11952, 11950, 11948, 11946, 11938])).
% 23.68/23.91 tff(11979,plain,
% 23.68/23.91 (rd(mult(mult(mult(mult(mult(b, c), b), a), unit), a), a) = rd(mult(mult(mult(c, mult(b, c)), mult(mult(unit, ld(c, mult(a, b))), unit)), a), a)),
% 23.68/23.91 inference(monotonicity,[status(thm)],[11978])).
% 23.68/23.91 tff(11980,plain,
% 23.68/23.91 (mult(mult(mult(mult(b, c), b), a), unit) = rd(mult(mult(mult(mult(mult(b, c), b), a), unit), a), a)),
% 23.68/23.91 inference(symmetry,[status(thm)],[3031])).
% 23.68/23.91 tff(11981,plain,
% 23.68/23.91 (mult(b, mult(mult(b, c), a)) = mult(b, mult(mult(a, b), c))),
% 23.68/23.91 inference(transitivity,[status(thm)],[7550, 6961, 3074, 11980, 11979, 11935, 10904, 10899, 3391, 10878, 3388])).
% 23.68/23.91 tff(11982,plain,
% 23.68/23.91 (ld(b, mult(b, mult(mult(b, c), a))) = ld(b, mult(b, mult(mult(a, b), c)))),
% 23.68/23.91 inference(monotonicity,[status(thm)],[11981])).
% 23.68/23.91 tff(11983,plain,
% 23.68/23.91 (mult(mult(b, c), a) = mult(mult(a, b), c)),
% 23.68/23.91 inference(transitivity,[status(thm)],[7553, 11982, 5605])).
% 23.68/23.91 tff(11984,plain,
% 23.68/23.91 (mult(mult(mult(b, c), a), b) = mult(mult(mult(a, b), c), b)),
% 23.68/23.91 inference(monotonicity,[status(thm)],[11983])).
% 23.68/23.91 tff(11985,plain,
% 23.68/23.91 (mult(mult(mult(a, b), c), b) = mult(mult(mult(b, c), a), b)),
% 23.68/23.91 inference(symmetry,[status(thm)],[11984])).
% 23.68/23.91 tff(11986,plain,
% 23.68/23.91 (mult(mult(c, mult(a, b)), b) = mult(mult(c, b), mult(a, b))),
% 23.68/23.91 inference(transitivity,[status(thm)],[10520, 11985, 1311, 7273])).
% 23.68/23.91 tff(11987,plain,
% 23.68/23.91 ($false),
% 23.68/23.91 inference(unit_resolution,[status(thm)],[7278, 11986])).
% 23.68/23.91 tff(11988,plain,((~(mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), b), a) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(b, a)))) | (mult(mult(c, mult(a, b)), b) = mult(mult(c, b), mult(a, b))) | (~(mult(mult(mult(b, c), a), b) = mult(mult(b, c), mult(a, b)))) | (~(mult(mult(b, mult(b, c)), a) = mult(b, mult(mult(b, c), a)))) | (~(mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(mult(a, c), mult(b, a)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(mult(a, b), c), a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, b), c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a)), a) = mult(mult(mult(a, b), c), mult(mult(rd(mult(b, c), mult(a, c)), a), a)))) | (~(mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), b) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), b)))) | (~(mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))) | (~(mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))) = mult(b, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))) | (~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(b, mult(a, c)), b) = mult(b, mult(mult(a, c), b)))) | (~(mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, mult(a, c))))))), inference(lemma,lemma(discharge,[]))).
% 23.68/23.91 tff(11989,plain,
% 23.68/23.91 (~(mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), b), a) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(b, a)))),
% 23.68/23.91 inference(unit_resolution,[status(thm)],[11988, 11933, 1311, 6990, 7278, 11932, 11931, 11930, 5557, 11929, 2187, 10365, 299, 8414, 6879, 4789, 10636])).
% 23.68/23.91 tff(11990,plain,
% 23.68/23.91 ((~(mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), b), a) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(b, a)))) | (~(mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a), b) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(a, b))))),
% 23.68/23.91 inference(unit_resolution,[status(thm)],[11385, 11989])).
% 23.68/23.91 tff(11991,plain,
% 23.68/23.91 (~((~(mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), b), a) = mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), a), b))) | (~(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(a, b)))))),
% 23.68/23.91 inference(unit_resolution,[status(thm)],[11287, 11990])).
% 23.68/23.91 tff(11992,plain,
% 23.68/23.91 (mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(a, b))),
% 23.68/23.91 inference(unit_resolution,[status(thm)],[11275, 11991])).
% 23.68/23.91 tff(11993,plain,
% 23.68/23.91 (ld(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(b, a))) = ld(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), mult(a, b)))),
% 23.68/23.91 inference(monotonicity,[status(thm)],[11992])).
% 23.68/23.91 tff(11994,plain,
% 23.68/23.91 (mult(b, a) = mult(a, b)),
% 23.68/23.91 inference(transitivity,[status(thm)],[11266, 11993, 11261])).
% 23.68/23.91 tff(11995,plain,
% 23.68/23.91 (mult(mult(mult(b, c), a), mult(b, a)) = mult(mult(mult(b, c), a), mult(a, b))),
% 23.68/23.91 inference(monotonicity,[status(thm)],[11994])).
% 23.68/23.91 tff(11996,plain,
% 23.68/23.91 (mult(mult(mult(a, c), mult(a, b)), b) = mult(mult(a, c), mult(mult(a, b), b))),
% 23.68/23.91 inference(unit_resolution,[status(thm)],[586, 11956])).
% 23.68/23.91 tff(11997,plain,
% 23.68/23.91 (mult(mult(a, c), mult(mult(a, b), b)) = mult(mult(mult(a, c), mult(a, b)), b)),
% 23.68/23.91 inference(symmetry,[status(thm)],[11996])).
% 23.68/23.91 tff(11998,plain,
% 23.68/23.91 (mult(mult(a, c), mult(b, mult(a, b))) = mult(mult(mult(a, c), b), mult(a, b))),
% 23.68/23.91 inference(symmetry,[status(thm)],[11957])).
% 23.68/23.91 tff(11999,plain,
% 23.68/23.91 ((mult(mult(a, c), mult(b, mult(a, b))) = mult(mult(a, c), mult(mult(a, b), b))) <=> (mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(mult(a, c), mult(a, b)), b))),
% 23.68/23.91 inference(monotonicity,[status(thm)],[11998, 11997])).
% 23.68/23.91 tff(12000,plain,
% 23.68/23.91 ((~(mult(mult(a, c), mult(b, mult(a, b))) = mult(mult(a, c), mult(mult(a, b), b)))) <=> (~(mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(mult(a, c), mult(a, b)), b)))),
% 23.68/23.91 inference(monotonicity,[status(thm)],[11999])).
% 23.68/23.91 tff(12001,plain,
% 23.68/23.91 (~(mult(mult(mult(a, c), b), mult(a, b)) = mult(mult(mult(a, c), mult(a, b)), b))),
% 23.68/23.91 inference(modus_ponens,[status(thm)],[11954, 12000])).
% 23.68/23.91 tff(12002,plain,
% 23.68/23.91 (~(mult(mult(mult(b, c), a), mult(b, a)) = mult(mult(mult(b, c), a), mult(a, b)))),
% 23.68/23.91 inference(unit_resolution,[status(thm)],[11246, 12001, 11996, 11957, 7293, 1311])).
% 23.68/23.91 tff(12003,plain,
% 23.68/23.91 ((~(mult(mult(mult(mult(b, c), a), b), a) = mult(mult(mult(mult(b, c), a), a), b))) | (~(mult(mult(mult(b, c), a), mult(b, a)) = mult(mult(mult(b, c), a), mult(a, b))))),
% 23.68/23.91 inference(unit_resolution,[status(thm)],[11248, 12002])).
% 23.68/23.91 tff(12004,plain,
% 23.68/23.91 (~((~(mult(mult(mult(mult(b, c), a), b), a) = mult(mult(mult(b, c), a), mult(b, a)))) | (~(mult(mult(mult(mult(b, c), a), a), b) = mult(mult(mult(b, c), a), mult(a, b)))))),
% 23.68/23.91 inference(unit_resolution,[status(thm)],[3115, 12003])).
% 23.68/23.91 tff(12005,plain,
% 23.68/23.91 (mult(mult(mult(mult(b, c), a), b), a) = mult(mult(mult(b, c), a), mult(b, a))),
% 23.68/23.91 inference(unit_resolution,[status(thm)],[3117, 12004])).
% 23.68/23.91 tff(12006,plain,
% 23.68/23.91 (mult(mult(mult(b, c), mult(a, b)), a) = mult(mult(mult(b, c), a), mult(a, b))),
% 23.68/23.91 inference(transitivity,[status(thm)],[1313, 12005, 11995])).
% 23.68/23.91 tff(12007,plain,
% 23.68/23.91 (mult(mult(mult(mult(b, c), a), b), a) = mult(mult(mult(b, c), mult(a, b)), a)),
% 23.68/23.91 inference(symmetry,[status(thm)],[1313])).
% 23.68/23.91 tff(12008,plain,
% 23.68/23.91 (mult(mult(mult(b, c), a), mult(b, a)) = mult(mult(mult(mult(b, c), a), b), a)),
% 23.68/23.91 inference(symmetry,[status(thm)],[12005])).
% 23.68/23.91 tff(12009,plain,
% 23.68/23.91 (mult(mult(mult(b, c), a), mult(b, a)) = mult(mult(mult(b, c), mult(a, b)), a)),
% 23.68/23.91 inference(transitivity,[status(thm)],[12008, 12007])).
% 23.68/23.91 tff(12010,plain,
% 23.68/23.91 ((mult(mult(mult(b, c), a), mult(b, a)) = mult(mult(mult(b, c), a), mult(a, b))) <=> (mult(mult(mult(b, c), mult(a, b)), a) = mult(mult(mult(b, c), a), mult(a, b)))),
% 23.68/23.91 inference(monotonicity,[status(thm)],[12009])).
% 23.68/23.91 tff(12011,plain,
% 23.68/23.91 ((~(mult(mult(mult(b, c), a), mult(b, a)) = mult(mult(mult(b, c), a), mult(a, b)))) <=> (~(mult(mult(mult(b, c), mult(a, b)), a) = mult(mult(mult(b, c), a), mult(a, b))))),
% 23.68/23.91 inference(monotonicity,[status(thm)],[12010])).
% 23.68/23.91 tff(12012,plain,
% 23.68/23.91 (~(mult(mult(mult(b, c), mult(a, b)), a) = mult(mult(mult(b, c), a), mult(a, b)))),
% 23.68/23.91 inference(modus_ponens,[status(thm)],[12002, 12011])).
% 23.68/23.91 tff(12013,plain,
% 23.68/23.91 ($false),
% 23.68/23.91 inference(unit_resolution,[status(thm)],[12012, 12006])).
% 23.68/23.91 tff(12014,plain,((~(mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(mult(a, c), mult(b, a)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(b, c), a), b) = mult(mult(b, c), mult(a, b)))) | (~(mult(mult(b, mult(b, c)), a) = mult(b, mult(mult(b, c), a)))) | (mult(mult(c, mult(a, b)), b) = mult(mult(c, b), mult(a, b))) | (~(mult(mult(mult(mult(a, b), c), a), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, b), c), mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a)), a) = mult(mult(mult(a, b), c), mult(mult(rd(mult(b, c), mult(a, c)), a), a)))) | (~(mult(a, mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, b), c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(a, c)), b) = mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), b)))) | (~(mult(mult(mult(mult(a, b), c), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(a, b), c), mult(rd(mult(b, c), mult(a, c)), a)))) | (~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))) | (~(mult(b, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))) = mult(b, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))) | (~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(b, mult(a, c)), b) = mult(b, mult(mult(a, c), b)))) | (~(mult(mult(c, a), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, mult(a, c))) = mult(rd(mult(b, c), mult(a, c)), mult(a, mult(c, mult(a, c))))))), inference(lemma,lemma(discharge,[]))).
% 23.68/23.91 tff(12015,plain,
% 23.68/23.91 (~(mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(mult(a, c), mult(b, a)), mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.68/23.91 inference(unit_resolution,[status(thm)],[12014, 10448, 9698, 10443, 11898, 11869, 11767, 11002, 11781, 8165, 11043, 281, 10584, 9662, 6583, 10627])).
% 23.68/23.91 tff(12016,plain,
% 23.68/23.91 (((~(mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(mult(a, c), mult(b, a)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, c), mult(mult(a, rd(mult(b, c), mult(a, c))), mult(b, a))) = mult(mult(a, c), mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))))))) | (mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(mult(a, c), mult(b, a)), mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.68/23.91 inference(tautology,[status(thm)],[])).
% 23.68/23.91 tff(12017,plain,
% 23.68/23.91 ((~(mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(mult(a, c), mult(b, a)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, c), mult(mult(a, rd(mult(b, c), mult(a, c))), mult(b, a))) = mult(mult(a, c), mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))))))),
% 23.68/23.91 inference(unit_resolution,[status(thm)],[12016, 12015])).
% 23.68/23.91 tff(12018,assumption,((~(mult(mult(mult(a, c), mult(b, a)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(a, c), mult(mult(a, rd(mult(b, c), mult(a, c))), mult(b, a)))))), introduced(assumption)).
% 23.68/23.91 tff(12019,assumption,((~(mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(mult(a, c), mult(b, a)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, c), mult(mult(a, rd(mult(b, c), mult(a, c))), mult(b, a))) = mult(mult(a, c), mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))))))), introduced(assumption)).
% 23.68/23.91 tff(12020,plain,
% 23.68/23.91 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, c), mult(b, a)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(a, c), mult(mult(a, rd(mult(b, c), mult(a, c))), mult(b, a))))))) | (~((~(mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(mult(a, c), mult(b, a)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, c), mult(mult(a, rd(mult(b, c), mult(a, c))), mult(b, a))) = mult(mult(a, c), mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c))))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(a, c), mult(b, a)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(a, c), mult(mult(a, rd(mult(b, c), mult(a, c))), mult(b, a))))))) | (~((~(mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(mult(a, c), mult(b, a)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, c), mult(mult(a, rd(mult(b, c), mult(a, c))), mult(b, a))) = mult(mult(a, c), mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c))))))))))),
% 23.68/23.92 inference(rewrite,[status(thm)],[])).
% 23.68/23.92 tff(12021,plain,
% 23.68/23.92 (((~((~(mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(mult(a, c), mult(b, a)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, c), mult(mult(a, rd(mult(b, c), mult(a, c))), mult(b, a))) = mult(mult(a, c), mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c))))))))) | (~((~(mult(mult(mult(a, c), mult(b, a)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(a, c), mult(mult(a, rd(mult(b, c), mult(a, c))), mult(b, a)))))))) <=> ((~((~(mult(mult(mult(a, c), mult(b, a)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(a, c), mult(mult(a, rd(mult(b, c), mult(a, c))), mult(b, a))))))) | (~((~(mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(mult(a, c), mult(b, a)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, c), mult(mult(a, rd(mult(b, c), mult(a, c))), mult(b, a))) = mult(mult(a, c), mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c))))))))))),
% 23.68/23.92 inference(rewrite,[status(thm)],[])).
% 23.68/23.92 tff(12022,plain,
% 23.68/23.92 ((~((~(mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(a, c), mult(mult(a, rd(mult(b, c), mult(a, c))), mult(b, a))))) | (~(mult(mult(mult(a, c), mult(b, a)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c))))))))) <=> (~((~(mult(mult(mult(a, c), mult(b, a)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(a, c), mult(mult(a, rd(mult(b, c), mult(a, c))), mult(b, a)))))))),
% 23.68/23.92 inference(rewrite,[status(thm)],[])).
% 23.68/23.92 tff(12023,plain,
% 23.68/23.92 ((~((~(mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(mult(a, c), mult(b, a)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, c), mult(mult(a, rd(mult(b, c), mult(a, c))), mult(b, a))) = mult(mult(a, c), mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c))))))))) <=> (~((~(mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(mult(a, c), mult(b, a)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, c), mult(mult(a, rd(mult(b, c), mult(a, c))), mult(b, a))) = mult(mult(a, c), mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))))))))),
% 23.68/23.92 inference(rewrite,[status(thm)],[])).
% 23.68/23.92 tff(12024,plain,
% 23.68/23.92 (((~((~(mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(mult(a, c), mult(b, a)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, c), mult(mult(a, rd(mult(b, c), mult(a, c))), mult(b, a))) = mult(mult(a, c), mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c))))))))) | (~((~(mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(a, c), mult(mult(a, rd(mult(b, c), mult(a, c))), mult(b, a))))) | (~(mult(mult(mult(a, c), mult(b, a)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))))))))) <=> ((~((~(mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(mult(a, c), mult(b, a)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, c), mult(mult(a, rd(mult(b, c), mult(a, c))), mult(b, a))) = mult(mult(a, c), mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c))))))))) | (~((~(mult(mult(mult(a, c), mult(b, a)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(a, c), mult(mult(a, rd(mult(b, c), mult(a, c))), mult(b, a))))))))),
% 23.68/23.92 inference(monotonicity,[status(thm)],[12023, 12022])).
% 23.68/23.92 tff(12025,plain,
% 23.68/23.92 (((~((~(mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(mult(a, c), mult(b, a)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, c), mult(mult(a, rd(mult(b, c), mult(a, c))), mult(b, a))) = mult(mult(a, c), mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c))))))))) | (~((~(mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(a, c), mult(mult(a, rd(mult(b, c), mult(a, c))), mult(b, a))))) | (~(mult(mult(mult(a, c), mult(b, a)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))))))))) <=> ((~((~(mult(mult(mult(a, c), mult(b, a)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(a, c), mult(mult(a, rd(mult(b, c), mult(a, c))), mult(b, a))))))) | (~((~(mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(mult(a, c), mult(b, a)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, c), mult(mult(a, rd(mult(b, c), mult(a, c))), mult(b, a))) = mult(mult(a, c), mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c))))))))))),
% 23.68/23.92 inference(transitivity,[status(thm)],[12024, 12021])).
% 23.68/23.92 tff(12026,plain,
% 23.68/23.92 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(mult(a, c), mult(b, a)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, c), mult(mult(a, rd(mult(b, c), mult(a, c))), mult(b, a))) = mult(mult(a, c), mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c))))))))) | (~((~(mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(a, c), mult(mult(a, rd(mult(b, c), mult(a, c))), mult(b, a))))) | (~(mult(mult(mult(a, c), mult(b, a)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c))))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, c), mult(b, a)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(a, c), mult(mult(a, rd(mult(b, c), mult(a, c))), mult(b, a))))))) | (~((~(mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(mult(a, c), mult(b, a)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, c), mult(mult(a, rd(mult(b, c), mult(a, c))), mult(b, a))) = mult(mult(a, c), mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))))))))))),
% 23.68/23.92 inference(monotonicity,[status(thm)],[12025])).
% 23.68/23.92 tff(12027,plain,
% 23.68/23.92 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(mult(a, c), mult(b, a)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, c), mult(mult(a, rd(mult(b, c), mult(a, c))), mult(b, a))) = mult(mult(a, c), mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c))))))))) | (~((~(mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(a, c), mult(mult(a, rd(mult(b, c), mult(a, c))), mult(b, a))))) | (~(mult(mult(mult(a, c), mult(b, a)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c))))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(a, c), mult(b, a)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(a, c), mult(mult(a, rd(mult(b, c), mult(a, c))), mult(b, a))))))) | (~((~(mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(mult(a, c), mult(b, a)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, c), mult(mult(a, rd(mult(b, c), mult(a, c))), mult(b, a))) = mult(mult(a, c), mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c))))))))))),
% 23.68/23.92 inference(transitivity,[status(thm)],[12026, 12020])).
% 23.68/23.92 tff(12028,plain,
% 23.68/23.92 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(mult(a, c), mult(b, a)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, c), mult(mult(a, rd(mult(b, c), mult(a, c))), mult(b, a))) = mult(mult(a, c), mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c))))))))) | (~((~(mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(a, c), mult(mult(a, rd(mult(b, c), mult(a, c))), mult(b, a))))) | (~(mult(mult(mult(a, c), mult(b, a)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c))))))))))),
% 23.68/23.92 inference(quant_inst,[status(thm)],[])).
% 23.68/23.92 tff(12029,plain,
% 23.68/23.92 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(a, c), mult(b, a)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(a, c), mult(mult(a, rd(mult(b, c), mult(a, c))), mult(b, a))))))) | (~((~(mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(mult(a, c), mult(b, a)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, c), mult(mult(a, rd(mult(b, c), mult(a, c))), mult(b, a))) = mult(mult(a, c), mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))))))))),
% 23.68/23.93 inference(modus_ponens,[status(thm)],[12028, 12027])).
% 23.68/23.93 tff(12030,plain,
% 23.68/23.93 ($false),
% 23.68/23.93 inference(unit_resolution,[status(thm)],[12029, 27, 12019, 12018])).
% 23.68/23.93 tff(12031,plain,((~((~(mult(mult(mult(a, c), mult(b, a)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(a, c), mult(mult(a, rd(mult(b, c), mult(a, c))), mult(b, a))))))) | (~((~(mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(mult(a, c), mult(b, a)), mult(a, rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, c), mult(mult(a, rd(mult(b, c), mult(a, c))), mult(b, a))) = mult(mult(a, c), mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))))))))), inference(lemma,lemma(discharge,[]))).
% 23.68/23.93 tff(12032,plain,
% 23.68/23.93 (~((~(mult(mult(mult(a, c), mult(b, a)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(a, c), mult(mult(a, rd(mult(b, c), mult(a, c))), mult(b, a))))))),
% 23.68/23.93 inference(unit_resolution,[status(thm)],[12031, 12017])).
% 23.68/23.93 tff(12033,plain,
% 23.68/23.93 (((~(mult(mult(mult(a, c), mult(b, a)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), mult(b, a)) = mult(mult(a, c), mult(mult(a, rd(mult(b, c), mult(a, c))), mult(b, a)))))) | (mult(mult(mult(a, c), mult(b, a)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c))))))),
% 23.68/23.93 inference(tautology,[status(thm)],[])).
% 23.68/23.93 tff(12034,plain,
% 23.68/23.93 (mult(mult(mult(a, c), mult(b, a)), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.68/23.93 inference(unit_resolution,[status(thm)],[12033, 12032])).
% 23.68/23.93 tff(12035,plain,
% 23.68/23.93 (mult(mult(a, c), mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c))))) = mult(mult(mult(a, c), mult(b, a)), mult(a, rd(mult(b, c), mult(a, c))))),
% 23.68/23.93 inference(symmetry,[status(thm)],[12034])).
% 23.68/23.93 tff(12036,plain,
% 23.68/23.93 (mult(mult(a, c), mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))) = mult(mult(a, c), mult(mult(b, a), mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.68/23.93 inference(monotonicity,[status(thm)],[11604])).
% 23.68/23.93 tff(12037,plain,
% 23.68/23.93 (mult(mult(a, c), mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))) = mult(mult(a, c), mult(mult(unit, a), mult(mult(b, unit), b)))),
% 23.68/23.93 inference(transitivity,[status(thm)],[12036, 12035, 11928, 11898, 11875, 11870, 11795, 11777, 11775, 11774, 3037, 3036, 11763, 11735, 11733, 11731, 11728, 11726, 10454, 11722, 11721])).
% 23.68/23.93 tff(12038,plain,
% 23.68/23.93 (ld(mult(a, c), mult(mult(a, c), mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))) = ld(mult(a, c), mult(mult(a, c), mult(mult(unit, a), mult(mult(b, unit), b))))),
% 23.68/23.93 inference(monotonicity,[status(thm)],[12037])).
% 23.68/23.93 tff(12039,plain,
% 23.68/23.93 (ld(mult(a, c), mult(mult(a, c), mult(mult(unit, a), mult(mult(b, unit), b)))) = ld(mult(a, c), mult(mult(a, c), mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))))),
% 23.68/23.93 inference(symmetry,[status(thm)],[12038])).
% 23.68/23.93 tff(12040,plain,
% 23.68/23.93 (mult(mult(unit, a), mult(mult(b, unit), b)) = ld(mult(a, c), mult(mult(a, c), mult(mult(unit, a), mult(mult(b, unit), b))))),
% 23.68/23.93 inference(symmetry,[status(thm)],[7277])).
% 23.68/23.93 tff(12041,plain,
% 23.68/23.93 (mult(a, mult(unit, mult(mult(b, unit), b))) = mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.68/23.93 inference(transitivity,[status(thm)],[829, 12040, 12039, 11720])).
% 23.68/23.93 tff(12042,plain,
% 23.68/23.93 (mult(c, mult(a, mult(unit, mult(mult(b, unit), b)))) = mult(c, mult(b, mult(a, mult(a, rd(mult(b, c), mult(a, c))))))),
% 23.68/23.93 inference(monotonicity,[status(thm)],[12041])).
% 23.68/23.93 tff(12043,plain,
% 23.68/23.93 (mult(c, mult(mult(a, b), b)) = mult(c, mult(a, mult(unit, mult(mult(b, unit), b))))),
% 23.68/23.93 inference(monotonicity,[status(thm)],[831])).
% 23.68/23.93 tff(12044,plain,
% 23.68/23.93 (mult(mult(mult(a, b), c), b) = mult(mult(c, mult(a, b)), b)),
% 23.68/23.93 inference(monotonicity,[status(thm)],[11311])).
% 23.68/23.93 tff(12045,plain,
% 23.68/23.93 (mult(mult(mult(a, b), b), c) = mult(mult(a, b), mult(b, c))),
% 23.68/23.93 inference(transitivity,[status(thm)],[828, 12044, 10446, 12043, 12042, 11718, 11608, 11607, 11605, 11603, 11495, 11493, 11492, 11013, 11491, 11421, 11090, 11087, 2943, 11068, 4287, 806])).
% 23.68/23.93 tff(12046,plain,
% 23.68/23.93 ($false),
% 23.68/23.93 inference(unit_resolution,[status(thm)],[1729, 12045])).
% 23.68/23.93 tff(12047,plain,(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))), inference(lemma,lemma(discharge,[]))).
% 23.68/23.93 tff(12048,plain,
% 23.68/23.93 (mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(b, c))),
% 23.68/23.93 inference(transitivity,[status(thm)],[12047, 142])).
% 23.68/23.93 tff(12049,plain,
% 23.68/23.93 (ld(a, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c))))) = ld(a, mult(a, mult(b, c)))),
% 23.68/23.93 inference(monotonicity,[status(thm)],[12048])).
% 23.68/23.93 tff(12050,plain,
% 23.68/23.93 (mult(mult(c, a), rd(mult(b, c), mult(a, c))) = mult(b, c)),
% 23.68/23.93 inference(transitivity,[status(thm)],[8637, 5650, 12049, 141])).
% 23.68/23.93 tff(12051,plain,
% 23.68/23.93 (mult(mult(mult(c, a), rd(mult(b, c), mult(a, c))), a) = mult(mult(b, c), a)),
% 23.68/23.93 inference(monotonicity,[status(thm)],[12050])).
% 23.68/23.93 tff(12052,plain,
% 23.68/23.93 (mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), a)) = mult(c, mult(b, a))),
% 23.68/23.93 inference(transitivity,[status(thm)],[5404, 12051, 3057, 4208])).
% 23.68/23.93 tff(12053,plain,
% 23.68/23.93 (ld(c, mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), a))) = ld(c, mult(c, mult(b, a)))),
% 23.68/23.93 inference(monotonicity,[status(thm)],[12052])).
% 23.68/23.93 tff(12054,plain,
% 23.68/23.93 (mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(b, a)),
% 23.68/23.93 inference(transitivity,[status(thm)],[5409, 12053, 1472])).
% 23.68/23.93 tff(12055,plain,
% 23.68/23.93 (rd(mult(mult(a, rd(mult(b, c), mult(a, c))), a), a) = rd(mult(b, a), a)),
% 23.68/23.93 inference(monotonicity,[status(thm)],[12054])).
% 23.68/23.93 tff(12056,plain,
% 23.68/23.93 (mult(a, rd(mult(b, c), mult(a, c))) = b),
% 23.68/23.93 inference(transitivity,[status(thm)],[1456, 12055, 1451])).
% 23.68/23.93 tff(12057,plain,
% 23.68/23.93 (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), b)),
% 23.68/23.93 inference(monotonicity,[status(thm)],[12056])).
% 23.68/23.93 tff(12058,plain,
% 23.68/23.93 (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), c)),
% 23.68/23.93 inference(transitivity,[status(thm)],[12057, 161, 215])).
% 23.68/23.93 tff(12059,plain,
% 23.68/23.93 (mult(unit, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = mult(unit, mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), c))),
% 23.68/23.93 inference(monotonicity,[status(thm)],[12058])).
