TSTP Solution File: GRP747+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP747+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n005.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 : Fri Sep 16 22:29:42 EDT 2022
% Result : Theorem 1.35s 1.08s
% Output : Proof 1.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GRP747+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n005.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 31 20:44:03 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 1.35/1.08 % SZS status Theorem
% 1.35/1.08 % SZS output start Proof
% 1.35/1.08 tff(mult_type, type, (
% 1.35/1.08 mult: ( $i * $i ) > $i)).
% 1.35/1.08 tff(c_type, type, (
% 1.35/1.08 c: $i)).
% 1.35/1.08 tff(b_type, type, (
% 1.35/1.08 b: $i)).
% 1.35/1.08 tff(rd_type, type, (
% 1.35/1.08 rd: ( $i * $i ) > $i)).
% 1.35/1.08 tff(a_type, type, (
% 1.35/1.08 a: $i)).
% 1.35/1.08 tff(unit_type, type, (
% 1.35/1.08 unit: $i)).
% 1.35/1.08 tff(ld_type, type, (
% 1.35/1.08 ld: ( $i * $i ) > $i)).
% 1.35/1.08 tff(1,plain,
% 1.35/1.08 (^[B: $i, A: $i] : refl((mult(rd(A, B), B) = A) <=> (mult(rd(A, B), B) = A))),
% 1.35/1.08 inference(bind,[status(th)],[])).
% 1.35/1.08 tff(2,plain,
% 1.35/1.08 (![B: $i, A: $i] : (mult(rd(A, B), B) = A) <=> ![B: $i, A: $i] : (mult(rd(A, B), B) = A)),
% 1.35/1.08 inference(quant_intro,[status(thm)],[1])).
% 1.35/1.08 tff(3,plain,
% 1.35/1.08 (![B: $i, A: $i] : (mult(rd(A, B), B) = A) <=> ![B: $i, A: $i] : (mult(rd(A, B), B) = A)),
% 1.35/1.08 inference(rewrite,[status(thm)],[])).
% 1.35/1.08 tff(4,axiom,(![B: $i, A: $i] : (mult(rd(A, B), B) = A)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','f03')).
% 1.35/1.08 tff(5,plain,
% 1.35/1.08 (![B: $i, A: $i] : (mult(rd(A, B), B) = A)),
% 1.35/1.08 inference(modus_ponens,[status(thm)],[4, 3])).
% 1.35/1.08 tff(6,plain,(
% 1.35/1.08 ![B: $i, A: $i] : (mult(rd(A, B), B) = A)),
% 1.35/1.08 inference(skolemize,[status(sab)],[5])).
% 1.35/1.08 tff(7,plain,
% 1.35/1.08 (![B: $i, A: $i] : (mult(rd(A, B), B) = A)),
% 1.35/1.08 inference(modus_ponens,[status(thm)],[6, 2])).
% 1.35/1.08 tff(8,plain,
% 1.35/1.08 ((~![B: $i, A: $i] : (mult(rd(A, B), B) = A)) | (mult(rd(mult(a, b), mult(b, c)), mult(b, c)) = mult(a, b))),
% 1.35/1.08 inference(quant_inst,[status(thm)],[])).
% 1.35/1.08 tff(9,plain,
% 1.35/1.08 (mult(rd(mult(a, b), mult(b, c)), mult(b, c)) = mult(a, b)),
% 1.35/1.08 inference(unit_resolution,[status(thm)],[8, 7])).
% 1.35/1.08 tff(10,plain,
% 1.35/1.08 (mult(a, b) = mult(rd(mult(a, b), mult(b, c)), mult(b, c))),
% 1.35/1.08 inference(symmetry,[status(thm)],[9])).
% 1.35/1.08 tff(11,plain,
% 1.35/1.08 (^[B: $i, A: $i] : refl((rd(mult(A, B), B) = A) <=> (rd(mult(A, B), B) = A))),
% 1.35/1.08 inference(bind,[status(th)],[])).
% 1.35/1.08 tff(12,plain,
% 1.35/1.08 (![B: $i, A: $i] : (rd(mult(A, B), B) = A) <=> ![B: $i, A: $i] : (rd(mult(A, B), B) = A)),
% 1.35/1.08 inference(quant_intro,[status(thm)],[11])).
% 1.35/1.08 tff(13,plain,
% 1.35/1.08 (![B: $i, A: $i] : (rd(mult(A, B), B) = A) <=> ![B: $i, A: $i] : (rd(mult(A, B), B) = A)),
% 1.35/1.08 inference(rewrite,[status(thm)],[])).
% 1.35/1.08 tff(14,axiom,(![B: $i, A: $i] : (rd(mult(A, B), B) = A)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','f04')).
% 1.35/1.08 tff(15,plain,
% 1.35/1.08 (![B: $i, A: $i] : (rd(mult(A, B), B) = A)),
% 1.35/1.08 inference(modus_ponens,[status(thm)],[14, 13])).
% 1.35/1.08 tff(16,plain,(
% 1.35/1.08 ![B: $i, A: $i] : (rd(mult(A, B), B) = A)),
% 1.35/1.08 inference(skolemize,[status(sab)],[15])).
% 1.35/1.08 tff(17,plain,
% 1.35/1.08 (![B: $i, A: $i] : (rd(mult(A, B), B) = A)),
% 1.35/1.08 inference(modus_ponens,[status(thm)],[16, 12])).
% 1.35/1.08 tff(18,plain,
% 1.35/1.08 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(a, b), c), c) = mult(a, b))),
% 1.35/1.08 inference(quant_inst,[status(thm)],[])).
% 1.35/1.08 tff(19,plain,
% 1.35/1.08 (rd(mult(mult(a, b), c), c) = mult(a, b)),
% 1.35/1.08 inference(unit_resolution,[status(thm)],[18, 17])).
% 1.35/1.08 tff(20,plain,
% 1.35/1.08 (^[A: $i] : refl((mult(unit, A) = A) <=> (mult(unit, A) = A))),
% 1.35/1.08 inference(bind,[status(th)],[])).
% 1.35/1.08 tff(21,plain,
% 1.35/1.08 (![A: $i] : (mult(unit, A) = A) <=> ![A: $i] : (mult(unit, A) = A)),
% 1.35/1.08 inference(quant_intro,[status(thm)],[20])).
% 1.35/1.08 tff(22,plain,
% 1.35/1.08 (![A: $i] : (mult(unit, A) = A) <=> ![A: $i] : (mult(unit, A) = A)),
% 1.35/1.08 inference(rewrite,[status(thm)],[])).
% 1.35/1.08 tff(23,axiom,(![A: $i] : (mult(unit, A) = A)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','f06')).
% 1.35/1.08 tff(24,plain,
% 1.35/1.08 (![A: $i] : (mult(unit, A) = A)),
% 1.35/1.08 inference(modus_ponens,[status(thm)],[23, 22])).
% 1.35/1.08 tff(25,plain,(
% 1.35/1.08 ![A: $i] : (mult(unit, A) = A)),
% 1.35/1.08 inference(skolemize,[status(sab)],[24])).
% 1.35/1.08 tff(26,plain,
% 1.35/1.08 (![A: $i] : (mult(unit, A) = A)),
% 1.35/1.08 inference(modus_ponens,[status(thm)],[25, 21])).
% 1.35/1.08 tff(27,plain,
% 1.35/1.08 ((~![A: $i] : (mult(unit, A) = A)) | (mult(unit, rd(mult(a, b), mult(b, c))) = rd(mult(a, b), mult(b, c)))),
% 1.35/1.08 inference(quant_inst,[status(thm)],[])).
% 1.35/1.08 tff(28,plain,
% 1.35/1.08 (mult(unit, rd(mult(a, b), mult(b, c))) = rd(mult(a, b), mult(b, c))),
% 1.35/1.08 inference(unit_resolution,[status(thm)],[27, 26])).
% 1.35/1.08 tff(29,plain,
% 1.35/1.08 (^[A: $i] : refl((mult(A, unit) = A) <=> (mult(A, unit) = A))),
% 1.35/1.08 inference(bind,[status(th)],[])).
% 1.35/1.08 tff(30,plain,
% 1.35/1.08 (![A: $i] : (mult(A, unit) = A) <=> ![A: $i] : (mult(A, unit) = A)),
% 1.35/1.08 inference(quant_intro,[status(thm)],[29])).
% 1.35/1.08 tff(31,plain,
% 1.35/1.08 (![A: $i] : (mult(A, unit) = A) <=> ![A: $i] : (mult(A, unit) = A)),
% 1.35/1.08 inference(rewrite,[status(thm)],[])).
% 1.35/1.08 tff(32,axiom,(![A: $i] : (mult(A, unit) = A)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','f05')).
% 1.35/1.08 tff(33,plain,
% 1.35/1.08 (![A: $i] : (mult(A, unit) = A)),
% 1.35/1.08 inference(modus_ponens,[status(thm)],[32, 31])).
% 1.35/1.08 tff(34,plain,(
% 1.35/1.08 ![A: $i] : (mult(A, unit) = A)),
% 1.35/1.08 inference(skolemize,[status(sab)],[33])).
% 1.35/1.08 tff(35,plain,
% 1.35/1.08 (![A: $i] : (mult(A, unit) = A)),
% 1.35/1.08 inference(modus_ponens,[status(thm)],[34, 30])).
% 1.35/1.08 tff(36,plain,
% 1.35/1.08 ((~![A: $i] : (mult(A, unit) = A)) | (mult(mult(unit, rd(mult(a, b), mult(b, c))), unit) = mult(unit, rd(mult(a, b), mult(b, c))))),
% 1.35/1.08 inference(quant_inst,[status(thm)],[])).
% 1.35/1.08 tff(37,plain,
% 1.35/1.08 (mult(mult(unit, rd(mult(a, b), mult(b, c))), unit) = mult(unit, rd(mult(a, b), mult(b, c)))),
% 1.35/1.08 inference(unit_resolution,[status(thm)],[36, 35])).
% 1.35/1.08 tff(38,plain,
% 1.35/1.08 (mult(mult(unit, rd(mult(a, b), mult(b, c))), unit) = rd(mult(a, b), mult(b, c))),
% 1.35/1.08 inference(transitivity,[status(thm)],[37, 28])).
% 1.35/1.08 tff(39,plain,
% 1.35/1.08 (mult(mult(mult(unit, rd(mult(a, b), mult(b, c))), unit), mult(b, c)) = mult(rd(mult(a, b), mult(b, c)), mult(b, c))),
% 1.35/1.08 inference(monotonicity,[status(thm)],[38])).
% 1.35/1.08 tff(40,plain,
% 1.35/1.08 (mult(unit, rd(mult(a, b), mult(b, c))) = mult(mult(unit, rd(mult(a, b), mult(b, c))), unit)),
% 1.35/1.08 inference(symmetry,[status(thm)],[37])).
% 1.35/1.08 tff(41,plain,
% 1.35/1.08 (mult(mult(unit, rd(mult(a, b), mult(b, c))), mult(b, c)) = mult(mult(mult(unit, rd(mult(a, b), mult(b, c))), unit), mult(b, c))),
% 1.35/1.08 inference(monotonicity,[status(thm)],[40])).
% 1.35/1.08 tff(42,plain,
% 1.35/1.08 (mult(mult(mult(unit, rd(mult(a, b), mult(b, c))), unit), mult(b, c)) = mult(mult(unit, rd(mult(a, b), mult(b, c))), mult(b, c))),
% 1.35/1.08 inference(symmetry,[status(thm)],[41])).
% 1.35/1.08 tff(43,plain,
% 1.35/1.08 (mult(rd(mult(a, b), mult(b, c)), mult(b, c)) = mult(mult(mult(unit, rd(mult(a, b), mult(b, c))), unit), mult(b, c))),
% 1.35/1.08 inference(symmetry,[status(thm)],[39])).
% 1.35/1.08 tff(44,plain,
% 1.35/1.08 ((~![A: $i] : (mult(unit, A) = A)) | (mult(unit, mult(a, b)) = mult(a, b))),
% 1.35/1.08 inference(quant_inst,[status(thm)],[])).
% 1.35/1.08 tff(45,plain,
% 1.35/1.08 (mult(unit, mult(a, b)) = mult(a, b)),
% 1.35/1.08 inference(unit_resolution,[status(thm)],[44, 26])).
% 1.35/1.08 tff(46,plain,
% 1.35/1.08 (mult(unit, mult(rd(mult(a, b), mult(b, c)), mult(b, c))) = mult(unit, mult(a, b))),
% 1.35/1.08 inference(monotonicity,[status(thm)],[9])).
% 1.35/1.08 tff(47,plain,
% 1.35/1.08 (mult(unit, mult(rd(mult(a, b), mult(b, c)), mult(b, c))) = mult(mult(unit, rd(mult(a, b), mult(b, c))), mult(b, c))),
% 1.35/1.08 inference(transitivity,[status(thm)],[46, 45, 10, 43, 42])).
% 1.35/1.08 tff(48,plain,
% 1.35/1.08 ((mult(mult(unit, mult(b, c)), rd(mult(a, b), mult(b, c))) = mult(unit, mult(rd(mult(a, b), mult(b, c)), mult(b, c)))) <=> (mult(mult(unit, mult(b, c)), rd(mult(a, b), mult(b, c))) = mult(mult(unit, rd(mult(a, b), mult(b, c))), mult(b, c)))),
% 1.35/1.08 inference(monotonicity,[status(thm)],[47])).
% 1.35/1.08 tff(49,assumption,(~(mult(mult(unit, mult(b, c)), rd(mult(a, b), mult(b, c))) = mult(mult(unit, rd(mult(a, b), mult(b, c))), mult(b, c)))), introduced(assumption)).
% 1.35/1.08 tff(50,plain,
% 1.35/1.08 (((~(mult(mult(unit, mult(b, c)), rd(mult(a, b), mult(b, c))) = mult(mult(unit, rd(mult(a, b), mult(b, c))), mult(b, c)))) | (~(mult(unit, mult(mult(b, c), rd(mult(a, b), mult(b, c)))) = mult(unit, mult(rd(mult(a, b), mult(b, c)), mult(b, c)))))) | (mult(mult(unit, mult(b, c)), rd(mult(a, b), mult(b, c))) = mult(mult(unit, rd(mult(a, b), mult(b, c))), mult(b, c)))),
% 1.35/1.08 inference(tautology,[status(thm)],[])).
% 1.35/1.08 tff(51,plain,
% 1.35/1.08 ((~(mult(mult(unit, mult(b, c)), rd(mult(a, b), mult(b, c))) = mult(mult(unit, rd(mult(a, b), mult(b, c))), mult(b, c)))) | (~(mult(unit, mult(mult(b, c), rd(mult(a, b), mult(b, c)))) = mult(unit, mult(rd(mult(a, b), mult(b, c)), mult(b, c)))))),
% 1.35/1.08 inference(unit_resolution,[status(thm)],[50, 49])).
% 1.35/1.08 tff(52,plain,
% 1.35/1.08 (^[X0: $i, X1: $i, X2: $i] : refl(((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2))))))) <=> ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2))))))))),
% 1.35/1.08 inference(bind,[status(th)],[])).
% 1.35/1.08 tff(53,plain,
% 1.35/1.08 (![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2))))))) <=> ![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))),
% 1.35/1.08 inference(quant_intro,[status(thm)],[52])).
% 1.35/1.08 tff(54,plain,
% 1.35/1.08 (^[X0: $i, X1: $i, X2: $i] : rewrite((((mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1)) & (mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))) | ((mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1))) & (mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2))))) <=> ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2))))))))),
% 1.35/1.08 inference(bind,[status(th)],[])).
% 1.35/1.08 tff(55,plain,
% 1.35/1.08 (![X0: $i, X1: $i, X2: $i] : (((mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1)) & (mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))) | ((mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1))) & (mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2))))) <=> ![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))),
% 1.35/1.08 inference(quant_intro,[status(thm)],[54])).
% 1.35/1.08 tff(56,plain,
% 1.35/1.08 (![X0: $i, X1: $i, X2: $i] : (((mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1)) & (mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))) | ((mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1))) & (mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2))))) <=> ![X0: $i, X1: $i, X2: $i] : (((mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1)) & (mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))) | ((mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1))) & (mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))),
% 1.35/1.08 inference(rewrite,[status(thm)],[])).
% 1.35/1.08 tff(57,plain,
% 1.35/1.08 (^[X0: $i, X1: $i, X2: $i] : rewrite((((mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1))) & (mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))) | ((mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1)) & (mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1))))) <=> (((mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1)) & (mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))) | ((mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1))) & (mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2))))))),
% 1.35/1.08 inference(bind,[status(th)],[])).
% 1.35/1.08 tff(58,plain,
% 1.35/1.08 (![X0: $i, X1: $i, X2: $i] : (((mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1))) & (mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))) | ((mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1)) & (mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1))))) <=> ![X0: $i, X1: $i, X2: $i] : (((mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1)) & (mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))) | ((mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1))) & (mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))),
% 1.35/1.08 inference(quant_intro,[status(thm)],[57])).
% 1.35/1.08 tff(59,axiom,(![X0: $i, X1: $i, X2: $i] : (((mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1))) & (mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))) | ((mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1)) & (mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','f08')).
% 1.35/1.08 tff(60,plain,
% 1.35/1.08 (![X0: $i, X1: $i, X2: $i] : (((mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1)) & (mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))) | ((mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1))) & (mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))),
% 1.35/1.09 inference(modus_ponens,[status(thm)],[59, 58])).
% 1.35/1.09 tff(61,plain,
% 1.35/1.09 (![X0: $i, X1: $i, X2: $i] : (((mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1)) & (mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))) | ((mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1))) & (mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))),
% 1.35/1.09 inference(modus_ponens,[status(thm)],[60, 56])).
% 1.35/1.09 tff(62,plain,(
% 1.35/1.09 ![X0: $i, X1: $i, X2: $i] : (((mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1)) & (mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))) | ((mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1))) & (mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))),
% 1.35/1.09 inference(skolemize,[status(sab)],[61])).
% 1.35/1.09 tff(63,plain,
% 1.35/1.09 (![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))),
% 1.35/1.09 inference(modus_ponens,[status(thm)],[62, 55])).
% 1.35/1.09 tff(64,plain,
% 1.35/1.09 (![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))),
% 1.35/1.09 inference(modus_ponens,[status(thm)],[63, 53])).
% 1.35/1.09 tff(65,plain,
% 1.35/1.09 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(mult(unit, mult(b, c)), rd(mult(a, b), mult(b, c))) = mult(mult(unit, rd(mult(a, b), mult(b, c))), mult(b, c)))) | (~(mult(unit, mult(mult(b, c), rd(mult(a, b), mult(b, c)))) = mult(unit, mult(rd(mult(a, b), mult(b, c)), mult(b, c))))))) | (~((~(mult(mult(unit, mult(b, c)), rd(mult(a, b), mult(b, c))) = mult(unit, mult(rd(mult(a, b), mult(b, c)), mult(b, c))))) | (~(mult(mult(unit, rd(mult(a, b), mult(b, c))), mult(b, c)) = mult(unit, mult(mult(b, c), rd(mult(a, b), mult(b, c)))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | (~((~(mult(mult(unit, mult(b, c)), rd(mult(a, b), mult(b, c))) = mult(mult(unit, rd(mult(a, b), mult(b, c))), mult(b, c)))) | (~(mult(unit, mult(mult(b, c), rd(mult(a, b), mult(b, c)))) = mult(unit, mult(rd(mult(a, b), mult(b, c)), mult(b, c))))))) | (~((~(mult(mult(unit, mult(b, c)), rd(mult(a, b), mult(b, c))) = mult(unit, mult(rd(mult(a, b), mult(b, c)), mult(b, c))))) | (~(mult(mult(unit, rd(mult(a, b), mult(b, c))), mult(b, c)) = mult(unit, mult(mult(b, c), rd(mult(a, b), mult(b, c)))))))))),
% 1.35/1.09 inference(rewrite,[status(thm)],[])).
% 1.35/1.09 tff(66,plain,
% 1.35/1.09 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(mult(unit, mult(b, c)), rd(mult(a, b), mult(b, c))) = mult(mult(unit, rd(mult(a, b), mult(b, c))), mult(b, c)))) | (~(mult(unit, mult(mult(b, c), rd(mult(a, b), mult(b, c)))) = mult(unit, mult(rd(mult(a, b), mult(b, c)), mult(b, c))))))) | (~((~(mult(mult(unit, mult(b, c)), rd(mult(a, b), mult(b, c))) = mult(unit, mult(rd(mult(a, b), mult(b, c)), mult(b, c))))) | (~(mult(mult(unit, rd(mult(a, b), mult(b, c))), mult(b, c)) = mult(unit, mult(mult(b, c), rd(mult(a, b), mult(b, c)))))))))),
% 1.35/1.09 inference(quant_inst,[status(thm)],[])).
% 1.35/1.09 tff(67,plain,
% 1.35/1.09 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | (~((~(mult(mult(unit, mult(b, c)), rd(mult(a, b), mult(b, c))) = mult(mult(unit, rd(mult(a, b), mult(b, c))), mult(b, c)))) | (~(mult(unit, mult(mult(b, c), rd(mult(a, b), mult(b, c)))) = mult(unit, mult(rd(mult(a, b), mult(b, c)), mult(b, c))))))) | (~((~(mult(mult(unit, mult(b, c)), rd(mult(a, b), mult(b, c))) = mult(unit, mult(rd(mult(a, b), mult(b, c)), mult(b, c))))) | (~(mult(mult(unit, rd(mult(a, b), mult(b, c))), mult(b, c)) = mult(unit, mult(mult(b, c), rd(mult(a, b), mult(b, c))))))))),
% 1.35/1.09 inference(modus_ponens,[status(thm)],[66, 65])).
% 1.35/1.09 tff(68,plain,
% 1.35/1.09 ((~((~(mult(mult(unit, mult(b, c)), rd(mult(a, b), mult(b, c))) = mult(mult(unit, rd(mult(a, b), mult(b, c))), mult(b, c)))) | (~(mult(unit, mult(mult(b, c), rd(mult(a, b), mult(b, c)))) = mult(unit, mult(rd(mult(a, b), mult(b, c)), mult(b, c))))))) | (~((~(mult(mult(unit, mult(b, c)), rd(mult(a, b), mult(b, c))) = mult(unit, mult(rd(mult(a, b), mult(b, c)), mult(b, c))))) | (~(mult(mult(unit, rd(mult(a, b), mult(b, c))), mult(b, c)) = mult(unit, mult(mult(b, c), rd(mult(a, b), mult(b, c))))))))),
% 1.35/1.09 inference(unit_resolution,[status(thm)],[67, 64])).
% 1.35/1.09 tff(69,plain,
% 1.35/1.09 (~((~(mult(mult(unit, mult(b, c)), rd(mult(a, b), mult(b, c))) = mult(unit, mult(rd(mult(a, b), mult(b, c)), mult(b, c))))) | (~(mult(mult(unit, rd(mult(a, b), mult(b, c))), mult(b, c)) = mult(unit, mult(mult(b, c), rd(mult(a, b), mult(b, c)))))))),
% 1.35/1.09 inference(unit_resolution,[status(thm)],[68, 51])).
% 1.35/1.09 tff(70,plain,
% 1.35/1.09 (((~(mult(mult(unit, mult(b, c)), rd(mult(a, b), mult(b, c))) = mult(unit, mult(rd(mult(a, b), mult(b, c)), mult(b, c))))) | (~(mult(mult(unit, rd(mult(a, b), mult(b, c))), mult(b, c)) = mult(unit, mult(mult(b, c), rd(mult(a, b), mult(b, c))))))) | (mult(mult(unit, mult(b, c)), rd(mult(a, b), mult(b, c))) = mult(unit, mult(rd(mult(a, b), mult(b, c)), mult(b, c))))),
% 1.35/1.09 inference(tautology,[status(thm)],[])).
% 1.35/1.09 tff(71,plain,
% 1.35/1.09 (mult(mult(unit, mult(b, c)), rd(mult(a, b), mult(b, c))) = mult(unit, mult(rd(mult(a, b), mult(b, c)), mult(b, c)))),
% 1.35/1.09 inference(unit_resolution,[status(thm)],[70, 69])).
% 1.35/1.09 tff(72,plain,
% 1.35/1.09 (mult(mult(unit, mult(b, c)), rd(mult(a, b), mult(b, c))) = mult(mult(unit, rd(mult(a, b), mult(b, c))), mult(b, c))),
% 1.35/1.09 inference(modus_ponens,[status(thm)],[71, 48])).
% 1.35/1.09 tff(73,plain,
% 1.35/1.09 ($false),
% 1.35/1.09 inference(unit_resolution,[status(thm)],[49, 72])).
% 1.35/1.09 tff(74,plain,(mult(mult(unit, mult(b, c)), rd(mult(a, b), mult(b, c))) = mult(mult(unit, rd(mult(a, b), mult(b, c))), mult(b, c))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.09 tff(75,plain,
% 1.35/1.09 ((~![A: $i] : (mult(unit, A) = A)) | (mult(unit, mult(b, c)) = mult(b, c))),
% 1.35/1.09 inference(quant_inst,[status(thm)],[])).
% 1.35/1.09 tff(76,plain,
% 1.35/1.09 (mult(unit, mult(b, c)) = mult(b, c)),
% 1.35/1.09 inference(unit_resolution,[status(thm)],[75, 26])).
% 1.35/1.09 tff(77,plain,
% 1.35/1.09 (mult(b, c) = mult(unit, mult(b, c))),
% 1.35/1.09 inference(symmetry,[status(thm)],[76])).
% 1.35/1.09 tff(78,plain,
% 1.35/1.09 (mult(mult(b, c), rd(mult(a, b), mult(b, c))) = mult(mult(unit, mult(b, c)), rd(mult(a, b), mult(b, c)))),
% 1.35/1.09 inference(monotonicity,[status(thm)],[77])).
% 1.35/1.09 tff(79,plain,
% 1.35/1.09 (mult(mult(b, c), rd(mult(a, b), mult(b, c))) = mult(a, b)),
% 1.35/1.09 inference(transitivity,[status(thm)],[78, 74, 41, 39, 9])).
% 1.35/1.09 tff(80,plain,
% 1.35/1.09 (mult(mult(mult(b, c), rd(mult(a, b), mult(b, c))), c) = mult(mult(a, b), c)),
% 1.35/1.09 inference(monotonicity,[status(thm)],[79])).
% 1.35/1.09 tff(81,plain,
% 1.35/1.09 (mult(mult(unit, mult(b, c)), ld(mult(b, c), mult(mult(a, b), c))) = mult(mult(b, c), ld(mult(b, c), mult(mult(a, b), c)))),
% 1.35/1.09 inference(monotonicity,[status(thm)],[76])).
% 1.35/1.09 tff(82,plain,
% 1.35/1.09 (mult(mult(b, c), ld(mult(b, c), mult(mult(a, b), c))) = mult(mult(unit, mult(b, c)), ld(mult(b, c), mult(mult(a, b), c)))),
% 1.35/1.09 inference(symmetry,[status(thm)],[81])).
% 1.35/1.09 tff(83,plain,
% 1.35/1.09 (^[B: $i, A: $i] : refl((mult(A, ld(A, B)) = B) <=> (mult(A, ld(A, B)) = B))),
% 1.35/1.09 inference(bind,[status(th)],[])).
% 1.35/1.09 tff(84,plain,
% 1.35/1.09 (![B: $i, A: $i] : (mult(A, ld(A, B)) = B) <=> ![B: $i, A: $i] : (mult(A, ld(A, B)) = B)),
% 1.35/1.09 inference(quant_intro,[status(thm)],[83])).
% 1.35/1.09 tff(85,plain,
% 1.35/1.09 (![B: $i, A: $i] : (mult(A, ld(A, B)) = B) <=> ![B: $i, A: $i] : (mult(A, ld(A, B)) = B)),
% 1.35/1.09 inference(rewrite,[status(thm)],[])).
% 1.35/1.09 tff(86,axiom,(![B: $i, A: $i] : (mult(A, ld(A, B)) = B)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','f01')).
% 1.35/1.09 tff(87,plain,
% 1.35/1.09 (![B: $i, A: $i] : (mult(A, ld(A, B)) = B)),
% 1.35/1.09 inference(modus_ponens,[status(thm)],[86, 85])).
% 1.35/1.09 tff(88,plain,(
% 1.35/1.09 ![B: $i, A: $i] : (mult(A, ld(A, B)) = B)),
% 1.35/1.09 inference(skolemize,[status(sab)],[87])).
% 1.35/1.09 tff(89,plain,
% 1.35/1.09 (![B: $i, A: $i] : (mult(A, ld(A, B)) = B)),
% 1.35/1.09 inference(modus_ponens,[status(thm)],[88, 84])).
% 1.35/1.09 tff(90,plain,
% 1.35/1.09 ((~![B: $i, A: $i] : (mult(A, ld(A, B)) = B)) | (mult(mult(b, c), ld(mult(b, c), mult(mult(a, b), c))) = mult(mult(a, b), c))),
% 1.35/1.09 inference(quant_inst,[status(thm)],[])).
% 1.35/1.09 tff(91,plain,
% 1.35/1.09 (mult(mult(b, c), ld(mult(b, c), mult(mult(a, b), c))) = mult(mult(a, b), c)),
% 1.35/1.09 inference(unit_resolution,[status(thm)],[90, 89])).
% 1.35/1.09 tff(92,plain,
% 1.35/1.09 (mult(mult(a, b), c) = mult(mult(b, c), ld(mult(b, c), mult(mult(a, b), c)))),
% 1.35/1.09 inference(symmetry,[status(thm)],[91])).
% 1.35/1.09 tff(93,plain,
% 1.35/1.09 (^[B: $i, A: $i] : refl((ld(A, mult(A, B)) = B) <=> (ld(A, mult(A, B)) = B))),
% 1.35/1.09 inference(bind,[status(th)],[])).
% 1.35/1.09 tff(94,plain,
% 1.35/1.09 (![B: $i, A: $i] : (ld(A, mult(A, B)) = B) <=> ![B: $i, A: $i] : (ld(A, mult(A, B)) = B)),
% 1.35/1.09 inference(quant_intro,[status(thm)],[93])).
% 1.35/1.09 tff(95,plain,
% 1.35/1.09 (![B: $i, A: $i] : (ld(A, mult(A, B)) = B) <=> ![B: $i, A: $i] : (ld(A, mult(A, B)) = B)),
% 1.35/1.09 inference(rewrite,[status(thm)],[])).
% 1.35/1.09 tff(96,axiom,(![B: $i, A: $i] : (ld(A, mult(A, B)) = B)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','f02')).
% 1.35/1.09 tff(97,plain,
% 1.35/1.09 (![B: $i, A: $i] : (ld(A, mult(A, B)) = B)),
% 1.35/1.09 inference(modus_ponens,[status(thm)],[96, 95])).
% 1.35/1.09 tff(98,plain,(
% 1.35/1.09 ![B: $i, A: $i] : (ld(A, mult(A, B)) = B)),
% 1.35/1.09 inference(skolemize,[status(sab)],[97])).
% 1.35/1.09 tff(99,plain,
% 1.35/1.09 (![B: $i, A: $i] : (ld(A, mult(A, B)) = B)),
% 1.35/1.09 inference(modus_ponens,[status(thm)],[98, 94])).
% 1.35/1.09 tff(100,plain,
% 1.35/1.09 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(b, mult(a, b)), mult(mult(b, mult(a, b)), mult(mult(a, b), c))) = mult(mult(a, b), c))),
% 1.35/1.09 inference(quant_inst,[status(thm)],[])).
% 1.35/1.09 tff(101,plain,
% 1.35/1.09 (ld(mult(b, mult(a, b)), mult(mult(b, mult(a, b)), mult(mult(a, b), c))) = mult(mult(a, b), c)),
% 1.35/1.09 inference(unit_resolution,[status(thm)],[100, 99])).
% 1.35/1.09 tff(102,plain,
% 1.35/1.09 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(b, mult(mult(a, b), c)), mult(a, b)), mult(a, b)) = mult(b, mult(mult(a, b), c)))),
% 1.35/1.09 inference(quant_inst,[status(thm)],[])).
% 1.35/1.09 tff(103,plain,
% 1.35/1.09 (rd(mult(mult(b, mult(mult(a, b), c)), mult(a, b)), mult(a, b)) = mult(b, mult(mult(a, b), c))),
% 1.35/1.09 inference(unit_resolution,[status(thm)],[102, 17])).
% 1.35/1.09 tff(104,plain,
% 1.35/1.09 ((mult(b, mult(mult(mult(a, b), c), mult(a, b))) = mult(b, mult(mult(a, b), mult(mult(a, b), c)))) <=> (mult(b, mult(mult(a, b), mult(mult(a, b), c))) = mult(b, mult(mult(mult(a, b), c), mult(a, b))))),
% 1.35/1.09 inference(commutativity,[status(thm)],[])).
% 1.35/1.09 tff(105,assumption,(~(mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(mult(b, mult(mult(a, b), c)), mult(a, b)))), introduced(assumption)).
% 1.35/1.09 tff(106,plain,
% 1.35/1.09 (((~(mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(mult(b, mult(mult(a, b), c)), mult(a, b)))) | (~(mult(b, mult(mult(a, b), mult(mult(a, b), c))) = mult(b, mult(mult(mult(a, b), c), mult(a, b)))))) | (mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(mult(b, mult(mult(a, b), c)), mult(a, b)))),
% 1.35/1.09 inference(tautology,[status(thm)],[])).
% 1.35/1.09 tff(107,plain,
% 1.35/1.09 ((~(mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(mult(b, mult(mult(a, b), c)), mult(a, b)))) | (~(mult(b, mult(mult(a, b), mult(mult(a, b), c))) = mult(b, mult(mult(mult(a, b), c), mult(a, b)))))),
% 1.35/1.09 inference(unit_resolution,[status(thm)],[106, 105])).
% 1.35/1.09 tff(108,plain,
% 1.35/1.09 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(b, mult(mult(mult(a, b), c), mult(a, b))))) | (~(mult(mult(b, mult(mult(a, b), c)), mult(a, b)) = mult(b, mult(mult(a, b), mult(mult(a, b), c))))))) | (~((~(mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(mult(b, mult(mult(a, b), c)), mult(a, b)))) | (~(mult(b, mult(mult(a, b), mult(mult(a, b), c))) = mult(b, mult(mult(mult(a, b), c), mult(a, b))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | (~((~(mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(b, mult(mult(mult(a, b), c), mult(a, b))))) | (~(mult(mult(b, mult(mult(a, b), c)), mult(a, b)) = mult(b, mult(mult(a, b), mult(mult(a, b), c))))))) | (~((~(mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(mult(b, mult(mult(a, b), c)), mult(a, b)))) | (~(mult(b, mult(mult(a, b), mult(mult(a, b), c))) = mult(b, mult(mult(mult(a, b), c), mult(a, b))))))))),
% 1.35/1.09 inference(rewrite,[status(thm)],[])).
% 1.35/1.09 tff(109,plain,
% 1.35/1.09 (((~((~(mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(mult(b, mult(mult(a, b), c)), mult(a, b)))) | (~(mult(b, mult(mult(a, b), mult(mult(a, b), c))) = mult(b, mult(mult(mult(a, b), c), mult(a, b))))))) | (~((~(mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(b, mult(mult(mult(a, b), c), mult(a, b))))) | (~(mult(mult(b, mult(mult(a, b), c)), mult(a, b)) = mult(b, mult(mult(a, b), mult(mult(a, b), c)))))))) <=> ((~((~(mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(b, mult(mult(mult(a, b), c), mult(a, b))))) | (~(mult(mult(b, mult(mult(a, b), c)), mult(a, b)) = mult(b, mult(mult(a, b), mult(mult(a, b), c))))))) | (~((~(mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(mult(b, mult(mult(a, b), c)), mult(a, b)))) | (~(mult(b, mult(mult(a, b), mult(mult(a, b), c))) = mult(b, mult(mult(mult(a, b), c), mult(a, b))))))))),
% 1.35/1.09 inference(rewrite,[status(thm)],[])).
