TSTP Solution File: GRP755-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP755-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n029.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 22:29:44 EDT 2022
% Result : Unsatisfiable 4.57s 3.15s
% Output : Proof 4.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP755-1 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Aug 31 21:00:28 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.19/0.34 Usage: tptp [options] [-file:]file
% 0.19/0.34 -h, -? prints this message.
% 0.19/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.19/0.34 -m, -model generate model.
% 0.19/0.34 -p, -proof generate proof.
% 0.19/0.34 -c, -core generate unsat core of named formulas.
% 0.19/0.34 -st, -statistics display statistics.
% 0.19/0.34 -t:timeout set timeout (in second).
% 0.19/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.19/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.19/0.34 -<param>:<value> configuration parameter and value.
% 0.19/0.34 -o:<output-file> file to place output in.
% 4.57/3.15 % SZS status Unsatisfiable
% 4.57/3.15 % SZS output start Proof
% 4.57/3.15 tff(mult_type, type, (
% 4.57/3.15 mult: ( $i * $i ) > $i)).
% 4.57/3.15 tff(b_type, type, (
% 4.57/3.15 b: $i)).
% 4.57/3.15 tff(ld_type, type, (
% 4.57/3.15 ld: ( $i * $i ) > $i)).
% 4.57/3.15 tff(unit_type, type, (
% 4.57/3.15 unit: $i)).
% 4.57/3.15 tff(a_type, type, (
% 4.57/3.15 a: $i)).
% 4.57/3.15 tff(i_type, type, (
% 4.57/3.15 i: $i > $i)).
% 4.57/3.15 tff(rd_type, type, (
% 4.57/3.15 rd: ( $i * $i ) > $i)).
% 4.57/3.15 tff(1,plain,
% 4.57/3.15 ((mult(mult(a, b), ld(mult(a, b), unit)) = mult(a, mult(ld(mult(a, b), unit), b))) <=> (mult(a, mult(ld(mult(a, b), unit), b)) = mult(mult(a, b), ld(mult(a, b), unit)))),
% 4.57/3.15 inference(commutativity,[status(thm)],[])).
% 4.57/3.15 tff(2,plain,
% 4.57/3.15 (^[A: $i] : refl((mult(A, unit) = A) <=> (mult(A, unit) = A))),
% 4.57/3.15 inference(bind,[status(th)],[])).
% 4.57/3.15 tff(3,plain,
% 4.57/3.15 (![A: $i] : (mult(A, unit) = A) <=> ![A: $i] : (mult(A, unit) = A)),
% 4.57/3.15 inference(quant_intro,[status(thm)],[2])).
% 4.57/3.15 tff(4,plain,
% 4.57/3.15 (![A: $i] : (mult(A, unit) = A) <=> ![A: $i] : (mult(A, unit) = A)),
% 4.57/3.15 inference(rewrite,[status(thm)],[])).
% 4.57/3.15 tff(5,axiom,(![A: $i] : (mult(A, unit) = A)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','f05')).
% 4.57/3.15 tff(6,plain,
% 4.57/3.15 (![A: $i] : (mult(A, unit) = A)),
% 4.57/3.15 inference(modus_ponens,[status(thm)],[5, 4])).
% 4.57/3.15 tff(7,plain,(
% 4.57/3.15 ![A: $i] : (mult(A, unit) = A)),
% 4.57/3.15 inference(skolemize,[status(sab)],[6])).
% 4.57/3.15 tff(8,plain,
% 4.57/3.15 (![A: $i] : (mult(A, unit) = A)),
% 4.57/3.15 inference(modus_ponens,[status(thm)],[7, 3])).
% 4.57/3.15 tff(9,plain,
% 4.57/3.15 ((~![A: $i] : (mult(A, unit) = A)) | (mult(a, unit) = a)),
% 4.57/3.15 inference(quant_inst,[status(thm)],[])).
% 4.57/3.15 tff(10,plain,
% 4.57/3.15 (mult(a, unit) = a),
% 4.57/3.15 inference(unit_resolution,[status(thm)],[9, 8])).
% 4.57/3.15 tff(11,plain,
% 4.57/3.15 (^[B: $i, A: $i] : refl((mult(A, ld(A, B)) = B) <=> (mult(A, ld(A, B)) = B))),
% 4.57/3.15 inference(bind,[status(th)],[])).
% 4.57/3.15 tff(12,plain,
% 4.57/3.15 (![B: $i, A: $i] : (mult(A, ld(A, B)) = B) <=> ![B: $i, A: $i] : (mult(A, ld(A, B)) = B)),
% 4.57/3.15 inference(quant_intro,[status(thm)],[11])).
% 4.57/3.15 tff(13,plain,
% 4.57/3.15 (![B: $i, A: $i] : (mult(A, ld(A, B)) = B) <=> ![B: $i, A: $i] : (mult(A, ld(A, B)) = B)),
% 4.57/3.15 inference(rewrite,[status(thm)],[])).
% 4.57/3.15 tff(14,axiom,(![B: $i, A: $i] : (mult(A, ld(A, B)) = B)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','f01')).
% 4.57/3.15 tff(15,plain,
% 4.57/3.15 (![B: $i, A: $i] : (mult(A, ld(A, B)) = B)),
% 4.57/3.15 inference(modus_ponens,[status(thm)],[14, 13])).
% 4.57/3.15 tff(16,plain,(
% 4.57/3.15 ![B: $i, A: $i] : (mult(A, ld(A, B)) = B)),
% 4.57/3.15 inference(skolemize,[status(sab)],[15])).
% 4.57/3.15 tff(17,plain,
% 4.57/3.15 (![B: $i, A: $i] : (mult(A, ld(A, B)) = B)),
% 4.57/3.15 inference(modus_ponens,[status(thm)],[16, 12])).
% 4.57/3.15 tff(18,plain,
% 4.57/3.15 ((~![B: $i, A: $i] : (mult(A, ld(A, B)) = B)) | (mult(b, ld(b, unit)) = unit)),
% 4.57/3.15 inference(quant_inst,[status(thm)],[])).
% 4.57/3.15 tff(19,plain,
% 4.57/3.15 (mult(b, ld(b, unit)) = unit),
% 4.57/3.15 inference(unit_resolution,[status(thm)],[18, 17])).
% 4.57/3.15 tff(20,plain,
% 4.57/3.15 (^[A: $i] : refl((i(A) = ld(A, unit)) <=> (i(A) = ld(A, unit)))),
% 4.57/3.15 inference(bind,[status(th)],[])).
% 4.57/3.15 tff(21,plain,
% 4.57/3.15 (![A: $i] : (i(A) = ld(A, unit)) <=> ![A: $i] : (i(A) = ld(A, unit))),
% 4.57/3.15 inference(quant_intro,[status(thm)],[20])).
% 4.57/3.15 tff(22,plain,
% 4.57/3.15 (![A: $i] : (i(A) = ld(A, unit)) <=> ![A: $i] : (i(A) = ld(A, unit))),
% 4.57/3.15 inference(rewrite,[status(thm)],[])).
% 4.57/3.15 tff(23,axiom,(![A: $i] : (i(A) = ld(A, unit))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','f09')).
% 4.57/3.15 tff(24,plain,
% 4.57/3.15 (![A: $i] : (i(A) = ld(A, unit))),
% 4.57/3.15 inference(modus_ponens,[status(thm)],[23, 22])).
% 4.57/3.15 tff(25,plain,(
% 4.57/3.15 ![A: $i] : (i(A) = ld(A, unit))),
% 4.57/3.15 inference(skolemize,[status(sab)],[24])).
% 4.57/3.15 tff(26,plain,
% 4.57/3.15 (![A: $i] : (i(A) = ld(A, unit))),
% 4.57/3.15 inference(modus_ponens,[status(thm)],[25, 21])).
% 4.57/3.15 tff(27,plain,
% 4.57/3.15 ((~![A: $i] : (i(A) = ld(A, unit))) | (i(b) = ld(b, unit))),
% 4.57/3.15 inference(quant_inst,[status(thm)],[])).
% 4.57/3.15 tff(28,plain,
% 4.57/3.15 (i(b) = ld(b, unit)),
% 4.57/3.15 inference(unit_resolution,[status(thm)],[27, 26])).
% 4.57/3.15 tff(29,plain,
% 4.57/3.15 (mult(b, i(b)) = mult(b, ld(b, unit))),
% 4.57/3.15 inference(monotonicity,[status(thm)],[28])).
% 4.57/3.15 tff(30,plain,
% 4.57/3.15 (mult(b, i(b)) = unit),
% 4.57/3.15 inference(transitivity,[status(thm)],[29, 19])).
% 4.57/3.15 tff(31,plain,
% 4.57/3.15 (mult(a, mult(b, i(b))) = mult(a, unit)),
% 4.57/3.15 inference(monotonicity,[status(thm)],[30])).
% 4.57/3.15 tff(32,plain,
% 4.57/3.15 (mult(b, ld(b, unit)) = mult(b, i(b))),
% 4.57/3.15 inference(symmetry,[status(thm)],[29])).
% 4.57/3.15 tff(33,assumption,(~(mult(unit, i(b)) = i(b))), introduced(assumption)).
% 4.57/3.15 tff(34,plain,
% 4.57/3.15 (^[A: $i] : refl((mult(unit, A) = A) <=> (mult(unit, A) = A))),
% 4.57/3.15 inference(bind,[status(th)],[])).
% 4.57/3.15 tff(35,plain,
% 4.57/3.15 (![A: $i] : (mult(unit, A) = A) <=> ![A: $i] : (mult(unit, A) = A)),
% 4.57/3.15 inference(quant_intro,[status(thm)],[34])).
% 4.57/3.15 tff(36,plain,
% 4.57/3.15 (![A: $i] : (mult(unit, A) = A) <=> ![A: $i] : (mult(unit, A) = A)),
% 4.57/3.15 inference(rewrite,[status(thm)],[])).
% 4.57/3.15 tff(37,axiom,(![A: $i] : (mult(unit, A) = A)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','f06')).
% 4.57/3.15 tff(38,plain,
% 4.57/3.15 (![A: $i] : (mult(unit, A) = A)),
% 4.57/3.15 inference(modus_ponens,[status(thm)],[37, 36])).
% 4.57/3.15 tff(39,plain,(
% 4.57/3.15 ![A: $i] : (mult(unit, A) = A)),
% 4.57/3.15 inference(skolemize,[status(sab)],[38])).
% 4.57/3.15 tff(40,plain,
% 4.57/3.15 (![A: $i] : (mult(unit, A) = A)),
% 4.57/3.15 inference(modus_ponens,[status(thm)],[39, 35])).
% 4.57/3.15 tff(41,plain,
% 4.57/3.15 ((~![A: $i] : (mult(unit, A) = A)) | (mult(unit, i(b)) = i(b))),
% 4.57/3.15 inference(quant_inst,[status(thm)],[])).
% 4.57/3.15 tff(42,plain,
% 4.57/3.15 ($false),
% 4.57/3.15 inference(unit_resolution,[status(thm)],[41, 40, 33])).
% 4.57/3.15 tff(43,plain,(mult(unit, i(b)) = i(b)), inference(lemma,lemma(discharge,[]))).
% 4.57/3.15 tff(44,plain,
% 4.57/3.15 (mult(mult(b, i(b)), i(b)) = mult(unit, i(b))),
% 4.57/3.15 inference(monotonicity,[status(thm)],[30])).
% 4.57/3.15 tff(45,plain,
% 4.57/3.15 (^[B: $i, A: $i, C: $i] : refl(((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C))) <=> ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C))))),
% 4.57/3.15 inference(bind,[status(th)],[])).
% 4.57/3.15 tff(46,plain,
% 4.57/3.15 (![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C))) <=> ![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))),
% 4.57/3.15 inference(quant_intro,[status(thm)],[45])).
% 4.57/3.15 tff(47,plain,
% 4.57/3.15 (![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C))) <=> ![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))),
% 4.57/3.15 inference(rewrite,[status(thm)],[])).
% 4.57/3.15 tff(48,axiom,(![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','f08')).
% 4.57/3.15 tff(49,plain,
% 4.57/3.15 (![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))),
% 4.57/3.15 inference(modus_ponens,[status(thm)],[48, 47])).
% 4.57/3.15 tff(50,plain,(
% 4.57/3.15 ![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))),
% 4.57/3.15 inference(skolemize,[status(sab)],[49])).
% 4.57/3.15 tff(51,plain,
% 4.57/3.15 (![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))),
% 4.57/3.15 inference(modus_ponens,[status(thm)],[50, 46])).
% 4.57/3.15 tff(52,plain,
% 4.57/3.15 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(b, mult(i(b), i(b))) = mult(mult(b, i(b)), i(b)))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(b, mult(i(b), i(b))) = mult(mult(b, i(b)), i(b))))),
% 4.57/3.15 inference(rewrite,[status(thm)],[])).
% 4.57/3.15 tff(53,plain,
% 4.57/3.15 (((mult(b, mult(i(b), i(b))) = mult(mult(b, i(b)), i(b))) | (mult(b, mult(i(b), i(b))) = mult(mult(b, i(b)), i(b)))) <=> (mult(b, mult(i(b), i(b))) = mult(mult(b, i(b)), i(b)))),
% 4.57/3.15 inference(rewrite,[status(thm)],[])).
% 4.57/3.15 tff(54,plain,
% 4.57/3.15 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(b, mult(i(b), i(b))) = mult(mult(b, i(b)), i(b))) | (mult(b, mult(i(b), i(b))) = mult(mult(b, i(b)), i(b))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(b, mult(i(b), i(b))) = mult(mult(b, i(b)), i(b))))),
% 4.57/3.15 inference(monotonicity,[status(thm)],[53])).
% 4.57/3.15 tff(55,plain,
% 4.57/3.15 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(b, mult(i(b), i(b))) = mult(mult(b, i(b)), i(b))) | (mult(b, mult(i(b), i(b))) = mult(mult(b, i(b)), i(b))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(b, mult(i(b), i(b))) = mult(mult(b, i(b)), i(b))))),
% 4.57/3.15 inference(transitivity,[status(thm)],[54, 52])).
% 4.57/3.15 tff(56,plain,
% 4.57/3.15 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(b, mult(i(b), i(b))) = mult(mult(b, i(b)), i(b))) | (mult(b, mult(i(b), i(b))) = mult(mult(b, i(b)), i(b))))),
% 4.57/3.15 inference(quant_inst,[status(thm)],[])).
% 4.57/3.15 tff(57,plain,
% 4.57/3.15 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(b, mult(i(b), i(b))) = mult(mult(b, i(b)), i(b)))),
% 4.57/3.15 inference(modus_ponens,[status(thm)],[56, 55])).
% 4.57/3.15 tff(58,plain,
% 4.57/3.15 (mult(b, mult(i(b), i(b))) = mult(mult(b, i(b)), i(b))),
% 4.57/3.15 inference(unit_resolution,[status(thm)],[57, 51])).
% 4.57/3.15 tff(59,plain,
% 4.57/3.15 (mult(b, mult(i(b), i(b))) = ld(b, unit)),
% 4.57/3.15 inference(transitivity,[status(thm)],[58, 44, 43, 28])).
% 4.57/3.15 tff(60,plain,
% 4.57/3.15 (mult(b, mult(b, mult(i(b), i(b)))) = mult(b, ld(b, unit))),
% 4.57/3.15 inference(monotonicity,[status(thm)],[59])).
% 4.57/3.15 tff(61,plain,
% 4.57/3.15 (mult(b, mult(i(b), i(b))) = i(b)),
% 4.57/3.15 inference(transitivity,[status(thm)],[58, 44, 43])).
% 4.57/3.15 tff(62,plain,
% 4.57/3.15 (mult(mult(b, mult(i(b), i(b))), b) = mult(i(b), b)),
% 4.57/3.15 inference(monotonicity,[status(thm)],[61])).
% 4.57/3.15 tff(63,plain,
% 4.57/3.15 (mult(i(b), b) = mult(mult(b, mult(i(b), i(b))), b)),
% 4.57/3.15 inference(symmetry,[status(thm)],[62])).
% 4.57/3.15 tff(64,plain,
% 4.57/3.15 (mult(mult(unit, i(b)), b) = mult(i(b), b)),
% 4.57/3.15 inference(monotonicity,[status(thm)],[43])).
% 4.57/3.15 tff(65,plain,
% 4.57/3.15 (mult(mult(unit, i(b)), b) = mult(mult(b, mult(i(b), i(b))), b)),
% 4.57/3.15 inference(transitivity,[status(thm)],[64, 63])).
% 4.57/3.15 tff(66,plain,
% 4.57/3.15 (mult(b, ld(b, unit)) = mult(b, mult(b, mult(i(b), i(b))))),
% 4.57/3.15 inference(symmetry,[status(thm)],[60])).
% 4.57/3.15 tff(67,plain,
% 4.57/3.15 (unit = mult(b, ld(b, unit))),
% 4.57/3.15 inference(symmetry,[status(thm)],[19])).
% 4.57/3.15 tff(68,plain,
% 4.57/3.15 ((~![A: $i] : (mult(unit, A) = A)) | (mult(unit, unit) = unit)),
% 4.57/3.15 inference(quant_inst,[status(thm)],[])).
% 4.57/3.15 tff(69,plain,
% 4.57/3.15 (mult(unit, unit) = unit),
% 4.57/3.15 inference(unit_resolution,[status(thm)],[68, 40])).
% 4.57/3.15 tff(70,plain,
% 4.57/3.15 (mult(unit, mult(b, i(b))) = mult(unit, unit)),
% 4.57/3.15 inference(monotonicity,[status(thm)],[30])).
% 4.57/3.15 tff(71,plain,
% 4.57/3.15 (mult(unit, mult(b, i(b))) = mult(b, mult(b, mult(i(b), i(b))))),
% 4.57/3.15 inference(transitivity,[status(thm)],[70, 69, 67, 66])).
% 4.57/3.15 tff(72,plain,
% 4.57/3.15 ((mult(unit, mult(b, i(b))) = mult(mult(unit, i(b)), b)) <=> (mult(b, mult(b, mult(i(b), i(b)))) = mult(mult(b, mult(i(b), i(b))), b))),
% 4.57/3.15 inference(monotonicity,[status(thm)],[71, 65])).
% 4.57/3.15 tff(73,assumption,(~(mult(b, mult(b, mult(i(b), i(b)))) = mult(mult(b, mult(i(b), i(b))), b))), introduced(assumption)).
% 4.57/3.15 tff(74,plain,
% 4.57/3.15 (^[B: $i, A: $i] : refl((rd(mult(A, B), B) = A) <=> (rd(mult(A, B), B) = A))),
% 4.57/3.15 inference(bind,[status(th)],[])).
% 4.57/3.15 tff(75,plain,
% 4.57/3.15 (![B: $i, A: $i] : (rd(mult(A, B), B) = A) <=> ![B: $i, A: $i] : (rd(mult(A, B), B) = A)),
% 4.57/3.15 inference(quant_intro,[status(thm)],[74])).
% 4.57/3.15 tff(76,plain,
% 4.57/3.15 (![B: $i, A: $i] : (rd(mult(A, B), B) = A) <=> ![B: $i, A: $i] : (rd(mult(A, B), B) = A)),
% 4.57/3.15 inference(rewrite,[status(thm)],[])).
% 4.57/3.15 tff(77,axiom,(![B: $i, A: $i] : (rd(mult(A, B), B) = A)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','f04')).
% 4.57/3.15 tff(78,plain,
% 4.57/3.15 (![B: $i, A: $i] : (rd(mult(A, B), B) = A)),
% 4.57/3.15 inference(modus_ponens,[status(thm)],[77, 76])).
% 4.57/3.15 tff(79,plain,(
% 4.57/3.15 ![B: $i, A: $i] : (rd(mult(A, B), B) = A)),
% 4.57/3.15 inference(skolemize,[status(sab)],[78])).
% 4.57/3.15 tff(80,plain,
% 4.57/3.15 (![B: $i, A: $i] : (rd(mult(A, B), B) = A)),
% 4.57/3.15 inference(modus_ponens,[status(thm)],[79, 75])).
% 4.57/3.15 tff(81,plain,
% 4.57/3.15 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(i(b), b), mult(i(b), i(b))), mult(i(b), i(b))) = mult(i(b), b))),
% 4.57/3.16 inference(quant_inst,[status(thm)],[])).
% 4.57/3.16 tff(82,plain,
% 4.57/3.16 (rd(mult(mult(i(b), b), mult(i(b), i(b))), mult(i(b), i(b))) = mult(i(b), b)),
% 4.57/3.16 inference(unit_resolution,[status(thm)],[81, 80])).
% 4.57/3.16 tff(83,plain,
% 4.57/3.16 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(unit, mult(i(b), i(b))) = mult(mult(unit, i(b)), i(b)))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(unit, mult(i(b), i(b))) = mult(mult(unit, i(b)), i(b))))),
% 4.57/3.16 inference(rewrite,[status(thm)],[])).
% 4.57/3.16 tff(84,plain,
% 4.57/3.16 (((mult(unit, mult(i(b), i(b))) = mult(mult(unit, i(b)), i(b))) | (mult(unit, mult(i(b), i(b))) = mult(mult(unit, i(b)), i(b)))) <=> (mult(unit, mult(i(b), i(b))) = mult(mult(unit, i(b)), i(b)))),
% 4.57/3.16 inference(rewrite,[status(thm)],[])).
% 4.57/3.16 tff(85,plain,
% 4.57/3.16 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(unit, mult(i(b), i(b))) = mult(mult(unit, i(b)), i(b))) | (mult(unit, mult(i(b), i(b))) = mult(mult(unit, i(b)), i(b))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(unit, mult(i(b), i(b))) = mult(mult(unit, i(b)), i(b))))),
% 4.57/3.16 inference(monotonicity,[status(thm)],[84])).
% 4.57/3.16 tff(86,plain,
% 4.57/3.16 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(unit, mult(i(b), i(b))) = mult(mult(unit, i(b)), i(b))) | (mult(unit, mult(i(b), i(b))) = mult(mult(unit, i(b)), i(b))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(unit, mult(i(b), i(b))) = mult(mult(unit, i(b)), i(b))))),
% 4.57/3.16 inference(transitivity,[status(thm)],[85, 83])).
% 4.57/3.16 tff(87,plain,
% 4.57/3.16 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(unit, mult(i(b), i(b))) = mult(mult(unit, i(b)), i(b))) | (mult(unit, mult(i(b), i(b))) = mult(mult(unit, i(b)), i(b))))),
% 4.57/3.16 inference(quant_inst,[status(thm)],[])).
% 4.57/3.16 tff(88,plain,
% 4.57/3.16 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(unit, mult(i(b), i(b))) = mult(mult(unit, i(b)), i(b)))),
% 4.57/3.16 inference(modus_ponens,[status(thm)],[87, 86])).
% 4.57/3.16 tff(89,plain,
% 4.57/3.16 (mult(unit, mult(i(b), i(b))) = mult(mult(unit, i(b)), i(b))),
% 4.57/3.16 inference(unit_resolution,[status(thm)],[88, 51])).
% 4.57/3.16 tff(90,plain,
% 4.57/3.16 (mult(mult(unit, i(b)), i(b)) = mult(unit, mult(i(b), i(b)))),
% 4.57/3.16 inference(symmetry,[status(thm)],[89])).
% 4.57/3.16 tff(91,plain,
% 4.57/3.16 (mult(mult(unit, i(b)), i(b)) = mult(i(b), i(b))),
% 4.57/3.16 inference(monotonicity,[status(thm)],[43])).
% 4.57/3.16 tff(92,plain,
% 4.57/3.16 (mult(i(b), i(b)) = mult(mult(unit, i(b)), i(b))),
% 4.57/3.16 inference(symmetry,[status(thm)],[91])).
% 4.57/3.16 tff(93,plain,
% 4.57/3.16 (mult(i(b), mult(b, mult(i(b), i(b)))) = mult(i(b), i(b))),
% 4.57/3.16 inference(monotonicity,[status(thm)],[61])).
% 4.57/3.16 tff(94,assumption,(mult(i(b), mult(b, mult(i(b), i(b)))) = mult(mult(i(b), b), mult(i(b), i(b)))), introduced(assumption)).
% 4.57/3.16 tff(95,plain,
% 4.57/3.16 (mult(mult(i(b), b), mult(i(b), i(b))) = mult(i(b), mult(b, mult(i(b), i(b))))),
% 4.57/3.16 inference(symmetry,[status(thm)],[94])).
% 4.57/3.16 tff(96,plain,
% 4.57/3.16 (mult(mult(i(b), b), mult(i(b), i(b))) = mult(unit, mult(i(b), i(b)))),
% 4.57/3.16 inference(transitivity,[status(thm)],[95, 93, 92, 90])).
% 4.57/3.16 tff(97,plain,
% 4.57/3.16 (rd(mult(mult(i(b), b), mult(i(b), i(b))), mult(i(b), i(b))) = rd(mult(unit, mult(i(b), i(b))), mult(i(b), i(b)))),
% 4.57/3.16 inference(monotonicity,[status(thm)],[96])).
% 4.57/3.16 tff(98,plain,
% 4.57/3.16 (rd(mult(unit, mult(i(b), i(b))), mult(i(b), i(b))) = rd(mult(mult(i(b), b), mult(i(b), i(b))), mult(i(b), i(b)))),
% 4.57/3.16 inference(symmetry,[status(thm)],[97])).
% 4.57/3.16 tff(99,plain,
% 4.57/3.16 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(unit, mult(i(b), i(b))), mult(i(b), i(b))) = unit)),
% 4.57/3.16 inference(quant_inst,[status(thm)],[])).
% 4.57/3.16 tff(100,plain,
% 4.57/3.16 (rd(mult(unit, mult(i(b), i(b))), mult(i(b), i(b))) = unit),
% 4.57/3.16 inference(unit_resolution,[status(thm)],[99, 80])).
% 4.57/3.16 tff(101,plain,
% 4.57/3.16 (unit = rd(mult(unit, mult(i(b), i(b))), mult(i(b), i(b)))),
% 4.57/3.16 inference(symmetry,[status(thm)],[100])).
% 4.57/3.16 tff(102,plain,
% 4.57/3.16 (mult(b, mult(b, mult(i(b), i(b)))) = mult(mult(b, mult(i(b), i(b))), b)),
% 4.57/3.16 inference(transitivity,[status(thm)],[60, 19, 101, 98, 82, 63])).
% 4.57/3.16 tff(103,plain,
% 4.57/3.16 ($false),
% 4.57/3.16 inference(unit_resolution,[status(thm)],[73, 102])).
% 4.57/3.16 tff(104,plain,((~(mult(i(b), mult(b, mult(i(b), i(b)))) = mult(mult(i(b), b), mult(i(b), i(b))))) | (mult(b, mult(b, mult(i(b), i(b)))) = mult(mult(b, mult(i(b), i(b))), b))), inference(lemma,lemma(discharge,[]))).
% 4.57/3.16 tff(105,plain,
% 4.57/3.16 (~(mult(i(b), mult(b, mult(i(b), i(b)))) = mult(mult(i(b), b), mult(i(b), i(b))))),
% 4.57/3.16 inference(unit_resolution,[status(thm)],[104, 73])).
% 4.57/3.16 tff(106,assumption,(~(mult(i(b), mult(b, mult(i(b), i(b)))) = mult(mult(i(b), b), mult(i(b), i(b))))), introduced(assumption)).
% 4.57/3.16 tff(107,plain,
% 4.57/3.16 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(i(b), mult(b, mult(i(b), i(b)))) = mult(mult(i(b), b), mult(i(b), i(b)))) | (mult(i(b), mult(mult(i(b), i(b)), b)) = mult(mult(i(b), b), mult(i(b), i(b)))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(i(b), mult(b, mult(i(b), i(b)))) = mult(mult(i(b), b), mult(i(b), i(b)))) | (mult(i(b), mult(mult(i(b), i(b)), b)) = mult(mult(i(b), b), mult(i(b), i(b)))))),
% 4.57/3.16 inference(rewrite,[status(thm)],[])).
% 4.57/3.16 tff(108,plain,
% 4.57/3.16 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(i(b), mult(b, mult(i(b), i(b)))) = mult(mult(i(b), b), mult(i(b), i(b)))) | (mult(i(b), mult(mult(i(b), i(b)), b)) = mult(mult(i(b), b), mult(i(b), i(b)))))),
% 4.57/3.16 inference(quant_inst,[status(thm)],[])).
% 4.57/3.16 tff(109,plain,
% 4.57/3.16 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(i(b), mult(b, mult(i(b), i(b)))) = mult(mult(i(b), b), mult(i(b), i(b)))) | (mult(i(b), mult(mult(i(b), i(b)), b)) = mult(mult(i(b), b), mult(i(b), i(b))))),
% 4.57/3.16 inference(modus_ponens,[status(thm)],[108, 107])).
% 4.57/3.16 tff(110,plain,
% 4.57/3.16 ((mult(i(b), mult(b, mult(i(b), i(b)))) = mult(mult(i(b), b), mult(i(b), i(b)))) | (mult(i(b), mult(mult(i(b), i(b)), b)) = mult(mult(i(b), b), mult(i(b), i(b))))),
% 4.57/3.16 inference(unit_resolution,[status(thm)],[109, 51])).
% 4.57/3.16 tff(111,plain,
% 4.57/3.16 (mult(i(b), mult(mult(i(b), i(b)), b)) = mult(mult(i(b), b), mult(i(b), i(b)))),
% 4.57/3.16 inference(unit_resolution,[status(thm)],[110, 106])).
% 4.57/3.16 tff(112,assumption,(mult(unit, mult(b, i(b))) = mult(mult(unit, b), i(b))), introduced(assumption)).
% 4.57/3.16 tff(113,plain,
% 4.57/3.16 (mult(mult(unit, b), i(b)) = mult(unit, mult(b, i(b)))),
% 4.57/3.16 inference(symmetry,[status(thm)],[112])).
% 4.57/3.16 tff(114,plain,
% 4.57/3.16 (mult(mult(unit, b), i(b)) = unit),
% 4.57/3.16 inference(transitivity,[status(thm)],[113, 70, 69])).
% 4.57/3.16 tff(115,plain,
% 4.57/3.16 (mult(mult(mult(unit, b), i(b)), i(b)) = mult(unit, i(b))),
% 4.57/3.16 inference(monotonicity,[status(thm)],[114])).
% 4.57/3.16 tff(116,plain,
% 4.57/3.16 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(unit, b), mult(i(b), i(b))) = mult(mult(mult(unit, b), i(b)), i(b)))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(unit, b), mult(i(b), i(b))) = mult(mult(mult(unit, b), i(b)), i(b))))),
% 4.57/3.16 inference(rewrite,[status(thm)],[])).
% 4.57/3.16 tff(117,plain,
% 4.57/3.16 (((mult(mult(unit, b), mult(i(b), i(b))) = mult(mult(mult(unit, b), i(b)), i(b))) | (mult(mult(unit, b), mult(i(b), i(b))) = mult(mult(mult(unit, b), i(b)), i(b)))) <=> (mult(mult(unit, b), mult(i(b), i(b))) = mult(mult(mult(unit, b), i(b)), i(b)))),
% 4.57/3.16 inference(rewrite,[status(thm)],[])).
% 4.57/3.16 tff(118,plain,
% 4.57/3.16 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(mult(unit, b), mult(i(b), i(b))) = mult(mult(mult(unit, b), i(b)), i(b))) | (mult(mult(unit, b), mult(i(b), i(b))) = mult(mult(mult(unit, b), i(b)), i(b))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(unit, b), mult(i(b), i(b))) = mult(mult(mult(unit, b), i(b)), i(b))))),
% 4.57/3.16 inference(monotonicity,[status(thm)],[117])).
% 4.57/3.16 tff(119,plain,
% 4.57/3.16 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(mult(unit, b), mult(i(b), i(b))) = mult(mult(mult(unit, b), i(b)), i(b))) | (mult(mult(unit, b), mult(i(b), i(b))) = mult(mult(mult(unit, b), i(b)), i(b))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(unit, b), mult(i(b), i(b))) = mult(mult(mult(unit, b), i(b)), i(b))))),
% 4.57/3.16 inference(transitivity,[status(thm)],[118, 116])).
% 4.57/3.16 tff(120,plain,
% 4.57/3.16 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(mult(unit, b), mult(i(b), i(b))) = mult(mult(mult(unit, b), i(b)), i(b))) | (mult(mult(unit, b), mult(i(b), i(b))) = mult(mult(mult(unit, b), i(b)), i(b))))),
% 4.57/3.16 inference(quant_inst,[status(thm)],[])).
% 4.57/3.16 tff(121,plain,
% 4.57/3.16 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(unit, b), mult(i(b), i(b))) = mult(mult(mult(unit, b), i(b)), i(b)))),
% 4.57/3.16 inference(modus_ponens,[status(thm)],[120, 119])).
% 4.57/3.16 tff(122,plain,
% 4.57/3.16 (mult(mult(unit, b), mult(i(b), i(b))) = mult(mult(mult(unit, b), i(b)), i(b))),
% 4.57/3.16 inference(unit_resolution,[status(thm)],[121, 51])).
% 4.57/3.16 tff(123,plain,
% 4.57/3.16 (^[B: $i, A: $i, C: $i] : refl(((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C))) <=> ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C))))),
% 4.57/3.16 inference(bind,[status(th)],[])).
% 4.57/3.16 tff(124,plain,
% 4.57/3.16 (![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C))) <=> ![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))),
% 4.57/3.16 inference(quant_intro,[status(thm)],[123])).
% 4.57/3.16 tff(125,plain,
% 4.57/3.16 (![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C))) <=> ![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))),
% 4.57/3.16 inference(rewrite,[status(thm)],[])).
% 4.57/3.16 tff(126,plain,
% 4.57/3.16 (^[B: $i, A: $i, C: $i] : rewrite(((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(B, C)) = mult(mult(A, C), B))) <=> ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C))))),
% 4.57/3.16 inference(bind,[status(th)],[])).
% 4.57/3.16 tff(127,plain,
% 4.57/3.16 (![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(B, C)) = mult(mult(A, C), B))) <=> ![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))),
% 4.57/3.16 inference(quant_intro,[status(thm)],[126])).
% 4.57/3.16 tff(128,axiom,(![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(B, C)) = mult(mult(A, C), B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','f07')).
% 4.57/3.16 tff(129,plain,
% 4.57/3.16 (![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))),
% 4.57/3.16 inference(modus_ponens,[status(thm)],[128, 127])).
% 4.57/3.16 tff(130,plain,
% 4.57/3.16 (![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))),
% 4.57/3.16 inference(modus_ponens,[status(thm)],[129, 125])).
% 4.57/3.16 tff(131,plain,(
% 4.57/3.16 ![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))),
% 4.57/3.16 inference(skolemize,[status(sab)],[130])).
