%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP755-1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:08:36 AM UTC 2025
% Result : Unsatisfiable 6.94s 7.18s
% Output : Proof 7.03s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP755-1 : TPTP v9.0.0. Released v4.0.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 17:03:18 EDT 2025
% 0.12/0.33 % CPUTime :
% 6.94/7.18 % SZS status Unsatisfiable
% 6.94/7.18 % SZS output start Proof
% 6.94/7.18 tff(mult_type, type, (
% 6.94/7.18 mult: ( $i * $i ) > $i)).
% 6.94/7.18 tff(i_type, type, (
% 6.94/7.18 i: $i > $i)).
% 6.94/7.18 tff(a_type, type, (
% 6.94/7.18 a: $i)).
% 6.94/7.18 tff(b_type, type, (
% 6.94/7.18 b: $i)).
% 6.94/7.18 tff(ld_type, type, (
% 6.94/7.18 ld: ( $i * $i ) > $i)).
% 6.94/7.18 tff(unit_type, type, (
% 6.94/7.18 unit: $i)).
% 6.94/7.18 tff(rd_type, type, (
% 6.94/7.18 rd: ( $i * $i ) > $i)).
% 6.94/7.18 tff(1,plain,
% 6.94/7.18 (^[A: $i] : refl((mult(unit, A) = A) <=> (mult(unit, A) = A))),
% 6.94/7.18 inference(bind,[status(th)],[])).
% 6.94/7.18 tff(2,plain,
% 6.94/7.18 (![A: $i] : (mult(unit, A) = A) <=> ![A: $i] : (mult(unit, A) = A)),
% 6.94/7.18 inference(quant_intro,[status(thm)],[1])).
% 6.94/7.18 tff(3,plain,
% 6.94/7.18 (![A: $i] : (mult(unit, A) = A) <=> ![A: $i] : (mult(unit, A) = A)),
% 6.94/7.18 inference(rewrite,[status(thm)],[])).
% 6.94/7.18 tff(4,axiom,(![A: $i] : (mult(unit, A) = A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','f06')).
% 6.94/7.18 tff(5,plain,
% 6.94/7.18 (![A: $i] : (mult(unit, A) = A)),
% 6.94/7.18 inference(modus_ponens,[status(thm)],[4, 3])).
% 6.94/7.18 tff(6,plain,(
% 6.94/7.18 ![A: $i] : (mult(unit, A) = A)),
% 6.94/7.18 inference(skolemize,[status(sab)],[5])).
% 6.94/7.18 tff(7,plain,
% 6.94/7.18 (![A: $i] : (mult(unit, A) = A)),
% 6.94/7.18 inference(modus_ponens,[status(thm)],[6, 2])).
% 6.94/7.18 tff(8,plain,
% 6.94/7.18 ((~![A: $i] : (mult(unit, A) = A)) | (mult(unit, ld(mult(a, b), unit)) = ld(mult(a, b), unit))),
% 6.94/7.18 inference(quant_inst,[status(thm)],[])).
% 6.94/7.18 tff(9,plain,
% 6.94/7.18 (mult(unit, ld(mult(a, b), unit)) = ld(mult(a, b), unit)),
% 6.94/7.18 inference(unit_resolution,[status(thm)],[8, 7])).
% 6.94/7.18 tff(10,plain,
% 6.94/7.18 (ld(mult(a, b), unit) = mult(unit, ld(mult(a, b), unit))),
% 6.94/7.18 inference(symmetry,[status(thm)],[9])).
% 6.94/7.18 tff(11,plain,
% 6.94/7.18 (mult(ld(mult(a, b), unit), b) = mult(mult(unit, ld(mult(a, b), unit)), b)),
% 6.94/7.18 inference(monotonicity,[status(thm)],[10])).
% 6.94/7.18 tff(12,plain,
% 6.94/7.18 (mult(mult(unit, ld(mult(a, b), unit)), b) = mult(ld(mult(a, b), unit), b)),
% 6.94/7.18 inference(symmetry,[status(thm)],[11])).
% 6.94/7.18 tff(13,plain,
% 6.94/7.18 (mult(mult(unit, ld(mult(a, b), unit)), b) = mult(ld(mult(a, b), unit), b)),
% 6.94/7.18 inference(monotonicity,[status(thm)],[9])).
% 6.94/7.18 tff(14,plain,
% 6.94/7.18 (mult(ld(mult(a, b), unit), b) = mult(mult(unit, ld(mult(a, b), unit)), b)),
% 6.94/7.18 inference(symmetry,[status(thm)],[13])).
% 6.94/7.18 tff(15,plain,
% 6.94/7.18 ((~![A: $i] : (mult(unit, A) = A)) | (mult(unit, i(b)) = i(b))),
% 6.94/7.18 inference(quant_inst,[status(thm)],[])).
% 6.94/7.18 tff(16,plain,
% 6.94/7.18 (mult(unit, i(b)) = i(b)),
% 6.94/7.18 inference(unit_resolution,[status(thm)],[15, 7])).
% 6.94/7.18 tff(17,plain,
% 6.94/7.18 (i(b) = mult(unit, i(b))),
% 6.94/7.18 inference(symmetry,[status(thm)],[16])).
% 6.94/7.18 tff(18,plain,
% 6.94/7.18 (mult(i(b), b) = mult(mult(unit, i(b)), b)),
% 6.94/7.18 inference(monotonicity,[status(thm)],[17])).
% 6.94/7.18 tff(19,plain,
% 6.94/7.18 (mult(mult(unit, i(b)), b) = mult(i(b), b)),
% 6.94/7.18 inference(symmetry,[status(thm)],[18])).
% 6.94/7.18 tff(20,assumption,(~(mult(unit, mult(b, i(b))) = mult(mult(unit, i(b)), b))), introduced(assumption)).
% 6.94/7.18 tff(21,plain,
% 6.94/7.18 (^[B: $i, A: $i, C: $i] : refl(((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C))) <=> ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C))))),
% 6.94/7.18 inference(bind,[status(th)],[])).
% 6.94/7.18 tff(22,plain,
% 6.94/7.18 (![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C))) <=> ![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))),
% 6.94/7.18 inference(quant_intro,[status(thm)],[21])).
% 6.94/7.18 tff(23,plain,
% 6.94/7.18 (![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C))) <=> ![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))),
% 6.94/7.18 inference(rewrite,[status(thm)],[])).
% 6.94/7.18 tff(24,axiom,(![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','f08')).
% 6.94/7.18 tff(25,plain,
% 6.94/7.18 (![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))),
% 6.94/7.18 inference(modus_ponens,[status(thm)],[24, 23])).
% 6.94/7.18 tff(26,plain,(
% 6.94/7.18 ![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))),
% 6.94/7.18 inference(skolemize,[status(sab)],[25])).
% 6.94/7.18 tff(27,plain,
% 6.94/7.18 (![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))),
% 6.94/7.18 inference(modus_ponens,[status(thm)],[26, 22])).
% 6.94/7.18 tff(28,plain,
% 6.94/7.18 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(unit, mult(b, i(b))) = mult(mult(unit, i(b)), b)) | (mult(unit, mult(i(b), b)) = mult(mult(unit, i(b)), b)))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(unit, mult(b, i(b))) = mult(mult(unit, i(b)), b)) | (mult(unit, mult(i(b), b)) = mult(mult(unit, i(b)), b)))),
% 6.94/7.18 inference(rewrite,[status(thm)],[])).
% 6.94/7.18 tff(29,plain,
% 6.94/7.18 (((mult(unit, mult(i(b), b)) = mult(mult(unit, i(b)), b)) | (mult(unit, mult(b, i(b))) = mult(mult(unit, i(b)), b))) <=> ((mult(unit, mult(b, i(b))) = mult(mult(unit, i(b)), b)) | (mult(unit, mult(i(b), b)) = mult(mult(unit, i(b)), b)))),
% 6.94/7.18 inference(rewrite,[status(thm)],[])).
% 6.94/7.18 tff(30,plain,
% 6.94/7.18 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(unit, mult(i(b), b)) = mult(mult(unit, i(b)), b)) | (mult(unit, mult(b, i(b))) = mult(mult(unit, i(b)), b)))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(unit, mult(b, i(b))) = mult(mult(unit, i(b)), b)) | (mult(unit, mult(i(b), b)) = mult(mult(unit, i(b)), b))))),
% 6.94/7.18 inference(monotonicity,[status(thm)],[29])).
% 6.94/7.18 tff(31,plain,
% 6.94/7.18 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(unit, mult(i(b), b)) = mult(mult(unit, i(b)), b)) | (mult(unit, mult(b, i(b))) = mult(mult(unit, i(b)), b)))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(unit, mult(b, i(b))) = mult(mult(unit, i(b)), b)) | (mult(unit, mult(i(b), b)) = mult(mult(unit, i(b)), b)))),
% 6.94/7.18 inference(transitivity,[status(thm)],[30, 28])).
% 6.94/7.18 tff(32,plain,
% 6.94/7.18 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(unit, mult(i(b), b)) = mult(mult(unit, i(b)), b)) | (mult(unit, mult(b, i(b))) = mult(mult(unit, i(b)), b)))),
% 6.94/7.18 inference(quant_inst,[status(thm)],[])).
% 6.94/7.18 tff(33,plain,
% 6.94/7.18 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(unit, mult(b, i(b))) = mult(mult(unit, i(b)), b)) | (mult(unit, mult(i(b), b)) = mult(mult(unit, i(b)), b))),
% 6.94/7.18 inference(modus_ponens,[status(thm)],[32, 31])).
% 6.94/7.18 tff(34,plain,
% 6.94/7.18 ((mult(unit, mult(b, i(b))) = mult(mult(unit, i(b)), b)) | (mult(unit, mult(i(b), b)) = mult(mult(unit, i(b)), b))),
% 6.94/7.18 inference(unit_resolution,[status(thm)],[33, 27])).
% 6.94/7.18 tff(35,plain,
% 6.94/7.18 (mult(unit, mult(i(b), b)) = mult(mult(unit, i(b)), b)),
% 6.94/7.18 inference(unit_resolution,[status(thm)],[34, 20])).
% 6.94/7.18 tff(36,plain,
% 6.94/7.18 ((~![A: $i] : (mult(unit, A) = A)) | (mult(unit, mult(i(b), b)) = mult(i(b), b))),
% 6.94/7.18 inference(quant_inst,[status(thm)],[])).
% 6.94/7.18 tff(37,plain,
% 6.94/7.18 (mult(unit, mult(i(b), b)) = mult(i(b), b)),
% 6.94/7.18 inference(unit_resolution,[status(thm)],[36, 7])).
% 6.94/7.18 tff(38,plain,
% 6.94/7.18 (mult(i(b), b) = mult(unit, mult(i(b), b))),
% 6.94/7.18 inference(symmetry,[status(thm)],[37])).
% 6.94/7.18 tff(39,plain,
% 6.94/7.18 (^[B: $i, A: $i] : refl((rd(mult(A, B), B) = A) <=> (rd(mult(A, B), B) = A))),
% 6.94/7.18 inference(bind,[status(th)],[])).
% 6.94/7.18 tff(40,plain,
% 6.94/7.18 (![B: $i, A: $i] : (rd(mult(A, B), B) = A) <=> ![B: $i, A: $i] : (rd(mult(A, B), B) = A)),
% 6.94/7.18 inference(quant_intro,[status(thm)],[39])).
% 6.94/7.18 tff(41,plain,
% 6.94/7.18 (![B: $i, A: $i] : (rd(mult(A, B), B) = A) <=> ![B: $i, A: $i] : (rd(mult(A, B), B) = A)),
% 6.94/7.18 inference(rewrite,[status(thm)],[])).
% 6.94/7.18 tff(42,axiom,(![B: $i, A: $i] : (rd(mult(A, B), B) = A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','f04')).
% 6.94/7.18 tff(43,plain,
% 6.94/7.18 (![B: $i, A: $i] : (rd(mult(A, B), B) = A)),
% 6.94/7.18 inference(modus_ponens,[status(thm)],[42, 41])).
% 6.94/7.18 tff(44,plain,(
% 6.94/7.18 ![B: $i, A: $i] : (rd(mult(A, B), B) = A)),
% 6.94/7.18 inference(skolemize,[status(sab)],[43])).
% 6.94/7.18 tff(45,plain,
% 6.94/7.18 (![B: $i, A: $i] : (rd(mult(A, B), B) = A)),
% 6.94/7.18 inference(modus_ponens,[status(thm)],[44, 40])).
% 6.94/7.18 tff(46,plain,
% 6.94/7.18 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(i(b), b), i(b)), i(b)) = mult(i(b), b))),
% 6.94/7.18 inference(quant_inst,[status(thm)],[])).
% 6.94/7.18 tff(47,plain,
% 6.94/7.18 (rd(mult(mult(i(b), b), i(b)), i(b)) = mult(i(b), b)),
% 6.94/7.18 inference(unit_resolution,[status(thm)],[46, 45])).
% 6.94/7.18 tff(48,plain,
% 6.94/7.18 (^[A: $i] : refl((mult(A, unit) = A) <=> (mult(A, unit) = A))),
% 6.94/7.18 inference(bind,[status(th)],[])).
% 6.94/7.18 tff(49,plain,
% 6.94/7.18 (![A: $i] : (mult(A, unit) = A) <=> ![A: $i] : (mult(A, unit) = A)),
% 6.94/7.18 inference(quant_intro,[status(thm)],[48])).
% 6.94/7.18 tff(50,plain,
% 6.94/7.18 (![A: $i] : (mult(A, unit) = A) <=> ![A: $i] : (mult(A, unit) = A)),
% 6.94/7.18 inference(rewrite,[status(thm)],[])).
% 6.94/7.18 tff(51,axiom,(![A: $i] : (mult(A, unit) = A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','f05')).
% 6.94/7.18 tff(52,plain,
% 6.94/7.18 (![A: $i] : (mult(A, unit) = A)),
% 6.94/7.18 inference(modus_ponens,[status(thm)],[51, 50])).
% 6.94/7.18 tff(53,plain,(
% 6.94/7.18 ![A: $i] : (mult(A, unit) = A)),
% 6.94/7.18 inference(skolemize,[status(sab)],[52])).
% 6.94/7.18 tff(54,plain,
% 6.94/7.18 (![A: $i] : (mult(A, unit) = A)),
% 6.94/7.18 inference(modus_ponens,[status(thm)],[53, 49])).
% 6.94/7.18 tff(55,plain,
% 6.94/7.18 ((~![A: $i] : (mult(A, unit) = A)) | (mult(i(b), unit) = i(b))),
% 6.94/7.18 inference(quant_inst,[status(thm)],[])).
% 6.94/7.18 tff(56,plain,
% 6.94/7.18 (mult(i(b), unit) = i(b)),
% 6.94/7.18 inference(unit_resolution,[status(thm)],[55, 54])).
% 6.94/7.18 tff(57,plain,
% 6.94/7.18 (^[B: $i, A: $i] : refl((mult(A, ld(A, B)) = B) <=> (mult(A, ld(A, B)) = B))),
% 6.94/7.18 inference(bind,[status(th)],[])).
% 6.94/7.18 tff(58,plain,
% 6.94/7.18 (![B: $i, A: $i] : (mult(A, ld(A, B)) = B) <=> ![B: $i, A: $i] : (mult(A, ld(A, B)) = B)),
% 6.94/7.18 inference(quant_intro,[status(thm)],[57])).
% 6.94/7.18 tff(59,plain,
% 6.94/7.18 (![B: $i, A: $i] : (mult(A, ld(A, B)) = B) <=> ![B: $i, A: $i] : (mult(A, ld(A, B)) = B)),
% 6.94/7.18 inference(rewrite,[status(thm)],[])).
% 6.94/7.18 tff(60,axiom,(![B: $i, A: $i] : (mult(A, ld(A, B)) = B)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','f01')).
% 6.94/7.18 tff(61,plain,
% 6.94/7.18 (![B: $i, A: $i] : (mult(A, ld(A, B)) = B)),
% 6.94/7.18 inference(modus_ponens,[status(thm)],[60, 59])).
% 6.94/7.18 tff(62,plain,(
% 6.94/7.18 ![B: $i, A: $i] : (mult(A, ld(A, B)) = B)),
% 6.94/7.18 inference(skolemize,[status(sab)],[61])).
% 6.94/7.18 tff(63,plain,
% 6.94/7.18 (![B: $i, A: $i] : (mult(A, ld(A, B)) = B)),
% 6.94/7.18 inference(modus_ponens,[status(thm)],[62, 58])).
% 6.94/7.18 tff(64,plain,
% 6.94/7.18 ((~![B: $i, A: $i] : (mult(A, ld(A, B)) = B)) | (mult(b, ld(b, unit)) = unit)),
% 6.94/7.18 inference(quant_inst,[status(thm)],[])).
% 6.94/7.18 tff(65,plain,
% 6.94/7.18 (mult(b, ld(b, unit)) = unit),
% 6.94/7.18 inference(unit_resolution,[status(thm)],[64, 63])).
% 6.94/7.18 tff(66,plain,
% 6.94/7.18 (^[A: $i] : refl((i(A) = ld(A, unit)) <=> (i(A) = ld(A, unit)))),
% 6.94/7.18 inference(bind,[status(th)],[])).
% 6.94/7.18 tff(67,plain,
% 6.94/7.18 (![A: $i] : (i(A) = ld(A, unit)) <=> ![A: $i] : (i(A) = ld(A, unit))),
% 6.94/7.18 inference(quant_intro,[status(thm)],[66])).
% 6.94/7.18 tff(68,plain,
% 6.94/7.18 (![A: $i] : (i(A) = ld(A, unit)) <=> ![A: $i] : (i(A) = ld(A, unit))),
% 6.94/7.18 inference(rewrite,[status(thm)],[])).
% 6.94/7.18 tff(69,axiom,(![A: $i] : (i(A) = ld(A, unit))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','f09')).
% 6.94/7.18 tff(70,plain,
% 6.94/7.18 (![A: $i] : (i(A) = ld(A, unit))),
% 6.94/7.18 inference(modus_ponens,[status(thm)],[69, 68])).
% 6.94/7.18 tff(71,plain,(
% 6.94/7.18 ![A: $i] : (i(A) = ld(A, unit))),
% 6.94/7.18 inference(skolemize,[status(sab)],[70])).
% 6.94/7.18 tff(72,plain,
% 6.94/7.18 (![A: $i] : (i(A) = ld(A, unit))),
% 6.94/7.18 inference(modus_ponens,[status(thm)],[71, 67])).
% 6.94/7.18 tff(73,plain,
% 6.94/7.18 ((~![A: $i] : (i(A) = ld(A, unit))) | (i(b) = ld(b, unit))),
% 6.94/7.18 inference(quant_inst,[status(thm)],[])).
% 6.94/7.18 tff(74,plain,
% 6.94/7.18 (i(b) = ld(b, unit)),
% 6.94/7.18 inference(unit_resolution,[status(thm)],[73, 72])).
% 6.94/7.18 tff(75,plain,
% 6.94/7.18 (mult(b, i(b)) = mult(b, ld(b, unit))),
% 6.94/7.18 inference(monotonicity,[status(thm)],[74])).
% 6.94/7.18 tff(76,plain,
% 6.94/7.18 (mult(b, i(b)) = unit),
% 6.94/7.18 inference(transitivity,[status(thm)],[75, 65])).
% 6.94/7.18 tff(77,plain,
% 6.94/7.18 (mult(i(b), mult(b, i(b))) = mult(i(b), unit)),
% 6.94/7.18 inference(monotonicity,[status(thm)],[76])).
% 6.94/7.18 tff(78,plain,
% 6.94/7.18 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(b, mult(i(b), i(b))) = mult(mult(b, i(b)), i(b)))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(b, mult(i(b), i(b))) = mult(mult(b, i(b)), i(b))))),
% 6.94/7.18 inference(rewrite,[status(thm)],[])).
% 6.94/7.18 tff(79,plain,
% 6.94/7.18 (((mult(b, mult(i(b), i(b))) = mult(mult(b, i(b)), i(b))) | (mult(b, mult(i(b), i(b))) = mult(mult(b, i(b)), i(b)))) <=> (mult(b, mult(i(b), i(b))) = mult(mult(b, i(b)), i(b)))),
% 6.94/7.18 inference(rewrite,[status(thm)],[])).
% 6.94/7.18 tff(80,plain,
% 6.94/7.18 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(b, mult(i(b), i(b))) = mult(mult(b, i(b)), i(b))) | (mult(b, mult(i(b), i(b))) = mult(mult(b, i(b)), i(b))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(b, mult(i(b), i(b))) = mult(mult(b, i(b)), i(b))))),
% 6.94/7.18 inference(monotonicity,[status(thm)],[79])).
% 6.94/7.18 tff(81,plain,
% 6.94/7.18 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(b, mult(i(b), i(b))) = mult(mult(b, i(b)), i(b))) | (mult(b, mult(i(b), i(b))) = mult(mult(b, i(b)), i(b))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(b, mult(i(b), i(b))) = mult(mult(b, i(b)), i(b))))),
% 6.94/7.18 inference(transitivity,[status(thm)],[80, 78])).
% 6.94/7.18 tff(82,plain,
% 6.94/7.18 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(b, mult(i(b), i(b))) = mult(mult(b, i(b)), i(b))) | (mult(b, mult(i(b), i(b))) = mult(mult(b, i(b)), i(b))))),
% 6.94/7.18 inference(quant_inst,[status(thm)],[])).
% 6.94/7.18 tff(83,plain,
% 6.94/7.18 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(b, mult(i(b), i(b))) = mult(mult(b, i(b)), i(b)))),
% 6.94/7.18 inference(modus_ponens,[status(thm)],[82, 81])).
% 6.94/7.18 tff(84,plain,
% 6.94/7.18 (mult(b, mult(i(b), i(b))) = mult(mult(b, i(b)), i(b))),
% 6.94/7.18 inference(unit_resolution,[status(thm)],[83, 27])).
% 6.94/7.18 tff(85,plain,
% 6.94/7.18 (mult(mult(b, i(b)), i(b)) = mult(b, mult(i(b), i(b)))),
% 6.94/7.18 inference(symmetry,[status(thm)],[84])).
% 6.94/7.18 tff(86,plain,
% 6.94/7.18 (mult(mult(b, i(b)), i(b)) = mult(unit, i(b))),
% 6.94/7.18 inference(monotonicity,[status(thm)],[76])).
% 6.94/7.18 tff(87,plain,
% 6.94/7.18 (mult(unit, i(b)) = mult(mult(b, i(b)), i(b))),
% 6.94/7.18 inference(symmetry,[status(thm)],[86])).
% 6.94/7.18 tff(88,plain,
% 6.94/7.18 (i(b) = mult(b, mult(i(b), i(b)))),
% 6.94/7.18 inference(transitivity,[status(thm)],[17, 87, 85])).
% 6.94/7.18 tff(89,plain,
% 6.94/7.18 (mult(i(b), b) = mult(mult(b, mult(i(b), i(b))), b)),
% 6.94/7.18 inference(monotonicity,[status(thm)],[88])).
% 6.94/7.18 tff(90,plain,
% 6.94/7.18 (mult(mult(b, mult(i(b), i(b))), b) = mult(i(b), b)),
% 6.94/7.18 inference(symmetry,[status(thm)],[89])).
% 6.94/7.18 tff(91,plain,
% 6.94/7.18 (mult(mult(b, mult(i(b), i(b))), b) = mult(mult(unit, i(b)), b)),
% 6.94/7.18 inference(transitivity,[status(thm)],[90, 38, 35])).
% 6.94/7.18 tff(92,plain,
% 6.94/7.18 ((~![A: $i] : (i(A) = ld(A, unit))) | (i(a) = ld(a, unit))),
% 6.94/7.18 inference(quant_inst,[status(thm)],[])).
% 6.94/7.18 tff(93,plain,
% 6.94/7.18 (i(a) = ld(a, unit)),
% 6.94/7.18 inference(unit_resolution,[status(thm)],[92, 72])).
% 6.94/7.18 tff(94,plain,
% 6.94/7.18 (mult(a, i(a)) = mult(a, ld(a, unit))),
% 6.94/7.18 inference(monotonicity,[status(thm)],[93])).