% 23.68/23.93 tff(12060,plain,
% 23.68/23.93 ((mult(unit, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = mult(unit, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))) <=> (mult(unit, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))) = mult(unit, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))))),
% 23.68/23.93 inference(commutativity,[status(thm)],[])).
% 23.68/23.93 tff(12061,plain,
% 23.68/23.93 ((mult(unit, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))) = mult(unit, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))) <=> (mult(unit, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = mult(unit, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))))),
% 23.68/23.93 inference(symmetry,[status(thm)],[12060])).
% 23.68/23.93 tff(12062,plain,
% 23.68/23.93 (mult(unit, mult(mult(a, c), b)) = mult(unit, mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), c))),
% 23.68/23.93 inference(monotonicity,[status(thm)],[3189])).
% 23.68/23.93 tff(12063,plain,
% 23.68/23.93 (mult(unit, mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), c)) = mult(unit, mult(mult(a, c), b))),
% 23.68/23.93 inference(symmetry,[status(thm)],[12062])).
% 23.68/23.93 tff(12064,plain,
% 23.68/23.93 (mult(unit, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = mult(unit, mult(mult(a, c), b))),
% 23.68/23.93 inference(transitivity,[status(thm)],[12059, 12063])).
% 23.68/23.93 tff(12065,plain,
% 23.68/23.93 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(b, mult(a, c))),
% 23.68/23.93 inference(monotonicity,[status(thm)],[12056])).
% 23.68/23.93 tff(12066,plain,
% 23.68/23.93 (mult(b, mult(a, c)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))),
% 23.68/23.93 inference(symmetry,[status(thm)],[12065])).
% 23.68/23.93 tff(12067,plain,
% 23.68/23.93 (mult(unit, mult(b, mult(a, c))) = mult(unit, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 23.68/23.93 inference(monotonicity,[status(thm)],[12066])).
% 23.68/23.93 tff(12068,plain,
% 23.68/23.93 (mult(unit, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))) = mult(unit, mult(b, mult(a, c)))),
% 23.68/23.93 inference(symmetry,[status(thm)],[12067])).
% 23.68/23.93 tff(12069,plain,
% 23.68/23.93 ((mult(unit, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))) = mult(unit, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))) <=> (mult(unit, mult(b, mult(a, c))) = mult(unit, mult(mult(a, c), b)))),
% 23.68/23.93 inference(monotonicity,[status(thm)],[12068, 12064])).
% 23.68/23.93 tff(12070,plain,
% 23.68/23.93 ((mult(unit, mult(b, mult(a, c))) = mult(unit, mult(mult(a, c), b))) <=> (mult(unit, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))) = mult(unit, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))))),
% 23.68/23.93 inference(symmetry,[status(thm)],[12069])).
% 23.68/23.93 tff(12071,plain,
% 23.68/23.93 (mult(unit, mult(mult(a, c), b)) = mult(mult(unit, mult(a, c)), b)),
% 23.68/23.93 inference(transitivity,[status(thm)],[12062, 228, 222, 227, 5517])).
% 23.68/23.93 tff(12072,plain,
% 23.68/23.93 ((~![A: $i] : (mult(unit, A) = A)) | (mult(unit, mult(b, mult(a, c))) = mult(b, mult(a, c)))),
% 23.68/23.93 inference(quant_inst,[status(thm)],[])).
% 23.68/23.93 tff(12073,plain,
% 23.68/23.93 (mult(unit, mult(b, mult(a, c))) = mult(b, mult(a, c))),
% 23.68/23.93 inference(unit_resolution,[status(thm)],[12072, 71])).
% 23.68/23.93 tff(12074,plain,
% 23.68/23.93 (mult(unit, mult(b, mult(a, c))) = mult(mult(unit, b), mult(a, c))),
% 23.68/23.93 inference(transitivity,[status(thm)],[12073, 8665])).
% 23.68/23.93 tff(12075,plain,
% 23.68/23.93 ((mult(unit, mult(b, mult(a, c))) = mult(unit, mult(mult(a, c), b))) <=> (mult(mult(unit, b), mult(a, c)) = mult(mult(unit, mult(a, c)), b))),
% 23.68/23.93 inference(monotonicity,[status(thm)],[12074, 12071])).
% 23.68/23.93 tff(12076,plain,
% 23.68/23.93 ((mult(mult(unit, b), mult(a, c)) = mult(mult(unit, mult(a, c)), b)) <=> (mult(unit, mult(b, mult(a, c))) = mult(unit, mult(mult(a, c), b)))),
% 23.68/23.93 inference(symmetry,[status(thm)],[12075])).
% 23.68/23.93 tff(12077,plain,
% 23.68/23.93 ((mult(mult(unit, b), mult(a, c)) = mult(mult(unit, mult(a, c)), b)) <=> (mult(unit, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = mult(unit, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))))),
% 23.68/23.93 inference(transitivity,[status(thm)],[12076, 12070, 12061])).
% 23.68/23.93 tff(12078,plain,
% 23.68/23.93 (mult(mult(unit, b), mult(a, c)) = mult(mult(unit, mult(a, c)), b)),
% 23.68/23.93 inference(unit_resolution,[status(thm)],[8688, 12047])).
% 23.68/23.93 tff(12079,plain,
% 23.68/23.93 (mult(unit, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = mult(unit, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 23.68/23.93 inference(modus_ponens,[status(thm)],[12078, 12077])).
% 23.68/23.93 tff(12080,plain,
% 23.68/23.93 (mult(unit, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))) = mult(unit, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.68/23.93 inference(symmetry,[status(thm)],[12079])).
% 23.68/23.93 tff(12081,plain,
% 23.68/23.93 (mult(b, mult(a, c)) = mult(unit, mult(b, mult(a, c)))),
% 23.68/23.93 inference(symmetry,[status(thm)],[12073])).
% 23.68/23.93 tff(12082,plain,
% 23.68/23.93 (mult(b, mult(a, c)) = mult(mult(a, c), b)),
% 23.68/23.93 inference(transitivity,[status(thm)],[12081, 12067, 12080, 12059, 228, 222, 227])).
% 23.68/23.93 tff(12083,plain,
% 23.68/23.93 (mult(mult(b, mult(a, c)), c) = mult(mult(mult(a, c), b), c)),
% 23.68/23.93 inference(monotonicity,[status(thm)],[12082])).
% 23.68/23.93 tff(12084,plain,
% 23.68/23.93 (mult(b, mult(c, a)) = mult(b, mult(a, c))),
% 23.68/23.93 inference(monotonicity,[status(thm)],[4268])).
% 23.68/23.93 tff(12085,plain,
% 23.68/23.93 (mult(mult(b, mult(c, a)), c) = mult(mult(b, mult(a, c)), c)),
% 23.68/23.93 inference(monotonicity,[status(thm)],[12084])).
% 23.68/23.93 tff(12086,plain,
% 23.68/23.93 (mult(mult(b, c), mult(a, c)) = mult(mult(b, c), mult(c, a))),
% 23.68/23.93 inference(monotonicity,[status(thm)],[8565])).
% 23.68/23.93 tff(12087,plain,
% 23.68/23.93 (mult(mult(b, c), mult(c, a)) = mult(mult(b, c), mult(a, c))),
% 23.68/23.93 inference(symmetry,[status(thm)],[12086])).
% 23.68/23.93 tff(12088,plain,
% 23.68/23.93 ((mult(mult(b, mult(c, a)), c) = mult(mult(b, c), mult(c, a))) <=> (mult(mult(b, mult(a, c)), c) = mult(mult(b, c), mult(a, c)))),
% 23.68/23.93 inference(monotonicity,[status(thm)],[12085, 12087])).
% 23.68/23.93 tff(12089,plain,
% 23.68/23.93 ((mult(mult(b, mult(a, c)), c) = mult(mult(b, c), mult(a, c))) <=> (mult(mult(b, mult(c, a)), c) = mult(mult(b, c), mult(c, a)))),
% 23.68/23.93 inference(symmetry,[status(thm)],[12088])).
% 23.68/23.93 tff(12090,plain,
% 23.68/23.93 (mult(mult(b, mult(c, a)), c) = mult(mult(b, c), mult(c, a))),
% 23.68/23.93 inference(modus_ponens,[status(thm)],[5435, 12089])).
% 23.68/23.93 tff(12091,plain,
% 23.68/23.93 (mult(mult(b, c), mult(c, a)) = mult(mult(b, mult(c, a)), c)),
% 23.68/23.93 inference(symmetry,[status(thm)],[12090])).
% 23.68/23.93 tff(12092,plain,
% 23.68/23.93 (mult(mult(rd(mult(b, c), mult(a, c)), a), c) = mult(b, c)),
% 23.68/23.93 inference(transitivity,[status(thm)],[76, 6555, 61, 137])).
% 23.68/23.93 tff(12093,plain,
% 23.68/23.93 (rd(mult(mult(rd(mult(b, c), mult(a, c)), a), c), c) = rd(mult(b, c), c)),
% 23.68/23.93 inference(monotonicity,[status(thm)],[12092])).
% 23.68/23.93 tff(12094,plain,
% 23.68/23.93 (mult(rd(mult(b, c), mult(a, c)), a) = b),
% 23.68/23.93 inference(transitivity,[status(thm)],[175, 12093, 170])).
% 23.68/23.93 tff(12095,plain,
% 23.68/23.93 (mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(a, c), b)),
% 23.68/23.93 inference(monotonicity,[status(thm)],[12094])).
% 23.68/23.93 tff(12096,plain,
% 23.68/23.93 (mult(mult(b, c), a) = mult(mult(a, c), b)),
% 23.68/23.93 inference(transitivity,[status(thm)],[4338, 5496, 12095])).
% 23.68/23.93 tff(12097,plain,
% 23.68/23.93 (mult(mult(mult(b, c), a), c) = mult(mult(mult(a, c), b), c)),
% 23.68/23.93 inference(monotonicity,[status(thm)],[12096])).
% 23.68/23.93 tff(12098,plain,
% 23.68/23.93 (mult(mult(mult(b, c), a), mult(mult(unit, c), unit)) = mult(mult(mult(b, c), a), c)),
% 23.68/23.93 inference(monotonicity,[status(thm)],[78])).
% 23.68/23.93 tff(12099,plain,
% 23.68/23.93 ((mult(mult(b, c), mult(a, mult(mult(unit, c), unit))) = mult(mult(b, c), mult(mult(mult(unit, c), unit), a))) <=> (mult(mult(b, c), mult(mult(mult(unit, c), unit), a)) = mult(mult(b, c), mult(a, mult(mult(unit, c), unit))))),
% 23.68/23.93 inference(commutativity,[status(thm)],[])).
% 23.68/23.93 tff(12100,plain,
% 23.68/23.93 ((mult(mult(b, c), mult(mult(mult(unit, c), unit), a)) = mult(mult(b, c), mult(a, mult(mult(unit, c), unit)))) <=> (mult(mult(b, c), mult(a, mult(mult(unit, c), unit))) = mult(mult(b, c), mult(mult(mult(unit, c), unit), a)))),
% 23.68/23.93 inference(symmetry,[status(thm)],[12099])).
% 23.68/23.93 tff(12101,plain,
% 23.68/23.93 (mult(mult(a, c), unit) = mult(mult(mult(a, unit), c), unit)),
% 23.68/23.93 inference(symmetry,[status(thm)],[49])).
% 23.68/23.93 tff(12102,plain,
% 23.68/23.93 (mult(a, c) = mult(mult(a, c), unit)),
% 23.68/23.93 inference(symmetry,[status(thm)],[45])).
% 23.68/23.93 tff(12103,plain,
% 23.68/23.93 (mult(a, c) = mult(a, mult(mult(unit, c), unit))),
% 23.68/23.93 inference(transitivity,[status(thm)],[12102, 12101, 58])).
% 23.68/23.93 tff(12104,plain,
% 23.68/23.93 (mult(mult(b, c), mult(a, c)) = mult(mult(b, c), mult(a, mult(mult(unit, c), unit)))),
% 23.68/23.93 inference(monotonicity,[status(thm)],[12103])).
% 23.68/23.93 tff(12105,plain,
% 23.68/23.93 (mult(mult(b, c), mult(a, mult(mult(unit, c), unit))) = mult(mult(b, c), mult(a, c))),
% 23.68/23.93 inference(symmetry,[status(thm)],[12104])).
% 23.68/23.93 tff(12106,plain,
% 23.68/23.93 (mult(mult(b, c), mult(c, a)) = mult(mult(b, c), mult(mult(mult(unit, c), unit), a))),
% 23.68/23.93 inference(monotonicity,[status(thm)],[3866])).
% 23.68/23.93 tff(12107,plain,
% 23.68/23.93 (mult(mult(b, c), mult(mult(mult(unit, c), unit), a)) = mult(mult(b, c), mult(c, a))),
% 23.68/23.93 inference(symmetry,[status(thm)],[12106])).
% 23.68/23.93 tff(12108,plain,
% 23.68/23.93 ((mult(mult(b, c), mult(mult(mult(unit, c), unit), a)) = mult(mult(b, c), mult(a, mult(mult(unit, c), unit)))) <=> (mult(mult(b, c), mult(c, a)) = mult(mult(b, c), mult(a, c)))),
% 23.68/23.93 inference(monotonicity,[status(thm)],[12107, 12105])).
% 23.68/23.93 tff(12109,plain,
% 23.68/23.93 ((mult(mult(b, c), mult(c, a)) = mult(mult(b, c), mult(a, c))) <=> (mult(mult(b, c), mult(mult(mult(unit, c), unit), a)) = mult(mult(b, c), mult(a, mult(mult(unit, c), unit))))),
% 23.68/23.93 inference(symmetry,[status(thm)],[12108])).
% 23.68/23.93 tff(12110,plain,
% 23.68/23.93 ((mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))) <=> (mult(mult(b, c), mult(c, a)) = mult(mult(b, c), mult(a, c)))),
% 23.68/23.93 inference(monotonicity,[status(thm)],[8875, 5652])).
% 23.68/23.93 tff(12111,plain,
% 23.68/23.94 ((mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))) <=> (mult(mult(b, c), mult(a, mult(mult(unit, c), unit))) = mult(mult(b, c), mult(mult(mult(unit, c), unit), a)))),
% 23.68/23.94 inference(transitivity,[status(thm)],[12110, 12109, 12100])).
% 23.68/23.94 tff(12112,plain,
% 23.68/23.94 ((~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))) <=> (~(mult(mult(b, c), mult(a, mult(mult(unit, c), unit))) = mult(mult(b, c), mult(mult(mult(unit, c), unit), a))))),
% 23.68/23.94 inference(monotonicity,[status(thm)],[12111])).
% 23.68/23.94 tff(12113,plain,
% 23.68/23.94 (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 23.68/23.94 inference(unit_resolution,[status(thm)],[6559, 6551])).
% 23.68/23.94 tff(12114,plain,
% 23.68/23.94 (~(mult(mult(b, c), mult(a, mult(mult(unit, c), unit))) = mult(mult(b, c), mult(mult(mult(unit, c), unit), a)))),
% 23.68/23.94 inference(modus_ponens,[status(thm)],[12113, 12112])).
% 23.68/23.94 tff(12115,plain,
% 23.68/23.94 (((~(mult(mult(mult(b, c), a), mult(mult(unit, c), unit)) = mult(mult(mult(b, c), mult(mult(unit, c), unit)), a))) | (~(mult(mult(b, c), mult(a, mult(mult(unit, c), unit))) = mult(mult(b, c), mult(mult(mult(unit, c), unit), a))))) | (mult(mult(b, c), mult(a, mult(mult(unit, c), unit))) = mult(mult(b, c), mult(mult(mult(unit, c), unit), a)))),
% 23.68/23.94 inference(tautology,[status(thm)],[])).
% 23.68/23.94 tff(12116,plain,
% 23.68/23.94 ((~(mult(mult(mult(b, c), a), mult(mult(unit, c), unit)) = mult(mult(mult(b, c), mult(mult(unit, c), unit)), a))) | (~(mult(mult(b, c), mult(a, mult(mult(unit, c), unit))) = mult(mult(b, c), mult(mult(mult(unit, c), unit), a))))),
% 23.68/23.94 inference(unit_resolution,[status(thm)],[12115, 12114])).
% 23.68/23.94 tff(12117,plain,
% 23.68/23.94 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(b, c), a), mult(mult(unit, c), unit)) = mult(mult(mult(b, c), mult(mult(unit, c), unit)), a))) | (~(mult(mult(b, c), mult(a, mult(mult(unit, c), unit))) = mult(mult(b, c), mult(mult(mult(unit, c), unit), a)))))) | (~((~(mult(mult(mult(b, c), a), mult(mult(unit, c), unit)) = mult(mult(b, c), mult(a, mult(mult(unit, c), unit))))) | (~(mult(mult(mult(b, c), mult(mult(unit, c), unit)), a) = mult(mult(b, c), mult(mult(mult(unit, c), unit), a)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(b, c), a), mult(mult(unit, c), unit)) = mult(mult(mult(b, c), mult(mult(unit, c), unit)), a))) | (~(mult(mult(b, c), mult(a, mult(mult(unit, c), unit))) = mult(mult(b, c), mult(mult(mult(unit, c), unit), a)))))) | (~((~(mult(mult(mult(b, c), a), mult(mult(unit, c), unit)) = mult(mult(b, c), mult(a, mult(mult(unit, c), unit))))) | (~(mult(mult(mult(b, c), mult(mult(unit, c), unit)), a) = mult(mult(b, c), mult(mult(mult(unit, c), unit), a)))))))),
% 23.68/23.94 inference(rewrite,[status(thm)],[])).
% 23.68/23.94 tff(12118,plain,
% 23.68/23.94 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(b, c), a), mult(mult(unit, c), unit)) = mult(mult(mult(b, c), mult(mult(unit, c), unit)), a))) | (~(mult(mult(b, c), mult(a, mult(mult(unit, c), unit))) = mult(mult(b, c), mult(mult(mult(unit, c), unit), a)))))) | (~((~(mult(mult(mult(b, c), a), mult(mult(unit, c), unit)) = mult(mult(b, c), mult(a, mult(mult(unit, c), unit))))) | (~(mult(mult(mult(b, c), mult(mult(unit, c), unit)), a) = mult(mult(b, c), mult(mult(mult(unit, c), unit), a)))))))),
% 23.68/23.94 inference(quant_inst,[status(thm)],[])).
% 23.68/23.94 tff(12119,plain,
% 23.68/23.94 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(b, c), a), mult(mult(unit, c), unit)) = mult(mult(mult(b, c), mult(mult(unit, c), unit)), a))) | (~(mult(mult(b, c), mult(a, mult(mult(unit, c), unit))) = mult(mult(b, c), mult(mult(mult(unit, c), unit), a)))))) | (~((~(mult(mult(mult(b, c), a), mult(mult(unit, c), unit)) = mult(mult(b, c), mult(a, mult(mult(unit, c), unit))))) | (~(mult(mult(mult(b, c), mult(mult(unit, c), unit)), a) = mult(mult(b, c), mult(mult(mult(unit, c), unit), a))))))),
% 23.68/23.94 inference(modus_ponens,[status(thm)],[12118, 12117])).
% 23.68/23.94 tff(12120,plain,
% 23.68/23.94 ((~((~(mult(mult(mult(b, c), a), mult(mult(unit, c), unit)) = mult(mult(mult(b, c), mult(mult(unit, c), unit)), a))) | (~(mult(mult(b, c), mult(a, mult(mult(unit, c), unit))) = mult(mult(b, c), mult(mult(mult(unit, c), unit), a)))))) | (~((~(mult(mult(mult(b, c), a), mult(mult(unit, c), unit)) = mult(mult(b, c), mult(a, mult(mult(unit, c), unit))))) | (~(mult(mult(mult(b, c), mult(mult(unit, c), unit)), a) = mult(mult(b, c), mult(mult(mult(unit, c), unit), a))))))),
% 23.68/23.94 inference(unit_resolution,[status(thm)],[12119, 27])).
% 23.68/23.94 tff(12121,plain,
% 23.68/23.94 (~((~(mult(mult(mult(b, c), a), mult(mult(unit, c), unit)) = mult(mult(b, c), mult(a, mult(mult(unit, c), unit))))) | (~(mult(mult(mult(b, c), mult(mult(unit, c), unit)), a) = mult(mult(b, c), mult(mult(mult(unit, c), unit), a)))))),
% 23.68/23.94 inference(unit_resolution,[status(thm)],[12120, 12116])).
% 23.68/23.94 tff(12122,plain,
% 23.68/23.94 (((~(mult(mult(mult(b, c), a), mult(mult(unit, c), unit)) = mult(mult(b, c), mult(a, mult(mult(unit, c), unit))))) | (~(mult(mult(mult(b, c), mult(mult(unit, c), unit)), a) = mult(mult(b, c), mult(mult(mult(unit, c), unit), a))))) | (mult(mult(mult(b, c), a), mult(mult(unit, c), unit)) = mult(mult(b, c), mult(a, mult(mult(unit, c), unit))))),
% 23.68/23.94 inference(tautology,[status(thm)],[])).
% 23.68/23.94 tff(12123,plain,
% 23.68/23.94 (mult(mult(mult(b, c), a), mult(mult(unit, c), unit)) = mult(mult(b, c), mult(a, mult(mult(unit, c), unit)))),
% 23.68/23.94 inference(unit_resolution,[status(thm)],[12122, 12121])).
% 23.68/23.94 tff(12124,plain,
% 23.68/23.94 (mult(mult(b, c), mult(a, mult(mult(unit, c), unit))) = mult(mult(mult(b, c), a), mult(mult(unit, c), unit))),
% 23.68/23.94 inference(symmetry,[status(thm)],[12123])).
% 23.68/23.94 tff(12125,plain,
% 23.68/23.94 (mult(mult(b, c), mult(a, c)) = mult(mult(unit, a), mult(mult(b, c), c))),
% 23.68/23.94 inference(transitivity,[status(thm)],[12104, 12124, 12098, 12097, 233, 2414, 3136])).
% 23.68/23.94 tff(12126,plain,
% 23.68/23.94 (mult(mult(b, c), mult(mult(unit, c), unit)) = mult(mult(b, c), c)),
% 23.68/23.94 inference(monotonicity,[status(thm)],[78])).
% 23.68/23.94 tff(12127,plain,
% 23.68/23.94 (mult(mult(mult(b, c), mult(mult(unit, c), unit)), a) = mult(mult(mult(b, c), c), a)),
% 23.68/23.94 inference(monotonicity,[status(thm)],[12126])).
% 23.68/23.94 tff(12128,plain,
% 23.68/23.94 (((~(mult(mult(mult(b, c), a), mult(mult(unit, c), unit)) = mult(mult(b, c), mult(a, mult(mult(unit, c), unit))))) | (~(mult(mult(mult(b, c), mult(mult(unit, c), unit)), a) = mult(mult(b, c), mult(mult(mult(unit, c), unit), a))))) | (mult(mult(mult(b, c), mult(mult(unit, c), unit)), a) = mult(mult(b, c), mult(mult(mult(unit, c), unit), a)))),
% 23.68/23.94 inference(tautology,[status(thm)],[])).
% 23.68/23.94 tff(12129,plain,
% 23.68/23.94 (mult(mult(mult(b, c), mult(mult(unit, c), unit)), a) = mult(mult(b, c), mult(mult(mult(unit, c), unit), a))),
% 23.68/23.94 inference(unit_resolution,[status(thm)],[12128, 12121])).
% 23.68/23.94 tff(12130,plain,
% 23.68/23.94 (mult(mult(b, c), mult(mult(mult(unit, c), unit), a)) = mult(mult(mult(b, c), mult(mult(unit, c), unit)), a)),
% 23.68/23.94 inference(symmetry,[status(thm)],[12129])).
% 23.68/23.94 tff(12131,plain,
% 23.68/23.94 (mult(mult(b, c), mult(c, a)) = mult(mult(unit, mult(mult(b, c), c)), a)),
% 23.68/23.94 inference(transitivity,[status(thm)],[12106, 12130, 12127, 3150])).
% 23.68/23.94 tff(12132,plain,
% 23.68/23.94 ((mult(mult(b, c), mult(c, a)) = mult(mult(b, c), mult(a, c))) <=> (mult(mult(unit, mult(mult(b, c), c)), a) = mult(mult(unit, a), mult(mult(b, c), c)))),
% 23.68/23.94 inference(monotonicity,[status(thm)],[12131, 12125])).
% 23.68/23.94 tff(12133,plain,
% 23.68/23.94 ((mult(mult(unit, mult(mult(b, c), c)), a) = mult(mult(unit, a), mult(mult(b, c), c))) <=> (mult(mult(b, c), mult(c, a)) = mult(mult(b, c), mult(a, c)))),
% 23.68/23.94 inference(symmetry,[status(thm)],[12132])).
% 23.68/23.94 tff(12134,plain,
% 23.68/23.94 (mult(mult(mult(a, c), b), c) = mult(mult(mult(b, c), a), c)),
% 23.68/23.94 inference(symmetry,[status(thm)],[12097])).
% 23.68/23.94 tff(12135,plain,
% 23.68/23.94 (mult(mult(unit, a), mult(mult(b, c), c)) = mult(mult(mult(b, c), a), c)),
% 23.68/23.94 inference(transitivity,[status(thm)],[3135, 4372, 234, 12134])).
% 23.68/23.94 tff(12136,plain,
% 23.68/23.94 ((mult(mult(unit, mult(mult(b, c), c)), a) = mult(mult(unit, a), mult(mult(b, c), c))) <=> (mult(mult(mult(b, c), c), a) = mult(mult(mult(b, c), a), c))),
% 23.68/23.94 inference(monotonicity,[status(thm)],[3149, 12135])).
% 23.68/23.94 tff(12137,plain,
% 23.68/23.94 ((mult(mult(mult(b, c), c), a) = mult(mult(mult(b, c), a), c)) <=> (mult(mult(unit, mult(mult(b, c), c)), a) = mult(mult(unit, a), mult(mult(b, c), c)))),
% 23.68/23.94 inference(symmetry,[status(thm)],[12136])).
% 23.68/23.94 tff(12138,plain,
% 23.68/23.94 (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(b, c), a), c)),
% 23.68/23.94 inference(monotonicity,[status(thm)],[4339])).
% 23.68/23.94 tff(12139,plain,
% 23.68/23.94 ((mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c)) <=> (mult(mult(mult(b, c), c), a) = mult(mult(mult(b, c), a), c))),
% 23.68/23.94 inference(monotonicity,[status(thm)],[8633, 12138])).
% 23.68/23.94 tff(12140,plain,
% 23.68/23.94 (mult(mult(mult(b, c), c), a) = mult(mult(mult(b, c), a), c)),
% 23.68/23.94 inference(modus_ponens,[status(thm)],[7692, 12139])).
% 23.68/23.94 tff(12141,plain,
% 23.68/23.94 (mult(mult(unit, mult(mult(b, c), c)), a) = mult(mult(unit, a), mult(mult(b, c), c))),
% 23.68/23.94 inference(modus_ponens,[status(thm)],[12140, 12137])).
% 23.68/23.94 tff(12142,plain,
% 23.68/23.94 (mult(mult(b, c), mult(c, a)) = mult(mult(b, c), mult(a, c))),
% 23.68/23.94 inference(modus_ponens,[status(thm)],[12141, 12133])).
% 23.68/23.94 tff(12143,plain,
% 23.68/23.94 ((~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))) <=> (~(mult(mult(b, c), mult(c, a)) = mult(mult(b, c), mult(a, c))))),
% 23.68/23.94 inference(monotonicity,[status(thm)],[12110])).
% 23.68/23.94 tff(12144,plain,
% 23.68/23.94 (~(mult(mult(b, c), mult(c, a)) = mult(mult(b, c), mult(a, c)))),
% 23.68/23.94 inference(modus_ponens,[status(thm)],[12113, 12143])).
% 23.68/23.94 tff(12145,plain,
% 23.68/23.94 ($false),
% 23.68/23.94 inference(unit_resolution,[status(thm)],[12144, 12142])).
% 23.68/23.94 tff(12146,plain,((mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit))) | (~(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))), inference(lemma,lemma(discharge,[]))).
% 23.68/23.94 tff(12147,plain,
% 23.68/23.94 (mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit))),
% 23.68/23.94 inference(unit_resolution,[status(thm)],[12146, 12047])).
% 23.68/23.94 tff(12148,plain,
% 23.68/23.94 (mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit)) = mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a)),
% 23.68/23.94 inference(symmetry,[status(thm)],[12147])).