% 4.57/3.16 tff(132,plain,
% 4.57/3.16 (![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))),
% 4.57/3.16 inference(modus_ponens,[status(thm)],[131, 124])).
% 4.57/3.16 tff(133,plain,
% 4.57/3.16 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | ((mult(i(b), mult(b, mult(i(b), i(b)))) = mult(mult(i(b), mult(i(b), i(b))), b)) | (mult(i(b), mult(b, mult(i(b), i(b)))) = mult(mult(i(b), b), mult(i(b), i(b)))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | (mult(i(b), mult(b, mult(i(b), i(b)))) = mult(mult(i(b), mult(i(b), i(b))), b)) | (mult(i(b), mult(b, mult(i(b), i(b)))) = mult(mult(i(b), b), mult(i(b), i(b)))))),
% 4.57/3.16 inference(rewrite,[status(thm)],[])).
% 4.57/3.16 tff(134,plain,
% 4.57/3.16 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | ((mult(i(b), mult(b, mult(i(b), i(b)))) = mult(mult(i(b), mult(i(b), i(b))), b)) | (mult(i(b), mult(b, mult(i(b), i(b)))) = mult(mult(i(b), b), mult(i(b), i(b)))))),
% 4.57/3.16 inference(quant_inst,[status(thm)],[])).
% 4.57/3.16 tff(135,plain,
% 4.57/3.16 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | (mult(i(b), mult(b, mult(i(b), i(b)))) = mult(mult(i(b), mult(i(b), i(b))), b)) | (mult(i(b), mult(b, mult(i(b), i(b)))) = mult(mult(i(b), b), mult(i(b), i(b))))),
% 4.57/3.16 inference(modus_ponens,[status(thm)],[134, 133])).
% 4.57/3.16 tff(136,plain,
% 4.57/3.16 ((mult(i(b), mult(b, mult(i(b), i(b)))) = mult(mult(i(b), mult(i(b), i(b))), b)) | (mult(i(b), mult(b, mult(i(b), i(b)))) = mult(mult(i(b), b), mult(i(b), i(b))))),
% 4.57/3.16 inference(unit_resolution,[status(thm)],[135, 132])).
% 4.57/3.16 tff(137,plain,
% 4.57/3.16 (mult(i(b), mult(b, mult(i(b), i(b)))) = mult(mult(i(b), mult(i(b), i(b))), b)),
% 4.57/3.16 inference(unit_resolution,[status(thm)],[136, 106])).
% 4.57/3.16 tff(138,plain,
% 4.57/3.16 (mult(unit, mult(i(b), i(b))) = mult(i(b), i(b))),
% 4.57/3.16 inference(transitivity,[status(thm)],[89, 91])).
% 4.57/3.16 tff(139,plain,
% 4.57/3.16 (mult(mult(unit, mult(i(b), i(b))), b) = mult(mult(i(b), i(b)), b)),
% 4.57/3.16 inference(monotonicity,[status(thm)],[138])).
% 4.57/3.16 tff(140,plain,
% 4.57/3.16 (mult(mult(i(b), i(b)), b) = mult(mult(unit, mult(i(b), i(b))), b)),
% 4.57/3.16 inference(symmetry,[status(thm)],[139])).
% 4.57/3.16 tff(141,plain,
% 4.57/3.16 (mult(mult(b, i(b)), mult(i(b), i(b))) = mult(unit, mult(i(b), i(b)))),
% 4.57/3.16 inference(monotonicity,[status(thm)],[30])).
% 4.57/3.16 tff(142,plain,
% 4.57/3.16 (mult(mult(b, mult(i(b), i(b))), i(b)) = mult(i(b), i(b))),
% 4.57/3.16 inference(monotonicity,[status(thm)],[61])).
% 4.57/3.16 tff(143,plain,
% 4.57/3.16 (mult(i(b), i(b)) = mult(mult(b, mult(i(b), i(b))), i(b))),
% 4.57/3.16 inference(symmetry,[status(thm)],[142])).
% 4.57/3.16 tff(144,plain,
% 4.57/3.16 (mult(mult(b, i(b)), mult(i(b), i(b))) = mult(mult(b, mult(i(b), i(b))), i(b))),
% 4.57/3.16 inference(transitivity,[status(thm)],[141, 89, 91, 143])).
% 4.57/3.16 tff(145,plain,
% 4.57/3.16 ((mult(b, mult(i(b), mult(i(b), i(b)))) = mult(mult(b, i(b)), mult(i(b), i(b)))) <=> (mult(b, mult(i(b), mult(i(b), i(b)))) = mult(mult(b, mult(i(b), i(b))), i(b)))),
% 4.57/3.16 inference(monotonicity,[status(thm)],[144])).
% 4.57/3.16 tff(146,plain,
% 4.57/3.16 ((mult(b, mult(i(b), mult(i(b), i(b)))) = mult(mult(b, mult(i(b), i(b))), i(b))) <=> (mult(b, mult(i(b), mult(i(b), i(b)))) = mult(mult(b, i(b)), mult(i(b), i(b))))),
% 4.57/3.16 inference(symmetry,[status(thm)],[145])).
% 4.57/3.16 tff(147,assumption,(~(mult(b, mult(i(b), mult(i(b), i(b)))) = mult(mult(b, i(b)), mult(i(b), i(b))))), introduced(assumption)).
% 4.57/3.16 tff(148,plain,
% 4.57/3.16 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | ((mult(b, mult(i(b), mult(i(b), i(b)))) = mult(mult(b, mult(i(b), i(b))), i(b))) | (mult(b, mult(i(b), mult(i(b), i(b)))) = mult(mult(b, i(b)), mult(i(b), i(b)))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | (mult(b, mult(i(b), mult(i(b), i(b)))) = mult(mult(b, mult(i(b), i(b))), i(b))) | (mult(b, mult(i(b), mult(i(b), i(b)))) = mult(mult(b, i(b)), mult(i(b), i(b)))))),
% 4.57/3.16 inference(rewrite,[status(thm)],[])).
% 4.57/3.16 tff(149,plain,
% 4.57/3.16 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | ((mult(b, mult(i(b), mult(i(b), i(b)))) = mult(mult(b, mult(i(b), i(b))), i(b))) | (mult(b, mult(i(b), mult(i(b), i(b)))) = mult(mult(b, i(b)), mult(i(b), i(b)))))),
% 4.57/3.16 inference(quant_inst,[status(thm)],[])).
% 4.57/3.16 tff(150,plain,
% 4.57/3.16 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | (mult(b, mult(i(b), mult(i(b), i(b)))) = mult(mult(b, mult(i(b), i(b))), i(b))) | (mult(b, mult(i(b), mult(i(b), i(b)))) = mult(mult(b, i(b)), mult(i(b), i(b))))),
% 4.57/3.16 inference(modus_ponens,[status(thm)],[149, 148])).
% 4.57/3.16 tff(151,plain,
% 4.57/3.16 ((mult(b, mult(i(b), mult(i(b), i(b)))) = mult(mult(b, mult(i(b), i(b))), i(b))) | (mult(b, mult(i(b), mult(i(b), i(b)))) = mult(mult(b, i(b)), mult(i(b), i(b))))),
% 4.57/3.16 inference(unit_resolution,[status(thm)],[150, 132])).
% 4.57/3.16 tff(152,plain,
% 4.57/3.16 (mult(b, mult(i(b), mult(i(b), i(b)))) = mult(mult(b, mult(i(b), i(b))), i(b))),
% 4.57/3.16 inference(unit_resolution,[status(thm)],[151, 147])).
% 4.57/3.16 tff(153,plain,
% 4.57/3.16 (mult(b, mult(i(b), mult(i(b), i(b)))) = mult(mult(b, i(b)), mult(i(b), i(b)))),
% 4.57/3.16 inference(modus_ponens,[status(thm)],[152, 146])).
% 4.57/3.16 tff(154,plain,
% 4.57/3.16 ($false),
% 4.57/3.16 inference(unit_resolution,[status(thm)],[147, 153])).
% 4.57/3.16 tff(155,plain,(mult(b, mult(i(b), mult(i(b), i(b)))) = mult(mult(b, i(b)), mult(i(b), i(b)))), inference(lemma,lemma(discharge,[]))).
% 4.57/3.16 tff(156,plain,
% 4.57/3.16 (mult(b, mult(i(b), mult(i(b), i(b)))) = mult(i(b), i(b))),
% 4.57/3.16 inference(transitivity,[status(thm)],[155, 141, 89, 91])).
% 4.57/3.16 tff(157,plain,
% 4.57/3.16 (mult(mult(b, mult(i(b), mult(i(b), i(b)))), b) = mult(mult(i(b), i(b)), b)),
% 4.57/3.16 inference(monotonicity,[status(thm)],[156])).
% 4.57/3.16 tff(158,plain,
% 4.57/3.16 (mult(mult(b, mult(i(b), mult(i(b), i(b)))), b) = mult(mult(unit, mult(i(b), i(b))), b)),
% 4.57/3.16 inference(transitivity,[status(thm)],[157, 140])).
% 4.57/3.16 tff(159,plain,
% 4.57/3.16 (mult(unit, mult(b, mult(i(b), i(b)))) = mult(unit, i(b))),
% 4.57/3.16 inference(monotonicity,[status(thm)],[61])).
% 4.57/3.16 tff(160,plain,
% 4.57/3.16 (mult(unit, i(b)) = mult(unit, mult(b, mult(i(b), i(b))))),
% 4.57/3.16 inference(symmetry,[status(thm)],[159])).
% 4.57/3.16 tff(161,assumption,(mult(i(b), mult(b, mult(i(b), i(b)))) = mult(mult(i(b), mult(i(b), i(b))), b)), introduced(assumption)).
% 4.57/3.16 tff(162,plain,
% 4.57/3.16 (mult(mult(i(b), mult(i(b), i(b))), b) = mult(i(b), mult(b, mult(i(b), i(b))))),
% 4.57/3.16 inference(symmetry,[status(thm)],[161])).
% 4.57/3.16 tff(163,plain,
% 4.57/3.16 (mult(mult(i(b), mult(i(b), i(b))), b) = mult(i(b), i(b))),
% 4.57/3.16 inference(transitivity,[status(thm)],[162, 93])).
% 4.57/3.16 tff(164,plain,
% 4.57/3.16 (mult(b, mult(mult(i(b), mult(i(b), i(b))), b)) = mult(b, mult(i(b), i(b)))),
% 4.57/3.16 inference(monotonicity,[status(thm)],[163])).
% 4.57/3.16 tff(165,plain,
% 4.57/3.16 (mult(b, mult(mult(i(b), mult(i(b), i(b))), b)) = mult(unit, mult(b, mult(i(b), i(b))))),
% 4.57/3.16 inference(transitivity,[status(thm)],[164, 58, 44, 160])).
% 4.57/3.16 tff(166,plain,
% 4.57/3.16 ((mult(b, mult(mult(i(b), mult(i(b), i(b))), b)) = mult(mult(b, mult(i(b), mult(i(b), i(b)))), b)) <=> (mult(unit, mult(b, mult(i(b), i(b)))) = mult(mult(unit, mult(i(b), i(b))), b))),
% 4.57/3.16 inference(monotonicity,[status(thm)],[165, 158])).
% 4.57/3.16 tff(167,plain,
% 4.57/3.16 ((mult(unit, mult(b, mult(i(b), i(b)))) = mult(mult(unit, mult(i(b), i(b))), b)) <=> (mult(b, mult(mult(i(b), mult(i(b), i(b))), b)) = mult(mult(b, mult(i(b), mult(i(b), i(b)))), b))),
% 4.57/3.16 inference(symmetry,[status(thm)],[166])).
% 4.57/3.16 tff(168,plain,
% 4.57/3.16 ((mult(mult(unit, mult(i(b), i(b))), b) = mult(unit, mult(b, mult(i(b), i(b))))) <=> (mult(unit, mult(b, mult(i(b), i(b)))) = mult(mult(unit, mult(i(b), i(b))), b))),
% 4.57/3.16 inference(commutativity,[status(thm)],[])).
% 4.57/3.16 tff(169,plain,
% 4.57/3.16 (mult(mult(unit, b), mult(i(b), i(b))) = mult(unit, mult(b, mult(i(b), i(b))))),
% 4.57/3.16 inference(transitivity,[status(thm)],[122, 115, 160])).
% 4.57/3.16 tff(170,assumption,(~(mult(unit, mult(mult(i(b), i(b)), b)) = mult(mult(unit, b), mult(i(b), i(b))))), introduced(assumption)).
% 4.57/3.17 tff(171,plain,
% 4.57/3.17 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | ((mult(unit, mult(mult(i(b), i(b)), b)) = mult(mult(unit, b), mult(i(b), i(b)))) | (mult(unit, mult(mult(i(b), i(b)), b)) = mult(mult(unit, mult(i(b), i(b))), b)))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | (mult(unit, mult(mult(i(b), i(b)), b)) = mult(mult(unit, b), mult(i(b), i(b)))) | (mult(unit, mult(mult(i(b), i(b)), b)) = mult(mult(unit, mult(i(b), i(b))), b)))),
% 4.57/3.17 inference(rewrite,[status(thm)],[])).
% 4.57/3.17 tff(172,plain,
% 4.57/3.17 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | ((mult(unit, mult(mult(i(b), i(b)), b)) = mult(mult(unit, b), mult(i(b), i(b)))) | (mult(unit, mult(mult(i(b), i(b)), b)) = mult(mult(unit, mult(i(b), i(b))), b)))),
% 4.57/3.17 inference(quant_inst,[status(thm)],[])).
% 4.57/3.17 tff(173,plain,
% 4.57/3.17 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | (mult(unit, mult(mult(i(b), i(b)), b)) = mult(mult(unit, b), mult(i(b), i(b)))) | (mult(unit, mult(mult(i(b), i(b)), b)) = mult(mult(unit, mult(i(b), i(b))), b))),
% 4.57/3.17 inference(modus_ponens,[status(thm)],[172, 171])).
% 4.57/3.17 tff(174,plain,
% 4.57/3.17 ((mult(unit, mult(mult(i(b), i(b)), b)) = mult(mult(unit, b), mult(i(b), i(b)))) | (mult(unit, mult(mult(i(b), i(b)), b)) = mult(mult(unit, mult(i(b), i(b))), b))),
% 4.57/3.17 inference(unit_resolution,[status(thm)],[173, 132])).
% 4.57/3.17 tff(175,plain,
% 4.57/3.17 (mult(unit, mult(mult(i(b), i(b)), b)) = mult(mult(unit, mult(i(b), i(b))), b)),
% 4.57/3.17 inference(unit_resolution,[status(thm)],[174, 170])).
% 4.57/3.17 tff(176,plain,
% 4.57/3.17 ((mult(unit, mult(mult(i(b), i(b)), b)) = mult(mult(unit, b), mult(i(b), i(b)))) <=> (mult(mult(unit, mult(i(b), i(b))), b) = mult(unit, mult(b, mult(i(b), i(b)))))),
% 4.57/3.17 inference(monotonicity,[status(thm)],[175, 169])).
% 4.57/3.17 tff(177,plain,
% 4.57/3.17 ((mult(unit, mult(mult(i(b), i(b)), b)) = mult(mult(unit, b), mult(i(b), i(b)))) <=> (mult(unit, mult(b, mult(i(b), i(b)))) = mult(mult(unit, mult(i(b), i(b))), b))),
% 4.57/3.17 inference(transitivity,[status(thm)],[176, 168])).
% 4.57/3.17 tff(178,plain,
% 4.57/3.17 ((mult(unit, mult(mult(i(b), i(b)), b)) = mult(mult(unit, b), mult(i(b), i(b)))) <=> (mult(b, mult(mult(i(b), mult(i(b), i(b))), b)) = mult(mult(b, mult(i(b), mult(i(b), i(b)))), b))),
% 4.57/3.17 inference(transitivity,[status(thm)],[177, 167])).
% 4.57/3.17 tff(179,plain,
% 4.57/3.17 ((~(mult(unit, mult(mult(i(b), i(b)), b)) = mult(mult(unit, b), mult(i(b), i(b))))) <=> (~(mult(b, mult(mult(i(b), mult(i(b), i(b))), b)) = mult(mult(b, mult(i(b), mult(i(b), i(b)))), b)))),
% 4.57/3.17 inference(monotonicity,[status(thm)],[178])).
% 4.57/3.17 tff(180,plain,
% 4.57/3.17 (~(mult(b, mult(mult(i(b), mult(i(b), i(b))), b)) = mult(mult(b, mult(i(b), mult(i(b), i(b)))), b))),
% 4.57/3.17 inference(modus_ponens,[status(thm)],[170, 179])).
% 4.57/3.17 tff(181,plain,
% 4.57/3.17 (mult(b, mult(b, mult(i(b), mult(i(b), i(b))))) = mult(b, mult(i(b), i(b)))),
% 4.57/3.17 inference(monotonicity,[status(thm)],[156])).
% 4.57/3.17 tff(182,plain,
% 4.57/3.17 (mult(b, mult(b, mult(i(b), mult(i(b), i(b))))) = mult(unit, mult(b, mult(i(b), i(b))))),
% 4.57/3.17 inference(transitivity,[status(thm)],[181, 58, 44, 160])).
% 4.57/3.17 tff(183,plain,
% 4.57/3.17 ((mult(b, mult(b, mult(i(b), mult(i(b), i(b))))) = mult(mult(b, mult(i(b), mult(i(b), i(b)))), b)) <=> (mult(unit, mult(b, mult(i(b), i(b)))) = mult(mult(unit, mult(i(b), i(b))), b))),
% 4.57/3.17 inference(monotonicity,[status(thm)],[182, 158])).
% 4.57/3.17 tff(184,plain,
% 4.57/3.17 ((mult(unit, mult(b, mult(i(b), i(b)))) = mult(mult(unit, mult(i(b), i(b))), b)) <=> (mult(b, mult(b, mult(i(b), mult(i(b), i(b))))) = mult(mult(b, mult(i(b), mult(i(b), i(b)))), b))),
% 4.57/3.17 inference(symmetry,[status(thm)],[183])).
% 4.57/3.17 tff(185,plain,
% 4.57/3.17 ((mult(unit, mult(mult(i(b), i(b)), b)) = mult(mult(unit, b), mult(i(b), i(b)))) <=> (mult(b, mult(b, mult(i(b), mult(i(b), i(b))))) = mult(mult(b, mult(i(b), mult(i(b), i(b)))), b))),
% 4.57/3.17 inference(transitivity,[status(thm)],[177, 184])).
% 4.57/3.17 tff(186,plain,
% 4.57/3.17 ((~(mult(unit, mult(mult(i(b), i(b)), b)) = mult(mult(unit, b), mult(i(b), i(b))))) <=> (~(mult(b, mult(b, mult(i(b), mult(i(b), i(b))))) = mult(mult(b, mult(i(b), mult(i(b), i(b)))), b)))),
% 4.57/3.17 inference(monotonicity,[status(thm)],[185])).
% 4.57/3.17 tff(187,plain,
% 4.57/3.17 (~(mult(b, mult(b, mult(i(b), mult(i(b), i(b))))) = mult(mult(b, mult(i(b), mult(i(b), i(b)))), b))),
% 4.57/3.17 inference(modus_ponens,[status(thm)],[170, 186])).
% 4.57/3.17 tff(188,plain,
% 4.57/3.17 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(b, mult(mult(i(b), mult(i(b), i(b))), b)) = mult(mult(b, mult(i(b), mult(i(b), i(b)))), b)) | (mult(b, mult(b, mult(i(b), mult(i(b), i(b))))) = mult(mult(b, mult(i(b), mult(i(b), i(b)))), b)))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(b, mult(mult(i(b), mult(i(b), i(b))), b)) = mult(mult(b, mult(i(b), mult(i(b), i(b)))), b)) | (mult(b, mult(b, mult(i(b), mult(i(b), i(b))))) = mult(mult(b, mult(i(b), mult(i(b), i(b)))), b)))),
% 4.57/3.17 inference(rewrite,[status(thm)],[])).
% 4.57/3.17 tff(189,plain,
% 4.57/3.17 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(b, mult(mult(i(b), mult(i(b), i(b))), b)) = mult(mult(b, mult(i(b), mult(i(b), i(b)))), b)) | (mult(b, mult(b, mult(i(b), mult(i(b), i(b))))) = mult(mult(b, mult(i(b), mult(i(b), i(b)))), b)))),
% 4.57/3.17 inference(quant_inst,[status(thm)],[])).
% 4.57/3.17 tff(190,plain,
% 4.57/3.17 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(b, mult(mult(i(b), mult(i(b), i(b))), b)) = mult(mult(b, mult(i(b), mult(i(b), i(b)))), b)) | (mult(b, mult(b, mult(i(b), mult(i(b), i(b))))) = mult(mult(b, mult(i(b), mult(i(b), i(b)))), b))),
% 4.57/3.17 inference(modus_ponens,[status(thm)],[189, 188])).
% 4.57/3.17 tff(191,plain,
% 4.57/3.17 ((mult(b, mult(mult(i(b), mult(i(b), i(b))), b)) = mult(mult(b, mult(i(b), mult(i(b), i(b)))), b)) | (mult(b, mult(b, mult(i(b), mult(i(b), i(b))))) = mult(mult(b, mult(i(b), mult(i(b), i(b)))), b))),
% 4.57/3.17 inference(unit_resolution,[status(thm)],[190, 51])).
% 4.57/3.17 tff(192,plain,
% 4.57/3.17 ($false),
% 4.57/3.17 inference(unit_resolution,[status(thm)],[191, 187, 180])).
% 4.57/3.17 tff(193,plain,((mult(unit, mult(mult(i(b), i(b)), b)) = mult(mult(unit, b), mult(i(b), i(b)))) | (~(mult(unit, mult(b, i(b))) = mult(mult(unit, b), i(b)))) | (~(mult(i(b), mult(b, mult(i(b), i(b)))) = mult(mult(i(b), mult(i(b), i(b))), b)))), inference(lemma,lemma(discharge,[]))).
% 4.57/3.17 tff(194,plain,
% 4.57/3.17 (mult(unit, mult(mult(i(b), i(b)), b)) = mult(mult(unit, b), mult(i(b), i(b)))),
% 4.57/3.17 inference(unit_resolution,[status(thm)],[193, 112, 137])).
% 4.57/3.17 tff(195,plain,
% 4.57/3.17 ((~![A: $i] : (mult(unit, A) = A)) | (mult(unit, mult(mult(i(b), i(b)), b)) = mult(mult(i(b), i(b)), b))),
% 4.57/3.17 inference(quant_inst,[status(thm)],[])).
% 4.57/3.17 tff(196,plain,
% 4.57/3.17 (mult(unit, mult(mult(i(b), i(b)), b)) = mult(mult(i(b), i(b)), b)),
% 4.57/3.17 inference(unit_resolution,[status(thm)],[195, 40])).
% 4.57/3.17 tff(197,plain,
% 4.57/3.17 (mult(mult(i(b), i(b)), b) = mult(unit, mult(mult(i(b), i(b)), b))),
% 4.57/3.17 inference(symmetry,[status(thm)],[196])).
% 4.57/3.17 tff(198,plain,
% 4.57/3.17 (mult(mult(i(b), i(b)), b) = i(b)),
% 4.57/3.17 inference(transitivity,[status(thm)],[197, 194, 122, 115, 43])).
% 4.57/3.17 tff(199,plain,
% 4.57/3.17 (mult(i(b), mult(mult(i(b), i(b)), b)) = mult(i(b), i(b))),
% 4.57/3.17 inference(monotonicity,[status(thm)],[198])).
% 4.57/3.17 tff(200,plain,
% 4.57/3.17 (mult(i(b), i(b)) = mult(i(b), mult(mult(i(b), i(b)), b))),
% 4.57/3.17 inference(symmetry,[status(thm)],[199])).
% 4.57/3.17 tff(201,plain,
% 4.57/3.17 (mult(i(b), mult(b, mult(i(b), i(b)))) = mult(mult(i(b), b), mult(i(b), i(b)))),
% 4.57/3.17 inference(transitivity,[status(thm)],[93, 200, 111])).
% 4.57/3.17 tff(202,plain,
% 4.57/3.17 ($false),
% 4.57/3.17 inference(unit_resolution,[status(thm)],[106, 201])).
% 4.57/3.17 tff(203,plain,((~(mult(unit, mult(b, i(b))) = mult(mult(unit, b), i(b)))) | (mult(i(b), mult(b, mult(i(b), i(b)))) = mult(mult(i(b), b), mult(i(b), i(b))))), inference(lemma,lemma(discharge,[]))).
% 4.57/3.17 tff(204,plain,
% 4.57/3.17 (~(mult(unit, mult(b, i(b))) = mult(mult(unit, b), i(b)))),
% 4.57/3.17 inference(unit_resolution,[status(thm)],[203, 105])).
% 4.57/3.17 tff(205,plain,
% 4.67/3.17 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | ((mult(unit, mult(b, i(b))) = mult(mult(unit, i(b)), b)) | (mult(unit, mult(b, i(b))) = mult(mult(unit, b), i(b))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | (mult(unit, mult(b, i(b))) = mult(mult(unit, i(b)), b)) | (mult(unit, mult(b, i(b))) = mult(mult(unit, b), i(b))))),
% 4.67/3.17 inference(rewrite,[status(thm)],[])).
% 4.67/3.17 tff(206,plain,
% 4.67/3.17 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | ((mult(unit, mult(b, i(b))) = mult(mult(unit, i(b)), b)) | (mult(unit, mult(b, i(b))) = mult(mult(unit, b), i(b))))),
% 4.67/3.17 inference(quant_inst,[status(thm)],[])).
% 4.67/3.17 tff(207,plain,
% 4.67/3.17 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | (mult(unit, mult(b, i(b))) = mult(mult(unit, i(b)), b)) | (mult(unit, mult(b, i(b))) = mult(mult(unit, b), i(b)))),
% 4.67/3.17 inference(modus_ponens,[status(thm)],[206, 205])).
% 4.67/3.17 tff(208,plain,
% 4.67/3.17 ((mult(unit, mult(b, i(b))) = mult(mult(unit, i(b)), b)) | (mult(unit, mult(b, i(b))) = mult(mult(unit, b), i(b)))),
% 4.67/3.17 inference(unit_resolution,[status(thm)],[207, 132])).
% 4.67/3.17 tff(209,plain,
% 4.67/3.17 (mult(unit, mult(b, i(b))) = mult(mult(unit, i(b)), b)),
% 4.67/3.17 inference(unit_resolution,[status(thm)],[208, 204])).
% 4.67/3.17 tff(210,plain,
% 4.67/3.17 (mult(b, mult(b, mult(i(b), i(b)))) = mult(mult(b, mult(i(b), i(b))), b)),
% 4.67/3.17 inference(modus_ponens,[status(thm)],[209, 72])).
% 4.67/3.17 tff(211,plain,
% 4.67/3.17 ($false),
% 4.67/3.17 inference(unit_resolution,[status(thm)],[73, 210])).
% 4.67/3.17 tff(212,plain,(mult(b, mult(b, mult(i(b), i(b)))) = mult(mult(b, mult(i(b), i(b))), b)), inference(lemma,lemma(discharge,[]))).
% 4.67/3.17 tff(213,plain,
% 4.67/3.17 (mult(mult(b, mult(i(b), i(b))), b) = mult(b, mult(b, mult(i(b), i(b))))),
% 4.67/3.17 inference(symmetry,[status(thm)],[212])).
% 4.67/3.17 tff(214,plain,
% 4.67/3.17 (mult(mult(b, i(b)), i(b)) = mult(b, mult(i(b), i(b)))),
% 4.67/3.17 inference(symmetry,[status(thm)],[58])).
% 4.67/3.17 tff(215,plain,
% 4.67/3.17 (mult(unit, i(b)) = mult(mult(b, i(b)), i(b))),
% 4.67/3.17 inference(symmetry,[status(thm)],[44])).
% 4.67/3.17 tff(216,plain,
% 4.67/3.17 (i(b) = mult(unit, i(b))),
% 4.67/3.17 inference(symmetry,[status(thm)],[43])).
% 4.67/3.17 tff(217,plain,
% 4.67/3.17 (i(b) = mult(b, mult(i(b), i(b)))),
% 4.67/3.17 inference(transitivity,[status(thm)],[216, 215, 214])).
% 4.67/3.17 tff(218,plain,
% 4.67/3.17 (mult(i(b), b) = mult(mult(b, mult(i(b), i(b))), b)),
% 4.67/3.17 inference(monotonicity,[status(thm)],[217])).
% 4.67/3.17 tff(219,plain,
% 4.67/3.17 (mult(i(b), b) = mult(b, i(b))),
% 4.67/3.17 inference(transitivity,[status(thm)],[218, 213, 60, 32])).
% 4.67/3.17 tff(220,plain,
% 4.67/3.17 (mult(a, mult(i(b), b)) = mult(a, mult(b, i(b)))),
% 4.67/3.17 inference(monotonicity,[status(thm)],[219])).
% 4.67/3.17 tff(221,plain,
% 4.67/3.17 ((mult(a, mult(i(b), b)) = mult(mult(a, b), i(b))) <=> (mult(a, mult(b, i(b))) = mult(mult(a, b), i(b)))),
% 4.67/3.17 inference(monotonicity,[status(thm)],[220])).
% 4.67/3.17 tff(222,assumption,(~(mult(a, mult(b, i(b))) = mult(mult(a, b), i(b)))), introduced(assumption)).
% 4.67/3.17 tff(223,plain,
% 4.67/3.17 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(a, mult(b, i(b))) = mult(mult(a, b), i(b))) | (mult(a, mult(i(b), b)) = mult(mult(a, b), i(b))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(a, mult(b, i(b))) = mult(mult(a, b), i(b))) | (mult(a, mult(i(b), b)) = mult(mult(a, b), i(b))))),
% 4.67/3.17 inference(rewrite,[status(thm)],[])).
% 4.67/3.17 tff(224,plain,
% 4.67/3.17 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(a, mult(b, i(b))) = mult(mult(a, b), i(b))) | (mult(a, mult(i(b), b)) = mult(mult(a, b), i(b))))),
% 4.67/3.17 inference(quant_inst,[status(thm)],[])).
% 4.67/3.17 tff(225,plain,
% 4.67/3.17 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(a, mult(b, i(b))) = mult(mult(a, b), i(b))) | (mult(a, mult(i(b), b)) = mult(mult(a, b), i(b)))),
% 4.67/3.17 inference(modus_ponens,[status(thm)],[224, 223])).
% 4.67/3.17 tff(226,plain,
% 4.67/3.17 ((mult(a, mult(b, i(b))) = mult(mult(a, b), i(b))) | (mult(a, mult(i(b), b)) = mult(mult(a, b), i(b)))),
% 4.67/3.17 inference(unit_resolution,[status(thm)],[225, 51])).
% 4.67/3.17 tff(227,plain,
% 4.67/3.17 (mult(a, mult(i(b), b)) = mult(mult(a, b), i(b))),
% 4.67/3.17 inference(unit_resolution,[status(thm)],[226, 222])).
% 4.67/3.17 tff(228,plain,
% 4.67/3.17 (mult(a, mult(b, i(b))) = mult(mult(a, b), i(b))),
% 4.67/3.17 inference(modus_ponens,[status(thm)],[227, 221])).
% 4.67/3.17 tff(229,plain,
% 4.67/3.17 ($false),
% 4.67/3.17 inference(unit_resolution,[status(thm)],[222, 228])).
% 4.67/3.17 tff(230,plain,(mult(a, mult(b, i(b))) = mult(mult(a, b), i(b))), inference(lemma,lemma(discharge,[]))).
% 4.67/3.17 tff(231,plain,
% 4.67/3.17 (mult(mult(a, b), i(b)) = mult(a, mult(b, i(b)))),
% 4.67/3.17 inference(symmetry,[status(thm)],[230])).
% 4.67/3.17 tff(232,plain,
% 4.67/3.17 (mult(mult(a, b), i(b)) = a),
% 4.67/3.17 inference(transitivity,[status(thm)],[231, 31, 10])).
% 4.67/3.17 tff(233,plain,
% 4.67/3.17 (mult(mult(mult(a, b), i(b)), mult(ld(mult(a, b), unit), b)) = mult(a, mult(ld(mult(a, b), unit), b))),
% 4.67/3.17 inference(monotonicity,[status(thm)],[232])).
% 4.67/3.17 tff(234,plain,
% 4.67/3.17 ((~![A: $i] : (mult(unit, A) = A)) | (mult(unit, ld(mult(a, b), unit)) = ld(mult(a, b), unit))),
% 4.67/3.17 inference(quant_inst,[status(thm)],[])).
% 4.67/3.17 tff(235,plain,
% 4.67/3.17 (mult(unit, ld(mult(a, b), unit)) = ld(mult(a, b), unit)),
% 4.67/3.17 inference(unit_resolution,[status(thm)],[234, 40])).
% 4.67/3.17 tff(236,plain,
% 4.67/3.17 (mult(i(b), b) = unit),
% 4.67/3.17 inference(transitivity,[status(thm)],[218, 213, 60, 19])).
% 4.67/3.17 tff(237,plain,
% 4.67/3.17 (mult(mult(i(b), b), ld(mult(a, b), unit)) = mult(unit, ld(mult(a, b), unit))),
% 4.67/3.17 inference(monotonicity,[status(thm)],[236])).
% 4.67/3.17 tff(238,assumption,(mult(i(b), mult(ld(mult(a, b), unit), b)) = mult(mult(i(b), b), ld(mult(a, b), unit))), introduced(assumption)).
% 4.67/3.17 tff(239,plain,
% 4.67/3.17 (mult(i(b), mult(ld(mult(a, b), unit), b)) = ld(mult(a, b), unit)),
% 4.67/3.17 inference(transitivity,[status(thm)],[238, 237, 235])).
% 4.67/3.17 tff(240,plain,
% 4.67/3.17 (mult(mult(a, b), mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(a, b), ld(mult(a, b), unit))),
% 4.67/3.17 inference(monotonicity,[status(thm)],[239])).
% 4.67/3.17 tff(241,plain,
% 4.67/3.17 ((mult(mult(a, b), mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(mult(a, b), i(b)), mult(ld(mult(a, b), unit), b))) <=> (mult(mult(a, b), ld(mult(a, b), unit)) = mult(a, mult(ld(mult(a, b), unit), b)))),
% 4.67/3.17 inference(monotonicity,[status(thm)],[240, 233])).
% 4.67/3.17 tff(242,plain,
% 4.67/3.17 ((mult(mult(a, b), mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(mult(a, b), i(b)), mult(ld(mult(a, b), unit), b))) <=> (mult(a, mult(ld(mult(a, b), unit), b)) = mult(mult(a, b), ld(mult(a, b), unit)))),
% 4.67/3.17 inference(transitivity,[status(thm)],[241, 1])).