% 6.94/7.18 tff(95,plain,
% 6.94/7.18 (mult(a, ld(a, unit)) = mult(a, i(a))),
% 6.94/7.18 inference(symmetry,[status(thm)],[94])).
% 6.94/7.18 tff(96,plain,
% 6.94/7.18 ((~![B: $i, A: $i] : (mult(A, ld(A, B)) = B)) | (mult(a, ld(a, unit)) = unit)),
% 6.94/7.18 inference(quant_inst,[status(thm)],[])).
% 6.94/7.18 tff(97,plain,
% 6.94/7.18 (mult(a, ld(a, unit)) = unit),
% 6.94/7.18 inference(unit_resolution,[status(thm)],[96, 63])).
% 6.94/7.18 tff(98,plain,
% 6.94/7.18 (unit = mult(a, ld(a, unit))),
% 6.94/7.18 inference(symmetry,[status(thm)],[97])).
% 6.94/7.18 tff(99,plain,
% 6.94/7.18 (unit = mult(a, i(a))),
% 6.94/7.18 inference(transitivity,[status(thm)],[98, 95])).
% 6.94/7.18 tff(100,plain,
% 6.94/7.18 (mult(unit, mult(b, i(b))) = mult(mult(a, i(a)), unit)),
% 6.94/7.18 inference(monotonicity,[status(thm)],[99, 76])).
% 6.94/7.18 tff(101,plain,
% 6.94/7.18 (mult(mult(a, i(a)), unit) = mult(unit, mult(b, i(b)))),
% 6.94/7.18 inference(symmetry,[status(thm)],[100])).
% 6.94/7.18 tff(102,plain,
% 6.94/7.18 (mult(a, i(a)) = unit),
% 6.94/7.18 inference(transitivity,[status(thm)],[94, 97])).
% 6.94/7.18 tff(103,plain,
% 6.94/7.18 (mult(mult(a, i(a)), unit) = mult(unit, unit)),
% 6.94/7.18 inference(monotonicity,[status(thm)],[102])).
% 6.94/7.18 tff(104,plain,
% 6.94/7.18 (mult(unit, unit) = mult(mult(a, i(a)), unit)),
% 6.94/7.18 inference(symmetry,[status(thm)],[103])).
% 6.94/7.18 tff(105,plain,
% 6.94/7.18 ((~![A: $i] : (mult(unit, A) = A)) | (mult(unit, unit) = unit)),
% 6.94/7.18 inference(quant_inst,[status(thm)],[])).
% 6.94/7.18 tff(106,plain,
% 6.94/7.18 (mult(unit, unit) = unit),
% 6.94/7.18 inference(unit_resolution,[status(thm)],[105, 7])).
% 6.94/7.18 tff(107,plain,
% 6.94/7.18 (unit = mult(unit, unit)),
% 6.94/7.18 inference(symmetry,[status(thm)],[106])).
% 6.94/7.18 tff(108,plain,
% 6.94/7.18 (mult(b, mult(i(b), i(b))) = ld(b, unit)),
% 6.94/7.18 inference(transitivity,[status(thm)],[84, 86, 16, 74])).
% 6.94/7.18 tff(109,plain,
% 6.94/7.18 (mult(b, mult(b, mult(i(b), i(b)))) = mult(b, ld(b, unit))),
% 6.94/7.18 inference(monotonicity,[status(thm)],[108])).
% 6.94/7.18 tff(110,plain,
% 6.94/7.18 (mult(b, mult(b, mult(i(b), i(b)))) = mult(unit, mult(b, i(b)))),
% 6.94/7.18 inference(transitivity,[status(thm)],[109, 65, 107, 104, 101])).
% 6.94/7.18 tff(111,plain,
% 6.94/7.18 ((mult(b, mult(b, mult(i(b), i(b)))) = mult(mult(b, mult(i(b), i(b))), b)) <=> (mult(unit, mult(b, i(b))) = mult(mult(unit, i(b)), b))),
% 6.94/7.18 inference(monotonicity,[status(thm)],[110, 91])).
% 6.94/7.18 tff(112,plain,
% 6.94/7.18 ((mult(unit, mult(b, i(b))) = mult(mult(unit, i(b)), b)) <=> (mult(b, mult(b, mult(i(b), i(b)))) = mult(mult(b, mult(i(b), i(b))), b))),
% 6.94/7.18 inference(symmetry,[status(thm)],[111])).
% 6.94/7.18 tff(113,plain,
% 6.94/7.18 ((~(mult(unit, mult(b, i(b))) = mult(mult(unit, i(b)), b))) <=> (~(mult(b, mult(b, mult(i(b), i(b)))) = mult(mult(b, mult(i(b), i(b))), b)))),
% 6.94/7.18 inference(monotonicity,[status(thm)],[112])).
% 6.94/7.18 tff(114,plain,
% 6.94/7.18 (~(mult(b, mult(b, mult(i(b), i(b)))) = mult(mult(b, mult(i(b), i(b))), b))),
% 6.94/7.18 inference(modus_ponens,[status(thm)],[20, 113])).
% 6.94/7.18 tff(115,plain,
% 6.94/7.18 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(b, mult(mult(i(b), i(b)), b)) = mult(mult(b, mult(i(b), i(b))), b)) | (mult(b, mult(b, mult(i(b), i(b)))) = mult(mult(b, mult(i(b), i(b))), b)))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(b, mult(mult(i(b), i(b)), b)) = mult(mult(b, mult(i(b), i(b))), b)) | (mult(b, mult(b, mult(i(b), i(b)))) = mult(mult(b, mult(i(b), i(b))), b)))),
% 6.94/7.18 inference(rewrite,[status(thm)],[])).
% 6.94/7.18 tff(116,plain,
% 6.94/7.18 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(b, mult(mult(i(b), i(b)), b)) = mult(mult(b, mult(i(b), i(b))), b)) | (mult(b, mult(b, mult(i(b), i(b)))) = mult(mult(b, mult(i(b), i(b))), b)))),
% 6.94/7.18 inference(quant_inst,[status(thm)],[])).
% 6.94/7.18 tff(117,plain,
% 6.94/7.18 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(b, mult(mult(i(b), i(b)), b)) = mult(mult(b, mult(i(b), i(b))), b)) | (mult(b, mult(b, mult(i(b), i(b)))) = mult(mult(b, mult(i(b), i(b))), b))),
% 6.94/7.18 inference(modus_ponens,[status(thm)],[116, 115])).
% 6.94/7.18 tff(118,plain,
% 6.94/7.18 ((mult(b, mult(mult(i(b), i(b)), b)) = mult(mult(b, mult(i(b), i(b))), b)) | (mult(b, mult(b, mult(i(b), i(b)))) = mult(mult(b, mult(i(b), i(b))), b))),
% 6.94/7.18 inference(unit_resolution,[status(thm)],[117, 27])).
% 6.94/7.18 tff(119,plain,
% 6.94/7.18 (mult(b, mult(mult(i(b), i(b)), b)) = mult(mult(b, mult(i(b), i(b))), b)),
% 6.94/7.18 inference(unit_resolution,[status(thm)],[118, 114])).
% 6.94/7.18 tff(120,assumption,(mult(i(b), mult(b, i(b))) = mult(mult(i(b), i(b)), b)), introduced(assumption)).
% 6.94/7.18 tff(121,plain,
% 6.94/7.18 (mult(mult(i(b), i(b)), b) = mult(i(b), mult(b, i(b)))),
% 6.94/7.18 inference(symmetry,[status(thm)],[120])).
% 6.94/7.18 tff(122,plain,
% 6.94/7.18 (mult(mult(i(b), i(b)), b) = ld(b, unit)),
% 6.94/7.18 inference(transitivity,[status(thm)],[121, 77, 56, 74])).
% 6.94/7.18 tff(123,plain,
% 6.94/7.18 (mult(b, mult(mult(i(b), i(b)), b)) = mult(b, ld(b, unit))),
% 6.94/7.18 inference(monotonicity,[status(thm)],[122])).
% 6.94/7.18 tff(124,plain,
% 6.94/7.18 (mult(b, ld(b, unit)) = mult(b, mult(mult(i(b), i(b)), b))),
% 6.94/7.18 inference(symmetry,[status(thm)],[123])).
% 6.94/7.18 tff(125,plain,
% 6.94/7.18 (unit = mult(b, ld(b, unit))),
% 6.94/7.18 inference(symmetry,[status(thm)],[65])).
% 6.94/7.18 tff(126,plain,
% 6.94/7.18 (mult(unit, mult(b, i(b))) = mult(mult(unit, i(b)), b)),
% 6.94/7.18 inference(transitivity,[status(thm)],[100, 103, 106, 125, 124, 119, 90, 38, 35])).
% 6.94/7.18 tff(127,plain,
% 6.94/7.18 ($false),
% 6.94/7.18 inference(unit_resolution,[status(thm)],[20, 126])).
% 6.94/7.18 tff(128,plain,((~(mult(i(b), mult(b, i(b))) = mult(mult(i(b), i(b)), b))) | (mult(unit, mult(b, i(b))) = mult(mult(unit, i(b)), b))), inference(lemma,lemma(discharge,[]))).
% 6.94/7.18 tff(129,plain,
% 6.94/7.18 (~(mult(i(b), mult(b, i(b))) = mult(mult(i(b), i(b)), b))),
% 6.94/7.18 inference(unit_resolution,[status(thm)],[128, 20])).
% 6.94/7.18 tff(130,plain,
% 6.94/7.18 (^[B: $i, A: $i, C: $i] : refl(((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C))) <=> ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C))))),
% 6.94/7.18 inference(bind,[status(th)],[])).
% 6.94/7.18 tff(131,plain,
% 6.94/7.18 (![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C))) <=> ![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))),
% 6.94/7.18 inference(quant_intro,[status(thm)],[130])).
% 6.94/7.18 tff(132,plain,
% 6.94/7.18 (![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C))) <=> ![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))),
% 6.94/7.18 inference(rewrite,[status(thm)],[])).
% 6.94/7.18 tff(133,plain,
% 6.94/7.18 (^[B: $i, A: $i, C: $i] : rewrite(((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(B, C)) = mult(mult(A, C), B))) <=> ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C))))),
% 6.94/7.18 inference(bind,[status(th)],[])).
% 6.94/7.18 tff(134,plain,
% 6.94/7.18 (![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(B, C)) = mult(mult(A, C), B))) <=> ![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))),
% 6.94/7.18 inference(quant_intro,[status(thm)],[133])).
% 6.94/7.18 tff(135,axiom,(![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(B, C)) = mult(mult(A, C), B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','f07')).
% 6.94/7.18 tff(136,plain,
% 6.94/7.18 (![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))),
% 6.94/7.18 inference(modus_ponens,[status(thm)],[135, 134])).
% 6.94/7.18 tff(137,plain,
% 6.94/7.18 (![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))),
% 6.94/7.18 inference(modus_ponens,[status(thm)],[136, 132])).
% 6.94/7.18 tff(138,plain,(
% 6.94/7.18 ![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))),
% 6.94/7.18 inference(skolemize,[status(sab)],[137])).
% 6.94/7.18 tff(139,plain,
% 6.94/7.18 (![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))),
% 6.94/7.18 inference(modus_ponens,[status(thm)],[138, 131])).
% 6.94/7.18 tff(140,plain,
% 6.94/7.18 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | ((mult(i(b), mult(b, i(b))) = mult(mult(i(b), i(b)), b)) | (mult(i(b), mult(b, i(b))) = mult(mult(i(b), b), i(b))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | (mult(i(b), mult(b, i(b))) = mult(mult(i(b), i(b)), b)) | (mult(i(b), mult(b, i(b))) = mult(mult(i(b), b), i(b))))),
% 6.94/7.18 inference(rewrite,[status(thm)],[])).
% 6.94/7.18 tff(141,plain,
% 6.94/7.18 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | ((mult(i(b), mult(b, i(b))) = mult(mult(i(b), i(b)), b)) | (mult(i(b), mult(b, i(b))) = mult(mult(i(b), b), i(b))))),
% 6.94/7.19 inference(quant_inst,[status(thm)],[])).
% 6.94/7.19 tff(142,plain,
% 6.94/7.19 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | (mult(i(b), mult(b, i(b))) = mult(mult(i(b), i(b)), b)) | (mult(i(b), mult(b, i(b))) = mult(mult(i(b), b), i(b)))),
% 6.94/7.19 inference(modus_ponens,[status(thm)],[141, 140])).
% 6.94/7.19 tff(143,plain,
% 6.94/7.19 ((mult(i(b), mult(b, i(b))) = mult(mult(i(b), i(b)), b)) | (mult(i(b), mult(b, i(b))) = mult(mult(i(b), b), i(b)))),
% 6.94/7.19 inference(unit_resolution,[status(thm)],[142, 139])).
% 6.94/7.19 tff(144,plain,
% 6.94/7.19 (mult(i(b), mult(b, i(b))) = mult(mult(i(b), b), i(b))),
% 6.94/7.19 inference(unit_resolution,[status(thm)],[143, 129])).
% 6.94/7.19 tff(145,plain,
% 6.94/7.19 (mult(mult(i(b), b), i(b)) = mult(i(b), mult(b, i(b)))),
% 6.94/7.19 inference(symmetry,[status(thm)],[144])).
% 6.94/7.19 tff(146,plain,
% 6.94/7.19 (mult(mult(i(b), b), i(b)) = mult(unit, i(b))),
% 6.94/7.19 inference(transitivity,[status(thm)],[145, 77, 56, 17])).
% 6.94/7.19 tff(147,plain,
% 6.94/7.19 (rd(mult(mult(i(b), b), i(b)), i(b)) = rd(mult(unit, i(b)), i(b))),
% 6.94/7.19 inference(monotonicity,[status(thm)],[146])).
% 6.94/7.19 tff(148,plain,
% 6.94/7.19 (rd(mult(unit, i(b)), i(b)) = rd(mult(mult(i(b), b), i(b)), i(b))),
% 6.94/7.19 inference(symmetry,[status(thm)],[147])).
% 6.94/7.19 tff(149,plain,
% 6.94/7.19 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(unit, i(b)), i(b)) = unit)),
% 6.94/7.19 inference(quant_inst,[status(thm)],[])).
% 6.94/7.19 tff(150,plain,
% 6.94/7.19 (rd(mult(unit, i(b)), i(b)) = unit),
% 6.94/7.19 inference(unit_resolution,[status(thm)],[149, 45])).
% 6.94/7.19 tff(151,plain,
% 6.94/7.19 (unit = rd(mult(unit, i(b)), i(b))),
% 6.94/7.19 inference(symmetry,[status(thm)],[150])).
% 6.94/7.19 tff(152,plain,
% 6.94/7.19 (mult(unit, mult(b, i(b))) = mult(mult(unit, i(b)), b)),
% 6.94/7.19 inference(transitivity,[status(thm)],[100, 103, 106, 151, 148, 47, 38, 35])).
% 6.94/7.19 tff(153,plain,
% 6.94/7.19 ($false),
% 6.94/7.19 inference(unit_resolution,[status(thm)],[20, 152])).
% 6.94/7.19 tff(154,plain,(mult(unit, mult(b, i(b))) = mult(mult(unit, i(b)), b)), inference(lemma,lemma(discharge,[]))).
% 6.94/7.19 tff(155,plain,
% 6.94/7.19 (unit = mult(i(b), b)),
% 6.94/7.19 inference(transitivity,[status(thm)],[107, 104, 101, 154, 19])).
% 6.94/7.19 tff(156,plain,
% 6.94/7.19 (mult(unit, ld(mult(a, b), unit)) = mult(mult(i(b), b), ld(mult(a, b), unit))),
% 6.94/7.19 inference(monotonicity,[status(thm)],[155])).
% 6.94/7.19 tff(157,plain,
% 6.94/7.19 (mult(mult(i(b), b), ld(mult(a, b), unit)) = mult(unit, ld(mult(a, b), unit))),
% 6.94/7.19 inference(symmetry,[status(thm)],[156])).
% 6.94/7.19 tff(158,plain,
% 6.94/7.19 (mult(mult(i(b), b), ld(mult(a, b), unit)) = ld(mult(a, b), unit)),
% 6.94/7.19 inference(transitivity,[status(thm)],[157, 9])).
% 6.94/7.19 tff(159,plain,
% 6.94/7.19 (mult(mult(mult(i(b), b), ld(mult(a, b), unit)), b) = mult(ld(mult(a, b), unit), b)),
% 6.94/7.19 inference(monotonicity,[status(thm)],[158])).
% 6.94/7.19 tff(160,plain,
% 6.94/7.19 (^[B: $i, A: $i] : refl((ld(A, mult(A, B)) = B) <=> (ld(A, mult(A, B)) = B))),
% 6.94/7.19 inference(bind,[status(th)],[])).
% 6.94/7.19 tff(161,plain,
% 6.94/7.19 (![B: $i, A: $i] : (ld(A, mult(A, B)) = B) <=> ![B: $i, A: $i] : (ld(A, mult(A, B)) = B)),
% 6.94/7.19 inference(quant_intro,[status(thm)],[160])).
% 6.94/7.19 tff(162,plain,
% 6.94/7.19 (![B: $i, A: $i] : (ld(A, mult(A, B)) = B) <=> ![B: $i, A: $i] : (ld(A, mult(A, B)) = B)),
% 6.94/7.19 inference(rewrite,[status(thm)],[])).
% 6.94/7.19 tff(163,axiom,(![B: $i, A: $i] : (ld(A, mult(A, B)) = B)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','f02')).
% 6.94/7.19 tff(164,plain,
% 6.94/7.19 (![B: $i, A: $i] : (ld(A, mult(A, B)) = B)),
% 6.94/7.19 inference(modus_ponens,[status(thm)],[163, 162])).
% 6.94/7.19 tff(165,plain,(
% 6.94/7.19 ![B: $i, A: $i] : (ld(A, mult(A, B)) = B)),
% 6.94/7.19 inference(skolemize,[status(sab)],[164])).
% 6.94/7.19 tff(166,plain,
% 6.94/7.19 (![B: $i, A: $i] : (ld(A, mult(A, B)) = B)),
% 6.94/7.19 inference(modus_ponens,[status(thm)],[165, 161])).
% 6.94/7.19 tff(167,plain,
% 6.94/7.19 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(b, mult(b, ld(mult(a, b), unit))) = ld(mult(a, b), unit))),
% 6.94/7.19 inference(quant_inst,[status(thm)],[])).
% 6.94/7.19 tff(168,plain,
% 6.94/7.19 (ld(b, mult(b, ld(mult(a, b), unit))) = ld(mult(a, b), unit)),
% 6.94/7.19 inference(unit_resolution,[status(thm)],[167, 166])).
% 6.94/7.19 tff(169,plain,
% 6.94/7.19 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(a, mult(a, mult(b, ld(mult(a, b), unit)))) = mult(b, ld(mult(a, b), unit)))),
% 6.94/7.19 inference(quant_inst,[status(thm)],[])).
% 6.94/7.19 tff(170,plain,
% 6.94/7.19 (ld(a, mult(a, mult(b, ld(mult(a, b), unit)))) = mult(b, ld(mult(a, b), unit))),
% 6.94/7.19 inference(unit_resolution,[status(thm)],[169, 166])).
% 6.94/7.19 tff(171,plain,
% 6.94/7.19 ((~![B: $i, A: $i] : (mult(A, ld(A, B)) = B)) | (mult(mult(a, b), ld(mult(a, b), unit)) = unit)),
% 6.94/7.19 inference(quant_inst,[status(thm)],[])).
% 6.94/7.19 tff(172,plain,
% 6.94/7.19 (mult(mult(a, b), ld(mult(a, b), unit)) = unit),
% 6.94/7.19 inference(unit_resolution,[status(thm)],[171, 63])).
% 6.94/7.19 tff(173,plain,
% 6.94/7.19 (unit = mult(mult(a, b), ld(mult(a, b), unit))),
% 6.94/7.19 inference(symmetry,[status(thm)],[172])).
% 6.94/7.19 tff(174,plain,
% 6.94/7.19 (mult(mult(unit, i(b)), b) = mult(unit, mult(b, i(b)))),
% 6.94/7.19 inference(symmetry,[status(thm)],[154])).
% 6.94/7.19 tff(175,plain,
% 6.94/7.19 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(a, b), mult(mult(a, b), i(b))) = i(b))),
% 6.94/7.19 inference(quant_inst,[status(thm)],[])).
% 6.94/7.19 tff(176,plain,
% 6.94/7.19 (ld(mult(a, b), mult(mult(a, b), i(b))) = i(b)),
% 6.94/7.19 inference(unit_resolution,[status(thm)],[175, 166])).
% 6.94/7.19 tff(177,plain,
% 6.94/7.19 (mult(a, mult(b, i(b))) = mult(a, unit)),
% 6.94/7.19 inference(monotonicity,[status(thm)],[76])).
% 6.94/7.19 tff(178,plain,
% 6.94/7.19 (mult(a, unit) = mult(a, mult(b, i(b)))),
% 6.94/7.19 inference(symmetry,[status(thm)],[177])).
% 6.94/7.19 tff(179,plain,
% 6.94/7.19 (mult(i(b), b) = unit),
% 6.94/7.19 inference(transitivity,[status(thm)],[18, 174, 100, 103, 106])).
% 6.94/7.19 tff(180,plain,
% 6.94/7.19 (mult(a, mult(i(b), b)) = mult(a, unit)),
% 6.94/7.19 inference(monotonicity,[status(thm)],[179])).
% 6.94/7.19 tff(181,plain,
% 6.94/7.19 (mult(a, mult(i(b), b)) = mult(a, mult(b, i(b)))),
% 6.94/7.19 inference(transitivity,[status(thm)],[180, 178])).
% 6.94/7.19 tff(182,plain,
% 6.94/7.19 ((mult(a, mult(i(b), b)) = mult(mult(a, b), i(b))) <=> (mult(a, mult(b, i(b))) = mult(mult(a, b), i(b)))),
% 6.94/7.19 inference(monotonicity,[status(thm)],[181])).
% 6.94/7.19 tff(183,assumption,(~(mult(a, mult(b, i(b))) = mult(mult(a, b), i(b)))), introduced(assumption)).
% 6.94/7.19 tff(184,plain,
% 6.94/7.19 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(a, mult(b, i(b))) = mult(mult(a, b), i(b))) | (mult(a, mult(i(b), b)) = mult(mult(a, b), i(b))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(a, mult(b, i(b))) = mult(mult(a, b), i(b))) | (mult(a, mult(i(b), b)) = mult(mult(a, b), i(b))))),
% 6.94/7.19 inference(rewrite,[status(thm)],[])).
% 6.94/7.19 tff(185,plain,
% 6.94/7.19 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(a, mult(b, i(b))) = mult(mult(a, b), i(b))) | (mult(a, mult(i(b), b)) = mult(mult(a, b), i(b))))),
% 6.94/7.19 inference(quant_inst,[status(thm)],[])).
% 6.94/7.19 tff(186,plain,
% 6.94/7.19 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(a, mult(b, i(b))) = mult(mult(a, b), i(b))) | (mult(a, mult(i(b), b)) = mult(mult(a, b), i(b)))),
% 6.94/7.19 inference(modus_ponens,[status(thm)],[185, 184])).
% 6.94/7.19 tff(187,plain,
% 6.94/7.19 ((mult(a, mult(b, i(b))) = mult(mult(a, b), i(b))) | (mult(a, mult(i(b), b)) = mult(mult(a, b), i(b)))),
% 6.94/7.19 inference(unit_resolution,[status(thm)],[186, 27])).
% 6.94/7.19 tff(188,plain,
% 6.94/7.19 (mult(a, mult(i(b), b)) = mult(mult(a, b), i(b))),
% 6.94/7.19 inference(unit_resolution,[status(thm)],[187, 183])).
% 6.94/7.19 tff(189,plain,
% 6.94/7.19 (mult(a, mult(b, i(b))) = mult(mult(a, b), i(b))),
% 6.94/7.19 inference(modus_ponens,[status(thm)],[188, 182])).
% 6.94/7.19 tff(190,plain,
% 6.94/7.19 ($false),
% 6.94/7.19 inference(unit_resolution,[status(thm)],[183, 189])).
% 6.94/7.19 tff(191,plain,(mult(a, mult(b, i(b))) = mult(mult(a, b), i(b))), inference(lemma,lemma(discharge,[]))).