% 1.35/1.09 tff(110,plain,
% 1.35/1.09 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(mult(b, mult(mult(a, b), c)), mult(a, b)))) | (~(mult(b, mult(mult(a, b), mult(mult(a, b), c))) = mult(b, mult(mult(mult(a, b), c), mult(a, b))))))) | (~((~(mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(b, mult(mult(mult(a, b), c), mult(a, b))))) | (~(mult(mult(b, mult(mult(a, b), c)), mult(a, b)) = mult(b, mult(mult(a, b), mult(mult(a, b), c))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(b, mult(mult(mult(a, b), c), mult(a, b))))) | (~(mult(mult(b, mult(mult(a, b), c)), mult(a, b)) = mult(b, mult(mult(a, b), mult(mult(a, b), c))))))) | (~((~(mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(mult(b, mult(mult(a, b), c)), mult(a, b)))) | (~(mult(b, mult(mult(a, b), mult(mult(a, b), c))) = mult(b, mult(mult(mult(a, b), c), mult(a, b)))))))))),
% 1.35/1.09 inference(monotonicity,[status(thm)],[109])).
% 1.35/1.09 tff(111,plain,
% 1.35/1.09 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(mult(b, mult(mult(a, b), c)), mult(a, b)))) | (~(mult(b, mult(mult(a, b), mult(mult(a, b), c))) = mult(b, mult(mult(mult(a, b), c), mult(a, b))))))) | (~((~(mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(b, mult(mult(mult(a, b), c), mult(a, b))))) | (~(mult(mult(b, mult(mult(a, b), c)), mult(a, b)) = mult(b, mult(mult(a, b), mult(mult(a, b), c))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | (~((~(mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(b, mult(mult(mult(a, b), c), mult(a, b))))) | (~(mult(mult(b, mult(mult(a, b), c)), mult(a, b)) = mult(b, mult(mult(a, b), mult(mult(a, b), c))))))) | (~((~(mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(mult(b, mult(mult(a, b), c)), mult(a, b)))) | (~(mult(b, mult(mult(a, b), mult(mult(a, b), c))) = mult(b, mult(mult(mult(a, b), c), mult(a, b))))))))),
% 1.35/1.10 inference(transitivity,[status(thm)],[110, 108])).
% 1.35/1.10 tff(112,plain,
% 1.35/1.10 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(mult(b, mult(mult(a, b), c)), mult(a, b)))) | (~(mult(b, mult(mult(a, b), mult(mult(a, b), c))) = mult(b, mult(mult(mult(a, b), c), mult(a, b))))))) | (~((~(mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(b, mult(mult(mult(a, b), c), mult(a, b))))) | (~(mult(mult(b, mult(mult(a, b), c)), mult(a, b)) = mult(b, mult(mult(a, b), mult(mult(a, b), c))))))))),
% 1.35/1.10 inference(quant_inst,[status(thm)],[])).
% 1.35/1.10 tff(113,plain,
% 1.35/1.10 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | (~((~(mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(b, mult(mult(mult(a, b), c), mult(a, b))))) | (~(mult(mult(b, mult(mult(a, b), c)), mult(a, b)) = mult(b, mult(mult(a, b), mult(mult(a, b), c))))))) | (~((~(mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(mult(b, mult(mult(a, b), c)), mult(a, b)))) | (~(mult(b, mult(mult(a, b), mult(mult(a, b), c))) = mult(b, mult(mult(mult(a, b), c), mult(a, b)))))))),
% 1.35/1.10 inference(modus_ponens,[status(thm)],[112, 111])).
% 1.35/1.10 tff(114,plain,
% 1.35/1.10 ((~((~(mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(b, mult(mult(mult(a, b), c), mult(a, b))))) | (~(mult(mult(b, mult(mult(a, b), c)), mult(a, b)) = mult(b, mult(mult(a, b), mult(mult(a, b), c))))))) | (~((~(mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(mult(b, mult(mult(a, b), c)), mult(a, b)))) | (~(mult(b, mult(mult(a, b), mult(mult(a, b), c))) = mult(b, mult(mult(mult(a, b), c), mult(a, b)))))))),
% 1.35/1.10 inference(unit_resolution,[status(thm)],[113, 64])).
% 1.35/1.10 tff(115,plain,
% 1.35/1.10 (~((~(mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(b, mult(mult(mult(a, b), c), mult(a, b))))) | (~(mult(mult(b, mult(mult(a, b), c)), mult(a, b)) = mult(b, mult(mult(a, b), mult(mult(a, b), c))))))),
% 1.35/1.10 inference(unit_resolution,[status(thm)],[114, 107])).
% 1.35/1.10 tff(116,plain,
% 1.35/1.10 (((~(mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(b, mult(mult(mult(a, b), c), mult(a, b))))) | (~(mult(mult(b, mult(mult(a, b), c)), mult(a, b)) = mult(b, mult(mult(a, b), mult(mult(a, b), c)))))) | (mult(mult(b, mult(mult(a, b), c)), mult(a, b)) = mult(b, mult(mult(a, b), mult(mult(a, b), c))))),
% 1.35/1.10 inference(tautology,[status(thm)],[])).
% 1.35/1.10 tff(117,plain,
% 1.35/1.10 (mult(mult(b, mult(mult(a, b), c)), mult(a, b)) = mult(b, mult(mult(a, b), mult(mult(a, b), c)))),
% 1.35/1.10 inference(unit_resolution,[status(thm)],[116, 115])).
% 1.35/1.10 tff(118,plain,
% 1.35/1.10 (^[C: $i, B: $i, A: $i] : refl((mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B))) <=> (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B))))),
% 1.35/1.10 inference(bind,[status(th)],[])).
% 1.35/1.10 tff(119,plain,
% 1.35/1.10 (![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B))) <=> ![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))),
% 1.35/1.10 inference(quant_intro,[status(thm)],[118])).
% 1.35/1.10 tff(120,plain,
% 1.35/1.10 (![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B))) <=> ![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))),
% 1.35/1.10 inference(rewrite,[status(thm)],[])).
% 1.35/1.10 tff(121,axiom,(![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','f07')).
% 1.35/1.10 tff(122,plain,
% 1.35/1.10 (![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))),
% 1.35/1.10 inference(modus_ponens,[status(thm)],[121, 120])).
% 1.35/1.10 tff(123,plain,(
% 1.35/1.10 ![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))),
% 1.35/1.10 inference(skolemize,[status(sab)],[122])).
% 1.35/1.10 tff(124,plain,
% 1.35/1.10 (![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))),
% 1.35/1.10 inference(modus_ponens,[status(thm)],[123, 119])).
% 1.35/1.10 tff(125,plain,
% 1.35/1.10 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(b, mult(a, b)), c), mult(a, b)) = mult(b, mult(mult(mult(a, b), c), mult(a, b))))),
% 1.35/1.10 inference(quant_inst,[status(thm)],[])).
% 1.35/1.10 tff(126,plain,
% 1.35/1.10 (mult(mult(mult(b, mult(a, b)), c), mult(a, b)) = mult(b, mult(mult(mult(a, b), c), mult(a, b)))),
% 1.35/1.10 inference(unit_resolution,[status(thm)],[125, 124])).
% 1.35/1.10 tff(127,plain,
% 1.35/1.10 ((mult(b, mult(mult(mult(a, b), c), mult(a, b))) = mult(mult(b, mult(a, b)), mult(mult(a, b), c))) <=> (mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(b, mult(mult(mult(a, b), c), mult(a, b))))),
% 1.35/1.10 inference(commutativity,[status(thm)],[])).
% 1.35/1.10 tff(128,assumption,(~(mult(mult(mult(b, mult(a, b)), c), mult(a, b)) = mult(mult(b, mult(a, b)), mult(mult(a, b), c)))), introduced(assumption)).
% 1.35/1.10 tff(129,plain,
% 1.35/1.10 (((~(mult(mult(mult(b, mult(a, b)), mult(a, b)), c) = mult(mult(b, mult(a, b)), mult(c, mult(a, b))))) | (~(mult(mult(mult(b, mult(a, b)), c), mult(a, b)) = mult(mult(b, mult(a, b)), mult(mult(a, b), c))))) | (mult(mult(mult(b, mult(a, b)), c), mult(a, b)) = mult(mult(b, mult(a, b)), mult(mult(a, b), c)))),
% 1.35/1.10 inference(tautology,[status(thm)],[])).
% 1.35/1.10 tff(130,plain,
% 1.35/1.10 ((~(mult(mult(mult(b, mult(a, b)), mult(a, b)), c) = mult(mult(b, mult(a, b)), mult(c, mult(a, b))))) | (~(mult(mult(mult(b, mult(a, b)), c), mult(a, b)) = mult(mult(b, mult(a, b)), mult(mult(a, b), c))))),
% 1.35/1.10 inference(unit_resolution,[status(thm)],[129, 128])).
% 1.35/1.10 tff(131,plain,
% 1.35/1.10 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(mult(b, mult(a, b)), mult(c, mult(a, b))))) | (~(mult(mult(mult(b, mult(a, b)), mult(a, b)), c) = mult(mult(mult(b, mult(a, b)), c), mult(a, b)))))) | (~((~(mult(mult(mult(b, mult(a, b)), mult(a, b)), c) = mult(mult(b, mult(a, b)), mult(c, mult(a, b))))) | (~(mult(mult(mult(b, mult(a, b)), c), mult(a, b)) = mult(mult(b, mult(a, b)), mult(mult(a, b), c)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | (~((~(mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(mult(b, mult(a, b)), mult(c, mult(a, b))))) | (~(mult(mult(mult(b, mult(a, b)), mult(a, b)), c) = mult(mult(mult(b, mult(a, b)), c), mult(a, b)))))) | (~((~(mult(mult(mult(b, mult(a, b)), mult(a, b)), c) = mult(mult(b, mult(a, b)), mult(c, mult(a, b))))) | (~(mult(mult(mult(b, mult(a, b)), c), mult(a, b)) = mult(mult(b, mult(a, b)), mult(mult(a, b), c)))))))),
% 1.35/1.10 inference(rewrite,[status(thm)],[])).
% 1.35/1.10 tff(132,plain,
% 1.35/1.10 (((~((~(mult(mult(mult(b, mult(a, b)), mult(a, b)), c) = mult(mult(mult(b, mult(a, b)), c), mult(a, b)))) | (~(mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(mult(b, mult(a, b)), mult(c, mult(a, b))))))) | (~((~(mult(mult(mult(b, mult(a, b)), mult(a, b)), c) = mult(mult(b, mult(a, b)), mult(c, mult(a, b))))) | (~(mult(mult(mult(b, mult(a, b)), c), mult(a, b)) = mult(mult(b, mult(a, b)), mult(mult(a, b), c))))))) <=> ((~((~(mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(mult(b, mult(a, b)), mult(c, mult(a, b))))) | (~(mult(mult(mult(b, mult(a, b)), mult(a, b)), c) = mult(mult(mult(b, mult(a, b)), c), mult(a, b)))))) | (~((~(mult(mult(mult(b, mult(a, b)), mult(a, b)), c) = mult(mult(b, mult(a, b)), mult(c, mult(a, b))))) | (~(mult(mult(mult(b, mult(a, b)), c), mult(a, b)) = mult(mult(b, mult(a, b)), mult(mult(a, b), c)))))))),
% 1.35/1.10 inference(rewrite,[status(thm)],[])).
% 1.35/1.10 tff(133,plain,
% 1.35/1.10 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(mult(mult(b, mult(a, b)), mult(a, b)), c) = mult(mult(mult(b, mult(a, b)), c), mult(a, b)))) | (~(mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(mult(b, mult(a, b)), mult(c, mult(a, b))))))) | (~((~(mult(mult(mult(b, mult(a, b)), mult(a, b)), c) = mult(mult(b, mult(a, b)), mult(c, mult(a, b))))) | (~(mult(mult(mult(b, mult(a, b)), c), mult(a, b)) = mult(mult(b, mult(a, b)), mult(mult(a, b), c)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(mult(b, mult(a, b)), mult(c, mult(a, b))))) | (~(mult(mult(mult(b, mult(a, b)), mult(a, b)), c) = mult(mult(mult(b, mult(a, b)), c), mult(a, b)))))) | (~((~(mult(mult(mult(b, mult(a, b)), mult(a, b)), c) = mult(mult(b, mult(a, b)), mult(c, mult(a, b))))) | (~(mult(mult(mult(b, mult(a, b)), c), mult(a, b)) = mult(mult(b, mult(a, b)), mult(mult(a, b), c))))))))),
% 1.35/1.10 inference(monotonicity,[status(thm)],[132])).
% 1.35/1.10 tff(134,plain,
% 1.35/1.10 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(mult(mult(b, mult(a, b)), mult(a, b)), c) = mult(mult(mult(b, mult(a, b)), c), mult(a, b)))) | (~(mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(mult(b, mult(a, b)), mult(c, mult(a, b))))))) | (~((~(mult(mult(mult(b, mult(a, b)), mult(a, b)), c) = mult(mult(b, mult(a, b)), mult(c, mult(a, b))))) | (~(mult(mult(mult(b, mult(a, b)), c), mult(a, b)) = mult(mult(b, mult(a, b)), mult(mult(a, b), c)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | (~((~(mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(mult(b, mult(a, b)), mult(c, mult(a, b))))) | (~(mult(mult(mult(b, mult(a, b)), mult(a, b)), c) = mult(mult(mult(b, mult(a, b)), c), mult(a, b)))))) | (~((~(mult(mult(mult(b, mult(a, b)), mult(a, b)), c) = mult(mult(b, mult(a, b)), mult(c, mult(a, b))))) | (~(mult(mult(mult(b, mult(a, b)), c), mult(a, b)) = mult(mult(b, mult(a, b)), mult(mult(a, b), c)))))))),
% 1.35/1.10 inference(transitivity,[status(thm)],[133, 131])).
% 1.35/1.10 tff(135,plain,
% 1.35/1.10 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(mult(mult(b, mult(a, b)), mult(a, b)), c) = mult(mult(mult(b, mult(a, b)), c), mult(a, b)))) | (~(mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(mult(b, mult(a, b)), mult(c, mult(a, b))))))) | (~((~(mult(mult(mult(b, mult(a, b)), mult(a, b)), c) = mult(mult(b, mult(a, b)), mult(c, mult(a, b))))) | (~(mult(mult(mult(b, mult(a, b)), c), mult(a, b)) = mult(mult(b, mult(a, b)), mult(mult(a, b), c)))))))),
% 1.35/1.10 inference(quant_inst,[status(thm)],[])).
% 1.35/1.10 tff(136,plain,
% 1.35/1.10 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | (~((~(mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(mult(b, mult(a, b)), mult(c, mult(a, b))))) | (~(mult(mult(mult(b, mult(a, b)), mult(a, b)), c) = mult(mult(mult(b, mult(a, b)), c), mult(a, b)))))) | (~((~(mult(mult(mult(b, mult(a, b)), mult(a, b)), c) = mult(mult(b, mult(a, b)), mult(c, mult(a, b))))) | (~(mult(mult(mult(b, mult(a, b)), c), mult(a, b)) = mult(mult(b, mult(a, b)), mult(mult(a, b), c))))))),
% 1.35/1.10 inference(modus_ponens,[status(thm)],[135, 134])).
% 1.35/1.10 tff(137,plain,
% 1.35/1.10 ((~((~(mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(mult(b, mult(a, b)), mult(c, mult(a, b))))) | (~(mult(mult(mult(b, mult(a, b)), mult(a, b)), c) = mult(mult(mult(b, mult(a, b)), c), mult(a, b)))))) | (~((~(mult(mult(mult(b, mult(a, b)), mult(a, b)), c) = mult(mult(b, mult(a, b)), mult(c, mult(a, b))))) | (~(mult(mult(mult(b, mult(a, b)), c), mult(a, b)) = mult(mult(b, mult(a, b)), mult(mult(a, b), c))))))),
% 1.35/1.10 inference(unit_resolution,[status(thm)],[136, 64])).
% 1.35/1.10 tff(138,plain,
% 1.35/1.10 (~((~(mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(mult(b, mult(a, b)), mult(c, mult(a, b))))) | (~(mult(mult(mult(b, mult(a, b)), mult(a, b)), c) = mult(mult(mult(b, mult(a, b)), c), mult(a, b)))))),
% 1.35/1.10 inference(unit_resolution,[status(thm)],[137, 130])).
% 1.35/1.10 tff(139,plain,
% 1.35/1.10 (((~(mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(mult(b, mult(a, b)), mult(c, mult(a, b))))) | (~(mult(mult(mult(b, mult(a, b)), mult(a, b)), c) = mult(mult(mult(b, mult(a, b)), c), mult(a, b))))) | (mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(mult(b, mult(a, b)), mult(c, mult(a, b))))),
% 1.35/1.10 inference(tautology,[status(thm)],[])).
% 1.35/1.10 tff(140,plain,
% 1.35/1.10 (mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(mult(b, mult(a, b)), mult(c, mult(a, b)))),
% 1.35/1.10 inference(unit_resolution,[status(thm)],[139, 138])).
% 1.35/1.10 tff(141,plain,
% 1.35/1.10 (mult(mult(b, mult(a, b)), mult(c, mult(a, b))) = mult(mult(b, mult(a, b)), mult(mult(a, b), c))),
% 1.35/1.10 inference(symmetry,[status(thm)],[140])).
% 1.35/1.10 tff(142,plain,
% 1.35/1.10 (((~(mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(mult(b, mult(a, b)), mult(c, mult(a, b))))) | (~(mult(mult(mult(b, mult(a, b)), mult(a, b)), c) = mult(mult(mult(b, mult(a, b)), c), mult(a, b))))) | (mult(mult(mult(b, mult(a, b)), mult(a, b)), c) = mult(mult(mult(b, mult(a, b)), c), mult(a, b)))),
% 1.35/1.10 inference(tautology,[status(thm)],[])).
% 1.35/1.10 tff(143,plain,
% 1.35/1.10 (mult(mult(mult(b, mult(a, b)), mult(a, b)), c) = mult(mult(mult(b, mult(a, b)), c), mult(a, b))),
% 1.35/1.10 inference(unit_resolution,[status(thm)],[142, 138])).
% 1.35/1.10 tff(144,plain,
% 1.35/1.10 (mult(mult(mult(b, mult(a, b)), mult(a, b)), c) = mult(b, mult(mult(mult(a, b), c), mult(a, b)))),
% 1.35/1.10 inference(transitivity,[status(thm)],[143, 126])).
% 1.35/1.10 tff(145,plain,
% 1.35/1.10 ((mult(mult(mult(b, mult(a, b)), mult(a, b)), c) = mult(mult(b, mult(a, b)), mult(c, mult(a, b)))) <=> (mult(b, mult(mult(mult(a, b), c), mult(a, b))) = mult(mult(b, mult(a, b)), mult(mult(a, b), c)))),
% 1.35/1.10 inference(monotonicity,[status(thm)],[144, 141])).
% 1.35/1.10 tff(146,plain,
% 1.35/1.10 ((mult(mult(mult(b, mult(a, b)), mult(a, b)), c) = mult(mult(b, mult(a, b)), mult(c, mult(a, b)))) <=> (mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(b, mult(mult(mult(a, b), c), mult(a, b))))),
% 1.35/1.10 inference(transitivity,[status(thm)],[145, 127])).
% 1.35/1.10 tff(147,plain,
% 1.35/1.10 ((mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(b, mult(mult(mult(a, b), c), mult(a, b)))) <=> (mult(mult(mult(b, mult(a, b)), mult(a, b)), c) = mult(mult(b, mult(a, b)), mult(c, mult(a, b))))),
% 1.35/1.11 inference(symmetry,[status(thm)],[146])).
% 1.35/1.11 tff(148,plain,
% 1.35/1.11 ((~(mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(b, mult(mult(mult(a, b), c), mult(a, b))))) <=> (~(mult(mult(mult(b, mult(a, b)), mult(a, b)), c) = mult(mult(b, mult(a, b)), mult(c, mult(a, b)))))),
% 1.35/1.11 inference(monotonicity,[status(thm)],[147])).
% 1.35/1.11 tff(149,plain,
% 1.35/1.11 ((mult(mult(mult(b, mult(a, b)), c), mult(a, b)) = mult(mult(b, mult(a, b)), mult(mult(a, b), c))) <=> (mult(b, mult(mult(mult(a, b), c), mult(a, b))) = mult(mult(b, mult(a, b)), mult(mult(a, b), c)))),
% 1.35/1.11 inference(monotonicity,[status(thm)],[126])).
% 1.35/1.11 tff(150,plain,
% 1.35/1.11 ((mult(mult(mult(b, mult(a, b)), c), mult(a, b)) = mult(mult(b, mult(a, b)), mult(mult(a, b), c))) <=> (mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(b, mult(mult(mult(a, b), c), mult(a, b))))),
% 1.35/1.11 inference(transitivity,[status(thm)],[149, 127])).
% 1.35/1.11 tff(151,plain,
% 1.35/1.11 ((mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(b, mult(mult(mult(a, b), c), mult(a, b)))) <=> (mult(mult(mult(b, mult(a, b)), c), mult(a, b)) = mult(mult(b, mult(a, b)), mult(mult(a, b), c)))),
% 1.35/1.11 inference(symmetry,[status(thm)],[150])).
% 1.35/1.11 tff(152,assumption,(mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(b, mult(mult(mult(a, b), c), mult(a, b)))), introduced(assumption)).
% 1.35/1.11 tff(153,plain,
% 1.35/1.11 (mult(mult(mult(b, mult(a, b)), c), mult(a, b)) = mult(mult(b, mult(a, b)), mult(mult(a, b), c))),
% 1.35/1.11 inference(modus_ponens,[status(thm)],[152, 151])).
% 1.35/1.11 tff(154,plain,
% 1.35/1.11 ($false),
% 1.35/1.11 inference(unit_resolution,[status(thm)],[128, 153])).
% 1.35/1.11 tff(155,plain,((~(mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(b, mult(mult(mult(a, b), c), mult(a, b))))) | (mult(mult(mult(b, mult(a, b)), c), mult(a, b)) = mult(mult(b, mult(a, b)), mult(mult(a, b), c)))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.11 tff(156,plain,
% 1.35/1.11 (~(mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(b, mult(mult(mult(a, b), c), mult(a, b))))),
% 1.35/1.11 inference(unit_resolution,[status(thm)],[155, 128])).
% 1.35/1.11 tff(157,plain,
% 1.35/1.11 (~(mult(mult(mult(b, mult(a, b)), mult(a, b)), c) = mult(mult(b, mult(a, b)), mult(c, mult(a, b))))),
% 1.35/1.11 inference(modus_ponens,[status(thm)],[156, 148])).
% 1.35/1.11 tff(158,plain,
% 1.35/1.11 (((~(mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(b, mult(mult(mult(a, b), c), mult(a, b))))) | (~(mult(mult(b, mult(mult(a, b), c)), mult(a, b)) = mult(b, mult(mult(a, b), mult(mult(a, b), c)))))) | (mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(b, mult(mult(mult(a, b), c), mult(a, b))))),
% 1.35/1.11 inference(tautology,[status(thm)],[])).
% 1.35/1.11 tff(159,plain,
% 1.35/1.11 ((~(mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(b, mult(mult(mult(a, b), c), mult(a, b))))) | (~(mult(mult(b, mult(mult(a, b), c)), mult(a, b)) = mult(b, mult(mult(a, b), mult(mult(a, b), c)))))),
% 1.35/1.11 inference(unit_resolution,[status(thm)],[158, 156])).
% 1.35/1.11 tff(160,plain,
% 1.35/1.11 (~((~(mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(mult(b, mult(mult(a, b), c)), mult(a, b)))) | (~(mult(b, mult(mult(a, b), mult(mult(a, b), c))) = mult(b, mult(mult(mult(a, b), c), mult(a, b))))))),
% 1.35/1.11 inference(unit_resolution,[status(thm)],[114, 159])).
% 1.35/1.11 tff(161,plain,
% 1.35/1.11 (mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(mult(b, mult(mult(a, b), c)), mult(a, b))),
% 1.35/1.11 inference(unit_resolution,[status(thm)],[106, 160])).
% 1.35/1.11 tff(162,plain,
% 1.35/1.11 ((~![A: $i] : (mult(unit, A) = A)) | (mult(unit, b) = b)),
% 1.35/1.11 inference(quant_inst,[status(thm)],[])).
% 1.35/1.11 tff(163,plain,
% 1.35/1.11 (mult(unit, b) = b),
% 1.35/1.11 inference(unit_resolution,[status(thm)],[162, 26])).
% 1.35/1.11 tff(164,plain,
% 1.35/1.11 (mult(mult(unit, b), mult(mult(mult(a, b), c), mult(a, b))) = mult(b, mult(mult(mult(a, b), c), mult(a, b)))),
% 1.35/1.11 inference(monotonicity,[status(thm)],[163])).
% 1.35/1.11 tff(165,plain,
% 1.35/1.11 (mult(b, mult(mult(mult(a, b), c), mult(a, b))) = mult(mult(unit, b), mult(mult(mult(a, b), c), mult(a, b)))),
% 1.35/1.11 inference(symmetry,[status(thm)],[164])).
% 1.35/1.11 tff(166,plain,
% 1.35/1.11 ((~![A: $i] : (mult(unit, A) = A)) | (mult(unit, mult(b, mult(mult(mult(a, b), c), mult(a, b)))) = mult(b, mult(mult(mult(a, b), c), mult(a, b))))),
% 1.35/1.11 inference(quant_inst,[status(thm)],[])).
% 1.35/1.11 tff(167,plain,
% 1.35/1.11 (mult(unit, mult(b, mult(mult(mult(a, b), c), mult(a, b)))) = mult(b, mult(mult(mult(a, b), c), mult(a, b)))),
% 1.35/1.11 inference(unit_resolution,[status(thm)],[166, 26])).
% 1.35/1.11 tff(168,assumption,(~(mult(mult(unit, mult(mult(mult(a, b), c), mult(a, b))), b) = mult(unit, mult(b, mult(mult(mult(a, b), c), mult(a, b)))))), introduced(assumption)).
% 1.35/1.11 tff(169,plain,
% 1.35/1.11 (((~(mult(mult(unit, b), mult(mult(mult(a, b), c), mult(a, b))) = mult(unit, mult(mult(mult(mult(a, b), c), mult(a, b)), b)))) | (~(mult(mult(unit, mult(mult(mult(a, b), c), mult(a, b))), b) = mult(unit, mult(b, mult(mult(mult(a, b), c), mult(a, b))))))) | (mult(mult(unit, mult(mult(mult(a, b), c), mult(a, b))), b) = mult(unit, mult(b, mult(mult(mult(a, b), c), mult(a, b)))))),
% 1.35/1.11 inference(tautology,[status(thm)],[])).
% 1.35/1.11 tff(170,plain,
% 1.35/1.11 ((~(mult(mult(unit, b), mult(mult(mult(a, b), c), mult(a, b))) = mult(unit, mult(mult(mult(mult(a, b), c), mult(a, b)), b)))) | (~(mult(mult(unit, mult(mult(mult(a, b), c), mult(a, b))), b) = mult(unit, mult(b, mult(mult(mult(a, b), c), mult(a, b))))))),
% 1.35/1.11 inference(unit_resolution,[status(thm)],[169, 168])).
% 1.35/1.11 tff(171,plain,
% 1.35/1.11 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(mult(unit, b), mult(mult(mult(a, b), c), mult(a, b))) = mult(unit, mult(mult(mult(mult(a, b), c), mult(a, b)), b)))) | (~(mult(mult(unit, mult(mult(mult(a, b), c), mult(a, b))), b) = mult(unit, mult(b, mult(mult(mult(a, b), c), mult(a, b)))))))) | (~((~(mult(mult(unit, mult(mult(mult(a, b), c), mult(a, b))), b) = mult(mult(unit, b), mult(mult(mult(a, b), c), mult(a, b))))) | (~(mult(unit, mult(mult(mult(mult(a, b), c), mult(a, b)), b)) = mult(unit, mult(b, mult(mult(mult(a, b), c), mult(a, b)))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | (~((~(mult(mult(unit, b), mult(mult(mult(a, b), c), mult(a, b))) = mult(unit, mult(mult(mult(mult(a, b), c), mult(a, b)), b)))) | (~(mult(mult(unit, mult(mult(mult(a, b), c), mult(a, b))), b) = mult(unit, mult(b, mult(mult(mult(a, b), c), mult(a, b)))))))) | (~((~(mult(mult(unit, mult(mult(mult(a, b), c), mult(a, b))), b) = mult(mult(unit, b), mult(mult(mult(a, b), c), mult(a, b))))) | (~(mult(unit, mult(mult(mult(mult(a, b), c), mult(a, b)), b)) = mult(unit, mult(b, mult(mult(mult(a, b), c), mult(a, b)))))))))),
% 1.35/1.11 inference(rewrite,[status(thm)],[])).
% 1.35/1.11 tff(172,plain,
% 1.35/1.11 (((~((~(mult(mult(unit, mult(mult(mult(a, b), c), mult(a, b))), b) = mult(mult(unit, b), mult(mult(mult(a, b), c), mult(a, b))))) | (~(mult(unit, mult(mult(mult(mult(a, b), c), mult(a, b)), b)) = mult(unit, mult(b, mult(mult(mult(a, b), c), mult(a, b)))))))) | (~((~(mult(mult(unit, b), mult(mult(mult(a, b), c), mult(a, b))) = mult(unit, mult(mult(mult(mult(a, b), c), mult(a, b)), b)))) | (~(mult(mult(unit, mult(mult(mult(a, b), c), mult(a, b))), b) = mult(unit, mult(b, mult(mult(mult(a, b), c), mult(a, b))))))))) <=> ((~((~(mult(mult(unit, b), mult(mult(mult(a, b), c), mult(a, b))) = mult(unit, mult(mult(mult(mult(a, b), c), mult(a, b)), b)))) | (~(mult(mult(unit, mult(mult(mult(a, b), c), mult(a, b))), b) = mult(unit, mult(b, mult(mult(mult(a, b), c), mult(a, b)))))))) | (~((~(mult(mult(unit, mult(mult(mult(a, b), c), mult(a, b))), b) = mult(mult(unit, b), mult(mult(mult(a, b), c), mult(a, b))))) | (~(mult(unit, mult(mult(mult(mult(a, b), c), mult(a, b)), b)) = mult(unit, mult(b, mult(mult(mult(a, b), c), mult(a, b)))))))))),
% 1.35/1.11 inference(rewrite,[status(thm)],[])).
% 1.35/1.11 tff(173,plain,
% 1.35/1.11 ((~((~(mult(mult(unit, mult(mult(mult(a, b), c), mult(a, b))), b) = mult(unit, mult(b, mult(mult(mult(a, b), c), mult(a, b)))))) | (~(mult(mult(unit, b), mult(mult(mult(a, b), c), mult(a, b))) = mult(unit, mult(mult(mult(mult(a, b), c), mult(a, b)), b)))))) <=> (~((~(mult(mult(unit, b), mult(mult(mult(a, b), c), mult(a, b))) = mult(unit, mult(mult(mult(mult(a, b), c), mult(a, b)), b)))) | (~(mult(mult(unit, mult(mult(mult(a, b), c), mult(a, b))), b) = mult(unit, mult(b, mult(mult(mult(a, b), c), mult(a, b))))))))),
% 1.35/1.11 inference(rewrite,[status(thm)],[])).
% 1.35/1.11 tff(174,plain,
% 1.35/1.11 ((~((~(mult(mult(unit, mult(mult(mult(a, b), c), mult(a, b))), b) = mult(mult(unit, b), mult(mult(mult(a, b), c), mult(a, b))))) | (~(mult(unit, mult(mult(mult(mult(a, b), c), mult(a, b)), b)) = mult(unit, mult(b, mult(mult(mult(a, b), c), mult(a, b)))))))) <=> (~((~(mult(mult(unit, mult(mult(mult(a, b), c), mult(a, b))), b) = mult(mult(unit, b), mult(mult(mult(a, b), c), mult(a, b))))) | (~(mult(unit, mult(mult(mult(mult(a, b), c), mult(a, b)), b)) = mult(unit, mult(b, mult(mult(mult(a, b), c), mult(a, b))))))))),
% 1.35/1.11 inference(rewrite,[status(thm)],[])).
% 1.35/1.11 tff(175,plain,
% 1.35/1.11 (((~((~(mult(mult(unit, mult(mult(mult(a, b), c), mult(a, b))), b) = mult(mult(unit, b), mult(mult(mult(a, b), c), mult(a, b))))) | (~(mult(unit, mult(mult(mult(mult(a, b), c), mult(a, b)), b)) = mult(unit, mult(b, mult(mult(mult(a, b), c), mult(a, b)))))))) | (~((~(mult(mult(unit, mult(mult(mult(a, b), c), mult(a, b))), b) = mult(unit, mult(b, mult(mult(mult(a, b), c), mult(a, b)))))) | (~(mult(mult(unit, b), mult(mult(mult(a, b), c), mult(a, b))) = mult(unit, mult(mult(mult(mult(a, b), c), mult(a, b)), b))))))) <=> ((~((~(mult(mult(unit, mult(mult(mult(a, b), c), mult(a, b))), b) = mult(mult(unit, b), mult(mult(mult(a, b), c), mult(a, b))))) | (~(mult(unit, mult(mult(mult(mult(a, b), c), mult(a, b)), b)) = mult(unit, mult(b, mult(mult(mult(a, b), c), mult(a, b)))))))) | (~((~(mult(mult(unit, b), mult(mult(mult(a, b), c), mult(a, b))) = mult(unit, mult(mult(mult(mult(a, b), c), mult(a, b)), b)))) | (~(mult(mult(unit, mult(mult(mult(a, b), c), mult(a, b))), b) = mult(unit, mult(b, mult(mult(mult(a, b), c), mult(a, b)))))))))),
% 1.35/1.11 inference(monotonicity,[status(thm)],[174, 173])).
% 1.35/1.11 tff(176,plain,
% 1.35/1.11 (((~((~(mult(mult(unit, mult(mult(mult(a, b), c), mult(a, b))), b) = mult(mult(unit, b), mult(mult(mult(a, b), c), mult(a, b))))) | (~(mult(unit, mult(mult(mult(mult(a, b), c), mult(a, b)), b)) = mult(unit, mult(b, mult(mult(mult(a, b), c), mult(a, b)))))))) | (~((~(mult(mult(unit, mult(mult(mult(a, b), c), mult(a, b))), b) = mult(unit, mult(b, mult(mult(mult(a, b), c), mult(a, b)))))) | (~(mult(mult(unit, b), mult(mult(mult(a, b), c), mult(a, b))) = mult(unit, mult(mult(mult(mult(a, b), c), mult(a, b)), b))))))) <=> ((~((~(mult(mult(unit, b), mult(mult(mult(a, b), c), mult(a, b))) = mult(unit, mult(mult(mult(mult(a, b), c), mult(a, b)), b)))) | (~(mult(mult(unit, mult(mult(mult(a, b), c), mult(a, b))), b) = mult(unit, mult(b, mult(mult(mult(a, b), c), mult(a, b)))))))) | (~((~(mult(mult(unit, mult(mult(mult(a, b), c), mult(a, b))), b) = mult(mult(unit, b), mult(mult(mult(a, b), c), mult(a, b))))) | (~(mult(unit, mult(mult(mult(mult(a, b), c), mult(a, b)), b)) = mult(unit, mult(b, mult(mult(mult(a, b), c), mult(a, b)))))))))),
% 1.35/1.11 inference(transitivity,[status(thm)],[175, 172])).