% 4.67/3.17 tff(243,plain,
% 4.67/3.17 ((mult(a, mult(ld(mult(a, b), unit), b)) = mult(mult(a, b), ld(mult(a, b), unit))) <=> (mult(mult(a, b), mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(mult(a, b), i(b)), mult(ld(mult(a, b), unit), b)))),
% 4.67/3.17 inference(symmetry,[status(thm)],[242])).
% 4.67/3.17 tff(244,plain,
% 4.67/3.17 ((~(mult(a, mult(ld(mult(a, b), unit), b)) = mult(mult(a, b), ld(mult(a, b), unit)))) <=> (~(mult(mult(a, b), mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(mult(a, b), i(b)), mult(ld(mult(a, b), unit), b))))),
% 4.67/3.17 inference(monotonicity,[status(thm)],[243])).
% 4.67/3.17 tff(245,plain,
% 4.67/3.17 (^[B: $i, A: $i] : refl((ld(A, mult(A, B)) = B) <=> (ld(A, mult(A, B)) = B))),
% 4.67/3.17 inference(bind,[status(th)],[])).
% 4.67/3.17 tff(246,plain,
% 4.67/3.17 (![B: $i, A: $i] : (ld(A, mult(A, B)) = B) <=> ![B: $i, A: $i] : (ld(A, mult(A, B)) = B)),
% 4.67/3.17 inference(quant_intro,[status(thm)],[245])).
% 4.67/3.17 tff(247,plain,
% 4.67/3.17 (![B: $i, A: $i] : (ld(A, mult(A, B)) = B) <=> ![B: $i, A: $i] : (ld(A, mult(A, B)) = B)),
% 4.67/3.17 inference(rewrite,[status(thm)],[])).
% 4.67/3.17 tff(248,axiom,(![B: $i, A: $i] : (ld(A, mult(A, B)) = B)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','f02')).
% 4.67/3.17 tff(249,plain,
% 4.67/3.17 (![B: $i, A: $i] : (ld(A, mult(A, B)) = B)),
% 4.67/3.17 inference(modus_ponens,[status(thm)],[248, 247])).
% 4.67/3.17 tff(250,plain,(
% 4.67/3.17 ![B: $i, A: $i] : (ld(A, mult(A, B)) = B)),
% 4.67/3.17 inference(skolemize,[status(sab)],[249])).
% 4.67/3.17 tff(251,plain,
% 4.67/3.17 (![B: $i, A: $i] : (ld(A, mult(A, B)) = B)),
% 4.67/3.17 inference(modus_ponens,[status(thm)],[250, 246])).
% 4.67/3.17 tff(252,plain,
% 4.67/3.17 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(a, mult(a, mult(ld(mult(a, b), unit), b))) = mult(ld(mult(a, b), unit), b))),
% 4.67/3.17 inference(quant_inst,[status(thm)],[])).
% 4.67/3.17 tff(253,plain,
% 4.67/3.17 (ld(a, mult(a, mult(ld(mult(a, b), unit), b))) = mult(ld(mult(a, b), unit), b)),
% 4.67/3.17 inference(unit_resolution,[status(thm)],[252, 251])).
% 4.67/3.17 tff(254,assumption,(mult(a, mult(ld(mult(a, b), unit), b)) = mult(mult(a, b), ld(mult(a, b), unit))), introduced(assumption)).
% 4.67/3.17 tff(255,plain,
% 4.67/3.17 (mult(mult(a, b), ld(mult(a, b), unit)) = mult(a, mult(ld(mult(a, b), unit), b))),
% 4.67/3.17 inference(symmetry,[status(thm)],[254])).
% 4.67/3.17 tff(256,plain,
% 4.67/3.17 ((~![B: $i, A: $i] : (mult(A, ld(A, B)) = B)) | (mult(mult(a, b), ld(mult(a, b), unit)) = unit)),
% 4.67/3.17 inference(quant_inst,[status(thm)],[])).
% 4.67/3.17 tff(257,plain,
% 4.67/3.17 (mult(mult(a, b), ld(mult(a, b), unit)) = unit),
% 4.67/3.17 inference(unit_resolution,[status(thm)],[256, 17])).
% 4.67/3.17 tff(258,plain,
% 4.67/3.17 (unit = mult(mult(a, b), ld(mult(a, b), unit))),
% 4.67/3.17 inference(symmetry,[status(thm)],[257])).
% 4.67/3.17 tff(259,plain,
% 4.67/3.17 (unit = mult(a, mult(ld(mult(a, b), unit), b))),
% 4.67/3.17 inference(transitivity,[status(thm)],[258, 255])).
% 4.67/3.17 tff(260,plain,
% 4.67/3.17 (ld(a, unit) = ld(a, mult(a, mult(ld(mult(a, b), unit), b)))),
% 4.67/3.17 inference(monotonicity,[status(thm)],[259])).
% 4.67/3.17 tff(261,plain,
% 4.67/3.17 ((~![A: $i] : (i(A) = ld(A, unit))) | (i(a) = ld(a, unit))),
% 4.67/3.17 inference(quant_inst,[status(thm)],[])).
% 4.67/3.17 tff(262,plain,
% 4.67/3.17 (i(a) = ld(a, unit)),
% 4.67/3.17 inference(unit_resolution,[status(thm)],[261, 26])).
% 4.67/3.17 tff(263,plain,
% 4.67/3.17 (i(a) = mult(ld(mult(a, b), unit), b)),
% 4.67/3.17 inference(transitivity,[status(thm)],[262, 260, 253])).
% 4.67/3.17 tff(264,plain,
% 4.67/3.17 (mult(i(b), i(a)) = mult(i(b), mult(ld(mult(a, b), unit), b))),
% 4.67/3.17 inference(monotonicity,[status(thm)],[263])).
% 4.67/3.17 tff(265,plain,
% 4.67/3.17 (mult(i(b), mult(ld(mult(a, b), unit), b)) = mult(i(b), i(a))),
% 4.67/3.17 inference(symmetry,[status(thm)],[264])).
% 4.67/3.17 tff(266,plain,
% 4.67/3.17 (mult(mult(i(b), b), ld(mult(a, b), unit)) = mult(i(b), mult(ld(mult(a, b), unit), b))),
% 4.67/3.17 inference(symmetry,[status(thm)],[238])).
% 4.67/3.17 tff(267,plain,
% 4.67/3.17 (mult(unit, ld(mult(a, b), unit)) = mult(mult(i(b), b), ld(mult(a, b), unit))),
% 4.67/3.17 inference(symmetry,[status(thm)],[237])).
% 4.67/3.17 tff(268,plain,
% 4.67/3.17 (ld(mult(a, b), unit) = mult(unit, ld(mult(a, b), unit))),
% 4.67/3.17 inference(symmetry,[status(thm)],[235])).
% 4.67/3.17 tff(269,plain,
% 4.67/3.17 ((~![A: $i] : (i(A) = ld(A, unit))) | (i(mult(a, b)) = ld(mult(a, b), unit))),
% 4.67/3.17 inference(quant_inst,[status(thm)],[])).
% 4.67/3.17 tff(270,plain,
% 4.67/3.17 (i(mult(a, b)) = ld(mult(a, b), unit)),
% 4.67/3.17 inference(unit_resolution,[status(thm)],[269, 26])).
% 4.67/3.17 tff(271,plain,
% 4.67/3.17 (i(mult(a, b)) = mult(i(b), i(a))),
% 4.67/3.17 inference(transitivity,[status(thm)],[270, 268, 267, 266, 265])).
% 4.67/3.17 tff(272,plain,
% 4.67/3.17 ((~(i(mult(a, b)) = mult(i(b), i(a)))) <=> (~(i(mult(a, b)) = mult(i(b), i(a))))),
% 4.67/3.17 inference(rewrite,[status(thm)],[])).
% 4.67/3.17 tff(273,axiom,(~(i(mult(a, b)) = mult(i(b), i(a)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','goals')).
% 4.67/3.17 tff(274,plain,
% 4.67/3.17 (~(i(mult(a, b)) = mult(i(b), i(a)))),
% 4.67/3.17 inference(modus_ponens,[status(thm)],[273, 272])).
% 4.67/3.17 tff(275,plain,
% 4.67/3.17 ($false),
% 4.67/3.17 inference(unit_resolution,[status(thm)],[274, 271])).
% 4.67/3.17 tff(276,plain,((~(mult(a, mult(ld(mult(a, b), unit), b)) = mult(mult(a, b), ld(mult(a, b), unit)))) | (~(mult(i(b), mult(ld(mult(a, b), unit), b)) = mult(mult(i(b), b), ld(mult(a, b), unit))))), inference(lemma,lemma(discharge,[]))).
% 4.67/3.17 tff(277,plain,
% 4.67/3.17 (~(mult(a, mult(ld(mult(a, b), unit), b)) = mult(mult(a, b), ld(mult(a, b), unit)))),
% 4.67/3.17 inference(unit_resolution,[status(thm)],[276, 238])).
% 4.67/3.17 tff(278,plain,
% 4.67/3.17 (~(mult(mult(a, b), mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(mult(a, b), i(b)), mult(ld(mult(a, b), unit), b)))),
% 4.67/3.17 inference(modus_ponens,[status(thm)],[277, 244])).
% 4.67/3.17 tff(279,plain,
% 4.67/3.17 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(ld(mult(a, b), unit), b), b) = ld(mult(a, b), unit))),
% 4.67/3.17 inference(quant_inst,[status(thm)],[])).
% 4.67/3.17 tff(280,plain,
% 4.67/3.17 (rd(mult(ld(mult(a, b), unit), b), b) = ld(mult(a, b), unit)),
% 4.67/3.17 inference(unit_resolution,[status(thm)],[279, 80])).
% 4.67/3.18 tff(281,plain,
% 4.67/3.18 ((~![A: $i] : (mult(A, unit) = A)) | (mult(mult(ld(mult(a, b), unit), b), unit) = mult(ld(mult(a, b), unit), b))),
% 4.67/3.18 inference(quant_inst,[status(thm)],[])).
% 4.67/3.18 tff(282,plain,
% 4.67/3.18 (mult(mult(ld(mult(a, b), unit), b), unit) = mult(ld(mult(a, b), unit), b)),
% 4.67/3.18 inference(unit_resolution,[status(thm)],[281, 8])).
% 4.67/3.18 tff(283,plain,
% 4.67/3.18 (mult(mult(ld(mult(a, b), unit), b), mult(b, i(b))) = mult(mult(ld(mult(a, b), unit), b), unit)),
% 4.67/3.18 inference(monotonicity,[status(thm)],[30])).
% 4.67/3.18 tff(284,plain,
% 4.67/3.18 (mult(mult(ld(mult(a, b), unit), b), mult(i(b), b)) = mult(mult(ld(mult(a, b), unit), b), mult(b, i(b)))),
% 4.67/3.18 inference(monotonicity,[status(thm)],[219])).
% 4.67/3.18 tff(285,plain,
% 4.67/3.18 ((mult(mult(ld(mult(a, b), unit), b), mult(i(b), b)) = mult(mult(mult(ld(mult(a, b), unit), b), i(b)), b)) <=> (mult(mult(ld(mult(a, b), unit), b), mult(b, i(b))) = mult(mult(mult(ld(mult(a, b), unit), b), i(b)), b))),
% 4.67/3.18 inference(monotonicity,[status(thm)],[284])).
% 4.67/3.18 tff(286,assumption,(~(mult(mult(ld(mult(a, b), unit), b), mult(b, i(b))) = mult(mult(mult(ld(mult(a, b), unit), b), i(b)), b))), introduced(assumption)).
% 4.67/3.18 tff(287,plain,
% 4.67/3.18 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(mult(ld(mult(a, b), unit), b), mult(b, i(b))) = mult(mult(mult(ld(mult(a, b), unit), b), i(b)), b)) | (mult(mult(ld(mult(a, b), unit), b), mult(i(b), b)) = mult(mult(mult(ld(mult(a, b), unit), b), i(b)), b)))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(ld(mult(a, b), unit), b), mult(b, i(b))) = mult(mult(mult(ld(mult(a, b), unit), b), i(b)), b)) | (mult(mult(ld(mult(a, b), unit), b), mult(i(b), b)) = mult(mult(mult(ld(mult(a, b), unit), b), i(b)), b)))),
% 4.67/3.18 inference(rewrite,[status(thm)],[])).
% 4.67/3.18 tff(288,plain,
% 4.67/3.18 (((mult(mult(ld(mult(a, b), unit), b), mult(i(b), b)) = mult(mult(mult(ld(mult(a, b), unit), b), i(b)), b)) | (mult(mult(ld(mult(a, b), unit), b), mult(b, i(b))) = mult(mult(mult(ld(mult(a, b), unit), b), i(b)), b))) <=> ((mult(mult(ld(mult(a, b), unit), b), mult(b, i(b))) = mult(mult(mult(ld(mult(a, b), unit), b), i(b)), b)) | (mult(mult(ld(mult(a, b), unit), b), mult(i(b), b)) = mult(mult(mult(ld(mult(a, b), unit), b), i(b)), b)))),
% 4.67/3.18 inference(rewrite,[status(thm)],[])).
% 4.67/3.18 tff(289,plain,
% 4.67/3.18 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(mult(ld(mult(a, b), unit), b), mult(i(b), b)) = mult(mult(mult(ld(mult(a, b), unit), b), i(b)), b)) | (mult(mult(ld(mult(a, b), unit), b), mult(b, i(b))) = mult(mult(mult(ld(mult(a, b), unit), b), i(b)), b)))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(mult(ld(mult(a, b), unit), b), mult(b, i(b))) = mult(mult(mult(ld(mult(a, b), unit), b), i(b)), b)) | (mult(mult(ld(mult(a, b), unit), b), mult(i(b), b)) = mult(mult(mult(ld(mult(a, b), unit), b), i(b)), b))))),
% 4.67/3.18 inference(monotonicity,[status(thm)],[288])).
% 4.67/3.18 tff(290,plain,
% 4.67/3.18 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(mult(ld(mult(a, b), unit), b), mult(i(b), b)) = mult(mult(mult(ld(mult(a, b), unit), b), i(b)), b)) | (mult(mult(ld(mult(a, b), unit), b), mult(b, i(b))) = mult(mult(mult(ld(mult(a, b), unit), b), i(b)), b)))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(ld(mult(a, b), unit), b), mult(b, i(b))) = mult(mult(mult(ld(mult(a, b), unit), b), i(b)), b)) | (mult(mult(ld(mult(a, b), unit), b), mult(i(b), b)) = mult(mult(mult(ld(mult(a, b), unit), b), i(b)), b)))),
% 4.67/3.18 inference(transitivity,[status(thm)],[289, 287])).
% 4.67/3.18 tff(291,plain,
% 4.67/3.18 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(mult(ld(mult(a, b), unit), b), mult(i(b), b)) = mult(mult(mult(ld(mult(a, b), unit), b), i(b)), b)) | (mult(mult(ld(mult(a, b), unit), b), mult(b, i(b))) = mult(mult(mult(ld(mult(a, b), unit), b), i(b)), b)))),
% 4.67/3.18 inference(quant_inst,[status(thm)],[])).
% 4.67/3.18 tff(292,plain,
% 4.67/3.18 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(ld(mult(a, b), unit), b), mult(b, i(b))) = mult(mult(mult(ld(mult(a, b), unit), b), i(b)), b)) | (mult(mult(ld(mult(a, b), unit), b), mult(i(b), b)) = mult(mult(mult(ld(mult(a, b), unit), b), i(b)), b))),
% 4.67/3.18 inference(modus_ponens,[status(thm)],[291, 290])).
% 4.67/3.18 tff(293,plain,
% 4.67/3.18 ((mult(mult(ld(mult(a, b), unit), b), mult(b, i(b))) = mult(mult(mult(ld(mult(a, b), unit), b), i(b)), b)) | (mult(mult(ld(mult(a, b), unit), b), mult(i(b), b)) = mult(mult(mult(ld(mult(a, b), unit), b), i(b)), b))),
% 4.67/3.18 inference(unit_resolution,[status(thm)],[292, 51])).
% 4.67/3.18 tff(294,plain,
% 4.67/3.18 (mult(mult(ld(mult(a, b), unit), b), mult(i(b), b)) = mult(mult(mult(ld(mult(a, b), unit), b), i(b)), b)),
% 4.67/3.18 inference(unit_resolution,[status(thm)],[293, 286])).
% 4.67/3.18 tff(295,plain,
% 4.67/3.18 (mult(mult(ld(mult(a, b), unit), b), mult(b, i(b))) = mult(mult(mult(ld(mult(a, b), unit), b), i(b)), b)),
% 4.67/3.18 inference(modus_ponens,[status(thm)],[294, 285])).
% 4.67/3.18 tff(296,plain,
% 4.67/3.18 ($false),
% 4.67/3.18 inference(unit_resolution,[status(thm)],[286, 295])).
% 4.67/3.18 tff(297,plain,(mult(mult(ld(mult(a, b), unit), b), mult(b, i(b))) = mult(mult(mult(ld(mult(a, b), unit), b), i(b)), b)), inference(lemma,lemma(discharge,[]))).
% 4.67/3.18 tff(298,plain,
% 4.67/3.18 (mult(mult(mult(ld(mult(a, b), unit), b), i(b)), b) = mult(mult(ld(mult(a, b), unit), b), mult(b, i(b)))),
% 4.67/3.18 inference(symmetry,[status(thm)],[297])).
% 4.67/3.18 tff(299,plain,
% 4.67/3.18 (mult(mult(mult(ld(mult(a, b), unit), b), i(b)), b) = mult(ld(mult(a, b), unit), b)),
% 4.67/3.18 inference(transitivity,[status(thm)],[298, 283, 282])).
% 4.67/3.18 tff(300,plain,
% 4.67/3.18 (rd(mult(mult(mult(ld(mult(a, b), unit), b), i(b)), b), b) = rd(mult(ld(mult(a, b), unit), b), b)),
% 4.67/3.18 inference(monotonicity,[status(thm)],[299])).
% 4.67/3.18 tff(301,plain,
% 4.67/3.18 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(ld(mult(a, b), unit), b), i(b)), b), b) = mult(mult(ld(mult(a, b), unit), b), i(b)))),
% 4.67/3.18 inference(quant_inst,[status(thm)],[])).
% 4.67/3.18 tff(302,plain,
% 4.67/3.18 (rd(mult(mult(mult(ld(mult(a, b), unit), b), i(b)), b), b) = mult(mult(ld(mult(a, b), unit), b), i(b))),
% 4.67/3.18 inference(unit_resolution,[status(thm)],[301, 80])).
% 4.67/3.18 tff(303,plain,
% 4.67/3.18 (mult(mult(ld(mult(a, b), unit), b), i(b)) = rd(mult(mult(mult(ld(mult(a, b), unit), b), i(b)), b), b)),
% 4.67/3.18 inference(symmetry,[status(thm)],[302])).
% 4.67/3.18 tff(304,plain,
% 4.67/3.18 (mult(mult(ld(mult(a, b), unit), b), i(b)) = ld(mult(a, b), unit)),
% 4.67/3.18 inference(transitivity,[status(thm)],[303, 300, 280])).
% 4.67/3.18 tff(305,plain,
% 4.67/3.18 (mult(mult(a, b), mult(mult(ld(mult(a, b), unit), b), i(b))) = mult(mult(a, b), ld(mult(a, b), unit))),
% 4.67/3.18 inference(monotonicity,[status(thm)],[304])).
% 4.67/3.18 tff(306,plain,
% 4.67/3.18 ((mult(mult(a, b), mult(mult(ld(mult(a, b), unit), b), i(b))) = mult(mult(mult(a, b), i(b)), mult(ld(mult(a, b), unit), b))) <=> (mult(mult(a, b), ld(mult(a, b), unit)) = mult(a, mult(ld(mult(a, b), unit), b)))),
% 4.67/3.18 inference(monotonicity,[status(thm)],[305, 233])).
% 4.67/3.18 tff(307,plain,
% 4.67/3.18 ((mult(mult(a, b), mult(mult(ld(mult(a, b), unit), b), i(b))) = mult(mult(mult(a, b), i(b)), mult(ld(mult(a, b), unit), b))) <=> (mult(a, mult(ld(mult(a, b), unit), b)) = mult(mult(a, b), ld(mult(a, b), unit)))),
% 4.67/3.18 inference(transitivity,[status(thm)],[306, 1])).
% 4.67/3.18 tff(308,plain,
% 4.67/3.18 ((mult(a, mult(ld(mult(a, b), unit), b)) = mult(mult(a, b), ld(mult(a, b), unit))) <=> (mult(mult(a, b), mult(mult(ld(mult(a, b), unit), b), i(b))) = mult(mult(mult(a, b), i(b)), mult(ld(mult(a, b), unit), b)))),
% 4.67/3.18 inference(symmetry,[status(thm)],[307])).
% 4.67/3.18 tff(309,plain,
% 4.67/3.18 ((~(mult(a, mult(ld(mult(a, b), unit), b)) = mult(mult(a, b), ld(mult(a, b), unit)))) <=> (~(mult(mult(a, b), mult(mult(ld(mult(a, b), unit), b), i(b))) = mult(mult(mult(a, b), i(b)), mult(ld(mult(a, b), unit), b))))),
% 4.67/3.18 inference(monotonicity,[status(thm)],[308])).
% 4.67/3.18 tff(310,plain,
% 4.67/3.18 (~(mult(mult(a, b), mult(mult(ld(mult(a, b), unit), b), i(b))) = mult(mult(mult(a, b), i(b)), mult(ld(mult(a, b), unit), b)))),
% 4.67/3.18 inference(modus_ponens,[status(thm)],[277, 309])).
% 4.67/3.18 tff(311,plain,
% 4.67/3.18 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(mult(a, b), mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(mult(a, b), i(b)), mult(ld(mult(a, b), unit), b))) | (mult(mult(a, b), mult(mult(ld(mult(a, b), unit), b), i(b))) = mult(mult(mult(a, b), i(b)), mult(ld(mult(a, b), unit), b))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(a, b), mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(mult(a, b), i(b)), mult(ld(mult(a, b), unit), b))) | (mult(mult(a, b), mult(mult(ld(mult(a, b), unit), b), i(b))) = mult(mult(mult(a, b), i(b)), mult(ld(mult(a, b), unit), b))))),
% 4.67/3.18 inference(rewrite,[status(thm)],[])).
% 4.67/3.18 tff(312,plain,
% 4.67/3.18 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(mult(a, b), mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(mult(a, b), i(b)), mult(ld(mult(a, b), unit), b))) | (mult(mult(a, b), mult(mult(ld(mult(a, b), unit), b), i(b))) = mult(mult(mult(a, b), i(b)), mult(ld(mult(a, b), unit), b))))),
% 4.67/3.18 inference(quant_inst,[status(thm)],[])).
% 4.67/3.18 tff(313,plain,
% 4.67/3.18 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(a, b), mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(mult(a, b), i(b)), mult(ld(mult(a, b), unit), b))) | (mult(mult(a, b), mult(mult(ld(mult(a, b), unit), b), i(b))) = mult(mult(mult(a, b), i(b)), mult(ld(mult(a, b), unit), b)))),
% 4.67/3.18 inference(modus_ponens,[status(thm)],[312, 311])).
% 4.67/3.18 tff(314,plain,
% 4.67/3.18 ((mult(mult(a, b), mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(mult(a, b), i(b)), mult(ld(mult(a, b), unit), b))) | (mult(mult(a, b), mult(mult(ld(mult(a, b), unit), b), i(b))) = mult(mult(mult(a, b), i(b)), mult(ld(mult(a, b), unit), b)))),
% 4.67/3.18 inference(unit_resolution,[status(thm)],[313, 51])).
% 4.67/3.18 tff(315,plain,
% 4.67/3.18 ($false),
% 4.67/3.18 inference(unit_resolution,[status(thm)],[314, 310, 278])).
% 4.67/3.18 tff(316,plain,(~(mult(i(b), mult(ld(mult(a, b), unit), b)) = mult(mult(i(b), b), ld(mult(a, b), unit)))), inference(lemma,lemma(discharge,[]))).
% 4.67/3.18 tff(317,plain,
% 4.67/3.18 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | ((mult(i(b), mult(ld(mult(a, b), unit), b)) = mult(mult(i(b), b), ld(mult(a, b), unit))) | (mult(i(b), mult(ld(mult(a, b), unit), b)) = mult(mult(i(b), ld(mult(a, b), unit)), b)))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | (mult(i(b), mult(ld(mult(a, b), unit), b)) = mult(mult(i(b), b), ld(mult(a, b), unit))) | (mult(i(b), mult(ld(mult(a, b), unit), b)) = mult(mult(i(b), ld(mult(a, b), unit)), b)))),
% 4.67/3.18 inference(rewrite,[status(thm)],[])).
% 4.67/3.18 tff(318,plain,
% 4.67/3.18 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | ((mult(i(b), mult(ld(mult(a, b), unit), b)) = mult(mult(i(b), b), ld(mult(a, b), unit))) | (mult(i(b), mult(ld(mult(a, b), unit), b)) = mult(mult(i(b), ld(mult(a, b), unit)), b)))),
% 4.67/3.18 inference(quant_inst,[status(thm)],[])).
% 4.67/3.18 tff(319,plain,
% 4.67/3.18 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | (mult(i(b), mult(ld(mult(a, b), unit), b)) = mult(mult(i(b), b), ld(mult(a, b), unit))) | (mult(i(b), mult(ld(mult(a, b), unit), b)) = mult(mult(i(b), ld(mult(a, b), unit)), b))),
% 4.67/3.18 inference(modus_ponens,[status(thm)],[318, 317])).
% 4.67/3.18 tff(320,plain,
% 4.67/3.18 ((mult(i(b), mult(ld(mult(a, b), unit), b)) = mult(mult(i(b), b), ld(mult(a, b), unit))) | (mult(i(b), mult(ld(mult(a, b), unit), b)) = mult(mult(i(b), ld(mult(a, b), unit)), b))),
% 4.67/3.18 inference(unit_resolution,[status(thm)],[319, 132])).
% 4.67/3.18 tff(321,plain,
% 4.67/3.18 (mult(i(b), mult(ld(mult(a, b), unit), b)) = mult(mult(i(b), ld(mult(a, b), unit)), b)),
% 4.67/3.18 inference(unit_resolution,[status(thm)],[320, 316])).
% 4.67/3.18 tff(322,plain,
% 4.67/3.18 (mult(mult(unit, i(b)), mult(ld(mult(a, b), unit), b)) = mult(i(b), mult(ld(mult(a, b), unit), b))),
% 4.67/3.18 inference(monotonicity,[status(thm)],[43])).
% 4.67/3.18 tff(323,plain,
% 4.67/3.18 ((mult(mult(i(b), b), ld(mult(a, b), unit)) = mult(i(b), mult(ld(mult(a, b), unit), b))) <=> (mult(i(b), mult(ld(mult(a, b), unit), b)) = mult(mult(i(b), b), ld(mult(a, b), unit)))),
% 4.67/3.18 inference(commutativity,[status(thm)],[])).
% 4.67/3.18 tff(324,plain,
% 4.67/3.18 (mult(unit, mult(mult(ld(mult(a, b), unit), b), i(b))) = mult(unit, ld(mult(a, b), unit))),
% 4.67/3.18 inference(monotonicity,[status(thm)],[304])).
% 4.67/3.18 tff(325,plain,
% 4.67/3.18 (mult(unit, mult(mult(ld(mult(a, b), unit), b), i(b))) = mult(mult(i(b), b), ld(mult(a, b), unit))),
% 4.67/3.18 inference(transitivity,[status(thm)],[324, 267])).
% 4.67/3.18 tff(326,plain,
% 4.67/3.18 ((mult(unit, mult(mult(ld(mult(a, b), unit), b), i(b))) = mult(mult(unit, i(b)), mult(ld(mult(a, b), unit), b))) <=> (mult(mult(i(b), b), ld(mult(a, b), unit)) = mult(i(b), mult(ld(mult(a, b), unit), b)))),
% 4.67/3.18 inference(monotonicity,[status(thm)],[325, 322])).
% 4.67/3.18 tff(327,plain,
% 4.67/3.18 ((mult(unit, mult(mult(ld(mult(a, b), unit), b), i(b))) = mult(mult(unit, i(b)), mult(ld(mult(a, b), unit), b))) <=> (mult(i(b), mult(ld(mult(a, b), unit), b)) = mult(mult(i(b), b), ld(mult(a, b), unit)))),
% 4.67/3.18 inference(transitivity,[status(thm)],[326, 323])).
% 4.67/3.18 tff(328,plain,
% 4.67/3.18 ((mult(i(b), mult(ld(mult(a, b), unit), b)) = mult(mult(i(b), b), ld(mult(a, b), unit))) <=> (mult(unit, mult(mult(ld(mult(a, b), unit), b), i(b))) = mult(mult(unit, i(b)), mult(ld(mult(a, b), unit), b)))),
% 4.67/3.18 inference(symmetry,[status(thm)],[327])).
% 4.67/3.18 tff(329,plain,
% 4.67/3.18 ((~(mult(i(b), mult(ld(mult(a, b), unit), b)) = mult(mult(i(b), b), ld(mult(a, b), unit)))) <=> (~(mult(unit, mult(mult(ld(mult(a, b), unit), b), i(b))) = mult(mult(unit, i(b)), mult(ld(mult(a, b), unit), b))))),
% 4.67/3.18 inference(monotonicity,[status(thm)],[328])).
% 4.67/3.18 tff(330,plain,
% 4.67/3.18 (~(mult(unit, mult(mult(ld(mult(a, b), unit), b), i(b))) = mult(mult(unit, i(b)), mult(ld(mult(a, b), unit), b)))),
% 4.67/3.18 inference(modus_ponens,[status(thm)],[316, 329])).
% 4.67/3.18 tff(331,plain,
% 4.67/3.18 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(unit, mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(unit, i(b)), mult(ld(mult(a, b), unit), b))) | (mult(unit, mult(mult(ld(mult(a, b), unit), b), i(b))) = mult(mult(unit, i(b)), mult(ld(mult(a, b), unit), b))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(unit, mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(unit, i(b)), mult(ld(mult(a, b), unit), b))) | (mult(unit, mult(mult(ld(mult(a, b), unit), b), i(b))) = mult(mult(unit, i(b)), mult(ld(mult(a, b), unit), b))))),
% 4.67/3.18 inference(rewrite,[status(thm)],[])).
% 4.67/3.18 tff(332,plain,
% 4.67/3.18 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(unit, mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(unit, i(b)), mult(ld(mult(a, b), unit), b))) | (mult(unit, mult(mult(ld(mult(a, b), unit), b), i(b))) = mult(mult(unit, i(b)), mult(ld(mult(a, b), unit), b))))),
% 4.67/3.18 inference(quant_inst,[status(thm)],[])).
% 4.67/3.18 tff(333,plain,
% 4.67/3.18 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(unit, mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(unit, i(b)), mult(ld(mult(a, b), unit), b))) | (mult(unit, mult(mult(ld(mult(a, b), unit), b), i(b))) = mult(mult(unit, i(b)), mult(ld(mult(a, b), unit), b)))),
% 4.67/3.18 inference(modus_ponens,[status(thm)],[332, 331])).
% 4.67/3.18 tff(334,plain,
% 4.67/3.18 ((mult(unit, mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(unit, i(b)), mult(ld(mult(a, b), unit), b))) | (mult(unit, mult(mult(ld(mult(a, b), unit), b), i(b))) = mult(mult(unit, i(b)), mult(ld(mult(a, b), unit), b)))),
% 4.67/3.19 inference(unit_resolution,[status(thm)],[333, 51])).
% 4.67/3.19 tff(335,plain,
% 4.67/3.19 (mult(unit, mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(unit, i(b)), mult(ld(mult(a, b), unit), b))),
% 4.67/3.19 inference(unit_resolution,[status(thm)],[334, 330])).
% 4.67/3.19 tff(336,plain,
% 4.67/3.19 (mult(mult(i(b), ld(mult(a, b), unit)), b) = mult(i(b), mult(ld(mult(a, b), unit), b))),
% 4.67/3.19 inference(symmetry,[status(thm)],[321])).
% 4.67/3.19 tff(337,plain,
% 4.67/3.19 (mult(unit, mult(mult(i(b), ld(mult(a, b), unit)), b)) = mult(unit, mult(i(b), mult(ld(mult(a, b), unit), b)))),
% 4.67/3.19 inference(monotonicity,[status(thm)],[336])).
% 4.67/3.19 tff(338,plain,
% 4.67/3.19 (mult(unit, unit) = mult(unit, mult(b, i(b)))),
% 4.67/3.19 inference(symmetry,[status(thm)],[70])).
% 4.67/3.19 tff(339,plain,
% 4.67/3.19 (mult(unit, mult(i(b), b)) = mult(unit, unit)),
% 4.67/3.19 inference(monotonicity,[status(thm)],[236])).
% 4.67/3.19 tff(340,plain,
% 4.67/3.19 (mult(unit, mult(i(b), b)) = mult(unit, mult(b, i(b)))),
% 4.67/3.19 inference(transitivity,[status(thm)],[339, 338])).
% 4.67/3.19 tff(341,plain,
% 4.67/3.19 ((mult(unit, mult(i(b), b)) = mult(mult(unit, b), i(b))) <=> (mult(unit, mult(b, i(b))) = mult(mult(unit, b), i(b)))),
% 4.67/3.19 inference(monotonicity,[status(thm)],[340])).
% 4.67/3.19 tff(342,assumption,(~(mult(unit, mult(b, i(b))) = mult(mult(unit, b), i(b)))), introduced(assumption)).
% 4.67/3.19 tff(343,plain,
% 4.67/3.19 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(unit, mult(b, i(b))) = mult(mult(unit, b), i(b))) | (mult(unit, mult(i(b), b)) = mult(mult(unit, b), i(b))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(unit, mult(b, i(b))) = mult(mult(unit, b), i(b))) | (mult(unit, mult(i(b), b)) = mult(mult(unit, b), i(b))))),
% 4.67/3.19 inference(rewrite,[status(thm)],[])).
% 4.67/3.19 tff(344,plain,
% 4.67/3.19 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(unit, mult(b, i(b))) = mult(mult(unit, b), i(b))) | (mult(unit, mult(i(b), b)) = mult(mult(unit, b), i(b))))),
% 4.67/3.19 inference(quant_inst,[status(thm)],[])).
% 4.67/3.19 tff(345,plain,
% 4.67/3.19 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(unit, mult(b, i(b))) = mult(mult(unit, b), i(b))) | (mult(unit, mult(i(b), b)) = mult(mult(unit, b), i(b)))),
% 4.67/3.19 inference(modus_ponens,[status(thm)],[344, 343])).
