%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP747+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 0.20s 0.49s
% Output : Proof 0.40s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP747+1 : TPTP v9.0.0. Released v4.0.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n015.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 17:02:55 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.49 % SZS status Theorem
% 0.20/0.49 % SZS output start Proof
% 0.20/0.49 tff(mult_type, type, (
% 0.20/0.49 mult: ( $i * $i ) > $i)).
% 0.20/0.49 tff(c_type, type, (
% 0.20/0.49 c: $i)).
% 0.20/0.49 tff(a_type, type, (
% 0.20/0.49 a: $i)).
% 0.20/0.49 tff(b_type, type, (
% 0.20/0.49 b: $i)).
% 0.20/0.49 tff(ld_type, type, (
% 0.20/0.49 ld: ( $i * $i ) > $i)).
% 0.20/0.49 tff(unit_type, type, (
% 0.20/0.49 unit: $i)).
% 0.20/0.49 tff(rd_type, type, (
% 0.20/0.49 rd: ( $i * $i ) > $i)).
% 0.20/0.49 tff(1,plain,
% 0.20/0.49 ((mult(b, mult(a, c)) = mult(b, mult(c, a))) <=> (mult(b, mult(c, a)) = mult(b, mult(a, c)))),
% 0.20/0.49 inference(commutativity,[status(thm)],[])).
% 0.20/0.49 tff(2,assumption,(~(ld(b, mult(b, mult(a, c))) = mult(a, c))), introduced(assumption)).
% 0.20/0.49 tff(3,plain,
% 0.20/0.49 (^[B: $i, A: $i] : refl((ld(A, mult(A, B)) = B) <=> (ld(A, mult(A, B)) = B))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(4,plain,
% 0.20/0.49 (![B: $i, A: $i] : (ld(A, mult(A, B)) = B) <=> ![B: $i, A: $i] : (ld(A, mult(A, B)) = B)),
% 0.20/0.49 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.49 tff(5,plain,
% 0.20/0.49 (![B: $i, A: $i] : (ld(A, mult(A, B)) = B) <=> ![B: $i, A: $i] : (ld(A, mult(A, B)) = B)),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(6,axiom,(![B: $i, A: $i] : (ld(A, mult(A, B)) = B)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','f02')).
% 0.20/0.49 tff(7,plain,
% 0.20/0.49 (![B: $i, A: $i] : (ld(A, mult(A, B)) = B)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.20/0.49 tff(8,plain,(
% 0.20/0.49 ![B: $i, A: $i] : (ld(A, mult(A, B)) = B)),
% 0.20/0.49 inference(skolemize,[status(sab)],[7])).
% 0.20/0.49 tff(9,plain,
% 0.20/0.49 (![B: $i, A: $i] : (ld(A, mult(A, B)) = B)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.20/0.49 tff(10,plain,
% 0.20/0.49 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(b, mult(b, mult(a, c))) = mult(a, c))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(11,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[10, 9, 2])).
% 0.20/0.49 tff(12,plain,(ld(b, mult(b, mult(a, c))) = mult(a, c)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(13,assumption,(ld(b, mult(b, mult(a, c))) = mult(a, c)), introduced(assumption)).
% 0.20/0.49 tff(14,assumption,(~(mult(mult(mult(b, a), c), a) = mult(mult(b, a), mult(a, c)))), introduced(assumption)).
% 0.20/0.49 tff(15,plain,
% 0.20/0.49 (((~(mult(mult(mult(b, a), a), c) = mult(mult(b, a), mult(c, a)))) | (~(mult(mult(mult(b, a), c), a) = mult(mult(b, a), mult(a, c))))) | (mult(mult(mult(b, a), c), a) = mult(mult(b, a), mult(a, c)))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(16,plain,
% 0.20/0.49 ((~(mult(mult(mult(b, a), a), c) = mult(mult(b, a), mult(c, a)))) | (~(mult(mult(mult(b, a), c), a) = mult(mult(b, a), mult(a, c))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[15, 14])).
% 0.20/0.49 tff(17,plain,
% 0.20/0.49 (^[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(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2))))))) <=> ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2))))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(18,plain,
% 0.20/0.49 (![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(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2))))))) <=> ![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[17])).
% 0.20/0.49 tff(19,plain,
% 0.20/0.49 (^[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(X2, X1))) & (mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2))))) <=> ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2))))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(20,plain,
% 0.20/0.49 (![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(X2, X1))) & (mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2))))) <=> ![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[19])).
% 0.20/0.49 tff(21,plain,
% 0.20/0.49 (![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(X2, X1))) & (mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2))))) <=> ![X0: $i, X1: $i, X2: $i] : (((mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1)) & (mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))) | ((mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1))) & (mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(22,plain,
% 0.20/0.49 (^[X0: $i, X1: $i, X2: $i] : rewrite((((mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1))) & (mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))) | ((mult(mult(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(X2, X1))) & (mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(23,plain,
% 0.20/0.49 (![X0: $i, X1: $i, X2: $i] : (((mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1))) & (mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))) | ((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(X2, X1))) & (mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[22])).
% 0.20/0.49 tff(24,axiom,(![X0: $i, X1: $i, X2: $i] : (((mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1))) & (mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))) | ((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')).
% 0.20/0.49 tff(25,plain,
% 0.20/0.49 (![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(X2, X1))) & (mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.20/0.49 tff(26,plain,
% 0.20/0.49 (![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(X2, X1))) & (mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.20/0.49 tff(27,plain,(
% 0.20/0.49 ![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(X2, X1))) & (mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))),
% 0.20/0.49 inference(skolemize,[status(sab)],[26])).
% 0.20/0.49 tff(28,plain,
% 0.20/0.49 (![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(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.20/0.49 tff(29,plain,
% 0.20/0.49 (![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(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[28, 18])).
% 0.20/0.50 tff(30,plain,
% 0.20/0.50 (((~![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(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(mult(mult(b, a), a), c) = mult(mult(b, a), mult(c, a)))) | (~(mult(mult(mult(b, a), c), a) = mult(mult(b, a), mult(a, c)))))) | (~((~(mult(mult(mult(b, a), a), c) = mult(mult(mult(b, a), c), a))) | (~(mult(mult(b, a), mult(a, c)) = mult(mult(b, 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(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | (~((~(mult(mult(mult(b, a), a), c) = mult(mult(b, a), mult(c, a)))) | (~(mult(mult(mult(b, a), c), a) = mult(mult(b, a), mult(a, c)))))) | (~((~(mult(mult(mult(b, a), a), c) = mult(mult(mult(b, a), c), a))) | (~(mult(mult(b, a), mult(a, c)) = mult(mult(b, a), mult(c, a)))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(31,plain,
% 0.20/0.50 (((~((~(mult(mult(mult(b, a), a), c) = mult(mult(mult(b, a), c), a))) | (~(mult(mult(b, a), mult(a, c)) = mult(mult(b, a), mult(c, a)))))) | (~((~(mult(mult(mult(b, a), a), c) = mult(mult(b, a), mult(c, a)))) | (~(mult(mult(mult(b, a), c), a) = mult(mult(b, a), mult(a, c))))))) <=> ((~((~(mult(mult(mult(b, a), a), c) = mult(mult(b, a), mult(c, a)))) | (~(mult(mult(mult(b, a), c), a) = mult(mult(b, a), mult(a, c)))))) | (~((~(mult(mult(mult(b, a), a), c) = mult(mult(mult(b, a), c), a))) | (~(mult(mult(b, a), mult(a, c)) = mult(mult(b, a), mult(c, a)))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(32,plain,
% 0.20/0.50 ((~((~(mult(mult(mult(b, a), a), c) = mult(mult(mult(b, a), c), a))) | (~(mult(mult(b, a), mult(a, c)) = mult(mult(b, a), mult(c, a)))))) <=> (~((~(mult(mult(mult(b, a), a), c) = mult(mult(mult(b, a), c), a))) | (~(mult(mult(b, a), mult(a, c)) = mult(mult(b, a), mult(c, a))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(33,plain,
% 0.20/0.50 (((~((~(mult(mult(mult(b, a), a), c) = mult(mult(mult(b, a), c), a))) | (~(mult(mult(b, a), mult(a, c)) = mult(mult(b, a), mult(c, a)))))) | (~((~(mult(mult(mult(b, a), a), c) = mult(mult(b, a), mult(c, a)))) | (~(mult(mult(mult(b, a), c), a) = mult(mult(b, a), mult(a, c))))))) <=> ((~((~(mult(mult(mult(b, a), a), c) = mult(mult(mult(b, a), c), a))) | (~(mult(mult(b, a), mult(a, c)) = mult(mult(b, a), mult(c, a)))))) | (~((~(mult(mult(mult(b, a), a), c) = mult(mult(b, a), mult(c, a)))) | (~(mult(mult(mult(b, a), c), a) = mult(mult(b, a), mult(a, c)))))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[32])).
% 0.20/0.50 tff(34,plain,
% 0.20/0.50 (((~((~(mult(mult(mult(b, a), a), c) = mult(mult(mult(b, a), c), a))) | (~(mult(mult(b, a), mult(a, c)) = mult(mult(b, a), mult(c, a)))))) | (~((~(mult(mult(mult(b, a), a), c) = mult(mult(b, a), mult(c, a)))) | (~(mult(mult(mult(b, a), c), a) = mult(mult(b, a), mult(a, c))))))) <=> ((~((~(mult(mult(mult(b, a), a), c) = mult(mult(b, a), mult(c, a)))) | (~(mult(mult(mult(b, a), c), a) = mult(mult(b, a), mult(a, c)))))) | (~((~(mult(mult(mult(b, a), a), c) = mult(mult(mult(b, a), c), a))) | (~(mult(mult(b, a), mult(a, c)) = mult(mult(b, a), mult(c, a)))))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[33, 31])).
% 0.20/0.50 tff(35,plain,
% 0.20/0.50 (((~![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(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(mult(mult(b, a), a), c) = mult(mult(mult(b, a), c), a))) | (~(mult(mult(b, a), mult(a, c)) = mult(mult(b, a), mult(c, a)))))) | (~((~(mult(mult(mult(b, a), a), c) = mult(mult(b, a), mult(c, a)))) | (~(mult(mult(mult(b, a), c), a) = mult(mult(b, 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(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(mult(mult(b, a), a), c) = mult(mult(b, a), mult(c, a)))) | (~(mult(mult(mult(b, a), c), a) = mult(mult(b, a), mult(a, c)))))) | (~((~(mult(mult(mult(b, a), a), c) = mult(mult(mult(b, a), c), a))) | (~(mult(mult(b, a), mult(a, c)) = mult(mult(b, a), mult(c, a))))))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[34])).
% 0.20/0.50 tff(36,plain,
% 0.20/0.50 (((~![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(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(mult(mult(b, a), a), c) = mult(mult(mult(b, a), c), a))) | (~(mult(mult(b, a), mult(a, c)) = mult(mult(b, a), mult(c, a)))))) | (~((~(mult(mult(mult(b, a), a), c) = mult(mult(b, a), mult(c, a)))) | (~(mult(mult(mult(b, a), c), a) = mult(mult(b, 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(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | (~((~(mult(mult(mult(b, a), a), c) = mult(mult(b, a), mult(c, a)))) | (~(mult(mult(mult(b, a), c), a) = mult(mult(b, a), mult(a, c)))))) | (~((~(mult(mult(mult(b, a), a), c) = mult(mult(mult(b, a), c), a))) | (~(mult(mult(b, a), mult(a, c)) = mult(mult(b, a), mult(c, a)))))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[35, 30])).
% 0.20/0.50 tff(37,plain,
% 0.20/0.50 ((~![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(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(mult(mult(b, a), a), c) = mult(mult(mult(b, a), c), a))) | (~(mult(mult(b, a), mult(a, c)) = mult(mult(b, a), mult(c, a)))))) | (~((~(mult(mult(mult(b, a), a), c) = mult(mult(b, a), mult(c, a)))) | (~(mult(mult(mult(b, a), c), a) = mult(mult(b, a), mult(a, c)))))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(38,plain,
% 0.20/0.50 ((~![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(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | (~((~(mult(mult(mult(b, a), a), c) = mult(mult(b, a), mult(c, a)))) | (~(mult(mult(mult(b, a), c), a) = mult(mult(b, a), mult(a, c)))))) | (~((~(mult(mult(mult(b, a), a), c) = mult(mult(mult(b, a), c), a))) | (~(mult(mult(b, a), mult(a, c)) = mult(mult(b, a), mult(c, a))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.20/0.50 tff(39,plain,
% 0.20/0.50 ((~((~(mult(mult(mult(b, a), a), c) = mult(mult(b, a), mult(c, a)))) | (~(mult(mult(mult(b, a), c), a) = mult(mult(b, a), mult(a, c)))))) | (~((~(mult(mult(mult(b, a), a), c) = mult(mult(mult(b, a), c), a))) | (~(mult(mult(b, a), mult(a, c)) = mult(mult(b, a), mult(c, a))))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[38, 29])).
% 0.20/0.50 tff(40,plain,
% 0.20/0.50 (~((~(mult(mult(mult(b, a), a), c) = mult(mult(mult(b, a), c), a))) | (~(mult(mult(b, a), mult(a, c)) = mult(mult(b, a), mult(c, a)))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[39, 16])).
% 0.20/0.50 tff(41,plain,
% 0.20/0.50 (((~(mult(mult(mult(b, a), a), c) = mult(mult(mult(b, a), c), a))) | (~(mult(mult(b, a), mult(a, c)) = mult(mult(b, a), mult(c, a))))) | (mult(mult(b, a), mult(a, c)) = mult(mult(b, a), mult(c, a)))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(42,plain,
% 0.20/0.50 (mult(mult(b, a), mult(a, c)) = mult(mult(b, a), mult(c, a))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.20/0.50 tff(43,plain,
% 0.20/0.50 ((mult(b, mult(mult(a, c), a)) = mult(mult(b, a), mult(a, c))) <=> (mult(mult(b, a), mult(a, c)) = mult(b, mult(mult(a, c), a)))),
% 0.20/0.50 inference(commutativity,[status(thm)],[])).
% 0.20/0.50 tff(44,plain,
% 0.20/0.50 (^[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))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(45,plain,
% 0.20/0.50 (![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)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[44])).
% 0.20/0.50 tff(46,plain,
% 0.20/0.50 (![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)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(47,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')).
% 0.20/0.50 tff(48,plain,
% 0.20/0.50 (![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.20/0.50 tff(49,plain,(
% 0.20/0.50 ![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))),
% 0.20/0.50 inference(skolemize,[status(sab)],[48])).
% 0.20/0.50 tff(50,plain,
% 0.20/0.50 (![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[49, 45])).
% 0.20/0.50 tff(51,plain,
% 0.20/0.50 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(b, a), c), a) = mult(b, mult(mult(a, c), a)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(52,plain,
% 0.20/0.50 (mult(mult(mult(b, a), c), a) = mult(b, mult(mult(a, c), a))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.20/0.50 tff(53,plain,
% 0.20/0.50 ((mult(mult(mult(b, a), c), a) = mult(mult(b, a), mult(a, c))) <=> (mult(b, mult(mult(a, c), a)) = mult(mult(b, a), mult(a, c)))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[52])).
% 0.20/0.50 tff(54,plain,
% 0.20/0.50 ((mult(mult(mult(b, a), c), a) = mult(mult(b, a), mult(a, c))) <=> (mult(mult(b, a), mult(a, c)) = mult(b, mult(mult(a, c), a)))),
% 0.20/0.50 inference(transitivity,[status(thm)],[53, 43])).