% 23.68/23.94 tff(12149,plain,
% 23.68/23.94 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), unit) = mult(mult(rd(mult(b, c), mult(a, c)), c), a)),
% 23.68/23.94 inference(transitivity,[status(thm)],[1875, 1871, 12148, 4488])).
% 23.68/23.94 tff(12150,plain,
% 23.68/23.94 (mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), unit), c) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c)),
% 23.68/23.94 inference(monotonicity,[status(thm)],[12149])).
% 23.68/23.94 tff(12151,plain,
% 23.68/23.94 (mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c) = mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), unit), c)),
% 23.68/23.94 inference(symmetry,[status(thm)],[12150])).
% 23.68/23.94 tff(12152,plain,
% 23.68/23.94 (mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c))),
% 23.68/23.94 inference(transitivity,[status(thm)],[12151, 4654, 5994])).
% 23.68/23.94 tff(12153,plain,
% 23.68/23.94 (mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), mult(c, c)), a)),
% 23.68/23.94 inference(monotonicity,[status(thm)],[12152])).
% 23.68/23.94 tff(12154,plain,
% 23.68/23.94 ((mult(mult(unit, b), mult(a, c)) = mult(mult(unit, mult(a, c)), b)) <=> (mult(unit, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))) = mult(unit, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))))),
% 23.68/23.94 inference(transitivity,[status(thm)],[12076, 12070])).
% 23.68/23.94 tff(12155,plain,
% 23.68/23.94 (mult(unit, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))) = mult(unit, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.68/23.94 inference(modus_ponens,[status(thm)],[12078, 12154])).
% 23.68/23.94 tff(12156,plain,
% 23.68/23.94 (mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), c)),
% 23.68/23.94 inference(transitivity,[status(thm)],[5709, 8645, 161, 215])).
% 23.68/23.94 tff(12157,plain,
% 23.68/23.94 (mult(unit, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))) = mult(unit, mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), c))),
% 23.68/23.94 inference(monotonicity,[status(thm)],[12156])).
% 23.68/23.94 tff(12158,plain,
% 23.68/23.94 (mult(unit, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = mult(unit, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))))),
% 23.68/23.94 inference(monotonicity,[status(thm)],[8170])).
% 23.68/23.94 tff(12159,assumption,(mult(unit, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))) = mult(unit, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))), introduced(assumption)).
% 23.68/23.94 tff(12160,plain,
% 23.68/23.94 ((~![A: $i] : (mult(unit, A) = A)) | (mult(unit, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 23.68/23.94 inference(quant_inst,[status(thm)],[])).
% 23.68/23.94 tff(12161,plain,
% 23.68/23.94 (mult(unit, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))),
% 23.68/23.94 inference(unit_resolution,[status(thm)],[12160, 71])).
% 23.68/23.94 tff(12162,plain,
% 23.68/23.94 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(unit, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 23.68/23.94 inference(symmetry,[status(thm)],[12161])).
% 23.68/23.94 tff(12163,plain,
% 23.68/23.94 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, c), b)),
% 23.68/23.94 inference(transitivity,[status(thm)],[12162, 12159, 12158, 12157, 228, 222, 227])).
% 23.68/23.94 tff(12164,plain,
% 23.68/23.94 (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)), c) = mult(mult(mult(a, c), b), c)),
% 23.68/23.94 inference(monotonicity,[status(thm)],[12163])).
% 23.68/23.94 tff(12165,plain,
% 23.68/23.94 (mult(mult(b, mult(a, c)), c) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)), c)),
% 23.68/23.94 inference(monotonicity,[status(thm)],[8660])).
% 23.68/23.94 tff(12166,plain,
% 23.68/23.94 ((mult(mult(unit, mult(b, c)), mult(a, c)) = mult(mult(unit, mult(a, c)), mult(b, c))) <=> (mult(mult(unit, mult(a, c)), mult(b, c)) = mult(mult(unit, mult(b, c)), mult(a, c)))),
% 23.68/23.94 inference(commutativity,[status(thm)],[])).
% 23.68/23.94 tff(12167,plain,
% 23.68/23.94 (mult(mult(unit, mult(a, c)), mult(b, c)) = mult(mult(a, c), mult(b, c))),
% 23.68/23.94 inference(monotonicity,[status(thm)],[1549])).
% 23.68/23.94 tff(12168,plain,
% 23.68/23.94 (mult(mult(a, c), mult(b, c)) = mult(mult(unit, mult(a, c)), mult(b, c))),
% 23.68/23.94 inference(symmetry,[status(thm)],[12167])).
% 23.68/23.94 tff(12169,plain,
% 23.68/23.94 (mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(c, a))) = mult(mult(a, c), mult(b, c))),
% 23.68/23.94 inference(monotonicity,[status(thm)],[7463])).
% 23.68/23.94 tff(12170,plain,
% 23.68/23.94 (mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(c, a))) = mult(mult(unit, mult(a, c)), mult(b, c))),
% 23.68/23.94 inference(transitivity,[status(thm)],[12169, 12168])).
% 23.68/23.94 tff(12171,plain,
% 23.68/23.94 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(unit, mult(b, c)), mult(a, c))),
% 23.68/23.94 inference(transitivity,[status(thm)],[8875, 12087, 10138])).
% 23.68/23.94 tff(12172,plain,
% 23.68/23.94 ((mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(c, a)))) <=> (mult(mult(unit, mult(b, c)), mult(a, c)) = mult(mult(unit, mult(a, c)), mult(b, c)))),
% 23.68/23.94 inference(monotonicity,[status(thm)],[12171, 12170])).
% 23.68/23.94 tff(12173,plain,
% 23.68/23.94 ((mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(c, a)))) <=> (mult(mult(unit, mult(a, c)), mult(b, c)) = mult(mult(unit, mult(b, c)), mult(a, c)))),
% 23.68/23.94 inference(transitivity,[status(thm)],[12172, 12166])).
% 23.68/23.94 tff(12174,plain,
% 23.68/23.94 ((mult(mult(unit, mult(a, c)), mult(b, c)) = mult(mult(unit, mult(b, c)), mult(a, c))) <=> (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(c, a))))),
% 23.68/23.94 inference(symmetry,[status(thm)],[12173])).
% 23.68/23.94 tff(12175,plain,
% 23.68/23.94 (mult(mult(b, mult(a, c)), c) = mult(mult(b, mult(c, a)), c)),
% 23.68/23.94 inference(symmetry,[status(thm)],[12085])).
% 23.68/23.94 tff(12176,plain,
% 23.68/23.94 (mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)), c) = mult(mult(b, mult(a, c)), c)),
% 23.68/23.94 inference(symmetry,[status(thm)],[12165])).
% 23.68/23.94 tff(12177,plain,
% 23.68/23.94 (mult(mult(mult(a, c), b), c) = mult(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)), c)),
% 23.68/23.94 inference(symmetry,[status(thm)],[12164])).
% 23.68/23.94 tff(12178,plain,
% 23.68/23.94 (mult(a, mult(mult(b, c), c)) = mult(mult(unit, mult(b, c)), mult(a, c))),
% 23.68/23.95 inference(transitivity,[status(thm)],[4372, 234, 12177, 12176, 12175, 12090, 12087, 10138])).
% 23.68/23.95 tff(12179,plain,
% 23.68/23.95 (mult(mult(a, mult(b, c)), c) = mult(mult(unit, mult(a, c)), mult(b, c))),
% 23.68/23.95 inference(transitivity,[status(thm)],[8159, 12168])).
% 23.68/23.95 tff(12180,plain,
% 23.68/23.95 ((mult(mult(a, mult(b, c)), c) = mult(a, mult(mult(b, c), c))) <=> (mult(mult(unit, mult(a, c)), mult(b, c)) = mult(mult(unit, mult(b, c)), mult(a, c)))),
% 23.68/23.95 inference(monotonicity,[status(thm)],[12179, 12178])).
% 23.68/23.95 tff(12181,plain,
% 23.68/23.95 ((mult(mult(a, mult(b, c)), c) = mult(a, mult(mult(b, c), c))) <=> (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(c, a))))),
% 23.68/23.95 inference(transitivity,[status(thm)],[12180, 12174])).
% 23.68/23.95 tff(12182,plain,
% 23.68/23.95 ((~(mult(mult(a, mult(b, c)), c) = mult(a, mult(mult(b, c), c)))) <=> (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(c, a)))))),
% 23.68/23.95 inference(monotonicity,[status(thm)],[12181])).
% 23.68/23.95 tff(12183,plain,
% 23.68/23.95 (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(c, a))))),
% 23.68/23.95 inference(modus_ponens,[status(thm)],[258, 12182])).
% 23.68/23.95 tff(12184,plain,
% 23.68/23.95 (((~(mult(mult(mult(a, c), mult(c, a)), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(mult(c, a), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(c, a)))))) | (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(c, a))))),
% 23.68/23.95 inference(tautology,[status(thm)],[])).
% 23.68/23.95 tff(12185,plain,
% 23.68/23.95 ((~(mult(mult(mult(a, c), mult(c, a)), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(mult(c, a), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(c, a)))))),
% 23.68/23.95 inference(unit_resolution,[status(thm)],[12184, 12183])).
% 23.68/23.95 tff(12186,plain,
% 23.68/23.95 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, c), mult(c, a)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)))) | (~(mult(mult(a, c), mult(mult(c, a), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(c, a))))))) | (~((~(mult(mult(mult(a, c), mult(c, a)), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(mult(c, a), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(c, a))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(a, c), mult(c, a)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)))) | (~(mult(mult(a, c), mult(mult(c, a), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(c, a))))))) | (~((~(mult(mult(mult(a, c), mult(c, a)), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(mult(c, a), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(c, a))))))))),
% 23.68/23.95 inference(rewrite,[status(thm)],[])).
% 23.68/23.95 tff(12187,plain,
% 23.68/23.95 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(a, c), mult(c, a)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)))) | (~(mult(mult(a, c), mult(mult(c, a), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(c, a))))))) | (~((~(mult(mult(mult(a, c), mult(c, a)), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(mult(c, a), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(c, a))))))))),
% 23.68/23.95 inference(quant_inst,[status(thm)],[])).
% 23.68/23.95 tff(12188,plain,
% 23.68/23.95 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(a, c), mult(c, a)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)))) | (~(mult(mult(a, c), mult(mult(c, a), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(c, a))))))) | (~((~(mult(mult(mult(a, c), mult(c, a)), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(mult(c, a), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(c, a)))))))),
% 23.68/23.95 inference(modus_ponens,[status(thm)],[12187, 12186])).
% 23.68/23.95 tff(12189,plain,
% 23.68/23.95 ((~((~(mult(mult(mult(a, c), mult(c, a)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)))) | (~(mult(mult(a, c), mult(mult(c, a), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(c, a))))))) | (~((~(mult(mult(mult(a, c), mult(c, a)), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(mult(c, a), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(c, a)))))))),
% 23.68/23.95 inference(unit_resolution,[status(thm)],[12188, 27])).
% 23.68/23.95 tff(12190,plain,
% 23.68/23.95 (~((~(mult(mult(mult(a, c), mult(c, a)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)))) | (~(mult(mult(a, c), mult(mult(c, a), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(c, a))))))),
% 23.68/23.95 inference(unit_resolution,[status(thm)],[12189, 12185])).
% 23.68/23.95 tff(12191,plain,
% 23.68/23.95 (((~(mult(mult(mult(a, c), mult(c, a)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)))) | (~(mult(mult(a, c), mult(mult(c, a), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(c, a)))))) | (mult(mult(mult(a, c), mult(c, a)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a)))),
% 23.68/23.95 inference(tautology,[status(thm)],[])).
% 23.68/23.95 tff(12192,plain,
% 23.68/23.95 (mult(mult(mult(a, c), mult(c, a)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(c, a))),
% 23.68/23.95 inference(unit_resolution,[status(thm)],[12191, 12190])).
% 23.68/23.95 tff(12193,plain,
% 23.68/23.95 (mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), mult(c, a)), rd(mult(b, c), mult(a, c)))),
% 23.68/23.95 inference(monotonicity,[status(thm)],[8723])).
% 23.68/23.95 tff(12194,plain,
% 23.68/23.95 (mult(c, mult(mult(a, c), a)) = mult(mult(a, c), mult(a, c))),
% 23.68/23.95 inference(transitivity,[status(thm)],[2562, 6842, 8731, 8721])).
% 23.68/23.95 tff(12195,plain,
% 23.68/23.95 (mult(mult(c, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 23.68/23.95 inference(monotonicity,[status(thm)],[12194])).
% 23.68/23.95 tff(12196,plain,
% 23.68/23.95 (((~(mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) = mult(c, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(mult(c, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c)))))) | (mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(mult(c, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c))))),
% 23.68/23.95 inference(tautology,[status(thm)],[])).
% 23.68/23.95 tff(12197,plain,
% 23.68/23.95 (mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(mult(c, mult(mult(a, c), a)), rd(mult(b, c), mult(a, c)))),
% 23.68/23.95 inference(unit_resolution,[status(thm)],[12196, 8764])).
% 23.68/23.95 tff(12198,plain,
% 23.68/23.95 (mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(c, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))))),
% 23.68/23.95 inference(transitivity,[status(thm)],[12197, 12195, 12193, 12192, 8875, 12091, 12085, 12165, 12164, 4285, 3187, 4274, 8748, 8746])).
% 23.68/23.95 tff(12199,plain,
% 23.68/23.95 ((mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) <=> (mult(c, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))),
% 23.68/23.95 inference(monotonicity,[status(thm)],[12198])).
% 23.68/23.95 tff(12200,plain,
% 23.68/23.95 ((mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) <=> (mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) = mult(c, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))))),
% 23.68/23.95 inference(transitivity,[status(thm)],[12199, 8744])).
% 23.68/23.95 tff(12201,plain,
% 23.68/23.95 ((mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) = mult(c, mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))))) <=> (mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))))),
% 23.68/23.95 inference(symmetry,[status(thm)],[12200])).
% 23.68/23.95 tff(12202,plain,
% 23.68/23.95 (mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))),
% 23.68/23.95 inference(modus_ponens,[status(thm)],[8766, 12201])).
% 23.68/23.95 tff(12203,plain,
% 23.68/23.95 ($false),
% 23.68/23.95 inference(unit_resolution,[status(thm)],[8754, 12202])).
% 23.68/23.95 tff(12204,plain,((mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) | (~(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (~(mult(unit, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))) = mult(unit, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))))), inference(lemma,lemma(discharge,[]))).
% 23.68/23.95 tff(12205,plain,
% 23.68/23.95 (mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))),
% 23.68/23.95 inference(unit_resolution,[status(thm)],[12204, 12155, 12047])).
% 23.68/23.95 tff(12206,plain,
% 23.68/23.95 (mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a))),
% 23.68/23.95 inference(symmetry,[status(thm)],[12205])).
% 23.68/23.95 tff(12207,plain,
% 23.68/23.95 (mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a))) = mult(c, mult(mult(a, b), c))),
% 23.68/23.95 inference(transitivity,[status(thm)],[12206, 10229, 2632, 12153, 4660, 8733, 2502, 2499, 12086, 12091, 12085, 12083, 4285, 3187, 4274, 5654])).
% 23.68/23.95 tff(12208,plain,
% 23.68/23.95 (ld(c, mult(c, mult(rd(mult(b, c), mult(a, c)), mult(mult(a, c), a)))) = ld(c, mult(c, mult(mult(a, b), c)))),
% 23.68/23.95 inference(monotonicity,[status(thm)],[12207])).
% 23.68/23.95 tff(12209,plain,
% 23.68/23.95 (mult(mult(c, a), mult(b, c)) = mult(mult(a, c), mult(b, c))),
% 23.68/23.95 inference(symmetry,[status(thm)],[8982])).
% 23.68/23.95 tff(12210,plain,
% 23.68/23.95 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)) = mult(b, mult(mult(c, unit), c))),
% 23.68/23.95 inference(monotonicity,[status(thm)],[12056, 2617])).
% 23.68/23.95 tff(12211,plain,
% 23.68/23.95 (mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))) = mult(mult(a, mult(c, c)), rd(mult(b, c), mult(a, c)))),
% 23.68/23.95 inference(monotonicity,[status(thm)],[9456])).
% 23.68/23.95 tff(12212,plain,
% 23.68/23.95 (mult(mult(a, mult(c, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c)))),
% 23.68/23.95 inference(symmetry,[status(thm)],[12211])).
% 23.68/23.95 tff(12213,plain,
% 23.68/23.95 (mult(mult(a, mult(c, c)), rd(mult(b, c), mult(a, c))) = mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 23.68/23.95 inference(transitivity,[status(thm)],[12212, 8570])).
% 23.68/23.95 tff(12214,plain,
% 23.68/23.95 (mult(mult(a, c), rd(mult(b, c), mult(a, c))) = mult(b, c)),
% 23.68/23.95 inference(transitivity,[status(thm)],[5650, 12049, 141])).
% 23.68/23.95 tff(12215,plain,
% 23.68/23.95 (mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(c, mult(b, c))),
% 23.68/23.95 inference(monotonicity,[status(thm)],[12214])).
% 23.68/23.95 tff(12216,plain,
% 23.68/23.95 (mult(c, mult(b, c)) = mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 23.68/23.95 inference(symmetry,[status(thm)],[12215])).
% 23.68/23.95 tff(12217,plain,
% 23.68/23.95 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)) = mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 23.68/23.95 inference(transitivity,[status(thm)],[12210, 7714, 7711, 8573, 4537, 4178, 12216])).
% 23.68/23.95 tff(12218,plain,
% 23.68/23.95 ((mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)) = mult(mult(a, mult(c, c)), rd(mult(b, c), mult(a, c)))) <=> (mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))))),
% 23.68/23.95 inference(monotonicity,[status(thm)],[12217, 12213])).
% 23.68/23.95 tff(12219,plain,
% 23.68/23.95 ((mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)) = mult(mult(a, mult(c, c)), rd(mult(b, c), mult(a, c)))) <=> (mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 23.68/23.95 inference(transitivity,[status(thm)],[12218, 8564])).
% 23.68/23.95 tff(12220,plain,
% 23.68/23.95 ((mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c))))) <=> (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)) = mult(mult(a, mult(c, c)), rd(mult(b, c), mult(a, c))))),
% 23.68/23.95 inference(symmetry,[status(thm)],[12219])).
% 23.68/23.95 tff(12221,plain,
% 23.68/23.95 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(b, c), c)),
% 23.68/23.95 inference(monotonicity,[status(thm)],[12214])).
% 23.68/23.95 tff(12222,plain,
% 23.68/23.95 (mult(mult(b, c), c) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)),
% 23.68/23.95 inference(symmetry,[status(thm)],[12221])).
% 23.68/23.95 tff(12223,plain,
% 23.68/23.95 (mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c)),
% 23.68/23.95 inference(transitivity,[status(thm)],[12215, 4179, 4176, 4173, 12222])).
% 23.68/23.95 tff(12224,plain,
% 23.68/23.95 ((mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c))))) <=> (mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c))),
% 23.68/23.95 inference(monotonicity,[status(thm)],[8569, 12223])).
% 23.68/23.95 tff(12225,plain,
% 23.68/23.95 ((mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c))))) <=> (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c))))),
% 23.68/23.95 inference(transitivity,[status(thm)],[12224, 5297])).
% 23.68/23.95 tff(12226,plain,
% 23.68/23.95 ((mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, c), c), rd(mult(b, c), mult(a, c)))) <=> (mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 23.68/23.95 inference(symmetry,[status(thm)],[12225])).
% 23.68/23.95 tff(12227,plain,
% 23.68/23.95 (mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 23.68/23.96 inference(modus_ponens,[status(thm)],[9754, 12226])).
% 23.68/23.96 tff(12228,plain,
% 23.68/23.96 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c)) = mult(mult(a, mult(c, c)), rd(mult(b, c), mult(a, c)))),
% 23.68/23.96 inference(modus_ponens,[status(thm)],[12227, 12220])).
% 23.68/23.96 tff(12229,plain,
% 23.68/23.96 (mult(mult(a, mult(c, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, c))),
% 23.68/23.96 inference(symmetry,[status(thm)],[12228])).
% 23.68/23.96 tff(12230,plain,
% 23.68/23.96 (mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(b, c), c)),
% 23.68/23.96 inference(transitivity,[status(thm)],[8569, 12211, 12229, 12210, 7714, 7711])).
% 23.68/23.96 tff(12231,plain,
% 23.68/23.96 (mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(b, c), c))),
% 23.68/23.96 inference(monotonicity,[status(thm)],[12230])).
% 23.68/23.96 tff(12232,plain,
% 23.68/23.96 (mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))),
% 23.68/23.96 inference(unit_resolution,[status(thm)],[2813, 12047])).
% 23.68/23.96 tff(12233,plain,
% 23.68/23.96 (mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 23.68/23.96 inference(symmetry,[status(thm)],[12232])).
% 23.68/23.96 tff(12234,plain,
% 23.68/23.96 (mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))) = mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))))),
% 23.68/23.96 inference(monotonicity,[status(thm)],[12233])).
% 23.68/23.96 tff(12235,plain,
% 23.68/23.96 (ld(a, mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, c)))) = ld(a, mult(a, mult(mult(c, c), rd(mult(b, c), mult(a, c)))))),
% 23.68/23.96 inference(monotonicity,[status(thm)],[9941])).
% 23.68/23.96 tff(12236,plain,
% 23.68/23.96 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(a, mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, c)))) = mult(rd(mult(b, c), mult(a, c)), mult(c, c)))),
% 23.68/23.96 inference(quant_inst,[status(thm)],[])).
% 23.68/23.96 tff(12237,plain,
% 23.68/23.96 (ld(a, mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, c)))) = mult(rd(mult(b, c), mult(a, c)), mult(c, c))),
% 23.68/23.96 inference(unit_resolution,[status(thm)],[12236, 7])).
% 23.68/23.96 tff(12238,plain,
% 23.68/23.96 (mult(rd(mult(b, c), mult(a, c)), mult(c, c)) = ld(a, mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, c))))),
% 23.68/23.96 inference(symmetry,[status(thm)],[12237])).
% 23.68/23.96 tff(12239,plain,
% 23.68/23.96 (mult(rd(mult(b, c), mult(a, c)), mult(mult(c, unit), c)) = mult(rd(mult(b, c), mult(a, c)), mult(c, c))),
% 23.68/23.96 inference(monotonicity,[status(thm)],[2616])).
% 23.68/23.96 tff(12240,plain,
% 23.68/23.96 (mult(mult(rd(mult(b, c), mult(a, c)), c), c) = mult(mult(c, c), rd(mult(b, c), mult(a, c)))),
% 23.68/23.96 inference(transitivity,[status(thm)],[3967, 3970, 12239, 12238, 12235, 9947])).
% 23.68/23.96 tff(12241,plain,
% 23.68/23.96 (mult(mult(mult(rd(mult(b, c), mult(a, c)), c), c), a) = mult(mult(mult(c, c), rd(mult(b, c), mult(a, c))), a)),
% 23.68/23.96 inference(monotonicity,[status(thm)],[12240])).
% 23.68/23.96 tff(12242,plain,
% 23.68/23.96 (mult(mult(mult(c, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), c), a)),
% 23.68/23.96 inference(symmetry,[status(thm)],[12241])).
% 23.68/23.96 tff(12243,plain,
% 23.68/23.96 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(a, mult(a, mult(mult(mult(c, c), rd(mult(b, c), mult(a, c))), a))) = mult(mult(mult(c, c), rd(mult(b, c), mult(a, c))), a))),
% 23.68/23.96 inference(quant_inst,[status(thm)],[])).
% 23.68/23.96 tff(12244,plain,
% 23.68/23.96 (ld(a, mult(a, mult(mult(mult(c, c), rd(mult(b, c), mult(a, c))), a))) = mult(mult(mult(c, c), rd(mult(b, c), mult(a, c))), a)),
% 23.68/23.96 inference(unit_resolution,[status(thm)],[12243, 7])).
% 23.68/23.96 tff(12245,plain,
% 23.68/23.96 (mult(mult(c, rd(mult(b, c), mult(a, c))), c) = mult(mult(c, c), rd(mult(b, c), mult(a, c)))),
% 23.68/23.96 inference(transitivity,[status(thm)],[9899, 3967, 3970, 12239, 12238, 12235, 9947])).
% 23.68/23.96 tff(12246,plain,
% 23.68/23.96 (mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(c, c), rd(mult(b, c), mult(a, c))), a)),
% 23.68/23.96 inference(monotonicity,[status(thm)],[12245])).
% 23.68/23.96 tff(12247,plain,
% 23.68/23.96 (mult(mult(mult(c, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a)),
% 23.68/23.96 inference(symmetry,[status(thm)],[12246])).
% 23.68/23.96 tff(12248,plain,
% 23.68/23.96 (mult(a, mult(mult(mult(c, c), rd(mult(b, c), mult(a, c))), a)) = mult(a, mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a))),
% 23.68/23.96 inference(monotonicity,[status(thm)],[12247])).
% 23.68/23.96 tff(12249,plain,
% 23.68/23.96 (mult(a, mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a)) = mult(a, mult(mult(mult(c, c), rd(mult(b, c), mult(a, c))), a))),
% 23.68/23.96 inference(symmetry,[status(thm)],[12248])).
% 23.68/23.96 tff(12250,plain,
% 23.68/23.96 (mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a) = mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))),
% 23.68/23.96 inference(transitivity,[status(thm)],[12246, 12242, 7658, 2627, 6170, 6169])).
% 23.68/23.96 tff(12251,plain,
% 23.68/23.96 (mult(a, mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))))),
% 23.68/23.96 inference(monotonicity,[status(thm)],[12250])).
% 23.68/23.96 tff(12252,plain,
% 23.68/23.96 (mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))) = mult(a, mult(mult(mult(c, rd(mult(b, c), mult(a, c))), c), a))),
% 23.68/23.96 inference(symmetry,[status(thm)],[12251])).
% 23.68/23.96 tff(12253,plain,
% 23.68/23.96 ((mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c)))) <=> (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))))),
% 23.68/23.96 inference(symmetry,[status(thm)],[9327])).
% 23.68/23.96 tff(12254,plain,
% 23.68/23.96 ((mult(mult(unit, a), mult(mult(b, c), c)) = mult(mult(unit, mult(mult(b, c), c)), a)) <=> (mult(mult(unit, mult(mult(b, c), c)), a) = mult(mult(unit, a), mult(mult(b, c), c)))),
% 23.68/23.96 inference(commutativity,[status(thm)],[])).
% 23.68/23.96 tff(12255,plain,
% 23.68/23.96 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a) = mult(mult(b, c), a)),
% 23.68/23.96 inference(monotonicity,[status(thm)],[12214])).
% 23.68/23.96 tff(12256,plain,
% 23.68/23.96 (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c) = mult(mult(mult(b, c), a), c)),
% 23.68/23.96 inference(monotonicity,[status(thm)],[12255])).
% 23.68/23.96 tff(12257,plain,
% 23.68/23.96 (mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(b, c), c), a)),
% 23.68/23.96 inference(monotonicity,[status(thm)],[12221])).
% 23.68/23.96 tff(12258,plain,
% 23.68/23.96 ((mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), c), a) = mult(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), a), c)) <=> (mult(mult(mult(b, c), c), a) = mult(mult(mult(b, c), a), c))),
% 23.68/23.96 inference(monotonicity,[status(thm)],[12257, 12256])).
% 23.68/23.96 tff(12259,plain,
% 23.68/23.96 (mult(mult(mult(b, c), c), a) = mult(mult(mult(b, c), a), c)),
% 23.68/23.96 inference(modus_ponens,[status(thm)],[7692, 12258])).
% 23.68/23.96 tff(12260,plain,
% 23.68/23.96 (mult(mult(mult(b, c), a), c) = mult(mult(mult(b, c), c), a)),
% 23.68/23.96 inference(symmetry,[status(thm)],[12259])).
% 23.68/23.96 tff(12261,plain,
% 23.68/23.96 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(b, mult(c, mult(a, c)))),
% 23.68/23.96 inference(monotonicity,[status(thm)],[12056])).
% 23.68/23.96 tff(12262,plain,
% 23.68/23.96 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(mult(unit, mult(mult(b, c), c)), a)),
% 23.68/23.96 inference(transitivity,[status(thm)],[12261, 8559, 4149, 12260, 3150])).
% 23.68/23.96 tff(12263,plain,
% 23.68/23.96 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(b, c), mult(a, c))),
% 23.68/23.96 inference(monotonicity,[status(thm)],[12214])).
% 23.68/23.96 tff(12264,plain,
% 23.68/23.96 (mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c))) = mult(mult(unit, mult(a, c)), mult(b, c))),
% 23.68/23.96 inference(transitivity,[status(thm)],[138, 12168])).