% 1.35/1.11 tff(177,plain,
% 1.35/1.11 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(mult(unit, mult(mult(mult(a, b), c), mult(a, b))), b) = mult(mult(unit, b), mult(mult(mult(a, b), c), mult(a, b))))) | (~(mult(unit, mult(mult(mult(mult(a, b), c), mult(a, b)), b)) = mult(unit, mult(b, mult(mult(mult(a, b), c), mult(a, b)))))))) | (~((~(mult(mult(unit, mult(mult(mult(a, b), c), mult(a, b))), b) = mult(unit, mult(b, mult(mult(mult(a, b), c), mult(a, b)))))) | (~(mult(mult(unit, b), mult(mult(mult(a, b), c), mult(a, b))) = mult(unit, mult(mult(mult(mult(a, b), c), mult(a, b)), b)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(mult(unit, b), mult(mult(mult(a, b), c), mult(a, b))) = mult(unit, mult(mult(mult(mult(a, b), c), mult(a, b)), b)))) | (~(mult(mult(unit, mult(mult(mult(a, b), c), mult(a, b))), b) = mult(unit, mult(b, mult(mult(mult(a, b), c), mult(a, b)))))))) | (~((~(mult(mult(unit, mult(mult(mult(a, b), c), mult(a, b))), b) = mult(mult(unit, b), mult(mult(mult(a, b), c), mult(a, b))))) | (~(mult(unit, mult(mult(mult(mult(a, b), c), mult(a, b)), b)) = mult(unit, mult(b, mult(mult(mult(a, b), c), mult(a, b))))))))))),
% 1.35/1.11 inference(monotonicity,[status(thm)],[176])).
% 1.35/1.11 tff(178,plain,
% 1.35/1.11 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(mult(unit, mult(mult(mult(a, b), c), mult(a, b))), b) = mult(mult(unit, b), mult(mult(mult(a, b), c), mult(a, b))))) | (~(mult(unit, mult(mult(mult(mult(a, b), c), mult(a, b)), b)) = mult(unit, mult(b, mult(mult(mult(a, b), c), mult(a, b)))))))) | (~((~(mult(mult(unit, mult(mult(mult(a, b), c), mult(a, b))), b) = mult(unit, mult(b, mult(mult(mult(a, b), c), mult(a, b)))))) | (~(mult(mult(unit, b), mult(mult(mult(a, b), c), mult(a, b))) = mult(unit, mult(mult(mult(mult(a, b), c), mult(a, b)), b)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | (~((~(mult(mult(unit, b), mult(mult(mult(a, b), c), mult(a, b))) = mult(unit, mult(mult(mult(mult(a, b), c), mult(a, b)), b)))) | (~(mult(mult(unit, mult(mult(mult(a, b), c), mult(a, b))), b) = mult(unit, mult(b, mult(mult(mult(a, b), c), mult(a, b)))))))) | (~((~(mult(mult(unit, mult(mult(mult(a, b), c), mult(a, b))), b) = mult(mult(unit, b), mult(mult(mult(a, b), c), mult(a, b))))) | (~(mult(unit, mult(mult(mult(mult(a, b), c), mult(a, b)), b)) = mult(unit, mult(b, mult(mult(mult(a, b), c), mult(a, b)))))))))),
% 1.35/1.11 inference(transitivity,[status(thm)],[177, 171])).
% 1.35/1.11 tff(179,plain,
% 1.35/1.11 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(mult(unit, mult(mult(mult(a, b), c), mult(a, b))), b) = mult(mult(unit, b), mult(mult(mult(a, b), c), mult(a, b))))) | (~(mult(unit, mult(mult(mult(mult(a, b), c), mult(a, b)), b)) = mult(unit, mult(b, mult(mult(mult(a, b), c), mult(a, b)))))))) | (~((~(mult(mult(unit, mult(mult(mult(a, b), c), mult(a, b))), b) = mult(unit, mult(b, mult(mult(mult(a, b), c), mult(a, b)))))) | (~(mult(mult(unit, b), mult(mult(mult(a, b), c), mult(a, b))) = mult(unit, mult(mult(mult(mult(a, b), c), mult(a, b)), b)))))))),
% 1.35/1.11 inference(quant_inst,[status(thm)],[])).
% 1.35/1.11 tff(180,plain,
% 1.35/1.11 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | (~((~(mult(mult(unit, b), mult(mult(mult(a, b), c), mult(a, b))) = mult(unit, mult(mult(mult(mult(a, b), c), mult(a, b)), b)))) | (~(mult(mult(unit, mult(mult(mult(a, b), c), mult(a, b))), b) = mult(unit, mult(b, mult(mult(mult(a, b), c), mult(a, b)))))))) | (~((~(mult(mult(unit, mult(mult(mult(a, b), c), mult(a, b))), b) = mult(mult(unit, b), mult(mult(mult(a, b), c), mult(a, b))))) | (~(mult(unit, mult(mult(mult(mult(a, b), c), mult(a, b)), b)) = mult(unit, mult(b, mult(mult(mult(a, b), c), mult(a, b))))))))),
% 1.35/1.11 inference(modus_ponens,[status(thm)],[179, 178])).
% 1.35/1.12 tff(181,plain,
% 1.35/1.12 ((~((~(mult(mult(unit, b), mult(mult(mult(a, b), c), mult(a, b))) = mult(unit, mult(mult(mult(mult(a, b), c), mult(a, b)), b)))) | (~(mult(mult(unit, mult(mult(mult(a, b), c), mult(a, b))), b) = mult(unit, mult(b, mult(mult(mult(a, b), c), mult(a, b)))))))) | (~((~(mult(mult(unit, mult(mult(mult(a, b), c), mult(a, b))), b) = mult(mult(unit, b), mult(mult(mult(a, b), c), mult(a, b))))) | (~(mult(unit, mult(mult(mult(mult(a, b), c), mult(a, b)), b)) = mult(unit, mult(b, mult(mult(mult(a, b), c), mult(a, b))))))))),
% 1.35/1.12 inference(unit_resolution,[status(thm)],[180, 64])).
% 1.35/1.12 tff(182,plain,
% 1.35/1.12 (~((~(mult(mult(unit, mult(mult(mult(a, b), c), mult(a, b))), b) = mult(mult(unit, b), mult(mult(mult(a, b), c), mult(a, b))))) | (~(mult(unit, mult(mult(mult(mult(a, b), c), mult(a, b)), b)) = mult(unit, mult(b, mult(mult(mult(a, b), c), mult(a, b)))))))),
% 1.35/1.12 inference(unit_resolution,[status(thm)],[181, 170])).
% 1.35/1.12 tff(183,plain,
% 1.35/1.12 (((~(mult(mult(unit, mult(mult(mult(a, b), c), mult(a, b))), b) = mult(mult(unit, b), mult(mult(mult(a, b), c), mult(a, b))))) | (~(mult(unit, mult(mult(mult(mult(a, b), c), mult(a, b)), b)) = mult(unit, mult(b, mult(mult(mult(a, b), c), mult(a, b))))))) | (mult(unit, mult(mult(mult(mult(a, b), c), mult(a, b)), b)) = mult(unit, mult(b, mult(mult(mult(a, b), c), mult(a, b)))))),
% 1.35/1.12 inference(tautology,[status(thm)],[])).
% 1.35/1.12 tff(184,plain,
% 1.35/1.12 (mult(unit, mult(mult(mult(mult(a, b), c), mult(a, b)), b)) = mult(unit, mult(b, mult(mult(mult(a, b), c), mult(a, b))))),
% 1.35/1.12 inference(unit_resolution,[status(thm)],[183, 182])).
% 1.35/1.12 tff(185,plain,
% 1.35/1.12 (mult(unit, mult(b, mult(mult(mult(a, b), c), mult(a, b)))) = mult(unit, mult(mult(mult(mult(a, b), c), mult(a, b)), b))),
% 1.35/1.12 inference(symmetry,[status(thm)],[184])).
% 1.35/1.12 tff(186,plain,
% 1.35/1.12 (mult(b, mult(mult(mult(a, b), c), mult(a, b))) = mult(unit, mult(b, mult(mult(mult(a, b), c), mult(a, b))))),
% 1.35/1.12 inference(symmetry,[status(thm)],[167])).
% 1.35/1.12 tff(187,plain,
% 1.35/1.12 (mult(mult(unit, b), mult(mult(mult(a, b), c), mult(a, b))) = mult(unit, mult(mult(mult(mult(a, b), c), mult(a, b)), b))),
% 1.35/1.12 inference(transitivity,[status(thm)],[164, 186, 185])).
% 1.35/1.12 tff(188,plain,
% 1.35/1.12 (((~(mult(mult(unit, mult(mult(mult(a, b), c), mult(a, b))), b) = mult(mult(unit, b), mult(mult(mult(a, b), c), mult(a, b))))) | (~(mult(unit, mult(mult(mult(mult(a, b), c), mult(a, b)), b)) = mult(unit, mult(b, mult(mult(mult(a, b), c), mult(a, b))))))) | (mult(mult(unit, mult(mult(mult(a, b), c), mult(a, b))), b) = mult(mult(unit, b), mult(mult(mult(a, b), c), mult(a, b))))),
% 1.35/1.12 inference(tautology,[status(thm)],[])).
% 1.35/1.12 tff(189,plain,
% 1.35/1.12 (mult(mult(unit, mult(mult(mult(a, b), c), mult(a, b))), b) = mult(mult(unit, b), mult(mult(mult(a, b), c), mult(a, b)))),
% 1.35/1.12 inference(unit_resolution,[status(thm)],[188, 182])).
% 1.35/1.12 tff(190,plain,
% 1.35/1.12 ((mult(mult(unit, mult(mult(mult(a, b), c), mult(a, b))), b) = mult(unit, mult(b, mult(mult(mult(a, b), c), mult(a, b))))) <=> (mult(mult(unit, b), mult(mult(mult(a, b), c), mult(a, b))) = mult(unit, mult(mult(mult(mult(a, b), c), mult(a, b)), b)))),
% 1.35/1.12 inference(monotonicity,[status(thm)],[189, 185])).
% 1.35/1.12 tff(191,plain,
% 1.35/1.12 ((~(mult(mult(unit, mult(mult(mult(a, b), c), mult(a, b))), b) = mult(unit, mult(b, mult(mult(mult(a, b), c), mult(a, b)))))) <=> (~(mult(mult(unit, b), mult(mult(mult(a, b), c), mult(a, b))) = mult(unit, mult(mult(mult(mult(a, b), c), mult(a, b)), b))))),
% 1.35/1.12 inference(monotonicity,[status(thm)],[190])).
% 1.35/1.12 tff(192,plain,
% 1.35/1.12 (~(mult(mult(unit, b), mult(mult(mult(a, b), c), mult(a, b))) = mult(unit, mult(mult(mult(mult(a, b), c), mult(a, b)), b)))),
% 1.35/1.12 inference(modus_ponens,[status(thm)],[168, 191])).
% 1.35/1.12 tff(193,plain,
% 1.35/1.12 ($false),
% 1.35/1.12 inference(unit_resolution,[status(thm)],[192, 187])).
% 1.35/1.12 tff(194,plain,(mult(mult(unit, mult(mult(mult(a, b), c), mult(a, b))), b) = mult(unit, mult(b, mult(mult(mult(a, b), c), mult(a, b))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.12 tff(195,plain,
% 1.35/1.12 (mult(mult(unit, mult(mult(mult(a, b), c), mult(a, b))), b) = mult(mult(unit, b), mult(mult(mult(a, b), c), mult(a, b)))),
% 1.35/1.12 inference(transitivity,[status(thm)],[194, 167, 165])).
% 1.35/1.12 tff(196,assumption,(~(mult(mult(unit, mult(mult(mult(a, b), c), mult(a, b))), b) = mult(mult(unit, b), mult(mult(mult(a, b), c), mult(a, b))))), introduced(assumption)).
% 1.35/1.12 tff(197,plain,
% 1.35/1.12 ($false),
% 1.35/1.12 inference(unit_resolution,[status(thm)],[196, 195])).
% 1.35/1.12 tff(198,plain,(mult(mult(unit, mult(mult(mult(a, b), c), mult(a, b))), b) = mult(mult(unit, b), mult(mult(mult(a, b), c), mult(a, b)))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.12 tff(199,plain,
% 1.35/1.12 (((~(mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(mult(b, mult(mult(a, b), c)), mult(a, b)))) | (~(mult(b, mult(mult(a, b), mult(mult(a, b), c))) = mult(b, mult(mult(mult(a, b), c), mult(a, b)))))) | (mult(b, mult(mult(a, b), mult(mult(a, b), c))) = mult(b, mult(mult(mult(a, b), c), mult(a, b))))),
% 1.35/1.12 inference(tautology,[status(thm)],[])).
% 1.35/1.12 tff(200,plain,
% 1.35/1.12 (mult(b, mult(mult(a, b), mult(mult(a, b), c))) = mult(b, mult(mult(mult(a, b), c), mult(a, b)))),
% 1.35/1.12 inference(unit_resolution,[status(thm)],[199, 160])).
% 1.35/1.12 tff(201,plain,
% 1.35/1.12 ((mult(mult(b, mult(a, b)), mult(c, mult(a, b))) = mult(mult(mult(b, mult(a, b)), mult(a, b)), c)) <=> (mult(mult(mult(b, mult(a, b)), mult(a, b)), c) = mult(mult(b, mult(a, b)), mult(c, mult(a, b))))),
% 1.35/1.12 inference(commutativity,[status(thm)],[])).
% 1.35/1.12 tff(202,assumption,(mult(mult(mult(b, mult(a, b)), mult(a, b)), c) = mult(mult(mult(b, mult(a, b)), c), mult(a, b))), introduced(assumption)).
% 1.35/1.12 tff(203,plain,
% 1.35/1.12 (mult(mult(mult(b, mult(a, b)), c), mult(a, b)) = mult(mult(mult(b, mult(a, b)), mult(a, b)), c)),
% 1.35/1.12 inference(symmetry,[status(thm)],[202])).
% 1.35/1.12 tff(204,plain,
% 1.35/1.12 (mult(b, mult(mult(mult(a, b), c), mult(a, b))) = mult(mult(mult(b, mult(a, b)), c), mult(a, b))),
% 1.35/1.12 inference(symmetry,[status(thm)],[126])).
% 1.35/1.12 tff(205,assumption,(mult(mult(unit, mult(mult(mult(a, b), c), mult(a, b))), b) = mult(mult(unit, b), mult(mult(mult(a, b), c), mult(a, b)))), introduced(assumption)).
% 1.35/1.12 tff(206,plain,
% 1.35/1.12 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(unit, mult(a, b)), c), mult(a, b)) = mult(unit, mult(mult(mult(a, b), c), mult(a, b))))),
% 1.35/1.12 inference(quant_inst,[status(thm)],[])).
% 1.35/1.12 tff(207,plain,
% 1.35/1.12 (mult(mult(mult(unit, mult(a, b)), c), mult(a, b)) = mult(unit, mult(mult(mult(a, b), c), mult(a, b)))),
% 1.35/1.12 inference(unit_resolution,[status(thm)],[206, 124])).
% 1.35/1.12 tff(208,plain,
% 1.35/1.12 (mult(mult(unit, mult(a, b)), c) = mult(mult(a, b), c)),
% 1.35/1.12 inference(monotonicity,[status(thm)],[45])).
% 1.35/1.12 tff(209,plain,
% 1.35/1.12 (mult(mult(mult(unit, mult(a, b)), c), mult(a, b)) = mult(mult(mult(a, b), c), mult(a, b))),
% 1.35/1.12 inference(monotonicity,[status(thm)],[208])).
% 1.35/1.12 tff(210,plain,
% 1.35/1.12 (mult(mult(mult(a, b), c), mult(a, b)) = mult(mult(mult(unit, mult(a, b)), c), mult(a, b))),
% 1.35/1.12 inference(symmetry,[status(thm)],[209])).
% 1.35/1.12 tff(211,plain,
% 1.35/1.12 (mult(mult(mult(a, b), c), mult(a, b)) = mult(unit, mult(mult(mult(a, b), c), mult(a, b)))),
% 1.35/1.12 inference(transitivity,[status(thm)],[210, 207])).
% 1.35/1.12 tff(212,plain,
% 1.35/1.12 (mult(mult(mult(mult(a, b), c), mult(a, b)), b) = mult(mult(unit, mult(mult(mult(a, b), c), mult(a, b))), b)),
% 1.35/1.12 inference(monotonicity,[status(thm)],[211])).
% 1.35/1.12 tff(213,plain,
% 1.35/1.12 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(b, mult(b, mult(mult(mult(a, b), c), mult(a, b)))) = mult(mult(mult(a, b), c), mult(a, b)))),
% 1.35/1.12 inference(quant_inst,[status(thm)],[])).
% 1.35/1.12 tff(214,plain,
% 1.35/1.12 (ld(b, mult(b, mult(mult(mult(a, b), c), mult(a, b)))) = mult(mult(mult(a, b), c), mult(a, b))),
% 1.35/1.12 inference(unit_resolution,[status(thm)],[213, 99])).
% 1.35/1.12 tff(215,assumption,(mult(b, mult(mult(a, b), mult(mult(a, b), c))) = mult(b, mult(mult(mult(a, b), c), mult(a, b)))), introduced(assumption)).
% 1.35/1.12 tff(216,plain,
% 1.35/1.12 (ld(b, mult(b, mult(mult(a, b), mult(mult(a, b), c)))) = ld(b, mult(b, mult(mult(mult(a, b), c), mult(a, b))))),
% 1.35/1.12 inference(monotonicity,[status(thm)],[215])).
% 1.35/1.12 tff(217,plain,
% 1.35/1.12 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(b, mult(b, mult(mult(a, b), mult(mult(a, b), c)))) = mult(mult(a, b), mult(mult(a, b), c)))),
% 1.35/1.12 inference(quant_inst,[status(thm)],[])).
% 1.35/1.12 tff(218,plain,
% 1.35/1.12 (ld(b, mult(b, mult(mult(a, b), mult(mult(a, b), c)))) = mult(mult(a, b), mult(mult(a, b), c))),
% 1.35/1.12 inference(unit_resolution,[status(thm)],[217, 99])).
% 1.35/1.12 tff(219,plain,
% 1.35/1.12 (mult(mult(a, b), mult(mult(a, b), c)) = ld(b, mult(b, mult(mult(a, b), mult(mult(a, b), c))))),
% 1.35/1.12 inference(symmetry,[status(thm)],[218])).
% 1.35/1.12 tff(220,plain,
% 1.35/1.12 (mult(mult(a, b), mult(mult(a, b), c)) = mult(mult(mult(a, b), c), mult(a, b))),
% 1.35/1.12 inference(transitivity,[status(thm)],[219, 216, 214])).
% 1.35/1.12 tff(221,plain,
% 1.35/1.12 (mult(mult(mult(a, b), mult(mult(a, b), c)), b) = mult(mult(mult(mult(a, b), c), mult(a, b)), b)),
% 1.35/1.12 inference(monotonicity,[status(thm)],[220])).
% 1.35/1.12 tff(222,assumption,(mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(mult(b, mult(a, b)), mult(c, mult(a, b)))), introduced(assumption)).
% 1.35/1.12 tff(223,plain,
% 1.35/1.12 ((~![A: $i] : (mult(unit, A) = A)) | (mult(unit, mult(b, mult(a, b))) = mult(b, mult(a, b)))),
% 1.35/1.12 inference(quant_inst,[status(thm)],[])).
% 1.35/1.12 tff(224,plain,
% 1.35/1.12 (mult(unit, mult(b, mult(a, b))) = mult(b, mult(a, b))),
% 1.35/1.12 inference(unit_resolution,[status(thm)],[223, 26])).
% 1.35/1.12 tff(225,plain,
% 1.35/1.12 ((mult(unit, mult(b, mult(a, b))) = mult(unit, mult(mult(a, b), b))) <=> (mult(unit, mult(mult(a, b), b)) = mult(unit, mult(b, mult(a, b))))),
% 1.35/1.12 inference(commutativity,[status(thm)],[])).
% 1.35/1.12 tff(226,plain,
% 1.35/1.12 ((mult(unit, mult(mult(a, b), b)) = mult(unit, mult(b, mult(a, b)))) <=> (mult(unit, mult(b, mult(a, b))) = mult(unit, mult(mult(a, b), b)))),
% 1.35/1.12 inference(symmetry,[status(thm)],[225])).
% 1.35/1.12 tff(227,plain,
% 1.35/1.12 ((mult(mult(unit, b), mult(a, b)) = mult(mult(unit, mult(a, b)), b)) <=> (mult(mult(unit, mult(a, b)), b) = mult(mult(unit, b), mult(a, b)))),
% 1.35/1.12 inference(commutativity,[status(thm)],[])).
% 1.35/1.12 tff(228,assumption,(~(mult(unit, mult(b, mult(a, b))) = mult(unit, mult(mult(a, b), b)))), introduced(assumption)).
% 1.35/1.12 tff(229,plain,
% 1.35/1.12 (((~(mult(mult(unit, b), mult(a, b)) = mult(mult(unit, mult(a, b)), b))) | (~(mult(unit, mult(b, mult(a, b))) = mult(unit, mult(mult(a, b), b))))) | (mult(unit, mult(b, mult(a, b))) = mult(unit, mult(mult(a, b), b)))),
% 1.35/1.12 inference(tautology,[status(thm)],[])).
% 1.35/1.12 tff(230,plain,
% 1.35/1.12 ((~(mult(mult(unit, b), mult(a, b)) = mult(mult(unit, mult(a, b)), b))) | (~(mult(unit, mult(b, mult(a, b))) = mult(unit, mult(mult(a, b), b))))),
% 1.35/1.12 inference(unit_resolution,[status(thm)],[229, 228])).
% 1.35/1.12 tff(231,plain,
% 1.35/1.12 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(mult(unit, b), mult(a, b)) = mult(unit, mult(mult(a, b), b)))) | (~(mult(mult(unit, mult(a, b)), b) = mult(unit, mult(b, mult(a, b))))))) | (~((~(mult(mult(unit, b), mult(a, b)) = mult(mult(unit, mult(a, b)), b))) | (~(mult(unit, mult(b, mult(a, b))) = mult(unit, mult(mult(a, b), b)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | (~((~(mult(mult(unit, b), mult(a, b)) = mult(unit, mult(mult(a, b), b)))) | (~(mult(mult(unit, mult(a, b)), b) = mult(unit, mult(b, mult(a, b))))))) | (~((~(mult(mult(unit, b), mult(a, b)) = mult(mult(unit, mult(a, b)), b))) | (~(mult(unit, mult(b, mult(a, b))) = mult(unit, mult(mult(a, b), b)))))))),
% 1.35/1.12 inference(rewrite,[status(thm)],[])).
% 1.35/1.12 tff(232,plain,
% 1.35/1.12 (((~((~(mult(mult(unit, b), mult(a, b)) = mult(mult(unit, mult(a, b)), b))) | (~(mult(unit, mult(b, mult(a, b))) = mult(unit, mult(mult(a, b), b)))))) | (~((~(mult(mult(unit, b), mult(a, b)) = mult(unit, mult(mult(a, b), b)))) | (~(mult(mult(unit, mult(a, b)), b) = mult(unit, mult(b, mult(a, b)))))))) <=> ((~((~(mult(mult(unit, b), mult(a, b)) = mult(unit, mult(mult(a, b), b)))) | (~(mult(mult(unit, mult(a, b)), b) = mult(unit, mult(b, mult(a, b))))))) | (~((~(mult(mult(unit, b), mult(a, b)) = mult(mult(unit, mult(a, b)), b))) | (~(mult(unit, mult(b, mult(a, b))) = mult(unit, mult(mult(a, b), b)))))))),
% 1.35/1.12 inference(rewrite,[status(thm)],[])).
% 1.35/1.12 tff(233,plain,
% 1.35/1.12 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(mult(unit, b), mult(a, b)) = mult(mult(unit, mult(a, b)), b))) | (~(mult(unit, mult(b, mult(a, b))) = mult(unit, mult(mult(a, b), b)))))) | (~((~(mult(mult(unit, b), mult(a, b)) = mult(unit, mult(mult(a, b), b)))) | (~(mult(mult(unit, mult(a, b)), b) = mult(unit, mult(b, mult(a, b))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(mult(unit, b), mult(a, b)) = mult(unit, mult(mult(a, b), b)))) | (~(mult(mult(unit, mult(a, b)), b) = mult(unit, mult(b, mult(a, b))))))) | (~((~(mult(mult(unit, b), mult(a, b)) = mult(mult(unit, mult(a, b)), b))) | (~(mult(unit, mult(b, mult(a, b))) = mult(unit, mult(mult(a, b), b))))))))),
% 1.35/1.12 inference(monotonicity,[status(thm)],[232])).
% 1.35/1.12 tff(234,plain,
% 1.35/1.12 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(mult(unit, b), mult(a, b)) = mult(mult(unit, mult(a, b)), b))) | (~(mult(unit, mult(b, mult(a, b))) = mult(unit, mult(mult(a, b), b)))))) | (~((~(mult(mult(unit, b), mult(a, b)) = mult(unit, mult(mult(a, b), b)))) | (~(mult(mult(unit, mult(a, b)), b) = mult(unit, mult(b, mult(a, b))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | (~((~(mult(mult(unit, b), mult(a, b)) = mult(unit, mult(mult(a, b), b)))) | (~(mult(mult(unit, mult(a, b)), b) = mult(unit, mult(b, mult(a, b))))))) | (~((~(mult(mult(unit, b), mult(a, b)) = mult(mult(unit, mult(a, b)), b))) | (~(mult(unit, mult(b, mult(a, b))) = mult(unit, mult(mult(a, b), b)))))))),
% 1.35/1.12 inference(transitivity,[status(thm)],[233, 231])).
% 1.35/1.12 tff(235,plain,
% 1.35/1.12 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(mult(unit, b), mult(a, b)) = mult(mult(unit, mult(a, b)), b))) | (~(mult(unit, mult(b, mult(a, b))) = mult(unit, mult(mult(a, b), b)))))) | (~((~(mult(mult(unit, b), mult(a, b)) = mult(unit, mult(mult(a, b), b)))) | (~(mult(mult(unit, mult(a, b)), b) = mult(unit, mult(b, mult(a, b))))))))),
% 1.35/1.12 inference(quant_inst,[status(thm)],[])).
% 1.35/1.12 tff(236,plain,
% 1.35/1.12 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | (~((~(mult(mult(unit, b), mult(a, b)) = mult(unit, mult(mult(a, b), b)))) | (~(mult(mult(unit, mult(a, b)), b) = mult(unit, mult(b, mult(a, b))))))) | (~((~(mult(mult(unit, b), mult(a, b)) = mult(mult(unit, mult(a, b)), b))) | (~(mult(unit, mult(b, mult(a, b))) = mult(unit, mult(mult(a, b), b))))))),
% 1.35/1.12 inference(modus_ponens,[status(thm)],[235, 234])).
% 1.35/1.12 tff(237,plain,
% 1.35/1.12 ((~((~(mult(mult(unit, b), mult(a, b)) = mult(unit, mult(mult(a, b), b)))) | (~(mult(mult(unit, mult(a, b)), b) = mult(unit, mult(b, mult(a, b))))))) | (~((~(mult(mult(unit, b), mult(a, b)) = mult(mult(unit, mult(a, b)), b))) | (~(mult(unit, mult(b, mult(a, b))) = mult(unit, mult(mult(a, b), b))))))),
% 1.35/1.12 inference(unit_resolution,[status(thm)],[236, 64])).
% 1.35/1.12 tff(238,plain,
% 1.35/1.12 (~((~(mult(mult(unit, b), mult(a, b)) = mult(unit, mult(mult(a, b), b)))) | (~(mult(mult(unit, mult(a, b)), b) = mult(unit, mult(b, mult(a, b))))))),
% 1.35/1.12 inference(unit_resolution,[status(thm)],[237, 230])).
% 1.35/1.12 tff(239,plain,
% 1.35/1.12 (((~(mult(mult(unit, b), mult(a, b)) = mult(unit, mult(mult(a, b), b)))) | (~(mult(mult(unit, mult(a, b)), b) = mult(unit, mult(b, mult(a, b)))))) | (mult(mult(unit, mult(a, b)), b) = mult(unit, mult(b, mult(a, b))))),
% 1.35/1.12 inference(tautology,[status(thm)],[])).
% 1.35/1.12 tff(240,plain,
% 1.35/1.12 (mult(mult(unit, mult(a, b)), b) = mult(unit, mult(b, mult(a, b)))),
% 1.35/1.12 inference(unit_resolution,[status(thm)],[239, 238])).
% 1.35/1.12 tff(241,plain,
% 1.35/1.12 (mult(unit, mult(b, mult(a, b))) = mult(mult(unit, mult(a, b)), b)),
% 1.35/1.12 inference(symmetry,[status(thm)],[240])).
% 1.35/1.12 tff(242,plain,
% 1.35/1.12 (((~(mult(mult(unit, b), mult(a, b)) = mult(unit, mult(mult(a, b), b)))) | (~(mult(mult(unit, mult(a, b)), b) = mult(unit, mult(b, mult(a, b)))))) | (mult(mult(unit, b), mult(a, b)) = mult(unit, mult(mult(a, b), b)))),
% 1.35/1.12 inference(tautology,[status(thm)],[])).
% 1.35/1.12 tff(243,plain,
% 1.35/1.12 (mult(mult(unit, b), mult(a, b)) = mult(unit, mult(mult(a, b), b))),
% 1.35/1.12 inference(unit_resolution,[status(thm)],[242, 238])).
% 1.35/1.12 tff(244,plain,
% 1.35/1.12 (mult(unit, mult(mult(a, b), b)) = mult(mult(unit, b), mult(a, b))),
% 1.35/1.12 inference(symmetry,[status(thm)],[243])).
% 1.35/1.12 tff(245,plain,
% 1.35/1.12 ((mult(unit, mult(mult(a, b), b)) = mult(unit, mult(b, mult(a, b)))) <=> (mult(mult(unit, b), mult(a, b)) = mult(mult(unit, mult(a, b)), b))),
% 1.35/1.12 inference(monotonicity,[status(thm)],[244, 241])).
% 1.35/1.12 tff(246,plain,
% 1.35/1.12 ((mult(unit, mult(mult(a, b), b)) = mult(unit, mult(b, mult(a, b)))) <=> (mult(mult(unit, mult(a, b)), b) = mult(mult(unit, b), mult(a, b)))),
% 1.35/1.12 inference(transitivity,[status(thm)],[245, 227])).
% 1.35/1.12 tff(247,plain,
% 1.35/1.12 ((mult(mult(unit, mult(a, b)), b) = mult(mult(unit, b), mult(a, b))) <=> (mult(unit, mult(mult(a, b), b)) = mult(unit, mult(b, mult(a, b))))),
% 1.35/1.12 inference(symmetry,[status(thm)],[246])).
% 1.35/1.12 tff(248,plain,
% 1.35/1.12 ((mult(mult(unit, mult(a, b)), b) = mult(mult(unit, b), mult(a, b))) <=> (mult(unit, mult(b, mult(a, b))) = mult(unit, mult(mult(a, b), b)))),
% 1.35/1.12 inference(transitivity,[status(thm)],[247, 226])).
% 1.35/1.12 tff(249,plain,
% 1.35/1.12 (mult(mult(unit, b), mult(a, b)) = mult(b, mult(a, b))),
% 1.35/1.12 inference(monotonicity,[status(thm)],[163])).
% 1.35/1.12 tff(250,plain,
% 1.35/1.12 (mult(b, mult(a, b)) = mult(mult(unit, b), mult(a, b))),
% 1.35/1.12 inference(symmetry,[status(thm)],[249])).
% 1.35/1.12 tff(251,plain,
% 1.35/1.12 (mult(mult(unit, mult(a, b)), b) = mult(mult(unit, b), mult(a, b))),
% 1.35/1.12 inference(transitivity,[status(thm)],[240, 224, 250])).
% 1.35/1.12 tff(252,plain,
% 1.35/1.12 (mult(unit, mult(b, mult(a, b))) = mult(unit, mult(mult(a, b), b))),
% 1.35/1.12 inference(modus_ponens,[status(thm)],[251, 248])).
% 1.35/1.12 tff(253,plain,
% 1.35/1.12 ($false),
% 1.35/1.12 inference(unit_resolution,[status(thm)],[228, 252])).
% 1.35/1.12 tff(254,plain,(mult(unit, mult(b, mult(a, b))) = mult(unit, mult(mult(a, b), b))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.12 tff(255,plain,
% 1.35/1.12 (mult(unit, mult(mult(a, b), b)) = mult(unit, mult(b, mult(a, b)))),
% 1.35/1.12 inference(symmetry,[status(thm)],[254])).
% 1.35/1.12 tff(256,plain,
% 1.35/1.12 ((~![A: $i] : (mult(unit, A) = A)) | (mult(unit, mult(mult(a, b), b)) = mult(mult(a, b), b))),
% 1.35/1.12 inference(quant_inst,[status(thm)],[])).
% 1.35/1.12 tff(257,plain,
% 1.35/1.12 (mult(unit, mult(mult(a, b), b)) = mult(mult(a, b), b)),
% 1.35/1.12 inference(unit_resolution,[status(thm)],[256, 26])).
% 1.35/1.12 tff(258,plain,
% 1.35/1.12 (mult(mult(a, b), b) = mult(unit, mult(mult(a, b), b))),
% 1.35/1.12 inference(symmetry,[status(thm)],[257])).
% 1.35/1.12 tff(259,plain,
% 1.35/1.12 (mult(mult(a, b), b) = mult(b, mult(a, b))),
% 1.35/1.12 inference(transitivity,[status(thm)],[258, 255, 224])).
% 1.35/1.12 tff(260,plain,
% 1.35/1.12 (mult(mult(mult(a, b), b), mult(mult(a, b), c)) = mult(mult(b, mult(a, b)), mult(mult(a, b), c))),
% 1.35/1.12 inference(monotonicity,[status(thm)],[259])).
% 1.35/1.12 tff(261,plain,
% 1.35/1.12 (mult(mult(mult(a, b), b), mult(mult(a, b), c)) = mult(mult(b, mult(a, b)), mult(c, mult(a, b)))),
% 1.35/1.12 inference(transitivity,[status(thm)],[260, 222])).
% 1.35/1.12 tff(262,plain,
% 1.35/1.12 (mult(mult(mult(a, b), mult(mult(a, b), c)), b) = mult(mult(mult(b, mult(a, b)), mult(a, b)), c)),
% 1.35/1.13 inference(transitivity,[status(thm)],[221, 212, 205, 164, 204, 203])).
% 1.35/1.13 tff(263,plain,
% 1.35/1.13 ((mult(mult(mult(a, b), mult(mult(a, b), c)), b) = mult(mult(mult(a, b), b), mult(mult(a, b), c))) <=> (mult(mult(mult(b, mult(a, b)), mult(a, b)), c) = mult(mult(b, mult(a, b)), mult(c, mult(a, b))))),
% 1.35/1.13 inference(monotonicity,[status(thm)],[262, 261])).
% 1.35/1.13 tff(264,plain,
% 1.35/1.13 ((mult(mult(mult(b, mult(a, b)), mult(a, b)), c) = mult(mult(b, mult(a, b)), mult(c, mult(a, b)))) <=> (mult(mult(mult(a, b), mult(mult(a, b), c)), b) = mult(mult(mult(a, b), b), mult(mult(a, b), c)))),
% 1.35/1.13 inference(symmetry,[status(thm)],[263])).
% 1.35/1.13 tff(265,plain,
% 1.35/1.13 ((~(mult(mult(mult(b, mult(a, b)), mult(a, b)), c) = mult(mult(b, mult(a, b)), mult(c, mult(a, b))))) <=> (~(mult(mult(mult(a, b), mult(mult(a, b), c)), b) = mult(mult(mult(a, b), b), mult(mult(a, b), c))))),
% 1.35/1.13 inference(monotonicity,[status(thm)],[264])).
% 1.35/1.13 tff(266,assumption,(~(mult(mult(mult(b, mult(a, b)), mult(a, b)), c) = mult(mult(b, mult(a, b)), mult(c, mult(a, b))))), introduced(assumption)).