% 0.20/0.50 tff(55,plain,
% 0.20/0.50 ((mult(mult(b, a), mult(a, c)) = mult(b, mult(mult(a, c), a))) <=> (mult(mult(mult(b, a), c), a) = mult(mult(b, a), mult(a, c)))),
% 0.20/0.50 inference(symmetry,[status(thm)],[54])).
% 0.20/0.50 tff(56,assumption,(mult(mult(b, a), mult(a, c)) = mult(b, mult(mult(a, c), a))), introduced(assumption)).
% 0.20/0.50 tff(57,plain,
% 0.20/0.50 (mult(mult(mult(b, a), c), a) = mult(mult(b, a), mult(a, c))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.20/0.50 tff(58,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[14, 57])).
% 0.20/0.50 tff(59,plain,((~(mult(mult(b, a), mult(a, c)) = mult(b, mult(mult(a, c), a)))) | (mult(mult(mult(b, a), c), a) = mult(mult(b, a), mult(a, c)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(60,plain,
% 0.20/0.50 (~(mult(mult(b, a), mult(a, c)) = mult(b, mult(mult(a, c), a)))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[59, 14])).
% 0.20/0.50 tff(61,assumption,(mult(mult(b, a), c) = mult(b, mult(c, a))), introduced(assumption)).
% 0.20/0.50 tff(62,plain,
% 0.20/0.50 (mult(b, mult(c, a)) = mult(mult(b, a), c)),
% 0.20/0.50 inference(symmetry,[status(thm)],[61])).
% 0.20/0.50 tff(63,plain,
% 0.20/0.50 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(b, a), mult(mult(b, a), mult(c, a))) = mult(c, a))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(64,plain,
% 0.20/0.50 (ld(mult(b, a), mult(mult(b, a), mult(c, a))) = mult(c, a)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[63, 9])).
% 0.20/0.50 tff(65,assumption,(mult(mult(b, a), mult(a, c)) = mult(mult(b, a), mult(c, a))), introduced(assumption)).
% 0.20/0.50 tff(66,plain,
% 0.20/0.50 (mult(mult(b, a), mult(c, a)) = mult(mult(b, a), mult(a, c))),
% 0.20/0.50 inference(symmetry,[status(thm)],[65])).
% 0.20/0.50 tff(67,plain,
% 0.20/0.50 (ld(mult(b, a), mult(mult(b, a), mult(c, a))) = ld(mult(b, a), mult(mult(b, a), mult(a, c)))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[66])).
% 0.20/0.50 tff(68,plain,
% 0.20/0.50 (ld(mult(b, a), mult(mult(b, a), mult(a, c))) = ld(mult(b, a), mult(mult(b, a), mult(c, a)))),
% 0.20/0.50 inference(symmetry,[status(thm)],[67])).
% 0.20/0.50 tff(69,plain,
% 0.20/0.50 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(b, a), mult(mult(b, a), mult(a, c))) = mult(a, c))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(70,plain,
% 0.20/0.51 (ld(mult(b, a), mult(mult(b, a), mult(a, c))) = mult(a, c)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[69, 9])).
% 0.20/0.51 tff(71,plain,
% 0.20/0.51 (mult(a, c) = ld(mult(b, a), mult(mult(b, a), mult(a, c)))),
% 0.20/0.51 inference(symmetry,[status(thm)],[70])).
% 0.20/0.51 tff(72,plain,
% 0.20/0.51 (mult(a, c) = mult(c, a)),
% 0.20/0.51 inference(transitivity,[status(thm)],[71, 68, 64])).
% 0.20/0.51 tff(73,plain,
% 0.20/0.51 (mult(b, mult(a, c)) = mult(b, mult(c, a))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[72])).
% 0.20/0.51 tff(74,plain,
% 0.20/0.51 (mult(b, mult(a, c)) = mult(mult(b, a), c)),
% 0.20/0.51 inference(transitivity,[status(thm)],[73, 62])).
% 0.20/0.51 tff(75,plain,
% 0.20/0.51 (mult(mult(b, mult(a, c)), a) = mult(mult(mult(b, a), c), a)),
% 0.20/0.51 inference(monotonicity,[status(thm)],[74])).
% 0.20/0.51 tff(76,assumption,(~(mult(mult(b, a), mult(a, c)) = mult(b, mult(mult(a, c), a)))), introduced(assumption)).
% 0.20/0.51 tff(77,plain,
% 0.20/0.51 (((~(mult(mult(b, a), mult(a, c)) = mult(b, mult(mult(a, c), a)))) | (~(mult(mult(b, mult(a, c)), a) = mult(b, mult(a, mult(a, c)))))) | (mult(mult(b, a), mult(a, c)) = mult(b, mult(mult(a, c), a)))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(78,plain,
% 0.20/0.51 ((~(mult(mult(b, a), mult(a, c)) = mult(b, mult(mult(a, c), a)))) | (~(mult(mult(b, mult(a, c)), a) = mult(b, mult(a, mult(a, c)))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.20/0.51 tff(79,plain,
% 0.20/0.51 (((~![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(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(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(mult(a, c), a)))) | (~(mult(mult(b, mult(a, c)), a) = mult(b, 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(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | (~((~(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(mult(a, c), a)))) | (~(mult(mult(b, mult(a, c)), a) = mult(b, mult(a, mult(a, c))))))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(80,plain,
% 0.20/0.51 ((~![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(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(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(mult(a, c), a)))) | (~(mult(mult(b, mult(a, c)), a) = mult(b, mult(a, mult(a, c))))))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(81,plain,
% 0.20/0.51 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | (~((~(mult(mult(b, a), mult(a, c)) = mult(mult(b, mult(a, c)), a))) | (~(mult(b, mult(a, mult(a, c))) = mult(b, mult(mult(a, c), a)))))) | (~((~(mult(mult(b, a), mult(a, c)) = mult(b, mult(mult(a, c), a)))) | (~(mult(mult(b, mult(a, c)), a) = mult(b, mult(a, mult(a, c)))))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.20/0.51 tff(82,plain,
% 0.20/0.51 ((~((~(mult(mult(b, a), mult(a, c)) = mult(mult(b, mult(a, c)), a))) | (~(mult(b, mult(a, mult(a, c))) = mult(b, mult(mult(a, c), a)))))) | (~((~(mult(mult(b, a), mult(a, c)) = mult(b, mult(mult(a, c), a)))) | (~(mult(mult(b, mult(a, c)), a) = mult(b, mult(a, mult(a, c)))))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[81, 29])).
% 0.20/0.51 tff(83,plain,
% 0.20/0.51 (~((~(mult(mult(b, a), mult(a, c)) = mult(mult(b, mult(a, c)), a))) | (~(mult(b, mult(a, mult(a, c))) = mult(b, mult(mult(a, c), a)))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[82, 78])).
% 0.20/0.51 tff(84,plain,
% 0.20/0.51 (((~(mult(mult(b, a), mult(a, c)) = mult(mult(b, mult(a, c)), a))) | (~(mult(b, mult(a, mult(a, c))) = mult(b, mult(mult(a, c), a))))) | (mult(mult(b, a), mult(a, c)) = mult(mult(b, mult(a, c)), a))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(85,plain,
% 0.20/0.51 (mult(mult(b, a), mult(a, c)) = mult(mult(b, mult(a, c)), a)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[84, 83])).
% 0.20/0.51 tff(86,plain,
% 0.20/0.51 (mult(mult(b, a), mult(a, c)) = mult(b, mult(mult(a, c), a))),
% 0.20/0.51 inference(transitivity,[status(thm)],[85, 75, 52])).
% 0.20/0.51 tff(87,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[76, 86])).
% 0.20/0.51 tff(88,plain,((~(mult(mult(b, a), c) = mult(b, mult(c, a)))) | (mult(mult(b, a), mult(a, c)) = mult(b, mult(mult(a, c), a))) | (~(mult(mult(b, a), mult(a, c)) = mult(mult(b, a), mult(c, a))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(89,plain,
% 0.20/0.51 (~(mult(mult(b, a), c) = mult(b, mult(c, a)))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[88, 60, 42])).
% 0.20/0.51 tff(90,plain,
% 0.20/0.51 (((~(mult(mult(b, c), a) = mult(b, mult(a, c)))) | (~(mult(mult(b, a), c) = mult(b, mult(c, a))))) | (mult(mult(b, a), c) = mult(b, mult(c, a)))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(91,plain,
% 0.20/0.51 ((~(mult(mult(b, c), a) = mult(b, mult(a, c)))) | (~(mult(mult(b, a), c) = mult(b, mult(c, a))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[90, 89])).
% 0.20/0.51 tff(92,plain,
% 0.20/0.51 (((~![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(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(b, mult(c, a)) = mult(b, mult(a, c)))) | (~(mult(mult(b, c), a) = mult(mult(b, a), c))))) | (~((~(mult(mult(b, c), a) = mult(b, mult(a, c)))) | (~(mult(mult(b, a), 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(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | (~((~(mult(b, mult(c, a)) = mult(b, mult(a, c)))) | (~(mult(mult(b, c), a) = mult(mult(b, a), c))))) | (~((~(mult(mult(b, c), a) = mult(b, mult(a, c)))) | (~(mult(mult(b, a), c) = mult(b, mult(c, a)))))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(93,plain,
% 0.20/0.51 (((~((~(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(a, c)))) | (~(mult(mult(b, a), c) = mult(b, mult(c, a))))))) <=> ((~((~(mult(b, mult(c, a)) = mult(b, mult(a, c)))) | (~(mult(mult(b, c), a) = mult(mult(b, a), c))))) | (~((~(mult(mult(b, c), a) = mult(b, mult(a, c)))) | (~(mult(mult(b, a), c) = mult(b, mult(c, a)))))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(94,plain,
% 0.20/0.51 (((~![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(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(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(a, c)))) | (~(mult(mult(b, a), 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(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(b, mult(c, a)) = mult(b, mult(a, c)))) | (~(mult(mult(b, c), a) = mult(mult(b, a), c))))) | (~((~(mult(mult(b, c), a) = mult(b, mult(a, c)))) | (~(mult(mult(b, a), c) = mult(b, mult(c, a))))))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[93])).
% 0.20/0.51 tff(95,plain,
% 0.20/0.51 (((~![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(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(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(a, c)))) | (~(mult(mult(b, a), 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(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | (~((~(mult(b, mult(c, a)) = mult(b, mult(a, c)))) | (~(mult(mult(b, c), a) = mult(mult(b, a), c))))) | (~((~(mult(mult(b, c), a) = mult(b, mult(a, c)))) | (~(mult(mult(b, a), c) = mult(b, mult(c, a)))))))),
% 0.20/0.51 inference(transitivity,[status(thm)],[94, 92])).
% 0.20/0.51 tff(96,plain,
% 0.20/0.51 ((~![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(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(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(a, c)))) | (~(mult(mult(b, a), c) = mult(b, mult(c, a)))))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(97,plain,
% 0.20/0.51 ((~![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(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | (~((~(mult(b, mult(c, a)) = mult(b, mult(a, c)))) | (~(mult(mult(b, c), a) = mult(mult(b, a), c))))) | (~((~(mult(mult(b, c), a) = mult(b, mult(a, c)))) | (~(mult(mult(b, a), c) = mult(b, mult(c, a))))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.20/0.51 tff(98,plain,
% 0.20/0.51 ((~((~(mult(b, mult(c, a)) = mult(b, mult(a, c)))) | (~(mult(mult(b, c), a) = mult(mult(b, a), c))))) | (~((~(mult(mult(b, c), a) = mult(b, mult(a, c)))) | (~(mult(mult(b, a), c) = mult(b, mult(c, a))))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[97, 29])).
% 0.20/0.51 tff(99,plain,
% 0.20/0.51 (~((~(mult(b, mult(c, a)) = mult(b, mult(a, c)))) | (~(mult(mult(b, c), a) = mult(mult(b, a), c))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[98, 91])).
% 0.20/0.51 tff(100,plain,
% 0.20/0.51 (((~(mult(b, mult(c, a)) = mult(b, mult(a, c)))) | (~(mult(mult(b, c), a) = mult(mult(b, a), c)))) | (mult(mult(b, c), a) = mult(mult(b, a), c))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(101,plain,
% 0.20/0.51 (mult(mult(b, c), a) = mult(mult(b, a), c)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[100, 99])).
% 0.20/0.51 tff(102,plain,
% 0.20/0.51 (^[A: $i] : refl((mult(unit, A) = A) <=> (mult(unit, A) = A))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(103,plain,
% 0.20/0.51 (![A: $i] : (mult(unit, A) = A) <=> ![A: $i] : (mult(unit, A) = A)),
% 0.20/0.51 inference(quant_intro,[status(thm)],[102])).
% 0.20/0.51 tff(104,plain,
% 0.20/0.51 (![A: $i] : (mult(unit, A) = A) <=> ![A: $i] : (mult(unit, A) = A)),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(105,axiom,(![A: $i] : (mult(unit, A) = A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','f06')).
% 0.20/0.51 tff(106,plain,
% 0.20/0.51 (![A: $i] : (mult(unit, A) = A)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.20/0.51 tff(107,plain,(
% 0.20/0.51 ![A: $i] : (mult(unit, A) = A)),
% 0.20/0.51 inference(skolemize,[status(sab)],[106])).
% 0.20/0.51 tff(108,plain,
% 0.20/0.51 (![A: $i] : (mult(unit, A) = A)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[107, 103])).
% 0.20/0.51 tff(109,plain,
% 0.20/0.51 ((~![A: $i] : (mult(unit, A) = A)) | (mult(unit, a) = a)),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(110,plain,
% 0.20/0.51 (mult(unit, a) = a),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[109, 108])).
% 0.20/0.51 tff(111,plain,
% 0.20/0.51 (a = mult(unit, a)),
% 0.20/0.51 inference(symmetry,[status(thm)],[110])).
% 0.20/0.51 tff(112,plain,
% 0.20/0.51 (mult(a, mult(b, c)) = mult(mult(unit, a), mult(b, c))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[111])).
% 0.20/0.51 tff(113,plain,
% 0.20/0.51 (mult(mult(unit, a), mult(b, c)) = mult(a, mult(b, c))),
% 0.20/0.51 inference(symmetry,[status(thm)],[112])).
% 0.20/0.51 tff(114,plain,
% 0.20/0.51 (^[B: $i, A: $i] : refl((rd(mult(A, B), B) = A) <=> (rd(mult(A, B), B) = A))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(115,plain,
% 0.20/0.51 (![B: $i, A: $i] : (rd(mult(A, B), B) = A) <=> ![B: $i, A: $i] : (rd(mult(A, B), B) = A)),
% 0.20/0.51 inference(quant_intro,[status(thm)],[114])).
% 0.20/0.51 tff(116,plain,
% 0.20/0.51 (![B: $i, A: $i] : (rd(mult(A, B), B) = A) <=> ![B: $i, A: $i] : (rd(mult(A, B), B) = A)),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(117,axiom,(![B: $i, A: $i] : (rd(mult(A, B), B) = A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','f04')).
% 0.20/0.51 tff(118,plain,
% 0.20/0.51 (![B: $i, A: $i] : (rd(mult(A, B), B) = A)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.20/0.51 tff(119,plain,(
% 0.20/0.51 ![B: $i, A: $i] : (rd(mult(A, B), B) = A)),
% 0.20/0.51 inference(skolemize,[status(sab)],[118])).
% 0.20/0.51 tff(120,plain,
% 0.20/0.51 (![B: $i, A: $i] : (rd(mult(A, B), B) = A)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[119, 115])).