% 6.94/7.19 tff(192,plain,
% 6.94/7.19 ((~![A: $i] : (mult(A, unit) = A)) | (mult(a, unit) = a)),
% 6.94/7.19 inference(quant_inst,[status(thm)],[])).
% 6.94/7.19 tff(193,plain,
% 6.94/7.19 (mult(a, unit) = a),
% 6.94/7.19 inference(unit_resolution,[status(thm)],[192, 54])).
% 6.94/7.19 tff(194,plain,
% 6.94/7.19 (a = mult(a, unit)),
% 6.94/7.19 inference(symmetry,[status(thm)],[193])).
% 6.94/7.19 tff(195,plain,
% 6.94/7.19 ((~![A: $i] : (mult(unit, A) = A)) | (mult(unit, a) = a)),
% 6.94/7.19 inference(quant_inst,[status(thm)],[])).
% 7.03/7.19 tff(196,plain,
% 7.03/7.19 (mult(unit, a) = a),
% 7.03/7.19 inference(unit_resolution,[status(thm)],[195, 7])).
% 7.03/7.19 tff(197,plain,
% 7.03/7.19 (mult(mult(mult(a, b), ld(mult(a, b), unit)), a) = mult(unit, a)),
% 7.03/7.19 inference(monotonicity,[status(thm)],[172])).
% 7.03/7.19 tff(198,plain,
% 7.03/7.19 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(i(b), i(a)), a), a) = mult(i(b), i(a)))),
% 7.03/7.19 inference(quant_inst,[status(thm)],[])).
% 7.03/7.19 tff(199,plain,
% 7.03/7.19 (rd(mult(mult(i(b), i(a)), a), a) = mult(i(b), i(a))),
% 7.03/7.19 inference(unit_resolution,[status(thm)],[198, 45])).
% 7.03/7.19 tff(200,plain,
% 7.03/7.19 ((~![A: $i] : (mult(unit, A) = A)) | (mult(unit, i(a)) = i(a))),
% 7.03/7.19 inference(quant_inst,[status(thm)],[])).
% 7.03/7.19 tff(201,plain,
% 7.03/7.19 (mult(unit, i(a)) = i(a)),
% 7.03/7.19 inference(unit_resolution,[status(thm)],[200, 7])).
% 7.03/7.19 tff(202,plain,
% 7.03/7.19 (mult(mult(a, i(a)), i(a)) = mult(unit, i(a))),
% 7.03/7.19 inference(monotonicity,[status(thm)],[102])).
% 7.03/7.19 tff(203,plain,
% 7.03/7.19 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(a, mult(i(a), i(a))) = mult(mult(a, i(a)), i(a)))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(a, mult(i(a), i(a))) = mult(mult(a, i(a)), i(a))))),
% 7.03/7.19 inference(rewrite,[status(thm)],[])).
% 7.03/7.19 tff(204,plain,
% 7.03/7.19 (((mult(a, mult(i(a), i(a))) = mult(mult(a, i(a)), i(a))) | (mult(a, mult(i(a), i(a))) = mult(mult(a, i(a)), i(a)))) <=> (mult(a, mult(i(a), i(a))) = mult(mult(a, i(a)), i(a)))),
% 7.03/7.19 inference(rewrite,[status(thm)],[])).
% 7.03/7.19 tff(205,plain,
% 7.03/7.19 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(a, mult(i(a), i(a))) = mult(mult(a, i(a)), i(a))) | (mult(a, mult(i(a), i(a))) = mult(mult(a, i(a)), i(a))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(a, mult(i(a), i(a))) = mult(mult(a, i(a)), i(a))))),
% 7.03/7.19 inference(monotonicity,[status(thm)],[204])).
% 7.03/7.19 tff(206,plain,
% 7.03/7.19 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(a, mult(i(a), i(a))) = mult(mult(a, i(a)), i(a))) | (mult(a, mult(i(a), i(a))) = mult(mult(a, i(a)), i(a))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(a, mult(i(a), i(a))) = mult(mult(a, i(a)), i(a))))),
% 7.03/7.19 inference(transitivity,[status(thm)],[205, 203])).
% 7.03/7.19 tff(207,plain,
% 7.03/7.19 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(a, mult(i(a), i(a))) = mult(mult(a, i(a)), i(a))) | (mult(a, mult(i(a), i(a))) = mult(mult(a, i(a)), i(a))))),
% 7.03/7.19 inference(quant_inst,[status(thm)],[])).
% 7.03/7.19 tff(208,plain,
% 7.03/7.19 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(a, mult(i(a), i(a))) = mult(mult(a, i(a)), i(a)))),
% 7.03/7.19 inference(modus_ponens,[status(thm)],[207, 206])).
% 7.03/7.19 tff(209,plain,
% 7.03/7.19 (mult(a, mult(i(a), i(a))) = mult(mult(a, i(a)), i(a))),
% 7.03/7.19 inference(unit_resolution,[status(thm)],[208, 27])).
% 7.03/7.19 tff(210,plain,
% 7.03/7.19 (mult(a, mult(i(a), i(a))) = i(a)),
% 7.03/7.19 inference(transitivity,[status(thm)],[209, 202, 201])).
% 7.03/7.19 tff(211,plain,
% 7.03/7.19 (mult(i(b), mult(a, mult(i(a), i(a)))) = mult(i(b), i(a))),
% 7.03/7.19 inference(monotonicity,[status(thm)],[210])).
% 7.03/7.19 tff(212,plain,
% 7.03/7.19 (mult(i(b), i(a)) = mult(i(b), mult(a, mult(i(a), i(a))))),
% 7.03/7.19 inference(symmetry,[status(thm)],[211])).
% 7.03/7.19 tff(213,plain,
% 7.03/7.19 (mult(mult(unit, a), mult(i(a), i(a))) = mult(a, mult(i(a), i(a)))),
% 7.03/7.19 inference(monotonicity,[status(thm)],[196])).
% 7.03/7.19 tff(214,plain,
% 7.03/7.19 (mult(mult(unit, i(a)), i(a)) = mult(i(a), i(a))),
% 7.03/7.19 inference(monotonicity,[status(thm)],[201])).
% 7.03/7.19 tff(215,plain,
% 7.03/7.19 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(unit, mult(i(a), i(a))) = mult(mult(unit, i(a)), i(a)))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(unit, mult(i(a), i(a))) = mult(mult(unit, i(a)), i(a))))),
% 7.03/7.19 inference(rewrite,[status(thm)],[])).
% 7.03/7.19 tff(216,plain,
% 7.03/7.19 (((mult(unit, mult(i(a), i(a))) = mult(mult(unit, i(a)), i(a))) | (mult(unit, mult(i(a), i(a))) = mult(mult(unit, i(a)), i(a)))) <=> (mult(unit, mult(i(a), i(a))) = mult(mult(unit, i(a)), i(a)))),
% 7.03/7.19 inference(rewrite,[status(thm)],[])).
% 7.03/7.19 tff(217,plain,
% 7.03/7.19 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(unit, mult(i(a), i(a))) = mult(mult(unit, i(a)), i(a))) | (mult(unit, mult(i(a), i(a))) = mult(mult(unit, i(a)), i(a))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(unit, mult(i(a), i(a))) = mult(mult(unit, i(a)), i(a))))),
% 7.03/7.19 inference(monotonicity,[status(thm)],[216])).
% 7.03/7.19 tff(218,plain,
% 7.03/7.19 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(unit, mult(i(a), i(a))) = mult(mult(unit, i(a)), i(a))) | (mult(unit, mult(i(a), i(a))) = mult(mult(unit, i(a)), i(a))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(unit, mult(i(a), i(a))) = mult(mult(unit, i(a)), i(a))))),
% 7.03/7.19 inference(transitivity,[status(thm)],[217, 215])).
% 7.03/7.19 tff(219,plain,
% 7.03/7.19 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(unit, mult(i(a), i(a))) = mult(mult(unit, i(a)), i(a))) | (mult(unit, mult(i(a), i(a))) = mult(mult(unit, i(a)), i(a))))),
% 7.03/7.19 inference(quant_inst,[status(thm)],[])).
% 7.03/7.19 tff(220,plain,
% 7.03/7.19 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(unit, mult(i(a), i(a))) = mult(mult(unit, i(a)), i(a)))),
% 7.03/7.19 inference(modus_ponens,[status(thm)],[219, 218])).
% 7.03/7.19 tff(221,plain,
% 7.03/7.19 (mult(unit, mult(i(a), i(a))) = mult(mult(unit, i(a)), i(a))),
% 7.03/7.19 inference(unit_resolution,[status(thm)],[220, 27])).
% 7.03/7.19 tff(222,plain,
% 7.03/7.19 (mult(unit, mult(i(a), i(a))) = mult(i(a), i(a))),
% 7.03/7.19 inference(transitivity,[status(thm)],[221, 214])).
% 7.03/7.19 tff(223,plain,
% 7.03/7.19 (mult(mult(unit, mult(i(a), i(a))), a) = mult(mult(i(a), i(a)), a)),
% 7.03/7.19 inference(monotonicity,[status(thm)],[222])).
% 7.03/7.19 tff(224,plain,
% 7.03/7.19 (mult(mult(i(a), i(a)), a) = mult(mult(unit, mult(i(a), i(a))), a)),
% 7.03/7.19 inference(symmetry,[status(thm)],[223])).
% 7.03/7.19 tff(225,plain,
% 7.03/7.19 (mult(unit, mult(a, mult(i(a), i(a)))) = mult(mult(a, i(a)), i(a))),
% 7.03/7.19 inference(monotonicity,[status(thm)],[99, 210])).
% 7.03/7.19 tff(226,plain,
% 7.03/7.19 (mult(mult(a, i(a)), i(a)) = mult(unit, mult(a, mult(i(a), i(a))))),
% 7.03/7.19 inference(symmetry,[status(thm)],[225])).
% 7.03/7.19 tff(227,plain,
% 7.03/7.19 (mult(unit, mult(unit, i(a))) = mult(mult(a, i(a)), i(a))),
% 7.03/7.19 inference(monotonicity,[status(thm)],[99, 201])).
% 7.03/7.19 tff(228,plain,
% 7.03/7.19 (mult(mult(unit, i(a)), unit) = mult(i(a), unit)),
% 7.03/7.19 inference(monotonicity,[status(thm)],[201])).
% 7.03/7.19 tff(229,plain,
% 7.03/7.19 (mult(i(a), unit) = mult(mult(unit, i(a)), unit)),
% 7.03/7.19 inference(symmetry,[status(thm)],[228])).
% 7.03/7.19 tff(230,plain,
% 7.03/7.19 ((~![A: $i] : (mult(A, unit) = A)) | (mult(i(a), unit) = i(a))),
% 7.03/7.19 inference(quant_inst,[status(thm)],[])).
% 7.03/7.19 tff(231,plain,
% 7.03/7.19 (mult(i(a), unit) = i(a)),
% 7.03/7.19 inference(unit_resolution,[status(thm)],[230, 54])).
% 7.03/7.19 tff(232,plain,
% 7.03/7.19 (i(a) = mult(i(a), unit)),
% 7.03/7.19 inference(symmetry,[status(thm)],[231])).
% 7.03/7.19 tff(233,plain,
% 7.03/7.19 (mult(unit, mult(unit, i(a))) = mult(mult(unit, i(a)), unit)),
% 7.03/7.19 inference(transitivity,[status(thm)],[227, 202, 201, 232, 229])).
% 7.03/7.19 tff(234,assumption,(~(mult(unit, mult(unit, i(a))) = mult(mult(unit, i(a)), unit))), introduced(assumption)).
% 7.03/7.19 tff(235,plain,
% 7.03/7.19 ($false),
% 7.03/7.19 inference(unit_resolution,[status(thm)],[234, 233])).
% 7.03/7.19 tff(236,plain,(mult(unit, mult(unit, i(a))) = mult(mult(unit, i(a)), unit)), inference(lemma,lemma(discharge,[]))).
% 7.03/7.19 tff(237,plain,
% 7.03/7.19 (mult(mult(unit, i(a)), unit) = mult(unit, mult(unit, i(a)))),
% 7.03/7.19 inference(symmetry,[status(thm)],[236])).
% 7.03/7.19 tff(238,plain,
% 7.03/7.19 (i(a) = mult(unit, i(a))),
% 7.03/7.19 inference(symmetry,[status(thm)],[201])).
% 7.03/7.19 tff(239,plain,
% 7.03/7.19 (mult(i(a), unit) = mult(mult(unit, i(a)), unit)),
% 7.03/7.19 inference(monotonicity,[status(thm)],[238])).
% 7.03/7.19 tff(240,plain,
% 7.03/7.19 (mult(a, mult(i(a), i(a))) = ld(a, unit)),
% 7.03/7.19 inference(transitivity,[status(thm)],[209, 202, 201, 93])).
% 7.03/7.19 tff(241,plain,
% 7.03/7.19 (mult(a, mult(a, mult(i(a), i(a)))) = mult(a, ld(a, unit))),
% 7.03/7.19 inference(monotonicity,[status(thm)],[240])).
% 7.03/7.19 tff(242,assumption,(~(mult(a, mult(a, mult(i(a), i(a)))) = mult(mult(a, mult(i(a), i(a))), a))), introduced(assumption)).
% 7.03/7.19 tff(243,plain,
% 7.03/7.19 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(a, mult(mult(i(a), i(a)), a)) = mult(mult(a, mult(i(a), i(a))), a)) | (mult(a, mult(a, mult(i(a), i(a)))) = mult(mult(a, mult(i(a), i(a))), a)))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(a, mult(mult(i(a), i(a)), a)) = mult(mult(a, mult(i(a), i(a))), a)) | (mult(a, mult(a, mult(i(a), i(a)))) = mult(mult(a, mult(i(a), i(a))), a)))),
% 7.03/7.19 inference(rewrite,[status(thm)],[])).
% 7.03/7.19 tff(244,plain,
% 7.03/7.19 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(a, mult(mult(i(a), i(a)), a)) = mult(mult(a, mult(i(a), i(a))), a)) | (mult(a, mult(a, mult(i(a), i(a)))) = mult(mult(a, mult(i(a), i(a))), a)))),
% 7.03/7.19 inference(quant_inst,[status(thm)],[])).
% 7.03/7.19 tff(245,plain,
% 7.03/7.19 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(a, mult(mult(i(a), i(a)), a)) = mult(mult(a, mult(i(a), i(a))), a)) | (mult(a, mult(a, mult(i(a), i(a)))) = mult(mult(a, mult(i(a), i(a))), a))),
% 7.03/7.19 inference(modus_ponens,[status(thm)],[244, 243])).
% 7.03/7.19 tff(246,plain,
% 7.03/7.19 ((mult(a, mult(mult(i(a), i(a)), a)) = mult(mult(a, mult(i(a), i(a))), a)) | (mult(a, mult(a, mult(i(a), i(a)))) = mult(mult(a, mult(i(a), i(a))), a))),
% 7.03/7.19 inference(unit_resolution,[status(thm)],[245, 27])).
% 7.03/7.19 tff(247,plain,
% 7.03/7.19 (mult(a, mult(mult(i(a), i(a)), a)) = mult(mult(a, mult(i(a), i(a))), a)),
% 7.03/7.19 inference(unit_resolution,[status(thm)],[246, 242])).
% 7.03/7.19 tff(248,plain,
% 7.03/7.19 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | ((mult(a, mult(a, mult(i(a), i(a)))) = mult(mult(a, mult(i(a), i(a))), a)) | (mult(a, mult(a, mult(i(a), i(a)))) = mult(mult(a, a), mult(i(a), i(a)))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | (mult(a, mult(a, mult(i(a), i(a)))) = mult(mult(a, mult(i(a), i(a))), a)) | (mult(a, mult(a, mult(i(a), i(a)))) = mult(mult(a, a), mult(i(a), i(a)))))),
% 7.03/7.19 inference(rewrite,[status(thm)],[])).
% 7.03/7.19 tff(249,plain,
% 7.03/7.19 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | ((mult(a, mult(a, mult(i(a), i(a)))) = mult(mult(a, mult(i(a), i(a))), a)) | (mult(a, mult(a, mult(i(a), i(a)))) = mult(mult(a, a), mult(i(a), i(a)))))),
% 7.03/7.19 inference(quant_inst,[status(thm)],[])).
% 7.03/7.19 tff(250,plain,
% 7.03/7.19 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | (mult(a, mult(a, mult(i(a), i(a)))) = mult(mult(a, mult(i(a), i(a))), a)) | (mult(a, mult(a, mult(i(a), i(a)))) = mult(mult(a, a), mult(i(a), i(a))))),
% 7.03/7.19 inference(modus_ponens,[status(thm)],[249, 248])).
% 7.03/7.19 tff(251,plain,
% 7.03/7.19 ((mult(a, mult(a, mult(i(a), i(a)))) = mult(mult(a, mult(i(a), i(a))), a)) | (mult(a, mult(a, mult(i(a), i(a)))) = mult(mult(a, a), mult(i(a), i(a))))),
% 7.03/7.19 inference(unit_resolution,[status(thm)],[250, 139])).
% 7.03/7.19 tff(252,plain,
% 7.03/7.19 (mult(a, mult(a, mult(i(a), i(a)))) = mult(mult(a, a), mult(i(a), i(a)))),
% 7.03/7.19 inference(unit_resolution,[status(thm)],[251, 242])).
% 7.03/7.19 tff(253,plain,
% 7.03/7.19 (mult(mult(a, a), mult(i(a), i(a))) = mult(a, mult(a, mult(i(a), i(a))))),
% 7.03/7.20 inference(symmetry,[status(thm)],[252])).
% 7.03/7.20 tff(254,plain,
% 7.03/7.20 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(a, a), mult(i(a), i(a))) = mult(mult(mult(a, a), i(a)), i(a)))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(a, a), mult(i(a), i(a))) = mult(mult(mult(a, a), i(a)), i(a))))),
% 7.03/7.20 inference(rewrite,[status(thm)],[])).
% 7.03/7.20 tff(255,plain,
% 7.03/7.20 (((mult(mult(a, a), mult(i(a), i(a))) = mult(mult(mult(a, a), i(a)), i(a))) | (mult(mult(a, a), mult(i(a), i(a))) = mult(mult(mult(a, a), i(a)), i(a)))) <=> (mult(mult(a, a), mult(i(a), i(a))) = mult(mult(mult(a, a), i(a)), i(a)))),
% 7.03/7.20 inference(rewrite,[status(thm)],[])).
% 7.03/7.20 tff(256,plain,
% 7.03/7.20 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(mult(a, a), mult(i(a), i(a))) = mult(mult(mult(a, a), i(a)), i(a))) | (mult(mult(a, a), mult(i(a), i(a))) = mult(mult(mult(a, a), i(a)), i(a))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(a, a), mult(i(a), i(a))) = mult(mult(mult(a, a), i(a)), i(a))))),
% 7.03/7.20 inference(monotonicity,[status(thm)],[255])).
% 7.03/7.20 tff(257,plain,
% 7.03/7.20 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(mult(a, a), mult(i(a), i(a))) = mult(mult(mult(a, a), i(a)), i(a))) | (mult(mult(a, a), mult(i(a), i(a))) = mult(mult(mult(a, a), i(a)), i(a))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(a, a), mult(i(a), i(a))) = mult(mult(mult(a, a), i(a)), i(a))))),
% 7.03/7.20 inference(transitivity,[status(thm)],[256, 254])).
% 7.03/7.20 tff(258,plain,
% 7.03/7.20 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(mult(a, a), mult(i(a), i(a))) = mult(mult(mult(a, a), i(a)), i(a))) | (mult(mult(a, a), mult(i(a), i(a))) = mult(mult(mult(a, a), i(a)), i(a))))),
% 7.03/7.20 inference(quant_inst,[status(thm)],[])).
% 7.03/7.20 tff(259,plain,
% 7.03/7.20 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(a, a), mult(i(a), i(a))) = mult(mult(mult(a, a), i(a)), i(a)))),
% 7.03/7.20 inference(modus_ponens,[status(thm)],[258, 257])).
% 7.03/7.20 tff(260,plain,
% 7.03/7.20 (mult(mult(a, a), mult(i(a), i(a))) = mult(mult(mult(a, a), i(a)), i(a))),
% 7.03/7.20 inference(unit_resolution,[status(thm)],[259, 27])).
% 7.03/7.20 tff(261,plain,
% 7.03/7.20 (mult(mult(mult(a, a), i(a)), i(a)) = mult(mult(a, a), mult(i(a), i(a)))),
% 7.03/7.20 inference(symmetry,[status(thm)],[260])).
% 7.03/7.20 tff(262,plain,
% 7.03/7.20 (mult(mult(mult(a, a), i(a)), i(a)) = unit),
% 7.03/7.20 inference(transitivity,[status(thm)],[261, 253, 241, 97])).
% 7.03/7.20 tff(263,plain,
% 7.03/7.20 (mult(unit, mult(mult(mult(a, a), i(a)), i(a))) = mult(mult(a, i(a)), unit)),
% 7.03/7.20 inference(monotonicity,[status(thm)],[99, 262])).
% 7.03/7.20 tff(264,plain,
% 7.03/7.20 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(a, i(a)), i(a)) = a)),
% 7.03/7.20 inference(quant_inst,[status(thm)],[])).
% 7.03/7.20 tff(265,plain,
% 7.03/7.20 (rd(mult(a, i(a)), i(a)) = a),
% 7.03/7.20 inference(unit_resolution,[status(thm)],[264, 45])).
% 7.03/7.20 tff(266,plain,
% 7.03/7.20 (mult(mult(mult(a, a), i(a)), i(a)) = mult(a, i(a))),
% 7.03/7.20 inference(transitivity,[status(thm)],[261, 253, 241, 95])).
% 7.03/7.20 tff(267,plain,
% 7.03/7.20 (rd(mult(mult(mult(a, a), i(a)), i(a)), i(a)) = rd(mult(a, i(a)), i(a))),
% 7.03/7.20 inference(monotonicity,[status(thm)],[266])).
% 7.03/7.20 tff(268,plain,
% 7.03/7.20 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(a, a), i(a)), i(a)), i(a)) = mult(mult(a, a), i(a)))),
% 7.03/7.20 inference(quant_inst,[status(thm)],[])).
% 7.03/7.20 tff(269,plain,
% 7.03/7.20 (rd(mult(mult(mult(a, a), i(a)), i(a)), i(a)) = mult(mult(a, a), i(a))),
% 7.03/7.20 inference(unit_resolution,[status(thm)],[268, 45])).
% 7.03/7.20 tff(270,plain,
% 7.03/7.20 (mult(mult(a, a), i(a)) = rd(mult(mult(mult(a, a), i(a)), i(a)), i(a))),
% 7.03/7.20 inference(symmetry,[status(thm)],[269])).
% 7.03/7.20 tff(271,plain,
% 7.03/7.20 (mult(mult(a, a), i(a)) = a),
% 7.03/7.20 inference(transitivity,[status(thm)],[270, 267, 265])).
% 7.03/7.20 tff(272,plain,
% 7.03/7.20 (mult(mult(a, i(a)), i(a)) = mult(a, mult(i(a), i(a)))),
% 7.03/7.20 inference(symmetry,[status(thm)],[209])).
% 7.03/7.20 tff(273,plain,
% 7.03/7.20 (mult(unit, i(a)) = mult(mult(a, i(a)), i(a))),
% 7.03/7.20 inference(symmetry,[status(thm)],[202])).
% 7.03/7.20 tff(274,plain,
% 7.03/7.20 (i(a) = mult(a, mult(i(a), i(a)))),
% 7.03/7.20 inference(transitivity,[status(thm)],[238, 273, 272])).
% 7.03/7.20 tff(275,plain,
% 7.03/7.20 (mult(i(a), mult(mult(a, a), i(a))) = mult(mult(a, mult(i(a), i(a))), a)),
% 7.03/7.20 inference(monotonicity,[status(thm)],[274, 271])).
% 7.03/7.20 tff(276,plain,
% 7.03/7.20 (mult(mult(unit, i(a)), mult(mult(a, a), i(a))) = mult(i(a), mult(mult(a, a), i(a)))),
% 7.03/7.20 inference(monotonicity,[status(thm)],[201])).