% 4.67/3.19 tff(346,plain,
% 4.67/3.19 ((mult(unit, mult(b, i(b))) = mult(mult(unit, b), i(b))) | (mult(unit, mult(i(b), b)) = mult(mult(unit, b), i(b)))),
% 4.67/3.19 inference(unit_resolution,[status(thm)],[345, 51])).
% 4.67/3.19 tff(347,plain,
% 4.67/3.19 (mult(unit, mult(i(b), b)) = mult(mult(unit, b), i(b))),
% 4.67/3.19 inference(unit_resolution,[status(thm)],[346, 342])).
% 4.67/3.19 tff(348,plain,
% 4.67/3.19 (mult(unit, mult(b, i(b))) = mult(mult(unit, b), i(b))),
% 4.67/3.19 inference(modus_ponens,[status(thm)],[347, 341])).
% 4.67/3.19 tff(349,plain,
% 4.67/3.19 ($false),
% 4.67/3.19 inference(unit_resolution,[status(thm)],[342, 348])).
% 4.67/3.19 tff(350,plain,(mult(unit, mult(b, i(b))) = mult(mult(unit, b), i(b))), inference(lemma,lemma(discharge,[]))).
% 4.67/3.19 tff(351,plain,
% 4.67/3.19 (mult(mult(unit, b), i(b)) = mult(unit, mult(b, i(b)))),
% 4.67/3.19 inference(symmetry,[status(thm)],[350])).
% 4.67/3.19 tff(352,plain,
% 4.67/3.19 (mult(mult(unit, b), i(b)) = unit),
% 4.67/3.19 inference(transitivity,[status(thm)],[351, 70, 69])).
% 4.67/3.19 tff(353,plain,
% 4.67/3.19 (mult(mult(mult(unit, b), i(b)), i(b)) = mult(unit, i(b))),
% 4.67/3.19 inference(monotonicity,[status(thm)],[352])).
% 4.67/3.19 tff(354,plain,
% 4.67/3.19 ((~![A: $i] : (mult(unit, A) = A)) | (mult(unit, b) = b)),
% 4.67/3.19 inference(quant_inst,[status(thm)],[])).
% 4.67/3.19 tff(355,plain,
% 4.67/3.19 (mult(unit, b) = b),
% 4.67/3.19 inference(unit_resolution,[status(thm)],[354, 40])).
% 4.67/3.19 tff(356,plain,
% 4.67/3.19 (mult(mult(i(b), i(b)), mult(unit, b)) = mult(mult(i(b), i(b)), b)),
% 4.67/3.19 inference(monotonicity,[status(thm)],[355])).
% 4.67/3.19 tff(357,plain,
% 4.67/3.19 (mult(mult(i(b), i(b)), mult(unit, b)) = mult(mult(unit, mult(i(b), i(b))), b)),
% 4.67/3.19 inference(transitivity,[status(thm)],[356, 140])).
% 4.67/3.19 tff(358,plain,
% 4.67/3.19 ((~![A: $i] : (mult(A, unit) = A)) | (mult(i(b), unit) = i(b))),
% 4.67/3.19 inference(quant_inst,[status(thm)],[])).
% 4.67/3.19 tff(359,plain,
% 4.67/3.19 (mult(i(b), unit) = i(b)),
% 4.67/3.19 inference(unit_resolution,[status(thm)],[358, 8])).
% 4.67/3.19 tff(360,plain,
% 4.67/3.19 (mult(i(b), mult(unit, b)) = mult(i(b), b)),
% 4.67/3.19 inference(monotonicity,[status(thm)],[355])).
% 4.67/3.19 tff(361,plain,
% 4.67/3.19 (mult(i(b), mult(unit, b)) = unit),
% 4.67/3.19 inference(transitivity,[status(thm)],[360, 218, 213, 60, 19])).
% 4.67/3.19 tff(362,plain,
% 4.67/3.19 (mult(i(b), mult(i(b), mult(unit, b))) = mult(i(b), unit)),
% 4.67/3.19 inference(monotonicity,[status(thm)],[361])).
% 4.67/3.19 tff(363,plain,
% 4.67/3.19 (mult(i(b), mult(i(b), mult(unit, b))) = mult(unit, mult(b, mult(i(b), i(b))))),
% 4.67/3.19 inference(transitivity,[status(thm)],[362, 359, 216, 160])).
% 4.67/3.19 tff(364,plain,
% 4.67/3.19 ((mult(i(b), mult(i(b), mult(unit, b))) = mult(mult(i(b), i(b)), mult(unit, b))) <=> (mult(unit, mult(b, mult(i(b), i(b)))) = mult(mult(unit, mult(i(b), i(b))), b))),
% 4.67/3.19 inference(monotonicity,[status(thm)],[363, 357])).
% 4.67/3.19 tff(365,plain,
% 4.67/3.19 ((mult(unit, mult(b, mult(i(b), i(b)))) = mult(mult(unit, mult(i(b), i(b))), b)) <=> (mult(i(b), mult(i(b), mult(unit, b))) = mult(mult(i(b), i(b)), mult(unit, b)))),
% 4.67/3.19 inference(symmetry,[status(thm)],[364])).
% 4.67/3.19 tff(366,plain,
% 4.67/3.19 (mult(mult(unit, b), mult(i(b), i(b))) = mult(unit, mult(b, mult(i(b), i(b))))),
% 4.67/3.19 inference(transitivity,[status(thm)],[122, 353, 160])).
% 4.67/3.19 tff(367,plain,
% 4.67/3.19 ((mult(unit, mult(mult(i(b), i(b)), b)) = mult(mult(unit, b), mult(i(b), i(b)))) <=> (mult(mult(unit, mult(i(b), i(b))), b) = mult(unit, mult(b, mult(i(b), i(b)))))),
% 4.67/3.19 inference(monotonicity,[status(thm)],[175, 366])).
% 4.67/3.19 tff(368,plain,
% 4.67/3.19 ((mult(unit, mult(mult(i(b), i(b)), b)) = mult(mult(unit, b), mult(i(b), i(b)))) <=> (mult(unit, mult(b, mult(i(b), i(b)))) = mult(mult(unit, mult(i(b), i(b))), b))),
% 4.67/3.19 inference(transitivity,[status(thm)],[367, 168])).
% 4.67/3.19 tff(369,plain,
% 4.67/3.19 ((mult(unit, mult(mult(i(b), i(b)), b)) = mult(mult(unit, b), mult(i(b), i(b)))) <=> (mult(i(b), mult(i(b), mult(unit, b))) = mult(mult(i(b), i(b)), mult(unit, b)))),
% 4.67/3.19 inference(transitivity,[status(thm)],[368, 365])).
% 4.67/3.19 tff(370,plain,
% 4.67/3.19 ((~(mult(unit, mult(mult(i(b), i(b)), b)) = mult(mult(unit, b), mult(i(b), i(b))))) <=> (~(mult(i(b), mult(i(b), mult(unit, b))) = mult(mult(i(b), i(b)), mult(unit, b))))),
% 4.67/3.19 inference(monotonicity,[status(thm)],[369])).
% 4.67/3.19 tff(371,plain,
% 4.67/3.19 (~(mult(i(b), mult(i(b), mult(unit, b))) = mult(mult(i(b), i(b)), mult(unit, b)))),
% 4.67/3.19 inference(modus_ponens,[status(thm)],[170, 370])).
% 4.67/3.19 tff(372,plain,
% 4.67/3.19 (mult(i(b), mult(mult(unit, b), i(b))) = mult(i(b), unit)),
% 4.67/3.19 inference(monotonicity,[status(thm)],[352])).
% 4.67/3.19 tff(373,plain,
% 4.67/3.19 (mult(i(b), mult(mult(unit, b), i(b))) = mult(unit, mult(b, mult(i(b), i(b))))),
% 4.67/3.19 inference(transitivity,[status(thm)],[372, 359, 216, 160])).
% 4.67/3.19 tff(374,plain,
% 4.67/3.19 ((mult(i(b), mult(mult(unit, b), i(b))) = mult(mult(i(b), i(b)), mult(unit, b))) <=> (mult(unit, mult(b, mult(i(b), i(b)))) = mult(mult(unit, mult(i(b), i(b))), b))),
% 4.67/3.19 inference(monotonicity,[status(thm)],[373, 357])).
% 4.67/3.19 tff(375,plain,
% 4.67/3.19 ((mult(unit, mult(b, mult(i(b), i(b)))) = mult(mult(unit, mult(i(b), i(b))), b)) <=> (mult(i(b), mult(mult(unit, b), i(b))) = mult(mult(i(b), i(b)), mult(unit, b)))),
% 4.67/3.19 inference(symmetry,[status(thm)],[374])).
% 4.67/3.19 tff(376,plain,
% 4.67/3.19 ((mult(unit, mult(mult(i(b), i(b)), b)) = mult(mult(unit, b), mult(i(b), i(b)))) <=> (mult(i(b), mult(mult(unit, b), i(b))) = mult(mult(i(b), i(b)), mult(unit, b)))),
% 4.67/3.19 inference(transitivity,[status(thm)],[368, 375])).
% 4.67/3.19 tff(377,plain,
% 4.67/3.19 ((~(mult(unit, mult(mult(i(b), i(b)), b)) = mult(mult(unit, b), mult(i(b), i(b))))) <=> (~(mult(i(b), mult(mult(unit, b), i(b))) = mult(mult(i(b), i(b)), mult(unit, b))))),
% 4.67/3.19 inference(monotonicity,[status(thm)],[376])).
% 4.67/3.19 tff(378,plain,
% 4.67/3.19 (~(mult(i(b), mult(mult(unit, b), i(b))) = mult(mult(i(b), i(b)), mult(unit, b)))),
% 4.67/3.19 inference(modus_ponens,[status(thm)],[170, 377])).
% 4.67/3.19 tff(379,plain,
% 4.67/3.19 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(i(b), mult(i(b), mult(unit, b))) = mult(mult(i(b), i(b)), mult(unit, b))) | (mult(i(b), mult(mult(unit, b), i(b))) = mult(mult(i(b), i(b)), mult(unit, b))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(i(b), mult(i(b), mult(unit, b))) = mult(mult(i(b), i(b)), mult(unit, b))) | (mult(i(b), mult(mult(unit, b), i(b))) = mult(mult(i(b), i(b)), mult(unit, b))))),
% 4.67/3.19 inference(rewrite,[status(thm)],[])).
% 4.67/3.19 tff(380,plain,
% 4.67/3.19 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(i(b), mult(i(b), mult(unit, b))) = mult(mult(i(b), i(b)), mult(unit, b))) | (mult(i(b), mult(mult(unit, b), i(b))) = mult(mult(i(b), i(b)), mult(unit, b))))),
% 4.67/3.19 inference(quant_inst,[status(thm)],[])).
% 4.67/3.19 tff(381,plain,
% 4.67/3.19 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(i(b), mult(i(b), mult(unit, b))) = mult(mult(i(b), i(b)), mult(unit, b))) | (mult(i(b), mult(mult(unit, b), i(b))) = mult(mult(i(b), i(b)), mult(unit, b)))),
% 4.67/3.19 inference(modus_ponens,[status(thm)],[380, 379])).
% 4.67/3.19 tff(382,plain,
% 4.67/3.19 ((mult(i(b), mult(i(b), mult(unit, b))) = mult(mult(i(b), i(b)), mult(unit, b))) | (mult(i(b), mult(mult(unit, b), i(b))) = mult(mult(i(b), i(b)), mult(unit, b)))),
% 4.67/3.19 inference(unit_resolution,[status(thm)],[381, 51])).
% 4.67/3.19 tff(383,plain,
% 4.67/3.19 ($false),
% 4.67/3.19 inference(unit_resolution,[status(thm)],[382, 378, 371])).
% 4.67/3.19 tff(384,plain,(mult(unit, mult(mult(i(b), i(b)), b)) = mult(mult(unit, b), mult(i(b), i(b)))), inference(lemma,lemma(discharge,[]))).
% 4.67/3.19 tff(385,plain,
% 4.67/3.19 (mult(mult(i(b), i(b)), b) = ld(b, unit)),
% 4.67/3.19 inference(transitivity,[status(thm)],[197, 384, 122, 353, 43, 28])).
% 4.67/3.19 tff(386,plain,
% 4.67/3.19 (mult(b, mult(mult(i(b), i(b)), b)) = mult(b, ld(b, unit))),
% 4.67/3.19 inference(monotonicity,[status(thm)],[385])).
% 4.67/3.19 tff(387,plain,
% 4.67/3.19 (mult(b, mult(mult(i(b), i(b)), b)) = mult(b, mult(b, mult(i(b), i(b))))),
% 4.67/3.19 inference(transitivity,[status(thm)],[386, 66])).
% 4.67/3.19 tff(388,plain,
% 4.67/3.19 ((mult(b, mult(mult(i(b), i(b)), b)) = mult(mult(b, b), mult(i(b), i(b)))) <=> (mult(b, mult(b, mult(i(b), i(b)))) = mult(mult(b, b), mult(i(b), i(b))))),
% 4.67/3.19 inference(monotonicity,[status(thm)],[387])).
% 4.67/3.19 tff(389,plain,
% 4.67/3.19 ((mult(b, mult(b, mult(i(b), i(b)))) = mult(mult(b, b), mult(i(b), i(b)))) <=> (mult(b, mult(mult(i(b), i(b)), b)) = mult(mult(b, b), mult(i(b), i(b))))),
% 4.67/3.19 inference(symmetry,[status(thm)],[388])).
% 4.67/3.19 tff(390,assumption,(~(mult(b, mult(mult(i(b), i(b)), b)) = mult(mult(b, b), mult(i(b), i(b))))), introduced(assumption)).
% 4.67/3.19 tff(391,plain,
% 4.67/3.19 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(b, mult(b, mult(i(b), i(b)))) = mult(mult(b, b), mult(i(b), i(b)))) | (mult(b, mult(mult(i(b), i(b)), b)) = mult(mult(b, b), mult(i(b), i(b)))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(b, mult(b, mult(i(b), i(b)))) = mult(mult(b, b), mult(i(b), i(b)))) | (mult(b, mult(mult(i(b), i(b)), b)) = mult(mult(b, b), mult(i(b), i(b)))))),
% 4.67/3.19 inference(rewrite,[status(thm)],[])).
% 4.67/3.19 tff(392,plain,
% 4.67/3.19 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(b, mult(b, mult(i(b), i(b)))) = mult(mult(b, b), mult(i(b), i(b)))) | (mult(b, mult(mult(i(b), i(b)), b)) = mult(mult(b, b), mult(i(b), i(b)))))),
% 4.67/3.19 inference(quant_inst,[status(thm)],[])).
% 4.67/3.19 tff(393,plain,
% 4.67/3.19 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(b, mult(b, mult(i(b), i(b)))) = mult(mult(b, b), mult(i(b), i(b)))) | (mult(b, mult(mult(i(b), i(b)), b)) = mult(mult(b, b), mult(i(b), i(b))))),
% 4.67/3.19 inference(modus_ponens,[status(thm)],[392, 391])).
% 4.67/3.19 tff(394,plain,
% 4.67/3.19 ((mult(b, mult(b, mult(i(b), i(b)))) = mult(mult(b, b), mult(i(b), i(b)))) | (mult(b, mult(mult(i(b), i(b)), b)) = mult(mult(b, b), mult(i(b), i(b))))),
% 4.67/3.19 inference(unit_resolution,[status(thm)],[393, 51])).
% 4.67/3.19 tff(395,plain,
% 4.67/3.19 (mult(b, mult(b, mult(i(b), i(b)))) = mult(mult(b, b), mult(i(b), i(b)))),
% 4.67/3.19 inference(unit_resolution,[status(thm)],[394, 390])).
% 4.67/3.19 tff(396,plain,
% 4.67/3.19 (mult(b, mult(mult(i(b), i(b)), b)) = mult(mult(b, b), mult(i(b), i(b)))),
% 4.67/3.19 inference(modus_ponens,[status(thm)],[395, 389])).
% 4.67/3.19 tff(397,plain,
% 4.67/3.19 ($false),
% 4.67/3.19 inference(unit_resolution,[status(thm)],[390, 396])).
% 4.67/3.19 tff(398,plain,(mult(b, mult(mult(i(b), i(b)), b)) = mult(mult(b, b), mult(i(b), i(b)))), inference(lemma,lemma(discharge,[]))).
% 4.67/3.19 tff(399,plain,
% 4.67/3.19 (mult(mult(b, b), mult(i(b), i(b))) = mult(b, mult(mult(i(b), i(b)), b))),
% 4.67/3.19 inference(symmetry,[status(thm)],[398])).
% 4.67/3.19 tff(400,plain,
% 4.67/3.19 ((~![B: $i, A: $i] : (mult(A, ld(A, B)) = B)) | (mult(a, ld(a, unit)) = unit)),
% 4.67/3.19 inference(quant_inst,[status(thm)],[])).
% 4.67/3.19 tff(401,plain,
% 4.67/3.19 (mult(a, ld(a, unit)) = unit),
% 4.67/3.19 inference(unit_resolution,[status(thm)],[400, 17])).
% 4.67/3.19 tff(402,plain,
% 4.67/3.19 (mult(a, i(a)) = mult(a, ld(a, unit))),
% 4.67/3.19 inference(monotonicity,[status(thm)],[262])).
% 4.67/3.19 tff(403,plain,
% 4.67/3.19 (mult(a, i(a)) = unit),
% 4.67/3.19 inference(transitivity,[status(thm)],[402, 401])).
% 4.67/3.19 tff(404,plain,
% 4.67/3.19 (mult(mult(a, i(a)), i(b)) = mult(unit, i(b))),
% 4.67/3.19 inference(monotonicity,[status(thm)],[403])).
% 4.67/3.19 tff(405,plain,
% 4.67/3.19 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(i(b), mult(b, ld(mult(a, b), unit))) = mult(mult(i(b), b), ld(mult(a, b), unit))) | (mult(i(b), mult(ld(mult(a, b), unit), b)) = mult(mult(i(b), b), ld(mult(a, b), unit))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(i(b), mult(b, ld(mult(a, b), unit))) = mult(mult(i(b), b), ld(mult(a, b), unit))) | (mult(i(b), mult(ld(mult(a, b), unit), b)) = mult(mult(i(b), b), ld(mult(a, b), unit))))),
% 4.67/3.19 inference(rewrite,[status(thm)],[])).
% 4.67/3.19 tff(406,plain,
% 4.67/3.19 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(i(b), mult(b, ld(mult(a, b), unit))) = mult(mult(i(b), b), ld(mult(a, b), unit))) | (mult(i(b), mult(ld(mult(a, b), unit), b)) = mult(mult(i(b), b), ld(mult(a, b), unit))))),
% 4.67/3.19 inference(quant_inst,[status(thm)],[])).
% 4.67/3.19 tff(407,plain,
% 4.67/3.19 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(i(b), mult(b, ld(mult(a, b), unit))) = mult(mult(i(b), b), ld(mult(a, b), unit))) | (mult(i(b), mult(ld(mult(a, b), unit), b)) = mult(mult(i(b), b), ld(mult(a, b), unit)))),
% 4.67/3.19 inference(modus_ponens,[status(thm)],[406, 405])).
% 4.67/3.19 tff(408,plain,
% 4.67/3.19 ((mult(i(b), mult(b, ld(mult(a, b), unit))) = mult(mult(i(b), b), ld(mult(a, b), unit))) | (mult(i(b), mult(ld(mult(a, b), unit), b)) = mult(mult(i(b), b), ld(mult(a, b), unit)))),
% 4.67/3.19 inference(unit_resolution,[status(thm)],[407, 51])).
% 4.67/3.19 tff(409,plain,
% 4.67/3.19 (mult(i(b), mult(b, ld(mult(a, b), unit))) = mult(mult(i(b), b), ld(mult(a, b), unit))),
% 4.67/3.19 inference(unit_resolution,[status(thm)],[408, 316])).
% 4.67/3.19 tff(410,plain,
% 4.67/3.19 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(a, mult(a, mult(b, ld(mult(a, b), unit)))) = mult(b, ld(mult(a, b), unit)))),
% 4.67/3.19 inference(quant_inst,[status(thm)],[])).
% 4.67/3.19 tff(411,plain,
% 4.67/3.19 (ld(a, mult(a, mult(b, ld(mult(a, b), unit)))) = mult(b, ld(mult(a, b), unit))),
% 4.67/3.19 inference(unit_resolution,[status(thm)],[410, 251])).
% 4.67/3.19 tff(412,assumption,(mult(a, mult(b, ld(mult(a, b), unit))) = mult(mult(a, b), ld(mult(a, b), unit))), introduced(assumption)).
% 4.67/3.19 tff(413,plain,
% 4.67/3.19 (mult(mult(a, b), ld(mult(a, b), unit)) = mult(a, mult(b, ld(mult(a, b), unit)))),
% 4.67/3.19 inference(symmetry,[status(thm)],[412])).
% 4.67/3.19 tff(414,plain,
% 4.67/3.19 (unit = mult(a, mult(b, ld(mult(a, b), unit)))),
% 4.67/3.19 inference(transitivity,[status(thm)],[258, 413])).
% 4.67/3.19 tff(415,plain,
% 4.67/3.19 (ld(a, unit) = ld(a, mult(a, mult(b, ld(mult(a, b), unit))))),
% 4.67/3.19 inference(monotonicity,[status(thm)],[414])).
% 4.67/3.19 tff(416,plain,
% 4.67/3.19 (i(a) = mult(b, ld(mult(a, b), unit))),
% 4.67/3.19 inference(transitivity,[status(thm)],[262, 415, 411])).
% 4.67/3.19 tff(417,plain,
% 4.67/3.19 (mult(i(b), i(a)) = mult(i(b), mult(b, ld(mult(a, b), unit)))),
% 4.67/3.20 inference(monotonicity,[status(thm)],[416])).
% 4.67/3.20 tff(418,plain,
% 4.67/3.20 (mult(i(b), mult(b, ld(mult(a, b), unit))) = mult(i(b), i(a))),
% 4.67/3.20 inference(symmetry,[status(thm)],[417])).
% 4.67/3.20 tff(419,assumption,(mult(i(b), mult(b, ld(mult(a, b), unit))) = mult(mult(i(b), b), ld(mult(a, b), unit))), introduced(assumption)).
% 4.67/3.20 tff(420,plain,
% 4.67/3.20 (mult(mult(i(b), b), ld(mult(a, b), unit)) = mult(i(b), mult(b, ld(mult(a, b), unit)))),
% 4.67/3.20 inference(symmetry,[status(thm)],[419])).
% 4.67/3.20 tff(421,plain,
% 4.67/3.20 (i(mult(a, b)) = mult(i(b), i(a))),
% 4.67/3.20 inference(transitivity,[status(thm)],[270, 268, 267, 420, 418])).
% 4.67/3.20 tff(422,plain,
% 4.67/3.20 ($false),
% 4.67/3.20 inference(unit_resolution,[status(thm)],[274, 421])).
% 4.67/3.20 tff(423,plain,((~(mult(a, mult(b, ld(mult(a, b), unit))) = mult(mult(a, b), ld(mult(a, b), unit)))) | (~(mult(i(b), mult(b, ld(mult(a, b), unit))) = mult(mult(i(b), b), ld(mult(a, b), unit))))), inference(lemma,lemma(discharge,[]))).
% 4.67/3.20 tff(424,plain,
% 4.67/3.20 (~(mult(a, mult(b, ld(mult(a, b), unit))) = mult(mult(a, b), ld(mult(a, b), unit)))),
% 4.67/3.20 inference(unit_resolution,[status(thm)],[423, 409])).
% 4.67/3.20 tff(425,plain,
% 4.67/3.20 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(a, mult(b, ld(mult(a, b), unit))) = mult(mult(a, b), ld(mult(a, b), unit))) | (mult(a, mult(ld(mult(a, b), unit), b)) = mult(mult(a, b), ld(mult(a, b), unit))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(a, mult(b, ld(mult(a, b), unit))) = mult(mult(a, b), ld(mult(a, b), unit))) | (mult(a, mult(ld(mult(a, b), unit), b)) = mult(mult(a, b), ld(mult(a, b), unit))))),
% 4.67/3.20 inference(rewrite,[status(thm)],[])).
% 4.67/3.20 tff(426,plain,
% 4.67/3.20 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(a, mult(b, ld(mult(a, b), unit))) = mult(mult(a, b), ld(mult(a, b), unit))) | (mult(a, mult(ld(mult(a, b), unit), b)) = mult(mult(a, b), ld(mult(a, b), unit))))),
% 4.67/3.20 inference(quant_inst,[status(thm)],[])).
% 4.67/3.20 tff(427,plain,
% 4.67/3.20 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(a, mult(b, ld(mult(a, b), unit))) = mult(mult(a, b), ld(mult(a, b), unit))) | (mult(a, mult(ld(mult(a, b), unit), b)) = mult(mult(a, b), ld(mult(a, b), unit)))),
% 4.67/3.20 inference(modus_ponens,[status(thm)],[426, 425])).
% 4.67/3.20 tff(428,plain,
% 4.67/3.20 ((mult(a, mult(b, ld(mult(a, b), unit))) = mult(mult(a, b), ld(mult(a, b), unit))) | (mult(a, mult(ld(mult(a, b), unit), b)) = mult(mult(a, b), ld(mult(a, b), unit)))),
% 4.67/3.20 inference(unit_resolution,[status(thm)],[427, 51])).
% 4.67/3.20 tff(429,plain,
% 4.67/3.20 (mult(a, mult(ld(mult(a, b), unit), b)) = mult(mult(a, b), ld(mult(a, b), unit))),
% 4.67/3.20 inference(unit_resolution,[status(thm)],[428, 424])).
% 4.67/3.20 tff(430,plain,
% 4.67/3.20 ((mult(mult(a, ld(mult(a, b), unit)), b) = mult(a, mult(ld(mult(a, b), unit), b))) <=> (mult(a, mult(ld(mult(a, b), unit), b)) = mult(mult(a, ld(mult(a, b), unit)), b))),
% 4.67/3.20 inference(commutativity,[status(thm)],[])).
% 4.67/3.20 tff(431,plain,
% 4.67/3.20 (mult(mult(a, b), ld(mult(a, b), unit)) = mult(a, mult(ld(mult(a, b), unit), b))),
% 4.67/3.20 inference(symmetry,[status(thm)],[429])).
% 4.67/3.20 tff(432,plain,
% 4.67/3.20 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | ((mult(a, mult(b, ld(mult(a, b), unit))) = mult(mult(a, b), ld(mult(a, b), unit))) | (mult(a, mult(b, ld(mult(a, b), unit))) = mult(mult(a, ld(mult(a, b), unit)), b)))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | (mult(a, mult(b, ld(mult(a, b), unit))) = mult(mult(a, b), ld(mult(a, b), unit))) | (mult(a, mult(b, ld(mult(a, b), unit))) = mult(mult(a, ld(mult(a, b), unit)), b)))),
% 4.67/3.20 inference(rewrite,[status(thm)],[])).
% 4.67/3.20 tff(433,plain,
% 4.67/3.20 (((mult(a, mult(b, ld(mult(a, b), unit))) = mult(mult(a, ld(mult(a, b), unit)), b)) | (mult(a, mult(b, ld(mult(a, b), unit))) = mult(mult(a, b), ld(mult(a, b), unit)))) <=> ((mult(a, mult(b, ld(mult(a, b), unit))) = mult(mult(a, b), ld(mult(a, b), unit))) | (mult(a, mult(b, ld(mult(a, b), unit))) = mult(mult(a, ld(mult(a, b), unit)), b)))),
% 4.67/3.20 inference(rewrite,[status(thm)],[])).
% 4.67/3.20 tff(434,plain,
% 4.67/3.20 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | ((mult(a, mult(b, ld(mult(a, b), unit))) = mult(mult(a, ld(mult(a, b), unit)), b)) | (mult(a, mult(b, ld(mult(a, b), unit))) = mult(mult(a, b), ld(mult(a, b), unit))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | ((mult(a, mult(b, ld(mult(a, b), unit))) = mult(mult(a, b), ld(mult(a, b), unit))) | (mult(a, mult(b, ld(mult(a, b), unit))) = mult(mult(a, ld(mult(a, b), unit)), b))))),
% 4.67/3.20 inference(monotonicity,[status(thm)],[433])).
% 4.67/3.20 tff(435,plain,
% 4.67/3.20 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | ((mult(a, mult(b, ld(mult(a, b), unit))) = mult(mult(a, ld(mult(a, b), unit)), b)) | (mult(a, mult(b, ld(mult(a, b), unit))) = mult(mult(a, b), ld(mult(a, b), unit))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | (mult(a, mult(b, ld(mult(a, b), unit))) = mult(mult(a, b), ld(mult(a, b), unit))) | (mult(a, mult(b, ld(mult(a, b), unit))) = mult(mult(a, ld(mult(a, b), unit)), b)))),
% 4.67/3.20 inference(transitivity,[status(thm)],[434, 432])).
% 4.67/3.20 tff(436,plain,
% 4.67/3.20 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | ((mult(a, mult(b, ld(mult(a, b), unit))) = mult(mult(a, ld(mult(a, b), unit)), b)) | (mult(a, mult(b, ld(mult(a, b), unit))) = mult(mult(a, b), ld(mult(a, b), unit))))),
% 4.67/3.20 inference(quant_inst,[status(thm)],[])).
% 4.67/3.20 tff(437,plain,
% 4.67/3.20 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | (mult(a, mult(b, ld(mult(a, b), unit))) = mult(mult(a, b), ld(mult(a, b), unit))) | (mult(a, mult(b, ld(mult(a, b), unit))) = mult(mult(a, ld(mult(a, b), unit)), b))),
% 4.67/3.20 inference(modus_ponens,[status(thm)],[436, 435])).
% 4.67/3.20 tff(438,plain,
% 4.67/3.20 ((mult(a, mult(b, ld(mult(a, b), unit))) = mult(mult(a, b), ld(mult(a, b), unit))) | (mult(a, mult(b, ld(mult(a, b), unit))) = mult(mult(a, ld(mult(a, b), unit)), b))),
% 4.67/3.20 inference(unit_resolution,[status(thm)],[437, 132])).
% 4.67/3.20 tff(439,plain,
% 4.67/3.20 (mult(a, mult(b, ld(mult(a, b), unit))) = mult(mult(a, ld(mult(a, b), unit)), b)),
% 4.67/3.20 inference(unit_resolution,[status(thm)],[438, 424])).
% 4.67/3.20 tff(440,plain,
% 4.67/3.20 ((mult(a, mult(b, ld(mult(a, b), unit))) = mult(mult(a, b), ld(mult(a, b), unit))) <=> (mult(mult(a, ld(mult(a, b), unit)), b) = mult(a, mult(ld(mult(a, b), unit), b)))),
% 4.67/3.20 inference(monotonicity,[status(thm)],[439, 431])).
% 4.67/3.20 tff(441,plain,
% 4.67/3.20 ((mult(a, mult(b, ld(mult(a, b), unit))) = mult(mult(a, b), ld(mult(a, b), unit))) <=> (mult(a, mult(ld(mult(a, b), unit), b)) = mult(mult(a, ld(mult(a, b), unit)), b))),
% 4.67/3.20 inference(transitivity,[status(thm)],[440, 430])).
% 4.67/3.20 tff(442,plain,
% 4.67/3.20 ((~(mult(a, mult(b, ld(mult(a, b), unit))) = mult(mult(a, b), ld(mult(a, b), unit)))) <=> (~(mult(a, mult(ld(mult(a, b), unit), b)) = mult(mult(a, ld(mult(a, b), unit)), b)))),
% 4.67/3.20 inference(monotonicity,[status(thm)],[441])).
% 4.67/3.20 tff(443,plain,
% 4.67/3.20 (~(mult(a, mult(ld(mult(a, b), unit), b)) = mult(mult(a, ld(mult(a, b), unit)), b))),
% 4.67/3.20 inference(modus_ponens,[status(thm)],[424, 442])).
% 4.67/3.20 tff(444,assumption,(mult(a, mult(i(a), i(b))) = mult(mult(a, i(a)), i(b))), introduced(assumption)).
% 4.67/3.20 tff(445,plain,
% 4.67/3.20 (mult(i(a), i(b)) = mult(mult(ld(mult(a, b), unit), b), i(b))),
% 4.67/3.20 inference(monotonicity,[status(thm)],[263])).
% 4.67/3.20 tff(446,plain,
% 4.67/3.20 (mult(mult(ld(mult(a, b), unit), b), i(b)) = mult(i(a), i(b))),
% 4.67/3.20 inference(symmetry,[status(thm)],[445])).
% 4.67/3.20 tff(447,plain,
% 4.67/3.20 (rd(mult(ld(mult(a, b), unit), b), b) = rd(mult(mult(mult(ld(mult(a, b), unit), b), i(b)), b), b)),
% 4.67/3.20 inference(symmetry,[status(thm)],[300])).
% 4.67/3.20 tff(448,plain,
% 4.67/3.20 (ld(mult(a, b), unit) = rd(mult(ld(mult(a, b), unit), b), b)),
% 4.67/3.20 inference(symmetry,[status(thm)],[280])).
% 4.67/3.20 tff(449,plain,
% 4.67/3.20 (ld(mult(a, b), unit) = mult(i(a), i(b))),
% 4.67/3.20 inference(transitivity,[status(thm)],[448, 447, 302, 446])).
% 4.67/3.20 tff(450,plain,
% 4.67/3.20 (mult(a, ld(mult(a, b), unit)) = mult(a, mult(i(a), i(b)))),
% 4.67/3.20 inference(monotonicity,[status(thm)],[449])).
% 4.67/3.20 tff(451,plain,
% 4.67/3.20 (mult(a, ld(mult(a, b), unit)) = i(b)),
% 4.67/3.20 inference(transitivity,[status(thm)],[450, 444, 404, 43])).
% 4.67/3.20 tff(452,plain,
% 4.67/3.20 (mult(mult(a, ld(mult(a, b), unit)), b) = mult(i(b), b)),
% 4.67/3.20 inference(monotonicity,[status(thm)],[451])).
% 4.67/3.20 tff(453,plain,
% 4.67/3.20 (mult(i(b), b) = mult(mult(a, ld(mult(a, b), unit)), b)),
% 4.67/3.20 inference(symmetry,[status(thm)],[452])).
% 4.67/3.20 tff(454,plain,
% 4.67/3.20 (mult(mult(b, mult(i(b), i(b))), b) = mult(i(b), b)),
% 4.67/3.20 inference(symmetry,[status(thm)],[218])).
% 4.67/3.20 tff(455,plain,
% 4.67/3.20 (mult(a, mult(ld(mult(a, b), unit), b)) = mult(mult(a, ld(mult(a, b), unit)), b)),
% 4.67/3.20 inference(transitivity,[status(thm)],[254, 257, 67, 66, 212, 454, 453])).