% 0.20/0.51 tff(121,plain,
% 0.20/0.51 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(a, b), c), c), c) = mult(mult(a, b), c))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(122,plain,
% 0.20/0.51 (rd(mult(mult(mult(a, b), c), c), c) = mult(mult(a, b), c)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[121, 120])).
% 0.20/0.51 tff(123,plain,
% 0.20/0.51 ((~![A: $i] : (mult(unit, A) = A)) | (mult(unit, mult(b, c)) = mult(b, c))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(124,plain,
% 0.20/0.51 (mult(unit, mult(b, c)) = mult(b, c)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[123, 108])).
% 0.20/0.51 tff(125,plain,
% 0.20/0.51 ((mult(unit, mult(c, b)) = mult(unit, mult(b, c))) <=> (mult(unit, mult(b, c)) = mult(unit, mult(c, b)))),
% 0.20/0.51 inference(commutativity,[status(thm)],[])).
% 0.20/0.51 tff(126,plain,
% 0.20/0.51 ((mult(unit, mult(b, c)) = mult(unit, mult(c, b))) <=> (mult(unit, mult(c, b)) = mult(unit, mult(b, c)))),
% 0.20/0.51 inference(symmetry,[status(thm)],[125])).
% 0.20/0.51 tff(127,plain,
% 0.20/0.51 ((mult(mult(unit, c), b) = mult(mult(unit, b), c)) <=> (mult(mult(unit, b), c) = mult(mult(unit, c), b))),
% 0.20/0.51 inference(commutativity,[status(thm)],[])).
% 0.20/0.51 tff(128,assumption,(~(mult(unit, mult(c, b)) = mult(unit, mult(b, c)))), introduced(assumption)).
% 0.20/0.51 tff(129,plain,
% 0.20/0.51 (((~(mult(mult(unit, c), b) = mult(mult(unit, b), c))) | (~(mult(unit, mult(c, b)) = mult(unit, mult(b, c))))) | (mult(unit, mult(c, b)) = mult(unit, mult(b, c)))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(130,plain,
% 0.20/0.51 ((~(mult(mult(unit, c), b) = mult(mult(unit, b), c))) | (~(mult(unit, mult(c, b)) = mult(unit, mult(b, c))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[129, 128])).
% 0.20/0.51 tff(131,plain,
% 0.20/0.51 (((~![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(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(mult(unit, c), b) = mult(mult(unit, b), c))) | (~(mult(unit, mult(c, b)) = mult(unit, mult(b, c)))))) | (~((~(mult(mult(unit, c), b) = mult(unit, mult(b, c)))) | (~(mult(mult(unit, b), c) = mult(unit, 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(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | (~((~(mult(mult(unit, c), b) = mult(mult(unit, b), c))) | (~(mult(unit, mult(c, b)) = mult(unit, mult(b, c)))))) | (~((~(mult(mult(unit, c), b) = mult(unit, mult(b, c)))) | (~(mult(mult(unit, b), c) = mult(unit, mult(c, b)))))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(132,plain,
% 0.20/0.51 ((~![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(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(mult(unit, c), b) = mult(mult(unit, b), c))) | (~(mult(unit, mult(c, b)) = mult(unit, mult(b, c)))))) | (~((~(mult(mult(unit, c), b) = mult(unit, mult(b, c)))) | (~(mult(mult(unit, b), c) = mult(unit, mult(c, b)))))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(133,plain,
% 0.20/0.52 ((~![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(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | (~((~(mult(mult(unit, c), b) = mult(mult(unit, b), c))) | (~(mult(unit, mult(c, b)) = mult(unit, mult(b, c)))))) | (~((~(mult(mult(unit, c), b) = mult(unit, mult(b, c)))) | (~(mult(mult(unit, b), c) = mult(unit, mult(c, b))))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.20/0.52 tff(134,plain,
% 0.20/0.52 ((~((~(mult(mult(unit, c), b) = mult(mult(unit, b), c))) | (~(mult(unit, mult(c, b)) = mult(unit, mult(b, c)))))) | (~((~(mult(mult(unit, c), b) = mult(unit, mult(b, c)))) | (~(mult(mult(unit, b), c) = mult(unit, mult(c, b))))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[133, 29])).
% 0.20/0.52 tff(135,plain,
% 0.20/0.52 (~((~(mult(mult(unit, c), b) = mult(unit, mult(b, c)))) | (~(mult(mult(unit, b), c) = mult(unit, mult(c, b)))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[134, 130])).
% 0.20/0.52 tff(136,plain,
% 0.20/0.52 (((~(mult(mult(unit, c), b) = mult(unit, mult(b, c)))) | (~(mult(mult(unit, b), c) = mult(unit, mult(c, b))))) | (mult(mult(unit, b), c) = mult(unit, mult(c, b)))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(137,plain,
% 0.20/0.52 (mult(mult(unit, b), c) = mult(unit, mult(c, b))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[136, 135])).
% 0.20/0.52 tff(138,plain,
% 0.20/0.52 (mult(unit, mult(c, b)) = mult(mult(unit, b), c)),
% 0.20/0.52 inference(symmetry,[status(thm)],[137])).
% 0.20/0.52 tff(139,plain,
% 0.20/0.52 (((~(mult(mult(unit, c), b) = mult(unit, mult(b, c)))) | (~(mult(mult(unit, b), c) = mult(unit, mult(c, b))))) | (mult(mult(unit, c), b) = mult(unit, mult(b, c)))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(140,plain,
% 0.20/0.52 (mult(mult(unit, c), b) = mult(unit, mult(b, c))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[139, 135])).
% 0.20/0.52 tff(141,plain,
% 0.20/0.52 (mult(unit, mult(b, c)) = mult(mult(unit, c), b)),
% 0.20/0.52 inference(symmetry,[status(thm)],[140])).
% 0.20/0.52 tff(142,plain,
% 0.20/0.52 ((mult(unit, mult(b, c)) = mult(unit, mult(c, b))) <=> (mult(mult(unit, c), b) = mult(mult(unit, b), c))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[141, 138])).
% 0.20/0.52 tff(143,plain,
% 0.20/0.52 ((mult(unit, mult(b, c)) = mult(unit, mult(c, b))) <=> (mult(mult(unit, b), c) = mult(mult(unit, c), b))),
% 0.20/0.52 inference(transitivity,[status(thm)],[142, 127])).
% 0.20/0.52 tff(144,plain,
% 0.20/0.52 ((mult(mult(unit, b), c) = mult(mult(unit, c), b)) <=> (mult(unit, mult(b, c)) = mult(unit, mult(c, b)))),
% 0.20/0.52 inference(symmetry,[status(thm)],[143])).
% 0.20/0.52 tff(145,plain,
% 0.20/0.52 ((mult(mult(unit, b), c) = mult(mult(unit, c), b)) <=> (mult(unit, mult(c, b)) = mult(unit, mult(b, c)))),
% 0.20/0.52 inference(transitivity,[status(thm)],[144, 126])).
% 0.20/0.52 tff(146,plain,
% 0.20/0.52 ((~![A: $i] : (mult(unit, A) = A)) | (mult(unit, c) = c)),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(147,plain,
% 0.20/0.52 (mult(unit, c) = c),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[146, 108])).
% 0.20/0.52 tff(148,plain,
% 0.20/0.52 (mult(mult(unit, c), b) = mult(c, b)),
% 0.20/0.52 inference(monotonicity,[status(thm)],[147])).
% 0.20/0.52 tff(149,plain,
% 0.20/0.52 (mult(c, b) = mult(mult(unit, c), b)),
% 0.20/0.52 inference(symmetry,[status(thm)],[148])).
% 0.20/0.52 tff(150,plain,
% 0.20/0.52 ((~![A: $i] : (mult(unit, A) = A)) | (mult(unit, mult(c, b)) = mult(c, b))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(151,plain,
% 0.20/0.52 (mult(unit, mult(c, b)) = mult(c, b)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[150, 108])).
% 0.20/0.52 tff(152,plain,
% 0.20/0.52 (mult(mult(unit, b), c) = mult(mult(unit, c), b)),
% 0.20/0.52 inference(transitivity,[status(thm)],[137, 151, 149])).
% 0.20/0.52 tff(153,plain,
% 0.20/0.52 (mult(unit, mult(c, b)) = mult(unit, mult(b, c))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[152, 145])).
% 0.20/0.52 tff(154,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[128, 153])).
% 0.20/0.52 tff(155,plain,(mult(unit, mult(c, b)) = mult(unit, mult(b, c))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(156,plain,
% 0.20/0.52 (mult(c, b) = mult(unit, mult(c, b))),
% 0.20/0.52 inference(symmetry,[status(thm)],[151])).
% 0.20/0.52 tff(157,plain,
% 0.20/0.52 (mult(c, b) = mult(b, c)),
% 0.20/0.52 inference(transitivity,[status(thm)],[156, 155, 124])).
% 0.20/0.52 tff(158,plain,
% 0.20/0.52 (mult(a, mult(c, b)) = mult(a, mult(b, c))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[157])).
% 0.20/0.52 tff(159,plain,
% 0.20/0.52 (mult(a, mult(b, c)) = mult(a, mult(c, b))),
% 0.20/0.52 inference(symmetry,[status(thm)],[158])).
% 0.20/0.52 tff(160,plain,
% 0.20/0.52 ((mult(mult(a, b), c) = mult(a, mult(b, c))) <=> (mult(mult(a, b), c) = mult(a, mult(c, b)))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[159])).
% 0.20/0.52 tff(161,plain,
% 0.20/0.52 ((~(mult(mult(a, b), c) = mult(a, mult(b, c)))) <=> (~(mult(mult(a, b), c) = mult(a, mult(c, b))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[160])).
% 0.20/0.52 tff(162,plain,
% 0.20/0.52 ((~(mult(mult(a, b), c) = mult(a, mult(b, c)))) <=> (~(mult(mult(a, b), c) = mult(a, mult(b, c))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(163,axiom,(~(mult(mult(a, b), c) = mult(a, mult(b, c)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goals')).
% 0.20/0.52 tff(164,plain,
% 0.20/0.52 (~(mult(mult(a, b), c) = mult(a, mult(b, c)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[163, 162])).
% 0.20/0.52 tff(165,plain,
% 0.20/0.52 (~(mult(mult(a, b), c) = mult(a, mult(c, b)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[164, 161])).
% 0.20/0.52 tff(166,plain,
% 0.20/0.52 (((~(mult(mult(a, c), b) = mult(a, mult(b, c)))) | (~(mult(mult(a, b), c) = mult(a, mult(c, b))))) | (mult(mult(a, b), c) = mult(a, mult(c, b)))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(167,plain,
% 0.20/0.52 ((~(mult(mult(a, c), b) = mult(a, mult(b, c)))) | (~(mult(mult(a, b), c) = mult(a, mult(c, b))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[166, 165])).
% 0.20/0.52 tff(168,plain,
% 0.20/0.52 (((~![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(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(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(b, c)))) | (~(mult(mult(a, b), c) = 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(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | (~((~(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(b, c)))) | (~(mult(mult(a, b), c) = mult(a, mult(c, b)))))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(169,plain,
% 0.20/0.52 ((~![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(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(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(b, c)))) | (~(mult(mult(a, b), c) = mult(a, mult(c, b)))))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(170,plain,
% 0.20/0.52 ((~![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(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | (~((~(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(b, c)))) | (~(mult(mult(a, b), c) = mult(a, mult(c, b))))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[169, 168])).
% 0.20/0.52 tff(171,plain,
% 0.20/0.52 ((~((~(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(b, c)))) | (~(mult(mult(a, b), c) = mult(a, mult(c, b))))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[170, 29])).
% 0.20/0.52 tff(172,plain,
% 0.20/0.52 (~((~(mult(mult(a, c), b) = mult(mult(a, b), c))) | (~(mult(a, mult(c, b)) = mult(a, mult(b, c)))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[171, 167])).
% 0.20/0.52 tff(173,plain,
% 0.20/0.52 (((~(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))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(174,plain,
% 0.20/0.52 (mult(mult(a, c), b) = mult(mult(a, b), c)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[173, 172])).
% 0.20/0.52 tff(175,plain,
% 0.20/0.52 (mult(mult(a, b), c) = mult(mult(a, c), b)),
% 0.20/0.52 inference(symmetry,[status(thm)],[174])).
% 0.20/0.52 tff(176,plain,
% 0.20/0.52 (mult(mult(mult(a, b), c), c) = mult(mult(mult(a, c), b), c)),
% 0.20/0.52 inference(monotonicity,[status(thm)],[175])).
% 0.20/0.52 tff(177,plain,
% 0.20/0.52 (mult(mult(mult(a, c), b), c) = mult(mult(mult(a, b), c), c)),
% 0.20/0.52 inference(symmetry,[status(thm)],[176])).
% 0.20/0.52 tff(178,plain,
% 0.20/0.52 ((~![A: $i] : (mult(unit, A) = A)) | (mult(unit, mult(mult(mult(a, c), b), c)) = mult(mult(mult(a, c), b), c))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(179,plain,
% 0.20/0.52 (mult(unit, mult(mult(mult(a, c), b), c)) = mult(mult(mult(a, c), b), c)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[178, 108])).
% 0.20/0.52 tff(180,plain,
% 0.20/0.52 ((~![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)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(181,plain,
% 0.20/0.52 (mult(mult(mult(a, c), b), c) = mult(a, mult(mult(c, b), c))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[180, 50])).
% 0.20/0.52 tff(182,plain,
% 0.20/0.52 (mult(a, mult(mult(c, b), c)) = mult(mult(mult(a, c), b), c)),
% 0.20/0.52 inference(symmetry,[status(thm)],[181])).
% 0.20/0.52 tff(183,plain,
% 0.20/0.52 (mult(mult(c, b), c) = mult(mult(b, c), c)),
% 0.20/0.52 inference(monotonicity,[status(thm)],[157])).
% 0.20/0.52 tff(184,plain,
% 0.20/0.52 (mult(mult(b, c), c) = mult(mult(c, b), c)),
% 0.20/0.52 inference(symmetry,[status(thm)],[183])).
% 0.20/0.52 tff(185,plain,
% 0.20/0.52 (mult(a, mult(mult(b, c), c)) = mult(a, mult(mult(c, b), c))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[184])).
% 0.20/0.52 tff(186,plain,
% 0.20/0.52 (mult(a, mult(mult(b, c), c)) = mult(mult(mult(a, c), b), c)),
% 0.20/0.52 inference(transitivity,[status(thm)],[185, 182])).
% 0.20/0.52 tff(187,plain,
% 0.20/0.52 (mult(unit, mult(a, mult(mult(b, c), c))) = mult(unit, mult(mult(mult(a, c), b), c))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[186])).
% 0.20/0.52 tff(188,plain,
% 0.20/0.52 (mult(a, mult(mult(c, b), c)) = mult(a, mult(mult(b, c), c))),
% 0.20/0.52 inference(symmetry,[status(thm)],[185])).
% 0.20/0.52 tff(189,plain,
% 0.20/0.52 ((mult(mult(mult(a, c), b), c) = mult(mult(mult(a, c), c), b)) <=> (mult(mult(mult(a, c), c), b) = mult(mult(mult(a, c), b), c))),
% 0.20/0.52 inference(commutativity,[status(thm)],[])).
% 0.20/0.52 tff(190,assumption,(~(mult(mult(mult(a, c), c), b) = mult(mult(mult(a, c), b), c))), introduced(assumption)).