% 7.03/7.20 tff(277,plain,
% 7.03/7.20 (mult(mult(unit, i(a)), mult(mult(a, a), i(a))) = mult(mult(a, mult(i(a), i(a))), a)),
% 7.03/7.20 inference(transitivity,[status(thm)],[276, 275])).
% 7.03/7.20 tff(278,plain,
% 7.03/7.20 (mult(a, ld(a, unit)) = mult(a, mult(a, mult(i(a), i(a))))),
% 7.03/7.20 inference(symmetry,[status(thm)],[241])).
% 7.03/7.20 tff(279,plain,
% 7.03/7.20 (mult(unit, mult(mult(mult(a, a), i(a)), i(a))) = mult(a, mult(a, mult(i(a), i(a))))),
% 7.03/7.20 inference(transitivity,[status(thm)],[263, 103, 106, 98, 278])).
% 7.03/7.20 tff(280,plain,
% 7.03/7.20 ((mult(unit, mult(mult(mult(a, a), i(a)), i(a))) = mult(mult(unit, i(a)), mult(mult(a, a), i(a)))) <=> (mult(a, mult(a, mult(i(a), i(a)))) = mult(mult(a, mult(i(a), i(a))), a))),
% 7.03/7.20 inference(monotonicity,[status(thm)],[279, 277])).
% 7.03/7.20 tff(281,plain,
% 7.03/7.20 ((mult(a, mult(a, mult(i(a), i(a)))) = mult(mult(a, mult(i(a), i(a))), a)) <=> (mult(unit, mult(mult(mult(a, a), i(a)), i(a))) = mult(mult(unit, i(a)), mult(mult(a, a), i(a))))),
% 7.03/7.20 inference(symmetry,[status(thm)],[280])).
% 7.03/7.20 tff(282,plain,
% 7.03/7.20 ((~(mult(a, mult(a, mult(i(a), i(a)))) = mult(mult(a, mult(i(a), i(a))), a))) <=> (~(mult(unit, mult(mult(mult(a, a), i(a)), i(a))) = mult(mult(unit, i(a)), mult(mult(a, a), i(a)))))),
% 7.03/7.20 inference(monotonicity,[status(thm)],[281])).
% 7.03/7.20 tff(283,plain,
% 7.03/7.20 (~(mult(unit, mult(mult(mult(a, a), i(a)), i(a))) = mult(mult(unit, i(a)), mult(mult(a, a), i(a))))),
% 7.03/7.20 inference(modus_ponens,[status(thm)],[242, 282])).
% 7.03/7.20 tff(284,plain,
% 7.03/7.20 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | ((mult(unit, mult(mult(mult(a, a), i(a)), i(a))) = mult(mult(unit, i(a)), mult(mult(a, a), i(a)))) | (mult(unit, mult(mult(mult(a, a), i(a)), i(a))) = mult(mult(unit, mult(mult(a, a), i(a))), i(a))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | (mult(unit, mult(mult(mult(a, a), i(a)), i(a))) = mult(mult(unit, i(a)), mult(mult(a, a), i(a)))) | (mult(unit, mult(mult(mult(a, a), i(a)), i(a))) = mult(mult(unit, mult(mult(a, a), i(a))), i(a))))),
% 7.03/7.20 inference(rewrite,[status(thm)],[])).
% 7.03/7.20 tff(285,plain,
% 7.03/7.20 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | ((mult(unit, mult(mult(mult(a, a), i(a)), i(a))) = mult(mult(unit, i(a)), mult(mult(a, a), i(a)))) | (mult(unit, mult(mult(mult(a, a), i(a)), i(a))) = mult(mult(unit, mult(mult(a, a), i(a))), i(a))))),
% 7.03/7.20 inference(quant_inst,[status(thm)],[])).
% 7.03/7.20 tff(286,plain,
% 7.03/7.20 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | (mult(unit, mult(mult(mult(a, a), i(a)), i(a))) = mult(mult(unit, i(a)), mult(mult(a, a), i(a)))) | (mult(unit, mult(mult(mult(a, a), i(a)), i(a))) = mult(mult(unit, mult(mult(a, a), i(a))), i(a)))),
% 7.03/7.20 inference(modus_ponens,[status(thm)],[285, 284])).
% 7.03/7.20 tff(287,plain,
% 7.03/7.20 ((mult(unit, mult(mult(mult(a, a), i(a)), i(a))) = mult(mult(unit, i(a)), mult(mult(a, a), i(a)))) | (mult(unit, mult(mult(mult(a, a), i(a)), i(a))) = mult(mult(unit, mult(mult(a, a), i(a))), i(a)))),
% 7.03/7.20 inference(unit_resolution,[status(thm)],[286, 139])).
% 7.03/7.20 tff(288,plain,
% 7.03/7.20 (mult(unit, mult(mult(mult(a, a), i(a)), i(a))) = mult(mult(unit, mult(mult(a, a), i(a))), i(a))),
% 7.03/7.20 inference(unit_resolution,[status(thm)],[287, 283])).
% 7.03/7.20 tff(289,plain,
% 7.03/7.20 (mult(mult(unit, mult(mult(a, a), i(a))), i(a)) = mult(unit, mult(mult(mult(a, a), i(a)), i(a)))),
% 7.03/7.20 inference(symmetry,[status(thm)],[288])).
% 7.03/7.20 tff(290,plain,
% 7.03/7.20 (mult(unit, mult(mult(a, a), i(a))) = mult(mult(mult(a, b), ld(mult(a, b), unit)), a)),
% 7.03/7.20 inference(monotonicity,[status(thm)],[173, 271])).
% 7.03/7.20 tff(291,plain,
% 7.03/7.20 (mult(mult(mult(a, b), ld(mult(a, b), unit)), a) = mult(unit, mult(mult(a, a), i(a)))),
% 7.03/7.20 inference(symmetry,[status(thm)],[290])).
% 7.03/7.20 tff(292,plain,
% 7.03/7.20 (mult(unit, a) = mult(mult(mult(a, b), ld(mult(a, b), unit)), a)),
% 7.03/7.20 inference(symmetry,[status(thm)],[197])).
% 7.03/7.20 tff(293,plain,
% 7.03/7.20 (mult(unit, a) = mult(unit, mult(mult(a, a), i(a)))),
% 7.03/7.20 inference(transitivity,[status(thm)],[292, 291])).
% 7.03/7.20 tff(294,plain,
% 7.03/7.20 (mult(mult(unit, a), i(a)) = mult(mult(unit, mult(mult(a, a), i(a))), i(a))),
% 7.03/7.20 inference(monotonicity,[status(thm)],[293])).
% 7.03/7.20 tff(295,plain,
% 7.03/7.20 (mult(mult(mult(mult(a, b), ld(mult(a, b), unit)), a), i(a)) = mult(mult(unit, a), i(a))),
% 7.03/7.20 inference(monotonicity,[status(thm)],[197])).
% 7.03/7.20 tff(296,plain,
% 7.03/7.20 (mult(mult(mult(mult(a, b), ld(mult(a, b), unit)), a), i(a)) = unit),
% 7.03/7.20 inference(transitivity,[status(thm)],[295, 294, 289, 263, 103, 106])).
% 7.03/7.20 tff(297,plain,
% 7.03/7.20 (mult(i(a), mult(mult(mult(mult(a, b), ld(mult(a, b), unit)), a), i(a))) = mult(i(a), unit)),
% 7.03/7.20 inference(monotonicity,[status(thm)],[296])).
% 7.03/7.20 tff(298,plain,
% 7.03/7.20 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(a, mult(i(a), i(a))), a), i(a)), i(a)) = mult(mult(a, mult(i(a), i(a))), a))),
% 7.03/7.20 inference(quant_inst,[status(thm)],[])).
% 7.03/7.20 tff(299,plain,
% 7.03/7.20 (rd(mult(mult(mult(a, mult(i(a), i(a))), a), i(a)), i(a)) = mult(mult(a, mult(i(a), i(a))), a)),
% 7.03/7.20 inference(unit_resolution,[status(thm)],[298, 45])).
% 7.03/7.20 tff(300,assumption,(mult(i(a), mult(mult(mult(mult(a, b), ld(mult(a, b), unit)), a), i(a))) = mult(mult(i(a), mult(mult(mult(a, b), ld(mult(a, b), unit)), a)), i(a))), introduced(assumption)).
% 7.03/7.20 tff(301,plain,
% 7.03/7.20 (mult(mult(i(a), mult(mult(mult(a, b), ld(mult(a, b), unit)), a)), i(a)) = mult(i(a), mult(mult(mult(mult(a, b), ld(mult(a, b), unit)), a), i(a)))),
% 7.03/7.20 inference(symmetry,[status(thm)],[300])).
% 7.03/7.20 tff(302,plain,
% 7.03/7.20 (mult(i(a), mult(mult(mult(a, b), ld(mult(a, b), unit)), a)) = mult(i(a), mult(unit, a))),
% 7.03/7.20 inference(monotonicity,[status(thm)],[197])).
% 7.03/7.20 tff(303,plain,
% 7.03/7.20 (mult(i(a), mult(unit, a)) = mult(i(a), mult(mult(mult(a, b), ld(mult(a, b), unit)), a))),
% 7.03/7.20 inference(symmetry,[status(thm)],[302])).
% 7.03/7.20 tff(304,plain,
% 7.03/7.20 (mult(i(a), mult(unit, a)) = mult(mult(a, mult(i(a), i(a))), a)),
% 7.03/7.20 inference(monotonicity,[status(thm)],[274, 196])).
% 7.03/7.20 tff(305,plain,
% 7.03/7.20 (mult(mult(a, mult(i(a), i(a))), a) = mult(i(a), mult(unit, a))),
% 7.03/7.20 inference(symmetry,[status(thm)],[304])).
% 7.03/7.20 tff(306,plain,
% 7.03/7.20 (mult(i(a), a) = mult(mult(a, mult(i(a), i(a))), a)),
% 7.03/7.20 inference(monotonicity,[status(thm)],[274])).
% 7.03/7.20 tff(307,plain,
% 7.03/7.20 (mult(i(a), a) = mult(i(a), mult(mult(mult(a, b), ld(mult(a, b), unit)), a))),
% 7.03/7.20 inference(transitivity,[status(thm)],[306, 305, 303])).
% 7.03/7.20 tff(308,plain,
% 7.03/7.20 (mult(mult(i(a), a), i(a)) = mult(mult(i(a), mult(mult(mult(a, b), ld(mult(a, b), unit)), a)), i(a))),
% 7.03/7.20 inference(monotonicity,[status(thm)],[307])).
% 7.03/7.20 tff(309,plain,
% 7.03/7.20 (mult(mult(a, mult(i(a), i(a))), a) = mult(i(a), a)),
% 7.03/7.20 inference(symmetry,[status(thm)],[306])).
% 7.03/7.20 tff(310,plain,
% 7.03/7.20 (mult(mult(mult(a, mult(i(a), i(a))), a), i(a)) = mult(mult(i(a), a), i(a))),
% 7.03/7.20 inference(monotonicity,[status(thm)],[309])).
% 7.03/7.20 tff(311,plain,
% 7.03/7.20 (mult(mult(mult(a, mult(i(a), i(a))), a), i(a)) = mult(unit, i(a))),
% 7.03/7.20 inference(transitivity,[status(thm)],[310, 308, 301, 297, 239, 237, 227, 202])).
% 7.03/7.20 tff(312,plain,
% 7.03/7.20 (rd(mult(mult(mult(a, mult(i(a), i(a))), a), i(a)), i(a)) = rd(mult(unit, i(a)), i(a))),
% 7.03/7.20 inference(monotonicity,[status(thm)],[311])).
% 7.03/7.20 tff(313,plain,
% 7.03/7.20 (rd(mult(unit, i(a)), i(a)) = rd(mult(mult(mult(a, mult(i(a), i(a))), a), i(a)), i(a))),
% 7.03/7.20 inference(symmetry,[status(thm)],[312])).
% 7.03/7.20 tff(314,plain,
% 7.03/7.20 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(unit, i(a)), i(a)) = unit)),
% 7.03/7.20 inference(quant_inst,[status(thm)],[])).
% 7.03/7.20 tff(315,plain,
% 7.03/7.20 (rd(mult(unit, i(a)), i(a)) = unit),
% 7.03/7.20 inference(unit_resolution,[status(thm)],[314, 45])).
% 7.03/7.20 tff(316,plain,
% 7.03/7.20 (unit = rd(mult(unit, i(a)), i(a))),
% 7.03/7.20 inference(symmetry,[status(thm)],[315])).
% 7.03/7.20 tff(317,plain,
% 7.03/7.20 (mult(a, mult(a, mult(i(a), i(a)))) = mult(mult(a, mult(i(a), i(a))), a)),
% 7.03/7.20 inference(transitivity,[status(thm)],[241, 97, 316, 313, 299])).
% 7.03/7.20 tff(318,plain,
% 7.03/7.20 ($false),
% 7.03/7.20 inference(unit_resolution,[status(thm)],[242, 317])).
% 7.03/7.20 tff(319,plain,((~(mult(i(a), mult(mult(mult(mult(a, b), ld(mult(a, b), unit)), a), i(a))) = mult(mult(i(a), mult(mult(mult(a, b), ld(mult(a, b), unit)), a)), i(a)))) | (mult(a, mult(a, mult(i(a), i(a)))) = mult(mult(a, mult(i(a), i(a))), a))), inference(lemma,lemma(discharge,[]))).
% 7.03/7.20 tff(320,plain,
% 7.03/7.20 (~(mult(i(a), mult(mult(mult(mult(a, b), ld(mult(a, b), unit)), a), i(a))) = mult(mult(i(a), mult(mult(mult(a, b), ld(mult(a, b), unit)), a)), i(a)))),
% 7.03/7.20 inference(unit_resolution,[status(thm)],[319, 242])).
% 7.03/7.20 tff(321,plain,
% 7.03/7.20 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | ((mult(i(a), mult(mult(mult(mult(a, b), ld(mult(a, b), unit)), a), i(a))) = mult(mult(i(a), i(a)), mult(mult(mult(a, b), ld(mult(a, b), unit)), a))) | (mult(i(a), mult(mult(mult(mult(a, b), ld(mult(a, b), unit)), a), i(a))) = mult(mult(i(a), mult(mult(mult(a, b), ld(mult(a, b), unit)), a)), i(a))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | (mult(i(a), mult(mult(mult(mult(a, b), ld(mult(a, b), unit)), a), i(a))) = mult(mult(i(a), i(a)), mult(mult(mult(a, b), ld(mult(a, b), unit)), a))) | (mult(i(a), mult(mult(mult(mult(a, b), ld(mult(a, b), unit)), a), i(a))) = mult(mult(i(a), mult(mult(mult(a, b), ld(mult(a, b), unit)), a)), i(a))))),
% 7.03/7.20 inference(rewrite,[status(thm)],[])).
% 7.03/7.20 tff(322,plain,
% 7.03/7.20 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | ((mult(i(a), mult(mult(mult(mult(a, b), ld(mult(a, b), unit)), a), i(a))) = mult(mult(i(a), i(a)), mult(mult(mult(a, b), ld(mult(a, b), unit)), a))) | (mult(i(a), mult(mult(mult(mult(a, b), ld(mult(a, b), unit)), a), i(a))) = mult(mult(i(a), mult(mult(mult(a, b), ld(mult(a, b), unit)), a)), i(a))))),
% 7.03/7.20 inference(quant_inst,[status(thm)],[])).
% 7.03/7.20 tff(323,plain,
% 7.03/7.20 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | (mult(i(a), mult(mult(mult(mult(a, b), ld(mult(a, b), unit)), a), i(a))) = mult(mult(i(a), i(a)), mult(mult(mult(a, b), ld(mult(a, b), unit)), a))) | (mult(i(a), mult(mult(mult(mult(a, b), ld(mult(a, b), unit)), a), i(a))) = mult(mult(i(a), mult(mult(mult(a, b), ld(mult(a, b), unit)), a)), i(a)))),
% 7.03/7.20 inference(modus_ponens,[status(thm)],[322, 321])).
% 7.03/7.20 tff(324,plain,
% 7.03/7.20 ((mult(i(a), mult(mult(mult(mult(a, b), ld(mult(a, b), unit)), a), i(a))) = mult(mult(i(a), i(a)), mult(mult(mult(a, b), ld(mult(a, b), unit)), a))) | (mult(i(a), mult(mult(mult(mult(a, b), ld(mult(a, b), unit)), a), i(a))) = mult(mult(i(a), mult(mult(mult(a, b), ld(mult(a, b), unit)), a)), i(a)))),
% 7.03/7.20 inference(unit_resolution,[status(thm)],[323, 139])).
% 7.03/7.20 tff(325,plain,
% 7.03/7.20 (mult(i(a), mult(mult(mult(mult(a, b), ld(mult(a, b), unit)), a), i(a))) = mult(mult(i(a), i(a)), mult(mult(mult(a, b), ld(mult(a, b), unit)), a))),
% 7.03/7.20 inference(unit_resolution,[status(thm)],[324, 320])).
% 7.03/7.20 tff(326,plain,
% 7.03/7.20 (mult(mult(i(a), i(a)), mult(mult(mult(a, b), ld(mult(a, b), unit)), a)) = mult(i(a), mult(mult(mult(mult(a, b), ld(mult(a, b), unit)), a), i(a)))),
% 7.03/7.20 inference(symmetry,[status(thm)],[325])).
% 7.03/7.20 tff(327,plain,
% 7.03/7.20 (mult(mult(i(a), i(a)), mult(unit, a)) = mult(mult(i(a), i(a)), mult(mult(mult(a, b), ld(mult(a, b), unit)), a))),
% 7.03/7.20 inference(monotonicity,[status(thm)],[292])).
% 7.03/7.20 tff(328,plain,
% 7.03/7.20 (a = mult(unit, a)),
% 7.03/7.20 inference(symmetry,[status(thm)],[196])).
% 7.03/7.20 tff(329,plain,
% 7.03/7.20 (mult(mult(i(a), i(a)), a) = mult(mult(i(a), i(a)), mult(unit, a))),
% 7.03/7.20 inference(monotonicity,[status(thm)],[328])).
% 7.03/7.20 tff(330,plain,
% 7.03/7.20 (mult(mult(i(a), i(a)), a) = ld(a, unit)),
% 7.03/7.20 inference(transitivity,[status(thm)],[329, 327, 326, 297, 239, 237, 227, 202, 201, 93])).
% 7.03/7.20 tff(331,plain,
% 7.03/7.20 (mult(a, mult(mult(i(a), i(a)), a)) = mult(a, ld(a, unit))),
% 7.03/7.20 inference(monotonicity,[status(thm)],[330])).
% 7.03/7.20 tff(332,plain,
% 7.03/7.20 (mult(a, ld(a, unit)) = mult(a, mult(mult(i(a), i(a)), a))),
% 7.03/7.20 inference(symmetry,[status(thm)],[331])).
% 7.03/7.20 tff(333,plain,
% 7.03/7.20 (mult(a, mult(a, mult(i(a), i(a)))) = mult(mult(a, mult(i(a), i(a))), a)),
% 7.03/7.20 inference(transitivity,[status(thm)],[241, 332, 247])).
% 7.03/7.20 tff(334,plain,
% 7.03/7.20 ($false),
% 7.03/7.20 inference(unit_resolution,[status(thm)],[242, 333])).
% 7.03/7.20 tff(335,plain,(mult(a, mult(a, mult(i(a), i(a)))) = mult(mult(a, mult(i(a), i(a))), a)), inference(lemma,lemma(discharge,[]))).
% 7.03/7.20 tff(336,plain,
% 7.03/7.20 (mult(mult(a, mult(i(a), i(a))), a) = mult(a, mult(a, mult(i(a), i(a))))),
% 7.03/7.20 inference(symmetry,[status(thm)],[335])).
% 7.03/7.20 tff(337,plain,
% 7.03/7.20 (mult(i(a), a) = unit),
% 7.03/7.20 inference(transitivity,[status(thm)],[306, 336, 241, 97])).
% 7.03/7.20 tff(338,plain,
% 7.03/7.20 (mult(i(a), mult(i(a), a)) = mult(i(a), unit)),
% 7.03/7.20 inference(monotonicity,[status(thm)],[337])).
% 7.03/7.20 tff(339,plain,
% 7.03/7.20 (mult(i(a), mult(i(a), a)) = mult(unit, mult(a, mult(i(a), i(a))))),
% 7.03/7.20 inference(transitivity,[status(thm)],[338, 239, 237, 227, 226])).
% 7.03/7.20 tff(340,plain,
% 7.03/7.20 ((mult(i(a), mult(i(a), a)) = mult(mult(i(a), i(a)), a)) <=> (mult(unit, mult(a, mult(i(a), i(a)))) = mult(mult(unit, mult(i(a), i(a))), a))),
% 7.03/7.20 inference(monotonicity,[status(thm)],[339, 224])).
% 7.03/7.20 tff(341,plain,
% 7.03/7.20 ((mult(unit, mult(a, mult(i(a), i(a)))) = mult(mult(unit, mult(i(a), i(a))), a)) <=> (mult(i(a), mult(i(a), a)) = mult(mult(i(a), i(a)), a))),
% 7.03/7.20 inference(symmetry,[status(thm)],[340])).
% 7.03/7.20 tff(342,plain,
% 7.03/7.20 ((mult(mult(unit, mult(i(a), i(a))), a) = mult(unit, mult(a, mult(i(a), i(a))))) <=> (mult(unit, mult(a, mult(i(a), i(a)))) = mult(mult(unit, mult(i(a), i(a))), a))),
% 7.03/7.20 inference(commutativity,[status(thm)],[])).
% 7.03/7.20 tff(343,assumption,(~(mult(unit, mult(mult(i(a), i(a)), a)) = mult(mult(unit, a), mult(i(a), i(a))))), introduced(assumption)).
% 7.03/7.20 tff(344,plain,
% 7.03/7.20 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(unit, mult(a, mult(i(a), i(a)))) = mult(mult(unit, a), mult(i(a), i(a)))) | (mult(unit, mult(mult(i(a), i(a)), a)) = mult(mult(unit, a), mult(i(a), i(a)))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(unit, mult(a, mult(i(a), i(a)))) = mult(mult(unit, a), mult(i(a), i(a)))) | (mult(unit, mult(mult(i(a), i(a)), a)) = mult(mult(unit, a), mult(i(a), i(a)))))),
% 7.03/7.20 inference(rewrite,[status(thm)],[])).
% 7.03/7.20 tff(345,plain,
% 7.03/7.20 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(unit, mult(a, mult(i(a), i(a)))) = mult(mult(unit, a), mult(i(a), i(a)))) | (mult(unit, mult(mult(i(a), i(a)), a)) = mult(mult(unit, a), mult(i(a), i(a)))))),
% 7.03/7.20 inference(quant_inst,[status(thm)],[])).
% 7.03/7.20 tff(346,plain,
% 7.03/7.20 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(unit, mult(a, mult(i(a), i(a)))) = mult(mult(unit, a), mult(i(a), i(a)))) | (mult(unit, mult(mult(i(a), i(a)), a)) = mult(mult(unit, a), mult(i(a), i(a))))),
% 7.03/7.20 inference(modus_ponens,[status(thm)],[345, 344])).
% 7.03/7.20 tff(347,plain,
% 7.03/7.20 ((mult(unit, mult(a, mult(i(a), i(a)))) = mult(mult(unit, a), mult(i(a), i(a)))) | (mult(unit, mult(mult(i(a), i(a)), a)) = mult(mult(unit, a), mult(i(a), i(a))))),
% 7.03/7.20 inference(unit_resolution,[status(thm)],[346, 27])).
% 7.03/7.20 tff(348,plain,
% 7.03/7.20 (mult(unit, mult(a, mult(i(a), i(a)))) = mult(mult(unit, a), mult(i(a), i(a)))),
% 7.03/7.20 inference(unit_resolution,[status(thm)],[347, 343])).
% 7.03/7.20 tff(349,plain,
% 7.03/7.20 (mult(mult(unit, a), mult(i(a), i(a))) = mult(unit, mult(a, mult(i(a), i(a))))),
% 7.03/7.20 inference(symmetry,[status(thm)],[348])).