% 23.68/23.96 tff(12265,plain,
% 23.68/23.96 (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(unit, mult(b, c)), mult(a, c))),
% 23.68/23.96 inference(transitivity,[status(thm)],[12263, 10138])).
% 23.68/23.96 tff(12266,plain,
% 23.68/23.96 ((mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))) <=> (mult(mult(unit, mult(b, c)), mult(a, c)) = mult(mult(unit, mult(a, c)), mult(b, c)))),
% 23.68/23.96 inference(monotonicity,[status(thm)],[12265, 12264])).
% 23.68/23.96 tff(12267,plain,
% 23.68/23.96 ((mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))) <=> (mult(mult(unit, mult(a, c)), mult(b, c)) = mult(mult(unit, mult(b, c)), mult(a, c)))),
% 23.68/23.96 inference(transitivity,[status(thm)],[12266, 12166])).
% 23.68/23.96 tff(12268,plain,
% 23.80/23.96 ((mult(mult(unit, mult(a, c)), mult(b, c)) = mult(mult(unit, mult(b, c)), mult(a, c))) <=> (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))),
% 23.80/23.96 inference(symmetry,[status(thm)],[12267])).
% 23.80/23.96 tff(12269,plain,
% 23.80/23.96 (mult(mult(unit, mult(b, c)), mult(a, c)) = mult(a, mult(mult(b, c), c))),
% 23.80/23.96 inference(transitivity,[status(thm)],[10137, 12086, 12091, 12085, 12083, 233, 2414])).
% 23.80/23.96 tff(12270,plain,
% 23.80/23.96 (mult(mult(unit, mult(a, c)), mult(b, c)) = mult(mult(a, mult(b, c)), c)),
% 23.80/23.96 inference(transitivity,[status(thm)],[12167, 266])).
% 23.80/23.96 tff(12271,plain,
% 23.80/23.96 ((mult(mult(unit, mult(a, c)), mult(b, c)) = mult(mult(unit, mult(b, c)), mult(a, c))) <=> (mult(mult(a, mult(b, c)), c) = mult(a, mult(mult(b, c), c)))),
% 23.80/23.96 inference(monotonicity,[status(thm)],[12270, 12269])).
% 23.80/23.96 tff(12272,plain,
% 23.80/23.96 ((mult(mult(a, mult(b, c)), c) = mult(a, mult(mult(b, c), c))) <=> (mult(mult(unit, mult(a, c)), mult(b, c)) = mult(mult(unit, mult(b, c)), mult(a, c)))),
% 23.80/23.96 inference(symmetry,[status(thm)],[12271])).
% 23.80/23.96 tff(12273,plain,
% 23.80/23.96 ((mult(mult(a, mult(b, c)), c) = mult(a, mult(mult(b, c), c))) <=> (mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))),
% 23.80/23.96 inference(transitivity,[status(thm)],[12272, 12268])).
% 23.80/23.96 tff(12274,plain,
% 23.80/23.96 ((~(mult(mult(a, mult(b, c)), c) = mult(a, mult(mult(b, c), c)))) <=> (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))),
% 23.80/23.96 inference(monotonicity,[status(thm)],[12273])).
% 23.80/23.96 tff(12275,plain,
% 23.80/23.96 (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))),
% 23.80/23.96 inference(modus_ponens,[status(thm)],[258, 12274])).
% 23.80/23.96 tff(12276,plain,
% 23.80/23.96 ((~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))),
% 23.80/23.96 inference(unit_resolution,[status(thm)],[315, 12275])).
% 23.80/23.96 tff(12277,plain,
% 23.80/23.96 (~((~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))),
% 23.80/23.96 inference(unit_resolution,[status(thm)],[313, 12276])).
% 23.80/23.96 tff(12278,plain,
% 23.80/23.96 (((~(mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(mult(a, c), mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))) | (mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 23.80/23.96 inference(tautology,[status(thm)],[])).
% 23.80/23.96 tff(12279,plain,
% 23.80/23.96 (mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), rd(mult(b, c), mult(a, c))), mult(a, c))),
% 23.80/23.96 inference(unit_resolution,[status(thm)],[12278, 12277])).
% 23.80/23.96 tff(12280,plain,
% 23.80/23.96 (mult(c, mult(c, a)) = mult(c, mult(a, c))),
% 23.80/23.96 inference(monotonicity,[status(thm)],[4268])).
% 23.80/23.96 tff(12281,plain,
% 23.80/23.96 (mult(c, mult(a, c)) = mult(c, mult(c, a))),
% 23.80/23.96 inference(symmetry,[status(thm)],[12280])).
% 23.80/23.96 tff(12282,plain,
% 23.80/23.96 (mult(a, mult(c, c)) = mult(mult(c, c), a)),
% 23.80/23.96 inference(transitivity,[status(thm)],[2618, 2615, 2612, 8566, 2690, 12281, 9268])).
% 23.80/23.96 tff(12283,plain,
% 23.80/23.96 (mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(a, mult(c, c))) = mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(c, c), a))),
% 23.80/23.96 inference(monotonicity,[status(thm)],[12282])).
% 23.80/23.96 tff(12284,plain,
% 23.80/23.96 (mult(a, mult(c, mult(c, a))) = mult(a, mult(c, mult(a, c)))),
% 23.80/23.96 inference(monotonicity,[status(thm)],[12280])).
% 23.80/23.96 tff(12285,plain,
% 23.80/23.96 ((mult(mult(a, c), mult(c, a)) = mult(a, mult(c, mult(c, a)))) <=> (mult(mult(a, c), mult(a, c)) = mult(a, mult(c, mult(a, c))))),
% 23.80/23.96 inference(monotonicity,[status(thm)],[8722, 12284])).
% 23.80/23.96 tff(12286,plain,
% 23.80/23.96 ((mult(mult(a, c), mult(a, c)) = mult(a, mult(c, mult(a, c)))) <=> (mult(mult(a, c), mult(c, a)) = mult(a, mult(c, mult(c, a))))),
% 23.80/23.96 inference(symmetry,[status(thm)],[12285])).
% 23.80/23.96 tff(12287,plain,
% 23.80/23.96 (mult(mult(a, c), mult(c, a)) = mult(a, mult(c, mult(c, a)))),
% 23.80/23.96 inference(modus_ponens,[status(thm)],[9264, 12286])).
% 23.80/23.96 tff(12288,plain,
% 23.80/23.96 (mult(mult(unit, mult(mult(a, c), c)), a) = mult(mult(unit, a), mult(mult(a, c), c))),
% 23.80/23.96 inference(unit_resolution,[status(thm)],[9287, 12287, 12283])).
% 23.80/23.96 tff(12289,plain,
% 23.80/23.96 (mult(mult(a, mult(c, c)), a) = mult(mult(a, a), mult(c, c))),
% 23.80/23.96 inference(unit_resolution,[status(thm)],[7898, 12288])).
% 23.80/23.96 tff(12290,plain,
% 23.80/23.96 (mult(mult(a, a), mult(c, c)) = mult(mult(a, mult(c, c)), a)),
% 23.80/23.96 inference(modus_ponens,[status(thm)],[12289, 9255])).
% 23.80/23.96 tff(12291,plain,
% 23.80/23.96 (mult(mult(a, c), b) = mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))),
% 23.80/23.96 inference(symmetry,[status(thm)],[12057])).
% 23.80/23.96 tff(12292,plain,
% 23.80/23.96 (mult(mult(a, rd(mult(b, c), mult(a, c))), c) = mult(b, c)),
% 23.80/23.96 inference(monotonicity,[status(thm)],[12056])).
% 23.80/23.96 tff(12293,plain,
% 23.80/23.96 (mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c)) = mult(a, mult(b, c))),
% 23.80/23.96 inference(monotonicity,[status(thm)],[12292])).
% 23.80/23.96 tff(12294,plain,
% 23.80/23.96 (mult(a, mult(a, rd(mult(b, c), mult(a, c)))) = mult(a, b)),
% 23.80/23.96 inference(monotonicity,[status(thm)],[12056])).
% 23.80/23.96 tff(12295,plain,
% 23.80/23.96 (mult(mult(a, a), rd(mult(b, c), mult(a, c))) = mult(a, b)),
% 23.80/23.96 inference(transitivity,[status(thm)],[10012, 12294])).
% 23.80/23.96 tff(12296,plain,
% 23.80/23.96 (mult(mult(mult(a, a), rd(mult(b, c), mult(a, c))), c) = mult(mult(a, b), c)),
% 23.80/23.96 inference(monotonicity,[status(thm)],[12295])).
% 23.80/23.96 tff(12297,plain,
% 23.80/23.96 (mult(a, mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, a), rd(mult(b, c), mult(a, c)))),
% 23.80/23.96 inference(symmetry,[status(thm)],[10012])).
% 23.80/23.96 tff(12298,plain,
% 23.80/23.96 (mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(mult(a, a), rd(mult(b, c), mult(a, c))), c)),
% 23.80/23.96 inference(monotonicity,[status(thm)],[12297])).
% 23.80/23.96 tff(12299,plain,
% 23.80/23.96 (mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(a, b), c)),
% 23.80/23.96 inference(transitivity,[status(thm)],[12298, 12296])).
% 23.80/23.96 tff(12300,plain,
% 23.80/23.96 ((mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c))) <=> (mult(mult(a, b), c) = mult(a, mult(b, c)))),
% 23.80/23.96 inference(monotonicity,[status(thm)],[12299, 12293])).
% 23.80/23.96 tff(12301,plain,
% 23.80/23.96 ((mult(mult(a, b), c) = mult(a, mult(b, c))) <=> (mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c)))),
% 23.80/23.96 inference(symmetry,[status(thm)],[12300])).
% 23.80/23.96 tff(12302,plain,
% 23.80/23.96 ((~(mult(mult(a, b), c) = mult(a, mult(b, c)))) <=> (~(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c))))),
% 23.80/23.96 inference(monotonicity,[status(thm)],[12301])).
% 23.80/23.96 tff(12303,plain,
% 23.80/23.96 (~(mult(mult(a, mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(a, mult(mult(a, rd(mult(b, c), mult(a, c))), c)))),
% 23.80/23.96 inference(modus_ponens,[status(thm)],[146, 12302])).
% 23.80/23.96 tff(12304,plain,
% 23.80/23.96 (ld(a, mult(a, mult(b, c))) = ld(a, mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 23.80/23.96 inference(symmetry,[status(thm)],[12049])).
% 23.80/23.96 tff(12305,plain,
% 23.80/23.96 (mult(mult(a, rd(mult(b, c), mult(a, c))), c) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))),
% 23.80/23.96 inference(transitivity,[status(thm)],[12292, 843, 12304, 4336])).
% 23.80/23.96 tff(12306,plain,
% 23.80/23.96 ((mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))) <=> (mult(mult(a, rd(mult(b, c), mult(a, c))), c) = mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 23.80/23.96 inference(monotonicity,[status(thm)],[6620, 6298])).
% 23.80/23.96 tff(12307,plain,
% 23.80/23.96 ((mult(mult(a, rd(mult(b, c), mult(a, c))), c) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))) <=> (mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))),
% 23.80/23.97 inference(symmetry,[status(thm)],[12306])).
% 23.80/23.97 tff(12308,plain,
% 23.80/23.97 (mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))),
% 23.80/23.97 inference(modus_ponens,[status(thm)],[4944, 12307])).
% 23.80/23.97 tff(12309,assumption,(~(mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)))), introduced(assumption)).
% 23.80/23.97 tff(12310,plain,
% 23.80/23.97 ($false),
% 23.80/23.97 inference(unit_resolution,[status(thm)],[12309, 12308])).
% 23.80/23.97 tff(12311,plain,((mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), c) = mult(mult(a, c), rd(mult(b, c), mult(a, c)))))), inference(lemma,lemma(discharge,[]))).
% 23.80/23.97 tff(12312,plain,
% 23.80/23.97 (mult(mult(a, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit)), c) = mult(mult(a, c), mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))),
% 23.80/23.97 inference(unit_resolution,[status(thm)],[12311, 12305])).
% 23.80/23.97 tff(12313,plain,
% 23.80/23.97 (~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 23.80/23.97 inference(unit_resolution,[status(thm)],[9500, 12312, 12303])).
% 23.80/23.97 tff(12314,plain,
% 23.80/23.97 ((~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))))),
% 23.80/23.97 inference(unit_resolution,[status(thm)],[280, 12313])).
% 23.80/23.97 tff(12315,plain,
% 23.80/23.97 (~((~(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))))),
% 23.80/23.97 inference(unit_resolution,[status(thm)],[276, 12314])).
% 23.80/23.97 tff(12316,plain,
% 23.80/23.97 (mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))),
% 23.80/23.97 inference(unit_resolution,[status(thm)],[6389, 12315])).
% 23.80/23.97 tff(12317,plain,
% 23.80/23.97 (mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c)))),
% 23.80/23.97 inference(transitivity,[status(thm)],[12316, 12065, 12081, 12067, 12080, 12059, 228, 222, 227, 12291, 8170])).
% 23.80/23.97 tff(12318,plain,
% 23.80/23.97 (rd(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))), rd(mult(b, c), mult(a, c))) = rd(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), rd(mult(b, c), mult(a, c)))),
% 23.80/23.97 inference(monotonicity,[status(thm)],[12317])).
% 23.80/23.97 tff(12319,plain,
% 23.80/23.97 (mult(mult(unit, a), mult(a, c)) = mult(mult(unit, mult(a, c)), a)),
% 23.80/23.97 inference(transitivity,[status(thm)],[8812, 8292, 12318, 8230, 8811])).
% 23.80/23.97 tff(12320,plain,
% 23.80/23.97 (mult(mult(a, a), c) = mult(a, mult(a, c))),
% 23.80/23.97 inference(unit_resolution,[status(thm)],[8833, 12319])).
% 23.80/23.97 tff(12321,plain,
% 23.80/23.97 (mult(mult(a, a), c) = mult(mult(a, c), a)),
% 23.80/23.97 inference(transitivity,[status(thm)],[12320, 8292, 12318, 8230])).
% 23.80/23.97 tff(12322,plain,
% 23.80/23.97 (mult(mult(mult(a, a), c), unit) = mult(mult(mult(a, c), a), unit)),
% 23.80/23.97 inference(monotonicity,[status(thm)],[12321])).
% 23.80/23.97 tff(12323,plain,
% 23.80/23.97 (mult(mult(mult(a, c), a), unit) = mult(mult(mult(a, a), c), unit)),
% 23.80/23.97 inference(symmetry,[status(thm)],[12322])).
% 23.80/23.97 tff(12324,plain,
% 23.80/23.97 (mult(mult(a, c), a) = mult(mult(mult(a, a), c), unit)),
% 23.80/23.97 inference(transitivity,[status(thm)],[9301, 9299, 9296, 12323])).
% 23.80/23.97 tff(12325,plain,
% 23.80/23.97 (mult(mult(mult(a, c), a), c) = mult(mult(mult(mult(a, a), c), unit), c)),
% 23.80/23.97 inference(monotonicity,[status(thm)],[12324])).
% 23.80/23.97 tff(12326,plain,
% 23.80/23.97 (mult(a, mult(c, mult(a, c))) = mult(mult(a, c), mult(a, c))),
% 23.80/23.97 inference(transitivity,[status(thm)],[4714, 4724, 12325, 7903, 7901, 12290, 4662, 8726, 8731, 8721])).
% 23.80/23.97 tff(12327,plain,
% 23.80/23.97 (mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(mult(a, c), mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 23.80/23.97 inference(monotonicity,[status(thm)],[12326])).
% 23.80/23.97 tff(12328,plain,
% 23.80/23.97 (mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(unit, a), mult(mult(b, c), c))),
% 23.80/23.97 inference(transitivity,[status(thm)],[12327, 12279, 12263, 12086, 12091, 12085, 12083, 233, 2414, 3136])).
% 23.80/23.97 tff(12329,plain,
% 23.80/23.97 ((mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c)))) <=> (mult(mult(unit, a), mult(mult(b, c), c)) = mult(mult(unit, mult(mult(b, c), c)), a))),
% 23.80/23.97 inference(monotonicity,[status(thm)],[12328, 12262])).
% 23.80/23.97 tff(12330,plain,
% 23.80/23.97 ((mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c)))) <=> (mult(mult(unit, mult(mult(b, c), c)), a) = mult(mult(unit, a), mult(mult(b, c), c)))),
% 23.80/23.97 inference(transitivity,[status(thm)],[12329, 12254])).
% 23.80/23.97 tff(12331,plain,
% 23.80/23.97 ((mult(mult(unit, mult(mult(b, c), c)), a) = mult(mult(unit, a), mult(mult(b, c), c))) <=> (mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))))),
% 23.80/23.97 inference(symmetry,[status(thm)],[12330])).
% 23.80/23.97 tff(12332,plain,
% 23.80/23.97 (mult(mult(a, mult(b, c)), c) = mult(mult(unit, mult(mult(b, c), c)), a)),
% 23.80/23.97 inference(transitivity,[status(thm)],[8159, 8982, 8981, 4181, 3150])).
% 23.80/23.97 tff(12333,plain,
% 23.80/23.97 ((mult(mult(a, mult(b, c)), c) = mult(a, mult(mult(b, c), c))) <=> (mult(mult(unit, mult(mult(b, c), c)), a) = mult(mult(unit, a), mult(mult(b, c), c)))),
% 23.80/23.97 inference(monotonicity,[status(thm)],[12332, 3136])).
% 23.80/23.97 tff(12334,plain,
% 23.80/23.97 ((mult(mult(a, mult(b, c)), c) = mult(a, mult(mult(b, c), c))) <=> (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))))),
% 23.80/23.97 inference(transitivity,[status(thm)],[12333, 12331, 12253])).
% 23.80/23.97 tff(12335,plain,
% 23.80/23.97 ((~(mult(mult(a, mult(b, c)), c) = mult(a, mult(mult(b, c), c)))) <=> (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c)))))),
% 23.80/23.97 inference(monotonicity,[status(thm)],[12334])).
% 23.80/23.97 tff(12336,plain,
% 23.80/23.97 (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))))),
% 23.80/23.97 inference(modus_ponens,[status(thm)],[258, 12335])).
% 23.80/23.97 tff(12337,plain,
% 23.80/23.97 ((~(mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))) = mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c)))))),
% 23.80/23.97 inference(unit_resolution,[status(thm)],[7766, 12336])).
% 23.80/23.97 tff(12338,plain,
% 23.80/23.97 (~((~(mult(mult(a, mult(c, mult(a, c))), rd(mult(b, c), mult(a, c))) = mult(a, mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))))) | (~(mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c)))))))),
% 23.80/23.97 inference(unit_resolution,[status(thm)],[7774, 12337])).
% 23.80/23.97 tff(12339,plain,
% 23.80/23.97 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c))) = mult(a, mult(rd(mult(b, c), mult(a, c)), mult(c, mult(a, c))))),
% 23.80/23.97 inference(unit_resolution,[status(thm)],[9801, 12338])).
% 23.80/23.97 tff(12340,plain,
% 23.80/23.97 (mult(b, mult(c, mult(a, c))) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(c, mult(a, c)))),
% 23.80/23.97 inference(symmetry,[status(thm)],[12261])).
% 23.80/23.97 tff(12341,plain,
% 23.80/23.97 (mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)) = mult(mult(b, c), a)),
% 23.80/23.97 inference(transitivity,[status(thm)],[5497, 12255])).
% 23.80/23.97 tff(12342,plain,
% 23.80/23.97 (mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c) = mult(mult(mult(b, c), a), c)),
% 23.80/23.97 inference(monotonicity,[status(thm)],[12341])).
% 23.80/23.97 tff(12343,plain,
% 23.80/23.97 (mult(a, mult(mult(c, mult(rd(mult(b, c), mult(a, c)), a)), c)) = mult(a, mult(mult(mult(c, c), rd(mult(b, c), mult(a, c))), a))),
% 23.80/23.97 inference(transitivity,[status(thm)],[8941, 12342, 2570, 8560, 12340, 12339, 12252, 12249])).
% 23.80/23.97 tff(12344,plain,
% 23.80/23.97 (ld(a, mult(a, mult(mult(c, mult(rd(mult(b, c), mult(a, c)), a)), c))) = ld(a, mult(a, mult(mult(mult(c, c), rd(mult(b, c), mult(a, c))), a)))),
% 23.80/23.97 inference(monotonicity,[status(thm)],[12343])).
% 23.80/23.97 tff(12345,plain,
% 23.80/23.97 (mult(mult(mult(b, c), a), c) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), a)), c)),
% 23.80/23.97 inference(symmetry,[status(thm)],[12342])).
% 23.80/23.97 tff(12346,plain,
% 23.80/23.97 (mult(mult(mult(a, c), b), c) = mult(mult(b, mult(a, c)), c)),
% 23.80/23.97 inference(symmetry,[status(thm)],[12083])).
% 23.80/23.97 tff(12347,assumption,(~((~(mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))))), introduced(assumption)).
% 23.80/23.97 tff(12348,plain,
% 23.80/23.97 (mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 23.80/23.97 inference(unit_resolution,[status(thm)],[4560, 12347])).
% 23.80/23.97 tff(12349,plain,
% 23.80/23.97 (mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), mult(a, c)) = mult(mult(b, c), mult(a, c))),
% 23.80/23.97 inference(transitivity,[status(thm)],[10683, 12348, 12234, 12231, 4372, 234, 12346, 12175, 12090, 12087])).
% 23.80/23.97 tff(12350,plain,
% 23.80/23.97 (rd(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), mult(a, c)), mult(a, c)) = rd(mult(mult(b, c), mult(a, c)), mult(a, c))),
% 23.80/23.97 inference(monotonicity,[status(thm)],[12349])).
% 23.80/23.97 tff(12351,plain,
% 23.80/23.97 (mult(a, mult(rd(mult(b, c), mult(a, c)), c)) = mult(b, c)),
% 23.80/23.97 inference(transitivity,[status(thm)],[10936, 12350, 4402])).
% 23.80/23.97 tff(12352,plain,
% 23.80/23.97 (mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))) = mult(mult(a, c), mult(b, c))),
% 23.80/23.97 inference(monotonicity,[status(thm)],[12351])).
% 23.80/23.97 tff(12353,plain,
% 23.80/23.97 (mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(b, c), c)),
% 23.80/23.97 inference(transitivity,[status(thm)],[12233, 8569, 12211, 12229, 12210, 7714, 7711])).
% 23.80/23.97 tff(12354,plain,
% 23.80/23.97 (mult(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)), a) = mult(mult(mult(b, c), c), a)),
% 23.80/23.97 inference(monotonicity,[status(thm)],[12353])).
% 23.80/23.97 tff(12355,plain,
% 23.80/23.97 (mult(mult(mult(b, c), c), a) = mult(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)), a)),
% 23.80/23.97 inference(symmetry,[status(thm)],[12354])).
% 23.80/23.97 tff(12356,plain,
% 23.80/23.97 (mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)) = mult(mult(b, c), c)),
% 23.80/23.97 inference(transitivity,[status(thm)],[10632, 12233, 8569, 12211, 12229, 12210, 7714, 7711])).
% 23.80/23.97 tff(12357,plain,
% 23.80/23.97 (mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)), a) = mult(mult(mult(b, c), c), a)),
% 23.80/23.97 inference(monotonicity,[status(thm)],[12356])).
% 23.80/23.97 tff(12358,plain,
% 23.80/23.97 (mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)), a) = mult(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)), a)),
% 23.80/23.97 inference(transitivity,[status(thm)],[12357, 12355])).
% 23.80/23.97 tff(12359,plain,
% 23.80/23.97 ((mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)), a) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a))) <=> (mult(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)), a) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)))),
% 23.80/23.97 inference(monotonicity,[status(thm)],[12358, 11684])).
% 23.80/23.97 tff(12360,plain,
% 23.80/23.97 ((mult(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)), a) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a))) <=> (mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)), a) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)))),
% 23.80/23.97 inference(symmetry,[status(thm)],[12359])).
% 23.80/23.97 tff(12361,plain,
% 23.80/23.97 (mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)) = mult(mult(unit, a), mult(mult(b, c), c))),
% 23.80/23.97 inference(transitivity,[status(thm)],[10229, 2632, 12153, 4660, 8733, 2502, 2499, 12086, 12091, 12085, 12083, 233, 2414, 3136])).
% 23.80/23.97 tff(12362,plain,
% 23.80/23.97 (mult(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)), a) = mult(mult(unit, mult(mult(b, c), c)), a)),
% 23.80/23.97 inference(transitivity,[status(thm)],[12354, 3150])).
% 23.80/23.97 tff(12363,plain,
% 23.80/23.97 ((mult(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)), a) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a))) <=> (mult(mult(unit, mult(mult(b, c), c)), a) = mult(mult(unit, a), mult(mult(b, c), c)))),
% 23.80/23.97 inference(monotonicity,[status(thm)],[12362, 12361])).
% 23.80/23.97 tff(12364,plain,
% 23.80/23.97 ((mult(mult(unit, mult(mult(b, c), c)), a) = mult(mult(unit, a), mult(mult(b, c), c))) <=> (mult(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)), a) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(mult(a, c), a)))),
% 23.80/23.97 inference(symmetry,[status(thm)],[12363])).
% 23.80/23.97 tff(12365,plain,
% 23.80/23.97 ((mult(mult(a, mult(b, c)), c) = mult(a, mult(mult(b, c), c))) <=> (mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)), a) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)))),
% 23.80/23.97 inference(transitivity,[status(thm)],[12333, 12364, 12360])).
% 23.80/23.97 tff(12366,plain,
% 23.80/23.97 ((~(mult(mult(a, mult(b, c)), c) = mult(a, mult(mult(b, c), c)))) <=> (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)), a) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a))))),
% 23.80/23.97 inference(monotonicity,[status(thm)],[12365])).
% 23.80/23.97 tff(12367,plain,
% 23.80/23.97 (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)), a) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)))),
% 23.80/23.97 inference(modus_ponens,[status(thm)],[258, 12366])).
% 23.80/23.97 tff(12368,plain,
% 23.80/23.97 (((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)), a) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a))))) | (mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)), a) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)))),
% 23.80/23.97 inference(tautology,[status(thm)],[])).
% 23.80/23.97 tff(12369,plain,
% 23.80/23.97 ((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)), a) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a))))),
% 23.80/23.97 inference(unit_resolution,[status(thm)],[12368, 12367])).
% 23.80/23.97 tff(12370,plain,
% 23.80/23.97 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, c)))))) | (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)), a) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, c)))))) | (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)), a) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)))))))),
% 23.80/23.97 inference(rewrite,[status(thm)],[])).
% 23.80/23.97 tff(12371,plain,
% 23.80/23.97 (((~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, c)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))))))) | (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)), a) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c)))))))) <=> ((~((~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, c)))))) | (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)), a) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)))))))),
% 23.80/23.98 inference(rewrite,[status(thm)],[])).
% 23.80/23.98 tff(12372,plain,
% 23.80/23.98 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, c)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))))))) | (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)), a) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, c)))))) | (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)), a) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a))))))))),
% 23.80/23.98 inference(monotonicity,[status(thm)],[12371])).
% 23.80/23.98 tff(12373,plain,
% 23.80/23.98 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, c)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))))))) | (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)), a) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, c)))))) | (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)), a) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)))))))),
% 23.80/23.98 inference(transitivity,[status(thm)],[12372, 12370])).
% 23.80/23.98 tff(12374,plain,
% 23.80/23.98 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, c)))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))))))) | (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)), a) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))))))))),
% 23.80/23.98 inference(quant_inst,[status(thm)],[])).
% 23.80/23.98 tff(12375,plain,
% 23.80/23.98 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, c)))))) | (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)), a) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a))))))),
% 23.80/23.98 inference(modus_ponens,[status(thm)],[12374, 12373])).
% 23.80/23.98 tff(12376,plain,
% 23.80/23.98 ((~((~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, c)))))) | (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)), a) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a))))))),
% 23.80/23.98 inference(unit_resolution,[status(thm)],[12375, 27])).
% 23.80/23.98 tff(12377,plain,
% 23.80/23.98 (~((~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, c)))))),
% 23.80/23.98 inference(unit_resolution,[status(thm)],[12376, 12369])).
% 23.80/23.98 tff(12378,plain,
% 23.80/23.98 (((~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, c))))) | (mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, c)))),
% 23.80/23.98 inference(tautology,[status(thm)],[])).
% 23.80/23.98 tff(12379,plain,
% 23.80/23.98 (mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, c))),
% 23.80/23.98 inference(unit_resolution,[status(thm)],[12378, 12377])).