% 4.67/3.20 tff(456,assumption,(~(mult(a, mult(ld(mult(a, b), unit), b)) = mult(mult(a, ld(mult(a, b), unit)), b))), introduced(assumption)).
% 4.67/3.20 tff(457,plain,
% 4.67/3.20 ($false),
% 4.67/3.20 inference(unit_resolution,[status(thm)],[456, 455])).
% 4.67/3.20 tff(458,plain,((~(mult(a, mult(i(a), i(b))) = mult(mult(a, i(a)), i(b)))) | (mult(a, mult(ld(mult(a, b), unit), b)) = mult(mult(a, ld(mult(a, b), unit)), b)) | (~(mult(a, mult(ld(mult(a, b), unit), b)) = mult(mult(a, b), ld(mult(a, b), unit))))), inference(lemma,lemma(discharge,[]))).
% 4.67/3.20 tff(459,plain,
% 4.67/3.20 (~(mult(a, mult(i(a), i(b))) = mult(mult(a, i(a)), i(b)))),
% 4.67/3.20 inference(unit_resolution,[status(thm)],[458, 443, 429])).
% 4.67/3.20 tff(460,plain,
% 4.67/3.20 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(a, mult(i(a), i(b))) = mult(mult(a, i(a)), i(b))) | (mult(a, mult(i(b), i(a))) = mult(mult(a, i(a)), i(b))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(a, mult(i(a), i(b))) = mult(mult(a, i(a)), i(b))) | (mult(a, mult(i(b), i(a))) = mult(mult(a, i(a)), i(b))))),
% 4.67/3.20 inference(rewrite,[status(thm)],[])).
% 4.67/3.20 tff(461,plain,
% 4.67/3.20 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(a, mult(i(a), i(b))) = mult(mult(a, i(a)), i(b))) | (mult(a, mult(i(b), i(a))) = mult(mult(a, i(a)), i(b))))),
% 4.67/3.20 inference(quant_inst,[status(thm)],[])).
% 4.67/3.20 tff(462,plain,
% 4.67/3.20 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(a, mult(i(a), i(b))) = mult(mult(a, i(a)), i(b))) | (mult(a, mult(i(b), i(a))) = mult(mult(a, i(a)), i(b)))),
% 4.67/3.20 inference(modus_ponens,[status(thm)],[461, 460])).
% 4.67/3.20 tff(463,plain,
% 4.67/3.20 ((mult(a, mult(i(a), i(b))) = mult(mult(a, i(a)), i(b))) | (mult(a, mult(i(b), i(a))) = mult(mult(a, i(a)), i(b)))),
% 4.67/3.20 inference(unit_resolution,[status(thm)],[462, 51])).
% 4.67/3.20 tff(464,plain,
% 4.67/3.20 (mult(a, mult(i(b), i(a))) = mult(mult(a, i(a)), i(b))),
% 4.67/3.20 inference(unit_resolution,[status(thm)],[463, 459])).
% 4.67/3.20 tff(465,plain,
% 4.67/3.20 (unit = mult(a, mult(ld(mult(a, b), unit), b))),
% 4.67/3.20 inference(transitivity,[status(thm)],[258, 431])).
% 4.67/3.20 tff(466,plain,
% 4.67/3.20 (ld(a, unit) = ld(a, mult(a, mult(ld(mult(a, b), unit), b)))),
% 4.67/3.20 inference(monotonicity,[status(thm)],[465])).
% 4.67/3.20 tff(467,plain,
% 4.67/3.20 (i(a) = mult(ld(mult(a, b), unit), b)),
% 4.67/3.20 inference(transitivity,[status(thm)],[262, 466, 253])).
% 4.67/3.20 tff(468,plain,
% 4.67/3.20 (mult(i(b), i(a)) = mult(i(b), mult(ld(mult(a, b), unit), b))),
% 4.67/3.20 inference(monotonicity,[status(thm)],[467])).
% 4.67/3.20 tff(469,plain,
% 4.67/3.20 (mult(i(b), mult(ld(mult(a, b), unit), b)) = mult(i(b), i(a))),
% 4.67/3.20 inference(symmetry,[status(thm)],[468])).
% 4.67/3.20 tff(470,plain,
% 4.67/3.20 (mult(a, mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(a, mult(i(b), i(a)))),
% 4.67/3.20 inference(monotonicity,[status(thm)],[469])).
% 4.67/3.20 tff(471,plain,
% 4.67/3.20 (mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b)) = mult(a, mult(i(b), mult(ld(mult(a, b), unit), b)))),
% 4.67/3.20 inference(monotonicity,[status(thm)],[336])).
% 4.67/3.20 tff(472,plain,
% 4.67/3.20 (mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b)) = i(b)),
% 4.67/3.20 inference(transitivity,[status(thm)],[471, 470, 464, 404, 43])).
% 4.67/3.20 tff(473,plain,
% 4.67/3.20 (mult(i(b), mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b))) = mult(i(b), i(b))),
% 4.67/3.20 inference(monotonicity,[status(thm)],[472])).
% 4.67/3.20 tff(474,plain,
% 4.67/3.20 (mult(a, mult(ld(mult(a, b), unit), b)) = unit),
% 4.67/3.20 inference(transitivity,[status(thm)],[429, 257])).
% 4.67/3.20 tff(475,plain,
% 4.67/3.20 (mult(i(b), mult(a, mult(ld(mult(a, b), unit), b))) = mult(i(b), unit)),
% 4.67/3.20 inference(monotonicity,[status(thm)],[474])).
% 4.67/3.20 tff(476,assumption,(~(mult(i(b), mult(a, mult(ld(mult(a, b), unit), b))) = mult(mult(i(b), mult(ld(mult(a, b), unit), b)), a))), introduced(assumption)).
% 4.67/3.20 tff(477,plain,
% 4.67/3.20 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | ((mult(i(b), mult(a, mult(ld(mult(a, b), unit), b))) = mult(mult(i(b), mult(ld(mult(a, b), unit), b)), a)) | (mult(i(b), mult(a, mult(ld(mult(a, b), unit), b))) = mult(mult(i(b), a), mult(ld(mult(a, b), unit), b))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | (mult(i(b), mult(a, mult(ld(mult(a, b), unit), b))) = mult(mult(i(b), mult(ld(mult(a, b), unit), b)), a)) | (mult(i(b), mult(a, mult(ld(mult(a, b), unit), b))) = mult(mult(i(b), a), mult(ld(mult(a, b), unit), b))))),
% 4.67/3.20 inference(rewrite,[status(thm)],[])).
% 4.67/3.20 tff(478,plain,
% 4.67/3.20 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | ((mult(i(b), mult(a, mult(ld(mult(a, b), unit), b))) = mult(mult(i(b), mult(ld(mult(a, b), unit), b)), a)) | (mult(i(b), mult(a, mult(ld(mult(a, b), unit), b))) = mult(mult(i(b), a), mult(ld(mult(a, b), unit), b))))),
% 4.67/3.20 inference(quant_inst,[status(thm)],[])).
% 4.67/3.20 tff(479,plain,
% 4.67/3.20 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | (mult(i(b), mult(a, mult(ld(mult(a, b), unit), b))) = mult(mult(i(b), mult(ld(mult(a, b), unit), b)), a)) | (mult(i(b), mult(a, mult(ld(mult(a, b), unit), b))) = mult(mult(i(b), a), mult(ld(mult(a, b), unit), b)))),
% 4.67/3.20 inference(modus_ponens,[status(thm)],[478, 477])).
% 4.67/3.20 tff(480,plain,
% 4.67/3.20 ((mult(i(b), mult(a, mult(ld(mult(a, b), unit), b))) = mult(mult(i(b), mult(ld(mult(a, b), unit), b)), a)) | (mult(i(b), mult(a, mult(ld(mult(a, b), unit), b))) = mult(mult(i(b), a), mult(ld(mult(a, b), unit), b)))),
% 4.67/3.20 inference(unit_resolution,[status(thm)],[479, 132])).
% 4.67/3.20 tff(481,plain,
% 4.67/3.20 (mult(i(b), mult(a, mult(ld(mult(a, b), unit), b))) = mult(mult(i(b), a), mult(ld(mult(a, b), unit), b))),
% 4.67/3.20 inference(unit_resolution,[status(thm)],[480, 476])).
% 4.67/3.20 tff(482,plain,
% 4.67/3.20 (mult(mult(i(b), a), mult(ld(mult(a, b), unit), b)) = mult(i(b), mult(a, mult(ld(mult(a, b), unit), b)))),
% 4.67/3.20 inference(symmetry,[status(thm)],[481])).
% 4.67/3.20 tff(483,plain,
% 4.67/3.20 (mult(mult(i(b), a), mult(ld(mult(a, b), unit), b)) = i(b)),
% 4.67/3.20 inference(transitivity,[status(thm)],[482, 475, 359])).
% 4.67/3.20 tff(484,plain,
% 4.67/3.20 (mult(mult(mult(i(b), a), mult(ld(mult(a, b), unit), b)), mult(ld(mult(a, b), unit), b)) = mult(i(b), mult(ld(mult(a, b), unit), b))),
% 4.67/3.20 inference(monotonicity,[status(thm)],[483])).
% 4.67/3.20 tff(485,plain,
% 4.67/3.20 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(i(b), a), mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b))) = mult(mult(mult(i(b), a), mult(ld(mult(a, b), unit), b)), mult(ld(mult(a, b), unit), b)))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(i(b), a), mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b))) = mult(mult(mult(i(b), a), mult(ld(mult(a, b), unit), b)), mult(ld(mult(a, b), unit), b))))),
% 4.67/3.20 inference(rewrite,[status(thm)],[])).
% 4.67/3.20 tff(486,plain,
% 4.67/3.20 (((mult(mult(i(b), a), mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b))) = mult(mult(mult(i(b), a), mult(ld(mult(a, b), unit), b)), mult(ld(mult(a, b), unit), b))) | (mult(mult(i(b), a), mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b))) = mult(mult(mult(i(b), a), mult(ld(mult(a, b), unit), b)), mult(ld(mult(a, b), unit), b)))) <=> (mult(mult(i(b), a), mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b))) = mult(mult(mult(i(b), a), mult(ld(mult(a, b), unit), b)), mult(ld(mult(a, b), unit), b)))),
% 4.67/3.21 inference(rewrite,[status(thm)],[])).
% 4.67/3.21 tff(487,plain,
% 4.67/3.21 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(mult(i(b), a), mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b))) = mult(mult(mult(i(b), a), mult(ld(mult(a, b), unit), b)), mult(ld(mult(a, b), unit), b))) | (mult(mult(i(b), a), mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b))) = mult(mult(mult(i(b), a), mult(ld(mult(a, b), unit), b)), mult(ld(mult(a, b), unit), b))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(i(b), a), mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b))) = mult(mult(mult(i(b), a), mult(ld(mult(a, b), unit), b)), mult(ld(mult(a, b), unit), b))))),
% 4.67/3.21 inference(monotonicity,[status(thm)],[486])).
% 4.67/3.21 tff(488,plain,
% 4.67/3.21 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(mult(i(b), a), mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b))) = mult(mult(mult(i(b), a), mult(ld(mult(a, b), unit), b)), mult(ld(mult(a, b), unit), b))) | (mult(mult(i(b), a), mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b))) = mult(mult(mult(i(b), a), mult(ld(mult(a, b), unit), b)), mult(ld(mult(a, b), unit), b))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(i(b), a), mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b))) = mult(mult(mult(i(b), a), mult(ld(mult(a, b), unit), b)), mult(ld(mult(a, b), unit), b))))),
% 4.67/3.21 inference(transitivity,[status(thm)],[487, 485])).
% 4.67/3.21 tff(489,plain,
% 4.67/3.21 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(mult(i(b), a), mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b))) = mult(mult(mult(i(b), a), mult(ld(mult(a, b), unit), b)), mult(ld(mult(a, b), unit), b))) | (mult(mult(i(b), a), mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b))) = mult(mult(mult(i(b), a), mult(ld(mult(a, b), unit), b)), mult(ld(mult(a, b), unit), b))))),
% 4.67/3.21 inference(quant_inst,[status(thm)],[])).
% 4.67/3.21 tff(490,plain,
% 4.67/3.21 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(i(b), a), mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b))) = mult(mult(mult(i(b), a), mult(ld(mult(a, b), unit), b)), mult(ld(mult(a, b), unit), b)))),
% 4.67/3.21 inference(modus_ponens,[status(thm)],[489, 488])).
% 4.67/3.21 tff(491,plain,
% 4.67/3.21 (mult(mult(i(b), a), mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b))) = mult(mult(mult(i(b), a), mult(ld(mult(a, b), unit), b)), mult(ld(mult(a, b), unit), b))),
% 4.67/3.21 inference(unit_resolution,[status(thm)],[490, 51])).
% 4.67/3.21 tff(492,plain,
% 4.67/3.21 (mult(mult(i(b), a), mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b))) = mult(i(b), mult(ld(mult(a, b), unit), b))),
% 4.67/3.21 inference(transitivity,[status(thm)],[491, 484])).
% 4.67/3.21 tff(493,plain,
% 4.67/3.21 (mult(mult(mult(i(b), a), mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b))), a) = mult(mult(i(b), mult(ld(mult(a, b), unit), b)), a)),
% 4.67/3.21 inference(monotonicity,[status(thm)],[492])).
% 4.67/3.21 tff(494,plain,
% 4.67/3.21 ((~![A: $i] : (mult(unit, A) = A)) | (mult(unit, mult(ld(mult(a, b), unit), b)) = mult(ld(mult(a, b), unit), b))),
% 4.67/3.21 inference(quant_inst,[status(thm)],[])).
% 4.67/3.21 tff(495,plain,
% 4.67/3.21 (mult(unit, mult(ld(mult(a, b), unit), b)) = mult(ld(mult(a, b), unit), b)),
% 4.67/3.21 inference(unit_resolution,[status(thm)],[494, 40])).
% 4.67/3.21 tff(496,plain,
% 4.67/3.21 (mult(mult(a, mult(ld(mult(a, b), unit), b)), mult(ld(mult(a, b), unit), b)) = mult(unit, mult(ld(mult(a, b), unit), b))),
% 4.67/3.21 inference(monotonicity,[status(thm)],[474])).
% 4.67/3.21 tff(497,plain,
% 4.67/3.21 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(a, mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b))) = mult(mult(a, mult(ld(mult(a, b), unit), b)), mult(ld(mult(a, b), unit), b)))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(a, mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b))) = mult(mult(a, mult(ld(mult(a, b), unit), b)), mult(ld(mult(a, b), unit), b))))),
% 4.67/3.21 inference(rewrite,[status(thm)],[])).
% 4.67/3.21 tff(498,plain,
% 4.67/3.21 (((mult(a, mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b))) = mult(mult(a, mult(ld(mult(a, b), unit), b)), mult(ld(mult(a, b), unit), b))) | (mult(a, mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b))) = mult(mult(a, mult(ld(mult(a, b), unit), b)), mult(ld(mult(a, b), unit), b)))) <=> (mult(a, mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b))) = mult(mult(a, mult(ld(mult(a, b), unit), b)), mult(ld(mult(a, b), unit), b)))),
% 4.67/3.21 inference(rewrite,[status(thm)],[])).
% 4.67/3.21 tff(499,plain,
% 4.67/3.21 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(a, mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b))) = mult(mult(a, mult(ld(mult(a, b), unit), b)), mult(ld(mult(a, b), unit), b))) | (mult(a, mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b))) = mult(mult(a, mult(ld(mult(a, b), unit), b)), mult(ld(mult(a, b), unit), b))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(a, mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b))) = mult(mult(a, mult(ld(mult(a, b), unit), b)), mult(ld(mult(a, b), unit), b))))),
% 4.67/3.21 inference(monotonicity,[status(thm)],[498])).
% 4.67/3.21 tff(500,plain,
% 4.67/3.21 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(a, mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b))) = mult(mult(a, mult(ld(mult(a, b), unit), b)), mult(ld(mult(a, b), unit), b))) | (mult(a, mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b))) = mult(mult(a, mult(ld(mult(a, b), unit), b)), mult(ld(mult(a, b), unit), b))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(a, mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b))) = mult(mult(a, mult(ld(mult(a, b), unit), b)), mult(ld(mult(a, b), unit), b))))),
% 4.67/3.21 inference(transitivity,[status(thm)],[499, 497])).
% 4.67/3.21 tff(501,plain,
% 4.67/3.21 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(a, mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b))) = mult(mult(a, mult(ld(mult(a, b), unit), b)), mult(ld(mult(a, b), unit), b))) | (mult(a, mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b))) = mult(mult(a, mult(ld(mult(a, b), unit), b)), mult(ld(mult(a, b), unit), b))))),
% 4.67/3.21 inference(quant_inst,[status(thm)],[])).
% 4.67/3.21 tff(502,plain,
% 4.67/3.21 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(a, mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b))) = mult(mult(a, mult(ld(mult(a, b), unit), b)), mult(ld(mult(a, b), unit), b)))),
% 4.67/3.21 inference(modus_ponens,[status(thm)],[501, 500])).
% 4.67/3.21 tff(503,plain,
% 4.67/3.21 (mult(a, mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b))) = mult(mult(a, mult(ld(mult(a, b), unit), b)), mult(ld(mult(a, b), unit), b))),
% 4.67/3.21 inference(unit_resolution,[status(thm)],[502, 51])).
% 4.67/3.21 tff(504,plain,
% 4.67/3.21 (mult(a, mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b))) = mult(ld(mult(a, b), unit), b)),
% 4.67/3.21 inference(transitivity,[status(thm)],[503, 496, 495])).
% 4.67/3.21 tff(505,plain,
% 4.67/3.21 (mult(mult(i(b), a), mult(a, mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b)))) = mult(mult(i(b), a), mult(ld(mult(a, b), unit), b))),
% 4.67/3.21 inference(monotonicity,[status(thm)],[504])).
% 4.67/3.21 tff(506,plain,
% 4.67/3.21 (mult(mult(i(b), a), mult(a, mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b)))) = mult(i(b), mult(a, mult(ld(mult(a, b), unit), b)))),
% 4.67/3.21 inference(transitivity,[status(thm)],[505, 482])).
% 4.67/3.21 tff(507,plain,
% 4.67/3.21 ((mult(mult(i(b), a), mult(a, mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b)))) = mult(mult(mult(i(b), a), mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b))), a)) <=> (mult(i(b), mult(a, mult(ld(mult(a, b), unit), b))) = mult(mult(i(b), mult(ld(mult(a, b), unit), b)), a))),
% 4.67/3.21 inference(monotonicity,[status(thm)],[506, 493])).
% 4.67/3.21 tff(508,plain,
% 4.67/3.21 ((mult(i(b), mult(a, mult(ld(mult(a, b), unit), b))) = mult(mult(i(b), mult(ld(mult(a, b), unit), b)), a)) <=> (mult(mult(i(b), a), mult(a, mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b)))) = mult(mult(mult(i(b), a), mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b))), a))),
% 4.67/3.21 inference(symmetry,[status(thm)],[507])).
% 4.67/3.21 tff(509,plain,
% 4.67/3.21 ((~(mult(i(b), mult(a, mult(ld(mult(a, b), unit), b))) = mult(mult(i(b), mult(ld(mult(a, b), unit), b)), a))) <=> (~(mult(mult(i(b), a), mult(a, mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b)))) = mult(mult(mult(i(b), a), mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b))), a)))),
% 4.67/3.21 inference(monotonicity,[status(thm)],[508])).
% 4.67/3.21 tff(510,plain,
% 4.67/3.21 (~(mult(mult(i(b), a), mult(a, mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b)))) = mult(mult(mult(i(b), a), mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b))), a))),
% 4.67/3.21 inference(modus_ponens,[status(thm)],[476, 509])).
% 4.67/3.21 tff(511,plain,
% 4.67/3.21 (mult(mult(i(b), a), mult(ld(mult(a, b), unit), b)) = mult(mult(i(b), a), mult(a, mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b))))),
% 4.67/3.21 inference(symmetry,[status(thm)],[505])).
% 4.67/3.21 tff(512,plain,
% 4.67/3.21 (mult(a, i(a)) = mult(b, i(b))),
% 4.67/3.21 inference(transitivity,[status(thm)],[402, 401, 67, 32])).
% 4.67/3.21 tff(513,plain,
% 4.67/3.21 (mult(mult(ld(mult(a, b), unit), b), mult(a, i(a))) = mult(mult(ld(mult(a, b), unit), b), mult(b, i(b)))),
% 4.67/3.21 inference(monotonicity,[status(thm)],[512])).
% 4.67/3.21 tff(514,plain,
% 4.67/3.21 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(i(b), mult(mult(ld(mult(a, b), unit), b), a)) = mult(mult(i(b), mult(ld(mult(a, b), unit), b)), a)) | (mult(i(b), mult(a, mult(ld(mult(a, b), unit), b))) = mult(mult(i(b), mult(ld(mult(a, b), unit), b)), a)))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(i(b), mult(mult(ld(mult(a, b), unit), b), a)) = mult(mult(i(b), mult(ld(mult(a, b), unit), b)), a)) | (mult(i(b), mult(a, mult(ld(mult(a, b), unit), b))) = mult(mult(i(b), mult(ld(mult(a, b), unit), b)), a)))),
% 4.67/3.21 inference(rewrite,[status(thm)],[])).
% 4.67/3.21 tff(515,plain,
% 4.67/3.21 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(i(b), mult(mult(ld(mult(a, b), unit), b), a)) = mult(mult(i(b), mult(ld(mult(a, b), unit), b)), a)) | (mult(i(b), mult(a, mult(ld(mult(a, b), unit), b))) = mult(mult(i(b), mult(ld(mult(a, b), unit), b)), a)))),
% 4.67/3.21 inference(quant_inst,[status(thm)],[])).
% 4.67/3.21 tff(516,plain,
% 4.67/3.21 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(i(b), mult(mult(ld(mult(a, b), unit), b), a)) = mult(mult(i(b), mult(ld(mult(a, b), unit), b)), a)) | (mult(i(b), mult(a, mult(ld(mult(a, b), unit), b))) = mult(mult(i(b), mult(ld(mult(a, b), unit), b)), a))),
% 4.67/3.21 inference(modus_ponens,[status(thm)],[515, 514])).
% 4.67/3.21 tff(517,plain,
% 4.67/3.21 ((mult(i(b), mult(mult(ld(mult(a, b), unit), b), a)) = mult(mult(i(b), mult(ld(mult(a, b), unit), b)), a)) | (mult(i(b), mult(a, mult(ld(mult(a, b), unit), b))) = mult(mult(i(b), mult(ld(mult(a, b), unit), b)), a))),
% 4.67/3.21 inference(unit_resolution,[status(thm)],[516, 51])).
% 4.67/3.21 tff(518,plain,
% 4.67/3.21 (mult(i(b), mult(mult(ld(mult(a, b), unit), b), a)) = mult(mult(i(b), mult(ld(mult(a, b), unit), b)), a)),
% 4.67/3.21 inference(unit_resolution,[status(thm)],[517, 476])).
% 4.67/3.21 tff(519,assumption,(mult(i(b), mult(mult(ld(mult(a, b), unit), b), a)) = mult(mult(i(b), mult(ld(mult(a, b), unit), b)), a)), introduced(assumption)).
% 4.67/3.21 tff(520,plain,
% 4.67/3.21 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(unit, mult(ld(mult(a, b), unit), b)), mult(ld(mult(a, b), unit), b)) = unit)),
% 4.67/3.21 inference(quant_inst,[status(thm)],[])).
% 4.67/3.21 tff(521,plain,
% 4.67/3.21 (rd(mult(unit, mult(ld(mult(a, b), unit), b)), mult(ld(mult(a, b), unit), b)) = unit),
% 4.67/3.21 inference(unit_resolution,[status(thm)],[520, 80])).
% 4.67/3.21 tff(522,plain,
% 4.67/3.21 (mult(ld(mult(a, b), unit), b) = mult(unit, mult(ld(mult(a, b), unit), b))),
% 4.67/3.21 inference(symmetry,[status(thm)],[495])).
% 4.67/3.21 tff(523,assumption,(mult(mult(ld(mult(a, b), unit), b), mult(a, i(a))) = mult(mult(mult(ld(mult(a, b), unit), b), a), i(a))), introduced(assumption)).
% 4.67/3.21 tff(524,plain,
% 4.67/3.21 (mult(mult(mult(ld(mult(a, b), unit), b), a), i(a)) = mult(mult(ld(mult(a, b), unit), b), mult(a, i(a)))),
% 4.67/3.21 inference(symmetry,[status(thm)],[523])).
% 4.67/3.21 tff(525,plain,
% 4.67/3.21 (ld(a, unit) = i(a)),
% 4.67/3.21 inference(symmetry,[status(thm)],[262])).
% 4.67/3.21 tff(526,plain,
% 4.67/3.21 (ld(a, mult(a, mult(ld(mult(a, b), unit), b))) = ld(a, unit)),
% 4.67/3.21 inference(symmetry,[status(thm)],[466])).
% 4.67/3.21 tff(527,plain,
% 4.67/3.21 (mult(ld(mult(a, b), unit), b) = ld(a, mult(a, mult(ld(mult(a, b), unit), b)))),
% 4.67/3.21 inference(symmetry,[status(thm)],[253])).
% 4.67/3.21 tff(528,plain,
% 4.67/3.21 (mult(ld(mult(a, b), unit), b) = i(a)),
% 4.67/3.21 inference(transitivity,[status(thm)],[527, 526, 525])).
% 4.67/3.21 tff(529,plain,
% 4.67/3.21 (mult(mult(mult(ld(mult(a, b), unit), b), a), mult(ld(mult(a, b), unit), b)) = mult(mult(mult(ld(mult(a, b), unit), b), a), i(a))),
% 4.67/3.21 inference(monotonicity,[status(thm)],[528])).
% 4.67/3.21 tff(530,plain,
% 4.67/3.21 (mult(mult(mult(ld(mult(a, b), unit), b), a), mult(ld(mult(a, b), unit), b)) = mult(unit, mult(ld(mult(a, b), unit), b))),
% 4.67/3.21 inference(transitivity,[status(thm)],[529, 524, 513, 283, 282, 522])).
% 4.67/3.21 tff(531,plain,
% 4.67/3.21 (rd(mult(mult(mult(ld(mult(a, b), unit), b), a), mult(ld(mult(a, b), unit), b)), mult(ld(mult(a, b), unit), b)) = rd(mult(unit, mult(ld(mult(a, b), unit), b)), mult(ld(mult(a, b), unit), b))),
% 4.67/3.21 inference(monotonicity,[status(thm)],[530])).
% 4.67/3.21 tff(532,plain,
% 4.67/3.21 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(ld(mult(a, b), unit), b), a), mult(ld(mult(a, b), unit), b)), mult(ld(mult(a, b), unit), b)) = mult(mult(ld(mult(a, b), unit), b), a))),
% 4.67/3.21 inference(quant_inst,[status(thm)],[])).
% 4.67/3.21 tff(533,plain,
% 4.67/3.21 (rd(mult(mult(mult(ld(mult(a, b), unit), b), a), mult(ld(mult(a, b), unit), b)), mult(ld(mult(a, b), unit), b)) = mult(mult(ld(mult(a, b), unit), b), a)),
% 4.67/3.21 inference(unit_resolution,[status(thm)],[532, 80])).
% 4.67/3.21 tff(534,plain,
% 4.67/3.21 (mult(mult(ld(mult(a, b), unit), b), a) = rd(mult(mult(mult(ld(mult(a, b), unit), b), a), mult(ld(mult(a, b), unit), b)), mult(ld(mult(a, b), unit), b))),
% 4.67/3.21 inference(symmetry,[status(thm)],[533])).
% 4.67/3.21 tff(535,plain,
% 4.67/3.21 (mult(mult(ld(mult(a, b), unit), b), a) = unit),
% 4.67/3.21 inference(transitivity,[status(thm)],[534, 531, 521])).
% 4.67/3.21 tff(536,plain,
% 4.67/3.21 (mult(i(b), mult(mult(ld(mult(a, b), unit), b), a)) = mult(i(b), unit)),
% 4.67/3.21 inference(monotonicity,[status(thm)],[535])).
% 4.67/3.21 tff(537,plain,
% 4.67/3.21 (mult(i(b), unit) = mult(i(b), mult(mult(ld(mult(a, b), unit), b), a))),
% 4.67/3.21 inference(symmetry,[status(thm)],[536])).
% 4.67/3.21 tff(538,plain,
% 4.67/3.21 (mult(i(b), mult(a, mult(ld(mult(a, b), unit), b))) = mult(mult(i(b), mult(ld(mult(a, b), unit), b)), a)),
% 4.67/3.21 inference(transitivity,[status(thm)],[475, 537, 519])).
% 4.67/3.21 tff(539,plain,
% 4.67/3.21 ($false),
% 4.67/3.21 inference(unit_resolution,[status(thm)],[476, 538])).
% 4.67/3.22 tff(540,plain,((~(mult(mult(ld(mult(a, b), unit), b), mult(a, i(a))) = mult(mult(mult(ld(mult(a, b), unit), b), a), i(a)))) | (mult(i(b), mult(a, mult(ld(mult(a, b), unit), b))) = mult(mult(i(b), mult(ld(mult(a, b), unit), b)), a)) | (~(mult(i(b), mult(mult(ld(mult(a, b), unit), b), a)) = mult(mult(i(b), mult(ld(mult(a, b), unit), b)), a)))), inference(lemma,lemma(discharge,[]))).
% 4.67/3.22 tff(541,plain,
% 4.67/3.22 (~(mult(mult(ld(mult(a, b), unit), b), mult(a, i(a))) = mult(mult(mult(ld(mult(a, b), unit), b), a), i(a)))),
% 4.67/3.22 inference(unit_resolution,[status(thm)],[540, 476, 518])).
% 4.67/3.22 tff(542,plain,
% 4.67/3.22 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | ((mult(mult(ld(mult(a, b), unit), b), mult(a, i(a))) = mult(mult(mult(ld(mult(a, b), unit), b), i(a)), a)) | (mult(mult(ld(mult(a, b), unit), b), mult(a, i(a))) = mult(mult(mult(ld(mult(a, b), unit), b), a), i(a))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | (mult(mult(ld(mult(a, b), unit), b), mult(a, i(a))) = mult(mult(mult(ld(mult(a, b), unit), b), i(a)), a)) | (mult(mult(ld(mult(a, b), unit), b), mult(a, i(a))) = mult(mult(mult(ld(mult(a, b), unit), b), a), i(a))))),
% 4.67/3.22 inference(rewrite,[status(thm)],[])).
% 4.67/3.22 tff(543,plain,
% 4.67/3.22 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | ((mult(mult(ld(mult(a, b), unit), b), mult(a, i(a))) = mult(mult(mult(ld(mult(a, b), unit), b), i(a)), a)) | (mult(mult(ld(mult(a, b), unit), b), mult(a, i(a))) = mult(mult(mult(ld(mult(a, b), unit), b), a), i(a))))),
% 4.67/3.22 inference(quant_inst,[status(thm)],[])).
% 4.67/3.22 tff(544,plain,
% 4.67/3.22 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | (mult(mult(ld(mult(a, b), unit), b), mult(a, i(a))) = mult(mult(mult(ld(mult(a, b), unit), b), i(a)), a)) | (mult(mult(ld(mult(a, b), unit), b), mult(a, i(a))) = mult(mult(mult(ld(mult(a, b), unit), b), a), i(a)))),
% 4.67/3.22 inference(modus_ponens,[status(thm)],[543, 542])).
% 4.67/3.22 tff(545,plain,
% 4.67/3.22 ((mult(mult(ld(mult(a, b), unit), b), mult(a, i(a))) = mult(mult(mult(ld(mult(a, b), unit), b), i(a)), a)) | (mult(mult(ld(mult(a, b), unit), b), mult(a, i(a))) = mult(mult(mult(ld(mult(a, b), unit), b), a), i(a)))),
% 4.67/3.22 inference(unit_resolution,[status(thm)],[544, 132])).
% 4.67/3.22 tff(546,plain,
% 4.67/3.22 (mult(mult(ld(mult(a, b), unit), b), mult(a, i(a))) = mult(mult(mult(ld(mult(a, b), unit), b), i(a)), a)),
% 4.67/3.22 inference(unit_resolution,[status(thm)],[545, 541])).
% 4.67/3.22 tff(547,plain,
% 4.67/3.22 (mult(mult(mult(ld(mult(a, b), unit), b), i(a)), a) = mult(mult(ld(mult(a, b), unit), b), mult(a, i(a)))),
% 4.67/3.22 inference(symmetry,[status(thm)],[546])).
% 4.67/3.22 tff(548,plain,
% 4.67/3.22 (mult(mult(ld(mult(a, b), unit), b), i(a)) = mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b))),
% 4.67/3.22 inference(monotonicity,[status(thm)],[467])).
% 4.67/3.22 tff(549,plain,
% 4.67/3.22 (mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b)) = mult(mult(ld(mult(a, b), unit), b), i(a))),
% 4.67/3.22 inference(symmetry,[status(thm)],[548])).
% 4.67/3.22 tff(550,plain,
% 4.67/3.22 (mult(mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b)), a) = mult(mult(mult(ld(mult(a, b), unit), b), i(a)), a)),
% 4.67/3.22 inference(monotonicity,[status(thm)],[549])).
% 4.67/3.22 tff(551,plain,
% 4.67/3.22 (mult(mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b)), a) = mult(ld(mult(a, b), unit), b)),
% 4.67/3.22 inference(transitivity,[status(thm)],[550, 547, 513, 283, 282])).
% 4.67/3.22 tff(552,plain,
% 4.67/3.22 (mult(mult(i(b), a), mult(mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b)), a)) = mult(mult(i(b), a), mult(ld(mult(a, b), unit), b))),
% 4.67/3.22 inference(monotonicity,[status(thm)],[551])).
% 4.67/3.22 tff(553,plain,
% 4.67/3.22 (mult(mult(i(b), a), mult(mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b)), a)) = mult(mult(i(b), a), mult(a, mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b))))),
% 4.67/3.22 inference(transitivity,[status(thm)],[552, 511])).
% 4.67/3.22 tff(554,plain,
% 4.67/3.22 ((mult(mult(i(b), a), mult(mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b)), a)) = mult(mult(mult(i(b), a), mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b))), a)) <=> (mult(mult(i(b), a), mult(a, mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b)))) = mult(mult(mult(i(b), a), mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b))), a))),
% 4.67/3.22 inference(monotonicity,[status(thm)],[553])).