% 0.20/0.52 tff(191,plain,
% 0.20/0.52 (((~(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)))) | (mult(mult(mult(a, c), c), b) = mult(mult(mult(a, c), b), c))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(192,plain,
% 0.20/0.52 ((~(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)))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[191, 190])).
% 0.20/0.52 tff(193,plain,
% 0.20/0.52 (((~![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(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(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))))) | (~((~(mult(mult(mult(a, c), b), c) = mult(mult(a, c), mult(c, b)))) | (~(mult(mult(mult(a, c), c), b) = 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(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | (~((~(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))))) | (~((~(mult(mult(mult(a, c), b), c) = mult(mult(a, c), mult(c, b)))) | (~(mult(mult(mult(a, c), c), b) = mult(mult(a, c), mult(b, c)))))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(194,plain,
% 0.20/0.52 (((~((~(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(b, c)))) | (~(mult(mult(mult(a, c), b), c) = mult(mult(a, c), mult(c, b))))))) <=> ((~((~(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))))) | (~((~(mult(mult(mult(a, c), b), c) = mult(mult(a, c), mult(c, b)))) | (~(mult(mult(mult(a, c), c), b) = mult(mult(a, c), mult(b, c)))))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(195,plain,
% 0.20/0.52 (((~![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(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(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(b, c)))) | (~(mult(mult(mult(a, c), b), c) = mult(mult(a, c), 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(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(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))))) | (~((~(mult(mult(mult(a, c), b), c) = mult(mult(a, c), mult(c, b)))) | (~(mult(mult(mult(a, c), c), b) = mult(mult(a, c), mult(b, c))))))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[194])).
% 0.20/0.52 tff(196,plain,
% 0.20/0.52 (((~![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(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(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(b, c)))) | (~(mult(mult(mult(a, c), b), c) = mult(mult(a, c), 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(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | (~((~(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))))) | (~((~(mult(mult(mult(a, c), b), c) = mult(mult(a, c), mult(c, b)))) | (~(mult(mult(mult(a, c), c), b) = mult(mult(a, c), mult(b, c)))))))),
% 0.20/0.52 inference(transitivity,[status(thm)],[195, 193])).
% 0.20/0.52 tff(197,plain,
% 0.20/0.52 ((~![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(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(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(b, c)))) | (~(mult(mult(mult(a, c), b), c) = mult(mult(a, c), mult(c, b)))))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(198,plain,
% 0.20/0.52 ((~![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(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | (~((~(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))))) | (~((~(mult(mult(mult(a, c), b), c) = mult(mult(a, c), mult(c, b)))) | (~(mult(mult(mult(a, c), c), b) = mult(mult(a, c), mult(b, c))))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[197, 196])).
% 0.20/0.53 tff(199,plain,
% 0.20/0.53 ((~((~(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))))) | (~((~(mult(mult(mult(a, c), b), c) = mult(mult(a, c), mult(c, b)))) | (~(mult(mult(mult(a, c), c), b) = mult(mult(a, c), mult(b, c))))))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[198, 29])).
% 0.20/0.53 tff(200,plain,
% 0.20/0.53 (~((~(mult(mult(mult(a, c), b), c) = mult(mult(a, c), mult(c, b)))) | (~(mult(mult(mult(a, c), c), b) = mult(mult(a, c), mult(b, c)))))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[199, 192])).
% 0.20/0.53 tff(201,plain,
% 0.20/0.53 (((~(mult(mult(mult(a, c), b), c) = mult(mult(a, c), mult(c, b)))) | (~(mult(mult(mult(a, c), c), b) = mult(mult(a, c), mult(b, c))))) | (mult(mult(mult(a, c), c), b) = mult(mult(a, c), mult(b, c)))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(202,plain,
% 0.20/0.53 (mult(mult(mult(a, c), c), b) = mult(mult(a, c), mult(b, c))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[201, 200])).
% 0.20/0.53 tff(203,plain,
% 0.20/0.53 (mult(mult(a, c), mult(b, c)) = mult(mult(mult(a, c), c), b)),
% 0.20/0.53 inference(symmetry,[status(thm)],[202])).
% 0.20/0.53 tff(204,plain,
% 0.20/0.53 (mult(mult(a, c), mult(c, b)) = mult(mult(a, c), mult(b, c))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[157])).
% 0.20/0.53 tff(205,plain,
% 0.20/0.53 (mult(mult(a, c), mult(c, b)) = mult(mult(mult(a, c), c), b)),
% 0.20/0.53 inference(transitivity,[status(thm)],[204, 203])).
% 0.20/0.53 tff(206,plain,
% 0.20/0.53 ((mult(mult(mult(a, c), b), c) = mult(mult(a, c), mult(c, b))) <=> (mult(mult(mult(a, c), b), c) = mult(mult(mult(a, c), c), b))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[205])).
% 0.20/0.53 tff(207,plain,
% 0.20/0.53 ((mult(mult(mult(a, c), b), c) = mult(mult(a, c), mult(c, b))) <=> (mult(mult(mult(a, c), c), b) = mult(mult(mult(a, c), b), c))),
% 0.20/0.53 inference(transitivity,[status(thm)],[206, 189])).
% 0.20/0.53 tff(208,plain,
% 0.20/0.53 ((mult(mult(mult(a, c), c), b) = mult(mult(mult(a, c), b), c)) <=> (mult(mult(mult(a, c), b), c) = mult(mult(a, c), mult(c, b)))),
% 0.20/0.53 inference(symmetry,[status(thm)],[207])).
% 0.20/0.53 tff(209,plain,
% 0.20/0.53 ((~(mult(mult(mult(a, c), c), b) = mult(mult(mult(a, c), b), c))) <=> (~(mult(mult(mult(a, c), b), c) = mult(mult(a, c), mult(c, b))))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[208])).
% 0.20/0.53 tff(210,plain,
% 0.20/0.53 (~(mult(mult(mult(a, c), b), c) = mult(mult(a, c), mult(c, b)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[190, 209])).
% 0.20/0.53 tff(211,plain,
% 0.20/0.53 (((~(mult(mult(mult(a, c), b), c) = mult(mult(a, c), mult(c, b)))) | (~(mult(mult(mult(a, c), c), b) = mult(mult(a, c), mult(b, c))))) | (mult(mult(mult(a, c), b), c) = mult(mult(a, c), mult(c, b)))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(212,plain,
% 0.20/0.53 (mult(mult(mult(a, c), b), c) = mult(mult(a, c), mult(c, b))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[211, 200])).
% 0.20/0.53 tff(213,plain,
% 0.20/0.53 ($false),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[212, 210])).
% 0.20/0.53 tff(214,plain,(mult(mult(mult(a, c), c), b) = mult(mult(mult(a, c), b), c)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.53 tff(215,plain,
% 0.20/0.53 (mult(mult(mult(a, c), c), b) = mult(a, mult(mult(b, c), c))),
% 0.20/0.53 inference(transitivity,[status(thm)],[214, 181, 188])).
% 0.20/0.53 tff(216,plain,
% 0.20/0.53 (mult(unit, mult(mult(mult(a, c), c), b)) = mult(unit, mult(a, mult(mult(b, c), c)))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[215])).
% 0.20/0.53 tff(217,assumption,(mult(mult(unit, b), mult(mult(a, c), c)) = mult(unit, mult(mult(mult(a, c), c), b))), introduced(assumption)).
% 0.20/0.53 tff(218,plain,
% 0.20/0.53 (mult(c, a) = ld(mult(b, a), mult(mult(b, a), mult(c, a)))),
% 0.20/0.53 inference(symmetry,[status(thm)],[64])).
% 0.20/0.53 tff(219,plain,
% 0.20/0.53 (mult(c, a) = mult(a, c)),
% 0.20/0.53 inference(transitivity,[status(thm)],[218, 67, 70])).
% 0.20/0.53 tff(220,plain,
% 0.20/0.53 (mult(mult(c, a), c) = mult(mult(a, c), c)),
% 0.20/0.53 inference(monotonicity,[status(thm)],[219])).
% 0.20/0.53 tff(221,plain,
% 0.20/0.53 ((~![A: $i] : (mult(unit, A) = A)) | (mult(unit, b) = b)),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(222,plain,
% 0.20/0.53 (mult(unit, b) = b),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[221, 108])).
% 0.20/0.53 tff(223,plain,
% 0.20/0.53 (b = mult(unit, b)),
% 0.20/0.53 inference(symmetry,[status(thm)],[222])).
% 0.20/0.53 tff(224,plain,
% 0.20/0.53 (mult(b, mult(mult(c, a), c)) = mult(mult(unit, b), mult(mult(a, c), c))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[223, 220])).
% 0.20/0.53 tff(225,plain,
% 0.20/0.53 ((~![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)))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(226,plain,
% 0.20/0.53 (mult(mult(mult(b, c), a), c) = mult(b, mult(mult(c, a), c))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[225, 50])).
% 0.20/0.53 tff(227,assumption,(mult(mult(b, c), a) = mult(mult(b, a), c)), introduced(assumption)).
% 0.20/0.53 tff(228,plain,
% 0.20/0.53 (mult(mult(b, a), c) = mult(mult(b, c), a)),
% 0.20/0.53 inference(symmetry,[status(thm)],[227])).
% 0.20/0.53 tff(229,plain,
% 0.20/0.53 (mult(mult(mult(b, a), c), c) = mult(mult(mult(b, c), a), c)),
% 0.20/0.53 inference(monotonicity,[status(thm)],[228])).
% 0.20/0.53 tff(230,plain,
% 0.20/0.53 (mult(mult(mult(b, a), c), c) = mult(mult(mult(a, b), c), c)),
% 0.20/0.53 inference(transitivity,[status(thm)],[229, 226, 224, 217, 216, 187, 179, 177])).
% 0.20/0.53 tff(231,plain,
% 0.20/0.53 (rd(mult(mult(mult(b, a), c), c), c) = rd(mult(mult(mult(a, b), c), c), c)),
% 0.20/0.53 inference(monotonicity,[status(thm)],[230])).
% 0.20/0.53 tff(232,plain,
% 0.20/0.53 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(b, a), c), c), c) = mult(mult(b, a), c))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(233,plain,
% 0.20/0.53 (rd(mult(mult(mult(b, a), c), c), c) = mult(mult(b, a), c)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[232, 120])).
% 0.20/0.53 tff(234,plain,
% 0.20/0.53 (mult(mult(b, a), c) = rd(mult(mult(mult(b, a), c), c), c)),
% 0.20/0.53 inference(symmetry,[status(thm)],[233])).
% 0.20/0.53 tff(235,plain,
% 0.20/0.53 (mult(mult(unit, mult(b, c)), a) = mult(mult(b, c), a)),
% 0.20/0.53 inference(monotonicity,[status(thm)],[124])).
% 0.20/0.53 tff(236,plain,
% 0.20/0.53 (mult(mult(unit, mult(b, c)), a) = mult(mult(a, b), c)),
% 0.20/0.53 inference(transitivity,[status(thm)],[235, 227, 234, 231, 122])).
% 0.20/0.53 tff(237,plain,
% 0.20/0.53 ((mult(mult(unit, mult(b, c)), a) = mult(mult(unit, a), mult(b, c))) <=> (mult(mult(a, b), c) = mult(a, mult(b, c)))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[236, 113])).
% 0.20/0.53 tff(238,plain,
% 0.20/0.53 ((mult(mult(a, b), c) = mult(a, mult(b, c))) <=> (mult(mult(unit, mult(b, c)), a) = mult(mult(unit, a), mult(b, c)))),
% 0.20/0.53 inference(symmetry,[status(thm)],[237])).
% 0.20/0.53 tff(239,plain,
% 0.20/0.53 ((~(mult(mult(a, b), c) = mult(a, mult(b, c)))) <=> (~(mult(mult(unit, mult(b, c)), a) = mult(mult(unit, a), mult(b, c))))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[238])).
% 0.20/0.53 tff(240,plain,
% 0.20/0.53 (~(mult(mult(unit, mult(b, c)), a) = mult(mult(unit, a), mult(b, c)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[164, 239])).
% 0.20/0.53 tff(241,plain,
% 0.20/0.53 (((~(mult(mult(unit, mult(b, c)), a) = mult(mult(unit, a), mult(b, c)))) | (~(mult(unit, mult(mult(b, c), a)) = mult(unit, mult(a, mult(b, c)))))) | (mult(mult(unit, mult(b, c)), a) = mult(mult(unit, a), mult(b, c)))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(242,plain,
% 0.20/0.53 ((~(mult(mult(unit, mult(b, c)), a) = mult(mult(unit, a), mult(b, c)))) | (~(mult(unit, mult(mult(b, c), a)) = mult(unit, mult(a, mult(b, c)))))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[241, 240])).
% 0.20/0.53 tff(243,plain,
% 0.20/0.53 (((~![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(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(mult(unit, mult(b, c)), a) = mult(mult(unit, a), mult(b, c)))) | (~(mult(unit, mult(mult(b, c), a)) = mult(unit, mult(a, mult(b, c))))))) | (~((~(mult(mult(unit, mult(b, c)), a) = mult(unit, mult(a, mult(b, c))))) | (~(mult(mult(unit, a), mult(b, c)) = mult(unit, 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(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | (~((~(mult(mult(unit, mult(b, c)), a) = mult(mult(unit, a), mult(b, c)))) | (~(mult(unit, mult(mult(b, c), a)) = mult(unit, mult(a, mult(b, c))))))) | (~((~(mult(mult(unit, mult(b, c)), a) = mult(unit, mult(a, mult(b, c))))) | (~(mult(mult(unit, a), mult(b, c)) = mult(unit, mult(mult(b, c), a)))))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(244,plain,
% 0.20/0.53 ((~![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(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(mult(unit, mult(b, c)), a) = mult(mult(unit, a), mult(b, c)))) | (~(mult(unit, mult(mult(b, c), a)) = mult(unit, mult(a, mult(b, c))))))) | (~((~(mult(mult(unit, mult(b, c)), a) = mult(unit, mult(a, mult(b, c))))) | (~(mult(mult(unit, a), mult(b, c)) = mult(unit, mult(mult(b, c), a)))))))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(245,plain,
% 0.20/0.53 ((~![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(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | (~((~(mult(mult(unit, mult(b, c)), a) = mult(mult(unit, a), mult(b, c)))) | (~(mult(unit, mult(mult(b, c), a)) = mult(unit, mult(a, mult(b, c))))))) | (~((~(mult(mult(unit, mult(b, c)), a) = mult(unit, mult(a, mult(b, c))))) | (~(mult(mult(unit, a), mult(b, c)) = mult(unit, mult(mult(b, c), a))))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[244, 243])).
% 0.20/0.53 tff(246,plain,
% 0.20/0.53 ((~((~(mult(mult(unit, mult(b, c)), a) = mult(mult(unit, a), mult(b, c)))) | (~(mult(unit, mult(mult(b, c), a)) = mult(unit, mult(a, mult(b, c))))))) | (~((~(mult(mult(unit, mult(b, c)), a) = mult(unit, mult(a, mult(b, c))))) | (~(mult(mult(unit, a), mult(b, c)) = mult(unit, mult(mult(b, c), a))))))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[245, 29])).
% 0.20/0.53 tff(247,plain,
% 0.20/0.53 (~((~(mult(mult(unit, mult(b, c)), a) = mult(unit, mult(a, mult(b, c))))) | (~(mult(mult(unit, a), mult(b, c)) = mult(unit, mult(mult(b, c), a)))))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[246, 242])).