% 1.35/1.13 tff(267,plain,
% 1.35/1.13 (~(mult(mult(mult(a, b), mult(mult(a, b), c)), b) = mult(mult(mult(a, b), b), mult(mult(a, b), c)))),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[266, 265])).
% 1.35/1.13 tff(268,plain,
% 1.35/1.13 (((~(mult(mult(a, b), mult(mult(mult(a, b), c), b)) = mult(mult(a, b), mult(b, mult(mult(a, b), c))))) | (~(mult(mult(mult(a, b), mult(mult(a, b), c)), b) = mult(mult(mult(a, b), b), mult(mult(a, b), c))))) | (mult(mult(mult(a, b), mult(mult(a, b), c)), b) = mult(mult(mult(a, b), b), mult(mult(a, b), c)))),
% 1.35/1.13 inference(tautology,[status(thm)],[])).
% 1.35/1.13 tff(269,plain,
% 1.35/1.13 ((~(mult(mult(a, b), mult(mult(mult(a, b), c), b)) = mult(mult(a, b), mult(b, mult(mult(a, b), c))))) | (~(mult(mult(mult(a, b), mult(mult(a, b), c)), b) = mult(mult(mult(a, b), b), mult(mult(a, b), c))))),
% 1.35/1.13 inference(unit_resolution,[status(thm)],[268, 267])).
% 1.35/1.13 tff(270,plain,
% 1.35/1.13 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(mult(a, b), mult(mult(mult(a, b), c), b)) = mult(mult(a, b), mult(b, mult(mult(a, b), c))))) | (~(mult(mult(mult(a, b), mult(mult(a, b), c)), b) = mult(mult(mult(a, b), b), mult(mult(a, b), c)))))) | (~((~(mult(mult(mult(a, b), mult(mult(a, b), c)), b) = mult(mult(a, b), mult(b, mult(mult(a, b), c))))) | (~(mult(mult(mult(a, b), b), mult(mult(a, b), c)) = mult(mult(a, b), mult(mult(mult(a, b), c), b)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | (~((~(mult(mult(a, b), mult(mult(mult(a, b), c), b)) = mult(mult(a, b), mult(b, mult(mult(a, b), c))))) | (~(mult(mult(mult(a, b), mult(mult(a, b), c)), b) = mult(mult(mult(a, b), b), mult(mult(a, b), c)))))) | (~((~(mult(mult(mult(a, b), mult(mult(a, b), c)), b) = mult(mult(a, b), mult(b, mult(mult(a, b), c))))) | (~(mult(mult(mult(a, b), b), mult(mult(a, b), c)) = mult(mult(a, b), mult(mult(mult(a, b), c), b)))))))),
% 1.35/1.13 inference(rewrite,[status(thm)],[])).
% 1.35/1.13 tff(271,plain,
% 1.35/1.13 (((~((~(mult(mult(mult(a, b), mult(mult(a, b), c)), b) = mult(mult(mult(a, b), b), mult(mult(a, b), c)))) | (~(mult(mult(a, b), mult(mult(mult(a, b), c), b)) = mult(mult(a, b), mult(b, mult(mult(a, b), c))))))) | (~((~(mult(mult(mult(a, b), mult(mult(a, b), c)), b) = mult(mult(a, b), mult(b, mult(mult(a, b), c))))) | (~(mult(mult(mult(a, b), b), mult(mult(a, b), c)) = mult(mult(a, b), mult(mult(mult(a, b), c), b))))))) <=> ((~((~(mult(mult(a, b), mult(mult(mult(a, b), c), b)) = mult(mult(a, b), mult(b, mult(mult(a, b), c))))) | (~(mult(mult(mult(a, b), mult(mult(a, b), c)), b) = mult(mult(mult(a, b), b), mult(mult(a, b), c)))))) | (~((~(mult(mult(mult(a, b), mult(mult(a, b), c)), b) = mult(mult(a, b), mult(b, mult(mult(a, b), c))))) | (~(mult(mult(mult(a, b), b), mult(mult(a, b), c)) = mult(mult(a, b), mult(mult(mult(a, b), c), b)))))))),
% 1.35/1.13 inference(rewrite,[status(thm)],[])).
% 1.35/1.13 tff(272,plain,
% 1.35/1.13 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(mult(mult(a, b), mult(mult(a, b), c)), b) = mult(mult(mult(a, b), b), mult(mult(a, b), c)))) | (~(mult(mult(a, b), mult(mult(mult(a, b), c), b)) = mult(mult(a, b), mult(b, mult(mult(a, b), c))))))) | (~((~(mult(mult(mult(a, b), mult(mult(a, b), c)), b) = mult(mult(a, b), mult(b, mult(mult(a, b), c))))) | (~(mult(mult(mult(a, b), b), mult(mult(a, b), c)) = mult(mult(a, b), mult(mult(mult(a, b), c), b)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(mult(a, b), mult(mult(mult(a, b), c), b)) = mult(mult(a, b), mult(b, mult(mult(a, b), c))))) | (~(mult(mult(mult(a, b), mult(mult(a, b), c)), b) = mult(mult(mult(a, b), b), mult(mult(a, b), c)))))) | (~((~(mult(mult(mult(a, b), mult(mult(a, b), c)), b) = mult(mult(a, b), mult(b, mult(mult(a, b), c))))) | (~(mult(mult(mult(a, b), b), mult(mult(a, b), c)) = mult(mult(a, b), mult(mult(mult(a, b), c), b))))))))),
% 1.35/1.13 inference(monotonicity,[status(thm)],[271])).
% 1.35/1.13 tff(273,plain,
% 1.35/1.13 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(mult(mult(a, b), mult(mult(a, b), c)), b) = mult(mult(mult(a, b), b), mult(mult(a, b), c)))) | (~(mult(mult(a, b), mult(mult(mult(a, b), c), b)) = mult(mult(a, b), mult(b, mult(mult(a, b), c))))))) | (~((~(mult(mult(mult(a, b), mult(mult(a, b), c)), b) = mult(mult(a, b), mult(b, mult(mult(a, b), c))))) | (~(mult(mult(mult(a, b), b), mult(mult(a, b), c)) = mult(mult(a, b), mult(mult(mult(a, b), c), b)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | (~((~(mult(mult(a, b), mult(mult(mult(a, b), c), b)) = mult(mult(a, b), mult(b, mult(mult(a, b), c))))) | (~(mult(mult(mult(a, b), mult(mult(a, b), c)), b) = mult(mult(mult(a, b), b), mult(mult(a, b), c)))))) | (~((~(mult(mult(mult(a, b), mult(mult(a, b), c)), b) = mult(mult(a, b), mult(b, mult(mult(a, b), c))))) | (~(mult(mult(mult(a, b), b), mult(mult(a, b), c)) = mult(mult(a, b), mult(mult(mult(a, b), c), b)))))))),
% 1.35/1.13 inference(transitivity,[status(thm)],[272, 270])).
% 1.35/1.13 tff(274,plain,
% 1.35/1.13 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(mult(mult(a, b), mult(mult(a, b), c)), b) = mult(mult(mult(a, b), b), mult(mult(a, b), c)))) | (~(mult(mult(a, b), mult(mult(mult(a, b), c), b)) = mult(mult(a, b), mult(b, mult(mult(a, b), c))))))) | (~((~(mult(mult(mult(a, b), mult(mult(a, b), c)), b) = mult(mult(a, b), mult(b, mult(mult(a, b), c))))) | (~(mult(mult(mult(a, b), b), mult(mult(a, b), c)) = mult(mult(a, b), mult(mult(mult(a, b), c), b)))))))),
% 1.35/1.13 inference(quant_inst,[status(thm)],[])).
% 1.35/1.13 tff(275,plain,
% 1.35/1.13 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | (~((~(mult(mult(a, b), mult(mult(mult(a, b), c), b)) = mult(mult(a, b), mult(b, mult(mult(a, b), c))))) | (~(mult(mult(mult(a, b), mult(mult(a, b), c)), b) = mult(mult(mult(a, b), b), mult(mult(a, b), c)))))) | (~((~(mult(mult(mult(a, b), mult(mult(a, b), c)), b) = mult(mult(a, b), mult(b, mult(mult(a, b), c))))) | (~(mult(mult(mult(a, b), b), mult(mult(a, b), c)) = mult(mult(a, b), mult(mult(mult(a, b), c), b))))))),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[274, 273])).
% 1.35/1.13 tff(276,plain,
% 1.35/1.13 ((~((~(mult(mult(a, b), mult(mult(mult(a, b), c), b)) = mult(mult(a, b), mult(b, mult(mult(a, b), c))))) | (~(mult(mult(mult(a, b), mult(mult(a, b), c)), b) = mult(mult(mult(a, b), b), mult(mult(a, b), c)))))) | (~((~(mult(mult(mult(a, b), mult(mult(a, b), c)), b) = mult(mult(a, b), mult(b, mult(mult(a, b), c))))) | (~(mult(mult(mult(a, b), b), mult(mult(a, b), c)) = mult(mult(a, b), mult(mult(mult(a, b), c), b))))))),
% 1.35/1.13 inference(unit_resolution,[status(thm)],[275, 64])).
% 1.35/1.13 tff(277,plain,
% 1.35/1.13 (~((~(mult(mult(mult(a, b), mult(mult(a, b), c)), b) = mult(mult(a, b), mult(b, mult(mult(a, b), c))))) | (~(mult(mult(mult(a, b), b), mult(mult(a, b), c)) = mult(mult(a, b), mult(mult(mult(a, b), c), b)))))),
% 1.35/1.13 inference(unit_resolution,[status(thm)],[276, 269])).
% 1.35/1.13 tff(278,plain,
% 1.35/1.13 (((~(mult(mult(mult(a, b), mult(mult(a, b), c)), b) = mult(mult(a, b), mult(b, mult(mult(a, b), c))))) | (~(mult(mult(mult(a, b), b), mult(mult(a, b), c)) = mult(mult(a, b), mult(mult(mult(a, b), c), b))))) | (mult(mult(mult(a, b), mult(mult(a, b), c)), b) = mult(mult(a, b), mult(b, mult(mult(a, b), c))))),
% 1.35/1.13 inference(tautology,[status(thm)],[])).
% 1.35/1.13 tff(279,plain,
% 1.35/1.13 (mult(mult(mult(a, b), mult(mult(a, b), c)), b) = mult(mult(a, b), mult(b, mult(mult(a, b), c)))),
% 1.35/1.13 inference(unit_resolution,[status(thm)],[278, 277])).
% 1.35/1.13 tff(280,plain,
% 1.35/1.13 (mult(mult(a, b), mult(b, mult(mult(a, b), c))) = mult(mult(mult(a, b), mult(mult(a, b), c)), b)),
% 1.35/1.13 inference(symmetry,[status(thm)],[279])).
% 1.35/1.13 tff(281,plain,
% 1.35/1.13 (mult(mult(unit, mult(a, b)), mult(b, mult(mult(a, b), c))) = mult(mult(a, b), mult(b, mult(mult(a, b), c)))),
% 1.35/1.13 inference(monotonicity,[status(thm)],[45])).
% 1.35/1.13 tff(282,plain,
% 1.35/1.13 (mult(mult(unit, mult(a, b)), mult(b, mult(mult(a, b), c))) = mult(mult(mult(b, mult(a, b)), mult(a, b)), c)),
% 1.35/1.13 inference(transitivity,[status(thm)],[281, 280, 221, 212, 205, 164, 204, 203])).
% 1.35/1.13 tff(283,assumption,(mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(mult(b, mult(mult(a, b), c)), mult(a, b))), introduced(assumption)).
% 1.35/1.13 tff(284,plain,
% 1.35/1.13 (mult(mult(b, mult(mult(a, b), c)), mult(a, b)) = mult(mult(b, mult(a, b)), mult(mult(a, b), c))),
% 1.35/1.13 inference(symmetry,[status(thm)],[283])).
% 1.35/1.13 tff(285,plain,
% 1.35/1.13 ((~![A: $i] : (mult(unit, A) = A)) | (mult(unit, mult(b, mult(mult(a, b), c))) = mult(b, mult(mult(a, b), c)))),
% 1.35/1.13 inference(quant_inst,[status(thm)],[])).
% 1.35/1.13 tff(286,plain,
% 1.35/1.13 (mult(unit, mult(b, mult(mult(a, b), c))) = mult(b, mult(mult(a, b), c))),
% 1.35/1.13 inference(unit_resolution,[status(thm)],[285, 26])).
% 1.35/1.13 tff(287,plain,
% 1.35/1.13 (mult(mult(unit, mult(b, mult(mult(a, b), c))), mult(a, b)) = mult(mult(b, mult(mult(a, b), c)), mult(a, b))),
% 1.35/1.13 inference(monotonicity,[status(thm)],[286])).
% 1.35/1.13 tff(288,plain,
% 1.35/1.13 (mult(mult(unit, mult(b, mult(mult(a, b), c))), mult(a, b)) = mult(mult(b, mult(a, b)), mult(c, mult(a, b)))),
% 1.35/1.13 inference(transitivity,[status(thm)],[287, 284, 222])).
% 1.35/1.13 tff(289,plain,
% 1.35/1.13 ((mult(mult(unit, mult(b, mult(mult(a, b), c))), mult(a, b)) = mult(mult(unit, mult(a, b)), mult(b, mult(mult(a, b), c)))) <=> (mult(mult(b, mult(a, b)), mult(c, mult(a, b))) = mult(mult(mult(b, mult(a, b)), mult(a, b)), c))),
% 1.35/1.13 inference(monotonicity,[status(thm)],[288, 282])).
% 1.35/1.13 tff(290,plain,
% 1.35/1.13 ((mult(mult(unit, mult(b, mult(mult(a, b), c))), mult(a, b)) = mult(mult(unit, mult(a, b)), mult(b, mult(mult(a, b), c)))) <=> (mult(mult(mult(b, mult(a, b)), mult(a, b)), c) = mult(mult(b, mult(a, b)), mult(c, mult(a, b))))),
% 1.35/1.13 inference(transitivity,[status(thm)],[289, 201])).
% 1.35/1.13 tff(291,plain,
% 1.35/1.13 ((mult(mult(mult(b, mult(a, b)), mult(a, b)), c) = mult(mult(b, mult(a, b)), mult(c, mult(a, b)))) <=> (mult(mult(unit, mult(b, mult(mult(a, b), c))), mult(a, b)) = mult(mult(unit, mult(a, b)), mult(b, mult(mult(a, b), c))))),
% 1.35/1.13 inference(symmetry,[status(thm)],[290])).
% 1.35/1.13 tff(292,plain,
% 1.35/1.13 ((~(mult(mult(mult(b, mult(a, b)), mult(a, b)), c) = mult(mult(b, mult(a, b)), mult(c, mult(a, b))))) <=> (~(mult(mult(unit, mult(b, mult(mult(a, b), c))), mult(a, b)) = mult(mult(unit, mult(a, b)), mult(b, mult(mult(a, b), c)))))),
% 1.35/1.13 inference(monotonicity,[status(thm)],[291])).
% 1.35/1.13 tff(293,plain,
% 1.35/1.13 (~(mult(mult(unit, mult(b, mult(mult(a, b), c))), mult(a, b)) = mult(mult(unit, mult(a, b)), mult(b, mult(mult(a, b), c))))),
% 1.35/1.13 inference(modus_ponens,[status(thm)],[266, 292])).
% 1.35/1.13 tff(294,plain,
% 1.35/1.13 (((~(mult(mult(unit, mult(b, mult(mult(a, b), c))), mult(a, b)) = mult(mult(unit, mult(a, b)), mult(b, mult(mult(a, b), c))))) | (~(mult(unit, mult(mult(b, mult(mult(a, b), c)), mult(a, b))) = mult(unit, mult(mult(a, b), mult(b, mult(mult(a, b), c))))))) | (mult(mult(unit, mult(b, mult(mult(a, b), c))), mult(a, b)) = mult(mult(unit, mult(a, b)), mult(b, mult(mult(a, b), c))))),
% 1.35/1.13 inference(tautology,[status(thm)],[])).
% 1.35/1.13 tff(295,plain,
% 1.35/1.13 ((~(mult(mult(unit, mult(b, mult(mult(a, b), c))), mult(a, b)) = mult(mult(unit, mult(a, b)), mult(b, mult(mult(a, b), c))))) | (~(mult(unit, mult(mult(b, mult(mult(a, b), c)), mult(a, b))) = mult(unit, mult(mult(a, b), mult(b, mult(mult(a, b), c))))))),
% 1.35/1.13 inference(unit_resolution,[status(thm)],[294, 293])).
% 1.35/1.13 tff(296,plain,
% 1.35/1.13 (mult(mult(a, b), mult(b, mult(mult(a, b), c))) = mult(mult(unit, mult(a, b)), mult(b, mult(mult(a, b), c)))),
% 1.35/1.13 inference(symmetry,[status(thm)],[281])).
% 1.35/1.13 tff(297,plain,
% 1.35/1.13 (mult(mult(mult(mult(a, b), c), mult(a, b)), b) = mult(mult(mult(a, b), mult(mult(a, b), c)), b)),
% 1.35/1.13 inference(symmetry,[status(thm)],[221])).
% 1.35/1.13 tff(298,plain,
% 1.35/1.13 (mult(mult(unit, mult(mult(mult(a, b), c), mult(a, b))), b) = mult(mult(mult(mult(a, b), c), mult(a, b)), b)),
% 1.35/1.13 inference(symmetry,[status(thm)],[212])).
% 1.35/1.13 tff(299,plain,
% 1.35/1.13 (mult(mult(unit, b), mult(mult(mult(a, b), c), mult(a, b))) = mult(mult(unit, mult(mult(mult(a, b), c), mult(a, b))), b)),
% 1.35/1.13 inference(symmetry,[status(thm)],[205])).
% 1.35/1.13 tff(300,plain,
% 1.35/1.13 (mult(mult(a, b), mult(b, mult(mult(a, b), c))) = mult(b, mult(mult(mult(a, b), c), mult(a, b)))),
% 1.35/1.13 inference(transitivity,[status(thm)],[280, 221, 212, 205, 164])).
% 1.35/1.13 tff(301,plain,
% 1.35/1.13 (mult(unit, mult(mult(a, b), mult(b, mult(mult(a, b), c)))) = mult(unit, mult(b, mult(mult(mult(a, b), c), mult(a, b))))),
% 1.35/1.13 inference(monotonicity,[status(thm)],[300])).
% 1.35/1.13 tff(302,plain,
% 1.35/1.13 (mult(unit, mult(mult(a, b), mult(b, mult(mult(a, b), c)))) = mult(mult(unit, mult(a, b)), mult(b, mult(mult(a, b), c)))),
% 1.35/1.13 inference(transitivity,[status(thm)],[301, 167, 165, 299, 298, 297, 279, 296])).
% 1.35/1.13 tff(303,plain,
% 1.35/1.13 ((mult(mult(unit, mult(b, mult(mult(a, b), c))), mult(a, b)) = mult(unit, mult(mult(a, b), mult(b, mult(mult(a, b), c))))) <=> (mult(mult(unit, mult(b, mult(mult(a, b), c))), mult(a, b)) = mult(mult(unit, mult(a, b)), mult(b, mult(mult(a, b), c))))),
% 1.35/1.13 inference(monotonicity,[status(thm)],[302])).
% 1.35/1.13 tff(304,plain,
% 1.35/1.13 ((mult(mult(unit, mult(b, mult(mult(a, b), c))), mult(a, b)) = mult(mult(unit, mult(a, b)), mult(b, mult(mult(a, b), c)))) <=> (mult(mult(unit, mult(b, mult(mult(a, b), c))), mult(a, b)) = mult(unit, mult(mult(a, b), mult(b, mult(mult(a, b), c)))))),
% 1.35/1.13 inference(symmetry,[status(thm)],[303])).
% 1.35/1.13 tff(305,plain,
% 1.35/1.13 ((mult(mult(mult(b, mult(a, b)), mult(a, b)), c) = mult(mult(b, mult(a, b)), mult(c, mult(a, b)))) <=> (mult(mult(unit, mult(b, mult(mult(a, b), c))), mult(a, b)) = mult(unit, mult(mult(a, b), mult(b, mult(mult(a, b), c)))))),
% 1.35/1.13 inference(transitivity,[status(thm)],[291, 304])).
% 1.35/1.13 tff(306,plain,
% 1.35/1.13 ((~(mult(mult(mult(b, mult(a, b)), mult(a, b)), c) = mult(mult(b, mult(a, b)), mult(c, mult(a, b))))) <=> (~(mult(mult(unit, mult(b, mult(mult(a, b), c))), mult(a, b)) = mult(unit, mult(mult(a, b), mult(b, mult(mult(a, b), c))))))),
% 1.35/1.13 inference(monotonicity,[status(thm)],[305])).
% 1.35/1.13 tff(307,plain,
% 1.35/1.13 (~(mult(mult(unit, mult(b, mult(mult(a, b), c))), mult(a, b)) = mult(unit, mult(mult(a, b), mult(b, mult(mult(a, b), c)))))),
% 1.35/1.14 inference(modus_ponens,[status(thm)],[266, 306])).
% 1.35/1.14 tff(308,plain,
% 1.35/1.14 (((~(mult(mult(unit, mult(b, mult(mult(a, b), c))), mult(a, b)) = mult(unit, mult(mult(a, b), mult(b, mult(mult(a, b), c)))))) | (~(mult(mult(unit, mult(a, b)), mult(b, mult(mult(a, b), c))) = mult(unit, mult(mult(b, mult(mult(a, b), c)), mult(a, b)))))) | (mult(mult(unit, mult(b, mult(mult(a, b), c))), mult(a, b)) = mult(unit, mult(mult(a, b), mult(b, mult(mult(a, b), c)))))),
% 1.35/1.14 inference(tautology,[status(thm)],[])).
% 1.35/1.14 tff(309,plain,
% 1.35/1.14 ((~(mult(mult(unit, mult(b, mult(mult(a, b), c))), mult(a, b)) = mult(unit, mult(mult(a, b), mult(b, mult(mult(a, b), c)))))) | (~(mult(mult(unit, mult(a, b)), mult(b, mult(mult(a, b), c))) = mult(unit, mult(mult(b, mult(mult(a, b), c)), mult(a, b)))))),
% 1.35/1.14 inference(unit_resolution,[status(thm)],[308, 307])).
% 1.35/1.14 tff(310,plain,
% 1.35/1.14 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(mult(unit, mult(b, mult(mult(a, b), c))), mult(a, b)) = mult(mult(unit, mult(a, b)), mult(b, mult(mult(a, b), c))))) | (~(mult(unit, mult(mult(b, mult(mult(a, b), c)), mult(a, b))) = mult(unit, mult(mult(a, b), mult(b, mult(mult(a, b), c)))))))) | (~((~(mult(mult(unit, mult(b, mult(mult(a, b), c))), mult(a, b)) = mult(unit, mult(mult(a, b), mult(b, mult(mult(a, b), c)))))) | (~(mult(mult(unit, mult(a, b)), mult(b, mult(mult(a, b), c))) = mult(unit, mult(mult(b, mult(mult(a, b), c)), mult(a, b))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | (~((~(mult(mult(unit, mult(b, mult(mult(a, b), c))), mult(a, b)) = mult(mult(unit, mult(a, b)), mult(b, mult(mult(a, b), c))))) | (~(mult(unit, mult(mult(b, mult(mult(a, b), c)), mult(a, b))) = mult(unit, mult(mult(a, b), mult(b, mult(mult(a, b), c)))))))) | (~((~(mult(mult(unit, mult(b, mult(mult(a, b), c))), mult(a, b)) = mult(unit, mult(mult(a, b), mult(b, mult(mult(a, b), c)))))) | (~(mult(mult(unit, mult(a, b)), mult(b, mult(mult(a, b), c))) = mult(unit, mult(mult(b, mult(mult(a, b), c)), mult(a, b))))))))),
% 1.35/1.14 inference(rewrite,[status(thm)],[])).
% 1.35/1.14 tff(311,plain,
% 1.35/1.14 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(mult(unit, mult(b, mult(mult(a, b), c))), mult(a, b)) = mult(mult(unit, mult(a, b)), mult(b, mult(mult(a, b), c))))) | (~(mult(unit, mult(mult(b, mult(mult(a, b), c)), mult(a, b))) = mult(unit, mult(mult(a, b), mult(b, mult(mult(a, b), c)))))))) | (~((~(mult(mult(unit, mult(b, mult(mult(a, b), c))), mult(a, b)) = mult(unit, mult(mult(a, b), mult(b, mult(mult(a, b), c)))))) | (~(mult(mult(unit, mult(a, b)), mult(b, mult(mult(a, b), c))) = mult(unit, mult(mult(b, mult(mult(a, b), c)), mult(a, b))))))))),
% 1.35/1.14 inference(quant_inst,[status(thm)],[])).
% 1.35/1.14 tff(312,plain,
% 1.35/1.14 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | (~((~(mult(mult(unit, mult(b, mult(mult(a, b), c))), mult(a, b)) = mult(mult(unit, mult(a, b)), mult(b, mult(mult(a, b), c))))) | (~(mult(unit, mult(mult(b, mult(mult(a, b), c)), mult(a, b))) = mult(unit, mult(mult(a, b), mult(b, mult(mult(a, b), c)))))))) | (~((~(mult(mult(unit, mult(b, mult(mult(a, b), c))), mult(a, b)) = mult(unit, mult(mult(a, b), mult(b, mult(mult(a, b), c)))))) | (~(mult(mult(unit, mult(a, b)), mult(b, mult(mult(a, b), c))) = mult(unit, mult(mult(b, mult(mult(a, b), c)), mult(a, b)))))))),
% 1.42/1.14 inference(modus_ponens,[status(thm)],[311, 310])).
% 1.42/1.14 tff(313,plain,
% 1.42/1.14 ((~((~(mult(mult(unit, mult(b, mult(mult(a, b), c))), mult(a, b)) = mult(mult(unit, mult(a, b)), mult(b, mult(mult(a, b), c))))) | (~(mult(unit, mult(mult(b, mult(mult(a, b), c)), mult(a, b))) = mult(unit, mult(mult(a, b), mult(b, mult(mult(a, b), c)))))))) | (~((~(mult(mult(unit, mult(b, mult(mult(a, b), c))), mult(a, b)) = mult(unit, mult(mult(a, b), mult(b, mult(mult(a, b), c)))))) | (~(mult(mult(unit, mult(a, b)), mult(b, mult(mult(a, b), c))) = mult(unit, mult(mult(b, mult(mult(a, b), c)), mult(a, b)))))))),
% 1.42/1.14 inference(unit_resolution,[status(thm)],[312, 64])).
% 1.42/1.14 tff(314,plain,
% 1.42/1.14 ($false),
% 1.42/1.14 inference(unit_resolution,[status(thm)],[313, 309, 295])).
% 1.42/1.14 tff(315,plain,((~(mult(mult(unit, mult(mult(mult(a, b), c), mult(a, b))), b) = mult(mult(unit, b), mult(mult(mult(a, b), c), mult(a, b))))) | (mult(mult(mult(b, mult(a, b)), mult(a, b)), c) = mult(mult(b, mult(a, b)), mult(c, mult(a, b)))) | (~(mult(mult(mult(b, mult(a, b)), mult(a, b)), c) = mult(mult(mult(b, mult(a, b)), c), mult(a, b)))) | (~(mult(b, mult(mult(a, b), mult(mult(a, b), c))) = mult(b, mult(mult(mult(a, b), c), mult(a, b))))) | (~(mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(mult(b, mult(mult(a, b), c)), mult(a, b)))) | (~(mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(mult(b, mult(a, b)), mult(c, mult(a, b)))))), inference(lemma,lemma(discharge,[]))).
% 1.42/1.14 tff(316,plain,
% 1.42/1.14 (mult(mult(mult(b, mult(a, b)), mult(a, b)), c) = mult(mult(b, mult(a, b)), mult(c, mult(a, b)))),
% 1.42/1.14 inference(unit_resolution,[status(thm)],[315, 200, 198, 143, 161, 140])).
% 1.42/1.14 tff(317,plain,
% 1.42/1.14 ($false),
% 1.42/1.14 inference(unit_resolution,[status(thm)],[316, 157])).
% 1.42/1.14 tff(318,plain,(mult(mult(mult(b, mult(a, b)), c), mult(a, b)) = mult(mult(b, mult(a, b)), mult(mult(a, b), c))), inference(lemma,lemma(discharge,[]))).
% 1.42/1.14 tff(319,plain,
% 1.42/1.14 (mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(mult(mult(b, mult(a, b)), c), mult(a, b))),
% 1.42/1.14 inference(symmetry,[status(thm)],[318])).
% 1.42/1.14 tff(320,plain,
% 1.42/1.14 (mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(b, mult(mult(mult(a, b), c), mult(a, b)))),
% 1.42/1.14 inference(transitivity,[status(thm)],[319, 126])).
% 1.42/1.14 tff(321,plain,
% 1.42/1.14 ((mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(mult(b, mult(mult(a, b), c)), mult(a, b))) <=> (mult(b, mult(mult(mult(a, b), c), mult(a, b))) = mult(b, mult(mult(a, b), mult(mult(a, b), c))))),
% 1.42/1.14 inference(monotonicity,[status(thm)],[320, 117])).
% 1.42/1.14 tff(322,plain,
% 1.42/1.14 ((mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(mult(b, mult(mult(a, b), c)), mult(a, b))) <=> (mult(b, mult(mult(a, b), mult(mult(a, b), c))) = mult(b, mult(mult(mult(a, b), c), mult(a, b))))),
% 1.42/1.14 inference(transitivity,[status(thm)],[321, 104])).
% 1.42/1.14 tff(323,plain,
% 1.42/1.14 ((mult(b, mult(mult(a, b), mult(mult(a, b), c))) = mult(b, mult(mult(mult(a, b), c), mult(a, b)))) <=> (mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(mult(b, mult(mult(a, b), c)), mult(a, b)))),
% 1.42/1.14 inference(symmetry,[status(thm)],[322])).
% 1.42/1.14 tff(324,plain,
% 1.42/1.14 ((mult(mult(a, b), mult(mult(a, b), c)) = mult(mult(mult(a, b), c), mult(a, b))) <=> (mult(mult(mult(a, b), c), mult(a, b)) = mult(mult(a, b), mult(mult(a, b), c)))),
% 1.42/1.14 inference(commutativity,[status(thm)],[])).
% 1.42/1.14 tff(325,plain,
% 1.42/1.14 (mult(unit, mult(mult(mult(a, b), c), mult(a, b))) = mult(mult(mult(unit, mult(a, b)), c), mult(a, b))),
% 1.42/1.14 inference(symmetry,[status(thm)],[207])).
% 1.42/1.14 tff(326,plain,
% 1.42/1.14 (mult(unit, mult(mult(mult(a, b), c), mult(a, b))) = mult(mult(mult(a, b), c), mult(a, b))),
% 1.42/1.14 inference(transitivity,[status(thm)],[325, 209])).
% 1.42/1.14 tff(327,plain,
% 1.42/1.14 (mult(mult(unit, mult(a, b)), mult(mult(a, b), c)) = mult(mult(a, b), mult(mult(a, b), c))),
% 1.42/1.14 inference(monotonicity,[status(thm)],[45])).
% 1.42/1.14 tff(328,plain,
% 1.42/1.14 ((mult(mult(unit, mult(a, b)), mult(mult(a, b), c)) = mult(unit, mult(mult(mult(a, b), c), mult(a, b)))) <=> (mult(mult(a, b), mult(mult(a, b), c)) = mult(mult(mult(a, b), c), mult(a, b)))),
% 1.42/1.14 inference(monotonicity,[status(thm)],[327, 326])).
% 1.42/1.14 tff(329,plain,
% 1.42/1.14 ((mult(mult(unit, mult(a, b)), mult(mult(a, b), c)) = mult(unit, mult(mult(mult(a, b), c), mult(a, b)))) <=> (mult(mult(mult(a, b), c), mult(a, b)) = mult(mult(a, b), mult(mult(a, b), c)))),
% 1.42/1.14 inference(transitivity,[status(thm)],[328, 324])).
% 1.42/1.14 tff(330,plain,
% 1.42/1.14 ((mult(mult(mult(a, b), c), mult(a, b)) = mult(mult(a, b), mult(mult(a, b), c))) <=> (mult(mult(unit, mult(a, b)), mult(mult(a, b), c)) = mult(unit, mult(mult(mult(a, b), c), mult(a, b))))),
% 1.42/1.14 inference(symmetry,[status(thm)],[329])).
% 1.42/1.14 tff(331,plain,
% 1.42/1.14 ((~![A: $i] : (mult(unit, A) = A)) | (mult(unit, mult(mult(a, b), mult(mult(a, b), c))) = mult(mult(a, b), mult(mult(a, b), c)))),
% 1.42/1.14 inference(quant_inst,[status(thm)],[])).
% 1.42/1.14 tff(332,plain,
% 1.42/1.14 (mult(unit, mult(mult(a, b), mult(mult(a, b), c))) = mult(mult(a, b), mult(mult(a, b), c))),
% 1.42/1.14 inference(unit_resolution,[status(thm)],[331, 26])).
% 1.42/1.14 tff(333,plain,
% 1.42/1.14 ((mult(unit, mult(mult(a, b), mult(mult(a, b), c))) = mult(unit, mult(mult(mult(a, b), c), mult(a, b)))) <=> (mult(mult(a, b), mult(mult(a, b), c)) = mult(mult(mult(a, b), c), mult(a, b)))),
% 1.42/1.14 inference(monotonicity,[status(thm)],[332, 326])).
% 1.42/1.14 tff(334,plain,
% 1.42/1.14 ((mult(unit, mult(mult(a, b), mult(mult(a, b), c))) = mult(unit, mult(mult(mult(a, b), c), mult(a, b)))) <=> (mult(mult(mult(a, b), c), mult(a, b)) = mult(mult(a, b), mult(mult(a, b), c)))),
% 1.42/1.14 inference(transitivity,[status(thm)],[333, 324])).
% 1.42/1.14 tff(335,plain,
% 1.42/1.14 ((mult(unit, mult(mult(mult(a, b), c), mult(a, b))) = mult(unit, mult(mult(a, b), mult(mult(a, b), c)))) <=> (mult(unit, mult(mult(a, b), mult(mult(a, b), c))) = mult(unit, mult(mult(mult(a, b), c), mult(a, b))))),
% 1.42/1.14 inference(commutativity,[status(thm)],[])).
% 1.42/1.14 tff(336,plain,
% 1.42/1.14 ((mult(unit, mult(mult(mult(a, b), c), mult(a, b))) = mult(unit, mult(mult(a, b), mult(mult(a, b), c)))) <=> (mult(mult(unit, mult(a, b)), mult(mult(a, b), c)) = mult(unit, mult(mult(mult(a, b), c), mult(a, b))))),
% 1.42/1.14 inference(transitivity,[status(thm)],[335, 334, 330])).
% 1.42/1.14 tff(337,plain,
% 1.42/1.14 ((~(mult(unit, mult(mult(mult(a, b), c), mult(a, b))) = mult(unit, mult(mult(a, b), mult(mult(a, b), c))))) <=> (~(mult(mult(unit, mult(a, b)), mult(mult(a, b), c)) = mult(unit, mult(mult(mult(a, b), c), mult(a, b)))))),
% 1.42/1.14 inference(monotonicity,[status(thm)],[336])).
% 1.42/1.14 tff(338,assumption,(~(mult(b, mult(mult(a, b), mult(mult(a, b), c))) = mult(b, mult(mult(mult(a, b), c), mult(a, b))))), introduced(assumption)).
% 1.42/1.14 tff(339,assumption,(mult(unit, mult(mult(mult(a, b), c), mult(a, b))) = mult(unit, mult(mult(a, b), mult(mult(a, b), c)))), introduced(assumption)).