% 23.80/23.98 tff(12380,plain,
% 23.80/23.98 (mult(unit, mult(mult(a, c), c)) = mult(unit, mult(c, mult(a, c)))),
% 23.80/23.98 inference(monotonicity,[status(thm)],[8725])).
% 23.80/23.98 tff(12381,plain,
% 23.80/23.98 (mult(unit, mult(mult(a, c), c)) = mult(c, mult(a, c))),
% 23.80/23.98 inference(transitivity,[status(thm)],[12380, 4366, 4365, 4362, 2690])).
% 23.80/23.98 tff(12382,plain,
% 23.80/23.98 (mult(mult(unit, mult(mult(a, c), c)), b) = mult(mult(c, mult(a, c)), b)),
% 23.80/23.98 inference(monotonicity,[status(thm)],[12381])).
% 23.80/23.98 tff(12383,plain,
% 23.80/23.98 (mult(mult(unit, mult(mult(a, c), c)), b) = mult(mult(unit, a), mult(mult(b, c), c))),
% 23.80/23.98 inference(transitivity,[status(thm)],[12382, 8847, 2759, 233, 2414, 3136])).
% 23.80/23.98 tff(12384,plain,
% 23.80/23.98 (mult(b, mult(mult(a, c), c)) = mult(b, mult(c, mult(a, c)))),
% 23.80/23.98 inference(monotonicity,[status(thm)],[8725])).
% 23.80/23.98 tff(12385,plain,
% 23.80/23.98 (mult(mult(unit, b), mult(mult(a, c), c)) = mult(mult(unit, mult(mult(b, c), c)), a)),
% 23.80/23.98 inference(transitivity,[status(thm)],[9615, 12384, 8559, 4149, 12260, 3150])).
% 23.80/23.98 tff(12386,plain,
% 23.80/23.98 ((mult(mult(unit, b), mult(mult(a, c), c)) = mult(mult(unit, mult(mult(a, c), c)), b)) <=> (mult(mult(unit, mult(mult(b, c), c)), a) = mult(mult(unit, a), mult(mult(b, c), c)))),
% 23.80/23.98 inference(monotonicity,[status(thm)],[12385, 12383])).
% 23.80/23.98 tff(12387,plain,
% 23.80/23.98 ((mult(mult(unit, mult(mult(b, c), c)), a) = mult(mult(unit, a), mult(mult(b, c), c))) <=> (mult(mult(unit, b), mult(mult(a, c), c)) = mult(mult(unit, mult(mult(a, c), c)), b))),
% 23.80/23.98 inference(symmetry,[status(thm)],[12386])).
% 23.80/23.98 tff(12388,plain,
% 23.80/23.98 ((mult(mult(a, mult(b, c)), c) = mult(a, mult(mult(b, c), c))) <=> (mult(mult(unit, b), mult(mult(a, c), c)) = mult(mult(unit, mult(mult(a, c), c)), b))),
% 23.80/23.98 inference(transitivity,[status(thm)],[12333, 12387])).
% 23.80/23.98 tff(12389,plain,
% 23.80/23.98 ((~(mult(mult(a, mult(b, c)), c) = mult(a, mult(mult(b, c), c)))) <=> (~(mult(mult(unit, b), mult(mult(a, c), c)) = mult(mult(unit, mult(mult(a, c), c)), b)))),
% 23.80/23.98 inference(monotonicity,[status(thm)],[12388])).
% 23.80/23.98 tff(12390,plain,
% 23.80/23.98 (~(mult(mult(unit, b), mult(mult(a, c), c)) = mult(mult(unit, mult(mult(a, c), c)), b))),
% 23.80/23.98 inference(modus_ponens,[status(thm)],[258, 12389])).
% 23.80/23.98 tff(12391,plain,
% 23.80/23.98 (mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c))) = mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c))))),
% 23.80/23.98 inference(transitivity,[status(thm)],[2802, 12216])).
% 23.80/23.98 tff(12392,plain,
% 23.80/23.98 ((mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))) <=> (mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c)))))),
% 23.80/23.98 inference(monotonicity,[status(thm)],[12233, 12391])).
% 23.80/23.98 tff(12393,plain,
% 23.80/23.98 ((mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c))) = mult(c, mult(mult(a, c), rd(mult(b, c), mult(a, c))))) <=> (mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))),
% 23.80/23.98 inference(symmetry,[status(thm)],[12392])).
% 23.80/23.98 tff(12394,plain,
% 23.80/23.98 (mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c)))),
% 23.80/23.98 inference(modus_ponens,[status(thm)],[12227, 12393])).
% 23.80/23.98 tff(12395,assumption,(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))), introduced(assumption)).
% 23.80/23.98 tff(12396,plain,
% 23.80/23.98 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(a, c), mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), c)))),
% 23.80/23.98 inference(quant_inst,[status(thm)],[])).
% 23.80/23.98 tff(12397,plain,
% 23.80/23.98 (ld(mult(a, c), mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c)))) = mult(a, mult(rd(mult(b, c), mult(a, c)), c))),
% 23.80/23.98 inference(unit_resolution,[status(thm)],[12396, 7])).
% 23.80/23.98 tff(12398,plain,
% 23.80/23.98 (mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), a), c)) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a))),
% 23.80/23.98 inference(monotonicity,[status(thm)],[7606])).
% 23.80/23.98 tff(12399,plain,
% 23.80/23.98 (mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), a), c))),
% 23.80/23.98 inference(symmetry,[status(thm)],[12398])).
% 23.80/23.98 tff(12400,plain,
% 23.80/23.98 (mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), a), c))),
% 23.80/23.98 inference(transitivity,[status(thm)],[6302, 12399])).
% 23.80/23.98 tff(12401,plain,
% 23.80/23.98 (ld(mult(a, c), mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c)))) = ld(mult(a, c), mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), a), c)))),
% 23.80/23.98 inference(monotonicity,[status(thm)],[12400])).
% 23.80/23.98 tff(12402,plain,
% 23.80/23.98 (ld(mult(a, c), mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), a), c))) = ld(mult(a, c), mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))),
% 23.80/23.98 inference(symmetry,[status(thm)],[12401])).
% 23.80/23.98 tff(12403,plain,
% 23.80/23.98 (mult(mult(rd(mult(b, c), mult(a, c)), a), c) = ld(mult(a, c), mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), a), c)))),
% 23.80/23.98 inference(symmetry,[status(thm)],[8780])).
% 23.80/23.98 tff(12404,plain,
% 23.80/23.98 (mult(mult(rd(mult(b, c), mult(a, c)), a), c) = mult(a, mult(c, rd(mult(b, c), mult(a, c))))),
% 23.80/23.98 inference(transitivity,[status(thm)],[12403, 12402, 12397, 10681, 5159, 6696])).
% 23.80/23.98 tff(12405,plain,
% 23.80/23.98 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), mult(a, c)) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c))),
% 23.80/23.98 inference(monotonicity,[status(thm)],[12404])).
% 23.80/23.98 tff(12406,plain,
% 23.80/23.98 (mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, c)) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), mult(a, c))),
% 23.80/23.98 inference(monotonicity,[status(thm)],[7721])).
% 23.80/23.98 tff(12407,assumption,(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, c))), introduced(assumption)).
% 23.80/23.98 tff(12408,plain,
% 23.80/23.98 (mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)) = mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))),
% 23.80/23.98 inference(monotonicity,[status(thm)],[10715])).
% 23.80/23.98 tff(12409,plain,
% 23.80/23.98 (mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c))),
% 23.80/23.98 inference(symmetry,[status(thm)],[12408])).
% 23.80/23.98 tff(12410,plain,
% 23.80/23.98 (mult(mult(b, c), c) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c))),
% 23.80/23.98 inference(transitivity,[status(thm)],[8573, 4537, 4178, 2803, 4536, 12409])).
% 23.80/23.98 tff(12411,plain,
% 23.80/23.98 (mult(mult(mult(b, c), c), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)), a)),
% 23.80/23.98 inference(monotonicity,[status(thm)],[12410])).
% 23.80/23.98 tff(12412,plain,
% 23.80/23.98 (mult(b, mult(mult(a, c), c)) = mult(b, mult(c, mult(a, c)))),
% 23.80/23.98 inference(monotonicity,[status(thm)],[6893])).
% 23.80/23.98 tff(12413,plain,
% 23.80/23.98 (mult(mult(unit, b), mult(mult(a, c), c)) = mult(mult(unit, mult(mult(a, c), c)), b)),
% 23.80/23.98 inference(transitivity,[status(thm)],[9615, 12412, 8559, 4149, 7719, 12411, 12407, 12406, 12405, 12395, 4539, 4372, 234, 4371, 7680, 9613])).
% 23.80/23.98 tff(12414,assumption,(~(mult(mult(unit, b), mult(mult(a, c), c)) = mult(mult(unit, mult(mult(a, c), c)), b))), introduced(assumption)).
% 23.80/23.98 tff(12415,plain,
% 23.80/23.98 ($false),
% 23.80/23.98 inference(unit_resolution,[status(thm)],[12414, 12413])).
% 23.80/23.98 tff(12416,plain,((~(mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)))) | (mult(mult(unit, b), mult(mult(a, c), c)) = mult(mult(unit, mult(mult(a, c), c)), b)) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, c)))) | (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (~(mult(a, mult(mult(mult(unit, rd(mult(b, c), mult(a, c))), unit), c)) = mult(a, mult(c, mult(mult(unit, rd(mult(b, c), mult(a, c))), unit))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit))))), inference(lemma,lemma(discharge,[]))).
% 23.80/23.99 tff(12417,plain,
% 23.80/23.99 ((~(mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)))) | (mult(mult(unit, b), mult(mult(a, c), c)) = mult(mult(unit, mult(mult(a, c), c)), b)) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, c)))) | (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))) | (~(mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(c, mult(rd(mult(b, c), mult(a, c)), mult(a, c))))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), mult(mult(unit, c), unit)), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), mult(mult(unit, c), unit))))),
% 23.80/23.99 inference(unit_resolution,[status(thm)],[12416, 9157])).
% 23.80/23.99 tff(12418,plain,
% 23.80/23.99 ((~(mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)))) | (mult(mult(unit, b), mult(mult(a, c), c)) = mult(mult(unit, mult(mult(a, c), c)), b)) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, c)))) | (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))))),
% 23.80/23.99 inference(unit_resolution,[status(thm)],[12417, 12147, 12394])).
% 23.80/23.99 tff(12419,plain,
% 23.80/23.99 (~(mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)))),
% 23.80/23.99 inference(unit_resolution,[status(thm)],[12418, 12348, 12390, 12379])).
% 23.80/23.99 tff(12420,plain,
% 23.80/23.99 ((~(mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a))) | (~(mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a))))),
% 23.80/23.99 inference(unit_resolution,[status(thm)],[5157, 12419])).
% 23.80/23.99 tff(12421,plain,
% 23.80/23.99 (~((~(mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))) | (~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)))))),
% 23.80/23.99 inference(unit_resolution,[status(thm)],[5220, 12420])).
% 23.80/23.99 tff(12422,plain,
% 23.80/23.99 (mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c)))),
% 23.80/23.99 inference(unit_resolution,[status(thm)],[5352, 12421])).
% 23.80/23.99 tff(12423,plain,
% 23.80/23.99 (mult(a, mult(a, c)) = mult(mult(a, c), a)),
% 23.80/23.99 inference(transitivity,[status(thm)],[8292, 12318, 8230])).
% 23.80/23.99 tff(12424,plain,
% 23.80/23.99 (mult(mult(a, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c))),
% 23.80/23.99 inference(monotonicity,[status(thm)],[12423])).
% 23.80/23.99 tff(12425,plain,
% 23.80/23.99 (mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), c))),
% 23.80/23.99 inference(monotonicity,[status(thm)],[9898])).
% 23.80/23.99 tff(12426,plain,
% 23.80/23.99 (mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))),
% 23.80/23.99 inference(unit_resolution,[status(thm)],[8924, 12347])).
% 23.80/23.99 tff(12427,plain,
% 23.80/23.99 (mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c))))),
% 23.80/23.99 inference(symmetry,[status(thm)],[12426])).
% 23.80/23.99 tff(12428,plain,
% 23.80/23.99 (mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(c, mult(rd(mult(b, c), mult(a, c)), a)), c))),
% 23.80/23.99 inference(transitivity,[status(thm)],[12427, 12425, 12424, 12422, 12352, 8982, 8981, 4181, 12259, 12345, 6220])).
% 23.80/23.99 tff(12429,plain,
% 23.80/23.99 (ld(a, mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))) = ld(a, mult(a, mult(mult(c, mult(rd(mult(b, c), mult(a, c)), a)), c)))),
% 23.80/23.99 inference(monotonicity,[status(thm)],[12428])).
% 23.80/23.99 tff(12430,plain,
% 23.80/23.99 (mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c)),
% 23.80/23.99 inference(transitivity,[status(thm)],[10670, 8954, 12429, 12344, 12244, 12242, 7658])).
% 23.80/23.99 tff(12431,plain,
% 23.80/23.99 (mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), c), a)),
% 23.80/23.99 inference(monotonicity,[status(thm)],[12430])).
% 23.80/23.99 tff(12432,plain,
% 23.80/23.99 (mult(mult(mult(c, a), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a)),
% 23.80/23.99 inference(monotonicity,[status(thm)],[8958])).
% 23.80/23.99 tff(12433,plain,
% 23.80/23.99 (mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(b, c), a)),
% 23.80/23.99 inference(monotonicity,[status(thm)],[12351])).
% 23.80/23.99 tff(12434,plain,
% 23.80/23.99 (mult(mult(b, c), a) = mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a)),
% 23.80/23.99 inference(symmetry,[status(thm)],[12433])).
% 23.80/23.99 tff(12435,plain,
% 23.80/23.99 (mult(c, mult(mult(b, c), a)) = mult(c, mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a))),
% 23.80/23.99 inference(monotonicity,[status(thm)],[12434])).
% 23.80/23.99 tff(12436,plain,
% 23.80/23.99 (mult(c, mult(mult(b, c), a)) = mult(c, mult(mult(a, b), c))),
% 23.80/23.99 inference(transitivity,[status(thm)],[12435, 5324, 12432, 12431, 12153, 4660, 8733, 2502, 2499, 12086, 12091, 12085, 12083, 4285, 3187, 4274, 5654])).
% 23.80/23.99 tff(12437,plain,
% 23.80/23.99 (ld(c, mult(c, mult(mult(b, c), a))) = ld(c, mult(c, mult(mult(a, b), c)))),
% 23.80/23.99 inference(monotonicity,[status(thm)],[12436])).
% 23.80/23.99 tff(12438,plain,
% 23.80/23.99 (mult(c, mult(b, a)) = mult(c, mult(a, b))),
% 23.80/23.99 inference(transitivity,[status(thm)],[4304, 2298, 2297, 12437, 4031, 227, 8636, 4221])).
% 23.80/23.99 tff(12439,plain,
% 23.80/23.99 ((mult(c, mult(a, b)) = mult(c, mult(b, a))) <=> (mult(c, mult(b, a)) = mult(c, mult(a, b)))),
% 23.80/23.99 inference(commutativity,[status(thm)],[])).
% 23.80/23.99 tff(12440,plain,
% 23.80/23.99 (mult(mult(a, mult(b, c)), c) = mult(mult(mult(b, c), a), c)),
% 23.80/23.99 inference(transitivity,[status(thm)],[8159, 8982, 8981, 4181, 12259])).
% 23.80/23.99 tff(12441,plain,
% 23.80/23.99 (rd(mult(mult(a, mult(b, c)), c), c) = rd(mult(mult(mult(b, c), a), c), c)),
% 23.80/23.99 inference(monotonicity,[status(thm)],[12440])).
% 23.80/23.99 tff(12442,plain,
% 23.80/23.99 (mult(a, mult(b, c)) = mult(c, mult(b, a))),
% 23.80/23.99 inference(transitivity,[status(thm)],[8985, 12441, 2676, 3057, 4208])).
% 23.80/23.99 tff(12443,plain,
% 23.80/23.99 (mult(mult(a, b), c) = mult(c, mult(a, b))),
% 23.80/23.99 inference(transitivity,[status(thm)],[227, 8636, 4221])).
% 23.80/23.99 tff(12444,plain,
% 23.80/23.99 ((mult(mult(a, b), c) = mult(a, mult(b, c))) <=> (mult(c, mult(a, b)) = mult(c, mult(b, a)))),
% 23.80/23.99 inference(monotonicity,[status(thm)],[12443, 12442])).
% 23.80/23.99 tff(12445,plain,
% 23.80/23.99 ((mult(mult(a, b), c) = mult(a, mult(b, c))) <=> (mult(c, mult(b, a)) = mult(c, mult(a, b)))),
% 23.80/23.99 inference(transitivity,[status(thm)],[12444, 12439])).
% 23.80/23.99 tff(12446,plain,
% 23.80/23.99 ((~(mult(mult(a, b), c) = mult(a, mult(b, c)))) <=> (~(mult(c, mult(b, a)) = mult(c, mult(a, b))))),
% 23.80/23.99 inference(monotonicity,[status(thm)],[12445])).
% 23.80/23.99 tff(12447,plain,
% 23.80/23.99 (~(mult(c, mult(b, a)) = mult(c, mult(a, b)))),
% 23.80/23.99 inference(modus_ponens,[status(thm)],[146, 12446])).
% 23.80/23.99 tff(12448,plain,
% 23.80/23.99 ($false),
% 23.80/23.99 inference(unit_resolution,[status(thm)],[12447, 12438])).
% 23.80/23.99 tff(12449,plain,(((~(mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))))) | (~(mult(mult(c, mult(b, c)), a) = mult(mult(c, a), mult(b, c))))), inference(lemma,lemma(discharge,[]))).
% 23.80/23.99 tff(12450,plain,
% 23.80/23.99 ((~(mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))))),
% 23.80/23.99 inference(unit_resolution,[status(thm)],[12449, 8980])).
% 23.80/23.99 tff(12451,plain,
% 23.80/23.99 (~((~(mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)))) | (~(mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))))),
% 23.80/23.99 inference(unit_resolution,[status(thm)],[4565, 12450])).
% 23.80/23.99 tff(12452,plain,
% 23.80/23.99 (mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 23.80/23.99 inference(unit_resolution,[status(thm)],[4567, 12451])).
% 23.80/23.99 tff(12453,plain,
% 23.80/23.99 (mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(b, c), c))),
% 23.80/23.99 inference(transitivity,[status(thm)],[12452, 12234, 12231])).
% 23.80/23.99 tff(12454,plain,
% 23.80/23.99 (ld(a, mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))) = ld(a, mult(a, mult(mult(b, c), c)))),
% 23.80/23.99 inference(monotonicity,[status(thm)],[12453])).
% 23.80/23.99 tff(12455,plain,
% 23.80/23.99 (mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(b, c), c)),
% 23.80/23.99 inference(transitivity,[status(thm)],[10670, 8954, 12454, 4173])).
% 23.80/23.99 tff(12456,plain,
% 23.80/23.99 (mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(b, c), c), a)),
% 23.80/23.99 inference(monotonicity,[status(thm)],[12455])).
% 23.80/23.99 tff(12457,plain,
% 23.80/23.99 (mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c))),
% 23.80/23.99 inference(unit_resolution,[status(thm)],[4606, 12451])).
% 23.80/23.99 tff(12458,plain,
% 23.80/23.99 (~((~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, c)) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)), a))) | (~(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, mult(a, c))) = mult(mult(rd(mult(b, c), mult(a, c)), c), mult(mult(a, c), a)))))),
% 23.80/23.99 inference(unit_resolution,[status(thm)],[10857, 12369])).
% 23.80/23.99 tff(12459,plain,
% 23.80/23.99 (mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, c)) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)), a)),
% 23.80/23.99 inference(unit_resolution,[status(thm)],[10859, 12458])).
% 23.80/23.99 tff(12460,plain,
% 23.80/23.99 ((~(mult(mult(a, mult(b, c)), c) = mult(a, mult(mult(b, c), c)))) <=> (~(mult(mult(unit, mult(mult(b, c), c)), a) = mult(mult(unit, a), mult(mult(b, c), c))))),
% 23.80/23.99 inference(monotonicity,[status(thm)],[12333])).
% 23.80/23.99 tff(12461,plain,
% 23.80/23.99 (~(mult(mult(unit, mult(mult(b, c), c)), a) = mult(mult(unit, a), mult(mult(b, c), c)))),
% 23.80/23.99 inference(modus_ponens,[status(thm)],[258, 12460])).
% 23.80/23.99 tff(12462,plain,
% 23.80/23.99 (mult(mult(rd(mult(b, c), mult(a, c)), a), c) = mult(mult(rd(mult(b, c), mult(a, c)), c), a)),
% 23.80/23.99 inference(transitivity,[status(thm)],[4490, 12148, 4488])).
% 23.80/23.99 tff(12463,plain,
% 23.80/23.99 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), mult(a, c)) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, c))),
% 23.80/23.99 inference(monotonicity,[status(thm)],[12462])).
% 23.80/23.99 tff(12464,plain,
% 23.80/23.99 (mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, c)) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), mult(a, c))),
% 23.80/23.99 inference(symmetry,[status(thm)],[12463])).
% 23.80/23.99 tff(12465,assumption,(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, c)) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)), a)), introduced(assumption)).
% 23.80/23.99 tff(12466,plain,
% 23.80/23.99 (mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, c))),
% 23.80/23.99 inference(symmetry,[status(thm)],[12465])).
% 23.80/23.99 tff(12467,plain,
% 23.80/23.99 (mult(mult(mult(b, c), c), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)), a)),
% 23.80/23.99 inference(symmetry,[status(thm)],[12357])).
% 23.80/23.99 tff(12468,plain,
% 23.80/23.99 (mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(b, c), c))),
% 23.80/23.99 inference(transitivity,[status(thm)],[10922, 12234, 12231])).
% 23.80/23.99 tff(12469,plain,
% 23.80/23.99 (ld(a, mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))) = ld(a, mult(a, mult(mult(b, c), c)))),
% 23.80/23.99 inference(monotonicity,[status(thm)],[12468])).
% 23.80/23.99 tff(12470,plain,
% 23.80/23.99 (mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(b, c), c)),
% 23.80/23.99 inference(transitivity,[status(thm)],[10670, 8954, 12469, 4173])).
% 23.80/23.99 tff(12471,plain,
% 23.80/23.99 (mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(b, c), c), a)),
% 23.80/23.99 inference(monotonicity,[status(thm)],[12470])).
% 23.80/23.99 tff(12472,assumption,(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c))), introduced(assumption)).
% 23.80/23.99 tff(12473,plain,
% 23.80/23.99 (mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a)),
% 23.80/23.99 inference(symmetry,[status(thm)],[12472])).
% 23.80/23.99 tff(12474,assumption,(mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c))), introduced(assumption)).
% 23.80/23.99 tff(12475,plain,
% 23.80/23.99 (mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c))))),
% 23.80/23.99 inference(symmetry,[status(thm)],[12474])).
% 23.80/23.99 tff(12476,plain,
% 23.80/23.99 (mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), mult(a, c)) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), mult(a, c))),
% 23.80/23.99 inference(transitivity,[status(thm)],[10683, 12475, 12425, 12424, 12473, 12471, 12467, 12466, 12464])).
% 23.80/23.99 tff(12477,plain,
% 23.80/23.99 (rd(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), mult(a, c)), mult(a, c)) = rd(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), mult(a, c)), mult(a, c))),
% 23.80/23.99 inference(monotonicity,[status(thm)],[12476])).
% 23.80/23.99 tff(12478,plain,
% 23.80/23.99 (mult(a, mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(rd(mult(b, c), mult(a, c)), a), c)),
% 23.80/23.99 inference(transitivity,[status(thm)],[10936, 12477, 10842])).
% 23.80/23.99 tff(12479,plain,
% 23.80/23.99 (mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a)),
% 23.80/23.99 inference(monotonicity,[status(thm)],[12478])).
% 23.80/23.99 tff(12480,plain,
% 23.80/23.99 (mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(a, c), b)),
% 23.80/23.99 inference(transitivity,[status(thm)],[12479, 1168, 6930, 12208, 4031, 227])).
% 23.80/23.99 tff(12481,plain,
% 23.80/23.99 (mult(c, mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a)) = mult(c, mult(mult(a, c), b))),
% 23.80/23.99 inference(monotonicity,[status(thm)],[12480])).
% 23.80/23.99 tff(12482,plain,
% 23.80/23.99 (ld(a, mult(a, mult(mult(b, c), c))) = ld(a, mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))))),
% 23.80/23.99 inference(symmetry,[status(thm)],[12469])).
% 23.80/23.99 tff(12483,plain,
% 23.80/23.99 (mult(mult(b, c), c) = mult(mult(c, a), mult(rd(mult(b, c), mult(a, c)), c))),
% 23.80/23.99 inference(transitivity,[status(thm)],[8573, 12482, 8953, 10942, 8998])).
% 23.80/23.99 tff(12484,plain,
% 23.80/23.99 (mult(mult(mult(b, c), c), a) = mult(mult(mult(c, a), mult(rd(mult(b, c), mult(a, c)), c)), a)),
% 23.80/23.99 inference(monotonicity,[status(thm)],[12483])).
% 23.80/23.99 tff(12485,plain,
% 23.80/23.99 (mult(mult(unit, mult(mult(b, c), c)), a) = mult(mult(unit, a), mult(mult(b, c), c))),
% 23.80/23.99 inference(transitivity,[status(thm)],[3149, 12484, 5195, 12481, 3190, 3188, 4284, 233, 2414, 3136])).
% 23.80/23.99 tff(12486,assumption,(~(mult(mult(unit, mult(mult(b, c), c)), a) = mult(mult(unit, a), mult(mult(b, c), c)))), introduced(assumption)).
% 23.80/23.99 tff(12487,plain,
% 23.80/23.99 ($false),
% 23.80/23.99 inference(unit_resolution,[status(thm)],[12486, 12485])).
% 23.80/23.99 tff(12488,plain,((~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)))) | (mult(mult(unit, mult(mult(b, c), c)), a) = mult(mult(unit, a), mult(mult(b, c), c))) | (~(mult(mult(mult(rd(mult(b, c), mult(a, c)), c), a), mult(a, c)) = mult(mult(mult(rd(mult(b, c), mult(a, c)), c), mult(a, c)), a))) | (~(mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)))) | (~(mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))))), inference(lemma,lemma(discharge,[]))).
% 23.80/23.99 tff(12489,plain,
% 23.80/23.99 (~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)))),
% 23.80/23.99 inference(unit_resolution,[status(thm)],[12488, 12461, 12459, 12457, 12452])).
% 23.80/23.99 tff(12490,plain,
% 23.80/23.99 ((~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)))) | (~(mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c)))))),
% 23.80/23.99 inference(unit_resolution,[status(thm)],[10701, 12489])).
% 23.80/23.99 tff(12491,plain,
% 23.80/23.99 (~((~(mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))) | (~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)))))),
% 23.80/23.99 inference(unit_resolution,[status(thm)],[8807, 12490])).
% 23.80/23.99 tff(12492,plain,
% 23.80/23.99 (mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a))),
% 23.80/23.99 inference(unit_resolution,[status(thm)],[5222, 12491])).
% 23.80/23.99 tff(12493,plain,
% 23.80/23.99 (mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a)),
% 23.80/24.00 inference(symmetry,[status(thm)],[12492])).
% 23.80/24.00 tff(12494,plain,
% 23.80/24.00 (mult(mult(unit, mult(a, c)), mult(mult(rd(mult(b, c), mult(a, c)), a), c)) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a))),
% 23.80/24.00 inference(monotonicity,[status(thm)],[1549, 12462])).
% 23.80/24.00 tff(12495,plain,
% 23.80/24.00 (mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), a), c)) = mult(mult(a, c), mult(b, c))),
% 23.80/24.00 inference(transitivity,[status(thm)],[8785, 12494, 12493, 12456, 10665, 8980, 12209])).
% 23.80/24.00 tff(12496,plain,
% 23.80/24.00 (ld(mult(a, c), mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), a), c))) = ld(mult(a, c), mult(mult(a, c), mult(b, c)))),
% 23.80/24.00 inference(monotonicity,[status(thm)],[12495])).
% 23.80/24.00 tff(12497,plain,
% 23.80/24.00 (ld(mult(a, c), mult(mult(a, c), mult(b, c))) = ld(mult(a, c), mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), a), c)))),
% 23.80/24.00 inference(symmetry,[status(thm)],[12496])).
% 23.80/24.00 tff(12498,plain,
% 23.80/24.00 (mult(b, c) = mult(mult(rd(mult(b, c), mult(a, c)), a), c)),
% 23.80/24.00 inference(transitivity,[status(thm)],[740, 12497, 8780])).