% 0.20/0.53 tff(248,plain,
% 0.20/0.53 (((~(mult(mult(unit, mult(b, c)), a) = mult(unit, mult(a, mult(b, c))))) | (~(mult(mult(unit, a), mult(b, c)) = mult(unit, mult(mult(b, c), a))))) | (mult(mult(unit, a), mult(b, c)) = mult(unit, mult(mult(b, c), a)))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(249,plain,
% 0.20/0.53 (mult(mult(unit, a), mult(b, c)) = mult(unit, mult(mult(b, c), a))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[248, 247])).
% 0.20/0.53 tff(250,plain,
% 0.20/0.53 (mult(unit, mult(mult(b, c), a)) = mult(mult(unit, a), mult(b, c))),
% 0.20/0.53 inference(symmetry,[status(thm)],[249])).
% 0.20/0.53 tff(251,plain,
% 0.20/0.53 (^[A: $i] : refl((mult(A, unit) = A) <=> (mult(A, unit) = A))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(252,plain,
% 0.20/0.53 (![A: $i] : (mult(A, unit) = A) <=> ![A: $i] : (mult(A, unit) = A)),
% 0.20/0.53 inference(quant_intro,[status(thm)],[251])).
% 0.20/0.53 tff(253,plain,
% 0.20/0.53 (![A: $i] : (mult(A, unit) = A) <=> ![A: $i] : (mult(A, unit) = A)),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(254,axiom,(![A: $i] : (mult(A, unit) = A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','f05')).
% 0.20/0.53 tff(255,plain,
% 0.20/0.53 (![A: $i] : (mult(A, unit) = A)),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[254, 253])).
% 0.20/0.53 tff(256,plain,(
% 0.20/0.53 ![A: $i] : (mult(A, unit) = A)),
% 0.20/0.53 inference(skolemize,[status(sab)],[255])).
% 0.20/0.53 tff(257,plain,
% 0.20/0.53 (![A: $i] : (mult(A, unit) = A)),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[256, 252])).
% 0.20/0.53 tff(258,plain,
% 0.20/0.53 ((~![A: $i] : (mult(A, unit) = A)) | (mult(mult(unit, ld(b, mult(mult(a, b), c))), unit) = mult(unit, ld(b, mult(mult(a, b), c))))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(259,plain,
% 0.20/0.53 (mult(mult(unit, ld(b, mult(mult(a, b), c))), unit) = mult(unit, ld(b, mult(mult(a, b), c)))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[258, 257])).
% 0.20/0.53 tff(260,plain,
% 0.20/0.53 (mult(unit, ld(b, mult(mult(a, b), c))) = mult(mult(unit, ld(b, mult(mult(a, b), c))), unit)),
% 0.20/0.54 inference(symmetry,[status(thm)],[259])).
% 0.20/0.54 tff(261,plain,
% 0.20/0.54 (mult(b, mult(unit, ld(b, mult(mult(a, b), c)))) = mult(b, mult(mult(unit, ld(b, mult(mult(a, b), c))), unit))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[260])).
% 0.20/0.54 tff(262,plain,
% 0.20/0.54 (mult(b, mult(mult(unit, ld(b, mult(mult(a, b), c))), unit)) = mult(b, mult(unit, ld(b, mult(mult(a, b), c))))),
% 0.20/0.54 inference(symmetry,[status(thm)],[261])).
% 0.20/0.54 tff(263,plain,
% 0.20/0.54 ((~![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), ld(b, mult(mult(a, b), c))), unit) = mult(b, mult(mult(unit, ld(b, mult(mult(a, b), c))), unit)))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(264,plain,
% 0.20/0.54 (mult(mult(mult(b, unit), ld(b, mult(mult(a, b), c))), unit) = mult(b, mult(mult(unit, ld(b, mult(mult(a, b), c))), unit))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[263, 50])).
% 0.20/0.54 tff(265,plain,
% 0.20/0.54 (^[B: $i, A: $i] : refl((mult(A, ld(A, B)) = B) <=> (mult(A, ld(A, B)) = B))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(266,plain,
% 0.20/0.54 (![B: $i, A: $i] : (mult(A, ld(A, B)) = B) <=> ![B: $i, A: $i] : (mult(A, ld(A, B)) = B)),
% 0.20/0.54 inference(quant_intro,[status(thm)],[265])).
% 0.20/0.54 tff(267,plain,
% 0.20/0.54 (![B: $i, A: $i] : (mult(A, ld(A, B)) = B) <=> ![B: $i, A: $i] : (mult(A, ld(A, B)) = B)),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(268,axiom,(![B: $i, A: $i] : (mult(A, ld(A, B)) = B)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','f01')).
% 0.20/0.54 tff(269,plain,
% 0.20/0.54 (![B: $i, A: $i] : (mult(A, ld(A, B)) = B)),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[268, 267])).
% 0.20/0.54 tff(270,plain,(
% 0.20/0.54 ![B: $i, A: $i] : (mult(A, ld(A, B)) = B)),
% 0.20/0.54 inference(skolemize,[status(sab)],[269])).
% 0.20/0.54 tff(271,plain,
% 0.20/0.54 (![B: $i, A: $i] : (mult(A, ld(A, B)) = B)),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[270, 266])).
% 0.20/0.54 tff(272,plain,
% 0.20/0.54 ((~![B: $i, A: $i] : (mult(A, ld(A, B)) = B)) | (mult(b, ld(b, mult(mult(a, b), c))) = mult(mult(a, b), c))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(273,plain,
% 0.20/0.54 (mult(b, ld(b, mult(mult(a, b), c))) = mult(mult(a, b), c)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[272, 271])).
% 0.20/0.54 tff(274,plain,
% 0.20/0.54 ((~![A: $i] : (mult(A, unit) = A)) | (mult(b, unit) = b)),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(275,plain,
% 0.20/0.54 (mult(b, unit) = b),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[274, 257])).
% 0.20/0.54 tff(276,plain,
% 0.20/0.54 (mult(mult(b, unit), ld(b, mult(mult(a, b), c))) = mult(b, ld(b, mult(mult(a, b), c)))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[275])).
% 0.20/0.54 tff(277,plain,
% 0.20/0.54 (mult(mult(b, unit), ld(b, mult(mult(a, b), c))) = mult(mult(a, b), c)),
% 0.20/0.54 inference(transitivity,[status(thm)],[276, 273])).
% 0.20/0.54 tff(278,plain,
% 0.20/0.54 (mult(mult(mult(b, unit), ld(b, mult(mult(a, b), c))), unit) = mult(mult(mult(a, b), c), unit)),
% 0.20/0.54 inference(monotonicity,[status(thm)],[277])).
% 0.20/0.54 tff(279,plain,
% 0.20/0.54 (mult(mult(mult(a, b), c), unit) = mult(mult(mult(b, unit), ld(b, mult(mult(a, b), c))), unit)),
% 0.20/0.54 inference(symmetry,[status(thm)],[278])).
% 0.20/0.54 tff(280,plain,
% 0.20/0.54 ((~![A: $i] : (mult(A, unit) = A)) | (mult(mult(mult(a, b), c), unit) = mult(mult(a, b), c))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(281,plain,
% 0.20/0.54 (mult(mult(mult(a, b), c), unit) = mult(mult(a, b), c)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[280, 257])).
% 0.20/0.54 tff(282,plain,
% 0.20/0.54 (mult(mult(a, b), c) = mult(mult(mult(a, b), c), unit)),
% 0.20/0.54 inference(symmetry,[status(thm)],[281])).
% 0.20/0.54 tff(283,plain,
% 0.20/0.54 (mult(mult(b, c), a) = mult(b, mult(unit, ld(b, mult(mult(a, b), c))))),
% 0.20/0.54 inference(transitivity,[status(thm)],[227, 234, 231, 122, 282, 279, 264, 262])).
% 0.20/0.54 tff(284,plain,
% 0.20/0.54 (mult(unit, mult(mult(b, c), a)) = mult(unit, mult(b, mult(unit, ld(b, mult(mult(a, b), c)))))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[283])).
% 0.20/0.54 tff(285,plain,
% 0.20/0.54 (mult(unit, mult(b, mult(unit, ld(b, mult(mult(a, b), c))))) = mult(unit, mult(mult(b, c), a))),
% 0.20/0.54 inference(symmetry,[status(thm)],[284])).
% 0.20/0.54 tff(286,plain,
% 0.20/0.54 (mult(b, mult(mult(unit, ld(b, mult(mult(a, b), c))), unit)) = mult(mult(mult(b, unit), ld(b, mult(mult(a, b), c))), unit)),
% 0.20/0.54 inference(symmetry,[status(thm)],[264])).
% 0.20/0.54 tff(287,plain,
% 0.20/0.54 (mult(b, mult(unit, ld(b, mult(mult(a, b), c)))) = mult(mult(a, b), c)),
% 0.20/0.54 inference(transitivity,[status(thm)],[261, 286, 278, 281])).
% 0.20/0.54 tff(288,plain,
% 0.20/0.54 (mult(unit, mult(b, mult(unit, ld(b, mult(mult(a, b), c))))) = mult(unit, mult(mult(a, b), c))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[287])).
% 0.20/0.54 tff(289,plain,
% 0.20/0.54 (mult(unit, mult(mult(a, b), c)) = mult(unit, mult(b, mult(unit, ld(b, mult(mult(a, b), c)))))),
% 0.20/0.54 inference(symmetry,[status(thm)],[288])).
% 0.20/0.54 tff(290,plain,
% 0.20/0.54 ((~![A: $i] : (mult(unit, A) = A)) | (mult(unit, mult(mult(a, b), c)) = mult(mult(a, b), c))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(291,plain,
% 0.20/0.54 (mult(unit, mult(mult(a, b), c)) = mult(mult(a, b), c)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[290, 108])).
% 0.20/0.54 tff(292,plain,
% 0.20/0.54 (mult(mult(a, b), c) = mult(unit, mult(mult(a, b), c))),
% 0.20/0.54 inference(symmetry,[status(thm)],[291])).
% 0.20/0.54 tff(293,plain,
% 0.20/0.54 (mult(mult(a, b), c) = mult(a, mult(b, c))),
% 0.20/0.54 inference(transitivity,[status(thm)],[292, 289, 285, 250, 113])).
% 0.20/0.54 tff(294,plain,
% 0.20/0.54 ($false),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[164, 293])).
% 0.20/0.54 tff(295,plain,((~(mult(mult(unit, b), mult(mult(a, c), c)) = mult(unit, mult(mult(mult(a, c), c), b)))) | (~(mult(mult(b, c), a) = mult(mult(b, a), c))) | (~(mult(mult(b, a), mult(a, c)) = mult(mult(b, a), mult(c, a))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.54 tff(296,plain,
% 0.20/0.54 (~(mult(mult(unit, b), mult(mult(a, c), c)) = mult(unit, mult(mult(mult(a, c), c), b)))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[295, 101, 42])).
% 0.20/0.54 tff(297,plain,
% 0.20/0.54 (((~(mult(mult(unit, b), mult(mult(a, c), c)) = mult(unit, mult(mult(mult(a, c), c), b)))) | (~(mult(mult(unit, mult(mult(a, c), c)), b) = mult(unit, mult(b, mult(mult(a, c), c)))))) | (mult(mult(unit, b), mult(mult(a, c), c)) = mult(unit, mult(mult(mult(a, c), c), b)))),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(298,plain,
% 0.20/0.54 ((~(mult(mult(unit, b), mult(mult(a, c), c)) = mult(unit, mult(mult(mult(a, c), c), b)))) | (~(mult(mult(unit, mult(mult(a, c), c)), b) = mult(unit, mult(b, mult(mult(a, c), c)))))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[297, 296])).
% 0.20/0.54 tff(299,plain,
% 0.20/0.54 (((~![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(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(mult(unit, b), mult(mult(a, c), c)) = mult(mult(unit, mult(mult(a, c), c)), b))) | (~(mult(unit, mult(b, mult(mult(a, c), c))) = mult(unit, mult(mult(mult(a, c), c), b)))))) | (~((~(mult(mult(unit, b), mult(mult(a, c), c)) = mult(unit, mult(mult(mult(a, c), c), b)))) | (~(mult(mult(unit, mult(mult(a, c), c)), b) = mult(unit, 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(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | (~((~(mult(mult(unit, b), mult(mult(a, c), c)) = mult(mult(unit, mult(mult(a, c), c)), b))) | (~(mult(unit, mult(b, mult(mult(a, c), c))) = mult(unit, mult(mult(mult(a, c), c), b)))))) | (~((~(mult(mult(unit, b), mult(mult(a, c), c)) = mult(unit, mult(mult(mult(a, c), c), b)))) | (~(mult(mult(unit, mult(mult(a, c), c)), b) = mult(unit, mult(b, mult(mult(a, c), c))))))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(300,plain,
% 0.20/0.54 ((~![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(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(mult(unit, b), mult(mult(a, c), c)) = mult(mult(unit, mult(mult(a, c), c)), b))) | (~(mult(unit, mult(b, mult(mult(a, c), c))) = mult(unit, mult(mult(mult(a, c), c), b)))))) | (~((~(mult(mult(unit, b), mult(mult(a, c), c)) = mult(unit, mult(mult(mult(a, c), c), b)))) | (~(mult(mult(unit, mult(mult(a, c), c)), b) = mult(unit, mult(b, mult(mult(a, c), c))))))))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(301,plain,
% 0.20/0.54 ((~![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(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | (~((~(mult(mult(unit, b), mult(mult(a, c), c)) = mult(mult(unit, mult(mult(a, c), c)), b))) | (~(mult(unit, mult(b, mult(mult(a, c), c))) = mult(unit, mult(mult(mult(a, c), c), b)))))) | (~((~(mult(mult(unit, b), mult(mult(a, c), c)) = mult(unit, mult(mult(mult(a, c), c), b)))) | (~(mult(mult(unit, mult(mult(a, c), c)), b) = mult(unit, mult(b, mult(mult(a, c), c)))))))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[300, 299])).
% 0.20/0.54 tff(302,plain,
% 0.20/0.54 ((~((~(mult(mult(unit, b), mult(mult(a, c), c)) = mult(mult(unit, mult(mult(a, c), c)), b))) | (~(mult(unit, mult(b, mult(mult(a, c), c))) = mult(unit, mult(mult(mult(a, c), c), b)))))) | (~((~(mult(mult(unit, b), mult(mult(a, c), c)) = mult(unit, mult(mult(mult(a, c), c), b)))) | (~(mult(mult(unit, mult(mult(a, c), c)), b) = mult(unit, mult(b, mult(mult(a, c), c)))))))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[301, 29])).
% 0.20/0.54 tff(303,plain,
% 0.20/0.54 (~((~(mult(mult(unit, b), mult(mult(a, c), c)) = mult(mult(unit, mult(mult(a, c), c)), b))) | (~(mult(unit, mult(b, mult(mult(a, c), c))) = mult(unit, mult(mult(mult(a, c), c), b)))))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[302, 298])).
% 0.20/0.54 tff(304,plain,
% 0.20/0.54 (((~(mult(mult(unit, b), mult(mult(a, c), c)) = mult(mult(unit, mult(mult(a, c), c)), b))) | (~(mult(unit, mult(b, mult(mult(a, c), c))) = mult(unit, mult(mult(mult(a, c), c), b))))) | (mult(unit, mult(b, mult(mult(a, c), c))) = mult(unit, mult(mult(mult(a, c), c), b)))),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(305,plain,
% 0.20/0.54 (mult(unit, mult(b, mult(mult(a, c), c))) = mult(unit, mult(mult(mult(a, c), c), b))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[304, 303])).