% 1.42/1.14 tff(340,plain,
% 1.42/1.14 (mult(unit, mult(mult(a, b), mult(mult(a, b), c))) = mult(unit, mult(mult(mult(a, b), c), mult(a, b)))),
% 1.42/1.14 inference(symmetry,[status(thm)],[339])).
% 1.42/1.14 tff(341,plain,
% 1.42/1.14 (mult(mult(a, b), mult(mult(a, b), c)) = mult(unit, mult(mult(a, b), mult(mult(a, b), c)))),
% 1.42/1.14 inference(symmetry,[status(thm)],[332])).
% 1.42/1.14 tff(342,plain,
% 1.42/1.14 (mult(mult(a, b), mult(mult(a, b), c)) = mult(mult(mult(a, b), c), mult(a, b))),
% 1.42/1.14 inference(transitivity,[status(thm)],[341, 340, 325, 209])).
% 1.42/1.14 tff(343,plain,
% 1.42/1.14 (mult(b, mult(mult(a, b), mult(mult(a, b), c))) = mult(b, mult(mult(mult(a, b), c), mult(a, b)))),
% 1.42/1.14 inference(monotonicity,[status(thm)],[342])).
% 1.42/1.14 tff(344,plain,
% 1.42/1.14 ($false),
% 1.42/1.14 inference(unit_resolution,[status(thm)],[338, 343])).
% 1.42/1.14 tff(345,plain,((~(mult(unit, mult(mult(mult(a, b), c), mult(a, b))) = mult(unit, mult(mult(a, b), mult(mult(a, b), c))))) | (mult(b, mult(mult(a, b), mult(mult(a, b), c))) = mult(b, mult(mult(mult(a, b), c), mult(a, b))))), inference(lemma,lemma(discharge,[]))).
% 1.42/1.14 tff(346,plain,
% 1.42/1.14 (~(mult(unit, mult(mult(mult(a, b), c), mult(a, b))) = mult(unit, mult(mult(a, b), mult(mult(a, b), c))))),
% 1.42/1.14 inference(unit_resolution,[status(thm)],[345, 338])).
% 1.42/1.14 tff(347,plain,
% 1.42/1.14 (~(mult(mult(unit, mult(a, b)), mult(mult(a, b), c)) = mult(unit, mult(mult(mult(a, b), c), mult(a, b))))),
% 1.42/1.14 inference(modus_ponens,[status(thm)],[346, 337])).
% 1.42/1.14 tff(348,plain,
% 1.42/1.14 (((~(mult(mult(unit, mult(mult(a, b), c)), mult(a, b)) = mult(mult(unit, mult(a, b)), mult(mult(a, b), c)))) | (~(mult(unit, mult(mult(mult(a, b), c), mult(a, b))) = mult(unit, mult(mult(a, b), mult(mult(a, b), c)))))) | (mult(unit, mult(mult(mult(a, b), c), mult(a, b))) = mult(unit, mult(mult(a, b), mult(mult(a, b), c))))),
% 1.42/1.14 inference(tautology,[status(thm)],[])).
% 1.42/1.14 tff(349,plain,
% 1.42/1.14 ((~(mult(mult(unit, mult(mult(a, b), c)), mult(a, b)) = mult(mult(unit, mult(a, b)), mult(mult(a, b), c)))) | (~(mult(unit, mult(mult(mult(a, b), c), mult(a, b))) = mult(unit, mult(mult(a, b), mult(mult(a, b), c)))))),
% 1.42/1.14 inference(unit_resolution,[status(thm)],[348, 346])).
% 1.42/1.14 tff(350,plain,
% 1.42/1.14 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(mult(unit, mult(mult(a, b), c)), mult(a, b)) = mult(mult(unit, mult(a, b)), mult(mult(a, b), c)))) | (~(mult(unit, mult(mult(mult(a, b), c), mult(a, b))) = mult(unit, mult(mult(a, b), mult(mult(a, b), c))))))) | (~((~(mult(mult(unit, mult(mult(a, b), c)), mult(a, b)) = mult(unit, mult(mult(a, b), mult(mult(a, b), c))))) | (~(mult(mult(unit, mult(a, b)), mult(mult(a, b), c)) = mult(unit, mult(mult(mult(a, b), c), mult(a, b))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | (~((~(mult(mult(unit, mult(mult(a, b), c)), mult(a, b)) = mult(mult(unit, mult(a, b)), mult(mult(a, b), c)))) | (~(mult(unit, mult(mult(mult(a, b), c), mult(a, b))) = mult(unit, mult(mult(a, b), mult(mult(a, b), c))))))) | (~((~(mult(mult(unit, mult(mult(a, b), c)), mult(a, b)) = mult(unit, mult(mult(a, b), mult(mult(a, b), c))))) | (~(mult(mult(unit, mult(a, b)), mult(mult(a, b), c)) = mult(unit, mult(mult(mult(a, b), c), mult(a, b))))))))),
% 1.42/1.14 inference(rewrite,[status(thm)],[])).
% 1.42/1.14 tff(351,plain,
% 1.42/1.14 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(mult(unit, mult(mult(a, b), c)), mult(a, b)) = mult(mult(unit, mult(a, b)), mult(mult(a, b), c)))) | (~(mult(unit, mult(mult(mult(a, b), c), mult(a, b))) = mult(unit, mult(mult(a, b), mult(mult(a, b), c))))))) | (~((~(mult(mult(unit, mult(mult(a, b), c)), mult(a, b)) = mult(unit, mult(mult(a, b), mult(mult(a, b), c))))) | (~(mult(mult(unit, mult(a, b)), mult(mult(a, b), c)) = mult(unit, mult(mult(mult(a, b), c), mult(a, b))))))))),
% 1.42/1.14 inference(quant_inst,[status(thm)],[])).
% 1.42/1.14 tff(352,plain,
% 1.42/1.14 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | (~((~(mult(mult(unit, mult(mult(a, b), c)), mult(a, b)) = mult(mult(unit, mult(a, b)), mult(mult(a, b), c)))) | (~(mult(unit, mult(mult(mult(a, b), c), mult(a, b))) = mult(unit, mult(mult(a, b), mult(mult(a, b), c))))))) | (~((~(mult(mult(unit, mult(mult(a, b), c)), mult(a, b)) = mult(unit, mult(mult(a, b), mult(mult(a, b), c))))) | (~(mult(mult(unit, mult(a, b)), mult(mult(a, b), c)) = mult(unit, mult(mult(mult(a, b), c), mult(a, b)))))))),
% 1.42/1.14 inference(modus_ponens,[status(thm)],[351, 350])).
% 1.42/1.14 tff(353,plain,
% 1.42/1.14 ((~((~(mult(mult(unit, mult(mult(a, b), c)), mult(a, b)) = mult(mult(unit, mult(a, b)), mult(mult(a, b), c)))) | (~(mult(unit, mult(mult(mult(a, b), c), mult(a, b))) = mult(unit, mult(mult(a, b), mult(mult(a, b), c))))))) | (~((~(mult(mult(unit, mult(mult(a, b), c)), mult(a, b)) = mult(unit, mult(mult(a, b), mult(mult(a, b), c))))) | (~(mult(mult(unit, mult(a, b)), mult(mult(a, b), c)) = mult(unit, mult(mult(mult(a, b), c), mult(a, b)))))))),
% 1.42/1.14 inference(unit_resolution,[status(thm)],[352, 64])).
% 1.42/1.15 tff(354,plain,
% 1.42/1.15 (~((~(mult(mult(unit, mult(mult(a, b), c)), mult(a, b)) = mult(unit, mult(mult(a, b), mult(mult(a, b), c))))) | (~(mult(mult(unit, mult(a, b)), mult(mult(a, b), c)) = mult(unit, mult(mult(mult(a, b), c), mult(a, b))))))),
% 1.42/1.15 inference(unit_resolution,[status(thm)],[353, 349])).
% 1.42/1.15 tff(355,plain,
% 1.42/1.15 (((~(mult(mult(unit, mult(mult(a, b), c)), mult(a, b)) = mult(unit, mult(mult(a, b), mult(mult(a, b), c))))) | (~(mult(mult(unit, mult(a, b)), mult(mult(a, b), c)) = mult(unit, mult(mult(mult(a, b), c), mult(a, b)))))) | (mult(mult(unit, mult(a, b)), mult(mult(a, b), c)) = mult(unit, mult(mult(mult(a, b), c), mult(a, b))))),
% 1.42/1.15 inference(tautology,[status(thm)],[])).
% 1.42/1.15 tff(356,plain,
% 1.42/1.15 (mult(mult(unit, mult(a, b)), mult(mult(a, b), c)) = mult(unit, mult(mult(mult(a, b), c), mult(a, b)))),
% 1.42/1.15 inference(unit_resolution,[status(thm)],[355, 354])).
% 1.42/1.15 tff(357,plain,
% 1.42/1.15 ($false),
% 1.42/1.15 inference(unit_resolution,[status(thm)],[356, 347])).
% 1.42/1.15 tff(358,plain,(mult(b, mult(mult(a, b), mult(mult(a, b), c))) = mult(b, mult(mult(mult(a, b), c), mult(a, b)))), inference(lemma,lemma(discharge,[]))).
% 1.42/1.15 tff(359,plain,
% 1.42/1.15 (mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(mult(b, mult(mult(a, b), c)), mult(a, b))),
% 1.42/1.15 inference(modus_ponens,[status(thm)],[358, 323])).
% 1.42/1.15 tff(360,plain,
% 1.42/1.15 ($false),
% 1.42/1.15 inference(unit_resolution,[status(thm)],[105, 359])).
% 1.42/1.15 tff(361,plain,(mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(mult(b, mult(mult(a, b), c)), mult(a, b))), inference(lemma,lemma(discharge,[]))).
% 1.42/1.15 tff(362,plain,
% 1.42/1.15 (mult(mult(mult(b, mult(a, b)), c), mult(a, b)) = mult(mult(b, mult(mult(a, b), c)), mult(a, b))),
% 1.42/1.15 inference(transitivity,[status(thm)],[318, 361])).
% 1.42/1.15 tff(363,plain,
% 1.42/1.15 (rd(mult(mult(mult(b, mult(a, b)), c), mult(a, b)), mult(a, b)) = rd(mult(mult(b, mult(mult(a, b), c)), mult(a, b)), mult(a, b))),
% 1.42/1.15 inference(monotonicity,[status(thm)],[362])).
% 1.42/1.15 tff(364,plain,
% 1.42/1.15 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(b, mult(a, b)), c), mult(a, b)), mult(a, b)) = mult(mult(b, mult(a, b)), c))),
% 1.42/1.15 inference(quant_inst,[status(thm)],[])).
% 1.42/1.15 tff(365,plain,
% 1.42/1.15 (rd(mult(mult(mult(b, mult(a, b)), c), mult(a, b)), mult(a, b)) = mult(mult(b, mult(a, b)), c)),
% 1.42/1.15 inference(unit_resolution,[status(thm)],[364, 17])).
% 1.42/1.15 tff(366,plain,
% 1.42/1.15 (mult(mult(b, mult(a, b)), c) = rd(mult(mult(mult(b, mult(a, b)), c), mult(a, b)), mult(a, b))),
% 1.42/1.15 inference(symmetry,[status(thm)],[365])).
% 1.42/1.15 tff(367,assumption,(~(mult(b, mult(c, mult(a, b))) = mult(b, mult(mult(a, b), c)))), introduced(assumption)).
% 1.42/1.15 tff(368,plain,
% 1.42/1.15 (((~(mult(mult(b, c), mult(a, b)) = mult(mult(b, mult(a, b)), c))) | (~(mult(b, mult(c, mult(a, b))) = mult(b, mult(mult(a, b), c))))) | (mult(b, mult(c, mult(a, b))) = mult(b, mult(mult(a, b), c)))),
% 1.42/1.15 inference(tautology,[status(thm)],[])).
% 1.42/1.15 tff(369,plain,
% 1.42/1.15 ((~(mult(mult(b, c), mult(a, b)) = mult(mult(b, mult(a, b)), c))) | (~(mult(b, mult(c, mult(a, b))) = mult(b, mult(mult(a, b), c))))),
% 1.42/1.15 inference(unit_resolution,[status(thm)],[368, 367])).
% 1.42/1.15 tff(370,plain,
% 1.42/1.15 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(mult(b, c), mult(a, b)) = mult(b, mult(mult(a, b), c)))) | (~(mult(mult(b, mult(a, b)), c) = mult(b, mult(c, mult(a, b))))))) | (~((~(mult(mult(b, c), mult(a, b)) = mult(mult(b, mult(a, b)), c))) | (~(mult(b, mult(c, mult(a, b))) = mult(b, mult(mult(a, b), c)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | (~((~(mult(mult(b, c), mult(a, b)) = mult(b, mult(mult(a, b), c)))) | (~(mult(mult(b, mult(a, b)), c) = mult(b, mult(c, mult(a, b))))))) | (~((~(mult(mult(b, c), mult(a, b)) = mult(mult(b, mult(a, b)), c))) | (~(mult(b, mult(c, mult(a, b))) = mult(b, mult(mult(a, b), c)))))))),
% 1.42/1.15 inference(rewrite,[status(thm)],[])).
% 1.42/1.15 tff(371,plain,
% 1.42/1.15 (((~((~(mult(mult(b, c), mult(a, b)) = mult(mult(b, mult(a, b)), c))) | (~(mult(b, mult(c, mult(a, b))) = mult(b, mult(mult(a, b), c)))))) | (~((~(mult(mult(b, c), mult(a, b)) = mult(b, mult(mult(a, b), c)))) | (~(mult(mult(b, mult(a, b)), c) = mult(b, mult(c, mult(a, b)))))))) <=> ((~((~(mult(mult(b, c), mult(a, b)) = mult(b, mult(mult(a, b), c)))) | (~(mult(mult(b, mult(a, b)), c) = mult(b, mult(c, mult(a, b))))))) | (~((~(mult(mult(b, c), mult(a, b)) = mult(mult(b, mult(a, b)), c))) | (~(mult(b, mult(c, mult(a, b))) = mult(b, mult(mult(a, b), c)))))))),
% 1.42/1.15 inference(rewrite,[status(thm)],[])).
% 1.42/1.15 tff(372,plain,
% 1.42/1.15 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(mult(b, c), mult(a, b)) = mult(mult(b, mult(a, b)), c))) | (~(mult(b, mult(c, mult(a, b))) = mult(b, mult(mult(a, b), c)))))) | (~((~(mult(mult(b, c), mult(a, b)) = mult(b, mult(mult(a, b), c)))) | (~(mult(mult(b, mult(a, b)), c) = mult(b, mult(c, mult(a, b))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(mult(b, c), mult(a, b)) = mult(b, mult(mult(a, b), c)))) | (~(mult(mult(b, mult(a, b)), c) = mult(b, mult(c, mult(a, b))))))) | (~((~(mult(mult(b, c), mult(a, b)) = mult(mult(b, mult(a, b)), c))) | (~(mult(b, mult(c, mult(a, b))) = mult(b, mult(mult(a, b), c))))))))),
% 1.42/1.15 inference(monotonicity,[status(thm)],[371])).
% 1.42/1.15 tff(373,plain,
% 1.42/1.15 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(mult(b, c), mult(a, b)) = mult(mult(b, mult(a, b)), c))) | (~(mult(b, mult(c, mult(a, b))) = mult(b, mult(mult(a, b), c)))))) | (~((~(mult(mult(b, c), mult(a, b)) = mult(b, mult(mult(a, b), c)))) | (~(mult(mult(b, mult(a, b)), c) = mult(b, mult(c, mult(a, b))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | (~((~(mult(mult(b, c), mult(a, b)) = mult(b, mult(mult(a, b), c)))) | (~(mult(mult(b, mult(a, b)), c) = mult(b, mult(c, mult(a, b))))))) | (~((~(mult(mult(b, c), mult(a, b)) = mult(mult(b, mult(a, b)), c))) | (~(mult(b, mult(c, mult(a, b))) = mult(b, mult(mult(a, b), c)))))))),
% 1.42/1.15 inference(transitivity,[status(thm)],[372, 370])).
% 1.42/1.15 tff(374,plain,
% 1.42/1.15 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(mult(b, c), mult(a, b)) = mult(mult(b, mult(a, b)), c))) | (~(mult(b, mult(c, mult(a, b))) = mult(b, mult(mult(a, b), c)))))) | (~((~(mult(mult(b, c), mult(a, b)) = mult(b, mult(mult(a, b), c)))) | (~(mult(mult(b, mult(a, b)), c) = mult(b, mult(c, mult(a, b))))))))),
% 1.42/1.15 inference(quant_inst,[status(thm)],[])).
% 1.42/1.15 tff(375,plain,
% 1.42/1.15 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | (~((~(mult(mult(b, c), mult(a, b)) = mult(b, mult(mult(a, b), c)))) | (~(mult(mult(b, mult(a, b)), c) = mult(b, mult(c, mult(a, b))))))) | (~((~(mult(mult(b, c), mult(a, b)) = mult(mult(b, mult(a, b)), c))) | (~(mult(b, mult(c, mult(a, b))) = mult(b, mult(mult(a, b), c))))))),
% 1.42/1.15 inference(modus_ponens,[status(thm)],[374, 373])).
% 1.42/1.15 tff(376,plain,
% 1.42/1.15 ((~((~(mult(mult(b, c), mult(a, b)) = mult(b, mult(mult(a, b), c)))) | (~(mult(mult(b, mult(a, b)), c) = mult(b, mult(c, mult(a, b))))))) | (~((~(mult(mult(b, c), mult(a, b)) = mult(mult(b, mult(a, b)), c))) | (~(mult(b, mult(c, mult(a, b))) = mult(b, mult(mult(a, b), c))))))),
% 1.42/1.15 inference(unit_resolution,[status(thm)],[375, 64])).
% 1.42/1.15 tff(377,plain,
% 1.42/1.15 (~((~(mult(mult(b, c), mult(a, b)) = mult(b, mult(mult(a, b), c)))) | (~(mult(mult(b, mult(a, b)), c) = mult(b, mult(c, mult(a, b))))))),
% 1.42/1.15 inference(unit_resolution,[status(thm)],[376, 369])).
% 1.42/1.15 tff(378,plain,
% 1.42/1.15 (((~(mult(mult(b, c), mult(a, b)) = mult(b, mult(mult(a, b), c)))) | (~(mult(mult(b, mult(a, b)), c) = mult(b, mult(c, mult(a, b)))))) | (mult(mult(b, mult(a, b)), c) = mult(b, mult(c, mult(a, b))))),
% 1.42/1.15 inference(tautology,[status(thm)],[])).
% 1.42/1.15 tff(379,plain,
% 1.42/1.15 (mult(mult(b, mult(a, b)), c) = mult(b, mult(c, mult(a, b)))),
% 1.42/1.15 inference(unit_resolution,[status(thm)],[378, 377])).
% 1.42/1.15 tff(380,plain,
% 1.42/1.15 (mult(b, mult(c, mult(a, b))) = mult(mult(b, mult(a, b)), c)),
% 1.42/1.15 inference(symmetry,[status(thm)],[379])).
% 1.42/1.15 tff(381,plain,
% 1.42/1.15 (mult(b, mult(c, mult(a, b))) = mult(b, mult(mult(a, b), c))),
% 1.42/1.15 inference(transitivity,[status(thm)],[380, 366, 363, 103])).
% 1.42/1.15 tff(382,plain,
% 1.42/1.15 ($false),
% 1.42/1.15 inference(unit_resolution,[status(thm)],[367, 381])).
% 1.42/1.15 tff(383,plain,(mult(b, mult(c, mult(a, b))) = mult(b, mult(mult(a, b), c))), inference(lemma,lemma(discharge,[]))).
% 1.42/1.15 tff(384,plain,
% 1.42/1.15 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(b, mult(b, mult(mult(a, b), c))) = mult(mult(a, b), c))),
% 1.42/1.15 inference(quant_inst,[status(thm)],[])).
% 1.42/1.15 tff(385,plain,
% 1.42/1.15 (ld(b, mult(b, mult(mult(a, b), c))) = mult(mult(a, b), c)),
% 1.42/1.15 inference(unit_resolution,[status(thm)],[384, 99])).
% 1.42/1.15 tff(386,assumption,(mult(b, mult(c, mult(a, b))) = mult(b, mult(mult(a, b), c))), introduced(assumption)).
% 1.42/1.15 tff(387,plain,
% 1.42/1.15 (ld(b, mult(b, mult(c, mult(a, b)))) = ld(b, mult(b, mult(mult(a, b), c)))),
% 1.42/1.15 inference(monotonicity,[status(thm)],[386])).
% 1.42/1.15 tff(388,plain,
% 1.42/1.15 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(b, mult(b, mult(c, mult(a, b)))) = mult(c, mult(a, b)))),
% 1.42/1.15 inference(quant_inst,[status(thm)],[])).
% 1.42/1.15 tff(389,plain,
% 1.42/1.15 (ld(b, mult(b, mult(c, mult(a, b)))) = mult(c, mult(a, b))),
% 1.42/1.15 inference(unit_resolution,[status(thm)],[388, 99])).
% 1.42/1.15 tff(390,plain,
% 1.42/1.15 (mult(c, mult(a, b)) = ld(b, mult(b, mult(c, mult(a, b))))),
% 1.42/1.15 inference(symmetry,[status(thm)],[389])).
% 1.42/1.15 tff(391,plain,
% 1.42/1.15 (mult(c, mult(a, b)) = mult(mult(a, b), c)),
% 1.42/1.15 inference(transitivity,[status(thm)],[390, 387, 385])).
% 1.42/1.15 tff(392,plain,
% 1.42/1.15 (mult(mult(b, mult(a, b)), mult(c, mult(a, b))) = mult(mult(b, mult(a, b)), mult(mult(a, b), c))),
% 1.42/1.15 inference(monotonicity,[status(thm)],[391])).
% 1.42/1.15 tff(393,plain,
% 1.42/1.15 (mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(mult(b, mult(a, b)), mult(c, mult(a, b)))),
% 1.42/1.15 inference(symmetry,[status(thm)],[392])).
% 1.42/1.15 tff(394,assumption,(~(mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(mult(b, mult(a, b)), mult(c, mult(a, b))))), introduced(assumption)).
% 1.42/1.15 tff(395,plain,
% 1.42/1.15 ($false),
% 1.42/1.15 inference(unit_resolution,[status(thm)],[394, 393])).
% 1.42/1.15 tff(396,plain,((~(mult(b, mult(c, mult(a, b))) = mult(b, mult(mult(a, b), c)))) | (mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(mult(b, mult(a, b)), mult(c, mult(a, b))))), inference(lemma,lemma(discharge,[]))).
% 1.42/1.15 tff(397,plain,
% 1.42/1.15 (mult(mult(b, mult(a, b)), mult(mult(a, b), c)) = mult(mult(b, mult(a, b)), mult(c, mult(a, b)))),
% 1.42/1.15 inference(unit_resolution,[status(thm)],[396, 383])).
% 1.42/1.15 tff(398,plain,
% 1.42/1.15 (mult(mult(b, mult(a, b)), mult(c, mult(a, b))) = mult(mult(b, mult(a, b)), mult(mult(a, b), c))),
% 1.42/1.15 inference(symmetry,[status(thm)],[397])).
% 1.42/1.15 tff(399,plain,
% 1.42/1.15 (ld(mult(b, mult(a, b)), mult(mult(b, mult(a, b)), mult(c, mult(a, b)))) = ld(mult(b, mult(a, b)), mult(mult(b, mult(a, b)), mult(mult(a, b), c)))),
% 1.42/1.15 inference(monotonicity,[status(thm)],[398])).
% 1.42/1.15 tff(400,plain,
% 1.42/1.15 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(b, mult(a, b)), mult(mult(b, mult(a, b)), mult(c, mult(a, b)))) = mult(c, mult(a, b)))),
% 1.42/1.15 inference(quant_inst,[status(thm)],[])).
% 1.42/1.15 tff(401,plain,
% 1.42/1.15 (ld(mult(b, mult(a, b)), mult(mult(b, mult(a, b)), mult(c, mult(a, b)))) = mult(c, mult(a, b))),
% 1.42/1.15 inference(unit_resolution,[status(thm)],[400, 99])).
% 1.42/1.15 tff(402,plain,
% 1.42/1.15 (mult(c, mult(a, b)) = ld(mult(b, mult(a, b)), mult(mult(b, mult(a, b)), mult(c, mult(a, b))))),
% 1.42/1.15 inference(symmetry,[status(thm)],[401])).
% 1.42/1.15 tff(403,plain,
% 1.42/1.15 (mult(c, mult(mult(b, c), rd(mult(a, b), mult(b, c)))) = mult(c, mult(a, b))),
% 1.42/1.15 inference(monotonicity,[status(thm)],[79])).
% 1.42/1.15 tff(404,plain,
% 1.42/1.15 (mult(c, mult(mult(b, c), rd(mult(a, b), mult(b, c)))) = mult(mult(unit, mult(b, c)), ld(mult(b, c), mult(mult(a, b), c)))),
% 1.42/1.15 inference(transitivity,[status(thm)],[403, 402, 399, 101, 92, 82])).
% 1.42/1.15 tff(405,plain,
% 1.42/1.15 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(b, c), mult(mult(b, c), mult(c, rd(mult(a, b), mult(b, c))))) = mult(c, rd(mult(a, b), mult(b, c))))),
% 1.42/1.15 inference(quant_inst,[status(thm)],[])).
% 1.42/1.15 tff(406,plain,
% 1.42/1.15 (ld(mult(b, c), mult(mult(b, c), mult(c, rd(mult(a, b), mult(b, c))))) = mult(c, rd(mult(a, b), mult(b, c)))),
% 1.42/1.15 inference(unit_resolution,[status(thm)],[405, 99])).
% 1.42/1.15 tff(407,assumption,(~(mult(mult(mult(b, c), c), rd(mult(a, b), mult(b, c))) = mult(mult(mult(b, c), rd(mult(a, b), mult(b, c))), c))), introduced(assumption)).
% 1.42/1.15 tff(408,plain,
% 1.42/1.15 (((~(mult(mult(mult(b, c), c), rd(mult(a, b), mult(b, c))) = mult(mult(mult(b, c), rd(mult(a, b), mult(b, c))), c))) | (~(mult(mult(b, c), mult(c, rd(mult(a, b), mult(b, c)))) = mult(mult(b, c), mult(rd(mult(a, b), mult(b, c)), c))))) | (mult(mult(mult(b, c), c), rd(mult(a, b), mult(b, c))) = mult(mult(mult(b, c), rd(mult(a, b), mult(b, c))), c))),
% 1.42/1.15 inference(tautology,[status(thm)],[])).
% 1.42/1.15 tff(409,plain,
% 1.42/1.15 ((~(mult(mult(mult(b, c), c), rd(mult(a, b), mult(b, c))) = mult(mult(mult(b, c), rd(mult(a, b), mult(b, c))), c))) | (~(mult(mult(b, c), mult(c, rd(mult(a, b), mult(b, c)))) = mult(mult(b, c), mult(rd(mult(a, b), mult(b, c)), c))))),
% 1.42/1.15 inference(unit_resolution,[status(thm)],[408, 407])).
% 1.42/1.15 tff(410,plain,
% 1.42/1.15 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(mult(mult(b, c), c), rd(mult(a, b), mult(b, c))) = mult(mult(mult(b, c), rd(mult(a, b), mult(b, c))), c))) | (~(mult(mult(b, c), mult(c, rd(mult(a, b), mult(b, c)))) = mult(mult(b, c), mult(rd(mult(a, b), mult(b, c)), c)))))) | (~((~(mult(mult(mult(b, c), c), rd(mult(a, b), mult(b, c))) = mult(mult(b, c), mult(rd(mult(a, b), mult(b, c)), c)))) | (~(mult(mult(mult(b, c), rd(mult(a, b), mult(b, c))), c) = mult(mult(b, c), mult(c, rd(mult(a, b), mult(b, c)))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | (~((~(mult(mult(mult(b, c), c), rd(mult(a, b), mult(b, c))) = mult(mult(mult(b, c), rd(mult(a, b), mult(b, c))), c))) | (~(mult(mult(b, c), mult(c, rd(mult(a, b), mult(b, c)))) = mult(mult(b, c), mult(rd(mult(a, b), mult(b, c)), c)))))) | (~((~(mult(mult(mult(b, c), c), rd(mult(a, b), mult(b, c))) = mult(mult(b, c), mult(rd(mult(a, b), mult(b, c)), c)))) | (~(mult(mult(mult(b, c), rd(mult(a, b), mult(b, c))), c) = mult(mult(b, c), mult(c, rd(mult(a, b), mult(b, c)))))))))),
% 1.42/1.15 inference(rewrite,[status(thm)],[])).
% 1.42/1.15 tff(411,plain,
% 1.42/1.15 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(mult(mult(b, c), c), rd(mult(a, b), mult(b, c))) = mult(mult(mult(b, c), rd(mult(a, b), mult(b, c))), c))) | (~(mult(mult(b, c), mult(c, rd(mult(a, b), mult(b, c)))) = mult(mult(b, c), mult(rd(mult(a, b), mult(b, c)), c)))))) | (~((~(mult(mult(mult(b, c), c), rd(mult(a, b), mult(b, c))) = mult(mult(b, c), mult(rd(mult(a, b), mult(b, c)), c)))) | (~(mult(mult(mult(b, c), rd(mult(a, b), mult(b, c))), c) = mult(mult(b, c), mult(c, rd(mult(a, b), mult(b, c)))))))))),
% 1.42/1.16 inference(quant_inst,[status(thm)],[])).
% 1.42/1.16 tff(412,plain,
% 1.42/1.16 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | (~((~(mult(mult(mult(b, c), c), rd(mult(a, b), mult(b, c))) = mult(mult(mult(b, c), rd(mult(a, b), mult(b, c))), c))) | (~(mult(mult(b, c), mult(c, rd(mult(a, b), mult(b, c)))) = mult(mult(b, c), mult(rd(mult(a, b), mult(b, c)), c)))))) | (~((~(mult(mult(mult(b, c), c), rd(mult(a, b), mult(b, c))) = mult(mult(b, c), mult(rd(mult(a, b), mult(b, c)), c)))) | (~(mult(mult(mult(b, c), rd(mult(a, b), mult(b, c))), c) = mult(mult(b, c), mult(c, rd(mult(a, b), mult(b, c))))))))),
% 1.42/1.16 inference(modus_ponens,[status(thm)],[411, 410])).
% 1.42/1.16 tff(413,plain,
% 1.42/1.16 ((~((~(mult(mult(mult(b, c), c), rd(mult(a, b), mult(b, c))) = mult(mult(mult(b, c), rd(mult(a, b), mult(b, c))), c))) | (~(mult(mult(b, c), mult(c, rd(mult(a, b), mult(b, c)))) = mult(mult(b, c), mult(rd(mult(a, b), mult(b, c)), c)))))) | (~((~(mult(mult(mult(b, c), c), rd(mult(a, b), mult(b, c))) = mult(mult(b, c), mult(rd(mult(a, b), mult(b, c)), c)))) | (~(mult(mult(mult(b, c), rd(mult(a, b), mult(b, c))), c) = mult(mult(b, c), mult(c, rd(mult(a, b), mult(b, c))))))))),
% 1.42/1.16 inference(unit_resolution,[status(thm)],[412, 64])).
% 1.42/1.16 tff(414,plain,
% 1.42/1.16 (~((~(mult(mult(mult(b, c), c), rd(mult(a, b), mult(b, c))) = mult(mult(b, c), mult(rd(mult(a, b), mult(b, c)), c)))) | (~(mult(mult(mult(b, c), rd(mult(a, b), mult(b, c))), c) = mult(mult(b, c), mult(c, rd(mult(a, b), mult(b, c)))))))),
% 1.42/1.16 inference(unit_resolution,[status(thm)],[413, 409])).
% 1.42/1.16 tff(415,plain,
% 1.42/1.16 (((~(mult(mult(mult(b, c), c), rd(mult(a, b), mult(b, c))) = mult(mult(b, c), mult(rd(mult(a, b), mult(b, c)), c)))) | (~(mult(mult(mult(b, c), rd(mult(a, b), mult(b, c))), c) = mult(mult(b, c), mult(c, rd(mult(a, b), mult(b, c))))))) | (mult(mult(mult(b, c), rd(mult(a, b), mult(b, c))), c) = mult(mult(b, c), mult(c, rd(mult(a, b), mult(b, c)))))),
% 1.42/1.16 inference(tautology,[status(thm)],[])).
% 1.42/1.16 tff(416,plain,
% 1.42/1.16 (mult(mult(mult(b, c), rd(mult(a, b), mult(b, c))), c) = mult(mult(b, c), mult(c, rd(mult(a, b), mult(b, c))))),
% 1.42/1.16 inference(unit_resolution,[status(thm)],[415, 414])).
% 1.42/1.16 tff(417,plain,
% 1.42/1.16 (mult(mult(b, c), mult(c, rd(mult(a, b), mult(b, c)))) = mult(mult(mult(b, c), rd(mult(a, b), mult(b, c))), c)),
% 1.42/1.16 inference(symmetry,[status(thm)],[416])).
% 1.42/1.16 tff(418,plain,
% 1.42/1.16 (mult(mult(b, c), mult(c, rd(mult(a, b), mult(b, c)))) = mult(mult(a, b), c)),
% 1.42/1.16 inference(transitivity,[status(thm)],[417, 80])).
% 1.42/1.16 tff(419,plain,
% 1.42/1.16 (ld(mult(b, c), mult(mult(b, c), mult(c, rd(mult(a, b), mult(b, c))))) = ld(mult(b, c), mult(mult(a, b), c))),
% 1.42/1.16 inference(monotonicity,[status(thm)],[418])).
% 1.42/1.16 tff(420,plain,
% 1.42/1.16 (ld(mult(b, c), mult(mult(a, b), c)) = ld(mult(b, c), mult(mult(b, c), mult(c, rd(mult(a, b), mult(b, c)))))),
% 1.42/1.16 inference(symmetry,[status(thm)],[419])).
% 1.42/1.16 tff(421,plain,
% 1.42/1.16 ((~![A: $i] : (mult(unit, A) = A)) | (mult(unit, ld(mult(b, c), mult(mult(a, b), c))) = ld(mult(b, c), mult(mult(a, b), c)))),
% 1.42/1.16 inference(quant_inst,[status(thm)],[])).
% 1.42/1.16 tff(422,plain,
% 1.42/1.16 (mult(unit, ld(mult(b, c), mult(mult(a, b), c))) = ld(mult(b, c), mult(mult(a, b), c))),
% 1.42/1.16 inference(unit_resolution,[status(thm)],[421, 26])).
% 1.42/1.16 tff(423,plain,
% 1.42/1.16 (mult(unit, ld(mult(b, c), mult(mult(a, b), c))) = mult(c, rd(mult(a, b), mult(b, c)))),
% 1.42/1.16 inference(transitivity,[status(thm)],[422, 420, 406])).
% 1.42/1.16 tff(424,plain,
% 1.42/1.16 (mult(mult(unit, ld(mult(b, c), mult(mult(a, b), c))), mult(b, c)) = mult(mult(c, rd(mult(a, b), mult(b, c))), mult(b, c))),
% 1.42/1.16 inference(monotonicity,[status(thm)],[423])).
% 1.42/1.16 tff(425,plain,
% 1.42/1.16 (mult(mult(c, rd(mult(a, b), mult(b, c))), mult(b, c)) = mult(mult(unit, ld(mult(b, c), mult(mult(a, b), c))), mult(b, c))),
% 1.42/1.16 inference(symmetry,[status(thm)],[424])).
% 1.42/1.16 tff(426,plain,
% 1.42/1.16 ((mult(mult(c, rd(mult(a, b), mult(b, c))), mult(b, c)) = mult(c, mult(mult(b, c), rd(mult(a, b), mult(b, c))))) <=> (mult(mult(unit, ld(mult(b, c), mult(mult(a, b), c))), mult(b, c)) = mult(mult(unit, mult(b, c)), ld(mult(b, c), mult(mult(a, b), c))))),
% 1.42/1.16 inference(monotonicity,[status(thm)],[425, 404])).