% 4.67/3.22 tff(555,plain,
% 4.67/3.22 ((mult(mult(i(b), a), mult(a, mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b)))) = mult(mult(mult(i(b), a), mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b))), a)) <=> (mult(mult(i(b), a), mult(mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b)), a)) = mult(mult(mult(i(b), a), mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b))), a))),
% 4.67/3.22 inference(symmetry,[status(thm)],[554])).
% 4.67/3.22 tff(556,plain,
% 4.67/3.22 ((mult(i(b), mult(a, mult(ld(mult(a, b), unit), b))) = mult(mult(i(b), mult(ld(mult(a, b), unit), b)), a)) <=> (mult(mult(i(b), a), mult(mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b)), a)) = mult(mult(mult(i(b), a), mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b))), a))),
% 4.67/3.22 inference(transitivity,[status(thm)],[508, 555])).
% 4.67/3.22 tff(557,plain,
% 4.67/3.22 ((~(mult(i(b), mult(a, mult(ld(mult(a, b), unit), b))) = mult(mult(i(b), mult(ld(mult(a, b), unit), b)), a))) <=> (~(mult(mult(i(b), a), mult(mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b)), a)) = mult(mult(mult(i(b), a), mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b))), a)))),
% 4.67/3.22 inference(monotonicity,[status(thm)],[556])).
% 4.67/3.22 tff(558,plain,
% 4.67/3.22 (~(mult(mult(i(b), a), mult(mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b)), a)) = mult(mult(mult(i(b), a), mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b))), a))),
% 4.67/3.22 inference(modus_ponens,[status(thm)],[476, 557])).
% 4.67/3.22 tff(559,plain,
% 4.67/3.22 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(mult(i(b), a), mult(a, mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b)))) = mult(mult(mult(i(b), a), mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b))), a)) | (mult(mult(i(b), a), mult(mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b)), a)) = mult(mult(mult(i(b), a), mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b))), a)))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(i(b), a), mult(a, mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b)))) = mult(mult(mult(i(b), a), mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b))), a)) | (mult(mult(i(b), a), mult(mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b)), a)) = mult(mult(mult(i(b), a), mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b))), a)))),
% 4.67/3.22 inference(rewrite,[status(thm)],[])).
% 4.67/3.22 tff(560,plain,
% 4.67/3.22 (((mult(mult(i(b), a), mult(mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b)), a)) = mult(mult(mult(i(b), a), mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b))), a)) | (mult(mult(i(b), a), mult(a, mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b)))) = mult(mult(mult(i(b), a), mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b))), a))) <=> ((mult(mult(i(b), a), mult(a, mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b)))) = mult(mult(mult(i(b), a), mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b))), a)) | (mult(mult(i(b), a), mult(mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b)), a)) = mult(mult(mult(i(b), a), mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b))), a)))),
% 4.67/3.22 inference(rewrite,[status(thm)],[])).
% 4.67/3.22 tff(561,plain,
% 4.67/3.22 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(mult(i(b), a), mult(mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b)), a)) = mult(mult(mult(i(b), a), mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b))), a)) | (mult(mult(i(b), a), mult(a, mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b)))) = mult(mult(mult(i(b), a), mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b))), a)))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(mult(i(b), a), mult(a, mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b)))) = mult(mult(mult(i(b), a), mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b))), a)) | (mult(mult(i(b), a), mult(mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b)), a)) = mult(mult(mult(i(b), a), mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b))), a))))),
% 4.67/3.22 inference(monotonicity,[status(thm)],[560])).
% 4.67/3.22 tff(562,plain,
% 4.67/3.22 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(mult(i(b), a), mult(mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b)), a)) = mult(mult(mult(i(b), a), mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b))), a)) | (mult(mult(i(b), a), mult(a, mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b)))) = mult(mult(mult(i(b), a), mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b))), a)))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(i(b), a), mult(a, mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b)))) = mult(mult(mult(i(b), a), mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b))), a)) | (mult(mult(i(b), a), mult(mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b)), a)) = mult(mult(mult(i(b), a), mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b))), a)))),
% 4.67/3.22 inference(transitivity,[status(thm)],[561, 559])).
% 4.67/3.22 tff(563,plain,
% 4.67/3.22 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(mult(i(b), a), mult(mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b)), a)) = mult(mult(mult(i(b), a), mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b))), a)) | (mult(mult(i(b), a), mult(a, mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b)))) = mult(mult(mult(i(b), a), mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b))), a)))),
% 4.67/3.22 inference(quant_inst,[status(thm)],[])).
% 4.67/3.22 tff(564,plain,
% 4.67/3.22 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(i(b), a), mult(a, mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b)))) = mult(mult(mult(i(b), a), mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b))), a)) | (mult(mult(i(b), a), mult(mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b)), a)) = mult(mult(mult(i(b), a), mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b))), a))),
% 4.67/3.22 inference(modus_ponens,[status(thm)],[563, 562])).
% 4.67/3.22 tff(565,plain,
% 4.67/3.22 ((mult(mult(i(b), a), mult(a, mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b)))) = mult(mult(mult(i(b), a), mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b))), a)) | (mult(mult(i(b), a), mult(mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b)), a)) = mult(mult(mult(i(b), a), mult(mult(ld(mult(a, b), unit), b), mult(ld(mult(a, b), unit), b))), a))),
% 4.67/3.22 inference(unit_resolution,[status(thm)],[564, 51])).
% 4.67/3.22 tff(566,plain,
% 4.67/3.22 ($false),
% 4.67/3.22 inference(unit_resolution,[status(thm)],[565, 558, 510])).
% 4.67/3.22 tff(567,plain,(mult(i(b), mult(a, mult(ld(mult(a, b), unit), b))) = mult(mult(i(b), mult(ld(mult(a, b), unit), b)), a)), inference(lemma,lemma(discharge,[]))).
% 4.67/3.22 tff(568,plain,
% 4.67/3.22 (mult(mult(i(b), b), mult(i(b), ld(mult(a, b), unit))) = mult(unit, mult(i(b), ld(mult(a, b), unit)))),
% 4.67/3.22 inference(monotonicity,[status(thm)],[236])).
% 4.67/3.22 tff(569,plain,
% 4.67/3.22 (mult(unit, mult(i(b), ld(mult(a, b), unit))) = mult(mult(i(b), b), mult(i(b), ld(mult(a, b), unit)))),
% 4.67/3.22 inference(symmetry,[status(thm)],[568])).
% 4.67/3.22 tff(570,plain,
% 4.67/3.22 ((~![A: $i] : (mult(unit, A) = A)) | (mult(unit, mult(i(b), ld(mult(a, b), unit))) = mult(i(b), ld(mult(a, b), unit)))),
% 4.67/3.22 inference(quant_inst,[status(thm)],[])).
% 4.67/3.22 tff(571,plain,
% 4.67/3.22 (mult(unit, mult(i(b), ld(mult(a, b), unit))) = mult(i(b), ld(mult(a, b), unit))),
% 4.67/3.22 inference(unit_resolution,[status(thm)],[570, 40])).
% 4.67/3.22 tff(572,plain,
% 4.67/3.22 (mult(i(b), ld(mult(a, b), unit)) = mult(unit, mult(i(b), ld(mult(a, b), unit)))),
% 4.67/3.22 inference(symmetry,[status(thm)],[571])).
% 4.67/3.22 tff(573,plain,
% 4.67/3.22 (mult(i(b), mult(mult(ld(mult(a, b), unit), b), i(b))) = mult(i(b), ld(mult(a, b), unit))),
% 4.67/3.22 inference(monotonicity,[status(thm)],[304])).
% 4.67/3.22 tff(574,assumption,(~(mult(i(b), mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(i(b), i(b)), mult(ld(mult(a, b), unit), b)))), introduced(assumption)).
% 4.67/3.22 tff(575,plain,
% 4.67/3.22 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(i(b), mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(i(b), i(b)), mult(ld(mult(a, b), unit), b))) | (mult(i(b), mult(mult(ld(mult(a, b), unit), b), i(b))) = mult(mult(i(b), i(b)), mult(ld(mult(a, b), unit), b))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(i(b), mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(i(b), i(b)), mult(ld(mult(a, b), unit), b))) | (mult(i(b), mult(mult(ld(mult(a, b), unit), b), i(b))) = mult(mult(i(b), i(b)), mult(ld(mult(a, b), unit), b))))),
% 4.67/3.22 inference(rewrite,[status(thm)],[])).
% 4.67/3.22 tff(576,plain,
% 4.67/3.22 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(i(b), mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(i(b), i(b)), mult(ld(mult(a, b), unit), b))) | (mult(i(b), mult(mult(ld(mult(a, b), unit), b), i(b))) = mult(mult(i(b), i(b)), mult(ld(mult(a, b), unit), b))))),
% 4.67/3.22 inference(quant_inst,[status(thm)],[])).
% 4.67/3.22 tff(577,plain,
% 4.67/3.22 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(i(b), mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(i(b), i(b)), mult(ld(mult(a, b), unit), b))) | (mult(i(b), mult(mult(ld(mult(a, b), unit), b), i(b))) = mult(mult(i(b), i(b)), mult(ld(mult(a, b), unit), b)))),
% 4.67/3.22 inference(modus_ponens,[status(thm)],[576, 575])).
% 4.67/3.22 tff(578,plain,
% 4.67/3.22 ((mult(i(b), mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(i(b), i(b)), mult(ld(mult(a, b), unit), b))) | (mult(i(b), mult(mult(ld(mult(a, b), unit), b), i(b))) = mult(mult(i(b), i(b)), mult(ld(mult(a, b), unit), b)))),
% 4.67/3.22 inference(unit_resolution,[status(thm)],[577, 51])).
% 4.67/3.22 tff(579,plain,
% 4.67/3.22 (mult(i(b), mult(mult(ld(mult(a, b), unit), b), i(b))) = mult(mult(i(b), i(b)), mult(ld(mult(a, b), unit), b))),
% 4.67/3.22 inference(unit_resolution,[status(thm)],[578, 574])).
% 4.67/3.22 tff(580,plain,
% 4.67/3.22 (mult(mult(i(b), i(b)), mult(ld(mult(a, b), unit), b)) = mult(i(b), mult(mult(ld(mult(a, b), unit), b), i(b)))),
% 4.67/3.22 inference(symmetry,[status(thm)],[579])).
% 4.67/3.22 tff(581,plain,
% 4.67/3.22 (mult(mult(i(b), i(b)), mult(ld(mult(a, b), unit), b)) = mult(mult(i(b), b), mult(i(b), ld(mult(a, b), unit)))),
% 4.67/3.22 inference(transitivity,[status(thm)],[580, 573, 572, 569])).
% 4.67/3.22 tff(582,plain,
% 4.67/3.22 (mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)) = mult(i(b), mult(i(b), mult(ld(mult(a, b), unit), b)))),
% 4.67/3.22 inference(monotonicity,[status(thm)],[336])).
% 4.67/3.22 tff(583,plain,
% 4.67/3.22 (mult(i(b), mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b))),
% 4.67/3.22 inference(symmetry,[status(thm)],[582])).
% 4.67/3.22 tff(584,plain,
% 4.67/3.22 ((mult(i(b), mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(i(b), i(b)), mult(ld(mult(a, b), unit), b))) <=> (mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)) = mult(mult(i(b), b), mult(i(b), ld(mult(a, b), unit))))),
% 4.67/3.23 inference(monotonicity,[status(thm)],[583, 581])).
% 4.67/3.23 tff(585,plain,
% 4.67/3.23 ((mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)) = mult(mult(i(b), b), mult(i(b), ld(mult(a, b), unit)))) <=> (mult(i(b), mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(i(b), i(b)), mult(ld(mult(a, b), unit), b)))),
% 4.67/3.23 inference(symmetry,[status(thm)],[584])).
% 4.67/3.23 tff(586,plain,
% 4.67/3.23 (mult(mult(i(b), unit), ld(mult(a, b), unit)) = mult(i(b), ld(mult(a, b), unit))),
% 4.67/3.23 inference(monotonicity,[status(thm)],[359])).
% 4.67/3.23 tff(587,plain,
% 4.67/3.23 (mult(i(b), ld(mult(a, b), unit)) = mult(mult(i(b), unit), ld(mult(a, b), unit))),
% 4.67/3.23 inference(symmetry,[status(thm)],[586])).
% 4.67/3.23 tff(588,plain,
% 4.67/3.23 ((~![A: $i] : (mult(A, unit) = A)) | (mult(mult(i(b), ld(mult(a, b), unit)), unit) = mult(i(b), ld(mult(a, b), unit)))),
% 4.67/3.23 inference(quant_inst,[status(thm)],[])).
% 4.67/3.23 tff(589,plain,
% 4.67/3.23 (mult(mult(i(b), ld(mult(a, b), unit)), unit) = mult(i(b), ld(mult(a, b), unit))),
% 4.67/3.23 inference(unit_resolution,[status(thm)],[588, 8])).
% 4.67/3.23 tff(590,assumption,(~(mult(i(b), mult(unit, ld(mult(a, b), unit))) = mult(mult(i(b), unit), ld(mult(a, b), unit)))), introduced(assumption)).
% 4.67/3.23 tff(591,plain,
% 4.67/3.23 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | ((mult(i(b), mult(unit, ld(mult(a, b), unit))) = mult(mult(i(b), ld(mult(a, b), unit)), unit)) | (mult(i(b), mult(unit, ld(mult(a, b), unit))) = mult(mult(i(b), unit), ld(mult(a, b), unit))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | (mult(i(b), mult(unit, ld(mult(a, b), unit))) = mult(mult(i(b), ld(mult(a, b), unit)), unit)) | (mult(i(b), mult(unit, ld(mult(a, b), unit))) = mult(mult(i(b), unit), ld(mult(a, b), unit))))),
% 4.67/3.23 inference(rewrite,[status(thm)],[])).
% 4.67/3.23 tff(592,plain,
% 4.67/3.23 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | ((mult(i(b), mult(unit, ld(mult(a, b), unit))) = mult(mult(i(b), ld(mult(a, b), unit)), unit)) | (mult(i(b), mult(unit, ld(mult(a, b), unit))) = mult(mult(i(b), unit), ld(mult(a, b), unit))))),
% 4.67/3.23 inference(quant_inst,[status(thm)],[])).
% 4.67/3.23 tff(593,plain,
% 4.67/3.23 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | (mult(i(b), mult(unit, ld(mult(a, b), unit))) = mult(mult(i(b), ld(mult(a, b), unit)), unit)) | (mult(i(b), mult(unit, ld(mult(a, b), unit))) = mult(mult(i(b), unit), ld(mult(a, b), unit)))),
% 4.67/3.23 inference(modus_ponens,[status(thm)],[592, 591])).
% 4.67/3.23 tff(594,plain,
% 4.67/3.23 ((mult(i(b), mult(unit, ld(mult(a, b), unit))) = mult(mult(i(b), ld(mult(a, b), unit)), unit)) | (mult(i(b), mult(unit, ld(mult(a, b), unit))) = mult(mult(i(b), unit), ld(mult(a, b), unit)))),
% 4.67/3.23 inference(unit_resolution,[status(thm)],[593, 132])).
% 4.67/3.23 tff(595,plain,
% 4.67/3.23 (mult(i(b), mult(unit, ld(mult(a, b), unit))) = mult(mult(i(b), ld(mult(a, b), unit)), unit)),
% 4.67/3.23 inference(unit_resolution,[status(thm)],[594, 590])).
% 4.67/3.23 tff(596,plain,
% 4.67/3.23 (mult(i(b), mult(unit, ld(mult(a, b), unit))) = mult(mult(i(b), unit), ld(mult(a, b), unit))),
% 4.67/3.23 inference(transitivity,[status(thm)],[595, 589, 587])).
% 4.67/3.23 tff(597,plain,
% 4.67/3.23 ($false),
% 4.67/3.23 inference(unit_resolution,[status(thm)],[590, 596])).
% 4.67/3.23 tff(598,plain,(mult(i(b), mult(unit, ld(mult(a, b), unit))) = mult(mult(i(b), unit), ld(mult(a, b), unit))), inference(lemma,lemma(discharge,[]))).
% 4.67/3.23 tff(599,plain,
% 4.67/3.23 (mult(i(b), ld(mult(a, b), unit)) = mult(mult(i(b), ld(mult(a, b), unit)), unit)),
% 4.67/3.23 inference(symmetry,[status(thm)],[589])).
% 4.67/3.23 tff(600,plain,
% 4.67/3.23 (mult(i(b), mult(unit, ld(mult(a, b), unit))) = mult(mult(i(b), ld(mult(a, b), unit)), unit)),
% 4.67/3.23 inference(transitivity,[status(thm)],[598, 586, 599])).
% 4.67/3.23 tff(601,assumption,(~(mult(i(b), mult(unit, ld(mult(a, b), unit))) = mult(mult(i(b), ld(mult(a, b), unit)), unit))), introduced(assumption)).
% 4.67/3.23 tff(602,plain,
% 4.67/3.23 ($false),
% 4.67/3.23 inference(unit_resolution,[status(thm)],[601, 600])).
% 4.67/3.23 tff(603,plain,(mult(i(b), mult(unit, ld(mult(a, b), unit))) = mult(mult(i(b), ld(mult(a, b), unit)), unit)), inference(lemma,lemma(discharge,[]))).
% 4.67/3.23 tff(604,plain,
% 4.67/3.23 (mult(mult(i(b), ld(mult(a, b), unit)), unit) = mult(i(b), mult(unit, ld(mult(a, b), unit)))),
% 4.67/3.23 inference(symmetry,[status(thm)],[603])).
% 4.67/3.23 tff(605,plain,
% 4.67/3.23 (mult(mult(i(b), ld(mult(a, b), unit)), mult(b, i(b))) = mult(mult(i(b), ld(mult(a, b), unit)), unit)),
% 4.67/3.23 inference(monotonicity,[status(thm)],[30])).
% 4.67/3.23 tff(606,plain,
% 4.67/3.23 (mult(mult(i(b), ld(mult(a, b), unit)), mult(i(b), b)) = mult(mult(i(b), ld(mult(a, b), unit)), mult(b, i(b)))),
% 4.67/3.23 inference(monotonicity,[status(thm)],[219])).
% 4.67/3.23 tff(607,plain,
% 4.67/3.23 ((mult(mult(i(b), ld(mult(a, b), unit)), mult(i(b), b)) = mult(mult(mult(i(b), ld(mult(a, b), unit)), b), i(b))) <=> (mult(mult(i(b), ld(mult(a, b), unit)), mult(b, i(b))) = mult(mult(mult(i(b), ld(mult(a, b), unit)), b), i(b)))),
% 4.67/3.23 inference(monotonicity,[status(thm)],[606])).
% 4.67/3.23 tff(608,plain,
% 4.67/3.23 ((mult(mult(i(b), ld(mult(a, b), unit)), mult(b, i(b))) = mult(mult(mult(i(b), ld(mult(a, b), unit)), b), i(b))) <=> (mult(mult(i(b), ld(mult(a, b), unit)), mult(i(b), b)) = mult(mult(mult(i(b), ld(mult(a, b), unit)), b), i(b)))),
% 4.67/3.23 inference(symmetry,[status(thm)],[607])).
% 4.67/3.23 tff(609,assumption,(~(mult(mult(i(b), ld(mult(a, b), unit)), mult(i(b), b)) = mult(mult(mult(i(b), ld(mult(a, b), unit)), b), i(b)))), introduced(assumption)).
% 4.67/3.23 tff(610,plain,
% 4.67/3.23 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(mult(i(b), ld(mult(a, b), unit)), mult(b, i(b))) = mult(mult(mult(i(b), ld(mult(a, b), unit)), b), i(b))) | (mult(mult(i(b), ld(mult(a, b), unit)), mult(i(b), b)) = mult(mult(mult(i(b), ld(mult(a, b), unit)), b), i(b))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(i(b), ld(mult(a, b), unit)), mult(b, i(b))) = mult(mult(mult(i(b), ld(mult(a, b), unit)), b), i(b))) | (mult(mult(i(b), ld(mult(a, b), unit)), mult(i(b), b)) = mult(mult(mult(i(b), ld(mult(a, b), unit)), b), i(b))))),
% 4.67/3.23 inference(rewrite,[status(thm)],[])).
% 4.67/3.23 tff(611,plain,
% 4.67/3.23 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(mult(i(b), ld(mult(a, b), unit)), mult(b, i(b))) = mult(mult(mult(i(b), ld(mult(a, b), unit)), b), i(b))) | (mult(mult(i(b), ld(mult(a, b), unit)), mult(i(b), b)) = mult(mult(mult(i(b), ld(mult(a, b), unit)), b), i(b))))),
% 4.67/3.23 inference(quant_inst,[status(thm)],[])).
% 4.67/3.23 tff(612,plain,
% 4.67/3.23 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(i(b), ld(mult(a, b), unit)), mult(b, i(b))) = mult(mult(mult(i(b), ld(mult(a, b), unit)), b), i(b))) | (mult(mult(i(b), ld(mult(a, b), unit)), mult(i(b), b)) = mult(mult(mult(i(b), ld(mult(a, b), unit)), b), i(b)))),
% 4.67/3.23 inference(modus_ponens,[status(thm)],[611, 610])).
% 4.67/3.23 tff(613,plain,
% 4.67/3.23 ((mult(mult(i(b), ld(mult(a, b), unit)), mult(b, i(b))) = mult(mult(mult(i(b), ld(mult(a, b), unit)), b), i(b))) | (mult(mult(i(b), ld(mult(a, b), unit)), mult(i(b), b)) = mult(mult(mult(i(b), ld(mult(a, b), unit)), b), i(b)))),
% 4.67/3.23 inference(unit_resolution,[status(thm)],[612, 51])).
% 4.67/3.23 tff(614,plain,
% 4.67/3.23 (mult(mult(i(b), ld(mult(a, b), unit)), mult(b, i(b))) = mult(mult(mult(i(b), ld(mult(a, b), unit)), b), i(b))),
% 4.67/3.23 inference(unit_resolution,[status(thm)],[613, 609])).
% 4.67/3.23 tff(615,plain,
% 4.67/3.23 (mult(mult(i(b), ld(mult(a, b), unit)), mult(i(b), b)) = mult(mult(mult(i(b), ld(mult(a, b), unit)), b), i(b))),
% 4.67/3.23 inference(modus_ponens,[status(thm)],[614, 608])).
% 4.67/3.23 tff(616,plain,
% 4.67/3.23 ($false),
% 4.67/3.23 inference(unit_resolution,[status(thm)],[609, 615])).
% 4.67/3.23 tff(617,plain,(mult(mult(i(b), ld(mult(a, b), unit)), mult(i(b), b)) = mult(mult(mult(i(b), ld(mult(a, b), unit)), b), i(b))), inference(lemma,lemma(discharge,[]))).
% 4.67/3.23 tff(618,plain,
% 4.67/3.23 (mult(mult(mult(i(b), ld(mult(a, b), unit)), b), i(b)) = mult(mult(i(b), ld(mult(a, b), unit)), mult(i(b), b))),
% 4.67/3.23 inference(symmetry,[status(thm)],[617])).
% 4.67/3.23 tff(619,plain,
% 4.67/3.23 (mult(mult(i(b), mult(ld(mult(a, b), unit), b)), i(b)) = mult(mult(mult(i(b), ld(mult(a, b), unit)), b), i(b))),
% 4.67/3.23 inference(monotonicity,[status(thm)],[321])).
% 4.67/3.23 tff(620,plain,
% 4.67/3.23 (mult(mult(i(b), mult(ld(mult(a, b), unit), b)), i(b)) = mult(mult(i(b), b), mult(i(b), ld(mult(a, b), unit)))),
% 4.67/3.23 inference(transitivity,[status(thm)],[619, 618, 606, 605, 604, 598, 586, 572, 569])).
% 4.67/3.23 tff(621,plain,
% 4.67/3.23 ((mult(i(b), mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(i(b), mult(ld(mult(a, b), unit), b)), i(b))) <=> (mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)) = mult(mult(i(b), b), mult(i(b), ld(mult(a, b), unit))))),
% 4.67/3.23 inference(monotonicity,[status(thm)],[583, 620])).
% 4.67/3.23 tff(622,plain,
% 4.67/3.23 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | ((mult(i(b), mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(i(b), i(b)), mult(ld(mult(a, b), unit), b))) | (mult(i(b), mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(i(b), mult(ld(mult(a, b), unit), b)), i(b))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | (mult(i(b), mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(i(b), i(b)), mult(ld(mult(a, b), unit), b))) | (mult(i(b), mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(i(b), mult(ld(mult(a, b), unit), b)), i(b))))),
% 4.67/3.23 inference(rewrite,[status(thm)],[])).
% 4.67/3.23 tff(623,plain,
% 4.67/3.23 (((mult(i(b), mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(i(b), mult(ld(mult(a, b), unit), b)), i(b))) | (mult(i(b), mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(i(b), i(b)), mult(ld(mult(a, b), unit), b)))) <=> ((mult(i(b), mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(i(b), i(b)), mult(ld(mult(a, b), unit), b))) | (mult(i(b), mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(i(b), mult(ld(mult(a, b), unit), b)), i(b))))),
% 4.67/3.23 inference(rewrite,[status(thm)],[])).
% 4.67/3.23 tff(624,plain,
% 4.67/3.23 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | ((mult(i(b), mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(i(b), mult(ld(mult(a, b), unit), b)), i(b))) | (mult(i(b), mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(i(b), i(b)), mult(ld(mult(a, b), unit), b))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | ((mult(i(b), mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(i(b), i(b)), mult(ld(mult(a, b), unit), b))) | (mult(i(b), mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(i(b), mult(ld(mult(a, b), unit), b)), i(b)))))),
% 4.67/3.23 inference(monotonicity,[status(thm)],[623])).
% 4.67/3.23 tff(625,plain,
% 4.67/3.23 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | ((mult(i(b), mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(i(b), mult(ld(mult(a, b), unit), b)), i(b))) | (mult(i(b), mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(i(b), i(b)), mult(ld(mult(a, b), unit), b))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | (mult(i(b), mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(i(b), i(b)), mult(ld(mult(a, b), unit), b))) | (mult(i(b), mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(i(b), mult(ld(mult(a, b), unit), b)), i(b))))),
% 4.67/3.23 inference(transitivity,[status(thm)],[624, 622])).
% 4.67/3.23 tff(626,plain,
% 4.67/3.23 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | ((mult(i(b), mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(i(b), mult(ld(mult(a, b), unit), b)), i(b))) | (mult(i(b), mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(i(b), i(b)), mult(ld(mult(a, b), unit), b))))),
% 4.67/3.23 inference(quant_inst,[status(thm)],[])).
% 4.67/3.23 tff(627,plain,
% 4.67/3.23 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | (mult(i(b), mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(i(b), i(b)), mult(ld(mult(a, b), unit), b))) | (mult(i(b), mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(i(b), mult(ld(mult(a, b), unit), b)), i(b)))),
% 4.67/3.23 inference(modus_ponens,[status(thm)],[626, 625])).
% 4.67/3.23 tff(628,plain,
% 4.67/3.23 ((mult(i(b), mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(i(b), i(b)), mult(ld(mult(a, b), unit), b))) | (mult(i(b), mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(i(b), mult(ld(mult(a, b), unit), b)), i(b)))),
% 4.67/3.23 inference(unit_resolution,[status(thm)],[627, 132])).
% 4.67/3.23 tff(629,plain,
% 4.67/3.23 (mult(i(b), mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(i(b), mult(ld(mult(a, b), unit), b)), i(b))),
% 4.67/3.23 inference(unit_resolution,[status(thm)],[628, 574])).
% 4.67/3.23 tff(630,plain,
% 4.67/3.23 (mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)) = mult(mult(i(b), b), mult(i(b), ld(mult(a, b), unit)))),
% 4.67/3.23 inference(modus_ponens,[status(thm)],[629, 621])).
% 4.67/3.23 tff(631,plain,
% 4.67/3.23 (mult(i(b), mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(i(b), i(b)), mult(ld(mult(a, b), unit), b))),
% 4.67/3.23 inference(modus_ponens,[status(thm)],[630, 585])).
% 4.67/3.23 tff(632,plain,
% 4.67/3.23 ($false),
% 4.67/3.23 inference(unit_resolution,[status(thm)],[574, 631])).
% 4.67/3.23 tff(633,plain,(mult(i(b), mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(i(b), i(b)), mult(ld(mult(a, b), unit), b))), inference(lemma,lemma(discharge,[]))).
% 4.67/3.23 tff(634,plain,
% 4.67/3.23 (mult(i(b), mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b))),
% 4.67/3.23 inference(monotonicity,[status(thm)],[321])).
% 4.67/3.23 tff(635,plain,
% 4.67/3.23 (mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)) = mult(i(b), mult(i(b), mult(ld(mult(a, b), unit), b)))),
% 4.67/3.23 inference(symmetry,[status(thm)],[634])).
% 4.67/3.23 tff(636,plain,
% 4.67/3.23 (mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)) = mult(mult(i(b), i(b)), mult(ld(mult(a, b), unit), b))),
% 4.67/3.23 inference(transitivity,[status(thm)],[635, 633])).
% 4.67/3.23 tff(637,plain,
% 4.67/3.23 (mult(mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)), a) = mult(mult(mult(i(b), i(b)), mult(ld(mult(a, b), unit), b)), a)),
% 4.67/3.23 inference(monotonicity,[status(thm)],[636])).
% 4.67/3.23 tff(638,plain,
% 4.67/3.23 (mult(mult(i(b), i(b)), mult(a, mult(ld(mult(a, b), unit), b))) = mult(mult(i(b), i(b)), unit)),
% 4.67/3.23 inference(monotonicity,[status(thm)],[474])).
% 4.67/3.23 tff(639,plain,
% 4.67/3.23 (mult(mult(i(b), i(b)), unit) = mult(mult(i(b), i(b)), mult(a, mult(ld(mult(a, b), unit), b)))),
% 4.67/3.23 inference(symmetry,[status(thm)],[638])).
% 4.67/3.23 tff(640,plain,
% 4.67/3.23 ((~![A: $i] : (mult(A, unit) = A)) | (mult(mult(i(b), i(b)), unit) = mult(i(b), i(b)))),
% 4.67/3.23 inference(quant_inst,[status(thm)],[])).
% 4.67/3.23 tff(641,plain,
% 4.67/3.23 (mult(mult(i(b), i(b)), unit) = mult(i(b), i(b))),
% 4.67/3.23 inference(unit_resolution,[status(thm)],[640, 8])).
% 4.67/3.23 tff(642,plain,
% 4.67/3.23 (mult(i(b), i(b)) = mult(mult(i(b), i(b)), unit)),
% 4.67/3.23 inference(symmetry,[status(thm)],[641])).
% 4.67/3.23 tff(643,plain,
% 4.67/3.23 (mult(i(b), mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b))) = mult(mult(i(b), i(b)), mult(a, mult(ld(mult(a, b), unit), b)))),
% 4.67/3.23 inference(transitivity,[status(thm)],[473, 642, 639])).
% 4.67/3.23 tff(644,plain,
% 4.67/3.23 ((mult(i(b), mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b))) = mult(mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)), a)) <=> (mult(mult(i(b), i(b)), mult(a, mult(ld(mult(a, b), unit), b))) = mult(mult(mult(i(b), i(b)), mult(ld(mult(a, b), unit), b)), a))),
% 4.67/3.23 inference(monotonicity,[status(thm)],[643, 637])).
% 4.67/3.23 tff(645,plain,
% 4.67/3.23 ((mult(mult(i(b), i(b)), mult(a, mult(ld(mult(a, b), unit), b))) = mult(mult(mult(i(b), i(b)), mult(ld(mult(a, b), unit), b)), a)) <=> (mult(i(b), mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b))) = mult(mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)), a))),
% 4.67/3.23 inference(symmetry,[status(thm)],[644])).
% 4.67/3.23 tff(646,assumption,(mult(i(b), mult(a, mult(ld(mult(a, b), unit), b))) = mult(mult(i(b), mult(ld(mult(a, b), unit), b)), a)), introduced(assumption)).
% 4.67/3.23 tff(647,plain,
% 4.67/3.23 (mult(mult(i(b), mult(ld(mult(a, b), unit), b)), a) = mult(i(b), mult(a, mult(ld(mult(a, b), unit), b)))),
% 4.67/3.23 inference(symmetry,[status(thm)],[646])).
% 4.67/3.24 tff(648,plain,
% 4.67/3.24 (mult(mult(mult(i(b), ld(mult(a, b), unit)), b), a) = mult(mult(i(b), mult(ld(mult(a, b), unit), b)), a)),
% 4.67/3.24 inference(monotonicity,[status(thm)],[336])).
% 4.67/3.24 tff(649,plain,
% 4.67/3.24 (mult(mult(mult(i(b), ld(mult(a, b), unit)), b), a) = i(b)),
% 4.67/3.24 inference(transitivity,[status(thm)],[648, 647, 475, 359])).
% 4.67/3.24 tff(650,plain,
% 4.67/3.24 (mult(i(b), mult(mult(mult(i(b), ld(mult(a, b), unit)), b), a)) = mult(i(b), i(b))),
% 4.67/3.24 inference(monotonicity,[status(thm)],[649])).
% 4.67/3.24 tff(651,plain,
% 4.67/3.24 (mult(i(b), mult(mult(mult(i(b), ld(mult(a, b), unit)), b), a)) = mult(mult(i(b), i(b)), mult(a, mult(ld(mult(a, b), unit), b)))),
% 4.67/3.24 inference(transitivity,[status(thm)],[650, 642, 639])).
% 4.67/3.24 tff(652,plain,
% 4.67/3.24 ((mult(i(b), mult(mult(mult(i(b), ld(mult(a, b), unit)), b), a)) = mult(mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)), a)) <=> (mult(mult(i(b), i(b)), mult(a, mult(ld(mult(a, b), unit), b))) = mult(mult(mult(i(b), i(b)), mult(ld(mult(a, b), unit), b)), a))),
% 4.67/3.24 inference(monotonicity,[status(thm)],[651, 637])).
% 4.67/3.24 tff(653,plain,
% 4.67/3.24 ((mult(i(b), mult(mult(mult(i(b), ld(mult(a, b), unit)), b), a)) = mult(mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)), a)) <=> (mult(i(b), mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b))) = mult(mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)), a))),
% 4.67/3.24 inference(transitivity,[status(thm)],[652, 645])).
% 4.67/3.24 tff(654,assumption,(~(mult(i(b), mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b))) = mult(mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)), a))), introduced(assumption)).
% 4.67/3.24 tff(655,plain,
% 4.67/3.24 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(i(b), mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b))) = mult(mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)), a)) | (mult(i(b), mult(mult(mult(i(b), ld(mult(a, b), unit)), b), a)) = mult(mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)), a)))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(i(b), mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b))) = mult(mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)), a)) | (mult(i(b), mult(mult(mult(i(b), ld(mult(a, b), unit)), b), a)) = mult(mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)), a)))),
% 4.67/3.24 inference(rewrite,[status(thm)],[])).