% 0.20/0.54 tff(306,plain,
% 0.20/0.54 (mult(unit, mult(mult(mult(a, c), c), b)) = mult(unit, mult(b, mult(mult(a, c), c)))),
% 0.20/0.54 inference(symmetry,[status(thm)],[305])).
% 0.20/0.54 tff(307,plain,
% 0.20/0.54 (mult(unit, mult(a, mult(mult(b, c), c))) = mult(unit, mult(mult(mult(a, c), c), b))),
% 0.20/0.54 inference(symmetry,[status(thm)],[216])).
% 0.20/0.54 tff(308,plain,
% 0.20/0.54 (mult(unit, mult(mult(mult(a, c), b), c)) = mult(unit, mult(a, mult(mult(b, c), c)))),
% 0.20/0.54 inference(symmetry,[status(thm)],[187])).
% 0.20/0.54 tff(309,plain,
% 0.20/0.54 (mult(mult(mult(a, c), b), c) = mult(unit, mult(mult(mult(a, c), b), c))),
% 0.20/0.54 inference(symmetry,[status(thm)],[179])).
% 0.20/0.54 tff(310,plain,
% 0.20/0.54 (mult(mult(b, a), mult(c, a)) = mult(mult(b, a), mult(a, c))),
% 0.20/0.54 inference(symmetry,[status(thm)],[42])).
% 0.20/0.54 tff(311,plain,
% 0.20/0.54 (ld(mult(b, a), mult(mult(b, a), mult(c, a))) = ld(mult(b, a), mult(mult(b, a), mult(a, c)))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[310])).
% 0.20/0.54 tff(312,plain,
% 0.20/0.54 (mult(mult(unit, c), a) = mult(c, a)),
% 0.20/0.54 inference(monotonicity,[status(thm)],[147])).
% 0.20/0.54 tff(313,plain,
% 0.20/0.54 (mult(mult(unit, c), a) = mult(a, c)),
% 0.20/0.54 inference(transitivity,[status(thm)],[312, 218, 311, 70])).
% 0.20/0.54 tff(314,plain,
% 0.20/0.54 (mult(mult(mult(unit, c), a), c) = mult(mult(a, c), c)),
% 0.20/0.54 inference(monotonicity,[status(thm)],[313])).
% 0.20/0.54 tff(315,plain,
% 0.20/0.54 ((~![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)))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(316,plain,
% 0.20/0.54 (mult(mult(mult(unit, c), a), c) = mult(unit, mult(mult(c, a), c))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[315, 50])).
% 0.20/0.54 tff(317,plain,
% 0.20/0.54 (mult(unit, mult(mult(c, a), c)) = mult(mult(mult(unit, c), a), c)),
% 0.20/0.54 inference(symmetry,[status(thm)],[316])).
% 0.20/0.54 tff(318,plain,
% 0.20/0.54 (mult(c, a) = mult(a, c)),
% 0.20/0.54 inference(transitivity,[status(thm)],[218, 311, 70])).
% 0.20/0.54 tff(319,plain,
% 0.20/0.54 (mult(mult(c, a), c) = mult(mult(a, c), c)),
% 0.20/0.54 inference(monotonicity,[status(thm)],[318])).
% 0.20/0.54 tff(320,plain,
% 0.20/0.54 (mult(mult(a, c), c) = mult(mult(c, a), c)),
% 0.20/0.54 inference(symmetry,[status(thm)],[319])).
% 0.20/0.54 tff(321,plain,
% 0.20/0.54 ((~![A: $i] : (mult(A, unit) = A)) | (mult(c, unit) = c)),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(322,plain,
% 0.20/0.54 (mult(c, unit) = c),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[321, 257])).
% 0.20/0.54 tff(323,plain,
% 0.20/0.54 (mult(mult(unit, c), unit) = mult(c, unit)),
% 0.20/0.54 inference(monotonicity,[status(thm)],[147])).
% 0.20/0.54 tff(324,plain,
% 0.20/0.54 (mult(mult(unit, c), unit) = c),
% 0.20/0.54 inference(transitivity,[status(thm)],[323, 322])).
% 0.20/0.54 tff(325,plain,
% 0.20/0.54 (mult(a, mult(mult(unit, c), unit)) = mult(a, c)),
% 0.20/0.54 inference(monotonicity,[status(thm)],[324])).
% 0.20/0.54 tff(326,plain,
% 0.20/0.54 ((~![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)))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(327,plain,
% 0.20/0.54 (mult(mult(mult(a, unit), c), unit) = mult(a, mult(mult(unit, c), unit))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[326, 50])).
% 0.20/0.54 tff(328,plain,
% 0.20/0.54 ((~![A: $i] : (mult(A, unit) = A)) | (mult(mult(mult(a, unit), c), unit) = mult(mult(a, unit), c))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(329,plain,
% 0.20/0.54 (mult(mult(mult(a, unit), c), unit) = mult(mult(a, unit), c)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[328, 257])).
% 0.20/0.54 tff(330,plain,
% 0.20/0.54 (mult(a, mult(mult(unit, c), unit)) = mult(mult(mult(a, unit), c), unit)),
% 0.20/0.54 inference(symmetry,[status(thm)],[327])).
% 0.20/0.54 tff(331,plain,
% 0.20/0.54 (mult(a, c) = mult(a, mult(mult(unit, c), unit))),
% 0.20/0.54 inference(symmetry,[status(thm)],[325])).
% 0.20/0.54 tff(332,plain,
% 0.20/0.54 (mult(a, c) = mult(mult(a, unit), c)),
% 0.20/0.54 inference(transitivity,[status(thm)],[331, 330, 329])).
% 0.20/0.54 tff(333,plain,
% 0.20/0.54 (mult(mult(a, c), unit) = mult(mult(mult(a, unit), c), unit)),
% 0.20/0.54 inference(monotonicity,[status(thm)],[332])).
% 0.20/0.54 tff(334,plain,
% 0.20/0.54 (mult(mult(a, c), unit) = mult(a, c)),
% 0.20/0.54 inference(transitivity,[status(thm)],[333, 327, 325])).
% 0.20/0.54 tff(335,plain,
% 0.20/0.54 (mult(mult(mult(a, c), unit), c) = mult(mult(a, c), c)),
% 0.20/0.54 inference(monotonicity,[status(thm)],[334])).
% 0.20/0.54 tff(336,plain,
% 0.20/0.54 ((~![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)))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(337,plain,
% 0.20/0.54 (mult(mult(mult(a, c), unit), c) = mult(a, mult(mult(c, unit), c))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[336, 50])).
% 0.20/0.54 tff(338,plain,
% 0.20/0.54 (mult(a, mult(mult(c, unit), c)) = mult(mult(mult(a, c), unit), c)),
% 0.20/0.54 inference(symmetry,[status(thm)],[337])).
% 0.20/0.54 tff(339,plain,
% 0.20/0.54 (mult(a, mult(mult(c, unit), c)) = mult(mult(c, a), c)),
% 0.20/0.54 inference(transitivity,[status(thm)],[338, 335, 320])).
% 0.20/0.54 tff(340,plain,
% 0.20/0.54 (mult(unit, mult(a, mult(mult(c, unit), c))) = mult(unit, mult(mult(c, a), c))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[339])).
% 0.20/0.54 tff(341,plain,
% 0.20/0.54 (mult(mult(a, c), c) = mult(mult(mult(a, c), unit), c)),
% 0.20/0.54 inference(symmetry,[status(thm)],[335])).
% 0.20/0.54 tff(342,plain,
% 0.20/0.54 (mult(mult(a, c), c) = mult(a, mult(mult(c, unit), c))),
% 0.20/0.54 inference(transitivity,[status(thm)],[341, 337])).
% 0.20/0.54 tff(343,plain,
% 0.20/0.54 (mult(unit, mult(mult(a, c), c)) = mult(unit, mult(a, mult(mult(c, unit), c)))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[342])).
% 0.20/0.54 tff(344,plain,
% 0.20/0.54 (mult(unit, mult(mult(a, c), c)) = mult(mult(a, c), c)),
% 0.20/0.54 inference(transitivity,[status(thm)],[343, 340, 317, 314])).
% 0.20/0.54 tff(345,plain,
% 0.20/0.54 (mult(mult(unit, mult(mult(a, c), c)), b) = mult(mult(mult(a, c), c), b)),
% 0.20/0.54 inference(monotonicity,[status(thm)],[344])).
% 0.20/0.54 tff(346,plain,
% 0.20/0.54 (mult(mult(unit, mult(mult(a, c), c)), b) = mult(unit, mult(b, mult(mult(a, c), c)))),
% 0.20/0.54 inference(transitivity,[status(thm)],[345, 214, 309, 308, 307, 306])).
% 0.20/0.54 tff(347,plain,
% 0.20/0.54 (((~(mult(mult(unit, b), mult(mult(a, c), c)) = mult(mult(unit, mult(mult(a, c), c)), b))) | (~(mult(unit, mult(b, mult(mult(a, c), c))) = mult(unit, mult(mult(mult(a, c), c), b))))) | (mult(mult(unit, b), mult(mult(a, c), c)) = mult(mult(unit, mult(mult(a, c), c)), b))),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(348,plain,
% 0.20/0.54 (mult(mult(unit, b), mult(mult(a, c), c)) = mult(mult(unit, mult(mult(a, c), c)), b)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[347, 303])).
% 0.20/0.55 tff(349,plain,
% 0.20/0.55 ((mult(mult(unit, b), mult(mult(a, c), c)) = mult(unit, mult(mult(mult(a, c), c), b))) <=> (mult(mult(unit, mult(mult(a, c), c)), b) = mult(unit, mult(b, mult(mult(a, c), c))))),
% 0.20/0.55 inference(monotonicity,[status(thm)],[348, 306])).
% 0.20/0.55 tff(350,plain,
% 0.20/0.55 ((~(mult(mult(unit, b), mult(mult(a, c), c)) = mult(unit, mult(mult(mult(a, c), c), b)))) <=> (~(mult(mult(unit, mult(mult(a, c), c)), b) = mult(unit, mult(b, mult(mult(a, c), c)))))),
% 0.20/0.55 inference(monotonicity,[status(thm)],[349])).
% 0.20/0.55 tff(351,plain,
% 0.20/0.55 (~(mult(mult(unit, mult(mult(a, c), c)), b) = mult(unit, mult(b, mult(mult(a, c), c))))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[296, 350])).
% 0.20/0.55 tff(352,plain,
% 0.20/0.55 ($false),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[351, 346])).
% 0.20/0.55 tff(353,plain,(mult(mult(mult(b, a), c), a) = mult(mult(b, a), mult(a, c))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.55 tff(354,plain,
% 0.20/0.55 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(b, mult(a, c)), a), a) = mult(b, mult(a, c)))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(355,plain,
% 0.20/0.55 (rd(mult(mult(b, mult(a, c)), a), a) = mult(b, mult(a, c))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[354, 120])).
% 0.20/0.55 tff(356,assumption,(mult(mult(mult(b, a), c), a) = mult(mult(b, a), mult(a, c))), introduced(assumption)).
% 0.20/0.55 tff(357,plain,
% 0.20/0.55 (mult(mult(b, a), mult(a, c)) = mult(mult(mult(b, a), c), a)),
% 0.20/0.55 inference(symmetry,[status(thm)],[356])).
% 0.20/0.55 tff(358,plain,
% 0.20/0.55 ((mult(mult(b, mult(a, c)), a) = mult(mult(b, a), mult(a, c))) <=> (mult(mult(b, a), mult(a, c)) = mult(mult(b, mult(a, c)), a))),
% 0.20/0.55 inference(commutativity,[status(thm)],[])).
% 0.20/0.55 tff(359,plain,
% 0.20/0.55 (mult(b, mult(mult(a, c), a)) = mult(mult(mult(b, a), c), a)),
% 0.20/0.55 inference(symmetry,[status(thm)],[52])).
% 0.20/0.55 tff(360,assumption,(~(mult(mult(a, c), a) = mult(a, mult(a, c)))), introduced(assumption)).
% 0.20/0.55 tff(361,plain,
% 0.20/0.55 (((~(mult(mult(a, a), c) = mult(a, mult(c, a)))) | (~(mult(mult(a, c), a) = mult(a, mult(a, c))))) | (mult(mult(a, c), a) = mult(a, mult(a, c)))),
% 0.20/0.55 inference(tautology,[status(thm)],[])).
% 0.20/0.55 tff(362,plain,
% 0.20/0.55 ((~(mult(mult(a, a), c) = mult(a, mult(c, a)))) | (~(mult(mult(a, c), a) = mult(a, mult(a, c))))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[361, 360])).
% 0.20/0.55 tff(363,plain,
% 0.20/0.55 (((~![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(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(mult(a, a), c) = mult(a, mult(c, a)))) | (~(mult(mult(a, c), a) = mult(a, mult(a, c)))))) | (~((~(mult(mult(a, a), c) = mult(mult(a, c), a))) | (~(mult(a, mult(a, c)) = 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(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | (~((~(mult(mult(a, a), c) = mult(a, mult(c, a)))) | (~(mult(mult(a, c), a) = mult(a, mult(a, c)))))) | (~((~(mult(mult(a, a), c) = mult(mult(a, c), a))) | (~(mult(a, mult(a, c)) = mult(a, mult(c, a)))))))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(364,plain,
% 0.20/0.55 (((~((~(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(c, a)))) | (~(mult(mult(a, c), a) = mult(a, mult(a, c))))))) <=> ((~((~(mult(mult(a, a), c) = mult(a, mult(c, a)))) | (~(mult(mult(a, c), a) = mult(a, mult(a, c)))))) | (~((~(mult(mult(a, a), c) = mult(mult(a, c), a))) | (~(mult(a, mult(a, c)) = mult(a, mult(c, a)))))))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(365,plain,
% 0.20/0.55 ((~((~(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))) | (~(mult(a, mult(a, c)) = mult(a, mult(c, a))))))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(366,plain,
% 0.20/0.55 (((~((~(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(c, a)))) | (~(mult(mult(a, c), a) = mult(a, mult(a, c))))))) <=> ((~((~(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(c, a)))) | (~(mult(mult(a, c), a) = mult(a, mult(a, c)))))))),
% 0.20/0.55 inference(monotonicity,[status(thm)],[365])).
% 0.20/0.55 tff(367,plain,
% 0.20/0.55 (((~((~(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(c, a)))) | (~(mult(mult(a, c), a) = mult(a, mult(a, c))))))) <=> ((~((~(mult(mult(a, a), c) = mult(a, mult(c, a)))) | (~(mult(mult(a, c), a) = mult(a, mult(a, c)))))) | (~((~(mult(mult(a, a), c) = mult(mult(a, c), a))) | (~(mult(a, mult(a, c)) = mult(a, mult(c, a)))))))),
% 0.20/0.55 inference(transitivity,[status(thm)],[366, 364])).
% 0.20/0.55 tff(368,plain,
% 0.20/0.55 (((~![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(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(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(c, a)))) | (~(mult(mult(a, c), a) = 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(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(mult(a, a), c) = mult(a, mult(c, a)))) | (~(mult(mult(a, c), a) = mult(a, mult(a, c)))))) | (~((~(mult(mult(a, a), c) = mult(mult(a, c), a))) | (~(mult(a, mult(a, c)) = mult(a, mult(c, a))))))))),
% 0.20/0.55 inference(monotonicity,[status(thm)],[367])).