% 1.42/1.16 tff(427,plain,
% 1.42/1.16 ((~(mult(mult(c, rd(mult(a, b), mult(b, c))), mult(b, c)) = mult(c, mult(mult(b, c), rd(mult(a, b), mult(b, c)))))) <=> (~(mult(mult(unit, ld(mult(b, c), mult(mult(a, b), c))), mult(b, c)) = mult(mult(unit, mult(b, c)), ld(mult(b, c), mult(mult(a, b), c)))))),
% 1.42/1.16 inference(monotonicity,[status(thm)],[426])).
% 1.42/1.16 tff(428,plain,
% 1.42/1.16 (mult(c, mult(a, b)) = mult(c, mult(mult(b, c), rd(mult(a, b), mult(b, c))))),
% 1.42/1.16 inference(symmetry,[status(thm)],[403])).
% 1.42/1.16 tff(429,plain,
% 1.42/1.16 (mult(c, mult(rd(mult(a, b), mult(b, c)), mult(b, c))) = mult(c, mult(a, b))),
% 1.42/1.16 inference(monotonicity,[status(thm)],[9])).
% 1.42/1.16 tff(430,plain,
% 1.42/1.16 (mult(c, mult(rd(mult(a, b), mult(b, c)), mult(b, c))) = mult(c, mult(mult(b, c), rd(mult(a, b), mult(b, c))))),
% 1.42/1.16 inference(transitivity,[status(thm)],[429, 428])).
% 1.42/1.16 tff(431,plain,
% 1.42/1.16 (mult(c, mult(a, b)) = mult(c, mult(rd(mult(a, b), mult(b, c)), mult(b, c)))),
% 1.42/1.16 inference(symmetry,[status(thm)],[429])).
% 1.42/1.16 tff(432,plain,
% 1.42/1.16 (ld(mult(b, mult(a, b)), mult(mult(b, mult(a, b)), mult(mult(a, b), c))) = ld(mult(b, mult(a, b)), mult(mult(b, mult(a, b)), mult(c, mult(a, b))))),
% 1.42/1.16 inference(symmetry,[status(thm)],[399])).
% 1.42/1.16 tff(433,plain,
% 1.42/1.16 (mult(mult(a, b), c) = ld(mult(b, mult(a, b)), mult(mult(b, mult(a, b)), mult(mult(a, b), c)))),
% 1.42/1.16 inference(symmetry,[status(thm)],[101])).
% 1.42/1.16 tff(434,plain,
% 1.42/1.16 (mult(mult(mult(b, c), rd(mult(a, b), mult(b, c))), c) = mult(c, mult(rd(mult(a, b), mult(b, c)), mult(b, c)))),
% 1.42/1.16 inference(transitivity,[status(thm)],[80, 433, 432, 401, 431])).
% 1.42/1.16 tff(435,plain,
% 1.42/1.16 ((~![A: $i] : (mult(unit, A) = A)) | (mult(unit, mult(c, mult(b, c))) = mult(c, mult(b, c)))),
% 1.42/1.16 inference(quant_inst,[status(thm)],[])).
% 1.42/1.16 tff(436,plain,
% 1.42/1.16 (mult(unit, mult(c, mult(b, c))) = mult(c, mult(b, c))),
% 1.42/1.16 inference(unit_resolution,[status(thm)],[435, 26])).
% 1.42/1.16 tff(437,plain,
% 1.42/1.16 (mult(mult(unit, mult(b, c)), c) = mult(mult(b, c), c)),
% 1.42/1.16 inference(monotonicity,[status(thm)],[76])).
% 1.42/1.16 tff(438,plain,
% 1.42/1.16 (mult(mult(b, c), c) = mult(mult(unit, mult(b, c)), c)),
% 1.42/1.16 inference(symmetry,[status(thm)],[437])).
% 1.42/1.16 tff(439,plain,
% 1.42/1.16 (mult(mult(unit, b), c) = mult(b, c)),
% 1.42/1.16 inference(monotonicity,[status(thm)],[163])).
% 1.42/1.16 tff(440,assumption,(~(mult(mult(unit, c), b) = mult(unit, mult(b, c)))), introduced(assumption)).
% 1.42/1.16 tff(441,plain,
% 1.42/1.16 (((~(mult(mult(unit, b), c) = mult(unit, mult(c, b)))) | (~(mult(mult(unit, c), b) = mult(unit, mult(b, c))))) | (mult(mult(unit, c), b) = mult(unit, mult(b, c)))),
% 1.42/1.16 inference(tautology,[status(thm)],[])).
% 1.42/1.16 tff(442,plain,
% 1.42/1.16 ((~(mult(mult(unit, b), c) = mult(unit, mult(c, b)))) | (~(mult(mult(unit, c), b) = mult(unit, mult(b, c))))),
% 1.42/1.16 inference(unit_resolution,[status(thm)],[441, 440])).
% 1.42/1.16 tff(443,plain,
% 1.42/1.16 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(unit, mult(c, b)) = mult(unit, mult(b, c)))) | (~(mult(mult(unit, c), b) = mult(mult(unit, b), c))))) | (~((~(mult(mult(unit, b), c) = mult(unit, mult(c, b)))) | (~(mult(mult(unit, c), b) = mult(unit, mult(b, c)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | (~((~(mult(unit, mult(c, b)) = mult(unit, mult(b, c)))) | (~(mult(mult(unit, c), b) = mult(mult(unit, b), c))))) | (~((~(mult(mult(unit, b), c) = mult(unit, mult(c, b)))) | (~(mult(mult(unit, c), b) = mult(unit, mult(b, c)))))))),
% 1.42/1.16 inference(rewrite,[status(thm)],[])).
% 1.42/1.16 tff(444,plain,
% 1.42/1.16 (((~((~(mult(mult(unit, c), b) = mult(mult(unit, b), c))) | (~(mult(unit, mult(c, b)) = mult(unit, mult(b, c)))))) | (~((~(mult(mult(unit, c), b) = mult(unit, mult(b, c)))) | (~(mult(mult(unit, b), c) = mult(unit, mult(c, b))))))) <=> ((~((~(mult(unit, mult(c, b)) = mult(unit, mult(b, c)))) | (~(mult(mult(unit, c), b) = mult(mult(unit, b), c))))) | (~((~(mult(mult(unit, b), c) = mult(unit, mult(c, b)))) | (~(mult(mult(unit, c), b) = mult(unit, mult(b, c)))))))),
% 1.42/1.16 inference(rewrite,[status(thm)],[])).
% 1.42/1.16 tff(445,plain,
% 1.42/1.16 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(mult(unit, c), b) = mult(mult(unit, b), c))) | (~(mult(unit, mult(c, b)) = mult(unit, mult(b, c)))))) | (~((~(mult(mult(unit, c), b) = mult(unit, mult(b, c)))) | (~(mult(mult(unit, b), c) = mult(unit, mult(c, b)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(unit, mult(c, b)) = mult(unit, mult(b, c)))) | (~(mult(mult(unit, c), b) = mult(mult(unit, b), c))))) | (~((~(mult(mult(unit, b), c) = mult(unit, mult(c, b)))) | (~(mult(mult(unit, c), b) = mult(unit, mult(b, c))))))))),
% 1.42/1.16 inference(monotonicity,[status(thm)],[444])).
% 1.42/1.16 tff(446,plain,
% 1.42/1.16 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(mult(unit, c), b) = mult(mult(unit, b), c))) | (~(mult(unit, mult(c, b)) = mult(unit, mult(b, c)))))) | (~((~(mult(mult(unit, c), b) = mult(unit, mult(b, c)))) | (~(mult(mult(unit, b), c) = mult(unit, mult(c, b)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | (~((~(mult(unit, mult(c, b)) = mult(unit, mult(b, c)))) | (~(mult(mult(unit, c), b) = mult(mult(unit, b), c))))) | (~((~(mult(mult(unit, b), c) = mult(unit, mult(c, b)))) | (~(mult(mult(unit, c), b) = mult(unit, mult(b, c)))))))),
% 1.42/1.16 inference(transitivity,[status(thm)],[445, 443])).
% 1.42/1.16 tff(447,plain,
% 1.42/1.16 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(mult(unit, c), b) = mult(mult(unit, b), c))) | (~(mult(unit, mult(c, b)) = mult(unit, mult(b, c)))))) | (~((~(mult(mult(unit, c), b) = mult(unit, mult(b, c)))) | (~(mult(mult(unit, b), c) = mult(unit, mult(c, b)))))))),
% 1.42/1.16 inference(quant_inst,[status(thm)],[])).
% 1.42/1.16 tff(448,plain,
% 1.42/1.16 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | (~((~(mult(unit, mult(c, b)) = mult(unit, mult(b, c)))) | (~(mult(mult(unit, c), b) = mult(mult(unit, b), c))))) | (~((~(mult(mult(unit, b), c) = mult(unit, mult(c, b)))) | (~(mult(mult(unit, c), b) = mult(unit, mult(b, c))))))),
% 1.42/1.16 inference(modus_ponens,[status(thm)],[447, 446])).
% 1.42/1.16 tff(449,plain,
% 1.42/1.16 ((~((~(mult(unit, mult(c, b)) = mult(unit, mult(b, c)))) | (~(mult(mult(unit, c), b) = mult(mult(unit, b), c))))) | (~((~(mult(mult(unit, b), c) = mult(unit, mult(c, b)))) | (~(mult(mult(unit, c), b) = mult(unit, mult(b, c))))))),
% 1.42/1.16 inference(unit_resolution,[status(thm)],[448, 64])).
% 1.42/1.16 tff(450,plain,
% 1.42/1.16 (~((~(mult(unit, mult(c, b)) = mult(unit, mult(b, c)))) | (~(mult(mult(unit, c), b) = mult(mult(unit, b), c))))),
% 1.42/1.16 inference(unit_resolution,[status(thm)],[449, 442])).
% 1.42/1.16 tff(451,plain,
% 1.42/1.16 (((~(mult(unit, mult(c, b)) = mult(unit, mult(b, c)))) | (~(mult(mult(unit, c), b) = mult(mult(unit, b), c)))) | (mult(mult(unit, c), b) = mult(mult(unit, b), c))),
% 1.42/1.16 inference(tautology,[status(thm)],[])).
% 1.42/1.16 tff(452,plain,
% 1.42/1.16 (mult(mult(unit, c), b) = mult(mult(unit, b), c)),
% 1.42/1.16 inference(unit_resolution,[status(thm)],[451, 450])).
% 1.42/1.16 tff(453,plain,
% 1.42/1.16 (mult(mult(unit, c), b) = mult(unit, mult(b, c))),
% 1.42/1.16 inference(transitivity,[status(thm)],[452, 439, 77])).
% 1.42/1.16 tff(454,plain,
% 1.42/1.16 ($false),
% 1.42/1.16 inference(unit_resolution,[status(thm)],[440, 453])).
% 1.42/1.16 tff(455,plain,(mult(mult(unit, c), b) = mult(unit, mult(b, c))), inference(lemma,lemma(discharge,[]))).
% 1.42/1.16 tff(456,plain,
% 1.42/1.16 (mult(mult(unit, c), b) = mult(b, c)),
% 1.42/1.16 inference(transitivity,[status(thm)],[455, 76])).
% 1.42/1.16 tff(457,plain,
% 1.42/1.16 (mult(mult(mult(unit, c), b), c) = mult(mult(b, c), c)),
% 1.42/1.16 inference(monotonicity,[status(thm)],[456])).
% 1.42/1.16 tff(458,plain,
% 1.42/1.16 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(unit, c), b), c) = mult(unit, mult(mult(c, b), c)))),
% 1.42/1.16 inference(quant_inst,[status(thm)],[])).
% 1.42/1.16 tff(459,plain,
% 1.42/1.16 (mult(mult(mult(unit, c), b), c) = mult(unit, mult(mult(c, b), c))),
% 1.42/1.16 inference(unit_resolution,[status(thm)],[458, 124])).
% 1.42/1.16 tff(460,plain,
% 1.42/1.16 (mult(unit, mult(mult(c, b), c)) = mult(mult(mult(unit, c), b), c)),
% 1.42/1.16 inference(symmetry,[status(thm)],[459])).
% 1.42/1.16 tff(461,plain,
% 1.42/1.16 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(rd(mult(a, b), mult(b, c)), mult(rd(mult(a, b), mult(b, c)), mult(b, c))) = mult(b, c))),
% 1.42/1.16 inference(quant_inst,[status(thm)],[])).
% 1.42/1.16 tff(462,plain,
% 1.42/1.16 (ld(rd(mult(a, b), mult(b, c)), mult(rd(mult(a, b), mult(b, c)), mult(b, c))) = mult(b, c)),
% 1.42/1.16 inference(unit_resolution,[status(thm)],[461, 99])).
% 1.42/1.16 tff(463,plain,
% 1.42/1.16 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(rd(mult(a, b), mult(b, c)), c), b), b) = mult(rd(mult(a, b), mult(b, c)), c))),
% 1.42/1.16 inference(quant_inst,[status(thm)],[])).
% 1.42/1.16 tff(464,plain,
% 1.42/1.16 (rd(mult(mult(rd(mult(a, b), mult(b, c)), c), b), b) = mult(rd(mult(a, b), mult(b, c)), c)),
% 1.42/1.16 inference(unit_resolution,[status(thm)],[463, 17])).
% 1.42/1.16 tff(465,assumption,(mult(mult(rd(mult(a, b), mult(b, c)), c), b) = mult(rd(mult(a, b), mult(b, c)), mult(b, c))), introduced(assumption)).
% 1.42/1.16 tff(466,plain,
% 1.42/1.16 (mult(mult(rd(mult(a, b), mult(b, c)), c), b) = mult(a, b)),
% 1.42/1.16 inference(transitivity,[status(thm)],[465, 9])).
% 1.42/1.16 tff(467,plain,
% 1.42/1.16 (rd(mult(mult(rd(mult(a, b), mult(b, c)), c), b), b) = rd(mult(a, b), b)),
% 1.42/1.16 inference(monotonicity,[status(thm)],[466])).
% 1.42/1.16 tff(468,plain,
% 1.42/1.16 (rd(mult(a, b), b) = rd(mult(mult(rd(mult(a, b), mult(b, c)), c), b), b)),
% 1.42/1.16 inference(symmetry,[status(thm)],[467])).
% 1.42/1.16 tff(469,plain,
% 1.42/1.16 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(a, b), b) = a)),
% 1.42/1.16 inference(quant_inst,[status(thm)],[])).
% 1.42/1.16 tff(470,plain,
% 1.42/1.16 (rd(mult(a, b), b) = a),
% 1.42/1.16 inference(unit_resolution,[status(thm)],[469, 17])).
% 1.42/1.16 tff(471,plain,
% 1.42/1.16 (a = rd(mult(a, b), b)),
% 1.42/1.16 inference(symmetry,[status(thm)],[470])).
% 1.42/1.16 tff(472,plain,
% 1.42/1.16 (a = mult(rd(mult(a, b), mult(b, c)), c)),
% 1.42/1.16 inference(transitivity,[status(thm)],[471, 468, 464])).
% 1.42/1.16 tff(473,plain,
% 1.42/1.16 (mult(a, mult(b, c)) = mult(mult(rd(mult(a, b), mult(b, c)), c), mult(b, c))),
% 1.42/1.16 inference(monotonicity,[status(thm)],[472])).
% 1.42/1.16 tff(474,plain,
% 1.42/1.16 (mult(mult(rd(mult(a, b), mult(b, c)), c), mult(b, c)) = mult(a, mult(b, c))),
% 1.42/1.16 inference(symmetry,[status(thm)],[473])).
% 1.42/1.16 tff(475,plain,
% 1.42/1.16 ((mult(mult(rd(mult(a, b), mult(b, c)), mult(b, c)), c) = mult(mult(rd(mult(a, b), mult(b, c)), c), mult(b, c))) <=> (mult(mult(rd(mult(a, b), mult(b, c)), c), mult(b, c)) = mult(mult(rd(mult(a, b), mult(b, c)), mult(b, c)), c))),
% 1.42/1.17 inference(commutativity,[status(thm)],[])).
% 1.42/1.17 tff(476,plain,
% 1.42/1.17 (mult(mult(rd(mult(a, b), mult(b, c)), mult(b, c)), c) = mult(mult(a, b), c)),
% 1.42/1.17 inference(monotonicity,[status(thm)],[9])).
% 1.42/1.17 tff(477,plain,
% 1.42/1.17 (mult(mult(a, b), c) = mult(mult(rd(mult(a, b), mult(b, c)), mult(b, c)), c)),
% 1.42/1.17 inference(symmetry,[status(thm)],[476])).
% 1.42/1.17 tff(478,plain,
% 1.42/1.17 ((mult(mult(a, b), c) = mult(a, mult(b, c))) <=> (mult(mult(rd(mult(a, b), mult(b, c)), mult(b, c)), c) = mult(mult(rd(mult(a, b), mult(b, c)), c), mult(b, c)))),
% 1.42/1.17 inference(monotonicity,[status(thm)],[477, 473])).
% 1.42/1.17 tff(479,plain,
% 1.42/1.17 ((mult(mult(a, b), c) = mult(a, mult(b, c))) <=> (mult(mult(rd(mult(a, b), mult(b, c)), c), mult(b, c)) = mult(mult(rd(mult(a, b), mult(b, c)), mult(b, c)), c))),
% 1.42/1.17 inference(transitivity,[status(thm)],[478, 475])).
% 1.42/1.17 tff(480,plain,
% 1.42/1.17 ((~(mult(mult(a, b), c) = mult(a, mult(b, c)))) <=> (~(mult(mult(rd(mult(a, b), mult(b, c)), c), mult(b, c)) = mult(mult(rd(mult(a, b), mult(b, c)), mult(b, c)), c)))),
% 1.42/1.17 inference(monotonicity,[status(thm)],[479])).
% 1.42/1.17 tff(481,plain,
% 1.42/1.17 ((~(mult(mult(a, b), c) = mult(a, mult(b, c)))) <=> (~(mult(mult(a, b), c) = mult(a, mult(b, c))))),
% 1.42/1.17 inference(rewrite,[status(thm)],[])).
% 1.42/1.17 tff(482,axiom,(~(mult(mult(a, b), c) = mult(a, mult(b, c)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','goals')).
% 1.42/1.17 tff(483,plain,
% 1.42/1.17 (~(mult(mult(a, b), c) = mult(a, mult(b, c)))),
% 1.42/1.17 inference(modus_ponens,[status(thm)],[482, 481])).
% 1.42/1.17 tff(484,plain,
% 1.42/1.17 (~(mult(mult(rd(mult(a, b), mult(b, c)), c), mult(b, c)) = mult(mult(rd(mult(a, b), mult(b, c)), mult(b, c)), c))),
% 1.42/1.17 inference(modus_ponens,[status(thm)],[483, 480])).
% 1.42/1.17 tff(485,plain,
% 1.42/1.17 (((~(mult(rd(mult(a, b), mult(b, c)), mult(c, mult(b, c))) = mult(rd(mult(a, b), mult(b, c)), mult(mult(b, c), c)))) | (~(mult(mult(rd(mult(a, b), mult(b, c)), c), mult(b, c)) = mult(mult(rd(mult(a, b), mult(b, c)), mult(b, c)), c)))) | (mult(mult(rd(mult(a, b), mult(b, c)), c), mult(b, c)) = mult(mult(rd(mult(a, b), mult(b, c)), mult(b, c)), c))),
% 1.42/1.17 inference(tautology,[status(thm)],[])).
% 1.42/1.17 tff(486,plain,
% 1.42/1.17 ((~(mult(rd(mult(a, b), mult(b, c)), mult(c, mult(b, c))) = mult(rd(mult(a, b), mult(b, c)), mult(mult(b, c), c)))) | (~(mult(mult(rd(mult(a, b), mult(b, c)), c), mult(b, c)) = mult(mult(rd(mult(a, b), mult(b, c)), mult(b, c)), c)))),
% 1.42/1.17 inference(unit_resolution,[status(thm)],[485, 484])).
% 1.42/1.17 tff(487,plain,
% 1.42/1.17 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(rd(mult(a, b), mult(b, c)), mult(c, mult(b, c))) = mult(rd(mult(a, b), mult(b, c)), mult(mult(b, c), c)))) | (~(mult(mult(rd(mult(a, b), mult(b, c)), c), mult(b, c)) = mult(mult(rd(mult(a, b), mult(b, c)), mult(b, c)), c))))) | (~((~(mult(mult(rd(mult(a, b), mult(b, c)), c), mult(b, c)) = mult(rd(mult(a, b), mult(b, c)), mult(mult(b, c), c)))) | (~(mult(mult(rd(mult(a, b), mult(b, c)), mult(b, c)), c) = mult(rd(mult(a, b), mult(b, c)), mult(c, mult(b, c))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | (~((~(mult(rd(mult(a, b), mult(b, c)), mult(c, mult(b, c))) = mult(rd(mult(a, b), mult(b, c)), mult(mult(b, c), c)))) | (~(mult(mult(rd(mult(a, b), mult(b, c)), c), mult(b, c)) = mult(mult(rd(mult(a, b), mult(b, c)), mult(b, c)), c))))) | (~((~(mult(mult(rd(mult(a, b), mult(b, c)), c), mult(b, c)) = mult(rd(mult(a, b), mult(b, c)), mult(mult(b, c), c)))) | (~(mult(mult(rd(mult(a, b), mult(b, c)), mult(b, c)), c) = mult(rd(mult(a, b), mult(b, c)), mult(c, mult(b, c))))))))),
% 1.42/1.17 inference(rewrite,[status(thm)],[])).
% 1.42/1.17 tff(488,plain,
% 1.42/1.17 (((~((~(mult(mult(rd(mult(a, b), mult(b, c)), c), mult(b, c)) = mult(mult(rd(mult(a, b), mult(b, c)), mult(b, c)), c))) | (~(mult(rd(mult(a, b), mult(b, c)), mult(c, mult(b, c))) = mult(rd(mult(a, b), mult(b, c)), mult(mult(b, c), c)))))) | (~((~(mult(mult(rd(mult(a, b), mult(b, c)), c), mult(b, c)) = mult(rd(mult(a, b), mult(b, c)), mult(mult(b, c), c)))) | (~(mult(mult(rd(mult(a, b), mult(b, c)), mult(b, c)), c) = mult(rd(mult(a, b), mult(b, c)), mult(c, mult(b, c)))))))) <=> ((~((~(mult(rd(mult(a, b), mult(b, c)), mult(c, mult(b, c))) = mult(rd(mult(a, b), mult(b, c)), mult(mult(b, c), c)))) | (~(mult(mult(rd(mult(a, b), mult(b, c)), c), mult(b, c)) = mult(mult(rd(mult(a, b), mult(b, c)), mult(b, c)), c))))) | (~((~(mult(mult(rd(mult(a, b), mult(b, c)), c), mult(b, c)) = mult(rd(mult(a, b), mult(b, c)), mult(mult(b, c), c)))) | (~(mult(mult(rd(mult(a, b), mult(b, c)), mult(b, c)), c) = mult(rd(mult(a, b), mult(b, c)), mult(c, mult(b, c))))))))),
% 1.42/1.17 inference(rewrite,[status(thm)],[])).
% 1.42/1.17 tff(489,plain,
% 1.42/1.17 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(mult(rd(mult(a, b), mult(b, c)), c), mult(b, c)) = mult(mult(rd(mult(a, b), mult(b, c)), mult(b, c)), c))) | (~(mult(rd(mult(a, b), mult(b, c)), mult(c, mult(b, c))) = mult(rd(mult(a, b), mult(b, c)), mult(mult(b, c), c)))))) | (~((~(mult(mult(rd(mult(a, b), mult(b, c)), c), mult(b, c)) = mult(rd(mult(a, b), mult(b, c)), mult(mult(b, c), c)))) | (~(mult(mult(rd(mult(a, b), mult(b, c)), mult(b, c)), c) = mult(rd(mult(a, b), mult(b, c)), mult(c, mult(b, c))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(rd(mult(a, b), mult(b, c)), mult(c, mult(b, c))) = mult(rd(mult(a, b), mult(b, c)), mult(mult(b, c), c)))) | (~(mult(mult(rd(mult(a, b), mult(b, c)), c), mult(b, c)) = mult(mult(rd(mult(a, b), mult(b, c)), mult(b, c)), c))))) | (~((~(mult(mult(rd(mult(a, b), mult(b, c)), c), mult(b, c)) = mult(rd(mult(a, b), mult(b, c)), mult(mult(b, c), c)))) | (~(mult(mult(rd(mult(a, b), mult(b, c)), mult(b, c)), c) = mult(rd(mult(a, b), mult(b, c)), mult(c, mult(b, c)))))))))),
% 1.42/1.17 inference(monotonicity,[status(thm)],[488])).
% 1.42/1.17 tff(490,plain,
% 1.42/1.17 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(mult(rd(mult(a, b), mult(b, c)), c), mult(b, c)) = mult(mult(rd(mult(a, b), mult(b, c)), mult(b, c)), c))) | (~(mult(rd(mult(a, b), mult(b, c)), mult(c, mult(b, c))) = mult(rd(mult(a, b), mult(b, c)), mult(mult(b, c), c)))))) | (~((~(mult(mult(rd(mult(a, b), mult(b, c)), c), mult(b, c)) = mult(rd(mult(a, b), mult(b, c)), mult(mult(b, c), c)))) | (~(mult(mult(rd(mult(a, b), mult(b, c)), mult(b, c)), c) = mult(rd(mult(a, b), mult(b, c)), mult(c, mult(b, c))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | (~((~(mult(rd(mult(a, b), mult(b, c)), mult(c, mult(b, c))) = mult(rd(mult(a, b), mult(b, c)), mult(mult(b, c), c)))) | (~(mult(mult(rd(mult(a, b), mult(b, c)), c), mult(b, c)) = mult(mult(rd(mult(a, b), mult(b, c)), mult(b, c)), c))))) | (~((~(mult(mult(rd(mult(a, b), mult(b, c)), c), mult(b, c)) = mult(rd(mult(a, b), mult(b, c)), mult(mult(b, c), c)))) | (~(mult(mult(rd(mult(a, b), mult(b, c)), mult(b, c)), c) = mult(rd(mult(a, b), mult(b, c)), mult(c, mult(b, c))))))))),
% 1.42/1.17 inference(transitivity,[status(thm)],[489, 487])).
% 1.42/1.17 tff(491,plain,
% 1.42/1.17 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(mult(rd(mult(a, b), mult(b, c)), c), mult(b, c)) = mult(mult(rd(mult(a, b), mult(b, c)), mult(b, c)), c))) | (~(mult(rd(mult(a, b), mult(b, c)), mult(c, mult(b, c))) = mult(rd(mult(a, b), mult(b, c)), mult(mult(b, c), c)))))) | (~((~(mult(mult(rd(mult(a, b), mult(b, c)), c), mult(b, c)) = mult(rd(mult(a, b), mult(b, c)), mult(mult(b, c), c)))) | (~(mult(mult(rd(mult(a, b), mult(b, c)), mult(b, c)), c) = mult(rd(mult(a, b), mult(b, c)), mult(c, mult(b, c))))))))),
% 1.42/1.17 inference(quant_inst,[status(thm)],[])).
% 1.42/1.17 tff(492,plain,
% 1.42/1.17 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | (~((~(mult(rd(mult(a, b), mult(b, c)), mult(c, mult(b, c))) = mult(rd(mult(a, b), mult(b, c)), mult(mult(b, c), c)))) | (~(mult(mult(rd(mult(a, b), mult(b, c)), c), mult(b, c)) = mult(mult(rd(mult(a, b), mult(b, c)), mult(b, c)), c))))) | (~((~(mult(mult(rd(mult(a, b), mult(b, c)), c), mult(b, c)) = mult(rd(mult(a, b), mult(b, c)), mult(mult(b, c), c)))) | (~(mult(mult(rd(mult(a, b), mult(b, c)), mult(b, c)), c) = mult(rd(mult(a, b), mult(b, c)), mult(c, mult(b, c)))))))),
% 1.42/1.17 inference(modus_ponens,[status(thm)],[491, 490])).
% 1.42/1.17 tff(493,plain,
% 1.42/1.17 ((~((~(mult(rd(mult(a, b), mult(b, c)), mult(c, mult(b, c))) = mult(rd(mult(a, b), mult(b, c)), mult(mult(b, c), c)))) | (~(mult(mult(rd(mult(a, b), mult(b, c)), c), mult(b, c)) = mult(mult(rd(mult(a, b), mult(b, c)), mult(b, c)), c))))) | (~((~(mult(mult(rd(mult(a, b), mult(b, c)), c), mult(b, c)) = mult(rd(mult(a, b), mult(b, c)), mult(mult(b, c), c)))) | (~(mult(mult(rd(mult(a, b), mult(b, c)), mult(b, c)), c) = mult(rd(mult(a, b), mult(b, c)), mult(c, mult(b, c)))))))),
% 1.42/1.17 inference(unit_resolution,[status(thm)],[492, 64])).
% 1.42/1.17 tff(494,plain,
% 1.42/1.17 (~((~(mult(mult(rd(mult(a, b), mult(b, c)), c), mult(b, c)) = mult(rd(mult(a, b), mult(b, c)), mult(mult(b, c), c)))) | (~(mult(mult(rd(mult(a, b), mult(b, c)), mult(b, c)), c) = mult(rd(mult(a, b), mult(b, c)), mult(c, mult(b, c))))))),
% 1.42/1.17 inference(unit_resolution,[status(thm)],[493, 486])).
% 1.42/1.17 tff(495,plain,
% 1.42/1.17 (((~(mult(mult(rd(mult(a, b), mult(b, c)), c), mult(b, c)) = mult(rd(mult(a, b), mult(b, c)), mult(mult(b, c), c)))) | (~(mult(mult(rd(mult(a, b), mult(b, c)), mult(b, c)), c) = mult(rd(mult(a, b), mult(b, c)), mult(c, mult(b, c)))))) | (mult(mult(rd(mult(a, b), mult(b, c)), c), mult(b, c)) = mult(rd(mult(a, b), mult(b, c)), mult(mult(b, c), c)))),
% 1.42/1.17 inference(tautology,[status(thm)],[])).
% 1.42/1.17 tff(496,plain,
% 1.42/1.17 (mult(mult(rd(mult(a, b), mult(b, c)), c), mult(b, c)) = mult(rd(mult(a, b), mult(b, c)), mult(mult(b, c), c))),
% 1.42/1.17 inference(unit_resolution,[status(thm)],[495, 494])).
% 1.42/1.17 tff(497,plain,
% 1.42/1.17 (mult(rd(mult(a, b), mult(b, c)), mult(mult(b, c), c)) = mult(mult(rd(mult(a, b), mult(b, c)), c), mult(b, c))),
% 1.42/1.17 inference(symmetry,[status(thm)],[496])).
% 1.42/1.17 tff(498,plain,
% 1.42/1.17 ((~![A: $i] : (mult(unit, A) = A)) | (mult(unit, c) = c)),
% 1.42/1.17 inference(quant_inst,[status(thm)],[])).
% 1.42/1.17 tff(499,plain,
% 1.42/1.17 (mult(unit, c) = c),
% 1.42/1.17 inference(unit_resolution,[status(thm)],[498, 26])).
% 1.42/1.17 tff(500,plain,
% 1.42/1.17 (mult(mult(unit, c), b) = mult(c, b)),
% 1.42/1.17 inference(monotonicity,[status(thm)],[499])).
% 1.42/1.17 tff(501,assumption,(mult(mult(unit, c), b) = mult(unit, mult(b, c))), introduced(assumption)).
% 1.42/1.17 tff(502,plain,
% 1.42/1.17 (mult(unit, mult(b, c)) = mult(mult(unit, c), b)),
% 1.42/1.17 inference(symmetry,[status(thm)],[501])).
% 1.42/1.17 tff(503,plain,
% 1.42/1.17 (mult(b, c) = mult(c, b)),
% 1.42/1.17 inference(transitivity,[status(thm)],[77, 502, 500])).
% 1.42/1.17 tff(504,plain,
% 1.42/1.17 (mult(mult(b, c), c) = mult(mult(c, b), c)),
% 1.42/1.17 inference(monotonicity,[status(thm)],[503])).
% 1.42/1.17 tff(505,plain,
% 1.42/1.17 (mult(rd(mult(a, b), mult(b, c)), mult(mult(b, c), c)) = mult(rd(mult(a, b), mult(b, c)), mult(mult(c, b), c))),
% 1.42/1.17 inference(monotonicity,[status(thm)],[504])).
% 1.42/1.17 tff(506,plain,
% 1.42/1.17 (mult(rd(mult(a, b), mult(b, c)), mult(mult(c, b), c)) = mult(rd(mult(a, b), mult(b, c)), mult(mult(b, c), c))),
% 1.42/1.17 inference(symmetry,[status(thm)],[505])).
% 1.42/1.17 tff(507,plain,
% 1.42/1.17 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(rd(mult(a, b), mult(b, c)), c), b), c) = mult(rd(mult(a, b), mult(b, c)), mult(mult(c, b), c)))),
% 1.42/1.17 inference(quant_inst,[status(thm)],[])).
% 1.42/1.17 tff(508,plain,
% 1.42/1.17 (mult(mult(mult(rd(mult(a, b), mult(b, c)), c), b), c) = mult(rd(mult(a, b), mult(b, c)), mult(mult(c, b), c))),
% 1.42/1.17 inference(unit_resolution,[status(thm)],[507, 124])).
% 1.42/1.17 tff(509,plain,
% 1.42/1.17 (mult(mult(mult(rd(mult(a, b), mult(b, c)), c), b), c) = mult(mult(a, b), c)),
% 1.42/1.17 inference(monotonicity,[status(thm)],[466])).
% 1.42/1.17 tff(510,plain,
% 1.42/1.17 (mult(mult(a, b), c) = mult(mult(mult(rd(mult(a, b), mult(b, c)), c), b), c)),
% 1.42/1.17 inference(symmetry,[status(thm)],[509])).
% 1.42/1.17 tff(511,plain,
% 1.42/1.17 (mult(mult(a, b), c) = mult(a, mult(b, c))),
% 1.42/1.17 inference(transitivity,[status(thm)],[510, 508, 506, 497, 474])).
% 1.42/1.17 tff(512,plain,
% 1.42/1.17 ($false),
% 1.42/1.17 inference(unit_resolution,[status(thm)],[483, 511])).
% 1.42/1.17 tff(513,plain,((~(mult(mult(unit, c), b) = mult(unit, mult(b, c)))) | (~(mult(mult(rd(mult(a, b), mult(b, c)), c), b) = mult(rd(mult(a, b), mult(b, c)), mult(b, c))))), inference(lemma,lemma(discharge,[]))).
% 1.42/1.17 tff(514,plain,
% 1.42/1.17 (~(mult(mult(rd(mult(a, b), mult(b, c)), c), b) = mult(rd(mult(a, b), mult(b, c)), mult(b, c)))),
% 1.42/1.17 inference(unit_resolution,[status(thm)],[513, 455])).
% 1.42/1.17 tff(515,plain,
% 1.42/1.17 (((~(mult(mult(rd(mult(a, b), mult(b, c)), b), c) = mult(rd(mult(a, b), mult(b, c)), mult(c, b)))) | (~(mult(mult(rd(mult(a, b), mult(b, c)), c), b) = mult(rd(mult(a, b), mult(b, c)), mult(b, c))))) | (mult(mult(rd(mult(a, b), mult(b, c)), c), b) = mult(rd(mult(a, b), mult(b, c)), mult(b, c)))),
% 1.42/1.17 inference(tautology,[status(thm)],[])).