% 7.03/7.20 tff(350,plain,
% 7.03/7.20 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | ((mult(unit, mult(mult(i(a), i(a)), a)) = mult(mult(unit, a), mult(i(a), i(a)))) | (mult(unit, mult(mult(i(a), i(a)), a)) = mult(mult(unit, mult(i(a), i(a))), a)))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | (mult(unit, mult(mult(i(a), i(a)), a)) = mult(mult(unit, a), mult(i(a), i(a)))) | (mult(unit, mult(mult(i(a), i(a)), a)) = mult(mult(unit, mult(i(a), i(a))), a)))),
% 7.03/7.21 inference(rewrite,[status(thm)],[])).
% 7.03/7.21 tff(351,plain,
% 7.03/7.21 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | ((mult(unit, mult(mult(i(a), i(a)), a)) = mult(mult(unit, a), mult(i(a), i(a)))) | (mult(unit, mult(mult(i(a), i(a)), a)) = mult(mult(unit, mult(i(a), i(a))), a)))),
% 7.03/7.21 inference(quant_inst,[status(thm)],[])).
% 7.03/7.21 tff(352,plain,
% 7.03/7.21 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | (mult(unit, mult(mult(i(a), i(a)), a)) = mult(mult(unit, a), mult(i(a), i(a)))) | (mult(unit, mult(mult(i(a), i(a)), a)) = mult(mult(unit, mult(i(a), i(a))), a))),
% 7.03/7.21 inference(modus_ponens,[status(thm)],[351, 350])).
% 7.03/7.21 tff(353,plain,
% 7.03/7.21 ((mult(unit, mult(mult(i(a), i(a)), a)) = mult(mult(unit, a), mult(i(a), i(a)))) | (mult(unit, mult(mult(i(a), i(a)), a)) = mult(mult(unit, mult(i(a), i(a))), a))),
% 7.03/7.21 inference(unit_resolution,[status(thm)],[352, 139])).
% 7.03/7.21 tff(354,plain,
% 7.03/7.21 (mult(unit, mult(mult(i(a), i(a)), a)) = mult(mult(unit, mult(i(a), i(a))), a)),
% 7.03/7.21 inference(unit_resolution,[status(thm)],[353, 343])).
% 7.03/7.21 tff(355,plain,
% 7.03/7.21 ((mult(unit, mult(mult(i(a), i(a)), a)) = mult(mult(unit, a), mult(i(a), i(a)))) <=> (mult(mult(unit, mult(i(a), i(a))), a) = mult(unit, mult(a, mult(i(a), i(a)))))),
% 7.03/7.21 inference(monotonicity,[status(thm)],[354, 349])).
% 7.03/7.21 tff(356,plain,
% 7.03/7.21 ((mult(unit, mult(mult(i(a), i(a)), a)) = mult(mult(unit, a), mult(i(a), i(a)))) <=> (mult(unit, mult(a, mult(i(a), i(a)))) = mult(mult(unit, mult(i(a), i(a))), a))),
% 7.03/7.21 inference(transitivity,[status(thm)],[355, 342])).
% 7.03/7.21 tff(357,plain,
% 7.03/7.21 ((mult(unit, mult(mult(i(a), i(a)), a)) = mult(mult(unit, a), mult(i(a), i(a)))) <=> (mult(i(a), mult(i(a), a)) = mult(mult(i(a), i(a)), a))),
% 7.03/7.21 inference(transitivity,[status(thm)],[356, 341])).
% 7.03/7.21 tff(358,plain,
% 7.03/7.21 ((~(mult(unit, mult(mult(i(a), i(a)), a)) = mult(mult(unit, a), mult(i(a), i(a))))) <=> (~(mult(i(a), mult(i(a), a)) = mult(mult(i(a), i(a)), a)))),
% 7.03/7.21 inference(monotonicity,[status(thm)],[357])).
% 7.03/7.21 tff(359,plain,
% 7.03/7.21 (~(mult(i(a), mult(i(a), a)) = mult(mult(i(a), i(a)), a))),
% 7.03/7.21 inference(modus_ponens,[status(thm)],[343, 358])).
% 7.03/7.21 tff(360,plain,
% 7.03/7.21 (mult(i(a), mult(a, i(a))) = mult(i(a), unit)),
% 7.03/7.21 inference(monotonicity,[status(thm)],[102])).
% 7.03/7.21 tff(361,plain,
% 7.03/7.21 (mult(i(a), mult(a, i(a))) = mult(unit, mult(a, mult(i(a), i(a))))),
% 7.03/7.21 inference(transitivity,[status(thm)],[360, 239, 237, 227, 226])).
% 7.03/7.21 tff(362,plain,
% 7.03/7.21 ((mult(i(a), mult(a, i(a))) = mult(mult(i(a), i(a)), a)) <=> (mult(unit, mult(a, mult(i(a), i(a)))) = mult(mult(unit, mult(i(a), i(a))), a))),
% 7.03/7.21 inference(monotonicity,[status(thm)],[361, 224])).
% 7.03/7.21 tff(363,plain,
% 7.03/7.21 ((mult(unit, mult(a, mult(i(a), i(a)))) = mult(mult(unit, mult(i(a), i(a))), a)) <=> (mult(i(a), mult(a, i(a))) = mult(mult(i(a), i(a)), a))),
% 7.03/7.21 inference(symmetry,[status(thm)],[362])).
% 7.03/7.21 tff(364,plain,
% 7.03/7.21 ((mult(unit, mult(mult(i(a), i(a)), a)) = mult(mult(unit, a), mult(i(a), i(a)))) <=> (mult(i(a), mult(a, i(a))) = mult(mult(i(a), i(a)), a))),
% 7.03/7.21 inference(transitivity,[status(thm)],[356, 363])).
% 7.03/7.21 tff(365,plain,
% 7.03/7.21 ((~(mult(unit, mult(mult(i(a), i(a)), a)) = mult(mult(unit, a), mult(i(a), i(a))))) <=> (~(mult(i(a), mult(a, i(a))) = mult(mult(i(a), i(a)), a)))),
% 7.03/7.21 inference(monotonicity,[status(thm)],[364])).
% 7.03/7.21 tff(366,plain,
% 7.03/7.21 (~(mult(i(a), mult(a, i(a))) = mult(mult(i(a), i(a)), a))),
% 7.03/7.21 inference(modus_ponens,[status(thm)],[343, 365])).
% 7.03/7.21 tff(367,plain,
% 7.03/7.21 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(i(a), mult(i(a), a)) = mult(mult(i(a), i(a)), a)) | (mult(i(a), mult(a, i(a))) = mult(mult(i(a), i(a)), a)))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(i(a), mult(i(a), a)) = mult(mult(i(a), i(a)), a)) | (mult(i(a), mult(a, i(a))) = mult(mult(i(a), i(a)), a)))),
% 7.03/7.21 inference(rewrite,[status(thm)],[])).
% 7.03/7.21 tff(368,plain,
% 7.03/7.21 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(i(a), mult(i(a), a)) = mult(mult(i(a), i(a)), a)) | (mult(i(a), mult(a, i(a))) = mult(mult(i(a), i(a)), a)))),
% 7.03/7.21 inference(quant_inst,[status(thm)],[])).
% 7.03/7.21 tff(369,plain,
% 7.03/7.21 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(i(a), mult(i(a), a)) = mult(mult(i(a), i(a)), a)) | (mult(i(a), mult(a, i(a))) = mult(mult(i(a), i(a)), a))),
% 7.03/7.21 inference(modus_ponens,[status(thm)],[368, 367])).
% 7.03/7.21 tff(370,plain,
% 7.03/7.21 ((mult(i(a), mult(i(a), a)) = mult(mult(i(a), i(a)), a)) | (mult(i(a), mult(a, i(a))) = mult(mult(i(a), i(a)), a))),
% 7.03/7.21 inference(unit_resolution,[status(thm)],[369, 27])).
% 7.03/7.21 tff(371,plain,
% 7.03/7.21 ($false),
% 7.03/7.21 inference(unit_resolution,[status(thm)],[370, 366, 359])).
% 7.03/7.21 tff(372,plain,(mult(unit, mult(mult(i(a), i(a)), a)) = mult(mult(unit, a), mult(i(a), i(a)))), inference(lemma,lemma(discharge,[]))).
% 7.03/7.21 tff(373,plain,
% 7.03/7.21 ((~![A: $i] : (mult(unit, A) = A)) | (mult(unit, mult(mult(i(a), i(a)), a)) = mult(mult(i(a), i(a)), a))),
% 7.03/7.21 inference(quant_inst,[status(thm)],[])).
% 7.03/7.21 tff(374,plain,
% 7.03/7.21 (mult(unit, mult(mult(i(a), i(a)), a)) = mult(mult(i(a), i(a)), a)),
% 7.03/7.21 inference(unit_resolution,[status(thm)],[373, 7])).
% 7.03/7.21 tff(375,plain,
% 7.03/7.21 (mult(mult(i(a), i(a)), a) = mult(unit, mult(mult(i(a), i(a)), a))),
% 7.03/7.21 inference(symmetry,[status(thm)],[374])).
% 7.03/7.21 tff(376,plain,
% 7.03/7.21 (mult(mult(i(a), i(a)), a) = i(a)),
% 7.03/7.21 inference(transitivity,[status(thm)],[375, 372, 213, 209, 202, 201])).
% 7.03/7.21 tff(377,plain,
% 7.03/7.21 (mult(i(b), mult(mult(i(a), i(a)), a)) = mult(i(b), i(a))),
% 7.03/7.21 inference(monotonicity,[status(thm)],[376])).
% 7.03/7.21 tff(378,plain,
% 7.03/7.21 (mult(i(b), mult(mult(i(a), i(a)), a)) = mult(i(b), mult(a, mult(i(a), i(a))))),
% 7.03/7.21 inference(transitivity,[status(thm)],[377, 212])).
% 7.03/7.21 tff(379,plain,
% 7.03/7.21 ((mult(i(b), mult(mult(i(a), i(a)), a)) = mult(mult(i(b), mult(i(a), i(a))), a)) <=> (mult(i(b), mult(a, mult(i(a), i(a)))) = mult(mult(i(b), mult(i(a), i(a))), a))),
% 7.03/7.21 inference(monotonicity,[status(thm)],[378])).
% 7.03/7.21 tff(380,plain,
% 7.03/7.21 ((mult(i(b), mult(a, mult(i(a), i(a)))) = mult(mult(i(b), mult(i(a), i(a))), a)) <=> (mult(i(b), mult(mult(i(a), i(a)), a)) = mult(mult(i(b), mult(i(a), i(a))), a))),
% 7.03/7.21 inference(symmetry,[status(thm)],[379])).
% 7.03/7.21 tff(381,assumption,(~(mult(i(b), mult(mult(i(a), i(a)), a)) = mult(mult(i(b), mult(i(a), i(a))), a))), introduced(assumption)).
% 7.03/7.21 tff(382,plain,
% 7.03/7.21 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(i(b), mult(mult(i(a), i(a)), a)) = mult(mult(i(b), mult(i(a), i(a))), a)) | (mult(i(b), mult(a, mult(i(a), i(a)))) = mult(mult(i(b), mult(i(a), i(a))), a)))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(i(b), mult(mult(i(a), i(a)), a)) = mult(mult(i(b), mult(i(a), i(a))), a)) | (mult(i(b), mult(a, mult(i(a), i(a)))) = mult(mult(i(b), mult(i(a), i(a))), a)))),
% 7.03/7.21 inference(rewrite,[status(thm)],[])).
% 7.03/7.21 tff(383,plain,
% 7.03/7.21 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(i(b), mult(mult(i(a), i(a)), a)) = mult(mult(i(b), mult(i(a), i(a))), a)) | (mult(i(b), mult(a, mult(i(a), i(a)))) = mult(mult(i(b), mult(i(a), i(a))), a)))),
% 7.03/7.21 inference(quant_inst,[status(thm)],[])).
% 7.03/7.21 tff(384,plain,
% 7.03/7.21 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(i(b), mult(mult(i(a), i(a)), a)) = mult(mult(i(b), mult(i(a), i(a))), a)) | (mult(i(b), mult(a, mult(i(a), i(a)))) = mult(mult(i(b), mult(i(a), i(a))), a))),
% 7.03/7.21 inference(modus_ponens,[status(thm)],[383, 382])).
% 7.03/7.21 tff(385,plain,
% 7.03/7.21 ((mult(i(b), mult(mult(i(a), i(a)), a)) = mult(mult(i(b), mult(i(a), i(a))), a)) | (mult(i(b), mult(a, mult(i(a), i(a)))) = mult(mult(i(b), mult(i(a), i(a))), a))),
% 7.03/7.21 inference(unit_resolution,[status(thm)],[384, 27])).
% 7.03/7.21 tff(386,plain,
% 7.03/7.21 (mult(i(b), mult(a, mult(i(a), i(a)))) = mult(mult(i(b), mult(i(a), i(a))), a)),
% 7.03/7.21 inference(unit_resolution,[status(thm)],[385, 381])).
% 7.03/7.21 tff(387,plain,
% 7.03/7.21 (mult(i(b), mult(mult(i(a), i(a)), a)) = mult(mult(i(b), mult(i(a), i(a))), a)),
% 7.03/7.21 inference(modus_ponens,[status(thm)],[386, 380])).
% 7.03/7.21 tff(388,plain,
% 7.03/7.21 ($false),
% 7.03/7.21 inference(unit_resolution,[status(thm)],[381, 387])).
% 7.03/7.21 tff(389,plain,(mult(i(b), mult(mult(i(a), i(a)), a)) = mult(mult(i(b), mult(i(a), i(a))), a)), inference(lemma,lemma(discharge,[]))).
% 7.03/7.21 tff(390,plain,
% 7.03/7.21 (mult(i(b), i(a)) = mult(i(b), mult(mult(i(a), i(a)), a))),
% 7.03/7.21 inference(symmetry,[status(thm)],[377])).
% 7.03/7.21 tff(391,plain,
% 7.03/7.21 (mult(i(b), i(a)) = mult(mult(i(b), mult(i(a), i(a))), a)),
% 7.03/7.21 inference(transitivity,[status(thm)],[390, 389])).
% 7.03/7.21 tff(392,plain,
% 7.03/7.21 (mult(mult(i(b), i(a)), a) = mult(mult(mult(i(b), mult(i(a), i(a))), a), a)),
% 7.03/7.21 inference(monotonicity,[status(thm)],[391])).
% 7.03/7.21 tff(393,plain,
% 7.03/7.21 (mult(mult(mult(i(b), mult(i(a), i(a))), a), a) = mult(mult(i(b), i(a)), a)),
% 7.03/7.21 inference(symmetry,[status(thm)],[392])).
% 7.03/7.21 tff(394,plain,
% 7.03/7.21 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(i(b), mult(i(a), i(a))), mult(a, a)) = mult(mult(mult(i(b), mult(i(a), i(a))), a), a))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(i(b), mult(i(a), i(a))), mult(a, a)) = mult(mult(mult(i(b), mult(i(a), i(a))), a), a)))),
% 7.03/7.21 inference(rewrite,[status(thm)],[])).
% 7.03/7.21 tff(395,plain,
% 7.03/7.21 (((mult(mult(i(b), mult(i(a), i(a))), mult(a, a)) = mult(mult(mult(i(b), mult(i(a), i(a))), a), a)) | (mult(mult(i(b), mult(i(a), i(a))), mult(a, a)) = mult(mult(mult(i(b), mult(i(a), i(a))), a), a))) <=> (mult(mult(i(b), mult(i(a), i(a))), mult(a, a)) = mult(mult(mult(i(b), mult(i(a), i(a))), a), a))),
% 7.03/7.21 inference(rewrite,[status(thm)],[])).
% 7.03/7.21 tff(396,plain,
% 7.03/7.21 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(mult(i(b), mult(i(a), i(a))), mult(a, a)) = mult(mult(mult(i(b), mult(i(a), i(a))), a), a)) | (mult(mult(i(b), mult(i(a), i(a))), mult(a, a)) = mult(mult(mult(i(b), mult(i(a), i(a))), a), a)))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(i(b), mult(i(a), i(a))), mult(a, a)) = mult(mult(mult(i(b), mult(i(a), i(a))), a), a)))),
% 7.03/7.21 inference(monotonicity,[status(thm)],[395])).
% 7.03/7.21 tff(397,plain,
% 7.03/7.21 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(mult(i(b), mult(i(a), i(a))), mult(a, a)) = mult(mult(mult(i(b), mult(i(a), i(a))), a), a)) | (mult(mult(i(b), mult(i(a), i(a))), mult(a, a)) = mult(mult(mult(i(b), mult(i(a), i(a))), a), a)))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(i(b), mult(i(a), i(a))), mult(a, a)) = mult(mult(mult(i(b), mult(i(a), i(a))), a), a)))),
% 7.03/7.21 inference(transitivity,[status(thm)],[396, 394])).
% 7.03/7.21 tff(398,plain,
% 7.03/7.21 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(mult(i(b), mult(i(a), i(a))), mult(a, a)) = mult(mult(mult(i(b), mult(i(a), i(a))), a), a)) | (mult(mult(i(b), mult(i(a), i(a))), mult(a, a)) = mult(mult(mult(i(b), mult(i(a), i(a))), a), a)))),
% 7.03/7.21 inference(quant_inst,[status(thm)],[])).
% 7.03/7.21 tff(399,plain,
% 7.03/7.21 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(i(b), mult(i(a), i(a))), mult(a, a)) = mult(mult(mult(i(b), mult(i(a), i(a))), a), a))),
% 7.03/7.21 inference(modus_ponens,[status(thm)],[398, 397])).
% 7.03/7.21 tff(400,plain,
% 7.03/7.21 (mult(mult(i(b), mult(i(a), i(a))), mult(a, a)) = mult(mult(mult(i(b), mult(i(a), i(a))), a), a)),
% 7.03/7.21 inference(unit_resolution,[status(thm)],[399, 27])).
% 7.03/7.21 tff(401,plain,
% 7.03/7.21 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(i(b), mult(i(a), i(a))), mult(a, a)), i(a)), i(a)) = mult(mult(i(b), mult(i(a), i(a))), mult(a, a)))),
% 7.03/7.21 inference(quant_inst,[status(thm)],[])).
% 7.03/7.21 tff(402,plain,
% 7.03/7.21 (rd(mult(mult(mult(i(b), mult(i(a), i(a))), mult(a, a)), i(a)), i(a)) = mult(mult(i(b), mult(i(a), i(a))), mult(a, a))),
% 7.03/7.21 inference(unit_resolution,[status(thm)],[401, 45])).
% 7.03/7.21 tff(403,plain,
% 7.03/7.21 (mult(mult(i(b), mult(i(a), i(a))), a) = mult(i(b), mult(mult(i(a), i(a)), a))),
% 7.03/7.21 inference(symmetry,[status(thm)],[389])).
% 7.03/7.21 tff(404,plain,
% 7.03/7.21 (mult(mult(i(a), i(a)), a) = ld(a, unit)),
% 7.03/7.21 inference(transitivity,[status(thm)],[375, 372, 213, 209, 202, 201, 93])).
% 7.03/7.21 tff(405,plain,
% 7.03/7.21 (mult(a, mult(mult(i(a), i(a)), a)) = mult(a, ld(a, unit))),
% 7.03/7.21 inference(monotonicity,[status(thm)],[404])).
% 7.03/7.21 tff(406,plain,
% 7.03/7.21 (mult(a, mult(mult(i(a), i(a)), a)) = mult(a, mult(a, mult(i(a), i(a))))),
% 7.03/7.21 inference(transitivity,[status(thm)],[405, 278])).
% 7.03/7.21 tff(407,plain,
% 7.03/7.21 ((mult(a, mult(mult(i(a), i(a)), a)) = mult(mult(a, a), mult(i(a), i(a)))) <=> (mult(a, mult(a, mult(i(a), i(a)))) = mult(mult(a, a), mult(i(a), i(a))))),
% 7.03/7.21 inference(monotonicity,[status(thm)],[406])).
% 7.03/7.21 tff(408,assumption,(~(mult(a, mult(a, mult(i(a), i(a)))) = mult(mult(a, a), mult(i(a), i(a))))), introduced(assumption)).
% 7.03/7.21 tff(409,plain,
% 7.03/7.21 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(a, mult(a, mult(i(a), i(a)))) = mult(mult(a, a), mult(i(a), i(a)))) | (mult(a, mult(mult(i(a), i(a)), a)) = mult(mult(a, a), mult(i(a), i(a)))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(a, mult(a, mult(i(a), i(a)))) = mult(mult(a, a), mult(i(a), i(a)))) | (mult(a, mult(mult(i(a), i(a)), a)) = mult(mult(a, a), mult(i(a), i(a)))))),
% 7.03/7.21 inference(rewrite,[status(thm)],[])).
% 7.03/7.21 tff(410,plain,
% 7.03/7.21 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(a, mult(a, mult(i(a), i(a)))) = mult(mult(a, a), mult(i(a), i(a)))) | (mult(a, mult(mult(i(a), i(a)), a)) = mult(mult(a, a), mult(i(a), i(a)))))),
% 7.03/7.21 inference(quant_inst,[status(thm)],[])).
% 7.03/7.21 tff(411,plain,
% 7.03/7.21 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(a, mult(a, mult(i(a), i(a)))) = mult(mult(a, a), mult(i(a), i(a)))) | (mult(a, mult(mult(i(a), i(a)), a)) = mult(mult(a, a), mult(i(a), i(a))))),
% 7.03/7.21 inference(modus_ponens,[status(thm)],[410, 409])).
% 7.03/7.21 tff(412,plain,
% 7.03/7.21 ((mult(a, mult(a, mult(i(a), i(a)))) = mult(mult(a, a), mult(i(a), i(a)))) | (mult(a, mult(mult(i(a), i(a)), a)) = mult(mult(a, a), mult(i(a), i(a))))),
% 7.03/7.21 inference(unit_resolution,[status(thm)],[411, 27])).
% 7.03/7.21 tff(413,plain,
% 7.03/7.21 (mult(a, mult(mult(i(a), i(a)), a)) = mult(mult(a, a), mult(i(a), i(a)))),
% 7.03/7.21 inference(unit_resolution,[status(thm)],[412, 408])).
% 7.03/7.21 tff(414,plain,
% 7.03/7.21 (mult(a, mult(a, mult(i(a), i(a)))) = mult(mult(a, a), mult(i(a), i(a)))),
% 7.03/7.21 inference(modus_ponens,[status(thm)],[413, 407])).
% 7.03/7.21 tff(415,plain,
% 7.03/7.21 ($false),
% 7.03/7.21 inference(unit_resolution,[status(thm)],[408, 414])).
% 7.03/7.21 tff(416,plain,(mult(a, mult(a, mult(i(a), i(a)))) = mult(mult(a, a), mult(i(a), i(a)))), inference(lemma,lemma(discharge,[]))).
% 7.03/7.21 tff(417,plain,
% 7.03/7.21 (mult(mult(a, a), mult(i(a), i(a))) = mult(a, mult(a, mult(i(a), i(a))))),
% 7.03/7.21 inference(symmetry,[status(thm)],[416])).
% 7.03/7.21 tff(418,plain,
% 7.03/7.21 (mult(mult(mult(a, a), i(a)), i(a)) = mult(a, i(a))),
% 7.03/7.21 inference(transitivity,[status(thm)],[261, 417, 241, 95])).
% 7.03/7.21 tff(419,plain,
% 7.03/7.21 (rd(mult(mult(mult(a, a), i(a)), i(a)), i(a)) = rd(mult(a, i(a)), i(a))),
% 7.03/7.21 inference(monotonicity,[status(thm)],[418])).
% 7.03/7.21 tff(420,plain,
% 7.03/7.21 (mult(mult(a, a), i(a)) = a),
% 7.03/7.21 inference(transitivity,[status(thm)],[270, 419, 265])).
% 7.03/7.21 tff(421,plain,
% 7.03/7.21 (mult(mult(i(b), mult(i(a), i(a))), mult(mult(a, a), i(a))) = mult(mult(i(b), mult(i(a), i(a))), a)),
% 7.03/7.21 inference(monotonicity,[status(thm)],[420])).
% 7.03/7.21 tff(422,plain,
% 7.03/7.21 (mult(i(a), a) = mult(mult(a, b), ld(mult(a, b), unit))),
% 7.03/7.21 inference(transitivity,[status(thm)],[306, 336, 241, 97, 173])).