% 0.20/0.55 tff(369,plain,
% 0.20/0.55 (((~![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(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(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(c, a)))) | (~(mult(mult(a, c), a) = 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(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | (~((~(mult(mult(a, a), c) = mult(a, mult(c, a)))) | (~(mult(mult(a, c), a) = mult(a, mult(a, c)))))) | (~((~(mult(mult(a, a), c) = mult(mult(a, c), a))) | (~(mult(a, mult(a, c)) = mult(a, mult(c, a)))))))),
% 0.20/0.55 inference(transitivity,[status(thm)],[368, 363])).
% 0.20/0.55 tff(370,plain,
% 0.20/0.55 ((~![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(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(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(c, a)))) | (~(mult(mult(a, c), a) = mult(a, mult(a, c)))))))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(371,plain,
% 0.20/0.55 ((~![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(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | (~((~(mult(mult(a, a), c) = mult(a, mult(c, a)))) | (~(mult(mult(a, c), a) = mult(a, mult(a, c)))))) | (~((~(mult(mult(a, a), c) = mult(mult(a, c), a))) | (~(mult(a, mult(a, c)) = mult(a, mult(c, a))))))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[370, 369])).
% 0.20/0.55 tff(372,plain,
% 0.20/0.55 ((~((~(mult(mult(a, a), c) = mult(a, mult(c, a)))) | (~(mult(mult(a, c), a) = mult(a, mult(a, c)))))) | (~((~(mult(mult(a, a), c) = mult(mult(a, c), a))) | (~(mult(a, mult(a, c)) = mult(a, mult(c, a))))))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[371, 29])).
% 0.20/0.55 tff(373,plain,
% 0.20/0.55 (~((~(mult(mult(a, a), c) = mult(mult(a, c), a))) | (~(mult(a, mult(a, c)) = mult(a, mult(c, a)))))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[372, 362])).
% 0.20/0.55 tff(374,plain,
% 0.20/0.55 (((~(mult(mult(a, a), c) = mult(mult(a, c), a))) | (~(mult(a, mult(a, c)) = mult(a, mult(c, a))))) | (mult(a, mult(a, c)) = mult(a, mult(c, a)))),
% 0.20/0.55 inference(tautology,[status(thm)],[])).
% 0.20/0.55 tff(375,plain,
% 0.20/0.55 (mult(a, mult(a, c)) = mult(a, mult(c, a))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[374, 373])).
% 0.20/0.55 tff(376,plain,
% 0.20/0.55 (mult(a, mult(c, a)) = mult(a, mult(a, c))),
% 0.20/0.55 inference(symmetry,[status(thm)],[375])).
% 0.20/0.55 tff(377,plain,
% 0.20/0.55 (mult(mult(unit, a), mult(c, a)) = mult(a, mult(c, a))),
% 0.20/0.55 inference(monotonicity,[status(thm)],[110])).
% 0.20/0.55 tff(378,plain,
% 0.20/0.55 (mult(mult(unit, a), mult(c, a)) = mult(a, mult(a, c))),
% 0.20/0.55 inference(transitivity,[status(thm)],[377, 376])).
% 0.20/0.55 tff(379,plain,
% 0.20/0.55 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(a, mult(a, mult(a, c))) = mult(a, c))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(380,plain,
% 0.20/0.55 (ld(a, mult(a, mult(a, c))) = mult(a, c)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[379, 9])).
% 0.20/0.55 tff(381,plain,
% 0.20/0.55 (ld(a, mult(a, mult(c, a))) = ld(a, mult(a, mult(a, c)))),
% 0.20/0.55 inference(monotonicity,[status(thm)],[376])).
% 0.20/0.55 tff(382,plain,
% 0.20/0.55 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(a, mult(a, mult(c, a))) = mult(c, a))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(383,plain,
% 0.20/0.55 (ld(a, mult(a, mult(c, a))) = mult(c, a)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[382, 9])).
% 0.20/0.55 tff(384,plain,
% 0.20/0.55 (mult(c, a) = ld(a, mult(a, mult(c, a)))),
% 0.20/0.55 inference(symmetry,[status(thm)],[383])).
% 0.20/0.55 tff(385,plain,
% 0.20/0.55 (mult(c, a) = mult(a, c)),
% 0.20/0.55 inference(transitivity,[status(thm)],[384, 381, 380])).
% 0.20/0.55 tff(386,plain,
% 0.20/0.55 (mult(mult(c, a), a) = mult(mult(a, c), a)),
% 0.20/0.55 inference(monotonicity,[status(thm)],[385])).
% 0.20/0.55 tff(387,plain,
% 0.20/0.55 ((~![A: $i] : (mult(unit, A) = A)) | (mult(unit, mult(c, a)) = mult(c, a))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(388,plain,
% 0.20/0.55 (mult(unit, mult(c, a)) = mult(c, a)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[387, 108])).
% 0.20/0.55 tff(389,plain,
% 0.20/0.55 (mult(mult(unit, mult(c, a)), a) = mult(mult(c, a), a)),
% 0.20/0.55 inference(monotonicity,[status(thm)],[388])).
% 0.20/0.55 tff(390,plain,
% 0.20/0.55 (mult(mult(unit, mult(c, a)), a) = mult(mult(a, c), a)),
% 0.20/0.55 inference(transitivity,[status(thm)],[389, 386])).
% 0.20/0.55 tff(391,plain,
% 0.20/0.55 ((mult(mult(unit, mult(c, a)), a) = mult(mult(unit, a), mult(c, a))) <=> (mult(mult(a, c), a) = mult(a, mult(a, c)))),
% 0.20/0.55 inference(monotonicity,[status(thm)],[390, 378])).
% 0.20/0.55 tff(392,plain,
% 0.20/0.55 ((mult(mult(a, c), a) = mult(a, mult(a, c))) <=> (mult(mult(unit, mult(c, a)), a) = mult(mult(unit, a), mult(c, a)))),
% 0.20/0.55 inference(symmetry,[status(thm)],[391])).
% 0.20/0.55 tff(393,plain,
% 0.20/0.55 ((~(mult(mult(a, c), a) = mult(a, mult(a, c)))) <=> (~(mult(mult(unit, mult(c, a)), a) = mult(mult(unit, a), mult(c, a))))),
% 0.20/0.55 inference(monotonicity,[status(thm)],[392])).
% 0.20/0.55 tff(394,plain,
% 0.20/0.55 (~(mult(mult(unit, mult(c, a)), a) = mult(mult(unit, a), mult(c, a)))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[360, 393])).
% 0.20/0.55 tff(395,plain,
% 0.20/0.55 (((~(mult(mult(unit, mult(c, a)), a) = mult(mult(unit, a), mult(c, a)))) | (~(mult(unit, mult(mult(c, a), a)) = mult(unit, mult(a, mult(c, a)))))) | (mult(mult(unit, mult(c, a)), a) = mult(mult(unit, a), mult(c, a)))),
% 0.20/0.55 inference(tautology,[status(thm)],[])).
% 0.20/0.55 tff(396,plain,
% 0.20/0.55 ((~(mult(mult(unit, mult(c, a)), a) = mult(mult(unit, a), mult(c, a)))) | (~(mult(unit, mult(mult(c, a), a)) = mult(unit, mult(a, mult(c, a)))))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[395, 394])).
% 0.20/0.55 tff(397,plain,
% 0.20/0.55 ((mult(a, mult(a, c)) = mult(mult(a, c), a)) <=> (mult(mult(a, c), a) = mult(a, mult(a, c)))),
% 0.20/0.55 inference(commutativity,[status(thm)],[])).
% 0.20/0.55 tff(398,plain,
% 0.20/0.55 (mult(mult(unit, a), c) = mult(a, c)),
% 0.40/0.55 inference(monotonicity,[status(thm)],[110])).
% 0.40/0.55 tff(399,plain,
% 0.40/0.55 (mult(mult(mult(unit, a), c), a) = mult(mult(a, c), a)),
% 0.40/0.55 inference(monotonicity,[status(thm)],[398])).
% 0.40/0.55 tff(400,plain,
% 0.40/0.55 ((~![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)))),
% 0.40/0.55 inference(quant_inst,[status(thm)],[])).
% 0.40/0.55 tff(401,plain,
% 0.40/0.55 (mult(mult(mult(unit, a), c), a) = mult(unit, mult(mult(a, c), a))),
% 0.40/0.55 inference(unit_resolution,[status(thm)],[400, 50])).
% 0.40/0.55 tff(402,plain,
% 0.40/0.55 (mult(unit, mult(mult(a, c), a)) = mult(mult(mult(unit, a), c), a)),
% 0.40/0.55 inference(symmetry,[status(thm)],[401])).
% 0.40/0.55 tff(403,plain,
% 0.40/0.55 (mult(unit, mult(mult(c, a), a)) = mult(unit, mult(mult(a, c), a))),
% 0.40/0.55 inference(monotonicity,[status(thm)],[386])).
% 0.40/0.55 tff(404,plain,
% 0.40/0.55 (mult(unit, mult(mult(c, a), a)) = mult(mult(a, c), a)),
% 0.40/0.55 inference(transitivity,[status(thm)],[403, 402, 399])).
% 0.40/0.55 tff(405,plain,
% 0.40/0.55 ((mult(mult(unit, a), mult(c, a)) = mult(unit, mult(mult(c, a), a))) <=> (mult(a, mult(a, c)) = mult(mult(a, c), a))),
% 0.40/0.55 inference(monotonicity,[status(thm)],[378, 404])).
% 0.40/0.55 tff(406,plain,
% 0.40/0.55 ((mult(mult(unit, a), mult(c, a)) = mult(unit, mult(mult(c, a), a))) <=> (mult(mult(a, c), a) = mult(a, mult(a, c)))),
% 0.40/0.55 inference(transitivity,[status(thm)],[405, 397])).
% 0.40/0.55 tff(407,plain,
% 0.40/0.55 ((mult(mult(a, c), a) = mult(a, mult(a, c))) <=> (mult(mult(unit, a), mult(c, a)) = mult(unit, mult(mult(c, a), a)))),
% 0.40/0.55 inference(symmetry,[status(thm)],[406])).
% 0.40/0.55 tff(408,plain,
% 0.40/0.55 ((~(mult(mult(a, c), a) = mult(a, mult(a, c)))) <=> (~(mult(mult(unit, a), mult(c, a)) = mult(unit, mult(mult(c, a), a))))),
% 0.40/0.55 inference(monotonicity,[status(thm)],[407])).
% 0.40/0.55 tff(409,plain,
% 0.40/0.55 (~(mult(mult(unit, a), mult(c, a)) = mult(unit, mult(mult(c, a), a)))),
% 0.40/0.55 inference(modus_ponens,[status(thm)],[360, 408])).
% 0.40/0.55 tff(410,plain,
% 0.40/0.55 (((~(mult(mult(unit, mult(c, a)), a) = mult(unit, mult(a, mult(c, a))))) | (~(mult(mult(unit, a), mult(c, a)) = mult(unit, mult(mult(c, a), a))))) | (mult(mult(unit, a), mult(c, a)) = mult(unit, mult(mult(c, a), a)))),
% 0.40/0.55 inference(tautology,[status(thm)],[])).
% 0.40/0.55 tff(411,plain,
% 0.40/0.55 ((~(mult(mult(unit, mult(c, a)), a) = mult(unit, mult(a, mult(c, a))))) | (~(mult(mult(unit, a), mult(c, a)) = mult(unit, mult(mult(c, a), a))))),
% 0.40/0.55 inference(unit_resolution,[status(thm)],[410, 409])).
% 0.40/0.55 tff(412,plain,
% 0.40/0.55 (((~![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(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(mult(unit, mult(c, a)), a) = mult(mult(unit, a), mult(c, a)))) | (~(mult(unit, mult(mult(c, a), a)) = mult(unit, mult(a, mult(c, a))))))) | (~((~(mult(mult(unit, mult(c, a)), a) = mult(unit, mult(a, mult(c, a))))) | (~(mult(mult(unit, a), mult(c, a)) = mult(unit, mult(mult(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(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | (~((~(mult(mult(unit, mult(c, a)), a) = mult(mult(unit, a), mult(c, a)))) | (~(mult(unit, mult(mult(c, a), a)) = mult(unit, mult(a, mult(c, a))))))) | (~((~(mult(mult(unit, mult(c, a)), a) = mult(unit, mult(a, mult(c, a))))) | (~(mult(mult(unit, a), mult(c, a)) = mult(unit, mult(mult(c, a), a)))))))),
% 0.40/0.55 inference(rewrite,[status(thm)],[])).
% 0.40/0.55 tff(413,plain,
% 0.40/0.55 ((~![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(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(mult(unit, mult(c, a)), a) = mult(mult(unit, a), mult(c, a)))) | (~(mult(unit, mult(mult(c, a), a)) = mult(unit, mult(a, mult(c, a))))))) | (~((~(mult(mult(unit, mult(c, a)), a) = mult(unit, mult(a, mult(c, a))))) | (~(mult(mult(unit, a), mult(c, a)) = mult(unit, mult(mult(c, a), a)))))))),
% 0.40/0.56 inference(quant_inst,[status(thm)],[])).
% 0.40/0.56 tff(414,plain,
% 0.40/0.56 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | (~((~(mult(mult(unit, mult(c, a)), a) = mult(mult(unit, a), mult(c, a)))) | (~(mult(unit, mult(mult(c, a), a)) = mult(unit, mult(a, mult(c, a))))))) | (~((~(mult(mult(unit, mult(c, a)), a) = mult(unit, mult(a, mult(c, a))))) | (~(mult(mult(unit, a), mult(c, a)) = mult(unit, mult(mult(c, a), a))))))),
% 0.40/0.56 inference(modus_ponens,[status(thm)],[413, 412])).
% 0.40/0.56 tff(415,plain,
% 0.40/0.56 ((~((~(mult(mult(unit, mult(c, a)), a) = mult(mult(unit, a), mult(c, a)))) | (~(mult(unit, mult(mult(c, a), a)) = mult(unit, mult(a, mult(c, a))))))) | (~((~(mult(mult(unit, mult(c, a)), a) = mult(unit, mult(a, mult(c, a))))) | (~(mult(mult(unit, a), mult(c, a)) = mult(unit, mult(mult(c, a), a))))))),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[414, 29])).
% 0.40/0.56 tff(416,plain,
% 0.40/0.56 ($false),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[415, 411, 396])).
% 0.40/0.56 tff(417,plain,(mult(mult(a, c), a) = mult(a, mult(a, c))), inference(lemma,lemma(discharge,[]))).
% 0.40/0.56 tff(418,plain,
% 0.40/0.56 (mult(a, mult(a, c)) = mult(mult(a, c), a)),
% 0.40/0.56 inference(symmetry,[status(thm)],[417])).
% 0.40/0.56 tff(419,plain,
% 0.40/0.56 (mult(b, mult(a, mult(a, c))) = mult(b, mult(mult(a, c), a))),
% 0.40/0.56 inference(monotonicity,[status(thm)],[418])).
% 0.40/0.56 tff(420,plain,
% 0.40/0.56 (mult(b, mult(a, mult(a, c))) = mult(mult(b, a), mult(a, c))),
% 0.40/0.56 inference(transitivity,[status(thm)],[419, 359, 356])).
% 0.40/0.56 tff(421,plain,
% 0.40/0.56 ((mult(mult(b, mult(a, c)), a) = mult(b, mult(a, mult(a, c)))) <=> (mult(mult(b, mult(a, c)), a) = mult(mult(b, a), mult(a, c)))),
% 0.40/0.56 inference(monotonicity,[status(thm)],[420])).