% 23.80/24.00 tff(12499,plain,
% 23.80/24.00 (mult(mult(b, c), a) = mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a)),
% 23.80/24.00 inference(monotonicity,[status(thm)],[12498])).
% 23.80/24.00 tff(12500,plain,
% 23.80/24.00 (mult(c, mult(b, a)) = mult(c, mult(a, b))),
% 23.80/24.00 inference(transitivity,[status(thm)],[4304, 2298, 12499, 1168, 6930, 12208, 4031, 227, 8636, 4221])).
% 23.80/24.00 tff(12501,plain,
% 23.80/24.00 ($false),
% 23.80/24.00 inference(unit_resolution,[status(thm)],[12447, 12500])).
% 23.80/24.00 tff(12502,plain,(~(mult(mult(c, mult(b, c)), a) = mult(mult(c, a), mult(b, c)))), inference(lemma,lemma(discharge,[]))).
% 23.80/24.00 tff(12503,plain,
% 23.80/24.00 ((~(mult(mult(c, mult(b, c)), a) = mult(mult(c, a), mult(b, c)))) | (~(mult(c, mult(mult(b, c), a)) = mult(c, mult(a, mult(b, c)))))),
% 23.80/24.00 inference(unit_resolution,[status(thm)],[4194, 12502])).
% 23.80/24.00 tff(12504,plain,
% 23.80/24.00 (~((~(mult(mult(c, mult(b, c)), a) = mult(c, mult(mult(b, c), a)))) | (~(mult(mult(c, a), mult(b, c)) = mult(c, mult(a, mult(b, c))))))),
% 23.80/24.00 inference(unit_resolution,[status(thm)],[4199, 12503])).
% 23.80/24.00 tff(12505,plain,
% 23.80/24.00 (mult(mult(c, mult(b, c)), a) = mult(c, mult(mult(b, c), a))),
% 23.80/24.00 inference(unit_resolution,[status(thm)],[4201, 12504])).
% 23.80/24.00 tff(12506,plain,
% 23.80/24.00 (mult(b, mult(a, c)) = mult(mult(a, b), c)),
% 23.80/24.00 inference(transitivity,[status(thm)],[12081, 12067, 12080, 12059, 228, 222])).
% 23.80/24.00 tff(12507,plain,
% 23.80/24.00 (mult(mult(b, mult(a, c)), b) = mult(mult(mult(a, b), c), b)),
% 23.80/24.00 inference(monotonicity,[status(thm)],[12506])).
% 23.80/24.00 tff(12508,assumption,(~(mult(mult(b, mult(a, c)), b) = mult(b, mult(mult(a, c), b)))), introduced(assumption)).
% 23.80/24.00 tff(12509,plain,
% 23.80/24.00 ((mult(mult(unit, mult(mult(a, b), c)), b) = mult(mult(unit, b), mult(mult(a, b), c))) <=> (mult(mult(unit, b), mult(mult(a, b), c)) = mult(mult(unit, mult(mult(a, b), c)), b))),
% 23.80/24.00 inference(commutativity,[status(thm)],[])).
% 23.80/24.00 tff(12510,plain,
% 23.80/24.00 (mult(unit, mult(mult(a, b), c)) = mult(mult(a, b), c)),
% 23.80/24.00 inference(transitivity,[status(thm)],[216, 228, 222])).
% 23.80/24.00 tff(12511,plain,
% 23.80/24.00 (mult(mult(unit, mult(mult(a, b), c)), b) = mult(mult(mult(a, b), c), b)),
% 23.80/24.00 inference(monotonicity,[status(thm)],[12510])).
% 23.80/24.00 tff(12512,plain,
% 23.80/24.00 (mult(mult(mult(a, b), c), b) = mult(mult(unit, mult(mult(a, b), c)), b)),
% 23.80/24.00 inference(symmetry,[status(thm)],[12511])).
% 23.80/24.00 tff(12513,plain,
% 23.80/24.00 (mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), a)) = mult(c, mult(b, a))),
% 23.80/24.00 inference(transitivity,[status(thm)],[5404, 12051, 3892, 4208])).
% 23.80/24.00 tff(12514,plain,
% 23.80/24.00 (ld(c, mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), a))) = ld(c, mult(c, mult(b, a)))),
% 23.80/24.00 inference(monotonicity,[status(thm)],[12513])).
% 23.80/24.00 tff(12515,plain,
% 23.80/24.00 (mult(mult(a, rd(mult(b, c), mult(a, c))), a) = mult(b, a)),
% 23.80/24.00 inference(transitivity,[status(thm)],[5409, 12514, 1472])).
% 23.80/24.00 tff(12516,plain,
% 23.80/24.00 (rd(mult(mult(a, rd(mult(b, c), mult(a, c))), a), a) = rd(mult(b, a), a)),
% 23.80/24.00 inference(monotonicity,[status(thm)],[12515])).
% 23.80/24.00 tff(12517,plain,
% 23.80/24.00 (mult(a, rd(mult(b, c), mult(a, c))) = b),
% 23.80/24.00 inference(transitivity,[status(thm)],[1456, 12516, 1451])).
% 23.80/24.00 tff(12518,plain,
% 23.80/24.00 (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(a, c), b)),
% 23.80/24.00 inference(monotonicity,[status(thm)],[12517])).
% 23.80/24.00 tff(12519,plain,
% 23.80/24.00 (mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))) = mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), c)),
% 23.80/24.00 inference(transitivity,[status(thm)],[12518, 161, 215])).
% 23.80/24.00 tff(12520,plain,
% 23.80/24.00 (mult(unit, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = mult(unit, mult(mult(c, mult(mult(unit, ld(c, mult(a, b))), unit)), c))),
% 23.80/24.00 inference(monotonicity,[status(thm)],[12519])).
% 23.80/24.00 tff(12521,plain,
% 23.80/24.00 (mult(unit, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = mult(unit, mult(mult(a, c), b))),
% 23.80/24.00 inference(transitivity,[status(thm)],[12520, 12063])).
% 23.80/24.00 tff(12522,plain,
% 23.80/24.00 (mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)) = mult(b, mult(a, c))),
% 23.80/24.00 inference(monotonicity,[status(thm)],[12517])).
% 23.80/24.00 tff(12523,plain,
% 23.80/24.00 (mult(b, mult(a, c)) = mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))),
% 23.80/24.00 inference(symmetry,[status(thm)],[12522])).
% 23.80/24.00 tff(12524,plain,
% 23.80/24.00 (mult(unit, mult(b, mult(a, c))) = mult(unit, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 23.80/24.00 inference(monotonicity,[status(thm)],[12523])).
% 23.80/24.00 tff(12525,plain,
% 23.80/24.00 (mult(unit, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))) = mult(unit, mult(b, mult(a, c)))),
% 23.80/24.00 inference(symmetry,[status(thm)],[12524])).
% 23.80/24.00 tff(12526,plain,
% 23.80/24.00 ((mult(unit, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))) = mult(unit, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))) <=> (mult(unit, mult(b, mult(a, c))) = mult(unit, mult(mult(a, c), b)))),
% 23.80/24.00 inference(monotonicity,[status(thm)],[12525, 12521])).
% 23.80/24.00 tff(12527,plain,
% 23.80/24.00 ((mult(unit, mult(b, mult(a, c))) = mult(unit, mult(mult(a, c), b))) <=> (mult(unit, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))) = mult(unit, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))))),
% 23.80/24.00 inference(symmetry,[status(thm)],[12526])).
% 23.80/24.00 tff(12528,plain,
% 23.80/24.00 ((mult(mult(unit, b), mult(a, c)) = mult(mult(unit, mult(a, c)), b)) <=> (mult(unit, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = mult(unit, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))))),
% 23.80/24.00 inference(transitivity,[status(thm)],[12076, 12527, 12061])).
% 23.80/24.00 tff(12529,plain,
% 23.80/24.00 (mult(unit, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c))))) = mult(unit, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 23.80/24.00 inference(modus_ponens,[status(thm)],[12078, 12528])).
% 23.80/24.00 tff(12530,plain,
% 23.80/24.00 (mult(unit, mult(mult(a, rd(mult(b, c), mult(a, c))), mult(a, c))) = mult(unit, mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))))),
% 23.80/24.00 inference(symmetry,[status(thm)],[12529])).
% 23.80/24.00 tff(12531,plain,
% 23.80/24.00 (mult(b, mult(a, c)) = mult(mult(a, b), c)),
% 23.80/24.00 inference(transitivity,[status(thm)],[12081, 12524, 12530, 12520, 228, 222])).
% 23.80/24.00 tff(12532,plain,
% 23.80/24.00 (mult(mult(b, mult(a, c)), b) = mult(mult(mult(a, b), c), b)),
% 23.80/24.00 inference(monotonicity,[status(thm)],[12531])).
% 23.80/24.00 tff(12533,plain,
% 23.80/24.00 (mult(mult(b, mult(a, c)), b) = mult(mult(unit, mult(mult(a, b), c)), b)),
% 23.80/24.00 inference(transitivity,[status(thm)],[12532, 12512])).
% 23.80/24.00 tff(12534,plain,
% 23.80/24.00 ((mult(mult(b, mult(a, c)), b) = mult(b, mult(mult(a, c), b))) <=> (mult(mult(unit, mult(mult(a, b), c)), b) = mult(mult(unit, b), mult(mult(a, b), c)))),
% 23.80/24.00 inference(monotonicity,[status(thm)],[12533, 5603])).
% 23.80/24.00 tff(12535,plain,
% 23.80/24.00 ((mult(mult(b, mult(a, c)), b) = mult(b, mult(mult(a, c), b))) <=> (mult(mult(unit, b), mult(mult(a, b), c)) = mult(mult(unit, mult(mult(a, b), c)), b))),
% 23.80/24.00 inference(transitivity,[status(thm)],[12534, 12509])).
% 23.80/24.00 tff(12536,plain,
% 23.80/24.00 ((mult(mult(unit, b), mult(mult(a, b), c)) = mult(mult(unit, mult(mult(a, b), c)), b)) <=> (mult(mult(b, mult(a, c)), b) = mult(b, mult(mult(a, c), b)))),
% 23.80/24.00 inference(symmetry,[status(thm)],[12535])).
% 23.80/24.00 tff(12537,assumption,(mult(mult(unit, b), mult(mult(a, b), c)) = mult(mult(unit, mult(mult(a, b), c)), b)), introduced(assumption)).
% 23.80/24.00 tff(12538,plain,
% 23.80/24.00 (mult(mult(b, mult(a, c)), b) = mult(b, mult(mult(a, c), b))),
% 23.80/24.00 inference(modus_ponens,[status(thm)],[12537, 12536])).
% 23.80/24.00 tff(12539,plain,
% 23.80/24.00 ($false),
% 23.80/24.00 inference(unit_resolution,[status(thm)],[12508, 12538])).
% 23.80/24.00 tff(12540,plain,((~(mult(mult(unit, b), mult(mult(a, b), c)) = mult(mult(unit, mult(mult(a, b), c)), b))) | (mult(mult(b, mult(a, c)), b) = mult(b, mult(mult(a, c), b)))), inference(lemma,lemma(discharge,[]))).
% 23.80/24.00 tff(12541,plain,
% 23.80/24.00 (~(mult(mult(unit, b), mult(mult(a, b), c)) = mult(mult(unit, mult(mult(a, b), c)), b))),
% 23.80/24.00 inference(unit_resolution,[status(thm)],[12540, 12508])).
% 23.80/24.00 tff(12542,plain,
% 23.80/24.00 (mult(mult(b, c), a) = mult(mult(a, b), c)),
% 23.80/24.00 inference(transitivity,[status(thm)],[3892, 4208, 8450, 4225, 4270, 4269, 161])).
% 23.80/24.00 tff(12543,plain,
% 23.80/24.00 (mult(mult(mult(b, c), a), b) = mult(mult(mult(a, b), c), b)),
% 23.80/24.00 inference(monotonicity,[status(thm)],[12542])).
% 23.80/24.00 tff(12544,plain,
% 23.80/24.00 (mult(mult(c, a), mult(b, c)) = mult(mult(a, c), mult(b, c))),
% 23.80/24.00 inference(monotonicity,[status(thm)],[4268])).
% 23.80/24.00 tff(12545,plain,
% 23.80/24.00 (mult(mult(a, c), mult(b, c)) = mult(mult(c, a), mult(b, c))),
% 23.80/24.00 inference(symmetry,[status(thm)],[12544])).
% 23.80/24.00 tff(12546,plain,
% 23.80/24.00 (mult(mult(mult(b, c), a), c) = mult(mult(a, mult(b, c)), c)),
% 23.80/24.00 inference(symmetry,[status(thm)],[8946])).
% 23.80/24.00 tff(12547,plain,
% 23.80/24.00 (mult(mult(c, mult(b, c)), a) = mult(mult(c, a), mult(b, c))),
% 23.80/24.00 inference(transitivity,[status(thm)],[4181, 12259, 12546, 8159, 12545])).
% 23.80/24.00 tff(12548,plain,
% 23.80/24.00 ($false),
% 23.80/24.00 inference(unit_resolution,[status(thm)],[12502, 12547])).
% 23.80/24.00 tff(12549,plain,(~(mult(b, mult(a, mult(b, c))) = mult(b, mult(mult(b, c), a)))), inference(lemma,lemma(discharge,[]))).
% 23.80/24.00 tff(12550,plain,
% 23.80/24.00 ((~(mult(mult(b, a), mult(b, c)) = mult(mult(b, mult(b, c)), a))) | (~(mult(b, mult(a, mult(b, c))) = mult(b, mult(mult(b, c), a))))),
% 23.80/24.00 inference(unit_resolution,[status(thm)],[7524, 12549])).
% 23.80/24.00 tff(12551,plain,
% 23.80/24.00 (~((~(mult(mult(b, a), mult(b, c)) = mult(b, mult(a, mult(b, c))))) | (~(mult(mult(b, mult(b, c)), a) = mult(b, mult(mult(b, c), a)))))),
% 23.80/24.00 inference(unit_resolution,[status(thm)],[6974, 12550])).
% 23.80/24.00 tff(12552,plain,
% 23.80/24.00 (mult(mult(b, mult(b, c)), a) = mult(b, mult(mult(b, c), a))),
% 23.80/24.00 inference(unit_resolution,[status(thm)],[6976, 12551])).
% 23.80/24.00 tff(12553,plain,
% 23.80/24.00 (mult(b, mult(mult(b, c), a)) = mult(mult(b, mult(b, c)), a)),
% 23.80/24.00 inference(symmetry,[status(thm)],[12552])).
% 23.80/24.00 tff(12554,plain,
% 23.80/24.00 (mult(mult(a, b), c) = mult(mult(b, c), a)),
% 23.80/24.00 inference(transitivity,[status(thm)],[227, 8636, 4221, 6985, 8466, 4304, 4975])).
% 23.80/24.00 tff(12555,plain,
% 23.80/24.00 (mult(mult(unit, b), mult(mult(a, b), c)) = mult(b, mult(mult(b, c), a))),
% 23.80/24.00 inference(monotonicity,[status(thm)],[184, 12554])).
% 23.80/24.00 tff(12556,plain,
% 23.80/24.00 (mult(mult(unit, b), mult(mult(a, b), c)) = mult(mult(unit, mult(mult(a, b), c)), b)),
% 23.80/24.00 inference(transitivity,[status(thm)],[12555, 12553, 6961, 8453, 12543, 12512])).
% 23.80/24.00 tff(12557,assumption,(~(mult(mult(unit, b), mult(mult(a, b), c)) = mult(mult(unit, mult(mult(a, b), c)), b))), introduced(assumption)).
% 23.80/24.00 tff(12558,plain,
% 23.80/24.00 ($false),
% 23.80/24.00 inference(unit_resolution,[status(thm)],[12557, 12556])).
% 23.80/24.00 tff(12559,plain,(((~(mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a))) | (~(mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a))))) | (mult(mult(unit, b), mult(mult(a, b), c)) = mult(mult(unit, mult(mult(a, b), c)), b))), inference(lemma,lemma(discharge,[]))).
% 23.80/24.00 tff(12560,plain,
% 23.80/24.00 ((~(mult(mult(mult(b, c), a), b) = mult(mult(mult(b, c), b), a))) | (~(mult(mult(b, c), mult(a, b)) = mult(mult(b, c), mult(b, a))))),
% 23.80/24.00 inference(unit_resolution,[status(thm)],[12559, 12541])).
% 23.80/24.00 tff(12561,plain,
% 23.80/24.00 (~((~(mult(mult(mult(b, c), a), b) = mult(mult(b, c), mult(a, b)))) | (~(mult(mult(mult(b, c), b), a) = mult(mult(b, c), mult(b, a)))))),
% 23.80/24.00 inference(unit_resolution,[status(thm)],[1205, 12560])).
% 23.80/24.00 tff(12562,plain,
% 23.80/24.00 (mult(mult(mult(b, c), a), b) = mult(mult(b, c), mult(a, b))),
% 23.80/24.00 inference(unit_resolution,[status(thm)],[1229, 12561])).
% 23.80/24.00 tff(12563,plain,
% 23.80/24.00 ((~(mult(mult(b, b), mult(a, c)) = mult(b, mult(b, mult(a, c))))) | (~(mult(mult(b, mult(a, c)), b) = mult(b, mult(mult(a, c), b))))),
% 23.80/24.00 inference(unit_resolution,[status(thm)],[5632, 12508])).
% 23.80/24.00 tff(12564,plain,
% 23.80/24.00 (~((~(mult(mult(b, mult(a, c)), b) = mult(mult(b, b), mult(a, c)))) | (~(mult(b, mult(mult(a, c), b)) = mult(b, mult(b, mult(a, c))))))),
% 23.80/24.00 inference(unit_resolution,[status(thm)],[5630, 12563])).
% 23.80/24.00 tff(12565,plain,
% 23.80/24.00 (mult(b, mult(mult(a, c), b)) = mult(b, mult(b, mult(a, c)))),
% 23.80/24.00 inference(unit_resolution,[status(thm)],[5618, 12564])).
% 23.80/24.00 tff(12566,plain,
% 23.80/24.00 ((~(mult(b, mult(mult(a, c), b)) = mult(b, mult(b, mult(a, c))))) | (mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(mult(c, mult(b, c)), a) = mult(c, mult(mult(b, c), a))))),
% 23.80/24.00 inference(unit_resolution,[status(thm)],[10950, 12394])).
% 23.80/24.00 tff(12567,plain,
% 23.80/24.00 (mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 23.80/24.00 inference(unit_resolution,[status(thm)],[12566, 12565, 12505])).
% 23.80/24.00 tff(12568,plain,
% 23.80/24.00 ((~(mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))) | (mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)))),
% 23.80/24.00 inference(unit_resolution,[status(thm)],[9037, 12394])).
% 23.80/24.00 tff(12569,plain,
% 23.80/24.00 (mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c))),
% 23.80/24.00 inference(unit_resolution,[status(thm)],[12568, 12567])).
% 23.80/24.00 tff(12570,plain,
% 23.80/24.00 (mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), c) = mult(mult(mult(a, c), b), c)),
% 23.80/24.00 inference(monotonicity,[status(thm)],[12057])).
% 23.80/24.00 tff(12571,plain,
% 23.80/24.00 (mult(mult(mult(a, c), b), c) = mult(mult(mult(a, c), mult(a, rd(mult(b, c), mult(a, c)))), c)),
% 23.80/24.00 inference(symmetry,[status(thm)],[12570])).
% 23.80/24.00 tff(12572,plain,
% 23.80/24.00 (mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))) = mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), c)),
% 23.80/24.00 inference(transitivity,[status(thm)],[12234, 12231, 4372, 234, 12571, 8886])).
% 23.80/24.00 tff(12573,assumption,(~(mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))), introduced(assumption)).
% 23.80/24.00 tff(12574,plain,
% 23.80/24.00 ((~(mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)))) | (~(mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))))),
% 23.80/24.00 inference(unit_resolution,[status(thm)],[4567, 12573])).
% 23.80/24.00 tff(12575,plain,
% 23.80/24.00 (~((~(mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))))) | (~(mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))))),
% 23.80/24.00 inference(unit_resolution,[status(thm)],[4565, 12574])).
% 23.80/24.00 tff(12576,plain,
% 23.80/24.00 (mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))),
% 23.80/24.00 inference(unit_resolution,[status(thm)],[8924, 12575])).
% 23.80/24.00 tff(12577,plain,
% 23.80/24.00 (mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c))))),
% 23.80/24.00 inference(symmetry,[status(thm)],[12576])).
% 23.80/24.00 tff(12578,plain,
% 23.80/24.00 (mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c))),
% 23.80/24.00 inference(transitivity,[status(thm)],[12577, 12425, 12424])).
% 23.80/24.00 tff(12579,plain,
% 23.80/24.00 ((mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))) <=> (mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), c))),
% 23.80/24.00 inference(monotonicity,[status(thm)],[12578, 12572])).
% 23.80/24.01 tff(12580,plain,
% 23.80/24.01 ((mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))) <=> (mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)))),
% 23.80/24.01 inference(transitivity,[status(thm)],[12579, 8884])).
% 23.80/24.01 tff(12581,plain,
% 23.80/24.01 ((mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c))) <=> (mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c))))),
% 23.80/24.01 inference(symmetry,[status(thm)],[12580])).
% 23.80/24.01 tff(12582,plain,
% 23.80/24.01 (mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 23.80/24.01 inference(unit_resolution,[status(thm)],[4560, 12575])).
% 23.80/24.01 tff(12583,plain,
% 23.80/24.01 (mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), c)),
% 23.80/24.01 inference(transitivity,[status(thm)],[12582, 12234, 12231, 4372, 234, 12571, 8886])).
% 23.80/24.01 tff(12584,plain,
% 23.80/24.01 (mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c))),
% 23.80/24.01 inference(transitivity,[status(thm)],[12425, 12424])).
% 23.80/24.01 tff(12585,plain,
% 23.80/24.01 ((mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c))) <=> (mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), c))),
% 23.80/24.01 inference(monotonicity,[status(thm)],[12584, 12583])).
% 23.80/24.01 tff(12586,plain,
% 23.80/24.01 ((mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c))) <=> (mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)))),
% 23.80/24.01 inference(transitivity,[status(thm)],[12585, 8884])).
% 23.80/24.01 tff(12587,plain,
% 23.80/24.01 (mult(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), c) = mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c))),
% 23.80/24.01 inference(modus_ponens,[status(thm)],[12474, 12586])).
% 23.80/24.01 tff(12588,plain,
% 23.80/24.01 (mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 23.80/24.01 inference(modus_ponens,[status(thm)],[12587, 12581])).
% 23.80/24.01 tff(12589,plain,
% 23.80/24.01 ($false),
% 23.80/24.01 inference(unit_resolution,[status(thm)],[12573, 12588])).
% 23.80/24.01 tff(12590,plain,((mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c))))), inference(lemma,lemma(discharge,[]))).
% 23.80/24.01 tff(12591,plain,
% 23.80/24.01 (mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 23.80/24.01 inference(unit_resolution,[status(thm)],[12590, 12569])).
% 23.80/24.01 tff(12592,plain,
% 23.80/24.01 (mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(b, c), c))),
% 23.80/24.01 inference(transitivity,[status(thm)],[12591, 12234, 12231])).
% 23.80/24.01 tff(12593,plain,
% 23.80/24.01 (ld(a, mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))) = ld(a, mult(a, mult(mult(b, c), c)))),
% 23.80/24.01 inference(monotonicity,[status(thm)],[12592])).
% 23.80/24.01 tff(12594,plain,
% 23.80/24.01 (mult(mult(c, a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(b, c), c)),
% 23.80/24.01 inference(transitivity,[status(thm)],[8958, 10670, 8954, 12593, 4173])).
% 23.80/24.01 tff(12595,plain,
% 23.80/24.01 (mult(mult(mult(c, a), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(b, c), c), a)),
% 23.80/24.01 inference(monotonicity,[status(thm)],[12594])).
% 23.80/24.01 tff(12596,plain,
% 23.80/24.01 (mult(c, mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a)) = mult(c, mult(mult(b, c), a))),
% 23.80/24.01 inference(transitivity,[status(thm)],[5324, 12595, 10665, 12505])).
% 23.80/24.01 tff(12597,plain,
% 23.80/24.01 (ld(c, mult(c, mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a))) = ld(c, mult(c, mult(mult(b, c), a)))),
% 23.80/24.01 inference(monotonicity,[status(thm)],[12596])).
% 23.80/24.01 tff(12598,plain,
% 23.80/24.01 (mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(b, c), a)),
% 23.80/24.01 inference(transitivity,[status(thm)],[5329, 12597, 2296])).
% 23.80/24.01 tff(12599,plain,
% 23.80/24.01 (rd(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a), a) = rd(mult(mult(b, c), a), a)),
% 23.80/24.01 inference(monotonicity,[status(thm)],[12598])).
% 23.80/24.01 tff(12600,plain,
% 23.80/24.01 (mult(a, mult(c, rd(mult(b, c), mult(a, c)))) = mult(b, c)),
% 23.80/24.01 inference(transitivity,[status(thm)],[2220, 9895, 2356, 9593, 12599, 1370])).
% 23.80/24.01 tff(12601,plain,
% 23.80/24.01 (mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(mult(b, c), mult(a, c))),
% 23.80/24.01 inference(monotonicity,[status(thm)],[12600])).
% 23.80/24.01 tff(12602,plain,
% 23.80/24.01 (rd(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), rd(mult(b, c), mult(a, c))) = rd(mult(mult(a, mult(a, c)), rd(mult(b, c), mult(a, c))), rd(mult(b, c), mult(a, c)))),
% 23.80/24.01 inference(symmetry,[status(thm)],[12318])).
% 23.80/24.01 tff(12603,plain,
% 23.80/24.01 (mult(mult(a, c), a) = rd(mult(mult(mult(a, c), a), rd(mult(b, c), mult(a, c))), rd(mult(b, c), mult(a, c)))),
% 23.80/24.01 inference(symmetry,[status(thm)],[8230])).
% 23.80/24.01 tff(12604,plain,
% 23.80/24.01 (mult(mult(a, c), a) = mult(a, mult(a, c))),
% 23.80/24.01 inference(transitivity,[status(thm)],[12603, 12602, 8291])).
% 23.80/24.01 tff(12605,plain,
% 23.80/24.01 (mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, mult(a, c)), mult(rd(mult(b, c), mult(a, c)), c))),
% 23.80/24.01 inference(monotonicity,[status(thm)],[12604])).
% 23.80/24.01 tff(12606,plain,
% 23.80/24.01 (mult(a, mult(rd(mult(b, c), mult(a, c)), c)) = mult(b, c)),
% 23.80/24.01 inference(transitivity,[status(thm)],[9593, 12599, 1370])).
% 23.80/24.01 tff(12607,plain,
% 23.80/24.01 (mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))) = mult(mult(a, c), mult(b, c))),
% 23.80/24.01 inference(monotonicity,[status(thm)],[12606])).
% 23.80/24.01 tff(12608,plain,
% 23.80/24.01 (mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))) = mult(mult(a, mult(b, c)), c)),
% 23.80/24.01 inference(transitivity,[status(thm)],[12607, 266])).
% 23.80/24.01 tff(12609,plain,
% 23.80/24.01 (mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(a, mult(mult(b, c), c))),
% 23.80/24.01 inference(transitivity,[status(thm)],[12605, 10686, 12569, 12601, 12086, 12091, 12085, 12083, 233, 2414])).
% 23.80/24.01 tff(12610,plain,
% 23.80/24.01 ((mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c)))) <=> (mult(a, mult(mult(b, c), c)) = mult(mult(a, mult(b, c)), c))),
% 23.80/24.01 inference(monotonicity,[status(thm)],[12609, 12608])).
% 23.80/24.01 tff(12611,plain,
% 23.80/24.01 ((mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c)))) <=> (mult(mult(a, mult(b, c)), c) = mult(a, mult(mult(b, c), c)))),
% 23.80/24.01 inference(transitivity,[status(thm)],[12610, 2412])).
% 23.80/24.01 tff(12612,plain,
% 23.80/24.01 ((mult(mult(a, mult(b, c)), c) = mult(a, mult(mult(b, c), c))) <=> (mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))),
% 23.80/24.01 inference(symmetry,[status(thm)],[12611])).
% 23.80/24.01 tff(12613,plain,
% 23.80/24.01 ((~(mult(mult(a, mult(b, c)), c) = mult(a, mult(mult(b, c), c)))) <=> (~(mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c)))))),
% 23.80/24.01 inference(monotonicity,[status(thm)],[12612])).