% 7.03/7.21 tff(423,plain,
% 7.03/7.21 (mult(mult(i(a), a), a) = mult(mult(mult(a, b), ld(mult(a, b), unit)), a)),
% 7.03/7.21 inference(monotonicity,[status(thm)],[422])).
% 7.03/7.21 tff(424,plain,
% 7.03/7.21 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(i(a), mult(a, a)) = mult(mult(i(a), a), a))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(i(a), mult(a, a)) = mult(mult(i(a), a), a)))),
% 7.03/7.21 inference(rewrite,[status(thm)],[])).
% 7.03/7.21 tff(425,plain,
% 7.03/7.21 (((mult(i(a), mult(a, a)) = mult(mult(i(a), a), a)) | (mult(i(a), mult(a, a)) = mult(mult(i(a), a), a))) <=> (mult(i(a), mult(a, a)) = mult(mult(i(a), a), a))),
% 7.03/7.21 inference(rewrite,[status(thm)],[])).
% 7.03/7.21 tff(426,plain,
% 7.03/7.21 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(i(a), mult(a, a)) = mult(mult(i(a), a), a)) | (mult(i(a), mult(a, a)) = mult(mult(i(a), a), a)))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(i(a), mult(a, a)) = mult(mult(i(a), a), a)))),
% 7.03/7.21 inference(monotonicity,[status(thm)],[425])).
% 7.03/7.21 tff(427,plain,
% 7.03/7.21 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(i(a), mult(a, a)) = mult(mult(i(a), a), a)) | (mult(i(a), mult(a, a)) = mult(mult(i(a), a), a)))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(i(a), mult(a, a)) = mult(mult(i(a), a), a)))),
% 7.03/7.21 inference(transitivity,[status(thm)],[426, 424])).
% 7.03/7.21 tff(428,plain,
% 7.03/7.21 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(i(a), mult(a, a)) = mult(mult(i(a), a), a)) | (mult(i(a), mult(a, a)) = mult(mult(i(a), a), a)))),
% 7.03/7.21 inference(quant_inst,[status(thm)],[])).
% 7.03/7.21 tff(429,plain,
% 7.03/7.21 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(i(a), mult(a, a)) = mult(mult(i(a), a), a))),
% 7.03/7.21 inference(modus_ponens,[status(thm)],[428, 427])).
% 7.03/7.21 tff(430,plain,
% 7.03/7.21 (mult(i(a), mult(a, a)) = mult(mult(i(a), a), a)),
% 7.03/7.21 inference(unit_resolution,[status(thm)],[429, 27])).
% 7.03/7.21 tff(431,plain,
% 7.03/7.21 (mult(i(a), mult(a, a)) = a),
% 7.03/7.21 inference(transitivity,[status(thm)],[430, 423, 197, 196])).
% 7.03/7.21 tff(432,plain,
% 7.03/7.21 (mult(mult(i(b), mult(i(a), i(a))), mult(i(a), mult(a, a))) = mult(mult(i(b), mult(i(a), i(a))), a)),
% 7.03/7.21 inference(monotonicity,[status(thm)],[431])).
% 7.03/7.21 tff(433,plain,
% 7.03/7.21 (mult(mult(i(b), mult(i(a), i(a))), a) = mult(mult(i(b), mult(i(a), i(a))), mult(i(a), mult(a, a)))),
% 7.03/7.21 inference(symmetry,[status(thm)],[432])).
% 7.03/7.21 tff(434,plain,
% 7.03/7.21 (mult(mult(i(b), mult(i(a), i(a))), mult(mult(a, a), i(a))) = mult(mult(i(b), mult(i(a), i(a))), mult(i(a), mult(a, a)))),
% 7.03/7.21 inference(transitivity,[status(thm)],[421, 433])).
% 7.03/7.21 tff(435,plain,
% 7.03/7.21 ((mult(mult(i(b), mult(i(a), i(a))), mult(mult(a, a), i(a))) = mult(mult(mult(i(b), mult(i(a), i(a))), mult(a, a)), i(a))) <=> (mult(mult(i(b), mult(i(a), i(a))), mult(i(a), mult(a, a))) = mult(mult(mult(i(b), mult(i(a), i(a))), mult(a, a)), i(a)))),
% 7.03/7.21 inference(monotonicity,[status(thm)],[434])).
% 7.03/7.21 tff(436,plain,
% 7.03/7.21 ((mult(mult(i(b), mult(i(a), i(a))), mult(i(a), mult(a, a))) = mult(mult(mult(i(b), mult(i(a), i(a))), mult(a, a)), i(a))) <=> (mult(mult(i(b), mult(i(a), i(a))), mult(mult(a, a), i(a))) = mult(mult(mult(i(b), mult(i(a), i(a))), mult(a, a)), i(a)))),
% 7.03/7.22 inference(symmetry,[status(thm)],[435])).
% 7.03/7.22 tff(437,assumption,(~(mult(mult(i(b), mult(i(a), i(a))), mult(mult(a, a), i(a))) = mult(mult(mult(i(b), mult(i(a), i(a))), mult(a, a)), i(a)))), introduced(assumption)).
% 7.03/7.22 tff(438,plain,
% 7.03/7.22 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(mult(i(b), mult(i(a), i(a))), mult(mult(a, a), i(a))) = mult(mult(mult(i(b), mult(i(a), i(a))), mult(a, a)), i(a))) | (mult(mult(i(b), mult(i(a), i(a))), mult(i(a), mult(a, a))) = mult(mult(mult(i(b), mult(i(a), i(a))), mult(a, a)), i(a))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(i(b), mult(i(a), i(a))), mult(mult(a, a), i(a))) = mult(mult(mult(i(b), mult(i(a), i(a))), mult(a, a)), i(a))) | (mult(mult(i(b), mult(i(a), i(a))), mult(i(a), mult(a, a))) = mult(mult(mult(i(b), mult(i(a), i(a))), mult(a, a)), i(a))))),
% 7.03/7.22 inference(rewrite,[status(thm)],[])).
% 7.03/7.22 tff(439,plain,
% 7.03/7.22 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(mult(i(b), mult(i(a), i(a))), mult(mult(a, a), i(a))) = mult(mult(mult(i(b), mult(i(a), i(a))), mult(a, a)), i(a))) | (mult(mult(i(b), mult(i(a), i(a))), mult(i(a), mult(a, a))) = mult(mult(mult(i(b), mult(i(a), i(a))), mult(a, a)), i(a))))),
% 7.03/7.22 inference(quant_inst,[status(thm)],[])).
% 7.03/7.22 tff(440,plain,
% 7.03/7.22 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(i(b), mult(i(a), i(a))), mult(mult(a, a), i(a))) = mult(mult(mult(i(b), mult(i(a), i(a))), mult(a, a)), i(a))) | (mult(mult(i(b), mult(i(a), i(a))), mult(i(a), mult(a, a))) = mult(mult(mult(i(b), mult(i(a), i(a))), mult(a, a)), i(a)))),
% 7.03/7.22 inference(modus_ponens,[status(thm)],[439, 438])).
% 7.03/7.22 tff(441,plain,
% 7.03/7.22 ((mult(mult(i(b), mult(i(a), i(a))), mult(mult(a, a), i(a))) = mult(mult(mult(i(b), mult(i(a), i(a))), mult(a, a)), i(a))) | (mult(mult(i(b), mult(i(a), i(a))), mult(i(a), mult(a, a))) = mult(mult(mult(i(b), mult(i(a), i(a))), mult(a, a)), i(a)))),
% 7.03/7.22 inference(unit_resolution,[status(thm)],[440, 27])).
% 7.03/7.22 tff(442,plain,
% 7.03/7.22 (mult(mult(i(b), mult(i(a), i(a))), mult(i(a), mult(a, a))) = mult(mult(mult(i(b), mult(i(a), i(a))), mult(a, a)), i(a))),
% 7.03/7.22 inference(unit_resolution,[status(thm)],[441, 437])).
% 7.03/7.22 tff(443,plain,
% 7.03/7.22 (mult(mult(i(b), mult(i(a), i(a))), mult(mult(a, a), i(a))) = mult(mult(mult(i(b), mult(i(a), i(a))), mult(a, a)), i(a))),
% 7.03/7.22 inference(modus_ponens,[status(thm)],[442, 436])).
% 7.03/7.22 tff(444,plain,
% 7.03/7.22 ($false),
% 7.03/7.22 inference(unit_resolution,[status(thm)],[437, 443])).
% 7.03/7.22 tff(445,plain,(mult(mult(i(b), mult(i(a), i(a))), mult(mult(a, a), i(a))) = mult(mult(mult(i(b), mult(i(a), i(a))), mult(a, a)), i(a))), inference(lemma,lemma(discharge,[]))).
% 7.03/7.22 tff(446,plain,
% 7.03/7.22 (mult(mult(mult(i(b), mult(i(a), i(a))), mult(a, a)), i(a)) = mult(mult(i(b), mult(i(a), i(a))), mult(mult(a, a), i(a)))),
% 7.03/7.22 inference(symmetry,[status(thm)],[445])).
% 7.03/7.22 tff(447,plain,
% 7.03/7.22 (mult(mult(mult(i(b), mult(i(a), i(a))), mult(a, a)), i(a)) = mult(i(b), i(a))),
% 7.03/7.22 inference(transitivity,[status(thm)],[446, 421, 403, 377])).
% 7.03/7.22 tff(448,plain,
% 7.03/7.22 (rd(mult(mult(mult(i(b), mult(i(a), i(a))), mult(a, a)), i(a)), i(a)) = rd(mult(i(b), i(a)), i(a))),
% 7.03/7.22 inference(monotonicity,[status(thm)],[447])).
% 7.03/7.22 tff(449,plain,
% 7.03/7.22 (rd(mult(i(b), i(a)), i(a)) = rd(mult(mult(mult(i(b), mult(i(a), i(a))), mult(a, a)), i(a)), i(a))),
% 7.03/7.22 inference(symmetry,[status(thm)],[448])).
% 7.03/7.22 tff(450,plain,
% 7.03/7.22 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(i(b), i(a)), i(a)) = i(b))),
% 7.03/7.22 inference(quant_inst,[status(thm)],[])).
% 7.03/7.22 tff(451,plain,
% 7.03/7.22 (rd(mult(i(b), i(a)), i(a)) = i(b)),
% 7.03/7.22 inference(unit_resolution,[status(thm)],[450, 45])).
% 7.03/7.22 tff(452,plain,
% 7.03/7.22 (i(b) = rd(mult(i(b), i(a)), i(a))),
% 7.03/7.22 inference(symmetry,[status(thm)],[451])).
% 7.03/7.22 tff(453,assumption,(mult(a, mult(b, i(b))) = mult(mult(a, b), i(b))), introduced(assumption)).
% 7.03/7.22 tff(454,assumption,(mult(mult(a, b), mult(ld(mult(a, b), unit), a)) = mult(mult(mult(a, b), ld(mult(a, b), unit)), a)), introduced(assumption)).
% 7.03/7.22 tff(455,plain,
% 7.03/7.22 (mult(mult(a, b), mult(ld(mult(a, b), unit), a)) = mult(mult(a, b), i(b))),
% 7.03/7.22 inference(transitivity,[status(thm)],[454, 197, 196, 194, 178, 453])).
% 7.03/7.22 tff(456,plain,
% 7.03/7.22 (ld(mult(a, b), mult(mult(a, b), mult(ld(mult(a, b), unit), a))) = ld(mult(a, b), mult(mult(a, b), i(b)))),
% 7.03/7.22 inference(monotonicity,[status(thm)],[455])).
% 7.03/7.22 tff(457,plain,
% 7.03/7.22 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(a, b), mult(mult(a, b), mult(ld(mult(a, b), unit), a))) = mult(ld(mult(a, b), unit), a))),
% 7.03/7.22 inference(quant_inst,[status(thm)],[])).
% 7.03/7.22 tff(458,plain,
% 7.03/7.22 (ld(mult(a, b), mult(mult(a, b), mult(ld(mult(a, b), unit), a))) = mult(ld(mult(a, b), unit), a)),
% 7.03/7.22 inference(unit_resolution,[status(thm)],[457, 166])).
% 7.03/7.22 tff(459,plain,
% 7.03/7.22 (mult(ld(mult(a, b), unit), a) = ld(mult(a, b), mult(mult(a, b), mult(ld(mult(a, b), unit), a)))),
% 7.03/7.22 inference(symmetry,[status(thm)],[458])).
% 7.03/7.22 tff(460,plain,
% 7.03/7.22 (mult(ld(mult(a, b), unit), a) = mult(mult(i(b), i(a)), a)),
% 7.03/7.22 inference(transitivity,[status(thm)],[459, 456, 176, 452, 449, 402, 400, 393])).
% 7.03/7.22 tff(461,plain,
% 7.03/7.22 (rd(mult(ld(mult(a, b), unit), a), a) = rd(mult(mult(i(b), i(a)), a), a)),
% 7.03/7.22 inference(monotonicity,[status(thm)],[460])).
% 7.03/7.22 tff(462,plain,
% 7.03/7.22 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(ld(mult(a, b), unit), a), a) = ld(mult(a, b), unit))),
% 7.03/7.22 inference(quant_inst,[status(thm)],[])).
% 7.03/7.22 tff(463,plain,
% 7.03/7.22 (rd(mult(ld(mult(a, b), unit), a), a) = ld(mult(a, b), unit)),
% 7.03/7.22 inference(unit_resolution,[status(thm)],[462, 45])).
% 7.03/7.22 tff(464,plain,
% 7.03/7.22 (ld(mult(a, b), unit) = rd(mult(ld(mult(a, b), unit), a), a)),
% 7.03/7.22 inference(symmetry,[status(thm)],[463])).
% 7.03/7.22 tff(465,plain,
% 7.03/7.22 ((~![A: $i] : (i(A) = ld(A, unit))) | (i(mult(a, b)) = ld(mult(a, b), unit))),
% 7.03/7.22 inference(quant_inst,[status(thm)],[])).
% 7.03/7.22 tff(466,plain,
% 7.03/7.22 (i(mult(a, b)) = ld(mult(a, b), unit)),
% 7.03/7.22 inference(unit_resolution,[status(thm)],[465, 72])).
% 7.03/7.22 tff(467,plain,
% 7.03/7.22 (i(mult(a, b)) = mult(i(b), i(a))),
% 7.03/7.22 inference(transitivity,[status(thm)],[466, 464, 461, 199])).
% 7.03/7.22 tff(468,plain,
% 7.03/7.22 ((~(i(mult(a, b)) = mult(i(b), i(a)))) <=> (~(i(mult(a, b)) = mult(i(b), i(a))))),
% 7.03/7.22 inference(rewrite,[status(thm)],[])).
% 7.03/7.22 tff(469,axiom,(~(i(mult(a, b)) = mult(i(b), i(a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goals')).
% 7.03/7.22 tff(470,plain,
% 7.03/7.22 (~(i(mult(a, b)) = mult(i(b), i(a)))),
% 7.03/7.22 inference(modus_ponens,[status(thm)],[469, 468])).
% 7.03/7.22 tff(471,plain,
% 7.03/7.22 ($false),
% 7.03/7.22 inference(unit_resolution,[status(thm)],[470, 467])).
% 7.03/7.22 tff(472,plain,((~(mult(mult(a, b), mult(ld(mult(a, b), unit), a)) = mult(mult(mult(a, b), ld(mult(a, b), unit)), a))) | (~(mult(a, mult(b, i(b))) = mult(mult(a, b), i(b))))), inference(lemma,lemma(discharge,[]))).
% 7.03/7.22 tff(473,plain,
% 7.03/7.22 (~(mult(mult(a, b), mult(ld(mult(a, b), unit), a)) = mult(mult(mult(a, b), ld(mult(a, b), unit)), a))),
% 7.03/7.22 inference(unit_resolution,[status(thm)],[472, 191])).
% 7.03/7.22 tff(474,plain,
% 7.03/7.22 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(mult(a, b), mult(ld(mult(a, b), unit), a)) = mult(mult(mult(a, b), ld(mult(a, b), unit)), a)) | (mult(mult(a, b), mult(a, ld(mult(a, b), unit))) = mult(mult(mult(a, b), ld(mult(a, b), unit)), a)))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(a, b), mult(ld(mult(a, b), unit), a)) = mult(mult(mult(a, b), ld(mult(a, b), unit)), a)) | (mult(mult(a, b), mult(a, ld(mult(a, b), unit))) = mult(mult(mult(a, b), ld(mult(a, b), unit)), a)))),
% 7.03/7.22 inference(rewrite,[status(thm)],[])).
% 7.03/7.22 tff(475,plain,
% 7.03/7.22 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(mult(a, b), mult(ld(mult(a, b), unit), a)) = mult(mult(mult(a, b), ld(mult(a, b), unit)), a)) | (mult(mult(a, b), mult(a, ld(mult(a, b), unit))) = mult(mult(mult(a, b), ld(mult(a, b), unit)), a)))),
% 7.03/7.22 inference(quant_inst,[status(thm)],[])).
% 7.03/7.22 tff(476,plain,
% 7.03/7.22 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(a, b), mult(ld(mult(a, b), unit), a)) = mult(mult(mult(a, b), ld(mult(a, b), unit)), a)) | (mult(mult(a, b), mult(a, ld(mult(a, b), unit))) = mult(mult(mult(a, b), ld(mult(a, b), unit)), a))),
% 7.03/7.22 inference(modus_ponens,[status(thm)],[475, 474])).
% 7.03/7.22 tff(477,plain,
% 7.03/7.22 ((mult(mult(a, b), mult(ld(mult(a, b), unit), a)) = mult(mult(mult(a, b), ld(mult(a, b), unit)), a)) | (mult(mult(a, b), mult(a, ld(mult(a, b), unit))) = mult(mult(mult(a, b), ld(mult(a, b), unit)), a))),
% 7.03/7.22 inference(unit_resolution,[status(thm)],[476, 27])).
% 7.03/7.22 tff(478,plain,
% 7.03/7.22 (mult(mult(a, b), mult(a, ld(mult(a, b), unit))) = mult(mult(mult(a, b), ld(mult(a, b), unit)), a)),
% 7.03/7.22 inference(unit_resolution,[status(thm)],[477, 473])).
% 7.03/7.22 tff(479,plain,
% 7.03/7.22 (mult(mult(a, b), mult(a, ld(mult(a, b), unit))) = mult(mult(a, b), i(b))),
% 7.03/7.22 inference(transitivity,[status(thm)],[478, 197, 196, 194, 178, 191])).
% 7.03/7.22 tff(480,plain,
% 7.03/7.22 (ld(mult(a, b), mult(mult(a, b), mult(a, ld(mult(a, b), unit)))) = ld(mult(a, b), mult(mult(a, b), i(b)))),
% 7.03/7.22 inference(monotonicity,[status(thm)],[479])).
% 7.03/7.22 tff(481,plain,
% 7.03/7.22 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(a, b), mult(mult(a, b), mult(a, ld(mult(a, b), unit)))) = mult(a, ld(mult(a, b), unit)))),
% 7.03/7.22 inference(quant_inst,[status(thm)],[])).
% 7.03/7.22 tff(482,plain,
% 7.03/7.22 (ld(mult(a, b), mult(mult(a, b), mult(a, ld(mult(a, b), unit)))) = mult(a, ld(mult(a, b), unit))),
% 7.03/7.22 inference(unit_resolution,[status(thm)],[481, 166])).
% 7.03/7.22 tff(483,plain,
% 7.03/7.22 (mult(a, ld(mult(a, b), unit)) = ld(mult(a, b), mult(mult(a, b), mult(a, ld(mult(a, b), unit))))),
% 7.03/7.22 inference(symmetry,[status(thm)],[482])).
% 7.03/7.22 tff(484,plain,
% 7.03/7.22 (mult(a, ld(mult(a, b), unit)) = i(b)),
% 7.03/7.22 inference(transitivity,[status(thm)],[483, 480, 176])).
% 7.03/7.22 tff(485,plain,
% 7.03/7.22 (mult(mult(a, ld(mult(a, b), unit)), b) = mult(i(b), b)),
% 7.03/7.22 inference(monotonicity,[status(thm)],[484])).
% 7.03/7.22 tff(486,plain,
% 7.03/7.22 (mult(mult(a, ld(mult(a, b), unit)), b) = mult(mult(a, b), ld(mult(a, b), unit))),
% 7.03/7.22 inference(transitivity,[status(thm)],[485, 18, 174, 100, 103, 106, 173])).
% 7.03/7.22 tff(487,plain,
% 7.03/7.22 ((mult(a, mult(b, ld(mult(a, b), unit))) = mult(mult(a, ld(mult(a, b), unit)), b)) <=> (mult(a, mult(b, ld(mult(a, b), unit))) = mult(mult(a, b), ld(mult(a, b), unit)))),
% 7.03/7.22 inference(monotonicity,[status(thm)],[486])).
% 7.03/7.22 tff(488,assumption,(~(mult(a, mult(b, ld(mult(a, b), unit))) = mult(mult(a, b), ld(mult(a, b), unit)))), introduced(assumption)).
% 7.03/7.22 tff(489,plain,
% 7.03/7.22 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | ((mult(a, mult(b, ld(mult(a, b), unit))) = mult(mult(a, b), ld(mult(a, b), unit))) | (mult(a, mult(b, ld(mult(a, b), unit))) = mult(mult(a, ld(mult(a, b), unit)), b)))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | (mult(a, mult(b, ld(mult(a, b), unit))) = mult(mult(a, b), ld(mult(a, b), unit))) | (mult(a, mult(b, ld(mult(a, b), unit))) = mult(mult(a, ld(mult(a, b), unit)), b)))),
% 7.03/7.22 inference(rewrite,[status(thm)],[])).
% 7.03/7.22 tff(490,plain,
% 7.03/7.22 (((mult(a, mult(b, ld(mult(a, b), unit))) = mult(mult(a, ld(mult(a, b), unit)), b)) | (mult(a, mult(b, ld(mult(a, b), unit))) = mult(mult(a, b), ld(mult(a, b), unit)))) <=> ((mult(a, mult(b, ld(mult(a, b), unit))) = mult(mult(a, b), ld(mult(a, b), unit))) | (mult(a, mult(b, ld(mult(a, b), unit))) = mult(mult(a, ld(mult(a, b), unit)), b)))),
% 7.03/7.22 inference(rewrite,[status(thm)],[])).
% 7.03/7.22 tff(491,plain,
% 7.03/7.22 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | ((mult(a, mult(b, ld(mult(a, b), unit))) = mult(mult(a, ld(mult(a, b), unit)), b)) | (mult(a, mult(b, ld(mult(a, b), unit))) = mult(mult(a, b), ld(mult(a, b), unit))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | ((mult(a, mult(b, ld(mult(a, b), unit))) = mult(mult(a, b), ld(mult(a, b), unit))) | (mult(a, mult(b, ld(mult(a, b), unit))) = mult(mult(a, ld(mult(a, b), unit)), b))))),
% 7.03/7.22 inference(monotonicity,[status(thm)],[490])).
% 7.03/7.22 tff(492,plain,
% 7.03/7.22 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | ((mult(a, mult(b, ld(mult(a, b), unit))) = mult(mult(a, ld(mult(a, b), unit)), b)) | (mult(a, mult(b, ld(mult(a, b), unit))) = mult(mult(a, b), ld(mult(a, b), unit))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | (mult(a, mult(b, ld(mult(a, b), unit))) = mult(mult(a, b), ld(mult(a, b), unit))) | (mult(a, mult(b, ld(mult(a, b), unit))) = mult(mult(a, ld(mult(a, b), unit)), b)))),
% 7.03/7.22 inference(transitivity,[status(thm)],[491, 489])).
% 7.03/7.22 tff(493,plain,
% 7.03/7.22 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | ((mult(a, mult(b, ld(mult(a, b), unit))) = mult(mult(a, ld(mult(a, b), unit)), b)) | (mult(a, mult(b, ld(mult(a, b), unit))) = mult(mult(a, b), ld(mult(a, b), unit))))),
% 7.03/7.22 inference(quant_inst,[status(thm)],[])).