% 4.67/3.24 tff(656,plain,
% 4.67/3.24 (((mult(i(b), mult(mult(mult(i(b), ld(mult(a, b), unit)), b), a)) = mult(mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)), a)) | (mult(i(b), mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b))) = mult(mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)), a))) <=> ((mult(i(b), mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b))) = mult(mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)), a)) | (mult(i(b), mult(mult(mult(i(b), ld(mult(a, b), unit)), b), a)) = mult(mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)), a)))),
% 4.67/3.24 inference(rewrite,[status(thm)],[])).
% 4.67/3.24 tff(657,plain,
% 4.67/3.24 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(i(b), mult(mult(mult(i(b), ld(mult(a, b), unit)), b), a)) = mult(mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)), a)) | (mult(i(b), mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b))) = mult(mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)), a)))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(i(b), mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b))) = mult(mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)), a)) | (mult(i(b), mult(mult(mult(i(b), ld(mult(a, b), unit)), b), a)) = mult(mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)), a))))),
% 4.67/3.24 inference(monotonicity,[status(thm)],[656])).
% 4.67/3.24 tff(658,plain,
% 4.67/3.24 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(i(b), mult(mult(mult(i(b), ld(mult(a, b), unit)), b), a)) = mult(mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)), a)) | (mult(i(b), mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b))) = mult(mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)), a)))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(i(b), mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b))) = mult(mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)), a)) | (mult(i(b), mult(mult(mult(i(b), ld(mult(a, b), unit)), b), a)) = mult(mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)), a)))),
% 4.67/3.24 inference(transitivity,[status(thm)],[657, 655])).
% 4.67/3.24 tff(659,plain,
% 4.67/3.24 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(i(b), mult(mult(mult(i(b), ld(mult(a, b), unit)), b), a)) = mult(mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)), a)) | (mult(i(b), mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b))) = mult(mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)), a)))),
% 4.67/3.24 inference(quant_inst,[status(thm)],[])).
% 4.67/3.24 tff(660,plain,
% 4.67/3.24 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(i(b), mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b))) = mult(mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)), a)) | (mult(i(b), mult(mult(mult(i(b), ld(mult(a, b), unit)), b), a)) = mult(mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)), a))),
% 4.67/3.24 inference(modus_ponens,[status(thm)],[659, 658])).
% 4.67/3.24 tff(661,plain,
% 4.67/3.24 ((mult(i(b), mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b))) = mult(mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)), a)) | (mult(i(b), mult(mult(mult(i(b), ld(mult(a, b), unit)), b), a)) = mult(mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)), a))),
% 4.67/3.24 inference(unit_resolution,[status(thm)],[660, 51])).
% 4.67/3.24 tff(662,plain,
% 4.67/3.24 (mult(i(b), mult(mult(mult(i(b), ld(mult(a, b), unit)), b), a)) = mult(mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)), a)),
% 4.67/3.24 inference(unit_resolution,[status(thm)],[661, 654])).
% 4.67/3.24 tff(663,plain,
% 4.67/3.24 (mult(i(b), mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b))) = mult(mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)), a)),
% 4.67/3.24 inference(modus_ponens,[status(thm)],[662, 653])).
% 4.67/3.24 tff(664,plain,
% 4.67/3.24 ($false),
% 4.67/3.24 inference(unit_resolution,[status(thm)],[654, 663])).
% 4.67/3.24 tff(665,plain,((mult(i(b), mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b))) = mult(mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)), a)) | (~(mult(i(b), mult(a, mult(ld(mult(a, b), unit), b))) = mult(mult(i(b), mult(ld(mult(a, b), unit), b)), a)))), inference(lemma,lemma(discharge,[]))).
% 4.67/3.24 tff(666,plain,
% 4.67/3.24 (mult(i(b), mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b))) = mult(mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)), a)),
% 4.67/3.24 inference(unit_resolution,[status(thm)],[665, 567])).
% 4.67/3.24 tff(667,plain,
% 4.67/3.24 (mult(mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)), a) = mult(i(b), mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b)))),
% 4.67/3.24 inference(symmetry,[status(thm)],[666])).
% 4.67/3.24 tff(668,plain,
% 4.67/3.24 (mult(mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)), a) = mult(i(b), i(b))),
% 4.67/3.24 inference(transitivity,[status(thm)],[667, 473])).
% 4.67/3.24 tff(669,plain,
% 4.67/3.24 (mult(mult(b, b), mult(mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)), a)) = mult(mult(b, b), mult(i(b), i(b)))),
% 4.67/3.24 inference(monotonicity,[status(thm)],[668])).
% 4.67/3.24 tff(670,plain,
% 4.67/3.24 (mult(mult(unit, mult(ld(mult(a, b), unit), b)), a) = mult(mult(ld(mult(a, b), unit), b), a)),
% 4.67/3.24 inference(monotonicity,[status(thm)],[495])).
% 4.67/3.24 tff(671,plain,
% 4.67/3.24 (mult(mult(ld(mult(a, b), unit), b), a) = mult(mult(unit, mult(ld(mult(a, b), unit), b)), a)),
% 4.67/3.24 inference(symmetry,[status(thm)],[670])).
% 4.67/3.24 tff(672,plain,
% 4.67/3.24 (mult(mult(b, i(b)), mult(ld(mult(a, b), unit), b)) = mult(unit, mult(ld(mult(a, b), unit), b))),
% 4.67/3.24 inference(monotonicity,[status(thm)],[30])).
% 4.67/3.24 tff(673,assumption,(mult(b, mult(mult(ld(mult(a, b), unit), b), i(b))) = mult(mult(b, i(b)), mult(ld(mult(a, b), unit), b))), introduced(assumption)).
% 4.67/3.24 tff(674,plain,
% 4.67/3.24 (ld(mult(a, b), unit) = mult(mult(ld(mult(a, b), unit), b), i(b))),
% 4.67/3.24 inference(transitivity,[status(thm)],[448, 447, 302])).
% 4.67/3.24 tff(675,plain,
% 4.67/3.24 (mult(b, ld(mult(a, b), unit)) = mult(b, mult(mult(ld(mult(a, b), unit), b), i(b)))),
% 4.67/3.24 inference(monotonicity,[status(thm)],[674])).
% 4.67/3.24 tff(676,plain,
% 4.67/3.24 (mult(b, ld(mult(a, b), unit)) = mult(ld(mult(a, b), unit), b)),
% 4.67/3.24 inference(transitivity,[status(thm)],[675, 673, 672, 495])).
% 4.67/3.24 tff(677,plain,
% 4.67/3.24 (mult(a, mult(b, ld(mult(a, b), unit))) = mult(a, mult(ld(mult(a, b), unit), b))),
% 4.67/3.24 inference(monotonicity,[status(thm)],[676])).
% 4.67/3.24 tff(678,plain,
% 4.67/3.24 (mult(a, mult(ld(mult(a, b), unit), b)) = mult(a, mult(b, ld(mult(a, b), unit)))),
% 4.67/3.24 inference(symmetry,[status(thm)],[677])).
% 4.67/3.24 tff(679,plain,
% 4.67/3.24 (mult(a, mult(ld(mult(a, b), unit), b)) = mult(mult(a, ld(mult(a, b), unit)), b)),
% 4.67/3.24 inference(transitivity,[status(thm)],[678, 439])).
% 4.67/3.24 tff(680,plain,
% 4.67/3.24 ($false),
% 4.67/3.24 inference(unit_resolution,[status(thm)],[443, 679])).
% 4.67/3.24 tff(681,plain,(~(mult(b, mult(mult(ld(mult(a, b), unit), b), i(b))) = mult(mult(b, i(b)), mult(ld(mult(a, b), unit), b)))), inference(lemma,lemma(discharge,[]))).
% 4.67/3.24 tff(682,plain,
% 4.67/3.24 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(b, mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(b, i(b)), mult(ld(mult(a, b), unit), b))) | (mult(b, mult(mult(ld(mult(a, b), unit), b), i(b))) = mult(mult(b, i(b)), mult(ld(mult(a, b), unit), b))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(b, mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(b, i(b)), mult(ld(mult(a, b), unit), b))) | (mult(b, mult(mult(ld(mult(a, b), unit), b), i(b))) = mult(mult(b, i(b)), mult(ld(mult(a, b), unit), b))))),
% 4.67/3.24 inference(rewrite,[status(thm)],[])).
% 4.67/3.24 tff(683,plain,
% 4.67/3.24 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(b, mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(b, i(b)), mult(ld(mult(a, b), unit), b))) | (mult(b, mult(mult(ld(mult(a, b), unit), b), i(b))) = mult(mult(b, i(b)), mult(ld(mult(a, b), unit), b))))),
% 4.67/3.24 inference(quant_inst,[status(thm)],[])).
% 4.67/3.24 tff(684,plain,
% 4.67/3.24 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(b, mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(b, i(b)), mult(ld(mult(a, b), unit), b))) | (mult(b, mult(mult(ld(mult(a, b), unit), b), i(b))) = mult(mult(b, i(b)), mult(ld(mult(a, b), unit), b)))),
% 4.67/3.24 inference(modus_ponens,[status(thm)],[683, 682])).
% 4.67/3.24 tff(685,plain,
% 4.67/3.24 ((mult(b, mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(b, i(b)), mult(ld(mult(a, b), unit), b))) | (mult(b, mult(mult(ld(mult(a, b), unit), b), i(b))) = mult(mult(b, i(b)), mult(ld(mult(a, b), unit), b)))),
% 4.67/3.24 inference(unit_resolution,[status(thm)],[684, 51])).
% 4.67/3.24 tff(686,plain,
% 4.67/3.24 (mult(b, mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(b, i(b)), mult(ld(mult(a, b), unit), b))),
% 4.67/3.24 inference(unit_resolution,[status(thm)],[685, 681])).
% 4.67/3.24 tff(687,plain,
% 4.67/3.24 ((~![A: $i] : (mult(A, unit) = A)) | (mult(b, unit) = b)),
% 4.67/3.24 inference(quant_inst,[status(thm)],[])).
% 4.67/3.24 tff(688,plain,
% 4.67/3.24 (mult(b, unit) = b),
% 4.67/3.24 inference(unit_resolution,[status(thm)],[687, 8])).
% 4.67/3.24 tff(689,plain,
% 4.67/3.24 (mult(b, mult(b, i(b))) = mult(b, unit)),
% 4.67/3.24 inference(monotonicity,[status(thm)],[30])).
% 4.67/3.24 tff(690,plain,
% 4.67/3.24 (mult(mult(b, b), mult(unit, i(b))) = mult(mult(b, b), i(b))),
% 4.67/3.24 inference(monotonicity,[status(thm)],[43])).
% 4.67/3.24 tff(691,plain,
% 4.67/3.24 (mult(mult(b, b), i(b)) = mult(mult(b, b), mult(unit, i(b)))),
% 4.67/3.24 inference(symmetry,[status(thm)],[690])).
% 4.67/3.24 tff(692,plain,
% 4.67/3.24 (mult(mult(b, b), mult(i(b), unit)) = mult(mult(b, b), i(b))),
% 4.67/3.24 inference(monotonicity,[status(thm)],[359])).
% 4.67/3.24 tff(693,plain,
% 4.67/3.24 (mult(mult(b, b), mult(i(b), unit)) = mult(mult(b, b), mult(unit, i(b)))),
% 4.67/3.24 inference(transitivity,[status(thm)],[692, 691])).
% 4.67/3.24 tff(694,plain,
% 4.67/3.24 ((mult(mult(b, b), mult(i(b), unit)) = mult(mult(mult(b, b), unit), i(b))) <=> (mult(mult(b, b), mult(unit, i(b))) = mult(mult(mult(b, b), unit), i(b)))),
% 4.67/3.24 inference(monotonicity,[status(thm)],[693])).
% 4.67/3.24 tff(695,plain,
% 4.67/3.24 ((mult(mult(b, b), mult(unit, i(b))) = mult(mult(mult(b, b), unit), i(b))) <=> (mult(mult(b, b), mult(i(b), unit)) = mult(mult(mult(b, b), unit), i(b)))),
% 4.67/3.24 inference(symmetry,[status(thm)],[694])).
% 4.67/3.24 tff(696,assumption,(~(mult(mult(b, b), mult(i(b), unit)) = mult(mult(mult(b, b), unit), i(b)))), introduced(assumption)).
% 4.67/3.24 tff(697,plain,
% 4.67/3.24 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(mult(b, b), mult(unit, i(b))) = mult(mult(mult(b, b), unit), i(b))) | (mult(mult(b, b), mult(i(b), unit)) = mult(mult(mult(b, b), unit), i(b))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(b, b), mult(unit, i(b))) = mult(mult(mult(b, b), unit), i(b))) | (mult(mult(b, b), mult(i(b), unit)) = mult(mult(mult(b, b), unit), i(b))))),
% 4.67/3.24 inference(rewrite,[status(thm)],[])).
% 4.67/3.24 tff(698,plain,
% 4.67/3.24 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(mult(b, b), mult(unit, i(b))) = mult(mult(mult(b, b), unit), i(b))) | (mult(mult(b, b), mult(i(b), unit)) = mult(mult(mult(b, b), unit), i(b))))),
% 4.67/3.24 inference(quant_inst,[status(thm)],[])).
% 4.67/3.24 tff(699,plain,
% 4.67/3.24 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(b, b), mult(unit, i(b))) = mult(mult(mult(b, b), unit), i(b))) | (mult(mult(b, b), mult(i(b), unit)) = mult(mult(mult(b, b), unit), i(b)))),
% 4.67/3.24 inference(modus_ponens,[status(thm)],[698, 697])).
% 4.67/3.24 tff(700,plain,
% 4.67/3.24 ((mult(mult(b, b), mult(unit, i(b))) = mult(mult(mult(b, b), unit), i(b))) | (mult(mult(b, b), mult(i(b), unit)) = mult(mult(mult(b, b), unit), i(b)))),
% 4.67/3.24 inference(unit_resolution,[status(thm)],[699, 51])).
% 4.67/3.24 tff(701,plain,
% 4.67/3.24 (mult(mult(b, b), mult(unit, i(b))) = mult(mult(mult(b, b), unit), i(b))),
% 4.67/3.24 inference(unit_resolution,[status(thm)],[700, 696])).
% 4.67/3.24 tff(702,plain,
% 4.67/3.24 (mult(mult(b, b), mult(i(b), unit)) = mult(mult(mult(b, b), unit), i(b))),
% 4.67/3.24 inference(modus_ponens,[status(thm)],[701, 695])).
% 4.67/3.24 tff(703,plain,
% 4.67/3.24 ($false),
% 4.67/3.24 inference(unit_resolution,[status(thm)],[696, 702])).
% 4.67/3.24 tff(704,plain,(mult(mult(b, b), mult(i(b), unit)) = mult(mult(mult(b, b), unit), i(b))), inference(lemma,lemma(discharge,[]))).
% 4.67/3.24 tff(705,plain,
% 4.67/3.24 (mult(mult(mult(b, b), unit), i(b)) = mult(mult(b, b), mult(i(b), unit))),
% 4.67/3.24 inference(symmetry,[status(thm)],[704])).
% 4.67/3.24 tff(706,plain,
% 4.67/3.24 ((~![A: $i] : (mult(A, unit) = A)) | (mult(mult(b, b), unit) = mult(b, b))),
% 4.67/3.24 inference(quant_inst,[status(thm)],[])).
% 4.67/3.24 tff(707,plain,
% 4.67/3.24 (mult(mult(b, b), unit) = mult(b, b)),
% 4.67/3.24 inference(unit_resolution,[status(thm)],[706, 8])).
% 4.67/3.24 tff(708,plain,
% 4.67/3.24 (mult(b, b) = mult(mult(b, b), unit)),
% 4.67/3.24 inference(symmetry,[status(thm)],[707])).
% 4.67/3.24 tff(709,plain,
% 4.67/3.24 (mult(mult(b, b), i(b)) = mult(mult(mult(b, b), unit), i(b))),
% 4.67/3.24 inference(monotonicity,[status(thm)],[708])).
% 4.67/3.24 tff(710,plain,
% 4.67/3.24 (mult(mult(b, b), i(b)) = mult(mult(b, b), mult(i(b), unit))),
% 4.67/3.24 inference(transitivity,[status(thm)],[709, 705])).
% 4.67/3.24 tff(711,plain,
% 4.67/3.24 (mult(i(b), unit) = ld(b, unit)),
% 4.67/3.24 inference(transitivity,[status(thm)],[359, 28])).
% 4.67/3.24 tff(712,plain,
% 4.67/3.24 (mult(b, mult(i(b), unit)) = mult(b, ld(b, unit))),
% 4.67/3.24 inference(monotonicity,[status(thm)],[711])).
% 4.67/3.24 tff(713,plain,
% 4.67/3.24 (mult(b, mult(i(b), unit)) = unit),
% 4.67/3.24 inference(transitivity,[status(thm)],[712, 19])).
% 4.67/3.24 tff(714,plain,
% 4.67/3.24 (mult(b, mult(b, mult(i(b), unit))) = mult(b, unit)),
% 4.67/3.24 inference(monotonicity,[status(thm)],[713])).
% 4.67/3.24 tff(715,plain,
% 4.67/3.24 (mult(b, unit) = mult(b, mult(b, mult(i(b), unit)))),
% 4.67/3.24 inference(symmetry,[status(thm)],[714])).
% 4.67/3.24 tff(716,plain,
% 4.67/3.24 (mult(b, mult(b, i(b))) = mult(b, mult(b, mult(i(b), unit)))),
% 4.67/3.24 inference(transitivity,[status(thm)],[689, 715])).
% 4.67/3.24 tff(717,plain,
% 4.67/3.24 ((mult(b, mult(b, i(b))) = mult(mult(b, b), i(b))) <=> (mult(b, mult(b, mult(i(b), unit))) = mult(mult(b, b), mult(i(b), unit)))),
% 4.67/3.25 inference(monotonicity,[status(thm)],[716, 710])).
% 4.67/3.25 tff(718,plain,
% 4.67/3.25 ((mult(b, mult(b, mult(i(b), unit))) = mult(mult(b, b), mult(i(b), unit))) <=> (mult(b, mult(b, i(b))) = mult(mult(b, b), i(b)))),
% 4.67/3.25 inference(symmetry,[status(thm)],[717])).
% 4.67/3.25 tff(719,plain,
% 4.67/3.25 (mult(b, mult(i(b), b)) = mult(b, unit)),
% 4.67/3.25 inference(monotonicity,[status(thm)],[236])).
% 4.67/3.25 tff(720,plain,
% 4.67/3.25 (mult(mult(i(b), unit), b) = mult(i(b), b)),
% 4.67/3.25 inference(monotonicity,[status(thm)],[359])).
% 4.67/3.25 tff(721,plain,
% 4.67/3.25 (mult(b, mult(mult(i(b), unit), b)) = mult(b, mult(i(b), b))),
% 4.67/3.25 inference(monotonicity,[status(thm)],[720])).
% 4.67/3.25 tff(722,plain,
% 4.67/3.25 (mult(b, mult(mult(i(b), unit), b)) = mult(b, mult(b, mult(i(b), unit)))),
% 4.67/3.25 inference(transitivity,[status(thm)],[721, 719, 715])).
% 4.67/3.25 tff(723,plain,
% 4.67/3.25 ((mult(b, mult(mult(i(b), unit), b)) = mult(mult(b, b), mult(i(b), unit))) <=> (mult(b, mult(b, mult(i(b), unit))) = mult(mult(b, b), mult(i(b), unit)))),
% 4.67/3.25 inference(monotonicity,[status(thm)],[722])).
% 4.67/3.25 tff(724,plain,
% 4.67/3.25 (mult(b, mult(i(b), b)) = mult(b, mult(mult(i(b), unit), b))),
% 4.67/3.25 inference(symmetry,[status(thm)],[721])).
% 4.67/3.25 tff(725,plain,
% 4.67/3.25 ((mult(b, mult(i(b), b)) = mult(mult(b, b), i(b))) <=> (mult(b, mult(mult(i(b), unit), b)) = mult(mult(b, b), mult(i(b), unit)))),
% 4.67/3.25 inference(monotonicity,[status(thm)],[724, 710])).
% 4.67/3.25 tff(726,plain,
% 4.67/3.25 ((mult(b, mult(i(b), b)) = mult(mult(b, b), i(b))) <=> (mult(b, mult(b, i(b))) = mult(mult(b, b), i(b)))),
% 4.67/3.25 inference(transitivity,[status(thm)],[725, 723, 718])).
% 4.67/3.25 tff(727,assumption,(~(mult(b, mult(b, i(b))) = mult(mult(b, b), i(b)))), introduced(assumption)).
% 4.67/3.25 tff(728,plain,
% 4.67/3.25 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(b, mult(b, i(b))) = mult(mult(b, b), i(b))) | (mult(b, mult(i(b), b)) = mult(mult(b, b), i(b))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(b, mult(b, i(b))) = mult(mult(b, b), i(b))) | (mult(b, mult(i(b), b)) = mult(mult(b, b), i(b))))),
% 4.67/3.25 inference(rewrite,[status(thm)],[])).
% 4.67/3.25 tff(729,plain,
% 4.67/3.25 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(b, mult(b, i(b))) = mult(mult(b, b), i(b))) | (mult(b, mult(i(b), b)) = mult(mult(b, b), i(b))))),
% 4.67/3.25 inference(quant_inst,[status(thm)],[])).
% 4.67/3.25 tff(730,plain,
% 4.67/3.25 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(b, mult(b, i(b))) = mult(mult(b, b), i(b))) | (mult(b, mult(i(b), b)) = mult(mult(b, b), i(b)))),
% 4.67/3.25 inference(modus_ponens,[status(thm)],[729, 728])).
% 4.67/3.25 tff(731,plain,
% 4.67/3.25 ((mult(b, mult(b, i(b))) = mult(mult(b, b), i(b))) | (mult(b, mult(i(b), b)) = mult(mult(b, b), i(b)))),
% 4.67/3.25 inference(unit_resolution,[status(thm)],[730, 51])).
% 4.67/3.25 tff(732,plain,
% 4.67/3.25 (mult(b, mult(i(b), b)) = mult(mult(b, b), i(b))),
% 4.67/3.25 inference(unit_resolution,[status(thm)],[731, 727])).
% 4.67/3.25 tff(733,plain,
% 4.67/3.25 (mult(b, mult(b, i(b))) = mult(mult(b, b), i(b))),
% 4.67/3.25 inference(modus_ponens,[status(thm)],[732, 726])).
% 4.67/3.25 tff(734,plain,
% 4.67/3.25 ($false),
% 4.67/3.25 inference(unit_resolution,[status(thm)],[727, 733])).
% 4.67/3.25 tff(735,plain,(mult(b, mult(b, i(b))) = mult(mult(b, b), i(b))), inference(lemma,lemma(discharge,[]))).
% 4.67/3.25 tff(736,plain,
% 4.67/3.25 (mult(mult(b, b), i(b)) = mult(b, mult(b, i(b)))),
% 4.67/3.25 inference(symmetry,[status(thm)],[735])).
% 4.67/3.25 tff(737,plain,
% 4.67/3.25 (mult(mult(b, b), i(b)) = b),
% 4.67/3.25 inference(transitivity,[status(thm)],[736, 689, 688])).
% 4.67/3.25 tff(738,plain,
% 4.67/3.25 (mult(mult(mult(b, b), i(b)), mult(mult(i(b), ld(mult(a, b), unit)), b)) = mult(b, mult(i(b), mult(ld(mult(a, b), unit), b)))),
% 4.67/3.25 inference(monotonicity,[status(thm)],[737, 336])).
% 4.67/3.25 tff(739,plain,
% 4.67/3.25 ((mult(mult(b, b), mult(i(b), ld(mult(a, b), unit))) = mult(b, mult(mult(i(b), ld(mult(a, b), unit)), b))) <=> (mult(b, mult(mult(i(b), ld(mult(a, b), unit)), b)) = mult(mult(b, b), mult(i(b), ld(mult(a, b), unit))))),
% 4.67/3.25 inference(commutativity,[status(thm)],[])).
% 4.67/3.25 tff(740,plain,
% 4.67/3.25 (mult(b, mult(mult(i(b), ld(mult(a, b), unit)), b)) = mult(b, mult(i(b), mult(ld(mult(a, b), unit), b)))),
% 4.67/3.25 inference(monotonicity,[status(thm)],[336])).
% 4.67/3.25 tff(741,plain,
% 4.67/3.25 (mult(b, mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(b, mult(mult(i(b), ld(mult(a, b), unit)), b))),
% 4.67/3.25 inference(symmetry,[status(thm)],[740])).
% 4.67/3.25 tff(742,plain,
% 4.67/3.25 (mult(mult(mult(b, b), i(b)), mult(mult(i(b), ld(mult(a, b), unit)), b)) = mult(b, mult(mult(i(b), ld(mult(a, b), unit)), b))),
% 4.67/3.25 inference(transitivity,[status(thm)],[738, 741])).
% 4.67/3.25 tff(743,plain,
% 4.67/3.25 (mult(mult(mult(i(b), ld(mult(a, b), unit)), b), i(b)) = mult(i(b), ld(mult(a, b), unit))),
% 4.67/3.25 inference(transitivity,[status(thm)],[618, 606, 605, 604, 598, 586])).
% 4.67/3.25 tff(744,plain,
% 4.67/3.25 (mult(mult(b, b), mult(mult(mult(i(b), ld(mult(a, b), unit)), b), i(b))) = mult(mult(b, b), mult(i(b), ld(mult(a, b), unit)))),
% 4.67/3.25 inference(monotonicity,[status(thm)],[743])).
% 4.67/3.25 tff(745,plain,
% 4.67/3.25 ((mult(mult(b, b), mult(mult(mult(i(b), ld(mult(a, b), unit)), b), i(b))) = mult(mult(mult(b, b), i(b)), mult(mult(i(b), ld(mult(a, b), unit)), b))) <=> (mult(mult(b, b), mult(i(b), ld(mult(a, b), unit))) = mult(b, mult(mult(i(b), ld(mult(a, b), unit)), b)))),
% 4.67/3.25 inference(monotonicity,[status(thm)],[744, 742])).
% 4.67/3.25 tff(746,plain,
% 4.67/3.25 ((mult(mult(b, b), mult(mult(mult(i(b), ld(mult(a, b), unit)), b), i(b))) = mult(mult(mult(b, b), i(b)), mult(mult(i(b), ld(mult(a, b), unit)), b))) <=> (mult(b, mult(mult(i(b), ld(mult(a, b), unit)), b)) = mult(mult(b, b), mult(i(b), ld(mult(a, b), unit))))),
% 4.67/3.25 inference(transitivity,[status(thm)],[745, 739])).
% 4.67/3.25 tff(747,plain,
% 4.67/3.25 ((mult(b, mult(mult(i(b), ld(mult(a, b), unit)), b)) = mult(mult(b, b), mult(i(b), ld(mult(a, b), unit)))) <=> (mult(mult(b, b), mult(mult(mult(i(b), ld(mult(a, b), unit)), b), i(b))) = mult(mult(mult(b, b), i(b)), mult(mult(i(b), ld(mult(a, b), unit)), b)))),
% 4.67/3.25 inference(symmetry,[status(thm)],[746])).
% 4.67/3.25 tff(748,plain,
% 4.67/3.25 (mult(mult(unit, b), ld(mult(a, b), unit)) = mult(b, ld(mult(a, b), unit))),
% 4.67/3.25 inference(monotonicity,[status(thm)],[355])).
% 4.67/3.25 tff(749,plain,
% 4.67/3.25 (mult(b, ld(mult(a, b), unit)) = mult(mult(unit, b), ld(mult(a, b), unit))),
% 4.67/3.25 inference(symmetry,[status(thm)],[748])).
% 4.67/3.25 tff(750,plain,
% 4.67/3.25 (mult(mult(mult(unit, b), i(b)), ld(mult(a, b), unit)) = mult(unit, ld(mult(a, b), unit))),
% 4.67/3.25 inference(monotonicity,[status(thm)],[352])).
% 4.67/3.25 tff(751,assumption,(~(mult(mult(unit, b), mult(i(b), ld(mult(a, b), unit))) = mult(mult(mult(unit, b), i(b)), ld(mult(a, b), unit)))), introduced(assumption)).
% 4.67/3.25 tff(752,plain,
% 4.67/3.25 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | ((mult(mult(unit, b), mult(i(b), ld(mult(a, b), unit))) = mult(mult(mult(unit, b), i(b)), ld(mult(a, b), unit))) | (mult(mult(unit, b), mult(i(b), ld(mult(a, b), unit))) = mult(mult(mult(unit, b), ld(mult(a, b), unit)), i(b))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | (mult(mult(unit, b), mult(i(b), ld(mult(a, b), unit))) = mult(mult(mult(unit, b), i(b)), ld(mult(a, b), unit))) | (mult(mult(unit, b), mult(i(b), ld(mult(a, b), unit))) = mult(mult(mult(unit, b), ld(mult(a, b), unit)), i(b))))),
% 4.67/3.25 inference(rewrite,[status(thm)],[])).
% 4.67/3.25 tff(753,plain,
% 4.67/3.25 (((mult(mult(unit, b), mult(i(b), ld(mult(a, b), unit))) = mult(mult(mult(unit, b), ld(mult(a, b), unit)), i(b))) | (mult(mult(unit, b), mult(i(b), ld(mult(a, b), unit))) = mult(mult(mult(unit, b), i(b)), ld(mult(a, b), unit)))) <=> ((mult(mult(unit, b), mult(i(b), ld(mult(a, b), unit))) = mult(mult(mult(unit, b), i(b)), ld(mult(a, b), unit))) | (mult(mult(unit, b), mult(i(b), ld(mult(a, b), unit))) = mult(mult(mult(unit, b), ld(mult(a, b), unit)), i(b))))),
% 4.67/3.25 inference(rewrite,[status(thm)],[])).
% 4.67/3.25 tff(754,plain,
% 4.67/3.25 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | ((mult(mult(unit, b), mult(i(b), ld(mult(a, b), unit))) = mult(mult(mult(unit, b), ld(mult(a, b), unit)), i(b))) | (mult(mult(unit, b), mult(i(b), ld(mult(a, b), unit))) = mult(mult(mult(unit, b), i(b)), ld(mult(a, b), unit))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | ((mult(mult(unit, b), mult(i(b), ld(mult(a, b), unit))) = mult(mult(mult(unit, b), i(b)), ld(mult(a, b), unit))) | (mult(mult(unit, b), mult(i(b), ld(mult(a, b), unit))) = mult(mult(mult(unit, b), ld(mult(a, b), unit)), i(b)))))),
% 4.67/3.25 inference(monotonicity,[status(thm)],[753])).
% 4.67/3.25 tff(755,plain,
% 4.67/3.25 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | ((mult(mult(unit, b), mult(i(b), ld(mult(a, b), unit))) = mult(mult(mult(unit, b), ld(mult(a, b), unit)), i(b))) | (mult(mult(unit, b), mult(i(b), ld(mult(a, b), unit))) = mult(mult(mult(unit, b), i(b)), ld(mult(a, b), unit))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | (mult(mult(unit, b), mult(i(b), ld(mult(a, b), unit))) = mult(mult(mult(unit, b), i(b)), ld(mult(a, b), unit))) | (mult(mult(unit, b), mult(i(b), ld(mult(a, b), unit))) = mult(mult(mult(unit, b), ld(mult(a, b), unit)), i(b))))),
% 4.67/3.25 inference(transitivity,[status(thm)],[754, 752])).
% 4.67/3.25 tff(756,plain,
% 4.67/3.25 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | ((mult(mult(unit, b), mult(i(b), ld(mult(a, b), unit))) = mult(mult(mult(unit, b), ld(mult(a, b), unit)), i(b))) | (mult(mult(unit, b), mult(i(b), ld(mult(a, b), unit))) = mult(mult(mult(unit, b), i(b)), ld(mult(a, b), unit))))),
% 4.67/3.25 inference(quant_inst,[status(thm)],[])).
% 4.67/3.25 tff(757,plain,
% 4.67/3.25 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | (mult(mult(unit, b), mult(i(b), ld(mult(a, b), unit))) = mult(mult(mult(unit, b), i(b)), ld(mult(a, b), unit))) | (mult(mult(unit, b), mult(i(b), ld(mult(a, b), unit))) = mult(mult(mult(unit, b), ld(mult(a, b), unit)), i(b)))),
% 4.67/3.25 inference(modus_ponens,[status(thm)],[756, 755])).
% 4.67/3.25 tff(758,plain,
% 4.67/3.25 ((mult(mult(unit, b), mult(i(b), ld(mult(a, b), unit))) = mult(mult(mult(unit, b), i(b)), ld(mult(a, b), unit))) | (mult(mult(unit, b), mult(i(b), ld(mult(a, b), unit))) = mult(mult(mult(unit, b), ld(mult(a, b), unit)), i(b)))),
% 4.67/3.25 inference(unit_resolution,[status(thm)],[757, 132])).
% 4.67/3.25 tff(759,plain,
% 4.67/3.25 (mult(mult(unit, b), mult(i(b), ld(mult(a, b), unit))) = mult(mult(mult(unit, b), ld(mult(a, b), unit)), i(b))),
% 4.67/3.25 inference(unit_resolution,[status(thm)],[758, 751])).
% 4.67/3.25 tff(760,plain,
% 4.67/3.25 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(mult(unit, b), mult(i(b), ld(mult(a, b), unit))) = mult(mult(mult(unit, b), i(b)), ld(mult(a, b), unit))) | (mult(mult(unit, b), mult(ld(mult(a, b), unit), i(b))) = mult(mult(mult(unit, b), i(b)), ld(mult(a, b), unit))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(unit, b), mult(i(b), ld(mult(a, b), unit))) = mult(mult(mult(unit, b), i(b)), ld(mult(a, b), unit))) | (mult(mult(unit, b), mult(ld(mult(a, b), unit), i(b))) = mult(mult(mult(unit, b), i(b)), ld(mult(a, b), unit))))),
% 4.67/3.25 inference(rewrite,[status(thm)],[])).
% 4.67/3.25 tff(761,plain,
% 4.67/3.25 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(mult(unit, b), mult(i(b), ld(mult(a, b), unit))) = mult(mult(mult(unit, b), i(b)), ld(mult(a, b), unit))) | (mult(mult(unit, b), mult(ld(mult(a, b), unit), i(b))) = mult(mult(mult(unit, b), i(b)), ld(mult(a, b), unit))))),
% 4.67/3.25 inference(quant_inst,[status(thm)],[])).