% 23.80/24.01 tff(12614,plain,
% 23.80/24.01 (~(mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))),
% 23.80/24.01 inference(modus_ponens,[status(thm)],[258, 12613])).
% 23.80/24.01 tff(12615,plain,
% 23.80/24.01 ((~(mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))) | (~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a))))),
% 23.80/24.01 inference(unit_resolution,[status(thm)],[5352, 12614])).
% 23.80/24.01 tff(12616,plain,
% 23.80/24.01 (~((~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)))) | (~(mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))))),
% 23.80/24.01 inference(unit_resolution,[status(thm)],[8807, 12615])).
% 23.80/24.01 tff(12617,plain,
% 23.80/24.01 (mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c))),
% 23.80/24.01 inference(unit_resolution,[status(thm)],[10701, 12616])).
% 23.80/24.01 tff(12618,plain,
% 23.80/24.01 (ld(a, mult(a, mult(mult(b, c), c))) = ld(a, mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))))),
% 23.80/24.01 inference(symmetry,[status(thm)],[12593])).
% 23.80/24.01 tff(12619,plain,
% 23.80/24.01 (mult(mult(b, c), c) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c))),
% 23.80/24.01 inference(transitivity,[status(thm)],[8573, 12618, 8953, 10942])).
% 23.80/24.01 tff(12620,plain,
% 23.80/24.01 (mult(mult(mult(b, c), c), a) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a)),
% 23.80/24.01 inference(monotonicity,[status(thm)],[12619])).
% 23.80/24.01 tff(12621,plain,
% 23.80/24.01 (mult(mult(mult(b, c), a), c) = mult(mult(mult(a, b), c), c)),
% 23.80/24.01 inference(transitivity,[status(thm)],[12260, 12620, 12617, 12605, 10686, 12569, 12601, 12086, 12091, 12085, 12083, 4023])).
% 23.80/24.01 tff(12622,plain,
% 23.80/24.01 (rd(mult(mult(mult(b, c), a), c), c) = rd(mult(mult(mult(a, b), c), c), c)),
% 23.80/24.01 inference(monotonicity,[status(thm)],[12621])).
% 23.80/24.01 tff(12623,plain,
% 23.80/24.01 (mult(mult(b, c), a) = mult(mult(a, b), c)),
% 23.80/24.01 inference(transitivity,[status(thm)],[10753, 12622, 254])).
% 23.80/24.01 tff(12624,plain,
% 23.80/24.01 (mult(mult(mult(b, c), a), b) = mult(mult(mult(a, b), c), b)),
% 23.80/24.01 inference(monotonicity,[status(thm)],[12623])).
% 23.80/24.01 tff(12625,plain,
% 23.80/24.01 (mult(mult(mult(a, b), c), b) = mult(mult(mult(b, c), a), b)),
% 23.80/24.01 inference(symmetry,[status(thm)],[12624])).
% 23.80/24.01 tff(12626,plain,
% 23.80/24.01 (mult(c, mult(a, b)) = mult(mult(a, b), c)),
% 23.80/24.01 inference(transitivity,[status(thm)],[4270, 4269, 161])).
% 23.80/24.01 tff(12627,plain,
% 23.80/24.01 (mult(mult(c, mult(a, b)), b) = mult(mult(mult(a, b), c), b)),
% 23.80/24.01 inference(monotonicity,[status(thm)],[12626])).
% 23.80/24.01 tff(12628,plain,
% 23.80/24.01 (mult(mult(c, mult(a, b)), b) = mult(mult(c, b), mult(a, b))),
% 23.80/24.01 inference(transitivity,[status(thm)],[12627, 12625, 12562, 7273])).
% 23.80/24.01 tff(12629,plain,
% 23.80/24.01 (~(mult(mult(c, mult(a, b)), b) = mult(mult(c, b), mult(a, b)))),
% 23.80/24.01 inference(unit_resolution,[status(thm)],[8542, 12560])).
% 23.80/24.01 tff(12630,plain,
% 23.80/24.01 ($false),
% 23.80/24.01 inference(unit_resolution,[status(thm)],[12629, 12628])).
% 23.80/24.01 tff(12631,plain,(mult(mult(b, mult(a, c)), b) = mult(b, mult(mult(a, c), b))), inference(lemma,lemma(discharge,[]))).
% 23.80/24.01 tff(12632,plain,
% 23.80/24.01 (mult(b, mult(mult(a, c), b)) = mult(mult(b, mult(a, c)), b)),
% 23.80/24.01 inference(symmetry,[status(thm)],[12631])).
% 23.80/24.01 tff(12633,plain,
% 23.80/24.01 (mult(b, mult(mult(a, b), c)) = mult(mult(mult(a, b), b), c)),
% 23.80/24.01 inference(transitivity,[status(thm)],[3387, 10914, 12632, 12507, 827])).
% 23.80/24.01 tff(12634,plain,
% 23.80/24.01 (mult(a, mult(b, mult(mult(a, b), c))) = mult(a, mult(mult(mult(a, b), b), c))),
% 23.80/24.01 inference(monotonicity,[status(thm)],[12633])).
% 23.80/24.01 tff(12635,plain,
% 23.80/24.01 (mult(a, mult(mult(mult(a, b), b), c)) = mult(a, mult(b, mult(mult(a, b), c)))),
% 23.80/24.01 inference(symmetry,[status(thm)],[12634])).
% 23.80/24.01 tff(12636,plain,
% 23.80/24.01 (mult(a, mult(mult(b, c), b)) = mult(mult(mult(a, b), b), c)),
% 23.80/24.01 inference(transitivity,[status(thm)],[783, 827])).
% 23.80/24.01 tff(12637,plain,
% 23.80/24.01 (mult(a, mult(a, mult(mult(b, c), b))) = mult(a, mult(mult(mult(a, b), b), c))),
% 23.80/24.01 inference(monotonicity,[status(thm)],[12636])).
% 23.80/24.01 tff(12638,plain,
% 23.80/24.01 (mult(a, mult(mult(mult(a, b), c), b)) = mult(a, mult(b, mult(mult(a, b), c)))),
% 23.80/24.01 inference(transitivity,[status(thm)],[10874, 12637, 12635])).
% 23.80/24.01 tff(12639,plain,
% 23.80/24.01 ((~(mult(a, mult(mult(mult(a, b), c), b)) = mult(a, mult(b, mult(mult(a, b), c))))) | (mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))) | (~(mult(mult(c, mult(b, c)), a) = mult(c, mult(mult(b, c), a))))),
% 23.80/24.01 inference(unit_resolution,[status(thm)],[10971, 12394])).
% 23.80/24.01 tff(12640,plain,
% 23.80/24.01 (mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(mult(mult(unit, ld(c, mult(a, b))), unit), mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 23.80/24.01 inference(unit_resolution,[status(thm)],[12639, 12638, 12505])).
% 23.80/24.01 tff(12641,plain,
% 23.80/24.01 (mult(mult(a, mult(a, c)), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c))),
% 23.80/24.01 inference(unit_resolution,[status(thm)],[12568, 12640])).
% 23.80/24.01 tff(12642,plain,
% 23.80/24.01 (mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(c, rd(mult(b, c), mult(a, c))), mult(a, c)))),
% 23.80/24.01 inference(unit_resolution,[status(thm)],[12590, 12641])).
% 23.80/24.01 tff(12643,plain,
% 23.80/24.01 (mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))) = mult(a, mult(mult(b, c), c))),
% 23.80/24.01 inference(transitivity,[status(thm)],[12642, 12234, 12231])).
% 23.80/24.01 tff(12644,plain,
% 23.80/24.01 (ld(a, mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c)))))) = ld(a, mult(a, mult(mult(b, c), c)))),
% 23.80/24.01 inference(monotonicity,[status(thm)],[12643])).
% 23.80/24.01 tff(12645,plain,
% 23.80/24.01 (mult(mult(c, a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(b, c), c)),
% 23.80/24.01 inference(transitivity,[status(thm)],[8958, 10670, 8954, 12644, 4173])).
% 23.80/24.01 tff(12646,plain,
% 23.80/24.01 (mult(mult(mult(c, a), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(b, c), c), a)),
% 23.80/24.01 inference(monotonicity,[status(thm)],[12645])).
% 23.80/24.01 tff(12647,plain,
% 23.80/24.01 (mult(c, mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a)) = mult(c, mult(mult(b, c), a))),
% 23.80/24.01 inference(transitivity,[status(thm)],[5324, 12646, 10665, 12505])).
% 23.80/24.01 tff(12648,plain,
% 23.80/24.01 (ld(c, mult(c, mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a))) = ld(c, mult(c, mult(mult(b, c), a)))),
% 23.80/24.01 inference(monotonicity,[status(thm)],[12647])).
% 23.80/24.01 tff(12649,plain,
% 23.80/24.01 (mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(b, c), a)),
% 23.80/24.01 inference(transitivity,[status(thm)],[5329, 12648, 2296])).
% 23.80/24.01 tff(12650,plain,
% 23.80/24.01 (rd(mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a), a) = rd(mult(mult(b, c), a), a)),
% 23.80/24.01 inference(monotonicity,[status(thm)],[12649])).
% 23.80/24.01 tff(12651,plain,
% 23.80/24.01 (mult(a, mult(c, rd(mult(b, c), mult(a, c)))) = mult(b, c)),
% 23.85/24.01 inference(transitivity,[status(thm)],[2220, 9895, 2356, 9593, 12650, 1370])).
% 23.85/24.01 tff(12652,plain,
% 23.85/24.01 (mult(mult(a, mult(c, rd(mult(b, c), mult(a, c)))), mult(a, c)) = mult(mult(b, c), mult(a, c))),
% 23.85/24.01 inference(monotonicity,[status(thm)],[12651])).
% 23.85/24.01 tff(12653,plain,
% 23.85/24.01 (mult(a, mult(rd(mult(b, c), mult(a, c)), c)) = mult(b, c)),
% 23.85/24.01 inference(transitivity,[status(thm)],[9593, 12650, 1370])).
% 23.85/24.01 tff(12654,plain,
% 23.85/24.01 (mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))) = mult(mult(a, c), mult(b, c))),
% 23.85/24.01 inference(monotonicity,[status(thm)],[12653])).
% 23.85/24.01 tff(12655,plain,
% 23.85/24.01 (mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))) = mult(mult(a, mult(b, c)), c)),
% 23.85/24.01 inference(transitivity,[status(thm)],[12654, 266])).
% 23.85/24.01 tff(12656,plain,
% 23.85/24.01 (mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(a, mult(mult(b, c), c))),
% 23.85/24.01 inference(transitivity,[status(thm)],[12605, 10686, 12641, 12652, 12086, 12091, 12085, 12083, 233, 2414])).
% 23.85/24.01 tff(12657,plain,
% 23.85/24.01 ((mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c)))) <=> (mult(a, mult(mult(b, c), c)) = mult(mult(a, mult(b, c)), c))),
% 23.85/24.01 inference(monotonicity,[status(thm)],[12656, 12655])).
% 23.85/24.01 tff(12658,plain,
% 23.85/24.01 ((mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c)))) <=> (mult(mult(a, mult(b, c)), c) = mult(a, mult(mult(b, c), c)))),
% 23.85/24.01 inference(transitivity,[status(thm)],[12657, 2412])).
% 23.85/24.01 tff(12659,plain,
% 23.85/24.01 ((mult(mult(a, mult(b, c)), c) = mult(a, mult(mult(b, c), c))) <=> (mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))),
% 23.85/24.01 inference(symmetry,[status(thm)],[12658])).
% 23.85/24.01 tff(12660,plain,
% 23.85/24.01 ((~(mult(mult(a, mult(b, c)), c) = mult(a, mult(mult(b, c), c)))) <=> (~(mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c)))))),
% 23.85/24.02 inference(monotonicity,[status(thm)],[12659])).
% 23.85/24.02 tff(12661,plain,
% 23.85/24.02 (~(mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))),
% 23.85/24.02 inference(modus_ponens,[status(thm)],[258, 12660])).
% 23.85/24.02 tff(12662,plain,
% 23.85/24.02 ((~(mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))) | (~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a))))),
% 23.85/24.02 inference(unit_resolution,[status(thm)],[5352, 12661])).
% 23.85/24.02 tff(12663,plain,
% 23.85/24.02 (~((~(mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c)))) | (~(mult(mult(a, c), mult(mult(rd(mult(b, c), mult(a, c)), c), a)) = mult(mult(a, c), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))))),
% 23.85/24.02 inference(unit_resolution,[status(thm)],[8807, 12662])).
% 23.85/24.02 tff(12664,plain,
% 23.85/24.02 (mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(a, c), a), mult(rd(mult(b, c), mult(a, c)), c))),
% 23.85/24.02 inference(unit_resolution,[status(thm)],[10701, 12663])).
% 23.85/24.02 tff(12665,plain,
% 23.85/24.02 (ld(a, mult(a, mult(mult(b, c), c))) = ld(a, mult(a, mult(mult(a, c), mult(c, rd(mult(b, c), mult(a, c))))))),
% 23.85/24.02 inference(symmetry,[status(thm)],[12644])).
% 23.85/24.02 tff(12666,plain,
% 23.85/24.02 (mult(mult(b, c), c) = mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c))),
% 23.85/24.02 inference(transitivity,[status(thm)],[8573, 12665, 8953, 10942])).
% 23.85/24.02 tff(12667,plain,
% 23.85/24.02 (mult(mult(mult(b, c), c), a) = mult(mult(mult(a, c), mult(rd(mult(b, c), mult(a, c)), c)), a)),
% 23.85/24.02 inference(monotonicity,[status(thm)],[12666])).
% 23.85/24.02 tff(12668,plain,
% 23.85/24.02 (mult(mult(c, c), a) = mult(c, mult(a, c))),
% 23.85/24.02 inference(transitivity,[status(thm)],[3911, 12280])).
% 23.85/24.02 tff(12669,plain,
% 23.85/24.02 (mult(mult(mult(c, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(c, mult(a, c)), rd(mult(b, c), mult(a, c)))),
% 23.85/24.02 inference(monotonicity,[status(thm)],[12668])).
% 23.85/24.02 tff(12670,plain,
% 23.85/24.02 (mult(mult(mult(c, c), a), rd(mult(b, c), mult(a, c))) = mult(mult(b, c), c)),
% 23.85/24.02 inference(transitivity,[status(thm)],[12669, 8569, 12211, 12229, 12210, 7714, 7711])).
% 23.85/24.02 tff(12671,plain,
% 23.85/24.02 (mult(mult(mult(mult(c, c), a), rd(mult(b, c), mult(a, c))), a) = mult(mult(mult(b, c), c), a)),
% 23.85/24.02 inference(monotonicity,[status(thm)],[12670])).
% 23.85/24.02 tff(12672,plain,
% 23.85/24.02 (ld(c, mult(c, mult(b, a))) = ld(c, mult(c, mult(mult(a, rd(mult(b, c), mult(a, c))), a)))),
% 23.85/24.02 inference(symmetry,[status(thm)],[12053])).
% 23.85/24.02 tff(12673,plain,
% 23.85/24.02 (mult(b, a) = mult(mult(a, rd(mult(b, c), mult(a, c))), a)),
% 23.85/24.02 inference(transitivity,[status(thm)],[1473, 12672, 5408])).
% 23.85/24.02 tff(12674,plain,
% 23.85/24.02 (mult(mult(c, c), mult(b, a)) = mult(mult(c, c), mult(mult(a, rd(mult(b, c), mult(a, c))), a))),
% 23.85/24.02 inference(monotonicity,[status(thm)],[12673])).
% 23.85/24.02 tff(12675,plain,
% 23.85/24.02 (mult(mult(c, c), mult(b, a)) = mult(mult(c, c), mult(a, b))),
% 23.85/24.02 inference(transitivity,[status(thm)],[12674, 5901, 12671, 12667, 12664, 12605, 10686, 12641, 12652, 12086, 12091, 12085, 12083, 4285, 3187, 4274, 4273, 4261])).
% 23.85/24.02 tff(12676,plain,
% 23.85/24.02 (ld(mult(c, c), mult(mult(c, c), mult(b, a))) = ld(mult(c, c), mult(mult(c, c), mult(a, b)))),
% 23.85/24.02 inference(monotonicity,[status(thm)],[12675])).
% 23.85/24.02 tff(12677,plain,
% 23.85/24.02 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(c, c), mult(mult(c, c), mult(b, a))) = mult(b, a))),
% 23.85/24.02 inference(quant_inst,[status(thm)],[])).
% 23.85/24.02 tff(12678,plain,
% 23.85/24.02 (ld(mult(c, c), mult(mult(c, c), mult(b, a))) = mult(b, a)),
% 23.85/24.02 inference(unit_resolution,[status(thm)],[12677, 7])).
% 23.85/24.02 tff(12679,plain,
% 23.85/24.02 (mult(b, a) = ld(mult(c, c), mult(mult(c, c), mult(b, a)))),
% 23.85/24.02 inference(symmetry,[status(thm)],[12678])).
% 23.85/24.02 tff(12680,plain,
% 23.85/24.02 (mult(b, a) = mult(a, b)),
% 23.85/24.02 inference(transitivity,[status(thm)],[12679, 12676, 11])).
% 23.85/24.02 tff(12681,plain,
% 23.85/24.02 (mult(mult(b, a), mult(mult(a, b), c)) = mult(mult(a, b), mult(mult(a, b), c))),
% 23.85/24.02 inference(monotonicity,[status(thm)],[12680])).
% 23.85/24.02 tff(12682,plain,
% 23.85/24.02 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a) = mult(mult(a, b), c)),
% 23.85/24.02 inference(transitivity,[status(thm)],[1168, 6930, 12208, 4031])).
% 23.85/24.02 tff(12683,plain,
% 23.85/24.02 (mult(mult(b, a), mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a)) = mult(mult(b, a), mult(mult(a, b), c))),
% 23.85/24.02 inference(monotonicity,[status(thm)],[12682])).
% 23.85/24.02 tff(12684,plain,
% 23.85/24.02 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(a, b), mult(b, c)), a), a) = mult(mult(a, b), mult(b, c)))),
% 23.85/24.02 inference(quant_inst,[status(thm)],[])).
% 23.85/24.02 tff(12685,plain,
% 23.85/24.02 (rd(mult(mult(mult(a, b), mult(b, c)), a), a) = mult(mult(a, b), mult(b, c))),
% 23.85/24.02 inference(unit_resolution,[status(thm)],[12684, 168])).
% 23.85/24.02 tff(12686,plain,
% 23.85/24.02 (mult(mult(mult(b, c), a), c) = mult(mult(mult(a, b), c), c)),
% 23.85/24.02 inference(transitivity,[status(thm)],[12260, 12667, 12664, 12605, 10686, 12641, 12652, 12086, 12091, 12085, 12083, 4023])).
% 23.85/24.02 tff(12687,plain,
% 23.85/24.02 (rd(mult(mult(mult(b, c), a), c), c) = rd(mult(mult(mult(a, b), c), c), c)),
% 23.85/24.02 inference(monotonicity,[status(thm)],[12686])).
% 23.85/24.02 tff(12688,plain,
% 23.85/24.02 (mult(mult(b, c), a) = mult(mult(a, b), c)),
% 23.85/24.02 inference(transitivity,[status(thm)],[10753, 12687, 254])).
% 23.85/24.02 tff(12689,plain,
% 23.85/24.02 (mult(mult(mult(b, c), a), b) = mult(mult(mult(a, b), c), b)),
% 23.85/24.02 inference(monotonicity,[status(thm)],[12688])).
% 23.85/24.02 tff(12690,plain,
% 23.85/24.02 (mult(mult(mult(mult(b, c), a), b), a) = mult(mult(mult(mult(a, b), c), b), a)),
% 23.85/24.02 inference(monotonicity,[status(thm)],[12689])).
% 23.85/24.02 tff(12691,plain,
% 23.85/24.02 (mult(mult(mult(mult(a, b), c), b), a) = mult(mult(mult(mult(b, c), a), b), a)),
% 23.85/24.02 inference(symmetry,[status(thm)],[12690])).
% 23.85/24.02 tff(12692,plain,
% 23.85/24.02 (mult(mult(b, a), a) = mult(mult(a, b), a)),
% 23.85/24.02 inference(monotonicity,[status(thm)],[12680])).
% 23.85/24.02 tff(12693,plain,
% 23.85/24.02 (mult(mult(a, b), a) = mult(mult(b, a), a)),
% 23.85/24.02 inference(symmetry,[status(thm)],[12692])).
% 23.85/24.02 tff(12694,plain,
% 23.85/24.02 (mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(b, a), a), mult(rd(mult(b, c), mult(a, c)), c))),
% 23.85/24.02 inference(monotonicity,[status(thm)],[12693, 9898])).
% 23.85/24.02 tff(12695,plain,
% 23.85/24.02 (mult(mult(mult(b, a), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c))))),
% 23.85/24.02 inference(symmetry,[status(thm)],[12694])).
% 23.85/24.02 tff(12696,plain,
% 23.85/24.02 (rd(mult(mult(mult(a, b), c), c), c) = rd(mult(mult(mult(b, c), a), c), c)),
% 23.85/24.02 inference(symmetry,[status(thm)],[12687])).
% 23.85/24.02 tff(12697,plain,
% 23.85/24.02 (mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a) = mult(mult(b, c), a)),
% 23.85/24.02 inference(transitivity,[status(thm)],[1168, 6930, 12208, 4031, 255, 12696, 2676])).
% 23.85/24.02 tff(12698,plain,
% 23.85/24.02 (rd(mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a), a) = rd(mult(mult(b, c), a), a)),
% 23.85/24.02 inference(monotonicity,[status(thm)],[12697])).
% 23.85/24.02 tff(12699,plain,
% 23.85/24.02 (mult(mult(rd(mult(b, c), mult(a, c)), a), c) = mult(b, c)),
% 23.85/24.02 inference(transitivity,[status(thm)],[1377, 12698, 1370])).
% 23.85/24.02 tff(12700,plain,
% 23.85/24.02 (mult(mult(a, b), mult(mult(rd(mult(b, c), mult(a, c)), a), c)) = mult(mult(a, b), mult(b, c))),
% 23.85/24.02 inference(monotonicity,[status(thm)],[12699])).
% 23.85/24.02 tff(12701,plain,
% 23.85/24.02 (mult(mult(b, a), mult(mult(rd(mult(b, c), mult(a, c)), a), c)) = mult(mult(a, b), mult(mult(rd(mult(b, c), mult(a, c)), a), c))),
% 23.85/24.02 inference(monotonicity,[status(thm)],[12680])).
% 23.85/24.02 tff(12702,plain,
% 23.85/24.02 (mult(mult(rd(mult(b, c), mult(a, c)), c), a) = mult(mult(rd(mult(b, c), mult(a, c)), a), c)),
% 23.85/24.02 inference(transitivity,[status(thm)],[83, 12147, 4340])).
% 23.85/24.02 tff(12703,plain,
% 23.85/24.02 (mult(mult(b, a), mult(mult(rd(mult(b, c), mult(a, c)), c), a)) = mult(mult(b, a), mult(mult(rd(mult(b, c), mult(a, c)), a), c))),
% 23.85/24.02 inference(monotonicity,[status(thm)],[12702])).
% 23.85/24.02 tff(12704,plain,
% 23.85/24.02 (mult(mult(b, a), mult(mult(rd(mult(b, c), mult(a, c)), c), a)) = mult(mult(a, b), mult(b, c))),
% 23.85/24.02 inference(transitivity,[status(thm)],[12703, 12701, 12700])).
% 23.85/24.02 tff(12705,plain,
% 23.85/24.02 (mult(b, mult(mult(b, c), a)) = mult(mult(unit, b), mult(mult(a, b), c))),
% 23.85/24.02 inference(monotonicity,[status(thm)],[3386, 12688])).
% 23.85/24.02 tff(12706,plain,
% 23.85/24.02 (mult(b, mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a)) = mult(b, mult(mult(b, c), a))),
% 23.85/24.02 inference(monotonicity,[status(thm)],[12649])).
% 23.85/24.02 tff(12707,plain,
% 23.85/24.02 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(b, mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a)))),
% 23.85/24.02 inference(quant_inst,[status(thm)],[])).
% 23.85/24.02 tff(12708,plain,
% 23.85/24.02 (mult(mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(b, mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a))),
% 23.85/24.02 inference(unit_resolution,[status(thm)],[12707, 56])).
% 23.85/24.02 tff(12709,plain,
% 23.85/24.02 (mult(mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(a, b), b), c)),
% 23.85/24.02 inference(transitivity,[status(thm)],[12708, 12706, 12705, 10914, 12632, 12507, 827])).
% 23.85/24.02 tff(12710,plain,
% 23.85/24.02 ((mult(mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(b, a), mult(mult(rd(mult(b, c), mult(a, c)), c), a))) <=> (mult(mult(mult(a, b), b), c) = mult(mult(a, b), mult(b, c)))),
% 23.85/24.02 inference(monotonicity,[status(thm)],[12709, 12704])).
% 23.85/24.02 tff(12711,plain,
% 23.85/24.02 ((mult(mult(mult(a, b), b), c) = mult(mult(a, b), mult(b, c))) <=> (mult(mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(b, a), mult(mult(rd(mult(b, c), mult(a, c)), c), a)))),
% 23.85/24.02 inference(symmetry,[status(thm)],[12710])).
% 23.85/24.02 tff(12712,plain,
% 23.85/24.02 ((~(mult(mult(mult(a, b), b), c) = mult(mult(a, b), mult(b, c)))) <=> (~(mult(mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(b, a), mult(mult(rd(mult(b, c), mult(a, c)), c), a))))),
% 23.85/24.02 inference(monotonicity,[status(thm)],[12711])).
% 23.85/24.02 tff(12713,plain,
% 23.85/24.02 (~(mult(mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(b, a), mult(mult(rd(mult(b, c), mult(a, c)), c), a)))),
% 23.85/24.02 inference(modus_ponens,[status(thm)],[1729, 12712])).
% 23.85/24.02 tff(12714,plain,
% 23.85/24.02 (((~(mult(mult(mult(b, a), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(b, a), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))) | (~(mult(mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(b, a), mult(mult(rd(mult(b, c), mult(a, c)), c), a))))) | (mult(mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(b, a), mult(mult(rd(mult(b, c), mult(a, c)), c), a)))),
% 23.85/24.02 inference(tautology,[status(thm)],[])).
% 23.85/24.02 tff(12715,plain,
% 23.85/24.02 ((~(mult(mult(mult(b, a), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(b, a), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))) | (~(mult(mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(b, a), mult(mult(rd(mult(b, c), mult(a, c)), c), a))))),
% 23.85/24.02 inference(unit_resolution,[status(thm)],[12714, 12713])).
% 23.85/24.02 tff(12716,plain,
% 23.85/24.02 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(b, a), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(b, a), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))) | (~(mult(mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(b, a), mult(mult(rd(mult(b, c), mult(a, c)), c), a)))))) | (~((~(mult(mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(b, a), a), mult(rd(mult(b, c), mult(a, c)), c)))) | (~(mult(mult(b, a), mult(mult(rd(mult(b, c), mult(a, c)), c), a)) = mult(mult(b, a), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(b, a), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(b, a), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))) | (~(mult(mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(b, a), mult(mult(rd(mult(b, c), mult(a, c)), c), a)))))) | (~((~(mult(mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(b, a), a), mult(rd(mult(b, c), mult(a, c)), c)))) | (~(mult(mult(b, a), mult(mult(rd(mult(b, c), mult(a, c)), c), a)) = mult(mult(b, a), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))))))),
% 23.85/24.02 inference(rewrite,[status(thm)],[])).
% 23.85/24.02 tff(12717,plain,
% 23.85/24.02 (((~((~(mult(mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(b, a), a), mult(rd(mult(b, c), mult(a, c)), c)))) | (~(mult(mult(b, a), mult(mult(rd(mult(b, c), mult(a, c)), c), a)) = mult(mult(b, a), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))))) | (~((~(mult(mult(mult(b, a), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(b, a), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))) | (~(mult(mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(b, a), mult(mult(rd(mult(b, c), mult(a, c)), c), a))))))) <=> ((~((~(mult(mult(mult(b, a), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(b, a), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))) | (~(mult(mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(b, a), mult(mult(rd(mult(b, c), mult(a, c)), c), a)))))) | (~((~(mult(mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(b, a), a), mult(rd(mult(b, c), mult(a, c)), c)))) | (~(mult(mult(b, a), mult(mult(rd(mult(b, c), mult(a, c)), c), a)) = mult(mult(b, a), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))))))),
% 23.85/24.02 inference(rewrite,[status(thm)],[])).