% 1.42/1.17 tff(516,plain,
% 1.42/1.17 ((~(mult(mult(rd(mult(a, b), mult(b, c)), b), c) = mult(rd(mult(a, b), mult(b, c)), mult(c, b)))) | (~(mult(mult(rd(mult(a, b), mult(b, c)), c), b) = mult(rd(mult(a, b), mult(b, c)), mult(b, c))))),
% 1.42/1.17 inference(unit_resolution,[status(thm)],[515, 514])).
% 1.42/1.17 tff(517,plain,
% 1.42/1.17 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(rd(mult(a, b), mult(b, c)), mult(c, b)) = mult(rd(mult(a, b), mult(b, c)), mult(b, c)))) | (~(mult(mult(rd(mult(a, b), mult(b, c)), c), b) = mult(mult(rd(mult(a, b), mult(b, c)), b), c))))) | (~((~(mult(mult(rd(mult(a, b), mult(b, c)), b), c) = mult(rd(mult(a, b), mult(b, c)), mult(c, b)))) | (~(mult(mult(rd(mult(a, b), mult(b, c)), c), b) = mult(rd(mult(a, b), mult(b, c)), mult(b, c)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | (~((~(mult(rd(mult(a, b), mult(b, c)), mult(c, b)) = mult(rd(mult(a, b), mult(b, c)), mult(b, c)))) | (~(mult(mult(rd(mult(a, b), mult(b, c)), c), b) = mult(mult(rd(mult(a, b), mult(b, c)), b), c))))) | (~((~(mult(mult(rd(mult(a, b), mult(b, c)), b), c) = mult(rd(mult(a, b), mult(b, c)), mult(c, b)))) | (~(mult(mult(rd(mult(a, b), mult(b, c)), c), b) = mult(rd(mult(a, b), mult(b, c)), mult(b, c)))))))),
% 1.42/1.17 inference(rewrite,[status(thm)],[])).
% 1.42/1.17 tff(518,plain,
% 1.42/1.17 (((~((~(mult(mult(rd(mult(a, b), mult(b, c)), c), b) = mult(mult(rd(mult(a, b), mult(b, c)), b), c))) | (~(mult(rd(mult(a, b), mult(b, c)), mult(c, b)) = mult(rd(mult(a, b), mult(b, c)), mult(b, c)))))) | (~((~(mult(mult(rd(mult(a, b), mult(b, c)), c), b) = mult(rd(mult(a, b), mult(b, c)), mult(b, c)))) | (~(mult(mult(rd(mult(a, b), mult(b, c)), b), c) = mult(rd(mult(a, b), mult(b, c)), mult(c, b))))))) <=> ((~((~(mult(rd(mult(a, b), mult(b, c)), mult(c, b)) = mult(rd(mult(a, b), mult(b, c)), mult(b, c)))) | (~(mult(mult(rd(mult(a, b), mult(b, c)), c), b) = mult(mult(rd(mult(a, b), mult(b, c)), b), c))))) | (~((~(mult(mult(rd(mult(a, b), mult(b, c)), b), c) = mult(rd(mult(a, b), mult(b, c)), mult(c, b)))) | (~(mult(mult(rd(mult(a, b), mult(b, c)), c), b) = mult(rd(mult(a, b), mult(b, c)), mult(b, c)))))))),
% 1.42/1.18 inference(rewrite,[status(thm)],[])).
% 1.42/1.18 tff(519,plain,
% 1.42/1.18 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(mult(rd(mult(a, b), mult(b, c)), c), b) = mult(mult(rd(mult(a, b), mult(b, c)), b), c))) | (~(mult(rd(mult(a, b), mult(b, c)), mult(c, b)) = mult(rd(mult(a, b), mult(b, c)), mult(b, c)))))) | (~((~(mult(mult(rd(mult(a, b), mult(b, c)), c), b) = mult(rd(mult(a, b), mult(b, c)), mult(b, c)))) | (~(mult(mult(rd(mult(a, b), mult(b, c)), b), c) = mult(rd(mult(a, b), mult(b, c)), mult(c, b)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(rd(mult(a, b), mult(b, c)), mult(c, b)) = mult(rd(mult(a, b), mult(b, c)), mult(b, c)))) | (~(mult(mult(rd(mult(a, b), mult(b, c)), c), b) = mult(mult(rd(mult(a, b), mult(b, c)), b), c))))) | (~((~(mult(mult(rd(mult(a, b), mult(b, c)), b), c) = mult(rd(mult(a, b), mult(b, c)), mult(c, b)))) | (~(mult(mult(rd(mult(a, b), mult(b, c)), c), b) = mult(rd(mult(a, b), mult(b, c)), mult(b, c))))))))),
% 1.42/1.18 inference(monotonicity,[status(thm)],[518])).
% 1.42/1.18 tff(520,plain,
% 1.42/1.18 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(mult(rd(mult(a, b), mult(b, c)), c), b) = mult(mult(rd(mult(a, b), mult(b, c)), b), c))) | (~(mult(rd(mult(a, b), mult(b, c)), mult(c, b)) = mult(rd(mult(a, b), mult(b, c)), mult(b, c)))))) | (~((~(mult(mult(rd(mult(a, b), mult(b, c)), c), b) = mult(rd(mult(a, b), mult(b, c)), mult(b, c)))) | (~(mult(mult(rd(mult(a, b), mult(b, c)), b), c) = mult(rd(mult(a, b), mult(b, c)), mult(c, b)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | (~((~(mult(rd(mult(a, b), mult(b, c)), mult(c, b)) = mult(rd(mult(a, b), mult(b, c)), mult(b, c)))) | (~(mult(mult(rd(mult(a, b), mult(b, c)), c), b) = mult(mult(rd(mult(a, b), mult(b, c)), b), c))))) | (~((~(mult(mult(rd(mult(a, b), mult(b, c)), b), c) = mult(rd(mult(a, b), mult(b, c)), mult(c, b)))) | (~(mult(mult(rd(mult(a, b), mult(b, c)), c), b) = mult(rd(mult(a, b), mult(b, c)), mult(b, c)))))))),
% 1.42/1.18 inference(transitivity,[status(thm)],[519, 517])).
% 1.42/1.18 tff(521,plain,
% 1.42/1.18 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(mult(rd(mult(a, b), mult(b, c)), c), b) = mult(mult(rd(mult(a, b), mult(b, c)), b), c))) | (~(mult(rd(mult(a, b), mult(b, c)), mult(c, b)) = mult(rd(mult(a, b), mult(b, c)), mult(b, c)))))) | (~((~(mult(mult(rd(mult(a, b), mult(b, c)), c), b) = mult(rd(mult(a, b), mult(b, c)), mult(b, c)))) | (~(mult(mult(rd(mult(a, b), mult(b, c)), b), c) = mult(rd(mult(a, b), mult(b, c)), mult(c, b)))))))),
% 1.42/1.18 inference(quant_inst,[status(thm)],[])).
% 1.42/1.18 tff(522,plain,
% 1.42/1.18 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | (~((~(mult(rd(mult(a, b), mult(b, c)), mult(c, b)) = mult(rd(mult(a, b), mult(b, c)), mult(b, c)))) | (~(mult(mult(rd(mult(a, b), mult(b, c)), c), b) = mult(mult(rd(mult(a, b), mult(b, c)), b), c))))) | (~((~(mult(mult(rd(mult(a, b), mult(b, c)), b), c) = mult(rd(mult(a, b), mult(b, c)), mult(c, b)))) | (~(mult(mult(rd(mult(a, b), mult(b, c)), c), b) = mult(rd(mult(a, b), mult(b, c)), mult(b, c))))))),
% 1.46/1.18 inference(modus_ponens,[status(thm)],[521, 520])).
% 1.46/1.18 tff(523,plain,
% 1.46/1.18 ((~((~(mult(rd(mult(a, b), mult(b, c)), mult(c, b)) = mult(rd(mult(a, b), mult(b, c)), mult(b, c)))) | (~(mult(mult(rd(mult(a, b), mult(b, c)), c), b) = mult(mult(rd(mult(a, b), mult(b, c)), b), c))))) | (~((~(mult(mult(rd(mult(a, b), mult(b, c)), b), c) = mult(rd(mult(a, b), mult(b, c)), mult(c, b)))) | (~(mult(mult(rd(mult(a, b), mult(b, c)), c), b) = mult(rd(mult(a, b), mult(b, c)), mult(b, c))))))),
% 1.46/1.18 inference(unit_resolution,[status(thm)],[522, 64])).
% 1.46/1.18 tff(524,plain,
% 1.46/1.18 (~((~(mult(rd(mult(a, b), mult(b, c)), mult(c, b)) = mult(rd(mult(a, b), mult(b, c)), mult(b, c)))) | (~(mult(mult(rd(mult(a, b), mult(b, c)), c), b) = mult(mult(rd(mult(a, b), mult(b, c)), b), c))))),
% 1.46/1.18 inference(unit_resolution,[status(thm)],[523, 516])).
% 1.46/1.18 tff(525,plain,
% 1.46/1.18 (((~(mult(rd(mult(a, b), mult(b, c)), mult(c, b)) = mult(rd(mult(a, b), mult(b, c)), mult(b, c)))) | (~(mult(mult(rd(mult(a, b), mult(b, c)), c), b) = mult(mult(rd(mult(a, b), mult(b, c)), b), c)))) | (mult(rd(mult(a, b), mult(b, c)), mult(c, b)) = mult(rd(mult(a, b), mult(b, c)), mult(b, c)))),
% 1.46/1.18 inference(tautology,[status(thm)],[])).
% 1.46/1.18 tff(526,plain,
% 1.46/1.18 (mult(rd(mult(a, b), mult(b, c)), mult(c, b)) = mult(rd(mult(a, b), mult(b, c)), mult(b, c))),
% 1.46/1.18 inference(unit_resolution,[status(thm)],[525, 524])).
% 1.46/1.18 tff(527,plain,
% 1.46/1.18 (ld(rd(mult(a, b), mult(b, c)), mult(rd(mult(a, b), mult(b, c)), mult(c, b))) = ld(rd(mult(a, b), mult(b, c)), mult(rd(mult(a, b), mult(b, c)), mult(b, c)))),
% 1.46/1.18 inference(monotonicity,[status(thm)],[526])).
% 1.46/1.18 tff(528,plain,
% 1.46/1.18 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(rd(mult(a, b), mult(b, c)), mult(rd(mult(a, b), mult(b, c)), mult(c, b))) = mult(c, b))),
% 1.46/1.18 inference(quant_inst,[status(thm)],[])).
% 1.46/1.18 tff(529,plain,
% 1.46/1.18 (ld(rd(mult(a, b), mult(b, c)), mult(rd(mult(a, b), mult(b, c)), mult(c, b))) = mult(c, b)),
% 1.46/1.18 inference(unit_resolution,[status(thm)],[528, 99])).
% 1.46/1.18 tff(530,plain,
% 1.46/1.18 (mult(c, b) = ld(rd(mult(a, b), mult(b, c)), mult(rd(mult(a, b), mult(b, c)), mult(c, b)))),
% 1.46/1.18 inference(symmetry,[status(thm)],[529])).
% 1.46/1.18 tff(531,plain,
% 1.46/1.18 (mult(c, b) = mult(b, c)),
% 1.46/1.18 inference(transitivity,[status(thm)],[530, 527, 462])).
% 1.46/1.18 tff(532,plain,
% 1.46/1.18 (mult(mult(c, b), c) = mult(mult(b, c), c)),
% 1.46/1.18 inference(monotonicity,[status(thm)],[531])).
% 1.46/1.18 tff(533,plain,
% 1.46/1.18 (mult(mult(b, c), c) = mult(mult(c, b), c)),
% 1.46/1.18 inference(symmetry,[status(thm)],[532])).
% 1.46/1.18 tff(534,plain,
% 1.46/1.18 (mult(unit, mult(mult(b, c), c)) = mult(unit, mult(mult(c, b), c))),
% 1.46/1.18 inference(monotonicity,[status(thm)],[533])).
% 1.46/1.18 tff(535,plain,
% 1.46/1.18 (mult(unit, mult(mult(b, c), c)) = mult(mult(unit, mult(b, c)), c)),
% 1.46/1.18 inference(transitivity,[status(thm)],[534, 460, 457, 438])).
% 1.46/1.18 tff(536,plain,
% 1.46/1.18 ((mult(unit, mult(mult(b, c), c)) = mult(unit, mult(c, mult(b, c)))) <=> (mult(mult(unit, mult(b, c)), c) = mult(unit, mult(c, mult(b, c))))),
% 1.46/1.18 inference(monotonicity,[status(thm)],[535])).
% 1.46/1.18 tff(537,plain,
% 1.46/1.18 ((mult(mult(unit, mult(b, c)), c) = mult(unit, mult(c, mult(b, c)))) <=> (mult(unit, mult(mult(b, c), c)) = mult(unit, mult(c, mult(b, c))))),
% 1.46/1.18 inference(symmetry,[status(thm)],[536])).
% 1.46/1.18 tff(538,plain,
% 1.46/1.18 (mult(c, mult(c, b)) = mult(c, mult(b, c))),
% 1.46/1.18 inference(monotonicity,[status(thm)],[531])).
% 1.46/1.18 tff(539,plain,
% 1.46/1.18 (mult(c, mult(b, c)) = mult(c, mult(c, b))),
% 1.46/1.18 inference(symmetry,[status(thm)],[538])).
% 1.46/1.18 tff(540,plain,
% 1.46/1.18 (mult(unit, mult(c, mult(b, c))) = mult(c, mult(c, b))),
% 1.46/1.18 inference(transitivity,[status(thm)],[436, 539])).
% 1.46/1.18 tff(541,plain,
% 1.46/1.18 (mult(mult(unit, mult(b, c)), c) = mult(mult(c, b), c)),
% 1.46/1.18 inference(transitivity,[status(thm)],[437, 533])).
% 1.46/1.18 tff(542,plain,
% 1.46/1.18 ((mult(mult(unit, mult(b, c)), c) = mult(unit, mult(c, mult(b, c)))) <=> (mult(mult(c, b), c) = mult(c, mult(c, b)))),
% 1.46/1.18 inference(monotonicity,[status(thm)],[541, 540])).
% 1.46/1.18 tff(543,plain,
% 1.46/1.18 ((mult(mult(c, b), c) = mult(c, mult(c, b))) <=> (mult(mult(unit, mult(b, c)), c) = mult(unit, mult(c, mult(b, c))))),
% 1.46/1.18 inference(symmetry,[status(thm)],[542])).
% 1.46/1.18 tff(544,plain,
% 1.46/1.18 ((mult(c, mult(c, b)) = mult(mult(c, b), c)) <=> (mult(mult(c, b), c) = mult(c, mult(c, b)))),
% 1.46/1.18 inference(commutativity,[status(thm)],[])).
% 1.46/1.18 tff(545,plain,
% 1.46/1.18 (mult(unit, mult(mult(b, c), c)) = mult(mult(c, b), c)),
% 1.46/1.18 inference(transitivity,[status(thm)],[534, 460, 457, 533])).
% 1.46/1.18 tff(546,plain,
% 1.46/1.18 (mult(mult(unit, c), mult(b, c)) = mult(c, mult(b, c))),
% 1.46/1.18 inference(monotonicity,[status(thm)],[499])).
% 1.46/1.18 tff(547,plain,
% 1.46/1.18 (mult(mult(unit, c), mult(b, c)) = mult(c, mult(c, b))),
% 1.46/1.18 inference(transitivity,[status(thm)],[546, 539])).
% 1.46/1.18 tff(548,plain,
% 1.46/1.18 ((mult(mult(unit, c), mult(b, c)) = mult(unit, mult(mult(b, c), c))) <=> (mult(c, mult(c, b)) = mult(mult(c, b), c))),
% 1.46/1.18 inference(monotonicity,[status(thm)],[547, 545])).
% 1.46/1.18 tff(549,plain,
% 1.46/1.18 ((mult(mult(unit, c), mult(b, c)) = mult(unit, mult(mult(b, c), c))) <=> (mult(mult(c, b), c) = mult(c, mult(c, b)))),
% 1.46/1.18 inference(transitivity,[status(thm)],[548, 544])).
% 1.46/1.18 tff(550,plain,
% 1.46/1.18 ((mult(mult(unit, c), mult(b, c)) = mult(unit, mult(mult(b, c), c))) <=> (mult(unit, mult(mult(b, c), c)) = mult(unit, mult(c, mult(b, c))))),
% 1.46/1.18 inference(transitivity,[status(thm)],[549, 543, 537])).
% 1.46/1.18 tff(551,assumption,(~(mult(unit, mult(mult(b, c), c)) = mult(unit, mult(c, mult(b, c))))), introduced(assumption)).
% 1.46/1.18 tff(552,plain,
% 1.46/1.18 (((~(mult(mult(unit, mult(b, c)), c) = mult(mult(unit, c), mult(b, c)))) | (~(mult(unit, mult(mult(b, c), c)) = mult(unit, mult(c, mult(b, c)))))) | (mult(unit, mult(mult(b, c), c)) = mult(unit, mult(c, mult(b, c))))),
% 1.46/1.18 inference(tautology,[status(thm)],[])).
% 1.46/1.18 tff(553,plain,
% 1.46/1.18 ((~(mult(mult(unit, mult(b, c)), c) = mult(mult(unit, c), mult(b, c)))) | (~(mult(unit, mult(mult(b, c), c)) = mult(unit, mult(c, mult(b, c)))))),
% 1.46/1.18 inference(unit_resolution,[status(thm)],[552, 551])).
% 1.46/1.18 tff(554,plain,
% 1.46/1.18 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(mult(unit, mult(b, c)), c) = mult(mult(unit, c), mult(b, c)))) | (~(mult(unit, mult(mult(b, c), c)) = mult(unit, mult(c, mult(b, c))))))) | (~((~(mult(mult(unit, mult(b, c)), c) = mult(unit, mult(c, mult(b, c))))) | (~(mult(mult(unit, c), mult(b, c)) = mult(unit, mult(mult(b, c), c)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | (~((~(mult(mult(unit, mult(b, c)), c) = mult(mult(unit, c), mult(b, c)))) | (~(mult(unit, mult(mult(b, c), c)) = mult(unit, mult(c, mult(b, c))))))) | (~((~(mult(mult(unit, mult(b, c)), c) = mult(unit, mult(c, mult(b, c))))) | (~(mult(mult(unit, c), mult(b, c)) = mult(unit, mult(mult(b, c), c)))))))),
% 1.46/1.18 inference(rewrite,[status(thm)],[])).
% 1.46/1.18 tff(555,plain,
% 1.46/1.18 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(mult(unit, mult(b, c)), c) = mult(mult(unit, c), mult(b, c)))) | (~(mult(unit, mult(mult(b, c), c)) = mult(unit, mult(c, mult(b, c))))))) | (~((~(mult(mult(unit, mult(b, c)), c) = mult(unit, mult(c, mult(b, c))))) | (~(mult(mult(unit, c), mult(b, c)) = mult(unit, mult(mult(b, c), c)))))))),
% 1.46/1.18 inference(quant_inst,[status(thm)],[])).
% 1.46/1.18 tff(556,plain,
% 1.46/1.18 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | (~((~(mult(mult(unit, mult(b, c)), c) = mult(mult(unit, c), mult(b, c)))) | (~(mult(unit, mult(mult(b, c), c)) = mult(unit, mult(c, mult(b, c))))))) | (~((~(mult(mult(unit, mult(b, c)), c) = mult(unit, mult(c, mult(b, c))))) | (~(mult(mult(unit, c), mult(b, c)) = mult(unit, mult(mult(b, c), c))))))),
% 1.46/1.18 inference(modus_ponens,[status(thm)],[555, 554])).
% 1.46/1.18 tff(557,plain,
% 1.46/1.18 ((~((~(mult(mult(unit, mult(b, c)), c) = mult(mult(unit, c), mult(b, c)))) | (~(mult(unit, mult(mult(b, c), c)) = mult(unit, mult(c, mult(b, c))))))) | (~((~(mult(mult(unit, mult(b, c)), c) = mult(unit, mult(c, mult(b, c))))) | (~(mult(mult(unit, c), mult(b, c)) = mult(unit, mult(mult(b, c), c))))))),
% 1.46/1.18 inference(unit_resolution,[status(thm)],[556, 64])).
% 1.46/1.18 tff(558,plain,
% 1.46/1.18 (~((~(mult(mult(unit, mult(b, c)), c) = mult(unit, mult(c, mult(b, c))))) | (~(mult(mult(unit, c), mult(b, c)) = mult(unit, mult(mult(b, c), c)))))),
% 1.46/1.18 inference(unit_resolution,[status(thm)],[557, 553])).
% 1.46/1.18 tff(559,plain,
% 1.46/1.18 (((~(mult(mult(unit, mult(b, c)), c) = mult(unit, mult(c, mult(b, c))))) | (~(mult(mult(unit, c), mult(b, c)) = mult(unit, mult(mult(b, c), c))))) | (mult(mult(unit, c), mult(b, c)) = mult(unit, mult(mult(b, c), c)))),
% 1.46/1.18 inference(tautology,[status(thm)],[])).
% 1.46/1.18 tff(560,plain,
% 1.46/1.18 (mult(mult(unit, c), mult(b, c)) = mult(unit, mult(mult(b, c), c))),
% 1.46/1.18 inference(unit_resolution,[status(thm)],[559, 558])).
% 1.46/1.18 tff(561,plain,
% 1.46/1.18 (mult(unit, mult(mult(b, c), c)) = mult(unit, mult(c, mult(b, c)))),
% 1.46/1.18 inference(modus_ponens,[status(thm)],[560, 550])).
% 1.46/1.18 tff(562,plain,
% 1.46/1.18 ($false),
% 1.46/1.18 inference(unit_resolution,[status(thm)],[551, 561])).
% 1.46/1.18 tff(563,plain,(mult(unit, mult(mult(b, c), c)) = mult(unit, mult(c, mult(b, c)))), inference(lemma,lemma(discharge,[]))).
% 1.46/1.18 tff(564,plain,
% 1.46/1.18 (mult(unit, mult(mult(c, b), c)) = mult(unit, mult(mult(b, c), c))),
% 1.46/1.18 inference(symmetry,[status(thm)],[534])).
% 1.46/1.18 tff(565,plain,
% 1.46/1.18 (mult(mult(b, c), c) = mult(mult(mult(unit, c), b), c)),
% 1.46/1.18 inference(symmetry,[status(thm)],[457])).
% 1.46/1.18 tff(566,plain,
% 1.46/1.18 (mult(mult(b, c), c) = mult(c, mult(b, c))),
% 1.46/1.18 inference(transitivity,[status(thm)],[565, 459, 564, 563, 436])).
% 1.46/1.18 tff(567,plain,
% 1.46/1.18 (mult(mult(mult(b, c), c), rd(mult(a, b), mult(b, c))) = mult(mult(c, mult(b, c)), rd(mult(a, b), mult(b, c)))),
% 1.46/1.18 inference(monotonicity,[status(thm)],[566])).
% 1.46/1.18 tff(568,plain,
% 1.46/1.18 ((mult(mult(mult(b, c), c), rd(mult(a, b), mult(b, c))) = mult(mult(mult(b, c), rd(mult(a, b), mult(b, c))), c)) <=> (mult(mult(c, mult(b, c)), rd(mult(a, b), mult(b, c))) = mult(c, mult(rd(mult(a, b), mult(b, c)), mult(b, c))))),
% 1.46/1.18 inference(monotonicity,[status(thm)],[567, 434])).
% 1.46/1.18 tff(569,plain,
% 1.46/1.18 ((~(mult(mult(mult(b, c), c), rd(mult(a, b), mult(b, c))) = mult(mult(mult(b, c), rd(mult(a, b), mult(b, c))), c))) <=> (~(mult(mult(c, mult(b, c)), rd(mult(a, b), mult(b, c))) = mult(c, mult(rd(mult(a, b), mult(b, c)), mult(b, c)))))),
% 1.46/1.18 inference(monotonicity,[status(thm)],[568])).
% 1.46/1.18 tff(570,plain,
% 1.46/1.18 (~(mult(mult(c, mult(b, c)), rd(mult(a, b), mult(b, c))) = mult(c, mult(rd(mult(a, b), mult(b, c)), mult(b, c))))),
% 1.46/1.18 inference(modus_ponens,[status(thm)],[407, 569])).
% 1.46/1.18 tff(571,plain,
% 1.46/1.18 (((~(mult(mult(c, mult(b, c)), rd(mult(a, b), mult(b, c))) = mult(c, mult(rd(mult(a, b), mult(b, c)), mult(b, c))))) | (~(mult(mult(c, rd(mult(a, b), mult(b, c))), mult(b, c)) = mult(c, mult(mult(b, c), rd(mult(a, b), mult(b, c))))))) | (mult(mult(c, mult(b, c)), rd(mult(a, b), mult(b, c))) = mult(c, mult(rd(mult(a, b), mult(b, c)), mult(b, c))))),
% 1.46/1.18 inference(tautology,[status(thm)],[])).
% 1.46/1.18 tff(572,plain,
% 1.46/1.18 ((~(mult(mult(c, mult(b, c)), rd(mult(a, b), mult(b, c))) = mult(c, mult(rd(mult(a, b), mult(b, c)), mult(b, c))))) | (~(mult(mult(c, rd(mult(a, b), mult(b, c))), mult(b, c)) = mult(c, mult(mult(b, c), rd(mult(a, b), mult(b, c))))))),
% 1.46/1.19 inference(unit_resolution,[status(thm)],[571, 570])).
% 1.46/1.19 tff(573,plain,
% 1.46/1.19 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(mult(c, mult(b, c)), rd(mult(a, b), mult(b, c))) = mult(mult(c, rd(mult(a, b), mult(b, c))), mult(b, c)))) | (~(mult(c, mult(mult(b, c), rd(mult(a, b), mult(b, c)))) = mult(c, mult(rd(mult(a, b), mult(b, c)), mult(b, c))))))) | (~((~(mult(mult(c, mult(b, c)), rd(mult(a, b), mult(b, c))) = mult(c, mult(rd(mult(a, b), mult(b, c)), mult(b, c))))) | (~(mult(mult(c, rd(mult(a, b), mult(b, c))), mult(b, c)) = mult(c, mult(mult(b, c), rd(mult(a, b), mult(b, c)))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | (~((~(mult(mult(c, mult(b, c)), rd(mult(a, b), mult(b, c))) = mult(mult(c, rd(mult(a, b), mult(b, c))), mult(b, c)))) | (~(mult(c, mult(mult(b, c), rd(mult(a, b), mult(b, c)))) = mult(c, mult(rd(mult(a, b), mult(b, c)), mult(b, c))))))) | (~((~(mult(mult(c, mult(b, c)), rd(mult(a, b), mult(b, c))) = mult(c, mult(rd(mult(a, b), mult(b, c)), mult(b, c))))) | (~(mult(mult(c, rd(mult(a, b), mult(b, c))), mult(b, c)) = mult(c, mult(mult(b, c), rd(mult(a, b), mult(b, c)))))))))),
% 1.46/1.19 inference(rewrite,[status(thm)],[])).
% 1.46/1.19 tff(574,plain,
% 1.46/1.19 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(mult(c, mult(b, c)), rd(mult(a, b), mult(b, c))) = mult(mult(c, rd(mult(a, b), mult(b, c))), mult(b, c)))) | (~(mult(c, mult(mult(b, c), rd(mult(a, b), mult(b, c)))) = mult(c, mult(rd(mult(a, b), mult(b, c)), mult(b, c))))))) | (~((~(mult(mult(c, mult(b, c)), rd(mult(a, b), mult(b, c))) = mult(c, mult(rd(mult(a, b), mult(b, c)), mult(b, c))))) | (~(mult(mult(c, rd(mult(a, b), mult(b, c))), mult(b, c)) = mult(c, mult(mult(b, c), rd(mult(a, b), mult(b, c)))))))))),
% 1.46/1.19 inference(quant_inst,[status(thm)],[])).
% 1.46/1.19 tff(575,plain,
% 1.46/1.19 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | (~((~(mult(mult(c, mult(b, c)), rd(mult(a, b), mult(b, c))) = mult(mult(c, rd(mult(a, b), mult(b, c))), mult(b, c)))) | (~(mult(c, mult(mult(b, c), rd(mult(a, b), mult(b, c)))) = mult(c, mult(rd(mult(a, b), mult(b, c)), mult(b, c))))))) | (~((~(mult(mult(c, mult(b, c)), rd(mult(a, b), mult(b, c))) = mult(c, mult(rd(mult(a, b), mult(b, c)), mult(b, c))))) | (~(mult(mult(c, rd(mult(a, b), mult(b, c))), mult(b, c)) = mult(c, mult(mult(b, c), rd(mult(a, b), mult(b, c))))))))),
% 1.46/1.19 inference(modus_ponens,[status(thm)],[574, 573])).
% 1.46/1.19 tff(576,plain,
% 1.46/1.19 ((~((~(mult(mult(c, mult(b, c)), rd(mult(a, b), mult(b, c))) = mult(mult(c, rd(mult(a, b), mult(b, c))), mult(b, c)))) | (~(mult(c, mult(mult(b, c), rd(mult(a, b), mult(b, c)))) = mult(c, mult(rd(mult(a, b), mult(b, c)), mult(b, c))))))) | (~((~(mult(mult(c, mult(b, c)), rd(mult(a, b), mult(b, c))) = mult(c, mult(rd(mult(a, b), mult(b, c)), mult(b, c))))) | (~(mult(mult(c, rd(mult(a, b), mult(b, c))), mult(b, c)) = mult(c, mult(mult(b, c), rd(mult(a, b), mult(b, c))))))))),
% 1.46/1.19 inference(unit_resolution,[status(thm)],[575, 64])).
% 1.46/1.19 tff(577,plain,
% 1.46/1.19 (~((~(mult(mult(c, mult(b, c)), rd(mult(a, b), mult(b, c))) = mult(mult(c, rd(mult(a, b), mult(b, c))), mult(b, c)))) | (~(mult(c, mult(mult(b, c), rd(mult(a, b), mult(b, c)))) = mult(c, mult(rd(mult(a, b), mult(b, c)), mult(b, c))))))),
% 1.46/1.19 inference(unit_resolution,[status(thm)],[576, 572])).
% 1.46/1.19 tff(578,plain,
% 1.46/1.19 (((~(mult(mult(c, mult(b, c)), rd(mult(a, b), mult(b, c))) = mult(mult(c, rd(mult(a, b), mult(b, c))), mult(b, c)))) | (~(mult(c, mult(mult(b, c), rd(mult(a, b), mult(b, c)))) = mult(c, mult(rd(mult(a, b), mult(b, c)), mult(b, c)))))) | (mult(mult(c, mult(b, c)), rd(mult(a, b), mult(b, c))) = mult(mult(c, rd(mult(a, b), mult(b, c))), mult(b, c)))),
% 1.46/1.19 inference(tautology,[status(thm)],[])).
% 1.46/1.19 tff(579,plain,
% 1.46/1.19 (mult(mult(c, mult(b, c)), rd(mult(a, b), mult(b, c))) = mult(mult(c, rd(mult(a, b), mult(b, c))), mult(b, c))),
% 1.46/1.19 inference(unit_resolution,[status(thm)],[578, 577])).
% 1.46/1.19 tff(580,plain,
% 1.46/1.19 ((mult(mult(c, mult(b, c)), rd(mult(a, b), mult(b, c))) = mult(c, mult(rd(mult(a, b), mult(b, c)), mult(b, c)))) <=> (mult(mult(c, rd(mult(a, b), mult(b, c))), mult(b, c)) = mult(c, mult(mult(b, c), rd(mult(a, b), mult(b, c)))))),
% 1.46/1.19 inference(monotonicity,[status(thm)],[579, 430])).
% 1.46/1.19 tff(581,plain,
% 1.46/1.19 ((~(mult(mult(c, mult(b, c)), rd(mult(a, b), mult(b, c))) = mult(c, mult(rd(mult(a, b), mult(b, c)), mult(b, c))))) <=> (~(mult(mult(c, rd(mult(a, b), mult(b, c))), mult(b, c)) = mult(c, mult(mult(b, c), rd(mult(a, b), mult(b, c))))))),
% 1.46/1.19 inference(monotonicity,[status(thm)],[580])).
% 1.46/1.19 tff(582,plain,
% 1.46/1.19 (~(mult(mult(c, rd(mult(a, b), mult(b, c))), mult(b, c)) = mult(c, mult(mult(b, c), rd(mult(a, b), mult(b, c)))))),
% 1.46/1.19 inference(modus_ponens,[status(thm)],[570, 581])).
% 1.46/1.19 tff(583,plain,
% 1.46/1.19 (~(mult(mult(unit, ld(mult(b, c), mult(mult(a, b), c))), mult(b, c)) = mult(mult(unit, mult(b, c)), ld(mult(b, c), mult(mult(a, b), c))))),
% 1.46/1.19 inference(modus_ponens,[status(thm)],[582, 427])).
% 1.46/1.19 tff(584,plain,
% 1.46/1.19 (((~(mult(mult(unit, ld(mult(b, c), mult(mult(a, b), c))), mult(b, c)) = mult(mult(unit, mult(b, c)), ld(mult(b, c), mult(mult(a, b), c))))) | (~(mult(unit, mult(ld(mult(b, c), mult(mult(a, b), c)), mult(b, c))) = mult(unit, mult(mult(b, c), ld(mult(b, c), mult(mult(a, b), c))))))) | (mult(mult(unit, ld(mult(b, c), mult(mult(a, b), c))), mult(b, c)) = mult(mult(unit, mult(b, c)), ld(mult(b, c), mult(mult(a, b), c))))),
% 1.46/1.19 inference(tautology,[status(thm)],[])).
% 1.46/1.19 tff(585,plain,
% 1.46/1.19 ((~(mult(mult(unit, ld(mult(b, c), mult(mult(a, b), c))), mult(b, c)) = mult(mult(unit, mult(b, c)), ld(mult(b, c), mult(mult(a, b), c))))) | (~(mult(unit, mult(ld(mult(b, c), mult(mult(a, b), c)), mult(b, c))) = mult(unit, mult(mult(b, c), ld(mult(b, c), mult(mult(a, b), c))))))),
% 1.46/1.19 inference(unit_resolution,[status(thm)],[584, 583])).
% 1.46/1.19 tff(586,plain,
% 1.46/1.19 ((~![A: $i] : (mult(unit, A) = A)) | (mult(unit, mult(mult(a, b), c)) = mult(mult(a, b), c))),
% 1.46/1.19 inference(quant_inst,[status(thm)],[])).
% 1.46/1.19 tff(587,plain,
% 1.46/1.19 (mult(unit, mult(mult(a, b), c)) = mult(mult(a, b), c)),
% 1.46/1.19 inference(unit_resolution,[status(thm)],[586, 26])).
% 1.46/1.19 tff(588,plain,
% 1.46/1.19 (mult(unit, mult(mult(b, c), ld(mult(b, c), mult(mult(a, b), c)))) = mult(unit, mult(mult(a, b), c))),
% 1.46/1.19 inference(monotonicity,[status(thm)],[91])).
% 1.46/1.19 tff(589,plain,
% 1.46/1.19 (mult(unit, mult(mult(b, c), ld(mult(b, c), mult(mult(a, b), c)))) = mult(mult(unit, mult(b, c)), ld(mult(b, c), mult(mult(a, b), c)))),
% 1.46/1.19 inference(transitivity,[status(thm)],[588, 587, 92, 82])).
% 1.46/1.19 tff(590,plain,
% 1.46/1.19 ((mult(mult(unit, ld(mult(b, c), mult(mult(a, b), c))), mult(b, c)) = mult(unit, mult(mult(b, c), ld(mult(b, c), mult(mult(a, b), c))))) <=> (mult(mult(unit, ld(mult(b, c), mult(mult(a, b), c))), mult(b, c)) = mult(mult(unit, mult(b, c)), ld(mult(b, c), mult(mult(a, b), c))))),
% 1.46/1.19 inference(monotonicity,[status(thm)],[589])).