% 0.40/0.56 tff(422,plain,
% 0.40/0.56 ((mult(mult(b, mult(a, c)), a) = mult(b, mult(a, mult(a, c)))) <=> (mult(mult(b, a), mult(a, c)) = mult(mult(b, mult(a, c)), a))),
% 0.40/0.56 inference(transitivity,[status(thm)],[421, 358])).
% 0.40/0.56 tff(423,assumption,(~(mult(mult(b, a), mult(a, c)) = mult(mult(b, mult(a, c)), a))), introduced(assumption)).
% 0.40/0.56 tff(424,plain,
% 0.40/0.56 ((~(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))))),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[84, 423])).
% 0.40/0.56 tff(425,plain,
% 0.40/0.56 (~((~(mult(mult(b, a), mult(a, c)) = mult(b, mult(mult(a, c), a)))) | (~(mult(mult(b, mult(a, c)), a) = mult(b, mult(a, mult(a, c))))))),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[82, 424])).
% 0.40/0.56 tff(426,plain,
% 0.40/0.56 (((~(mult(mult(b, a), mult(a, c)) = mult(b, mult(mult(a, c), a)))) | (~(mult(mult(b, mult(a, c)), a) = mult(b, mult(a, mult(a, c)))))) | (mult(mult(b, mult(a, c)), a) = mult(b, mult(a, mult(a, c))))),
% 0.40/0.56 inference(tautology,[status(thm)],[])).
% 0.40/0.56 tff(427,plain,
% 0.40/0.56 (mult(mult(b, mult(a, c)), a) = mult(b, mult(a, mult(a, c)))),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[426, 425])).
% 0.40/0.56 tff(428,plain,
% 0.40/0.56 (mult(mult(b, a), mult(a, c)) = mult(mult(b, mult(a, c)), a)),
% 0.40/0.56 inference(modus_ponens,[status(thm)],[427, 422])).
% 0.40/0.56 tff(429,plain,
% 0.40/0.56 ($false),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[423, 428])).
% 0.40/0.56 tff(430,plain,((mult(mult(b, a), mult(a, c)) = mult(mult(b, mult(a, c)), a)) | (~(mult(mult(mult(b, a), c), a) = mult(mult(b, a), mult(a, c))))), inference(lemma,lemma(discharge,[]))).
% 0.40/0.56 tff(431,plain,
% 0.40/0.56 (mult(mult(b, a), mult(a, c)) = mult(mult(b, mult(a, c)), a)),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[430, 356])).
% 0.40/0.56 tff(432,plain,
% 0.40/0.56 (mult(mult(b, mult(a, c)), a) = mult(mult(b, a), mult(a, c))),
% 0.40/0.56 inference(symmetry,[status(thm)],[431])).
% 0.40/0.56 tff(433,plain,
% 0.40/0.56 (mult(mult(b, mult(a, c)), a) = mult(mult(mult(b, a), c), a)),
% 0.40/0.56 inference(transitivity,[status(thm)],[432, 357])).
% 0.40/0.56 tff(434,plain,
% 0.40/0.56 (rd(mult(mult(b, mult(a, c)), a), a) = rd(mult(mult(mult(b, a), c), a), a)),
% 0.40/0.56 inference(monotonicity,[status(thm)],[433])).
% 0.40/0.56 tff(435,plain,
% 0.40/0.56 (rd(mult(mult(mult(b, a), c), a), a) = rd(mult(mult(b, mult(a, c)), a), a)),
% 0.40/0.56 inference(symmetry,[status(thm)],[434])).
% 0.40/0.56 tff(436,plain,
% 0.40/0.56 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(b, a), c), a), a) = mult(mult(b, a), c))),
% 0.40/0.56 inference(quant_inst,[status(thm)],[])).
% 0.40/0.56 tff(437,plain,
% 0.40/0.56 (rd(mult(mult(mult(b, a), c), a), a) = mult(mult(b, a), c)),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[436, 120])).
% 0.40/0.56 tff(438,plain,
% 0.40/0.56 (mult(mult(b, a), c) = rd(mult(mult(mult(b, a), c), a), a)),
% 0.40/0.56 inference(symmetry,[status(thm)],[437])).
% 0.40/0.56 tff(439,plain,
% 0.40/0.56 (mult(mult(b, a), c) = mult(b, mult(a, c))),
% 0.40/0.56 inference(transitivity,[status(thm)],[438, 435, 355])).
% 0.40/0.56 tff(440,plain,
% 0.40/0.56 ((mult(mult(b, a), c) = mult(b, mult(c, a))) <=> (mult(b, mult(a, c)) = mult(b, mult(c, a)))),
% 0.40/0.56 inference(monotonicity,[status(thm)],[439])).
% 0.40/0.56 tff(441,plain,
% 0.40/0.56 ((mult(mult(b, a), c) = mult(b, mult(c, a))) <=> (mult(b, mult(c, a)) = mult(b, mult(a, c)))),
% 0.40/0.56 inference(transitivity,[status(thm)],[440, 1])).
% 0.40/0.56 tff(442,assumption,(~(mult(b, mult(c, a)) = mult(b, mult(a, c)))), introduced(assumption)).
% 0.40/0.56 tff(443,plain,
% 0.40/0.56 (((~(mult(b, mult(c, a)) = mult(b, mult(a, c)))) | (~(mult(mult(b, c), a) = mult(mult(b, a), c)))) | (mult(b, mult(c, a)) = mult(b, mult(a, c)))),
% 0.40/0.56 inference(tautology,[status(thm)],[])).
% 0.40/0.56 tff(444,plain,
% 0.40/0.56 ((~(mult(b, mult(c, a)) = mult(b, mult(a, c)))) | (~(mult(mult(b, c), a) = mult(mult(b, a), c)))),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[443, 442])).
% 0.40/0.56 tff(445,plain,
% 0.40/0.56 (~((~(mult(mult(b, c), a) = mult(b, mult(a, c)))) | (~(mult(mult(b, a), c) = mult(b, mult(c, a)))))),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[98, 444])).
% 0.40/0.56 tff(446,plain,
% 0.40/0.56 (mult(mult(b, a), c) = mult(b, mult(c, a))),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[90, 445])).
% 0.40/0.56 tff(447,plain,
% 0.40/0.56 (mult(b, mult(c, a)) = mult(b, mult(a, c))),
% 0.40/0.56 inference(modus_ponens,[status(thm)],[446, 441])).
% 0.40/0.56 tff(448,plain,
% 0.40/0.56 ($false),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[442, 447])).
% 0.40/0.56 tff(449,plain,((mult(b, mult(c, a)) = mult(b, mult(a, c))) | (~(mult(mult(mult(b, a), c), a) = mult(mult(b, a), mult(a, c))))), inference(lemma,lemma(discharge,[]))).
% 0.40/0.56 tff(450,plain,
% 0.40/0.56 (mult(b, mult(c, a)) = mult(b, mult(a, c))),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[449, 353])).
% 0.40/0.56 tff(451,plain,
% 0.40/0.56 (ld(b, mult(b, mult(c, a))) = ld(b, mult(b, mult(a, c)))),
% 0.40/0.56 inference(monotonicity,[status(thm)],[450])).
% 0.40/0.56 tff(452,plain,
% 0.40/0.56 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(b, mult(b, mult(c, a))) = mult(c, a))),
% 0.40/0.56 inference(quant_inst,[status(thm)],[])).
% 0.40/0.56 tff(453,plain,
% 0.40/0.56 (ld(b, mult(b, mult(c, a))) = mult(c, a)),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[452, 9])).
% 0.40/0.56 tff(454,plain,
% 0.40/0.56 (mult(c, a) = ld(b, mult(b, mult(c, a)))),
% 0.40/0.56 inference(symmetry,[status(thm)],[453])).
% 0.40/0.56 tff(455,plain,
% 0.40/0.56 (mult(c, a) = mult(a, c)),
% 0.40/0.56 inference(transitivity,[status(thm)],[454, 451, 13])).
% 0.40/0.56 tff(456,plain,
% 0.40/0.56 (mult(mult(b, a), mult(c, a)) = mult(mult(b, a), mult(a, c))),
% 0.40/0.56 inference(monotonicity,[status(thm)],[455])).
% 0.40/0.56 tff(457,plain,
% 0.40/0.56 (mult(mult(b, a), mult(a, c)) = mult(mult(b, a), mult(c, a))),
% 0.40/0.56 inference(symmetry,[status(thm)],[456])).
% 0.40/0.56 tff(458,assumption,(~(mult(mult(b, a), mult(a, c)) = mult(mult(b, a), mult(c, a)))), introduced(assumption)).
% 0.40/0.56 tff(459,plain,
% 0.40/0.56 ($false),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[458, 457])).
% 0.40/0.56 tff(460,plain,((~(ld(b, mult(b, mult(a, c))) = mult(a, c))) | (mult(mult(b, a), mult(a, c)) = mult(mult(b, a), mult(c, a)))), inference(lemma,lemma(discharge,[]))).
% 0.40/0.56 tff(461,plain,
% 0.40/0.56 (mult(mult(b, a), mult(a, c)) = mult(mult(b, a), mult(c, a))),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[460, 12])).
% 0.40/0.56 tff(462,plain,
% 0.40/0.56 (mult(mult(unit, c), a) = mult(a, c)),
% 0.40/0.56 inference(transitivity,[status(thm)],[312, 454, 451, 12])).
% 0.40/0.56 tff(463,plain,
% 0.40/0.56 (mult(mult(mult(unit, c), a), c) = mult(mult(a, c), c)),
% 0.40/0.56 inference(monotonicity,[status(thm)],[462])).
% 0.40/0.56 tff(464,plain,
% 0.40/0.56 (mult(c, a) = mult(a, c)),
% 0.40/0.56 inference(transitivity,[status(thm)],[454, 451, 12])).
% 0.40/0.56 tff(465,plain,
% 0.40/0.56 (mult(mult(c, a), c) = mult(mult(a, c), c)),
% 0.40/0.56 inference(monotonicity,[status(thm)],[464])).
% 0.40/0.56 tff(466,plain,
% 0.40/0.56 (mult(mult(a, c), c) = mult(mult(c, a), c)),
% 0.40/0.56 inference(symmetry,[status(thm)],[465])).
% 0.40/0.56 tff(467,plain,
% 0.40/0.56 (mult(a, mult(mult(c, unit), c)) = mult(mult(c, a), c)),
% 0.40/0.56 inference(transitivity,[status(thm)],[338, 335, 466])).
% 0.40/0.56 tff(468,plain,
% 0.40/0.56 (mult(unit, mult(a, mult(mult(c, unit), c))) = mult(unit, mult(mult(c, a), c))),
% 0.40/0.56 inference(monotonicity,[status(thm)],[467])).
% 0.40/0.56 tff(469,plain,
% 0.40/0.56 (mult(unit, mult(mult(a, c), c)) = mult(mult(a, c), c)),
% 0.40/0.56 inference(transitivity,[status(thm)],[343, 468, 317, 463])).
% 0.40/0.56 tff(470,plain,
% 0.40/0.56 (mult(mult(unit, mult(mult(a, c), c)), b) = mult(mult(mult(a, c), c), b)),
% 0.40/0.56 inference(monotonicity,[status(thm)],[469])).
% 0.40/0.56 tff(471,assumption,(~(mult(mult(unit, b), mult(mult(a, c), c)) = mult(unit, mult(mult(mult(a, c), c), b)))), introduced(assumption)).
% 0.40/0.56 tff(472,plain,
% 0.40/0.56 ((~(mult(mult(unit, b), mult(mult(a, c), c)) = mult(unit, mult(mult(mult(a, c), c), b)))) | (~(mult(mult(unit, mult(mult(a, c), c)), b) = mult(unit, mult(b, mult(mult(a, c), c)))))),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[297, 471])).
% 0.40/0.56 tff(473,plain,
% 0.40/0.56 (~((~(mult(mult(unit, b), mult(mult(a, c), c)) = mult(mult(unit, mult(mult(a, c), c)), b))) | (~(mult(unit, mult(b, mult(mult(a, c), c))) = mult(unit, mult(mult(mult(a, c), c), b)))))),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[301, 29, 472])).
% 0.40/0.56 tff(474,plain,
% 0.40/0.56 (mult(mult(unit, b), mult(mult(a, c), c)) = mult(mult(unit, mult(mult(a, c), c)), b)),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[347, 473])).
% 0.40/0.56 tff(475,plain,
% 0.40/0.56 (mult(mult(unit, b), mult(mult(a, c), c)) = mult(unit, mult(mult(mult(a, c), c), b))),
% 0.40/0.56 inference(transitivity,[status(thm)],[474, 470, 214, 309, 308, 307])).
% 0.40/0.56 tff(476,plain,
% 0.40/0.56 ($false),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[471, 475])).
% 0.40/0.56 tff(477,plain,(mult(mult(unit, b), mult(mult(a, c), c)) = mult(unit, mult(mult(mult(a, c), c), b))), inference(lemma,lemma(discharge,[]))).
% 0.40/0.56 tff(478,plain,
% 0.40/0.56 (~(mult(mult(b, c), a) = mult(mult(b, a), c))),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[295, 477, 461])).
% 0.40/0.56 tff(479,plain,
% 0.40/0.56 ((~(mult(b, mult(c, a)) = mult(b, mult(a, c)))) | (~(mult(mult(b, c), a) = mult(mult(b, a), c)))),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[100, 478])).
% 0.40/0.56 tff(480,plain,
% 0.40/0.56 (~((~(mult(mult(b, c), a) = mult(b, mult(a, c)))) | (~(mult(mult(b, a), c) = mult(b, mult(c, a)))))),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[98, 479])).
% 0.40/0.56 tff(481,plain,
% 0.40/0.56 (mult(mult(b, a), c) = mult(b, mult(c, a))),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[90, 480])).
% 0.40/0.56 tff(482,plain,
% 0.40/0.56 (((~(mult(mult(b, c), a) = mult(b, mult(a, c)))) | (~(mult(mult(b, a), c) = mult(b, mult(c, a))))) | (mult(mult(b, c), a) = mult(b, mult(a, c)))),
% 0.40/0.56 inference(tautology,[status(thm)],[])).
% 0.40/0.56 tff(483,plain,
% 0.40/0.56 (mult(mult(b, c), a) = mult(b, mult(a, c))),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[482, 480])).
% 0.40/0.56 tff(484,plain,
% 0.40/0.56 ((mult(mult(b, c), a) = mult(mult(b, a), c)) <=> (mult(b, mult(a, c)) = mult(b, mult(c, a)))),
% 0.40/0.56 inference(monotonicity,[status(thm)],[483, 481])).
% 0.40/0.56 tff(485,plain,
% 0.40/0.56 ((mult(mult(b, c), a) = mult(mult(b, a), c)) <=> (mult(b, mult(c, a)) = mult(b, mult(a, c)))),
% 0.40/0.56 inference(transitivity,[status(thm)],[484, 1])).
% 0.40/0.56 tff(486,plain,
% 0.40/0.56 ((mult(b, mult(c, a)) = mult(b, mult(a, c))) <=> (mult(mult(b, c), a) = mult(mult(b, a), c))),
% 0.40/0.56 inference(symmetry,[status(thm)],[485])).
% 0.40/0.56 tff(487,plain,
% 0.40/0.56 (mult(mult(b, c), a) = mult(mult(b, a), c)),
% 0.40/0.56 inference(modus_ponens,[status(thm)],[450, 486])).
% 0.40/0.56 tff(488,plain,
% 0.40/0.56 ($false),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[478, 487])).
% 0.40/0.56 % SZS output end Proof
% 0.40/0.57 % E exiting
%------------------------------------------------------------------------------