% 23.85/24.02 tff(12718,plain,
% 23.85/24.02 ((~((~(mult(mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(b, a), mult(mult(rd(mult(b, c), mult(a, c)), c), a)))) | (~(mult(mult(mult(b, a), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(b, a), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))))) <=> (~((~(mult(mult(mult(b, a), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(b, a), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))) | (~(mult(mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(b, a), mult(mult(rd(mult(b, c), mult(a, c)), c), a))))))),
% 23.85/24.02 inference(rewrite,[status(thm)],[])).
% 23.85/24.02 tff(12719,plain,
% 23.85/24.02 ((~((~(mult(mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(b, a), a), mult(rd(mult(b, c), mult(a, c)), c)))) | (~(mult(mult(b, a), mult(mult(rd(mult(b, c), mult(a, c)), c), a)) = mult(mult(b, a), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))))) <=> (~((~(mult(mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(b, a), a), mult(rd(mult(b, c), mult(a, c)), c)))) | (~(mult(mult(b, a), mult(mult(rd(mult(b, c), mult(a, c)), c), a)) = mult(mult(b, a), mult(a, mult(rd(mult(b, c), mult(a, c)), c)))))))),
% 23.85/24.02 inference(rewrite,[status(thm)],[])).
% 23.85/24.02 tff(12720,plain,
% 23.85/24.02 (((~((~(mult(mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(b, a), a), mult(rd(mult(b, c), mult(a, c)), c)))) | (~(mult(mult(b, a), mult(mult(rd(mult(b, c), mult(a, c)), c), a)) = mult(mult(b, a), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))))) | (~((~(mult(mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(b, a), mult(mult(rd(mult(b, c), mult(a, c)), c), a)))) | (~(mult(mult(mult(b, a), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(b, a), mult(a, mult(rd(mult(b, c), mult(a, c)), c)))))))) <=> ((~((~(mult(mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(b, a), a), mult(rd(mult(b, c), mult(a, c)), c)))) | (~(mult(mult(b, a), mult(mult(rd(mult(b, c), mult(a, c)), c), a)) = mult(mult(b, a), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))))) | (~((~(mult(mult(mult(b, a), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(b, a), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))) | (~(mult(mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(b, a), mult(mult(rd(mult(b, c), mult(a, c)), c), a)))))))),
% 23.85/24.02 inference(monotonicity,[status(thm)],[12719, 12718])).
% 23.85/24.02 tff(12721,plain,
% 23.85/24.02 (((~((~(mult(mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(b, a), a), mult(rd(mult(b, c), mult(a, c)), c)))) | (~(mult(mult(b, a), mult(mult(rd(mult(b, c), mult(a, c)), c), a)) = mult(mult(b, a), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))))) | (~((~(mult(mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(b, a), mult(mult(rd(mult(b, c), mult(a, c)), c), a)))) | (~(mult(mult(mult(b, a), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(b, a), mult(a, mult(rd(mult(b, c), mult(a, c)), c)))))))) <=> ((~((~(mult(mult(mult(b, a), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(b, a), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))) | (~(mult(mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(b, a), mult(mult(rd(mult(b, c), mult(a, c)), c), a)))))) | (~((~(mult(mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(b, a), a), mult(rd(mult(b, c), mult(a, c)), c)))) | (~(mult(mult(b, a), mult(mult(rd(mult(b, c), mult(a, c)), c), a)) = mult(mult(b, a), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))))))),
% 23.85/24.03 inference(transitivity,[status(thm)],[12720, 12717])).
% 23.85/24.03 tff(12722,plain,
% 23.85/24.03 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(b, a), a), mult(rd(mult(b, c), mult(a, c)), c)))) | (~(mult(mult(b, a), mult(mult(rd(mult(b, c), mult(a, c)), c), a)) = mult(mult(b, a), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))))) | (~((~(mult(mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(b, a), mult(mult(rd(mult(b, c), mult(a, c)), c), a)))) | (~(mult(mult(mult(b, a), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(b, a), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(b, a), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(b, a), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))) | (~(mult(mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(b, a), mult(mult(rd(mult(b, c), mult(a, c)), c), a)))))) | (~((~(mult(mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(b, a), a), mult(rd(mult(b, c), mult(a, c)), c)))) | (~(mult(mult(b, a), mult(mult(rd(mult(b, c), mult(a, c)), c), a)) = mult(mult(b, a), mult(a, mult(rd(mult(b, c), mult(a, c)), c)))))))))),
% 23.85/24.03 inference(monotonicity,[status(thm)],[12721])).
% 23.85/24.03 tff(12723,plain,
% 23.85/24.03 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(b, a), a), mult(rd(mult(b, c), mult(a, c)), c)))) | (~(mult(mult(b, a), mult(mult(rd(mult(b, c), mult(a, c)), c), a)) = mult(mult(b, a), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))))) | (~((~(mult(mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(b, a), mult(mult(rd(mult(b, c), mult(a, c)), c), a)))) | (~(mult(mult(mult(b, a), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(b, a), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(b, a), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(b, a), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))) | (~(mult(mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(b, a), mult(mult(rd(mult(b, c), mult(a, c)), c), a)))))) | (~((~(mult(mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(b, a), a), mult(rd(mult(b, c), mult(a, c)), c)))) | (~(mult(mult(b, a), mult(mult(rd(mult(b, c), mult(a, c)), c), a)) = mult(mult(b, a), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))))))),
% 23.85/24.03 inference(transitivity,[status(thm)],[12722, 12716])).
% 23.85/24.03 tff(12724,plain,
% 23.85/24.03 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(b, a), a), mult(rd(mult(b, c), mult(a, c)), c)))) | (~(mult(mult(b, a), mult(mult(rd(mult(b, c), mult(a, c)), c), a)) = mult(mult(b, a), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))))) | (~((~(mult(mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(b, a), mult(mult(rd(mult(b, c), mult(a, c)), c), a)))) | (~(mult(mult(mult(b, a), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(b, a), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))))))),
% 23.85/24.03 inference(quant_inst,[status(thm)],[])).
% 23.85/24.03 tff(12725,plain,
% 23.85/24.03 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(b, a), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(b, a), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))) | (~(mult(mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(b, a), mult(mult(rd(mult(b, c), mult(a, c)), c), a)))))) | (~((~(mult(mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(b, a), a), mult(rd(mult(b, c), mult(a, c)), c)))) | (~(mult(mult(b, a), mult(mult(rd(mult(b, c), mult(a, c)), c), a)) = mult(mult(b, a), mult(a, mult(rd(mult(b, c), mult(a, c)), c)))))))),
% 23.85/24.03 inference(modus_ponens,[status(thm)],[12724, 12723])).
% 23.85/24.03 tff(12726,plain,
% 23.85/24.03 ((~((~(mult(mult(mult(b, a), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(b, a), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))) | (~(mult(mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(b, a), mult(mult(rd(mult(b, c), mult(a, c)), c), a)))))) | (~((~(mult(mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(b, a), a), mult(rd(mult(b, c), mult(a, c)), c)))) | (~(mult(mult(b, a), mult(mult(rd(mult(b, c), mult(a, c)), c), a)) = mult(mult(b, a), mult(a, mult(rd(mult(b, c), mult(a, c)), c)))))))),
% 23.85/24.03 inference(unit_resolution,[status(thm)],[12725, 27])).
% 23.85/24.03 tff(12727,plain,
% 23.85/24.03 (~((~(mult(mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(b, a), a), mult(rd(mult(b, c), mult(a, c)), c)))) | (~(mult(mult(b, a), mult(mult(rd(mult(b, c), mult(a, c)), c), a)) = mult(mult(b, a), mult(a, mult(rd(mult(b, c), mult(a, c)), c))))))),
% 23.85/24.03 inference(unit_resolution,[status(thm)],[12726, 12715])).
% 23.85/24.03 tff(12728,plain,
% 23.85/24.03 (((~(mult(mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(b, a), a), mult(rd(mult(b, c), mult(a, c)), c)))) | (~(mult(mult(b, a), mult(mult(rd(mult(b, c), mult(a, c)), c), a)) = mult(mult(b, a), mult(a, mult(rd(mult(b, c), mult(a, c)), c)))))) | (mult(mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(b, a), a), mult(rd(mult(b, c), mult(a, c)), c)))),
% 23.85/24.03 inference(tautology,[status(thm)],[])).
% 23.85/24.03 tff(12729,plain,
% 23.85/24.03 (mult(mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(b, a), a), mult(rd(mult(b, c), mult(a, c)), c))),
% 23.85/24.03 inference(unit_resolution,[status(thm)],[12728, 12727])).
% 23.85/24.03 tff(12730,plain,
% 23.85/24.03 (mult(b, mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a)) = mult(mult(mult(b, a), mult(rd(mult(b, c), mult(a, c)), c)), a)),
% 23.85/24.03 inference(symmetry,[status(thm)],[12708])).
% 23.85/24.03 tff(12731,plain,
% 23.85/24.03 (mult(b, mult(mult(b, c), a)) = mult(b, mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a))),
% 23.85/24.03 inference(symmetry,[status(thm)],[12706])).
% 23.85/24.03 tff(12732,plain,
% 23.85/24.03 (mult(mult(unit, b), mult(mult(a, b), c)) = mult(b, mult(mult(b, c), a))),
% 23.85/24.03 inference(symmetry,[status(thm)],[12705])).
% 23.85/24.03 tff(12733,plain,
% 23.85/24.03 (mult(mult(mult(a, b), c), b) = mult(mult(b, mult(a, c)), b)),
% 23.85/24.03 inference(symmetry,[status(thm)],[12507])).
% 23.85/24.03 tff(12734,plain,
% 23.85/24.03 (mult(mult(mult(a, b), c), b) = mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c))))),
% 23.85/24.03 inference(transitivity,[status(thm)],[12733, 12631, 10915, 12732, 12731, 12730, 12729, 12695])).
% 23.85/24.03 tff(12735,plain,
% 23.85/24.03 (mult(mult(mult(mult(a, b), c), b), a) = mult(mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))), a)),
% 23.85/24.03 inference(monotonicity,[status(thm)],[12734])).
% 23.85/24.03 tff(12736,plain,
% 23.85/24.03 (mult(mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(mult(a, b), c), b), a)),
% 23.85/24.03 inference(symmetry,[status(thm)],[12735])).
% 23.85/24.03 tff(12737,plain,
% 23.85/24.03 (mult(mult(mult(a, b), a), mult(rd(mult(b, c), mult(a, c)), c)) = mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c))))),
% 23.85/24.03 inference(monotonicity,[status(thm)],[10631])).
% 23.85/24.03 tff(12738,plain,
% 23.85/24.03 (mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))) = mult(mult(mult(a, b), a), mult(rd(mult(b, c), mult(a, c)), c))),
% 23.85/24.03 inference(symmetry,[status(thm)],[12737])).
% 23.85/24.03 tff(12739,plain,
% 23.85/24.03 (mult(mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))), a) = mult(mult(mult(mult(a, b), a), mult(rd(mult(b, c), mult(a, c)), c)), a)),
% 23.85/24.03 inference(monotonicity,[status(thm)],[12738])).
% 23.85/24.03 tff(12740,plain,
% 23.85/24.03 (mult(mult(mult(mult(a, b), a), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(mult(mult(a, b), a), mult(c, rd(mult(b, c), mult(a, c)))), a)),
% 23.85/24.03 inference(symmetry,[status(thm)],[12739])).
% 23.85/24.03 tff(12741,plain,
% 23.85/24.03 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(a, b), a), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(a, b), mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a)))),
% 23.85/24.03 inference(quant_inst,[status(thm)],[])).
% 23.85/24.03 tff(12742,plain,
% 23.85/24.03 (mult(mult(mult(mult(a, b), a), mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(a, b), mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a))),
% 23.85/24.03 inference(unit_resolution,[status(thm)],[12741, 56])).
% 23.85/24.03 tff(12743,plain,
% 23.85/24.03 (mult(mult(a, b), mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a)) = mult(mult(mult(mult(a, b), a), mult(rd(mult(b, c), mult(a, c)), c)), a)),
% 23.85/24.03 inference(symmetry,[status(thm)],[12742])).
% 23.85/24.03 tff(12744,plain,
% 23.85/24.03 (mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a) = mult(mult(a, b), c)),
% 23.85/24.03 inference(transitivity,[status(thm)],[5329, 12648, 2296, 10753, 12687, 254])).
% 23.85/24.03 tff(12745,plain,
% 23.85/24.03 (mult(mult(a, b), mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a)) = mult(mult(a, b), mult(mult(a, b), c))),
% 23.85/24.03 inference(monotonicity,[status(thm)],[12744])).
% 23.85/24.03 tff(12746,plain,
% 23.85/24.03 (mult(mult(a, b), mult(mult(a, b), c)) = mult(mult(a, b), mult(mult(a, mult(rd(mult(b, c), mult(a, c)), c)), a))),
% 23.85/24.03 inference(symmetry,[status(thm)],[12745])).
% 23.85/24.03 tff(12747,assumption,(mult(mult(mult(b, a), mult(mult(rd(mult(b, c), mult(a, c)), a), c)), a) = mult(mult(b, a), mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a))), introduced(assumption)).
% 23.85/24.03 tff(12748,plain,
% 23.85/24.03 (mult(mult(a, b), mult(mult(rd(mult(b, c), mult(a, c)), a), c)) = mult(mult(b, a), mult(mult(rd(mult(b, c), mult(a, c)), a), c))),
% 23.85/24.03 inference(symmetry,[status(thm)],[12701])).
% 23.85/24.03 tff(12749,plain,
% 23.85/24.03 (mult(mult(mult(a, b), mult(mult(rd(mult(b, c), mult(a, c)), a), c)), a) = mult(mult(mult(b, a), mult(mult(rd(mult(b, c), mult(a, c)), a), c)), a)),
% 23.85/24.03 inference(monotonicity,[status(thm)],[12748])).
% 23.85/24.03 tff(12750,plain,
% 23.85/24.03 (mult(mult(a, b), mult(b, c)) = mult(mult(a, b), mult(mult(rd(mult(b, c), mult(a, c)), a), c))),
% 23.85/24.03 inference(symmetry,[status(thm)],[12700])).
% 23.85/24.03 tff(12751,plain,
% 23.85/24.03 (mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), b) = mult(mult(a, mult(b, c)), b)),
% 23.85/24.03 inference(monotonicity,[status(thm)],[12048])).
% 23.85/24.03 tff(12752,plain,
% 23.85/24.03 (mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), b) = mult(mult(a, b), mult(mult(rd(mult(b, c), mult(a, c)), a), c))),
% 23.85/24.03 inference(transitivity,[status(thm)],[12751, 806, 12750])).
% 23.85/24.03 tff(12753,plain,
% 23.85/24.03 (mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), b), a) = mult(mult(mult(a, b), mult(mult(rd(mult(b, c), mult(a, c)), a), c)), a)),
% 23.85/24.03 inference(monotonicity,[status(thm)],[12752])).
% 23.85/24.03 tff(12754,plain,
% 23.85/24.03 (mult(mult(a, mult(b, c)), b) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), b)),
% 23.85/24.03 inference(symmetry,[status(thm)],[12751])).
% 23.85/24.03 tff(12755,plain,
% 23.85/24.03 (mult(mult(a, b), mult(b, c)) = mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), b)),
% 23.85/24.03 inference(transitivity,[status(thm)],[805, 12754])).
% 23.85/24.03 tff(12756,plain,
% 23.85/24.03 (mult(mult(mult(a, b), mult(b, c)), a) = mult(mult(mult(a, mult(mult(a, c), rd(mult(b, c), mult(a, c)))), b), a)),
% 23.85/24.03 inference(monotonicity,[status(thm)],[12755])).
% 23.85/24.03 tff(12757,plain,
% 23.85/24.03 (mult(mult(mult(a, b), mult(b, c)), a) = mult(mult(mult(mult(b, c), a), b), a)),
% 23.85/24.03 inference(transitivity,[status(thm)],[12756, 12753, 12749, 12747, 12683, 12681, 12746, 12743, 12740, 12736, 12691])).
% 23.85/24.03 tff(12758,plain,
% 23.85/24.03 (rd(mult(mult(mult(a, b), mult(b, c)), a), a) = rd(mult(mult(mult(mult(b, c), a), b), a), a)),
% 23.85/24.03 inference(monotonicity,[status(thm)],[12757])).
% 23.85/24.03 tff(12759,plain,
% 23.85/24.03 (rd(mult(mult(mult(mult(b, c), a), b), a), a) = rd(mult(mult(mult(a, b), mult(b, c)), a), a)),
% 23.85/24.03 inference(symmetry,[status(thm)],[12758])).
% 23.85/24.03 tff(12760,plain,
% 23.85/24.03 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(mult(b, c), a), b), a), a) = mult(mult(mult(b, c), a), b))),
% 23.85/24.03 inference(quant_inst,[status(thm)],[])).
% 23.85/24.03 tff(12761,plain,
% 23.85/24.03 (rd(mult(mult(mult(mult(b, c), a), b), a), a) = mult(mult(mult(b, c), a), b)),
% 23.85/24.03 inference(unit_resolution,[status(thm)],[12760, 168])).
% 23.85/24.03 tff(12762,plain,
% 23.85/24.03 (mult(mult(mult(b, c), a), b) = rd(mult(mult(mult(mult(b, c), a), b), a), a)),
% 23.85/24.03 inference(symmetry,[status(thm)],[12761])).
% 23.85/24.03 tff(12763,plain,
% 23.85/24.03 (mult(mult(mult(a, b), c), b) = mult(mult(mult(b, c), a), b)),
% 23.85/24.03 inference(symmetry,[status(thm)],[12689])).
% 23.85/24.03 tff(12764,plain,
% 23.85/24.03 (mult(mult(mult(a, b), b), c) = mult(mult(a, b), mult(b, c))),
% 23.85/24.03 inference(transitivity,[status(thm)],[828, 12763, 12762, 12759, 12685])).
% 23.85/24.04 tff(12765,plain,
% 23.85/24.04 ($false),
% 23.85/24.04 inference(unit_resolution,[status(thm)],[1729, 12764])).
% 23.85/24.04 tff(12766,plain,(~(mult(mult(mult(b, a), mult(mult(rd(mult(b, c), mult(a, c)), a), c)), a) = mult(mult(b, a), mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a)))), inference(lemma,lemma(discharge,[]))).
% 23.85/24.04 tff(12767,plain,
% 23.85/24.04 (((~(mult(mult(mult(b, a), a), mult(mult(rd(mult(b, c), mult(a, c)), a), c)) = mult(mult(b, a), mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), c))))) | (~(mult(mult(mult(b, a), mult(mult(rd(mult(b, c), mult(a, c)), a), c)), a) = mult(mult(b, a), mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a))))) | (mult(mult(mult(b, a), mult(mult(rd(mult(b, c), mult(a, c)), a), c)), a) = mult(mult(b, a), mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a)))),
% 23.85/24.04 inference(tautology,[status(thm)],[])).
% 23.85/24.04 tff(12768,plain,
% 23.85/24.04 ((~(mult(mult(mult(b, a), a), mult(mult(rd(mult(b, c), mult(a, c)), a), c)) = mult(mult(b, a), mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), c))))) | (~(mult(mult(mult(b, a), mult(mult(rd(mult(b, c), mult(a, c)), a), c)), a) = mult(mult(b, a), mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a))))),
% 23.85/24.04 inference(unit_resolution,[status(thm)],[12767, 12766])).
% 23.85/24.04 tff(12769,plain,
% 23.85/24.04 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(b, a), a), mult(mult(rd(mult(b, c), mult(a, c)), a), c)) = mult(mult(mult(b, a), mult(mult(rd(mult(b, c), mult(a, c)), a), c)), a))) | (~(mult(mult(b, a), mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), c))) = mult(mult(b, a), mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a)))))) | (~((~(mult(mult(mult(b, a), a), mult(mult(rd(mult(b, c), mult(a, c)), a), c)) = mult(mult(b, a), mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), c))))) | (~(mult(mult(mult(b, a), mult(mult(rd(mult(b, c), mult(a, c)), a), c)), a) = mult(mult(b, a), mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(b, a), a), mult(mult(rd(mult(b, c), mult(a, c)), a), c)) = mult(mult(mult(b, a), mult(mult(rd(mult(b, c), mult(a, c)), a), c)), a))) | (~(mult(mult(b, a), mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), c))) = mult(mult(b, a), mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a)))))) | (~((~(mult(mult(mult(b, a), a), mult(mult(rd(mult(b, c), mult(a, c)), a), c)) = mult(mult(b, a), mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), c))))) | (~(mult(mult(mult(b, a), mult(mult(rd(mult(b, c), mult(a, c)), a), c)), a) = mult(mult(b, a), mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a)))))))),
% 23.85/24.04 inference(rewrite,[status(thm)],[])).
% 23.85/24.04 tff(12770,plain,
% 23.85/24.04 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | ((~((~(mult(mult(mult(b, a), a), mult(mult(rd(mult(b, c), mult(a, c)), a), c)) = mult(mult(mult(b, a), mult(mult(rd(mult(b, c), mult(a, c)), a), c)), a))) | (~(mult(mult(b, a), mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), c))) = mult(mult(b, a), mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a)))))) | (~((~(mult(mult(mult(b, a), a), mult(mult(rd(mult(b, c), mult(a, c)), a), c)) = mult(mult(b, a), mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), c))))) | (~(mult(mult(mult(b, a), mult(mult(rd(mult(b, c), mult(a, c)), a), c)), a) = mult(mult(b, a), mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a)))))))),
% 23.85/24.04 inference(quant_inst,[status(thm)],[])).
% 23.85/24.04 tff(12771,plain,
% 23.85/24.04 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X1, X2)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X2, X1)))))))) | (~((~(mult(mult(mult(b, a), a), mult(mult(rd(mult(b, c), mult(a, c)), a), c)) = mult(mult(mult(b, a), mult(mult(rd(mult(b, c), mult(a, c)), a), c)), a))) | (~(mult(mult(b, a), mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), c))) = mult(mult(b, a), mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a)))))) | (~((~(mult(mult(mult(b, a), a), mult(mult(rd(mult(b, c), mult(a, c)), a), c)) = mult(mult(b, a), mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), c))))) | (~(mult(mult(mult(b, a), mult(mult(rd(mult(b, c), mult(a, c)), a), c)), a) = mult(mult(b, a), mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a))))))),
% 23.85/24.04 inference(modus_ponens,[status(thm)],[12770, 12769])).
% 23.85/24.04 tff(12772,plain,
% 23.85/24.04 ((~((~(mult(mult(mult(b, a), a), mult(mult(rd(mult(b, c), mult(a, c)), a), c)) = mult(mult(mult(b, a), mult(mult(rd(mult(b, c), mult(a, c)), a), c)), a))) | (~(mult(mult(b, a), mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), c))) = mult(mult(b, a), mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a)))))) | (~((~(mult(mult(mult(b, a), a), mult(mult(rd(mult(b, c), mult(a, c)), a), c)) = mult(mult(b, a), mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), c))))) | (~(mult(mult(mult(b, a), mult(mult(rd(mult(b, c), mult(a, c)), a), c)), a) = mult(mult(b, a), mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a))))))),
% 23.85/24.04 inference(unit_resolution,[status(thm)],[12771, 27])).
% 23.85/24.04 tff(12773,plain,
% 23.85/24.04 (~((~(mult(mult(mult(b, a), a), mult(mult(rd(mult(b, c), mult(a, c)), a), c)) = mult(mult(mult(b, a), mult(mult(rd(mult(b, c), mult(a, c)), a), c)), a))) | (~(mult(mult(b, a), mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), c))) = mult(mult(b, a), mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a)))))),
% 23.85/24.04 inference(unit_resolution,[status(thm)],[12772, 12768])).
% 23.85/24.04 tff(12774,plain,
% 23.85/24.04 (((~(mult(mult(mult(b, a), a), mult(mult(rd(mult(b, c), mult(a, c)), a), c)) = mult(mult(mult(b, a), mult(mult(rd(mult(b, c), mult(a, c)), a), c)), a))) | (~(mult(mult(b, a), mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), c))) = mult(mult(b, a), mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a))))) | (mult(mult(b, a), mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), c))) = mult(mult(b, a), mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a)))),
% 23.85/24.05 inference(tautology,[status(thm)],[])).
% 23.85/24.05 tff(12775,plain,
% 23.85/24.05 (mult(mult(b, a), mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), c))) = mult(mult(b, a), mult(mult(mult(rd(mult(b, c), mult(a, c)), a), c), a))),
% 23.85/24.05 inference(unit_resolution,[status(thm)],[12774, 12773])).
% 23.85/24.05 tff(12776,plain,
% 23.85/24.05 (ld(mult(c, c), mult(mult(c, c), mult(a, b))) = ld(mult(c, c), mult(mult(c, c), mult(b, a)))),
% 23.85/24.05 inference(symmetry,[status(thm)],[12676])).
% 23.85/24.05 tff(12777,plain,
% 23.85/24.05 (mult(a, b) = ld(mult(c, c), mult(mult(c, c), mult(a, b)))),
% 23.85/24.05 inference(symmetry,[status(thm)],[11])).
% 23.85/24.05 tff(12778,plain,
% 23.85/24.05 (mult(a, b) = mult(b, a)),
% 23.85/24.05 inference(transitivity,[status(thm)],[12777, 12776, 12678])).
% 23.85/24.05 tff(12779,plain,
% 23.85/24.05 (mult(mult(a, b), mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), c))) = mult(mult(b, a), mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), c)))),
% 23.85/24.05 inference(monotonicity,[status(thm)],[12778])).
% 23.85/24.05 tff(12780,plain,
% 23.85/24.05 (mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), c)) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), c), a))),
% 23.85/24.05 inference(monotonicity,[status(thm)],[12462])).
% 23.85/24.05 tff(12781,plain,
% 23.85/24.05 (mult(a, mult(mult(rd(mult(b, c), mult(a, c)), c), a)) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), c))),
% 23.85/24.05 inference(symmetry,[status(thm)],[12780])).
% 23.85/24.05 tff(12782,plain,
% 23.85/24.05 (mult(mult(rd(mult(b, c), mult(a, c)), c), a) = mult(b, c)),
% 23.85/24.05 inference(transitivity,[status(thm)],[83, 12147, 4340, 1377, 12698, 1370])).
% 23.85/24.05 tff(12783,plain,
% 23.85/24.05 (mult(a, mult(mult(rd(mult(b, c), mult(a, c)), c), a)) = mult(a, mult(b, c))),
% 23.85/24.05 inference(monotonicity,[status(thm)],[12782])).
% 23.85/24.05 tff(12784,plain,
% 23.85/24.05 (mult(a, mult(b, c)) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), c), a))),
% 23.85/24.05 inference(symmetry,[status(thm)],[12783])).
% 23.85/24.05 tff(12785,plain,
% 23.85/24.05 (mult(a, mult(b, c)) = mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), c))),
% 23.85/24.05 inference(transitivity,[status(thm)],[12784, 12781])).
% 23.85/24.05 tff(12786,plain,
% 23.85/24.05 (mult(mult(a, b), mult(a, mult(b, c))) = mult(mult(a, b), mult(a, mult(mult(rd(mult(b, c), mult(a, c)), a), c)))),
% 23.85/24.05 inference(monotonicity,[status(thm)],[12785])).
% 23.85/24.05 tff(12787,plain,
% 23.85/24.05 (mult(mult(a, b), mult(a, mult(b, c))) = mult(mult(a, b), mult(mult(a, b), c))),
% 23.85/24.05 inference(transitivity,[status(thm)],[12786, 12779, 12775, 12683, 12681])).
% 23.85/24.05 tff(12788,plain,
% 23.85/24.05 (ld(mult(a, b), mult(mult(a, b), mult(a, mult(b, c)))) = ld(mult(a, b), mult(mult(a, b), mult(mult(a, b), c)))),
% 23.85/24.05 inference(monotonicity,[status(thm)],[12787])).
% 23.85/24.05 tff(12789,plain,
% 23.85/24.05 (ld(mult(a, b), mult(mult(a, b), mult(mult(a, b), c))) = ld(mult(a, b), mult(mult(a, b), mult(a, mult(b, c))))),
% 23.85/24.05 inference(symmetry,[status(thm)],[12788])).
% 23.85/24.05 tff(12790,plain,
% 23.85/24.05 (mult(mult(a, b), c) = mult(a, mult(b, c))),
% 23.85/24.05 inference(transitivity,[status(thm)],[10353, 12789, 9])).
% 23.85/24.05 tff(12791,plain,
% 23.85/24.05 ($false),
% 23.85/24.05 inference(unit_resolution,[status(thm)],[146, 12790])).
% 23.85/24.05 % SZS output end Proof
% 23.85/24.05 % E exiting
%------------------------------------------------------------------------------