% 1.46/1.19 tff(591,plain,
% 1.46/1.19 ((mult(mult(unit, ld(mult(b, c), mult(mult(a, b), c))), mult(b, c)) = mult(mult(unit, mult(b, c)), ld(mult(b, c), mult(mult(a, b), c)))) <=> (mult(mult(unit, ld(mult(b, c), mult(mult(a, b), c))), mult(b, c)) = mult(unit, mult(mult(b, c), ld(mult(b, c), mult(mult(a, b), c)))))),
% 1.46/1.19 inference(symmetry,[status(thm)],[590])).
% 1.46/1.19 tff(592,plain,
% 1.46/1.19 ((mult(mult(c, rd(mult(a, b), mult(b, c))), mult(b, c)) = mult(c, mult(mult(b, c), rd(mult(a, b), mult(b, c))))) <=> (mult(mult(unit, ld(mult(b, c), mult(mult(a, b), c))), mult(b, c)) = mult(unit, mult(mult(b, c), ld(mult(b, c), mult(mult(a, b), c)))))),
% 1.46/1.19 inference(transitivity,[status(thm)],[426, 591])).
% 1.46/1.19 tff(593,plain,
% 1.46/1.19 ((~(mult(mult(c, rd(mult(a, b), mult(b, c))), mult(b, c)) = mult(c, mult(mult(b, c), rd(mult(a, b), mult(b, c)))))) <=> (~(mult(mult(unit, ld(mult(b, c), mult(mult(a, b), c))), mult(b, c)) = mult(unit, mult(mult(b, c), ld(mult(b, c), mult(mult(a, b), c))))))),
% 1.46/1.19 inference(monotonicity,[status(thm)],[592])).
% 1.46/1.19 tff(594,plain,
% 1.46/1.19 (~(mult(mult(unit, ld(mult(b, c), mult(mult(a, b), c))), mult(b, c)) = mult(unit, mult(mult(b, c), ld(mult(b, c), mult(mult(a, b), c)))))),
% 1.46/1.19 inference(modus_ponens,[status(thm)],[582, 593])).
% 1.46/1.19 tff(595,plain,
% 1.46/1.19 (((~(mult(mult(unit, ld(mult(b, c), mult(mult(a, b), c))), mult(b, c)) = mult(unit, mult(mult(b, c), ld(mult(b, c), mult(mult(a, b), c)))))) | (~(mult(mult(unit, mult(b, c)), ld(mult(b, c), mult(mult(a, b), c))) = mult(unit, mult(ld(mult(b, c), mult(mult(a, b), c)), mult(b, c)))))) | (mult(mult(unit, ld(mult(b, c), mult(mult(a, b), c))), mult(b, c)) = mult(unit, mult(mult(b, c), ld(mult(b, c), mult(mult(a, b), c)))))),
% 1.46/1.19 inference(tautology,[status(thm)],[])).
% 1.46/1.19 tff(596,plain,
% 1.46/1.19 ((~(mult(mult(unit, ld(mult(b, c), mult(mult(a, b), c))), mult(b, c)) = mult(unit, mult(mult(b, c), ld(mult(b, c), mult(mult(a, b), c)))))) | (~(mult(mult(unit, mult(b, c)), ld(mult(b, c), mult(mult(a, b), c))) = mult(unit, mult(ld(mult(b, c), mult(mult(a, b), c)), mult(b, c)))))),
% 1.46/1.19 inference(unit_resolution,[status(thm)],[595, 594])).
% 1.46/1.19 tff(597,plain,
% 1.46/1.19 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(mult(unit, ld(mult(b, c), mult(mult(a, b), c))), mult(b, c)) = mult(mult(unit, mult(b, c)), ld(mult(b, c), mult(mult(a, b), c))))) | (~(mult(unit, mult(ld(mult(b, c), mult(mult(a, b), c)), mult(b, c))) = mult(unit, mult(mult(b, c), ld(mult(b, c), mult(mult(a, b), c)))))))) | (~((~(mult(mult(unit, ld(mult(b, c), mult(mult(a, b), c))), mult(b, c)) = mult(unit, mult(mult(b, c), ld(mult(b, c), mult(mult(a, b), c)))))) | (~(mult(mult(unit, mult(b, c)), ld(mult(b, c), mult(mult(a, b), c))) = mult(unit, mult(ld(mult(b, c), mult(mult(a, b), c)), mult(b, c))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | (~((~(mult(mult(unit, ld(mult(b, c), mult(mult(a, b), c))), mult(b, c)) = mult(mult(unit, mult(b, c)), ld(mult(b, c), mult(mult(a, b), c))))) | (~(mult(unit, mult(ld(mult(b, c), mult(mult(a, b), c)), mult(b, c))) = mult(unit, mult(mult(b, c), ld(mult(b, c), mult(mult(a, b), c)))))))) | (~((~(mult(mult(unit, ld(mult(b, c), mult(mult(a, b), c))), mult(b, c)) = mult(unit, mult(mult(b, c), ld(mult(b, c), mult(mult(a, b), c)))))) | (~(mult(mult(unit, mult(b, c)), ld(mult(b, c), mult(mult(a, b), c))) = mult(unit, mult(ld(mult(b, c), mult(mult(a, b), c)), mult(b, c))))))))),
% 1.46/1.19 inference(rewrite,[status(thm)],[])).
% 1.46/1.19 tff(598,plain,
% 1.46/1.19 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(mult(unit, ld(mult(b, c), mult(mult(a, b), c))), mult(b, c)) = mult(mult(unit, mult(b, c)), ld(mult(b, c), mult(mult(a, b), c))))) | (~(mult(unit, mult(ld(mult(b, c), mult(mult(a, b), c)), mult(b, c))) = mult(unit, mult(mult(b, c), ld(mult(b, c), mult(mult(a, b), c)))))))) | (~((~(mult(mult(unit, ld(mult(b, c), mult(mult(a, b), c))), mult(b, c)) = mult(unit, mult(mult(b, c), ld(mult(b, c), mult(mult(a, b), c)))))) | (~(mult(mult(unit, mult(b, c)), ld(mult(b, c), mult(mult(a, b), c))) = mult(unit, mult(ld(mult(b, c), mult(mult(a, b), c)), mult(b, c))))))))),
% 1.46/1.19 inference(quant_inst,[status(thm)],[])).
% 1.46/1.19 tff(599,plain,
% 1.46/1.19 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | (~((~(mult(mult(unit, ld(mult(b, c), mult(mult(a, b), c))), mult(b, c)) = mult(mult(unit, mult(b, c)), ld(mult(b, c), mult(mult(a, b), c))))) | (~(mult(unit, mult(ld(mult(b, c), mult(mult(a, b), c)), mult(b, c))) = mult(unit, mult(mult(b, c), ld(mult(b, c), mult(mult(a, b), c)))))))) | (~((~(mult(mult(unit, ld(mult(b, c), mult(mult(a, b), c))), mult(b, c)) = mult(unit, mult(mult(b, c), ld(mult(b, c), mult(mult(a, b), c)))))) | (~(mult(mult(unit, mult(b, c)), ld(mult(b, c), mult(mult(a, b), c))) = mult(unit, mult(ld(mult(b, c), mult(mult(a, b), c)), mult(b, c)))))))),
% 1.46/1.19 inference(modus_ponens,[status(thm)],[598, 597])).
% 1.46/1.19 tff(600,plain,
% 1.46/1.19 ((~((~(mult(mult(unit, ld(mult(b, c), mult(mult(a, b), c))), mult(b, c)) = mult(mult(unit, mult(b, c)), ld(mult(b, c), mult(mult(a, b), c))))) | (~(mult(unit, mult(ld(mult(b, c), mult(mult(a, b), c)), mult(b, c))) = mult(unit, mult(mult(b, c), ld(mult(b, c), mult(mult(a, b), c)))))))) | (~((~(mult(mult(unit, ld(mult(b, c), mult(mult(a, b), c))), mult(b, c)) = mult(unit, mult(mult(b, c), ld(mult(b, c), mult(mult(a, b), c)))))) | (~(mult(mult(unit, mult(b, c)), ld(mult(b, c), mult(mult(a, b), c))) = mult(unit, mult(ld(mult(b, c), mult(mult(a, b), c)), mult(b, c)))))))),
% 1.46/1.19 inference(unit_resolution,[status(thm)],[599, 64])).
% 1.46/1.19 tff(601,plain,
% 1.46/1.19 ($false),
% 1.46/1.19 inference(unit_resolution,[status(thm)],[600, 596, 585])).
% 1.46/1.19 tff(602,plain,(mult(mult(mult(b, c), c), rd(mult(a, b), mult(b, c))) = mult(mult(mult(b, c), rd(mult(a, b), mult(b, c))), c)), inference(lemma,lemma(discharge,[]))).
% 1.46/1.19 tff(603,plain,
% 1.46/1.19 (mult(unit, mult(c, mult(b, c))) = mult(unit, mult(mult(b, c), c))),
% 1.46/1.19 inference(symmetry,[status(thm)],[563])).
% 1.46/1.19 tff(604,plain,
% 1.46/1.19 (mult(c, mult(b, c)) = mult(unit, mult(c, mult(b, c)))),
% 1.46/1.19 inference(symmetry,[status(thm)],[436])).
% 1.46/1.19 tff(605,plain,
% 1.46/1.19 (mult(c, mult(b, c)) = mult(mult(b, c), c)),
% 1.46/1.19 inference(transitivity,[status(thm)],[604, 603, 534, 460, 457])).
% 1.46/1.19 tff(606,plain,
% 1.46/1.19 (mult(mult(c, mult(b, c)), rd(mult(a, b), mult(b, c))) = mult(mult(mult(b, c), c), rd(mult(a, b), mult(b, c)))),
% 1.46/1.19 inference(monotonicity,[status(thm)],[605])).
% 1.46/1.19 tff(607,plain,
% 1.46/1.19 (mult(unit, mult(mult(b, c), c)) = mult(c, mult(b, c))),
% 1.46/1.19 inference(transitivity,[status(thm)],[563, 436])).
% 1.46/1.19 tff(608,plain,
% 1.46/1.19 (mult(mult(unit, mult(mult(b, c), c)), rd(mult(a, b), mult(b, c))) = mult(mult(c, mult(b, c)), rd(mult(a, b), mult(b, c)))),
% 1.46/1.19 inference(monotonicity,[status(thm)],[607])).
% 1.46/1.19 tff(609,plain,
% 1.46/1.19 ((mult(mult(unit, rd(mult(a, b), mult(b, c))), mult(mult(b, c), c)) = mult(mult(unit, mult(mult(b, c), c)), rd(mult(a, b), mult(b, c)))) <=> (mult(mult(unit, mult(mult(b, c), c)), rd(mult(a, b), mult(b, c))) = mult(mult(unit, rd(mult(a, b), mult(b, c))), mult(mult(b, c), c)))),
% 1.46/1.19 inference(commutativity,[status(thm)],[])).
% 1.46/1.19 tff(610,plain,
% 1.46/1.19 ((mult(mult(unit, mult(mult(b, c), c)), rd(mult(a, b), mult(b, c))) = mult(mult(unit, rd(mult(a, b), mult(b, c))), mult(mult(b, c), c))) <=> (mult(mult(unit, rd(mult(a, b), mult(b, c))), mult(mult(b, c), c)) = mult(mult(unit, mult(mult(b, c), c)), rd(mult(a, b), mult(b, c))))),
% 1.46/1.19 inference(symmetry,[status(thm)],[609])).
% 1.46/1.19 tff(611,plain,
% 1.46/1.19 (mult(rd(mult(a, b), mult(b, c)), mult(c, mult(b, c))) = mult(rd(mult(a, b), mult(b, c)), mult(mult(b, c), c))),
% 1.46/1.19 inference(monotonicity,[status(thm)],[605])).
% 1.46/1.19 tff(612,plain,
% 1.46/1.19 (mult(rd(mult(a, b), mult(b, c)), mult(mult(b, c), c)) = mult(rd(mult(a, b), mult(b, c)), mult(c, mult(b, c)))),
% 1.46/1.19 inference(symmetry,[status(thm)],[611])).
% 1.46/1.19 tff(613,plain,
% 1.46/1.19 (rd(mult(a, b), mult(b, c)) = mult(unit, rd(mult(a, b), mult(b, c)))),
% 1.46/1.19 inference(symmetry,[status(thm)],[28])).
% 1.46/1.19 tff(614,plain,
% 1.46/1.19 (mult(rd(mult(a, b), mult(b, c)), mult(mult(b, c), c)) = mult(mult(unit, rd(mult(a, b), mult(b, c))), mult(mult(b, c), c))),
% 1.46/1.20 inference(monotonicity,[status(thm)],[613])).
% 1.46/1.20 tff(615,plain,
% 1.46/1.20 (mult(mult(unit, rd(mult(a, b), mult(b, c))), mult(mult(b, c), c)) = mult(rd(mult(a, b), mult(b, c)), mult(mult(b, c), c))),
% 1.46/1.20 inference(symmetry,[status(thm)],[614])).
% 1.46/1.20 tff(616,plain,
% 1.46/1.20 (mult(mult(unit, rd(mult(a, b), mult(b, c))), mult(mult(b, c), c)) = mult(rd(mult(a, b), mult(b, c)), mult(c, mult(b, c)))),
% 1.46/1.20 inference(transitivity,[status(thm)],[615, 612])).
% 1.46/1.20 tff(617,plain,
% 1.46/1.20 (mult(mult(unit, mult(mult(b, c), c)), rd(mult(a, b), mult(b, c))) = mult(mult(rd(mult(a, b), mult(b, c)), mult(b, c)), c)),
% 1.46/1.20 inference(transitivity,[status(thm)],[608, 606, 602, 80, 477])).
% 1.46/1.20 tff(618,plain,
% 1.46/1.20 ((mult(mult(unit, mult(mult(b, c), c)), rd(mult(a, b), mult(b, c))) = mult(mult(unit, rd(mult(a, b), mult(b, c))), mult(mult(b, c), c))) <=> (mult(mult(rd(mult(a, b), mult(b, c)), mult(b, c)), c) = mult(rd(mult(a, b), mult(b, c)), mult(c, mult(b, c))))),
% 1.46/1.20 inference(monotonicity,[status(thm)],[617, 616])).
% 1.46/1.20 tff(619,plain,
% 1.46/1.20 ((mult(mult(rd(mult(a, b), mult(b, c)), mult(b, c)), c) = mult(rd(mult(a, b), mult(b, c)), mult(c, mult(b, c)))) <=> (mult(mult(unit, mult(mult(b, c), c)), rd(mult(a, b), mult(b, c))) = mult(mult(unit, rd(mult(a, b), mult(b, c))), mult(mult(b, c), c)))),
% 1.46/1.20 inference(symmetry,[status(thm)],[618])).
% 1.46/1.20 tff(620,plain,
% 1.46/1.20 ((mult(mult(rd(mult(a, b), mult(b, c)), mult(b, c)), c) = mult(rd(mult(a, b), mult(b, c)), mult(c, mult(b, c)))) <=> (mult(mult(unit, rd(mult(a, b), mult(b, c))), mult(mult(b, c), c)) = mult(mult(unit, mult(mult(b, c), c)), rd(mult(a, b), mult(b, c))))),
% 1.46/1.20 inference(transitivity,[status(thm)],[619, 610])).
% 1.46/1.20 tff(621,plain,
% 1.46/1.20 (mult(mult(unit, rd(mult(a, b), mult(b, c))), mult(mult(b, c), c)) = mult(rd(mult(a, b), mult(b, c)), mult(mult(b, c), c))),
% 1.46/1.20 inference(monotonicity,[status(thm)],[28])).
% 1.46/1.20 tff(622,plain,
% 1.46/1.20 (mult(mult(unit, rd(mult(a, b), mult(b, c))), mult(mult(b, c), c)) = mult(rd(mult(a, b), mult(b, c)), mult(c, mult(b, c)))),
% 1.46/1.20 inference(transitivity,[status(thm)],[621, 612])).
% 1.46/1.20 tff(623,assumption,(mult(mult(mult(b, c), c), rd(mult(a, b), mult(b, c))) = mult(mult(mult(b, c), rd(mult(a, b), mult(b, c))), c)), introduced(assumption)).
% 1.46/1.20 tff(624,plain,
% 1.46/1.20 (mult(mult(unit, mult(mult(b, c), c)), rd(mult(a, b), mult(b, c))) = mult(mult(rd(mult(a, b), mult(b, c)), mult(b, c)), c)),
% 1.46/1.20 inference(transitivity,[status(thm)],[608, 606, 623, 80, 477])).
% 1.46/1.20 tff(625,plain,
% 1.46/1.20 ((mult(mult(unit, mult(mult(b, c), c)), rd(mult(a, b), mult(b, c))) = mult(mult(unit, rd(mult(a, b), mult(b, c))), mult(mult(b, c), c))) <=> (mult(mult(rd(mult(a, b), mult(b, c)), mult(b, c)), c) = mult(rd(mult(a, b), mult(b, c)), mult(c, mult(b, c))))),
% 1.46/1.20 inference(monotonicity,[status(thm)],[624, 622])).
% 1.46/1.20 tff(626,plain,
% 1.46/1.20 ((mult(mult(rd(mult(a, b), mult(b, c)), mult(b, c)), c) = mult(rd(mult(a, b), mult(b, c)), mult(c, mult(b, c)))) <=> (mult(mult(unit, mult(mult(b, c), c)), rd(mult(a, b), mult(b, c))) = mult(mult(unit, rd(mult(a, b), mult(b, c))), mult(mult(b, c), c)))),
% 1.46/1.20 inference(symmetry,[status(thm)],[625])).
% 1.46/1.20 tff(627,plain,
% 1.46/1.20 ((~(mult(mult(rd(mult(a, b), mult(b, c)), mult(b, c)), c) = mult(rd(mult(a, b), mult(b, c)), mult(c, mult(b, c))))) <=> (~(mult(mult(unit, mult(mult(b, c), c)), rd(mult(a, b), mult(b, c))) = mult(mult(unit, rd(mult(a, b), mult(b, c))), mult(mult(b, c), c))))),
% 1.46/1.20 inference(monotonicity,[status(thm)],[626])).
% 1.46/1.20 tff(628,assumption,(~(mult(mult(rd(mult(a, b), mult(b, c)), mult(b, c)), c) = mult(rd(mult(a, b), mult(b, c)), mult(c, mult(b, c))))), introduced(assumption)).
% 1.46/1.20 tff(629,plain,
% 1.46/1.20 (~(mult(mult(unit, mult(mult(b, c), c)), rd(mult(a, b), mult(b, c))) = mult(mult(unit, rd(mult(a, b), mult(b, c))), mult(mult(b, c), c)))),
% 1.46/1.20 inference(modus_ponens,[status(thm)],[628, 627])).
% 1.46/1.20 tff(630,plain,
% 1.46/1.20 (((~(mult(mult(unit, mult(mult(b, c), c)), rd(mult(a, b), mult(b, c))) = mult(mult(unit, rd(mult(a, b), mult(b, c))), mult(mult(b, c), c)))) | (~(mult(unit, mult(mult(mult(b, c), c), rd(mult(a, b), mult(b, c)))) = mult(unit, mult(rd(mult(a, b), mult(b, c)), mult(mult(b, c), c)))))) | (mult(mult(unit, mult(mult(b, c), c)), rd(mult(a, b), mult(b, c))) = mult(mult(unit, rd(mult(a, b), mult(b, c))), mult(mult(b, c), c)))),
% 1.46/1.20 inference(tautology,[status(thm)],[])).
% 1.46/1.20 tff(631,plain,
% 1.46/1.20 ((~(mult(mult(unit, mult(mult(b, c), c)), rd(mult(a, b), mult(b, c))) = mult(mult(unit, rd(mult(a, b), mult(b, c))), mult(mult(b, c), c)))) | (~(mult(unit, mult(mult(mult(b, c), c), rd(mult(a, b), mult(b, c)))) = mult(unit, mult(rd(mult(a, b), mult(b, c)), mult(mult(b, c), c)))))),
% 1.46/1.20 inference(unit_resolution,[status(thm)],[630, 629])).
% 1.46/1.20 tff(632,plain,
% 1.46/1.20 ((mult(rd(mult(a, b), mult(b, c)), mult(c, mult(b, c))) = mult(mult(rd(mult(a, b), mult(b, c)), mult(b, c)), c)) <=> (mult(mult(rd(mult(a, b), mult(b, c)), mult(b, c)), c) = mult(rd(mult(a, b), mult(b, c)), mult(c, mult(b, c))))),
% 1.46/1.20 inference(commutativity,[status(thm)],[])).
% 1.46/1.20 tff(633,plain,
% 1.46/1.20 (mult(mult(mult(b, c), c), rd(mult(a, b), mult(b, c))) = mult(mult(b, c), ld(mult(b, c), mult(mult(a, b), c)))),
% 1.46/1.20 inference(transitivity,[status(thm)],[623, 80, 92])).
% 1.46/1.20 tff(634,plain,
% 1.46/1.20 (mult(unit, mult(mult(mult(b, c), c), rd(mult(a, b), mult(b, c)))) = mult(unit, mult(mult(b, c), ld(mult(b, c), mult(mult(a, b), c))))),
% 1.46/1.20 inference(monotonicity,[status(thm)],[633])).
% 1.46/1.20 tff(635,plain,
% 1.46/1.20 (mult(unit, mult(mult(mult(b, c), c), rd(mult(a, b), mult(b, c)))) = mult(mult(rd(mult(a, b), mult(b, c)), mult(b, c)), c)),
% 1.46/1.20 inference(transitivity,[status(thm)],[634, 588, 587, 477])).
% 1.46/1.20 tff(636,plain,
% 1.46/1.20 ((mult(mult(unit, rd(mult(a, b), mult(b, c))), mult(mult(b, c), c)) = mult(unit, mult(mult(mult(b, c), c), rd(mult(a, b), mult(b, c))))) <=> (mult(rd(mult(a, b), mult(b, c)), mult(c, mult(b, c))) = mult(mult(rd(mult(a, b), mult(b, c)), mult(b, c)), c))),
% 1.46/1.20 inference(monotonicity,[status(thm)],[622, 635])).
% 1.46/1.20 tff(637,plain,
% 1.46/1.20 ((mult(mult(unit, rd(mult(a, b), mult(b, c))), mult(mult(b, c), c)) = mult(unit, mult(mult(mult(b, c), c), rd(mult(a, b), mult(b, c))))) <=> (mult(mult(rd(mult(a, b), mult(b, c)), mult(b, c)), c) = mult(rd(mult(a, b), mult(b, c)), mult(c, mult(b, c))))),
% 1.46/1.20 inference(transitivity,[status(thm)],[636, 632])).
% 1.46/1.20 tff(638,plain,
% 1.46/1.20 ((mult(mult(rd(mult(a, b), mult(b, c)), mult(b, c)), c) = mult(rd(mult(a, b), mult(b, c)), mult(c, mult(b, c)))) <=> (mult(mult(unit, rd(mult(a, b), mult(b, c))), mult(mult(b, c), c)) = mult(unit, mult(mult(mult(b, c), c), rd(mult(a, b), mult(b, c)))))),
% 1.46/1.20 inference(symmetry,[status(thm)],[637])).
% 1.46/1.20 tff(639,plain,
% 1.46/1.20 ((~(mult(mult(rd(mult(a, b), mult(b, c)), mult(b, c)), c) = mult(rd(mult(a, b), mult(b, c)), mult(c, mult(b, c))))) <=> (~(mult(mult(unit, rd(mult(a, b), mult(b, c))), mult(mult(b, c), c)) = mult(unit, mult(mult(mult(b, c), c), rd(mult(a, b), mult(b, c))))))),
% 1.46/1.20 inference(monotonicity,[status(thm)],[638])).
% 1.46/1.20 tff(640,plain,
% 1.46/1.20 (~(mult(mult(unit, rd(mult(a, b), mult(b, c))), mult(mult(b, c), c)) = mult(unit, mult(mult(mult(b, c), c), rd(mult(a, b), mult(b, c)))))),
% 1.46/1.20 inference(modus_ponens,[status(thm)],[628, 639])).
% 1.46/1.20 tff(641,plain,
% 1.46/1.20 (((~(mult(mult(unit, mult(mult(b, c), c)), rd(mult(a, b), mult(b, c))) = mult(unit, mult(rd(mult(a, b), mult(b, c)), mult(mult(b, c), c))))) | (~(mult(mult(unit, rd(mult(a, b), mult(b, c))), mult(mult(b, c), c)) = mult(unit, mult(mult(mult(b, c), c), rd(mult(a, b), mult(b, c))))))) | (mult(mult(unit, rd(mult(a, b), mult(b, c))), mult(mult(b, c), c)) = mult(unit, mult(mult(mult(b, c), c), rd(mult(a, b), mult(b, c)))))),
% 1.46/1.20 inference(tautology,[status(thm)],[])).
% 1.46/1.20 tff(642,plain,
% 1.46/1.20 ((~(mult(mult(unit, mult(mult(b, c), c)), rd(mult(a, b), mult(b, c))) = mult(unit, mult(rd(mult(a, b), mult(b, c)), mult(mult(b, c), c))))) | (~(mult(mult(unit, rd(mult(a, b), mult(b, c))), mult(mult(b, c), c)) = mult(unit, mult(mult(mult(b, c), c), rd(mult(a, b), mult(b, c))))))),
% 1.46/1.20 inference(unit_resolution,[status(thm)],[641, 640])).
% 1.46/1.20 tff(643,plain,
% 1.46/1.20 (((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(mult(unit, mult(mult(b, c), c)), rd(mult(a, b), mult(b, c))) = mult(mult(unit, rd(mult(a, b), mult(b, c))), mult(mult(b, c), c)))) | (~(mult(unit, mult(mult(mult(b, c), c), rd(mult(a, b), mult(b, c)))) = mult(unit, mult(rd(mult(a, b), mult(b, c)), mult(mult(b, c), c))))))) | (~((~(mult(mult(unit, mult(mult(b, c), c)), rd(mult(a, b), mult(b, c))) = mult(unit, mult(rd(mult(a, b), mult(b, c)), mult(mult(b, c), c))))) | (~(mult(mult(unit, rd(mult(a, b), mult(b, c))), mult(mult(b, c), c)) = mult(unit, mult(mult(mult(b, c), c), rd(mult(a, b), mult(b, c)))))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | (~((~(mult(mult(unit, mult(mult(b, c), c)), rd(mult(a, b), mult(b, c))) = mult(mult(unit, rd(mult(a, b), mult(b, c))), mult(mult(b, c), c)))) | (~(mult(unit, mult(mult(mult(b, c), c), rd(mult(a, b), mult(b, c)))) = mult(unit, mult(rd(mult(a, b), mult(b, c)), mult(mult(b, c), c))))))) | (~((~(mult(mult(unit, mult(mult(b, c), c)), rd(mult(a, b), mult(b, c))) = mult(unit, mult(rd(mult(a, b), mult(b, c)), mult(mult(b, c), c))))) | (~(mult(mult(unit, rd(mult(a, b), mult(b, c))), mult(mult(b, c), c)) = mult(unit, mult(mult(mult(b, c), c), rd(mult(a, b), mult(b, c)))))))))),
% 1.46/1.20 inference(rewrite,[status(thm)],[])).
% 1.46/1.20 tff(644,plain,
% 1.46/1.20 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | ((~((~(mult(mult(unit, mult(mult(b, c), c)), rd(mult(a, b), mult(b, c))) = mult(mult(unit, rd(mult(a, b), mult(b, c))), mult(mult(b, c), c)))) | (~(mult(unit, mult(mult(mult(b, c), c), rd(mult(a, b), mult(b, c)))) = mult(unit, mult(rd(mult(a, b), mult(b, c)), mult(mult(b, c), c))))))) | (~((~(mult(mult(unit, mult(mult(b, c), c)), rd(mult(a, b), mult(b, c))) = mult(unit, mult(rd(mult(a, b), mult(b, c)), mult(mult(b, c), c))))) | (~(mult(mult(unit, rd(mult(a, b), mult(b, c))), mult(mult(b, c), c)) = mult(unit, mult(mult(mult(b, c), c), rd(mult(a, b), mult(b, c)))))))))),
% 1.46/1.20 inference(quant_inst,[status(thm)],[])).
% 1.46/1.20 tff(645,plain,
% 1.46/1.20 ((~![X0: $i, X1: $i, X2: $i] : ((~((~(mult(mult(X0, X1), X2) = mult(mult(X0, X2), X1))) | (~(mult(X0, mult(X1, X2)) = mult(X0, mult(X2, X1)))))) | (~((~(mult(mult(X0, X1), X2) = mult(X0, mult(X2, X1)))) | (~(mult(mult(X0, X2), X1) = mult(X0, mult(X1, X2)))))))) | (~((~(mult(mult(unit, mult(mult(b, c), c)), rd(mult(a, b), mult(b, c))) = mult(mult(unit, rd(mult(a, b), mult(b, c))), mult(mult(b, c), c)))) | (~(mult(unit, mult(mult(mult(b, c), c), rd(mult(a, b), mult(b, c)))) = mult(unit, mult(rd(mult(a, b), mult(b, c)), mult(mult(b, c), c))))))) | (~((~(mult(mult(unit, mult(mult(b, c), c)), rd(mult(a, b), mult(b, c))) = mult(unit, mult(rd(mult(a, b), mult(b, c)), mult(mult(b, c), c))))) | (~(mult(mult(unit, rd(mult(a, b), mult(b, c))), mult(mult(b, c), c)) = mult(unit, mult(mult(mult(b, c), c), rd(mult(a, b), mult(b, c))))))))),
% 1.46/1.20 inference(modus_ponens,[status(thm)],[644, 643])).
% 1.46/1.20 tff(646,plain,
% 1.46/1.20 ((~((~(mult(mult(unit, mult(mult(b, c), c)), rd(mult(a, b), mult(b, c))) = mult(mult(unit, rd(mult(a, b), mult(b, c))), mult(mult(b, c), c)))) | (~(mult(unit, mult(mult(mult(b, c), c), rd(mult(a, b), mult(b, c)))) = mult(unit, mult(rd(mult(a, b), mult(b, c)), mult(mult(b, c), c))))))) | (~((~(mult(mult(unit, mult(mult(b, c), c)), rd(mult(a, b), mult(b, c))) = mult(unit, mult(rd(mult(a, b), mult(b, c)), mult(mult(b, c), c))))) | (~(mult(mult(unit, rd(mult(a, b), mult(b, c))), mult(mult(b, c), c)) = mult(unit, mult(mult(mult(b, c), c), rd(mult(a, b), mult(b, c))))))))),
% 1.46/1.20 inference(unit_resolution,[status(thm)],[645, 64])).
% 1.46/1.20 tff(647,plain,
% 1.46/1.20 ($false),
% 1.46/1.20 inference(unit_resolution,[status(thm)],[646, 642, 631])).
% 1.46/1.20 tff(648,plain,((~(mult(mult(mult(b, c), c), rd(mult(a, b), mult(b, c))) = mult(mult(mult(b, c), rd(mult(a, b), mult(b, c))), c))) | (mult(mult(rd(mult(a, b), mult(b, c)), mult(b, c)), c) = mult(rd(mult(a, b), mult(b, c)), mult(c, mult(b, c))))), inference(lemma,lemma(discharge,[]))).
% 1.46/1.21 tff(649,plain,
% 1.46/1.21 (mult(mult(rd(mult(a, b), mult(b, c)), mult(b, c)), c) = mult(rd(mult(a, b), mult(b, c)), mult(c, mult(b, c)))),
% 1.46/1.21 inference(unit_resolution,[status(thm)],[648, 602])).
% 1.46/1.21 tff(650,plain,
% 1.46/1.21 (mult(mult(unit, rd(mult(a, b), mult(b, c))), mult(mult(b, c), c)) = mult(mult(unit, mult(mult(b, c), c)), rd(mult(a, b), mult(b, c)))),
% 1.46/1.21 inference(modus_ponens,[status(thm)],[649, 620])).
% 1.46/1.21 tff(651,plain,
% 1.46/1.21 (mult(rd(mult(a, b), mult(b, c)), mult(mult(c, b), c)) = mult(rd(mult(a, b), mult(b, c)), mult(mult(b, c), c))),
% 1.46/1.21 inference(monotonicity,[status(thm)],[532])).
% 1.46/1.21 tff(652,plain,
% 1.46/1.21 (((~(mult(rd(mult(a, b), mult(b, c)), mult(c, b)) = mult(rd(mult(a, b), mult(b, c)), mult(b, c)))) | (~(mult(mult(rd(mult(a, b), mult(b, c)), c), b) = mult(mult(rd(mult(a, b), mult(b, c)), b), c)))) | (mult(mult(rd(mult(a, b), mult(b, c)), c), b) = mult(mult(rd(mult(a, b), mult(b, c)), b), c))),
% 1.46/1.21 inference(tautology,[status(thm)],[])).
% 1.46/1.21 tff(653,plain,
% 1.46/1.21 (mult(mult(rd(mult(a, b), mult(b, c)), c), b) = mult(mult(rd(mult(a, b), mult(b, c)), b), c)),
% 1.46/1.21 inference(unit_resolution,[status(thm)],[652, 524])).
% 1.46/1.21 tff(654,plain,
% 1.46/1.21 (mult(mult(rd(mult(a, b), mult(b, c)), b), c) = mult(mult(rd(mult(a, b), mult(b, c)), c), b)),
% 1.46/1.21 inference(symmetry,[status(thm)],[653])).
% 1.46/1.21 tff(655,plain,
% 1.46/1.21 (mult(mult(mult(rd(mult(a, b), mult(b, c)), b), c), c) = mult(mult(mult(rd(mult(a, b), mult(b, c)), c), b), c)),
% 1.46/1.21 inference(monotonicity,[status(thm)],[654])).
% 1.46/1.21 tff(656,plain,
% 1.46/1.21 (mult(mult(mult(rd(mult(a, b), mult(b, c)), b), c), c) = mult(mult(a, b), c)),
% 1.46/1.21 inference(transitivity,[status(thm)],[655, 508, 651, 614, 650, 608, 606, 602, 80])).
% 1.46/1.21 tff(657,plain,
% 1.46/1.21 (rd(mult(mult(mult(rd(mult(a, b), mult(b, c)), b), c), c), c) = rd(mult(mult(a, b), c), c)),
% 1.46/1.21 inference(monotonicity,[status(thm)],[656])).
% 1.46/1.21 tff(658,plain,
% 1.46/1.21 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(rd(mult(a, b), mult(b, c)), b), c), c), c) = mult(mult(rd(mult(a, b), mult(b, c)), b), c))),
% 1.46/1.21 inference(quant_inst,[status(thm)],[])).
% 1.46/1.21 tff(659,plain,
% 1.46/1.21 (rd(mult(mult(mult(rd(mult(a, b), mult(b, c)), b), c), c), c) = mult(mult(rd(mult(a, b), mult(b, c)), b), c)),
% 1.46/1.21 inference(unit_resolution,[status(thm)],[658, 17])).
% 1.46/1.21 tff(660,plain,
% 1.46/1.21 (mult(mult(rd(mult(a, b), mult(b, c)), b), c) = rd(mult(mult(mult(rd(mult(a, b), mult(b, c)), b), c), c), c)),
% 1.46/1.21 inference(symmetry,[status(thm)],[659])).
% 1.46/1.21 tff(661,plain,
% 1.46/1.21 (mult(mult(rd(mult(a, b), mult(b, c)), c), b) = mult(rd(mult(a, b), mult(b, c)), mult(b, c))),
% 1.46/1.21 inference(transitivity,[status(thm)],[653, 660, 657, 19, 10])).
% 1.46/1.21 tff(662,plain,
% 1.46/1.21 ($false),
% 1.46/1.21 inference(unit_resolution,[status(thm)],[514, 661])).
% 1.46/1.21 % SZS output end Proof
%------------------------------------------------------------------------------