% 7.03/7.22 tff(494,plain,
% 7.03/7.22 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | (mult(a, mult(b, ld(mult(a, b), unit))) = mult(mult(a, b), ld(mult(a, b), unit))) | (mult(a, mult(b, ld(mult(a, b), unit))) = mult(mult(a, ld(mult(a, b), unit)), b))),
% 7.03/7.22 inference(modus_ponens,[status(thm)],[493, 492])).
% 7.03/7.22 tff(495,plain,
% 7.03/7.22 ((mult(a, mult(b, ld(mult(a, b), unit))) = mult(mult(a, b), ld(mult(a, b), unit))) | (mult(a, mult(b, ld(mult(a, b), unit))) = mult(mult(a, ld(mult(a, b), unit)), b))),
% 7.03/7.22 inference(unit_resolution,[status(thm)],[494, 139])).
% 7.03/7.22 tff(496,plain,
% 7.03/7.22 (mult(a, mult(b, ld(mult(a, b), unit))) = mult(mult(a, ld(mult(a, b), unit)), b)),
% 7.03/7.22 inference(unit_resolution,[status(thm)],[495, 488])).
% 7.03/7.22 tff(497,plain,
% 7.03/7.22 (mult(a, mult(b, ld(mult(a, b), unit))) = mult(mult(a, b), ld(mult(a, b), unit))),
% 7.03/7.22 inference(modus_ponens,[status(thm)],[496, 487])).
% 7.03/7.22 tff(498,plain,
% 7.03/7.22 ($false),
% 7.03/7.22 inference(unit_resolution,[status(thm)],[488, 497])).
% 7.03/7.22 tff(499,plain,(mult(a, mult(b, ld(mult(a, b), unit))) = mult(mult(a, b), ld(mult(a, b), unit))), inference(lemma,lemma(discharge,[]))).
% 7.03/7.22 tff(500,plain,
% 7.03/7.22 (mult(a, mult(b, ld(mult(a, b), unit))) = unit),
% 7.03/7.22 inference(transitivity,[status(thm)],[499, 172])).
% 7.03/7.22 tff(501,plain,
% 7.03/7.22 (ld(a, mult(a, mult(b, ld(mult(a, b), unit)))) = ld(a, unit)),
% 7.03/7.22 inference(monotonicity,[status(thm)],[500])).
% 7.03/7.22 tff(502,plain,
% 7.03/7.22 (ld(a, unit) = ld(a, mult(a, mult(b, ld(mult(a, b), unit))))),
% 7.03/7.22 inference(symmetry,[status(thm)],[501])).
% 7.03/7.22 tff(503,plain,
% 7.03/7.22 (mult(b, i(b)) = mult(a, i(a))),
% 7.03/7.22 inference(transitivity,[status(thm)],[75, 65, 98, 95])).
% 7.03/7.22 tff(504,plain,
% 7.03/7.22 (mult(mult(b, i(b)), i(a)) = mult(mult(a, i(a)), i(a))),
% 7.03/7.22 inference(monotonicity,[status(thm)],[503])).
% 7.03/7.22 tff(505,plain,
% 7.03/7.22 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(b, mult(b, mult(i(b), i(a)))) = mult(i(b), i(a)))),
% 7.03/7.22 inference(quant_inst,[status(thm)],[])).
% 7.03/7.22 tff(506,plain,
% 7.03/7.22 (ld(b, mult(b, mult(i(b), i(a)))) = mult(i(b), i(a))),
% 7.03/7.22 inference(unit_resolution,[status(thm)],[505, 166])).
% 7.03/7.22 tff(507,assumption,(mult(b, mult(i(b), i(a))) = mult(mult(b, i(b)), i(a))), introduced(assumption)).
% 7.03/7.22 tff(508,plain,
% 7.03/7.22 (mult(mult(b, i(b)), i(a)) = mult(b, mult(i(b), i(a)))),
% 7.03/7.22 inference(symmetry,[status(thm)],[507])).
% 7.03/7.22 tff(509,plain,
% 7.03/7.22 (mult(mult(a, i(a)), i(a)) = mult(mult(b, i(b)), i(a))),
% 7.03/7.22 inference(symmetry,[status(thm)],[504])).
% 7.03/7.22 tff(510,plain,
% 7.03/7.22 (ld(a, unit) = i(a)),
% 7.03/7.22 inference(symmetry,[status(thm)],[93])).
% 7.03/7.22 tff(511,assumption,(mult(a, mult(b, ld(mult(a, b), unit))) = mult(mult(a, b), ld(mult(a, b), unit))), introduced(assumption)).
% 7.03/7.22 tff(512,plain,
% 7.03/7.22 (mult(a, mult(b, ld(mult(a, b), unit))) = unit),
% 7.03/7.22 inference(transitivity,[status(thm)],[511, 172])).
% 7.03/7.23 tff(513,plain,
% 7.03/7.23 (ld(a, mult(a, mult(b, ld(mult(a, b), unit)))) = ld(a, unit)),
% 7.03/7.23 inference(monotonicity,[status(thm)],[512])).
% 7.03/7.23 tff(514,plain,
% 7.03/7.23 (mult(b, ld(mult(a, b), unit)) = ld(a, mult(a, mult(b, ld(mult(a, b), unit))))),
% 7.03/7.23 inference(symmetry,[status(thm)],[170])).
% 7.03/7.23 tff(515,plain,
% 7.03/7.23 (mult(b, ld(mult(a, b), unit)) = mult(b, mult(i(b), i(a)))),
% 7.03/7.23 inference(transitivity,[status(thm)],[514, 513, 510, 238, 273, 509, 508])).
% 7.03/7.23 tff(516,plain,
% 7.03/7.23 (ld(b, mult(b, ld(mult(a, b), unit))) = ld(b, mult(b, mult(i(b), i(a))))),
% 7.03/7.23 inference(monotonicity,[status(thm)],[515])).
% 7.03/7.23 tff(517,plain,
% 7.03/7.23 (ld(mult(a, b), unit) = ld(b, mult(b, ld(mult(a, b), unit)))),
% 7.03/7.23 inference(symmetry,[status(thm)],[168])).
% 7.03/7.23 tff(518,plain,
% 7.03/7.23 (i(mult(a, b)) = mult(i(b), i(a))),
% 7.03/7.23 inference(transitivity,[status(thm)],[466, 517, 516, 506])).
% 7.03/7.23 tff(519,plain,
% 7.03/7.23 ($false),
% 7.03/7.23 inference(unit_resolution,[status(thm)],[470, 518])).
% 7.03/7.23 tff(520,plain,((~(mult(a, mult(b, ld(mult(a, b), unit))) = mult(mult(a, b), ld(mult(a, b), unit)))) | (~(mult(b, mult(i(b), i(a))) = mult(mult(b, i(b)), i(a))))), inference(lemma,lemma(discharge,[]))).
% 7.03/7.23 tff(521,plain,
% 7.03/7.23 (~(mult(b, mult(i(b), i(a))) = mult(mult(b, i(b)), i(a)))),
% 7.03/7.23 inference(unit_resolution,[status(thm)],[520, 499])).
% 7.03/7.23 tff(522,plain,
% 7.03/7.23 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(b, mult(i(b), i(a))) = mult(mult(b, i(b)), i(a))) | (mult(b, mult(i(a), i(b))) = mult(mult(b, i(b)), i(a))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(b, mult(i(b), i(a))) = mult(mult(b, i(b)), i(a))) | (mult(b, mult(i(a), i(b))) = mult(mult(b, i(b)), i(a))))),
% 7.03/7.23 inference(rewrite,[status(thm)],[])).
% 7.03/7.23 tff(523,plain,
% 7.03/7.23 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(b, mult(i(b), i(a))) = mult(mult(b, i(b)), i(a))) | (mult(b, mult(i(a), i(b))) = mult(mult(b, i(b)), i(a))))),
% 7.03/7.23 inference(quant_inst,[status(thm)],[])).
% 7.03/7.23 tff(524,plain,
% 7.03/7.23 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(b, mult(i(b), i(a))) = mult(mult(b, i(b)), i(a))) | (mult(b, mult(i(a), i(b))) = mult(mult(b, i(b)), i(a)))),
% 7.03/7.23 inference(modus_ponens,[status(thm)],[523, 522])).
% 7.03/7.23 tff(525,plain,
% 7.03/7.23 ((mult(b, mult(i(b), i(a))) = mult(mult(b, i(b)), i(a))) | (mult(b, mult(i(a), i(b))) = mult(mult(b, i(b)), i(a)))),
% 7.03/7.23 inference(unit_resolution,[status(thm)],[524, 27])).
% 7.03/7.23 tff(526,plain,
% 7.03/7.23 (mult(b, mult(i(a), i(b))) = mult(mult(b, i(b)), i(a))),
% 7.03/7.23 inference(unit_resolution,[status(thm)],[525, 521])).
% 7.03/7.23 tff(527,plain,
% 7.03/7.23 (mult(b, mult(i(a), i(b))) = mult(b, ld(mult(a, b), unit))),
% 7.03/7.23 inference(transitivity,[status(thm)],[526, 504, 202, 201, 93, 502, 170])).
% 7.03/7.23 tff(528,plain,
% 7.03/7.23 (ld(b, mult(b, mult(i(a), i(b)))) = ld(b, mult(b, ld(mult(a, b), unit)))),
% 7.03/7.23 inference(monotonicity,[status(thm)],[527])).
% 7.03/7.23 tff(529,plain,
% 7.03/7.23 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(b, mult(b, mult(i(a), i(b)))) = mult(i(a), i(b)))),
% 7.03/7.23 inference(quant_inst,[status(thm)],[])).
% 7.03/7.23 tff(530,plain,
% 7.03/7.23 (ld(b, mult(b, mult(i(a), i(b)))) = mult(i(a), i(b))),
% 7.03/7.23 inference(unit_resolution,[status(thm)],[529, 166])).
% 7.03/7.23 tff(531,plain,
% 7.03/7.23 (mult(i(a), i(b)) = ld(b, mult(b, mult(i(a), i(b))))),
% 7.03/7.23 inference(symmetry,[status(thm)],[530])).
% 7.03/7.23 tff(532,plain,
% 7.03/7.23 ((mult(mult(i(b), b), ld(mult(a, b), unit)) = mult(i(b), mult(b, ld(mult(a, b), unit)))) <=> (mult(i(b), mult(b, ld(mult(a, b), unit))) = mult(mult(i(b), b), ld(mult(a, b), unit)))),
% 7.03/7.23 inference(commutativity,[status(thm)],[])).
% 7.03/7.23 tff(533,plain,
% 7.03/7.23 (mult(b, ld(mult(a, b), unit)) = i(a)),
% 7.03/7.23 inference(transitivity,[status(thm)],[514, 501, 510])).
% 7.03/7.23 tff(534,plain,
% 7.03/7.23 (mult(i(b), mult(b, ld(mult(a, b), unit))) = mult(i(b), i(a))),
% 7.03/7.23 inference(monotonicity,[status(thm)],[533])).
% 7.03/7.23 tff(535,plain,
% 7.03/7.23 (mult(i(b), i(a)) = mult(i(b), mult(b, ld(mult(a, b), unit)))),
% 7.03/7.23 inference(symmetry,[status(thm)],[534])).
% 7.03/7.23 tff(536,plain,
% 7.03/7.23 (i(mult(a, b)) = mult(mult(i(b), b), ld(mult(a, b), unit))),
% 7.03/7.23 inference(transitivity,[status(thm)],[466, 10, 156])).
% 7.03/7.23 tff(537,plain,
% 7.03/7.23 ((i(mult(a, b)) = mult(i(b), i(a))) <=> (mult(mult(i(b), b), ld(mult(a, b), unit)) = mult(i(b), mult(b, ld(mult(a, b), unit))))),
% 7.03/7.23 inference(monotonicity,[status(thm)],[536, 535])).
% 7.03/7.23 tff(538,plain,
% 7.03/7.23 ((i(mult(a, b)) = mult(i(b), i(a))) <=> (mult(i(b), mult(b, ld(mult(a, b), unit))) = mult(mult(i(b), b), ld(mult(a, b), unit)))),
% 7.03/7.23 inference(transitivity,[status(thm)],[537, 532])).
% 7.03/7.23 tff(539,plain,
% 7.03/7.23 ((~(i(mult(a, b)) = mult(i(b), i(a)))) <=> (~(mult(i(b), mult(b, ld(mult(a, b), unit))) = mult(mult(i(b), b), ld(mult(a, b), unit))))),
% 7.03/7.23 inference(monotonicity,[status(thm)],[538])).
% 7.03/7.23 tff(540,plain,
% 7.03/7.23 (~(mult(i(b), mult(b, ld(mult(a, b), unit))) = mult(mult(i(b), b), ld(mult(a, b), unit)))),
% 7.03/7.23 inference(modus_ponens,[status(thm)],[470, 539])).
% 7.03/7.23 tff(541,plain,
% 7.03/7.23 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(i(b), mult(b, ld(mult(a, b), unit))) = mult(mult(i(b), b), ld(mult(a, b), unit))) | (mult(i(b), mult(ld(mult(a, b), unit), b)) = mult(mult(i(b), b), ld(mult(a, b), unit))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(i(b), mult(b, ld(mult(a, b), unit))) = mult(mult(i(b), b), ld(mult(a, b), unit))) | (mult(i(b), mult(ld(mult(a, b), unit), b)) = mult(mult(i(b), b), ld(mult(a, b), unit))))),
% 7.03/7.23 inference(rewrite,[status(thm)],[])).
% 7.03/7.23 tff(542,plain,
% 7.03/7.23 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(i(b), mult(b, ld(mult(a, b), unit))) = mult(mult(i(b), b), ld(mult(a, b), unit))) | (mult(i(b), mult(ld(mult(a, b), unit), b)) = mult(mult(i(b), b), ld(mult(a, b), unit))))),
% 7.03/7.23 inference(quant_inst,[status(thm)],[])).
% 7.03/7.23 tff(543,plain,
% 7.03/7.23 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(i(b), mult(b, ld(mult(a, b), unit))) = mult(mult(i(b), b), ld(mult(a, b), unit))) | (mult(i(b), mult(ld(mult(a, b), unit), b)) = mult(mult(i(b), b), ld(mult(a, b), unit)))),
% 7.03/7.23 inference(modus_ponens,[status(thm)],[542, 541])).
% 7.03/7.23 tff(544,plain,
% 7.03/7.23 ((mult(i(b), mult(b, ld(mult(a, b), unit))) = mult(mult(i(b), b), ld(mult(a, b), unit))) | (mult(i(b), mult(ld(mult(a, b), unit), b)) = mult(mult(i(b), b), ld(mult(a, b), unit)))),
% 7.03/7.23 inference(unit_resolution,[status(thm)],[543, 27])).
% 7.03/7.23 tff(545,plain,
% 7.03/7.23 (mult(i(b), mult(ld(mult(a, b), unit), b)) = mult(mult(i(b), b), ld(mult(a, b), unit))),
% 7.03/7.23 inference(unit_resolution,[status(thm)],[544, 540])).
% 7.03/7.23 tff(546,plain,
% 7.03/7.23 (mult(i(b), mult(ld(mult(a, b), unit), b)) = ld(mult(a, b), unit)),
% 7.03/7.23 inference(transitivity,[status(thm)],[545, 157, 9])).
% 7.03/7.23 tff(547,plain,
% 7.03/7.23 (mult(b, mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(b, ld(mult(a, b), unit))),
% 7.03/7.23 inference(monotonicity,[status(thm)],[546])).
% 7.03/7.23 tff(548,plain,
% 7.03/7.23 ((mult(mult(unit, b), ld(mult(a, b), unit)) = mult(unit, mult(ld(mult(a, b), unit), b))) <=> (mult(unit, mult(ld(mult(a, b), unit), b)) = mult(mult(unit, b), ld(mult(a, b), unit)))),
% 7.03/7.23 inference(commutativity,[status(thm)],[])).
% 7.03/7.23 tff(549,plain,
% 7.03/7.23 (mult(mult(b, i(b)), mult(ld(mult(a, b), unit), b)) = mult(unit, mult(ld(mult(a, b), unit), b))),
% 7.03/7.23 inference(monotonicity,[status(thm)],[76])).
% 7.03/7.23 tff(550,plain,
% 7.03/7.23 ((~![A: $i] : (mult(unit, A) = A)) | (mult(unit, b) = b)),
% 7.03/7.23 inference(quant_inst,[status(thm)],[])).
% 7.03/7.23 tff(551,plain,
% 7.03/7.23 (mult(unit, b) = b),
% 7.03/7.23 inference(unit_resolution,[status(thm)],[550, 7])).
% 7.03/7.23 tff(552,plain,
% 7.03/7.23 (mult(mult(unit, b), ld(mult(a, b), unit)) = mult(b, ld(mult(a, b), unit))),
% 7.03/7.23 inference(monotonicity,[status(thm)],[551])).
% 7.03/7.23 tff(553,plain,
% 7.03/7.23 (mult(b, ld(mult(a, b), unit)) = mult(mult(unit, b), ld(mult(a, b), unit))),
% 7.03/7.23 inference(symmetry,[status(thm)],[552])).
% 7.03/7.23 tff(554,plain,
% 7.03/7.23 (mult(b, mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(unit, b), ld(mult(a, b), unit))),
% 7.03/7.23 inference(transitivity,[status(thm)],[547, 553])).
% 7.03/7.23 tff(555,plain,
% 7.03/7.23 ((mult(b, mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(b, i(b)), mult(ld(mult(a, b), unit), b))) <=> (mult(mult(unit, b), ld(mult(a, b), unit)) = mult(unit, mult(ld(mult(a, b), unit), b)))),
% 7.03/7.23 inference(monotonicity,[status(thm)],[554, 549])).
% 7.03/7.23 tff(556,plain,
% 7.03/7.23 ((mult(b, mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(b, i(b)), mult(ld(mult(a, b), unit), b))) <=> (mult(unit, mult(ld(mult(a, b), unit), b)) = mult(mult(unit, b), ld(mult(a, b), unit)))),
% 7.03/7.23 inference(transitivity,[status(thm)],[555, 548])).
% 7.03/7.23 tff(557,plain,
% 7.03/7.23 ((mult(unit, mult(ld(mult(a, b), unit), b)) = mult(mult(unit, b), ld(mult(a, b), unit))) <=> (mult(b, mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(b, i(b)), mult(ld(mult(a, b), unit), b)))),
% 7.03/7.23 inference(symmetry,[status(thm)],[556])).
% 7.03/7.23 tff(558,plain,
% 7.03/7.23 ((mult(mult(unit, ld(mult(a, b), unit)), b) = mult(unit, mult(b, ld(mult(a, b), unit)))) <=> (mult(unit, mult(b, ld(mult(a, b), unit))) = mult(mult(unit, ld(mult(a, b), unit)), b))),
% 7.03/7.23 inference(commutativity,[status(thm)],[])).
% 7.03/7.23 tff(559,plain,
% 7.03/7.23 ((~![A: $i] : (mult(unit, A) = A)) | (mult(unit, ld(mult(i(b), b), mult(b, ld(mult(a, b), unit)))) = ld(mult(i(b), b), mult(b, ld(mult(a, b), unit))))),
% 7.03/7.23 inference(quant_inst,[status(thm)],[])).
% 7.03/7.23 tff(560,plain,
% 7.03/7.23 (mult(unit, ld(mult(i(b), b), mult(b, ld(mult(a, b), unit)))) = ld(mult(i(b), b), mult(b, ld(mult(a, b), unit)))),
% 7.03/7.23 inference(unit_resolution,[status(thm)],[559, 7])).
% 7.03/7.23 tff(561,plain,
% 7.03/7.23 (mult(unit, ld(mult(i(b), b), mult(b, ld(mult(a, b), unit)))) = mult(mult(i(b), b), ld(mult(i(b), b), mult(b, ld(mult(a, b), unit))))),
% 7.03/7.23 inference(monotonicity,[status(thm)],[155])).
% 7.03/7.23 tff(562,plain,
% 7.03/7.23 (mult(mult(i(b), b), ld(mult(i(b), b), mult(b, ld(mult(a, b), unit)))) = mult(unit, ld(mult(i(b), b), mult(b, ld(mult(a, b), unit))))),
% 7.03/7.23 inference(symmetry,[status(thm)],[561])).
% 7.03/7.23 tff(563,plain,
% 7.03/7.23 ((~![B: $i, A: $i] : (mult(A, ld(A, B)) = B)) | (mult(mult(i(b), b), ld(mult(i(b), b), mult(b, ld(mult(a, b), unit)))) = mult(b, ld(mult(a, b), unit)))),
% 7.03/7.23 inference(quant_inst,[status(thm)],[])).
% 7.03/7.23 tff(564,plain,
% 7.03/7.23 (mult(mult(i(b), b), ld(mult(i(b), b), mult(b, ld(mult(a, b), unit)))) = mult(b, ld(mult(a, b), unit))),
% 7.03/7.23 inference(unit_resolution,[status(thm)],[563, 63])).
% 7.03/7.23 tff(565,plain,
% 7.03/7.23 (mult(b, ld(mult(a, b), unit)) = mult(mult(i(b), b), ld(mult(i(b), b), mult(b, ld(mult(a, b), unit))))),
% 7.03/7.23 inference(symmetry,[status(thm)],[564])).
% 7.03/7.23 tff(566,plain,
% 7.03/7.23 (mult(b, ld(mult(a, b), unit)) = ld(mult(i(b), b), mult(b, ld(mult(a, b), unit)))),
% 7.03/7.23 inference(transitivity,[status(thm)],[565, 562, 560])).
% 7.03/7.23 tff(567,plain,
% 7.03/7.23 (mult(unit, mult(b, ld(mult(a, b), unit))) = mult(unit, ld(mult(i(b), b), mult(b, ld(mult(a, b), unit))))),
% 7.03/7.23 inference(monotonicity,[status(thm)],[566])).
% 7.03/7.23 tff(568,plain,
% 7.03/7.23 (mult(unit, ld(mult(i(b), b), mult(b, ld(mult(a, b), unit)))) = mult(unit, mult(b, ld(mult(a, b), unit)))),
% 7.03/7.23 inference(symmetry,[status(thm)],[567])).
% 7.03/7.23 tff(569,plain,
% 7.03/7.23 (mult(mult(unit, b), ld(mult(a, b), unit)) = mult(unit, mult(b, ld(mult(a, b), unit)))),
% 7.03/7.23 inference(transitivity,[status(thm)],[552, 565, 562, 568])).
% 7.03/7.23 tff(570,assumption,(~(mult(unit, mult(b, ld(mult(a, b), unit))) = mult(mult(unit, ld(mult(a, b), unit)), b))), introduced(assumption)).
% 7.03/7.23 tff(571,plain,
% 7.03/7.23 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(unit, mult(ld(mult(a, b), unit), b)) = mult(mult(unit, ld(mult(a, b), unit)), b)) | (mult(unit, mult(b, ld(mult(a, b), unit))) = mult(mult(unit, ld(mult(a, b), unit)), b)))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(unit, mult(ld(mult(a, b), unit), b)) = mult(mult(unit, ld(mult(a, b), unit)), b)) | (mult(unit, mult(b, ld(mult(a, b), unit))) = mult(mult(unit, ld(mult(a, b), unit)), b)))),
% 7.03/7.23 inference(rewrite,[status(thm)],[])).
% 7.03/7.23 tff(572,plain,
% 7.03/7.23 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(unit, mult(ld(mult(a, b), unit), b)) = mult(mult(unit, ld(mult(a, b), unit)), b)) | (mult(unit, mult(b, ld(mult(a, b), unit))) = mult(mult(unit, ld(mult(a, b), unit)), b)))),
% 7.03/7.23 inference(quant_inst,[status(thm)],[])).
% 7.03/7.23 tff(573,plain,
% 7.03/7.23 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(unit, mult(ld(mult(a, b), unit), b)) = mult(mult(unit, ld(mult(a, b), unit)), b)) | (mult(unit, mult(b, ld(mult(a, b), unit))) = mult(mult(unit, ld(mult(a, b), unit)), b))),
% 7.03/7.23 inference(modus_ponens,[status(thm)],[572, 571])).
% 7.03/7.23 tff(574,plain,
% 7.03/7.23 ((mult(unit, mult(ld(mult(a, b), unit), b)) = mult(mult(unit, ld(mult(a, b), unit)), b)) | (mult(unit, mult(b, ld(mult(a, b), unit))) = mult(mult(unit, ld(mult(a, b), unit)), b))),
% 7.03/7.23 inference(unit_resolution,[status(thm)],[573, 27])).
% 7.03/7.23 tff(575,plain,
% 7.03/7.23 (mult(unit, mult(ld(mult(a, b), unit), b)) = mult(mult(unit, ld(mult(a, b), unit)), b)),
% 7.03/7.23 inference(unit_resolution,[status(thm)],[574, 570])).
% 7.03/7.23 tff(576,plain,
% 7.03/7.23 ((mult(unit, mult(ld(mult(a, b), unit), b)) = mult(mult(unit, b), ld(mult(a, b), unit))) <=> (mult(mult(unit, ld(mult(a, b), unit)), b) = mult(unit, mult(b, ld(mult(a, b), unit))))),
% 7.03/7.23 inference(monotonicity,[status(thm)],[575, 569])).
% 7.03/7.23 tff(577,plain,
% 7.03/7.23 ((mult(unit, mult(ld(mult(a, b), unit), b)) = mult(mult(unit, b), ld(mult(a, b), unit))) <=> (mult(unit, mult(b, ld(mult(a, b), unit))) = mult(mult(unit, ld(mult(a, b), unit)), b))),
% 7.03/7.23 inference(transitivity,[status(thm)],[576, 558])).
% 7.03/7.23 tff(578,plain,
% 7.03/7.23 ((mult(unit, mult(b, ld(mult(a, b), unit))) = mult(mult(unit, ld(mult(a, b), unit)), b)) <=> (mult(unit, mult(ld(mult(a, b), unit), b)) = mult(mult(unit, b), ld(mult(a, b), unit)))),
% 7.03/7.23 inference(symmetry,[status(thm)],[577])).
% 7.03/7.23 tff(579,plain,
% 7.03/7.23 ((mult(unit, mult(b, ld(mult(a, b), unit))) = mult(mult(unit, ld(mult(a, b), unit)), b)) <=> (mult(b, mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(b, i(b)), mult(ld(mult(a, b), unit), b)))),
% 7.03/7.23 inference(transitivity,[status(thm)],[578, 557])).
% 7.03/7.23 tff(580,plain,
% 7.03/7.23 ((~(mult(unit, mult(b, ld(mult(a, b), unit))) = mult(mult(unit, ld(mult(a, b), unit)), b))) <=> (~(mult(b, mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(b, i(b)), mult(ld(mult(a, b), unit), b))))),
% 7.03/7.23 inference(monotonicity,[status(thm)],[579])).
% 7.03/7.23 tff(581,plain,
% 7.03/7.23 (~(mult(b, mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(b, i(b)), mult(ld(mult(a, b), unit), b)))),
% 7.03/7.23 inference(modus_ponens,[status(thm)],[570, 580])).
% 7.03/7.23 tff(582,plain,
% 7.03/7.23 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | ((mult(b, mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(b, i(b)), mult(ld(mult(a, b), unit), b))) | (mult(b, mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(b, mult(ld(mult(a, b), unit), b)), i(b))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | (mult(b, mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(b, i(b)), mult(ld(mult(a, b), unit), b))) | (mult(b, mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(b, mult(ld(mult(a, b), unit), b)), i(b))))),
% 7.03/7.23 inference(rewrite,[status(thm)],[])).
% 7.03/7.23 tff(583,plain,
% 7.03/7.23 (((mult(b, mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(b, mult(ld(mult(a, b), unit), b)), i(b))) | (mult(b, mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(b, i(b)), mult(ld(mult(a, b), unit), b)))) <=> ((mult(b, mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(b, i(b)), mult(ld(mult(a, b), unit), b))) | (mult(b, mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(b, mult(ld(mult(a, b), unit), b)), i(b))))),
% 7.03/7.23 inference(rewrite,[status(thm)],[])).
% 7.03/7.23 tff(584,plain,
% 7.03/7.23 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | ((mult(b, mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(b, mult(ld(mult(a, b), unit), b)), i(b))) | (mult(b, mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(b, i(b)), mult(ld(mult(a, b), unit), b))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | ((mult(b, mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(b, i(b)), mult(ld(mult(a, b), unit), b))) | (mult(b, mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(b, mult(ld(mult(a, b), unit), b)), i(b)))))),
% 7.03/7.23 inference(monotonicity,[status(thm)],[583])).
% 7.03/7.23 tff(585,plain,
% 7.03/7.23 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | ((mult(b, mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(b, mult(ld(mult(a, b), unit), b)), i(b))) | (mult(b, mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(b, i(b)), mult(ld(mult(a, b), unit), b))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | (mult(b, mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(b, i(b)), mult(ld(mult(a, b), unit), b))) | (mult(b, mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(b, mult(ld(mult(a, b), unit), b)), i(b))))),
% 7.03/7.23 inference(transitivity,[status(thm)],[584, 582])).
% 7.03/7.23 tff(586,plain,
% 7.03/7.23 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | ((mult(b, mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(b, mult(ld(mult(a, b), unit), b)), i(b))) | (mult(b, mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(b, i(b)), mult(ld(mult(a, b), unit), b))))),
% 7.03/7.23 inference(quant_inst,[status(thm)],[])).
% 7.03/7.23 tff(587,plain,
% 7.03/7.23 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | (mult(b, mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(b, i(b)), mult(ld(mult(a, b), unit), b))) | (mult(b, mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(b, mult(ld(mult(a, b), unit), b)), i(b)))),
% 7.03/7.23 inference(modus_ponens,[status(thm)],[586, 585])).
% 7.03/7.23 tff(588,plain,
% 7.03/7.23 (mult(b, mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(b, mult(ld(mult(a, b), unit), b)), i(b))),
% 7.03/7.23 inference(unit_resolution,[status(thm)],[587, 139, 581])).
% 7.03/7.23 tff(589,plain,
% 7.03/7.23 (mult(mult(b, mult(ld(mult(a, b), unit), b)), i(b)) = mult(b, mult(i(b), mult(ld(mult(a, b), unit), b)))),
% 7.03/7.23 inference(symmetry,[status(thm)],[588])).
% 7.03/7.23 tff(590,plain,
% 7.03/7.23 (mult(mult(b, mult(ld(mult(a, b), unit), b)), i(b)) = i(a)),
% 7.03/7.23 inference(transitivity,[status(thm)],[589, 547, 514, 501, 510])).
% 7.03/7.23 tff(591,plain,
% 7.03/7.23 (mult(mult(mult(b, mult(ld(mult(a, b), unit), b)), i(b)), i(b)) = mult(i(a), i(b))),
% 7.03/7.23 inference(monotonicity,[status(thm)],[590])).
% 7.03/7.23 tff(592,plain,
% 7.03/7.23 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(i(b), i(b))) = mult(mult(mult(b, mult(ld(mult(a, b), unit), b)), i(b)), i(b)))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(i(b), i(b))) = mult(mult(mult(b, mult(ld(mult(a, b), unit), b)), i(b)), i(b))))),
% 7.03/7.23 inference(rewrite,[status(thm)],[])).
% 7.03/7.23 tff(593,plain,
% 7.03/7.23 (((mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(i(b), i(b))) = mult(mult(mult(b, mult(ld(mult(a, b), unit), b)), i(b)), i(b))) | (mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(i(b), i(b))) = mult(mult(mult(b, mult(ld(mult(a, b), unit), b)), i(b)), i(b)))) <=> (mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(i(b), i(b))) = mult(mult(mult(b, mult(ld(mult(a, b), unit), b)), i(b)), i(b)))),
% 7.03/7.23 inference(rewrite,[status(thm)],[])).
% 7.03/7.23 tff(594,plain,
% 7.03/7.23 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(i(b), i(b))) = mult(mult(mult(b, mult(ld(mult(a, b), unit), b)), i(b)), i(b))) | (mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(i(b), i(b))) = mult(mult(mult(b, mult(ld(mult(a, b), unit), b)), i(b)), i(b))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(i(b), i(b))) = mult(mult(mult(b, mult(ld(mult(a, b), unit), b)), i(b)), i(b))))),
% 7.03/7.24 inference(monotonicity,[status(thm)],[593])).
% 7.03/7.24 tff(595,plain,
% 7.03/7.24 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(i(b), i(b))) = mult(mult(mult(b, mult(ld(mult(a, b), unit), b)), i(b)), i(b))) | (mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(i(b), i(b))) = mult(mult(mult(b, mult(ld(mult(a, b), unit), b)), i(b)), i(b))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(i(b), i(b))) = mult(mult(mult(b, mult(ld(mult(a, b), unit), b)), i(b)), i(b))))),
% 7.03/7.24 inference(transitivity,[status(thm)],[594, 592])).
% 7.03/7.24 tff(596,plain,
% 7.03/7.24 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(i(b), i(b))) = mult(mult(mult(b, mult(ld(mult(a, b), unit), b)), i(b)), i(b))) | (mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(i(b), i(b))) = mult(mult(mult(b, mult(ld(mult(a, b), unit), b)), i(b)), i(b))))),
% 7.03/7.24 inference(quant_inst,[status(thm)],[])).
% 7.03/7.24 tff(597,plain,
% 7.03/7.24 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(i(b), i(b))) = mult(mult(mult(b, mult(ld(mult(a, b), unit), b)), i(b)), i(b)))),
% 7.03/7.24 inference(modus_ponens,[status(thm)],[596, 595])).
% 7.03/7.24 tff(598,plain,
% 7.03/7.24 (mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(i(b), i(b))) = mult(mult(mult(b, mult(ld(mult(a, b), unit), b)), i(b)), i(b))),
% 7.03/7.24 inference(unit_resolution,[status(thm)],[597, 27])).
% 7.03/7.24 tff(599,plain,
% 7.03/7.24 (mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(i(b), i(b))) = mult(mult(i(b), b), ld(mult(a, b), unit))),
% 7.03/7.24 inference(transitivity,[status(thm)],[598, 591, 531, 528, 168, 10, 156])).
% 7.03/7.24 tff(600,plain,
% 7.03/7.24 (mult(mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(i(b), i(b))), b) = mult(mult(mult(i(b), b), ld(mult(a, b), unit)), b)),
% 7.03/7.24 inference(monotonicity,[status(thm)],[599])).
% 7.03/7.24 tff(601,plain,
% 7.03/7.24 (mult(mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(i(b), i(b))), b) = mult(mult(unit, ld(mult(a, b), unit)), b)),
% 7.03/7.24 inference(transitivity,[status(thm)],[600, 159, 14])).
% 7.03/7.24 tff(602,plain,
% 7.03/7.24 (mult(b, mult(i(b), i(b))) = i(b)),
% 7.03/7.24 inference(transitivity,[status(thm)],[84, 86, 16])).
% 7.03/7.24 tff(603,plain,
% 7.03/7.24 (mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(b, mult(i(b), i(b)))) = mult(mult(b, mult(ld(mult(a, b), unit), b)), i(b))),
% 7.03/7.24 inference(monotonicity,[status(thm)],[602])).
% 7.03/7.24 tff(604,plain,
% 7.03/7.24 (mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(b, mult(i(b), i(b)))) = mult(unit, mult(b, ld(mult(a, b), unit)))),
% 7.03/7.24 inference(transitivity,[status(thm)],[603, 589, 547, 565, 562, 568])).
% 7.03/7.24 tff(605,plain,
% 7.03/7.24 ((mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(b, mult(i(b), i(b)))) = mult(mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(i(b), i(b))), b)) <=> (mult(unit, mult(b, ld(mult(a, b), unit))) = mult(mult(unit, ld(mult(a, b), unit)), b))),
% 7.03/7.24 inference(monotonicity,[status(thm)],[604, 601])).
% 7.03/7.24 tff(606,plain,
% 7.03/7.24 ((mult(unit, mult(b, ld(mult(a, b), unit))) = mult(mult(unit, ld(mult(a, b), unit)), b)) <=> (mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(b, mult(i(b), i(b)))) = mult(mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(i(b), i(b))), b))),
% 7.03/7.24 inference(symmetry,[status(thm)],[605])).
% 7.03/7.24 tff(607,plain,
% 7.03/7.24 ((~(mult(unit, mult(b, ld(mult(a, b), unit))) = mult(mult(unit, ld(mult(a, b), unit)), b))) <=> (~(mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(b, mult(i(b), i(b)))) = mult(mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(i(b), i(b))), b)))),
% 7.03/7.24 inference(monotonicity,[status(thm)],[606])).
% 7.03/7.24 tff(608,plain,
% 7.03/7.24 (~(mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(b, mult(i(b), i(b)))) = mult(mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(i(b), i(b))), b))),
% 7.03/7.24 inference(modus_ponens,[status(thm)],[570, 607])).
% 7.03/7.24 tff(609,plain,
% 7.03/7.24 (mult(mult(b, mult(ld(mult(a, b), unit), b)), i(b)) = mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(b, mult(i(b), i(b))))),
% 7.03/7.24 inference(symmetry,[status(thm)],[603])).
% 7.03/7.24 tff(610,plain,
% 7.03/7.24 (mult(i(b), unit) = mult(i(b), mult(b, i(b)))),
% 7.03/7.24 inference(symmetry,[status(thm)],[77])).
% 7.03/7.24 tff(611,plain,
% 7.03/7.24 (mult(i(b), mult(i(b), b)) = mult(i(b), unit)),
% 7.03/7.24 inference(monotonicity,[status(thm)],[179])).
% 7.03/7.24 tff(612,plain,
% 7.03/7.24 (mult(i(b), mult(i(b), b)) = mult(i(b), mult(b, i(b)))),
% 7.03/7.24 inference(transitivity,[status(thm)],[611, 610])).
% 7.03/7.24 tff(613,plain,
% 7.03/7.24 ((mult(i(b), mult(i(b), b)) = mult(mult(i(b), i(b)), b)) <=> (mult(i(b), mult(b, i(b))) = mult(mult(i(b), i(b)), b))),
% 7.03/7.24 inference(monotonicity,[status(thm)],[612])).
% 7.03/7.24 tff(614,assumption,(~(mult(i(b), mult(b, i(b))) = mult(mult(i(b), i(b)), b))), introduced(assumption)).
% 7.03/7.24 tff(615,plain,
% 7.03/7.24 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(i(b), mult(i(b), b)) = mult(mult(i(b), i(b)), b)) | (mult(i(b), mult(b, i(b))) = mult(mult(i(b), i(b)), b)))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(i(b), mult(i(b), b)) = mult(mult(i(b), i(b)), b)) | (mult(i(b), mult(b, i(b))) = mult(mult(i(b), i(b)), b)))),
% 7.03/7.24 inference(rewrite,[status(thm)],[])).
% 7.03/7.24 tff(616,plain,
% 7.03/7.24 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(i(b), mult(i(b), b)) = mult(mult(i(b), i(b)), b)) | (mult(i(b), mult(b, i(b))) = mult(mult(i(b), i(b)), b)))),
% 7.03/7.24 inference(quant_inst,[status(thm)],[])).
% 7.03/7.24 tff(617,plain,
% 7.03/7.24 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(i(b), mult(i(b), b)) = mult(mult(i(b), i(b)), b)) | (mult(i(b), mult(b, i(b))) = mult(mult(i(b), i(b)), b))),
% 7.03/7.24 inference(modus_ponens,[status(thm)],[616, 615])).
% 7.03/7.24 tff(618,plain,
% 7.03/7.24 ((mult(i(b), mult(i(b), b)) = mult(mult(i(b), i(b)), b)) | (mult(i(b), mult(b, i(b))) = mult(mult(i(b), i(b)), b))),
% 7.03/7.24 inference(unit_resolution,[status(thm)],[617, 27])).
% 7.03/7.24 tff(619,plain,
% 7.03/7.24 (mult(i(b), mult(i(b), b)) = mult(mult(i(b), i(b)), b)),
% 7.03/7.24 inference(unit_resolution,[status(thm)],[618, 614])).
% 7.03/7.24 tff(620,plain,
% 7.03/7.24 (mult(i(b), mult(b, i(b))) = mult(mult(i(b), i(b)), b)),
% 7.03/7.24 inference(modus_ponens,[status(thm)],[619, 613])).
% 7.03/7.24 tff(621,plain,
% 7.03/7.24 ($false),
% 7.03/7.24 inference(unit_resolution,[status(thm)],[614, 620])).
% 7.03/7.24 tff(622,plain,(mult(i(b), mult(b, i(b))) = mult(mult(i(b), i(b)), b)), inference(lemma,lemma(discharge,[]))).
% 7.03/7.24 tff(623,plain,
% 7.03/7.24 (mult(mult(i(b), i(b)), b) = mult(i(b), mult(b, i(b)))),
% 7.03/7.24 inference(symmetry,[status(thm)],[622])).
% 7.03/7.24 tff(624,plain,
% 7.03/7.24 (mult(mult(i(b), i(b)), b) = i(b)),
% 7.03/7.24 inference(transitivity,[status(thm)],[623, 77, 56])).
% 7.03/7.24 tff(625,plain,
% 7.03/7.24 (mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(mult(i(b), i(b)), b)) = mult(mult(b, mult(ld(mult(a, b), unit), b)), i(b))),
% 7.03/7.24 inference(monotonicity,[status(thm)],[624])).
% 7.03/7.24 tff(626,plain,
% 7.03/7.24 (mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(mult(i(b), i(b)), b)) = mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(b, mult(i(b), i(b))))),
% 7.03/7.24 inference(transitivity,[status(thm)],[625, 609])).
% 7.03/7.24 tff(627,plain,
% 7.03/7.24 ((mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(mult(i(b), i(b)), b)) = mult(mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(i(b), i(b))), b)) <=> (mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(b, mult(i(b), i(b)))) = mult(mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(i(b), i(b))), b))),
% 7.03/7.24 inference(monotonicity,[status(thm)],[626])).
% 7.03/7.24 tff(628,plain,
% 7.03/7.24 ((mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(b, mult(i(b), i(b)))) = mult(mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(i(b), i(b))), b)) <=> (mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(mult(i(b), i(b)), b)) = mult(mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(i(b), i(b))), b))),
% 7.03/7.24 inference(symmetry,[status(thm)],[627])).
% 7.03/7.24 tff(629,plain,
% 7.03/7.24 ((mult(unit, mult(b, ld(mult(a, b), unit))) = mult(mult(unit, ld(mult(a, b), unit)), b)) <=> (mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(mult(i(b), i(b)), b)) = mult(mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(i(b), i(b))), b))),
% 7.03/7.24 inference(transitivity,[status(thm)],[606, 628])).
% 7.03/7.24 tff(630,plain,
% 7.03/7.24 ((~(mult(unit, mult(b, ld(mult(a, b), unit))) = mult(mult(unit, ld(mult(a, b), unit)), b))) <=> (~(mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(mult(i(b), i(b)), b)) = mult(mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(i(b), i(b))), b)))),
% 7.03/7.24 inference(monotonicity,[status(thm)],[629])).
% 7.03/7.24 tff(631,plain,
% 7.03/7.24 (~(mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(mult(i(b), i(b)), b)) = mult(mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(i(b), i(b))), b))),
% 7.03/7.24 inference(modus_ponens,[status(thm)],[570, 630])).
% 7.03/7.24 tff(632,plain,
% 7.03/7.24 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(b, mult(i(b), i(b)))) = mult(mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(i(b), i(b))), b)) | (mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(mult(i(b), i(b)), b)) = mult(mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(i(b), i(b))), b)))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(b, mult(i(b), i(b)))) = mult(mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(i(b), i(b))), b)) | (mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(mult(i(b), i(b)), b)) = mult(mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(i(b), i(b))), b)))),
% 7.03/7.24 inference(rewrite,[status(thm)],[])).
% 7.03/7.24 tff(633,plain,
% 7.03/7.24 (((mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(mult(i(b), i(b)), b)) = mult(mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(i(b), i(b))), b)) | (mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(b, mult(i(b), i(b)))) = mult(mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(i(b), i(b))), b))) <=> ((mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(b, mult(i(b), i(b)))) = mult(mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(i(b), i(b))), b)) | (mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(mult(i(b), i(b)), b)) = mult(mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(i(b), i(b))), b)))),
% 7.03/7.24 inference(rewrite,[status(thm)],[])).
% 7.03/7.24 tff(634,plain,
% 7.03/7.24 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(mult(i(b), i(b)), b)) = mult(mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(i(b), i(b))), b)) | (mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(b, mult(i(b), i(b)))) = mult(mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(i(b), i(b))), b)))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(b, mult(i(b), i(b)))) = mult(mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(i(b), i(b))), b)) | (mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(mult(i(b), i(b)), b)) = mult(mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(i(b), i(b))), b))))),
% 7.03/7.24 inference(monotonicity,[status(thm)],[633])).
% 7.03/7.24 tff(635,plain,
% 7.03/7.24 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(mult(i(b), i(b)), b)) = mult(mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(i(b), i(b))), b)) | (mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(b, mult(i(b), i(b)))) = mult(mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(i(b), i(b))), b)))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(b, mult(i(b), i(b)))) = mult(mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(i(b), i(b))), b)) | (mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(mult(i(b), i(b)), b)) = mult(mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(i(b), i(b))), b)))),
% 7.03/7.25 inference(transitivity,[status(thm)],[634, 632])).
% 7.03/7.25 tff(636,plain,
% 7.03/7.25 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(mult(i(b), i(b)), b)) = mult(mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(i(b), i(b))), b)) | (mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(b, mult(i(b), i(b)))) = mult(mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(i(b), i(b))), b)))),
% 7.03/7.25 inference(quant_inst,[status(thm)],[])).
% 7.03/7.25 tff(637,plain,
% 7.03/7.25 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(b, mult(i(b), i(b)))) = mult(mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(i(b), i(b))), b)) | (mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(mult(i(b), i(b)), b)) = mult(mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(i(b), i(b))), b))),
% 7.03/7.25 inference(modus_ponens,[status(thm)],[636, 635])).
% 7.03/7.25 tff(638,plain,
% 7.03/7.25 ((mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(b, mult(i(b), i(b)))) = mult(mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(i(b), i(b))), b)) | (mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(mult(i(b), i(b)), b)) = mult(mult(mult(b, mult(ld(mult(a, b), unit), b)), mult(i(b), i(b))), b))),
% 7.03/7.25 inference(unit_resolution,[status(thm)],[637, 27])).
% 7.03/7.25 tff(639,plain,
% 7.03/7.25 ($false),
% 7.03/7.25 inference(unit_resolution,[status(thm)],[638, 631, 608])).
% 7.03/7.25 tff(640,plain,(mult(unit, mult(b, ld(mult(a, b), unit))) = mult(mult(unit, ld(mult(a, b), unit)), b)), inference(lemma,lemma(discharge,[]))).
% 7.03/7.25 tff(641,plain,
% 7.03/7.25 (i(a) = mult(ld(mult(a, b), unit), b)),
% 7.03/7.25 inference(transitivity,[status(thm)],[93, 502, 170, 565, 562, 568, 640, 12])).
% 7.03/7.25 tff(642,plain,
% 7.03/7.25 (mult(i(b), i(a)) = mult(i(b), mult(ld(mult(a, b), unit), b))),
% 7.03/7.25 inference(monotonicity,[status(thm)],[641])).
% 7.03/7.25 tff(643,plain,
% 7.03/7.25 (mult(i(b), mult(ld(mult(a, b), unit), b)) = mult(i(b), i(a))),
% 7.03/7.25 inference(symmetry,[status(thm)],[642])).
% 7.03/7.25 tff(644,plain,
% 7.03/7.25 (mult(mult(i(b), b), ld(mult(a, b), unit)) = mult(i(b), mult(ld(mult(a, b), unit), b))),
% 7.03/7.25 inference(symmetry,[status(thm)],[545])).
% 7.03/7.25 tff(645,plain,
% 7.03/7.25 (i(mult(a, b)) = mult(i(b), i(a))),
% 7.03/7.25 inference(transitivity,[status(thm)],[466, 10, 156, 644, 643])).
% 7.03/7.25 tff(646,plain,
% 7.03/7.25 ($false),
% 7.03/7.25 inference(unit_resolution,[status(thm)],[470, 645])).
% 7.03/7.25 % SZS output end Proof
% 7.03/7.25 % E exiting
%------------------------------------------------------------------------------