% 4.67/3.25 tff(762,plain,
% 4.67/3.25 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(unit, b), mult(i(b), ld(mult(a, b), unit))) = mult(mult(mult(unit, b), i(b)), ld(mult(a, b), unit))) | (mult(mult(unit, b), mult(ld(mult(a, b), unit), i(b))) = mult(mult(mult(unit, b), i(b)), ld(mult(a, b), unit)))),
% 4.67/3.26 inference(modus_ponens,[status(thm)],[761, 760])).
% 4.67/3.26 tff(763,plain,
% 4.67/3.26 ((mult(mult(unit, b), mult(i(b), ld(mult(a, b), unit))) = mult(mult(mult(unit, b), i(b)), ld(mult(a, b), unit))) | (mult(mult(unit, b), mult(ld(mult(a, b), unit), i(b))) = mult(mult(mult(unit, b), i(b)), ld(mult(a, b), unit)))),
% 4.67/3.26 inference(unit_resolution,[status(thm)],[762, 51])).
% 4.67/3.26 tff(764,plain,
% 4.67/3.26 (mult(mult(unit, b), mult(ld(mult(a, b), unit), i(b))) = mult(mult(mult(unit, b), i(b)), ld(mult(a, b), unit))),
% 4.67/3.26 inference(unit_resolution,[status(thm)],[763, 751])).
% 4.67/3.26 tff(765,plain,
% 4.67/3.26 (mult(mult(a, mult(ld(mult(a, b), unit), b)), i(b)) = mult(unit, i(b))),
% 4.67/3.26 inference(monotonicity,[status(thm)],[474])).
% 4.67/3.26 tff(766,plain,
% 4.67/3.26 (mult(unit, i(b)) = mult(mult(a, mult(ld(mult(a, b), unit), b)), i(b))),
% 4.67/3.26 inference(symmetry,[status(thm)],[765])).
% 4.67/3.26 tff(767,plain,
% 4.67/3.26 (mult(mult(b, i(b)), mult(mult(i(b), ld(mult(a, b), unit)), b)) = mult(unit, mult(mult(i(b), ld(mult(a, b), unit)), b))),
% 4.67/3.26 inference(monotonicity,[status(thm)],[30])).
% 4.67/3.26 tff(768,plain,
% 4.67/3.26 (mult(mult(b, i(b)), mult(mult(i(b), ld(mult(a, b), unit)), b)) = mult(mult(i(b), ld(mult(a, b), unit)), b)),
% 4.67/3.26 inference(transitivity,[status(thm)],[767, 337, 335, 322, 321])).
% 4.67/3.26 tff(769,plain,
% 4.67/3.26 (mult(mult(i(b), b), ld(mult(a, b), unit)) = mult(i(b), mult(b, ld(mult(a, b), unit)))),
% 4.67/3.26 inference(symmetry,[status(thm)],[409])).
% 4.67/3.26 tff(770,assumption,(mult(mult(unit, b), mult(ld(mult(a, b), unit), i(b))) = mult(mult(mult(unit, b), i(b)), ld(mult(a, b), unit))), introduced(assumption)).
% 4.67/3.26 tff(771,plain,
% 4.67/3.26 (b = mult(unit, b)),
% 4.67/3.26 inference(symmetry,[status(thm)],[355])).
% 4.67/3.26 tff(772,plain,
% 4.67/3.26 (mult(b, mult(ld(mult(a, b), unit), i(b))) = mult(mult(unit, b), mult(ld(mult(a, b), unit), i(b)))),
% 4.67/3.26 inference(monotonicity,[status(thm)],[771])).
% 4.67/3.26 tff(773,plain,
% 4.67/3.26 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(a, b), mult(mult(a, b), mult(ld(mult(a, b), unit), i(b)))) = mult(ld(mult(a, b), unit), i(b)))),
% 4.67/3.26 inference(quant_inst,[status(thm)],[])).
% 4.67/3.26 tff(774,plain,
% 4.67/3.26 (ld(mult(a, b), mult(mult(a, b), mult(ld(mult(a, b), unit), i(b)))) = mult(ld(mult(a, b), unit), i(b))),
% 4.67/3.26 inference(unit_resolution,[status(thm)],[773, 251])).
% 4.67/3.26 tff(775,plain,
% 4.67/3.26 (mult(mult(i(b), i(b)), b) = i(b)),
% 4.67/3.26 inference(transitivity,[status(thm)],[197, 384, 122, 353, 43])).
% 4.67/3.26 tff(776,plain,
% 4.67/3.26 (mult(ld(mult(a, b), unit), mult(mult(i(b), i(b)), b)) = mult(ld(mult(a, b), unit), i(b))),
% 4.67/3.26 inference(monotonicity,[status(thm)],[775])).
% 4.67/3.26 tff(777,plain,
% 4.67/3.26 (mult(ld(mult(a, b), unit), i(b)) = mult(ld(mult(a, b), unit), mult(mult(i(b), i(b)), b))),
% 4.67/3.26 inference(symmetry,[status(thm)],[776])).
% 4.67/3.26 tff(778,plain,
% 4.67/3.26 (mult(mult(a, b), mult(ld(mult(a, b), unit), i(b))) = mult(mult(a, b), mult(ld(mult(a, b), unit), mult(mult(i(b), i(b)), b)))),
% 4.67/3.26 inference(monotonicity,[status(thm)],[777])).
% 4.67/3.26 tff(779,plain,
% 4.67/3.26 (mult(mult(a, b), mult(ld(mult(a, b), unit), mult(mult(i(b), i(b)), b))) = mult(mult(a, b), mult(ld(mult(a, b), unit), i(b)))),
% 4.67/3.26 inference(symmetry,[status(thm)],[778])).
% 4.67/3.26 tff(780,assumption,(~(mult(mult(a, b), mult(mult(mult(i(b), i(b)), b), ld(mult(a, b), unit))) = mult(mult(mult(a, b), ld(mult(a, b), unit)), mult(mult(i(b), i(b)), b)))), introduced(assumption)).
% 4.67/3.26 tff(781,plain,
% 4.67/3.26 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(mult(a, b), mult(ld(mult(a, b), unit), mult(mult(i(b), i(b)), b))) = mult(mult(mult(a, b), ld(mult(a, b), unit)), mult(mult(i(b), i(b)), b))) | (mult(mult(a, b), mult(mult(mult(i(b), i(b)), b), ld(mult(a, b), unit))) = mult(mult(mult(a, b), ld(mult(a, b), unit)), mult(mult(i(b), i(b)), b))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(a, b), mult(ld(mult(a, b), unit), mult(mult(i(b), i(b)), b))) = mult(mult(mult(a, b), ld(mult(a, b), unit)), mult(mult(i(b), i(b)), b))) | (mult(mult(a, b), mult(mult(mult(i(b), i(b)), b), ld(mult(a, b), unit))) = mult(mult(mult(a, b), ld(mult(a, b), unit)), mult(mult(i(b), i(b)), b))))),
% 4.67/3.26 inference(rewrite,[status(thm)],[])).
% 4.67/3.26 tff(782,plain,
% 4.67/3.26 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(mult(a, b), mult(ld(mult(a, b), unit), mult(mult(i(b), i(b)), b))) = mult(mult(mult(a, b), ld(mult(a, b), unit)), mult(mult(i(b), i(b)), b))) | (mult(mult(a, b), mult(mult(mult(i(b), i(b)), b), ld(mult(a, b), unit))) = mult(mult(mult(a, b), ld(mult(a, b), unit)), mult(mult(i(b), i(b)), b))))),
% 4.67/3.26 inference(quant_inst,[status(thm)],[])).
% 4.67/3.26 tff(783,plain,
% 4.67/3.26 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(a, b), mult(ld(mult(a, b), unit), mult(mult(i(b), i(b)), b))) = mult(mult(mult(a, b), ld(mult(a, b), unit)), mult(mult(i(b), i(b)), b))) | (mult(mult(a, b), mult(mult(mult(i(b), i(b)), b), ld(mult(a, b), unit))) = mult(mult(mult(a, b), ld(mult(a, b), unit)), mult(mult(i(b), i(b)), b)))),
% 4.67/3.26 inference(modus_ponens,[status(thm)],[782, 781])).
% 4.67/3.26 tff(784,plain,
% 4.67/3.26 ((mult(mult(a, b), mult(ld(mult(a, b), unit), mult(mult(i(b), i(b)), b))) = mult(mult(mult(a, b), ld(mult(a, b), unit)), mult(mult(i(b), i(b)), b))) | (mult(mult(a, b), mult(mult(mult(i(b), i(b)), b), ld(mult(a, b), unit))) = mult(mult(mult(a, b), ld(mult(a, b), unit)), mult(mult(i(b), i(b)), b)))),
% 4.67/3.26 inference(unit_resolution,[status(thm)],[783, 51])).
% 4.67/3.26 tff(785,plain,
% 4.67/3.26 (mult(mult(a, b), mult(ld(mult(a, b), unit), mult(mult(i(b), i(b)), b))) = mult(mult(mult(a, b), ld(mult(a, b), unit)), mult(mult(i(b), i(b)), b))),
% 4.67/3.26 inference(unit_resolution,[status(thm)],[784, 780])).
% 4.67/3.26 tff(786,plain,
% 4.67/3.26 (mult(mult(mult(a, b), ld(mult(a, b), unit)), mult(mult(i(b), i(b)), b)) = mult(mult(a, b), mult(ld(mult(a, b), unit), mult(mult(i(b), i(b)), b)))),
% 4.67/3.26 inference(symmetry,[status(thm)],[785])).
% 4.67/3.26 tff(787,plain,
% 4.67/3.26 (mult(mult(mult(a, b), ld(mult(a, b), unit)), mult(mult(i(b), i(b)), b)) = mult(unit, mult(mult(i(b), i(b)), b))),
% 4.67/3.26 inference(monotonicity,[status(thm)],[257])).
% 4.67/3.26 tff(788,plain,
% 4.67/3.26 (mult(unit, mult(mult(i(b), i(b)), b)) = mult(mult(mult(a, b), ld(mult(a, b), unit)), mult(mult(i(b), i(b)), b))),
% 4.67/3.26 inference(symmetry,[status(thm)],[787])).
% 4.67/3.26 tff(789,plain,
% 4.67/3.26 (mult(mult(unit, b), mult(i(b), i(b))) = mult(unit, mult(mult(i(b), i(b)), b))),
% 4.67/3.26 inference(symmetry,[status(thm)],[384])).
% 4.67/3.26 tff(790,plain,
% 4.67/3.26 (mult(mult(mult(unit, b), i(b)), i(b)) = mult(mult(unit, b), mult(i(b), i(b)))),
% 4.67/3.26 inference(symmetry,[status(thm)],[122])).
% 4.67/3.26 tff(791,plain,
% 4.67/3.26 (mult(unit, i(b)) = mult(mult(mult(unit, b), i(b)), i(b))),
% 4.67/3.26 inference(symmetry,[status(thm)],[353])).
% 4.67/3.26 tff(792,plain,
% 4.67/3.26 (mult(mult(mult(a, b), i(b)), mult(mult(i(b), ld(mult(a, b), unit)), b)) = mult(a, mult(i(b), mult(ld(mult(a, b), unit), b)))),
% 4.67/3.26 inference(monotonicity,[status(thm)],[232, 336])).
% 4.67/3.26 tff(793,plain,
% 4.67/3.26 (mult(mult(mult(a, b), ld(mult(a, b), unit)), i(b)) = mult(unit, i(b))),
% 4.67/3.26 inference(monotonicity,[status(thm)],[257])).
% 4.67/3.26 tff(794,plain,
% 4.67/3.26 (mult(unit, i(b)) = mult(mult(mult(a, b), ld(mult(a, b), unit)), i(b))),
% 4.67/3.26 inference(symmetry,[status(thm)],[793])).
% 4.67/3.26 tff(795,plain,
% 4.67/3.26 (mult(mult(mult(a, b), i(b)), mult(mult(i(b), ld(mult(a, b), unit)), b)) = mult(mult(mult(a, b), ld(mult(a, b), unit)), i(b))),
% 4.67/3.26 inference(transitivity,[status(thm)],[792, 470, 464, 404, 794])).
% 4.67/3.26 tff(796,plain,
% 4.67/3.26 (mult(mult(a, b), mult(mult(mult(i(b), ld(mult(a, b), unit)), b), i(b))) = mult(mult(a, b), mult(i(b), ld(mult(a, b), unit)))),
% 4.67/3.26 inference(monotonicity,[status(thm)],[743])).
% 4.67/3.26 tff(797,plain,
% 4.67/3.26 ((mult(mult(a, b), mult(mult(mult(i(b), ld(mult(a, b), unit)), b), i(b))) = mult(mult(mult(a, b), i(b)), mult(mult(i(b), ld(mult(a, b), unit)), b))) <=> (mult(mult(a, b), mult(i(b), ld(mult(a, b), unit))) = mult(mult(mult(a, b), ld(mult(a, b), unit)), i(b)))),
% 4.67/3.26 inference(monotonicity,[status(thm)],[796, 795])).
% 4.67/3.26 tff(798,plain,
% 4.67/3.26 ((mult(mult(a, b), mult(i(b), ld(mult(a, b), unit))) = mult(mult(mult(a, b), ld(mult(a, b), unit)), i(b))) <=> (mult(mult(a, b), mult(mult(mult(i(b), ld(mult(a, b), unit)), b), i(b))) = mult(mult(mult(a, b), i(b)), mult(mult(i(b), ld(mult(a, b), unit)), b)))),
% 4.67/3.26 inference(symmetry,[status(thm)],[797])).
% 4.67/3.26 tff(799,plain,
% 4.67/3.26 (mult(mult(mult(a, b), ld(mult(a, b), unit)), mult(mult(i(b), i(b)), b)) = mult(mult(mult(a, b), ld(mult(a, b), unit)), i(b))),
% 4.67/3.26 inference(transitivity,[status(thm)],[787, 384, 122, 353, 794])).
% 4.67/3.26 tff(800,plain,
% 4.67/3.26 (mult(mult(mult(i(b), i(b)), b), ld(mult(a, b), unit)) = mult(i(b), ld(mult(a, b), unit))),
% 4.67/3.26 inference(monotonicity,[status(thm)],[775])).
% 4.67/3.26 tff(801,plain,
% 4.67/3.26 (mult(mult(a, b), mult(mult(mult(i(b), i(b)), b), ld(mult(a, b), unit))) = mult(mult(a, b), mult(i(b), ld(mult(a, b), unit)))),
% 4.67/3.26 inference(monotonicity,[status(thm)],[800])).
% 4.67/3.26 tff(802,plain,
% 4.67/3.26 ((mult(mult(a, b), mult(mult(mult(i(b), i(b)), b), ld(mult(a, b), unit))) = mult(mult(mult(a, b), ld(mult(a, b), unit)), mult(mult(i(b), i(b)), b))) <=> (mult(mult(a, b), mult(i(b), ld(mult(a, b), unit))) = mult(mult(mult(a, b), ld(mult(a, b), unit)), i(b)))),
% 4.67/3.26 inference(monotonicity,[status(thm)],[801, 799])).
% 4.67/3.26 tff(803,plain,
% 4.67/3.26 ((mult(mult(a, b), mult(mult(mult(i(b), i(b)), b), ld(mult(a, b), unit))) = mult(mult(mult(a, b), ld(mult(a, b), unit)), mult(mult(i(b), i(b)), b))) <=> (mult(mult(a, b), mult(mult(mult(i(b), ld(mult(a, b), unit)), b), i(b))) = mult(mult(mult(a, b), i(b)), mult(mult(i(b), ld(mult(a, b), unit)), b)))),
% 4.67/3.26 inference(transitivity,[status(thm)],[802, 798])).
% 4.67/3.26 tff(804,plain,
% 4.67/3.26 ((~(mult(mult(a, b), mult(mult(mult(i(b), i(b)), b), ld(mult(a, b), unit))) = mult(mult(mult(a, b), ld(mult(a, b), unit)), mult(mult(i(b), i(b)), b)))) <=> (~(mult(mult(a, b), mult(mult(mult(i(b), ld(mult(a, b), unit)), b), i(b))) = mult(mult(mult(a, b), i(b)), mult(mult(i(b), ld(mult(a, b), unit)), b))))),
% 4.67/3.26 inference(monotonicity,[status(thm)],[803])).
% 4.67/3.26 tff(805,plain,
% 4.67/3.26 (~(mult(mult(a, b), mult(mult(mult(i(b), ld(mult(a, b), unit)), b), i(b))) = mult(mult(mult(a, b), i(b)), mult(mult(i(b), ld(mult(a, b), unit)), b)))),
% 4.67/3.26 inference(modus_ponens,[status(thm)],[780, 804])).
% 4.67/3.26 tff(806,plain,
% 4.67/3.26 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(mult(a, b), mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b))) = mult(mult(mult(a, b), i(b)), mult(mult(i(b), ld(mult(a, b), unit)), b))) | (mult(mult(a, b), mult(mult(mult(i(b), ld(mult(a, b), unit)), b), i(b))) = mult(mult(mult(a, b), i(b)), mult(mult(i(b), ld(mult(a, b), unit)), b))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(a, b), mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b))) = mult(mult(mult(a, b), i(b)), mult(mult(i(b), ld(mult(a, b), unit)), b))) | (mult(mult(a, b), mult(mult(mult(i(b), ld(mult(a, b), unit)), b), i(b))) = mult(mult(mult(a, b), i(b)), mult(mult(i(b), ld(mult(a, b), unit)), b))))),
% 4.67/3.26 inference(rewrite,[status(thm)],[])).
% 4.67/3.26 tff(807,plain,
% 4.67/3.26 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(mult(a, b), mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b))) = mult(mult(mult(a, b), i(b)), mult(mult(i(b), ld(mult(a, b), unit)), b))) | (mult(mult(a, b), mult(mult(mult(i(b), ld(mult(a, b), unit)), b), i(b))) = mult(mult(mult(a, b), i(b)), mult(mult(i(b), ld(mult(a, b), unit)), b))))),
% 4.67/3.26 inference(quant_inst,[status(thm)],[])).
% 4.67/3.26 tff(808,plain,
% 4.67/3.26 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(a, b), mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b))) = mult(mult(mult(a, b), i(b)), mult(mult(i(b), ld(mult(a, b), unit)), b))) | (mult(mult(a, b), mult(mult(mult(i(b), ld(mult(a, b), unit)), b), i(b))) = mult(mult(mult(a, b), i(b)), mult(mult(i(b), ld(mult(a, b), unit)), b)))),
% 4.67/3.26 inference(modus_ponens,[status(thm)],[807, 806])).
% 4.67/3.26 tff(809,plain,
% 4.67/3.26 ((mult(mult(a, b), mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b))) = mult(mult(mult(a, b), i(b)), mult(mult(i(b), ld(mult(a, b), unit)), b))) | (mult(mult(a, b), mult(mult(mult(i(b), ld(mult(a, b), unit)), b), i(b))) = mult(mult(mult(a, b), i(b)), mult(mult(i(b), ld(mult(a, b), unit)), b)))),
% 4.67/3.26 inference(unit_resolution,[status(thm)],[808, 51])).
% 4.67/3.26 tff(810,plain,
% 4.67/3.26 (mult(mult(a, b), mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b))) = mult(mult(mult(a, b), i(b)), mult(mult(i(b), ld(mult(a, b), unit)), b))),
% 4.67/3.26 inference(unit_resolution,[status(thm)],[809, 805])).
% 4.67/3.26 tff(811,plain,
% 4.67/3.26 (mult(mult(a, b), mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b))) = mult(mult(a, b), mult(ld(mult(a, b), unit), i(b)))),
% 4.67/3.26 inference(transitivity,[status(thm)],[810, 792, 470, 464, 404, 791, 790, 789, 788, 786, 779])).
% 4.67/3.26 tff(812,plain,
% 4.67/3.26 (ld(mult(a, b), mult(mult(a, b), mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)))) = ld(mult(a, b), mult(mult(a, b), mult(ld(mult(a, b), unit), i(b))))),
% 4.67/3.26 inference(monotonicity,[status(thm)],[811])).
% 4.67/3.26 tff(813,plain,
% 4.67/3.26 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(a, b), mult(mult(a, b), mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)))) = mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)))),
% 4.67/3.26 inference(quant_inst,[status(thm)],[])).
% 4.67/3.26 tff(814,plain,
% 4.67/3.26 (ld(mult(a, b), mult(mult(a, b), mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)))) = mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b))),
% 4.67/3.26 inference(unit_resolution,[status(thm)],[813, 251])).
% 4.67/3.26 tff(815,plain,
% 4.67/3.26 (mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)) = ld(mult(a, b), mult(mult(a, b), mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b))))),
% 4.67/3.26 inference(symmetry,[status(thm)],[814])).
% 4.67/3.26 tff(816,plain,
% 4.67/3.26 (mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)) = mult(ld(mult(a, b), unit), i(b))),
% 4.67/3.26 inference(transitivity,[status(thm)],[815, 812, 774])).
% 4.67/3.26 tff(817,plain,
% 4.67/3.26 (mult(b, mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b))) = mult(b, mult(ld(mult(a, b), unit), i(b)))),
% 4.67/3.26 inference(monotonicity,[status(thm)],[816])).
% 4.67/3.26 tff(818,plain,
% 4.67/3.26 (mult(b, mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b))) = mult(i(b), mult(b, ld(mult(a, b), unit)))),
% 4.67/3.26 inference(transitivity,[status(thm)],[817, 772, 770, 750, 267, 769])).
% 4.67/3.26 tff(819,plain,
% 4.67/3.26 ((mult(b, mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b))) = mult(mult(b, i(b)), mult(mult(i(b), ld(mult(a, b), unit)), b))) <=> (mult(i(b), mult(b, ld(mult(a, b), unit))) = mult(mult(i(b), ld(mult(a, b), unit)), b))),
% 4.67/3.26 inference(monotonicity,[status(thm)],[818, 768])).
% 4.67/3.26 tff(820,plain,
% 4.67/3.26 ((mult(i(b), mult(b, ld(mult(a, b), unit))) = mult(mult(i(b), ld(mult(a, b), unit)), b)) <=> (mult(b, mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b))) = mult(mult(b, i(b)), mult(mult(i(b), ld(mult(a, b), unit)), b)))),
% 4.67/3.26 inference(symmetry,[status(thm)],[819])).
% 4.67/3.26 tff(821,plain,
% 4.67/3.26 ((~(mult(i(b), mult(b, ld(mult(a, b), unit))) = mult(mult(i(b), ld(mult(a, b), unit)), b))) <=> (~(mult(b, mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b))) = mult(mult(b, i(b)), mult(mult(i(b), ld(mult(a, b), unit)), b))))),
% 4.67/3.26 inference(monotonicity,[status(thm)],[820])).
% 4.67/3.26 tff(822,plain,
% 4.67/3.26 ((mult(i(b), mult(b, ld(mult(a, b), unit))) = mult(mult(i(b), ld(mult(a, b), unit)), b)) <=> (mult(mult(i(b), b), ld(mult(a, b), unit)) = mult(i(b), mult(ld(mult(a, b), unit), b)))),
% 4.67/3.26 inference(monotonicity,[status(thm)],[409, 336])).
% 4.67/3.26 tff(823,plain,
% 4.67/3.26 ((mult(i(b), mult(b, ld(mult(a, b), unit))) = mult(mult(i(b), ld(mult(a, b), unit)), b)) <=> (mult(i(b), mult(ld(mult(a, b), unit), b)) = mult(mult(i(b), b), ld(mult(a, b), unit)))),
% 4.67/3.26 inference(transitivity,[status(thm)],[822, 323])).
% 4.67/3.26 tff(824,plain,
% 4.67/3.26 ((mult(i(b), mult(ld(mult(a, b), unit), b)) = mult(mult(i(b), b), ld(mult(a, b), unit))) <=> (mult(i(b), mult(b, ld(mult(a, b), unit))) = mult(mult(i(b), ld(mult(a, b), unit)), b))),
% 4.67/3.26 inference(symmetry,[status(thm)],[823])).
% 4.67/3.26 tff(825,plain,
% 4.67/3.26 ((~(mult(i(b), mult(ld(mult(a, b), unit), b)) = mult(mult(i(b), b), ld(mult(a, b), unit)))) <=> (~(mult(i(b), mult(b, ld(mult(a, b), unit))) = mult(mult(i(b), ld(mult(a, b), unit)), b)))),
% 4.67/3.27 inference(monotonicity,[status(thm)],[824])).
% 4.67/3.27 tff(826,plain,
% 4.67/3.27 (~(mult(i(b), mult(b, ld(mult(a, b), unit))) = mult(mult(i(b), ld(mult(a, b), unit)), b))),
% 4.67/3.27 inference(modus_ponens,[status(thm)],[316, 825])).
% 4.67/3.27 tff(827,plain,
% 4.67/3.27 (~(mult(b, mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b))) = mult(mult(b, i(b)), mult(mult(i(b), ld(mult(a, b), unit)), b)))),
% 4.67/3.27 inference(modus_ponens,[status(thm)],[826, 821])).
% 4.67/3.27 tff(828,plain,
% 4.67/3.27 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(b, mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b))) = mult(mult(b, i(b)), mult(mult(i(b), ld(mult(a, b), unit)), b))) | (mult(b, mult(mult(mult(i(b), ld(mult(a, b), unit)), b), i(b))) = mult(mult(b, i(b)), mult(mult(i(b), ld(mult(a, b), unit)), b))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(b, mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b))) = mult(mult(b, i(b)), mult(mult(i(b), ld(mult(a, b), unit)), b))) | (mult(b, mult(mult(mult(i(b), ld(mult(a, b), unit)), b), i(b))) = mult(mult(b, i(b)), mult(mult(i(b), ld(mult(a, b), unit)), b))))),
% 4.67/3.27 inference(rewrite,[status(thm)],[])).
% 4.67/3.27 tff(829,plain,
% 4.67/3.27 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(b, mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b))) = mult(mult(b, i(b)), mult(mult(i(b), ld(mult(a, b), unit)), b))) | (mult(b, mult(mult(mult(i(b), ld(mult(a, b), unit)), b), i(b))) = mult(mult(b, i(b)), mult(mult(i(b), ld(mult(a, b), unit)), b))))),
% 4.67/3.27 inference(quant_inst,[status(thm)],[])).
% 4.67/3.27 tff(830,plain,
% 4.67/3.27 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(b, mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b))) = mult(mult(b, i(b)), mult(mult(i(b), ld(mult(a, b), unit)), b))) | (mult(b, mult(mult(mult(i(b), ld(mult(a, b), unit)), b), i(b))) = mult(mult(b, i(b)), mult(mult(i(b), ld(mult(a, b), unit)), b)))),
% 4.67/3.27 inference(modus_ponens,[status(thm)],[829, 828])).
% 4.67/3.27 tff(831,plain,
% 4.67/3.27 ((mult(b, mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b))) = mult(mult(b, i(b)), mult(mult(i(b), ld(mult(a, b), unit)), b))) | (mult(b, mult(mult(mult(i(b), ld(mult(a, b), unit)), b), i(b))) = mult(mult(b, i(b)), mult(mult(i(b), ld(mult(a, b), unit)), b)))),
% 4.67/3.27 inference(unit_resolution,[status(thm)],[830, 51])).
% 4.67/3.27 tff(832,plain,
% 4.67/3.27 (mult(b, mult(mult(mult(i(b), ld(mult(a, b), unit)), b), i(b))) = mult(mult(b, i(b)), mult(mult(i(b), ld(mult(a, b), unit)), b))),
% 4.67/3.27 inference(unit_resolution,[status(thm)],[831, 827])).
% 4.67/3.27 tff(833,plain,
% 4.67/3.27 (mult(mult(i(b), ld(mult(a, b), unit)), mult(b, i(b))) = mult(mult(i(b), ld(mult(a, b), unit)), mult(i(b), b))),
% 4.67/3.27 inference(symmetry,[status(thm)],[606])).
% 4.67/3.27 tff(834,plain,
% 4.67/3.27 (mult(mult(i(b), ld(mult(a, b), unit)), unit) = mult(mult(i(b), ld(mult(a, b), unit)), mult(b, i(b)))),
% 4.67/3.27 inference(symmetry,[status(thm)],[605])).
% 4.67/3.27 tff(835,plain,
% 4.67/3.27 (mult(mult(i(b), unit), ld(mult(a, b), unit)) = mult(i(b), mult(unit, ld(mult(a, b), unit)))),
% 4.67/3.27 inference(symmetry,[status(thm)],[598])).
% 4.67/3.27 tff(836,plain,
% 4.67/3.27 (mult(i(b), ld(mult(a, b), unit)) = mult(mult(mult(i(b), ld(mult(a, b), unit)), b), i(b))),
% 4.67/3.27 inference(transitivity,[status(thm)],[587, 835, 603, 834, 833, 617])).
% 4.67/3.27 tff(837,plain,
% 4.67/3.27 (mult(b, mult(i(b), ld(mult(a, b), unit))) = mult(b, mult(mult(mult(i(b), ld(mult(a, b), unit)), b), i(b)))),
% 4.67/3.27 inference(monotonicity,[status(thm)],[836])).
% 4.67/3.27 tff(838,plain,
% 4.67/3.27 (mult(mult(unit, b), mult(i(b), ld(mult(a, b), unit))) = mult(b, mult(i(b), ld(mult(a, b), unit)))),
% 4.67/3.27 inference(monotonicity,[status(thm)],[355])).
% 4.67/3.27 tff(839,assumption,(mult(mult(unit, b), mult(i(b), ld(mult(a, b), unit))) = mult(mult(mult(unit, b), ld(mult(a, b), unit)), i(b))), introduced(assumption)).
% 4.67/3.27 tff(840,plain,
% 4.67/3.27 (mult(mult(mult(unit, b), ld(mult(a, b), unit)), i(b)) = mult(mult(unit, b), mult(i(b), ld(mult(a, b), unit)))),
% 4.67/3.27 inference(symmetry,[status(thm)],[839])).
% 4.67/3.27 tff(841,plain,
% 4.67/3.27 (mult(mult(b, ld(mult(a, b), unit)), i(b)) = mult(mult(mult(unit, b), ld(mult(a, b), unit)), i(b))),
% 4.67/3.27 inference(monotonicity,[status(thm)],[749])).
% 4.67/3.27 tff(842,plain,
% 4.67/3.27 (mult(mult(b, ld(mult(a, b), unit)), i(b)) = mult(i(b), mult(ld(mult(a, b), unit), b))),
% 4.67/3.27 inference(transitivity,[status(thm)],[841, 840, 838, 837, 832, 767, 337, 335, 322])).
% 4.67/3.27 tff(843,plain,
% 4.67/3.27 (mult(a, mult(mult(b, ld(mult(a, b), unit)), i(b))) = mult(a, mult(i(b), mult(ld(mult(a, b), unit), b)))),
% 4.67/3.27 inference(monotonicity,[status(thm)],[842])).
% 4.67/3.27 tff(844,plain,
% 4.67/3.27 (mult(mult(mult(unit, b), ld(mult(a, b), unit)), i(b)) = mult(mult(b, ld(mult(a, b), unit)), i(b))),
% 4.67/3.27 inference(symmetry,[status(thm)],[841])).
% 4.67/3.27 tff(845,plain,
% 4.67/3.27 (mult(b, mult(i(b), ld(mult(a, b), unit))) = mult(mult(unit, b), mult(i(b), ld(mult(a, b), unit)))),
% 4.67/3.27 inference(symmetry,[status(thm)],[838])).
% 4.67/3.27 tff(846,plain,
% 4.67/3.27 (mult(b, mult(i(b), ld(mult(a, b), unit))) = mult(mult(b, ld(mult(a, b), unit)), i(b))),
% 4.67/3.27 inference(transitivity,[status(thm)],[845, 839, 844])).
% 4.67/3.27 tff(847,plain,
% 4.67/3.27 (mult(a, mult(b, mult(i(b), ld(mult(a, b), unit)))) = mult(a, mult(mult(b, ld(mult(a, b), unit)), i(b)))),
% 4.67/3.27 inference(monotonicity,[status(thm)],[846])).
% 4.67/3.27 tff(848,plain,
% 4.67/3.27 ((mult(mult(mult(a, b), ld(mult(a, b), unit)), i(b)) = mult(mult(a, b), mult(i(b), ld(mult(a, b), unit)))) <=> (mult(mult(a, b), mult(i(b), ld(mult(a, b), unit))) = mult(mult(mult(a, b), ld(mult(a, b), unit)), i(b)))),
% 4.67/3.27 inference(commutativity,[status(thm)],[])).
% 4.67/3.27 tff(849,plain,
% 4.67/3.27 (mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b)) = mult(mult(mult(a, b), ld(mult(a, b), unit)), i(b))),
% 4.67/3.27 inference(transitivity,[status(thm)],[471, 470, 464, 404, 794])).
% 4.67/3.27 tff(850,plain,
% 4.67/3.27 ((mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b)) = mult(mult(a, b), mult(i(b), ld(mult(a, b), unit)))) <=> (mult(mult(mult(a, b), ld(mult(a, b), unit)), i(b)) = mult(mult(a, b), mult(i(b), ld(mult(a, b), unit))))),
% 4.67/3.27 inference(monotonicity,[status(thm)],[849])).
% 4.67/3.27 tff(851,plain,
% 4.67/3.27 ((mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b)) = mult(mult(a, b), mult(i(b), ld(mult(a, b), unit)))) <=> (mult(mult(a, b), mult(i(b), ld(mult(a, b), unit))) = mult(mult(mult(a, b), ld(mult(a, b), unit)), i(b)))),
% 4.67/3.27 inference(transitivity,[status(thm)],[850, 848])).
% 4.67/3.27 tff(852,plain,
% 4.67/3.27 ((mult(mult(a, b), mult(i(b), ld(mult(a, b), unit))) = mult(mult(mult(a, b), ld(mult(a, b), unit)), i(b))) <=> (mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b)) = mult(mult(a, b), mult(i(b), ld(mult(a, b), unit))))),
% 4.67/3.27 inference(symmetry,[status(thm)],[851])).
% 4.67/3.27 tff(853,plain,
% 4.67/3.27 ((mult(mult(a, b), mult(mult(mult(i(b), i(b)), b), ld(mult(a, b), unit))) = mult(mult(mult(a, b), ld(mult(a, b), unit)), mult(mult(i(b), i(b)), b))) <=> (mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b)) = mult(mult(a, b), mult(i(b), ld(mult(a, b), unit))))),
% 4.67/3.27 inference(transitivity,[status(thm)],[802, 852])).
% 4.67/3.27 tff(854,plain,
% 4.67/3.27 ((~(mult(mult(a, b), mult(mult(mult(i(b), i(b)), b), ld(mult(a, b), unit))) = mult(mult(mult(a, b), ld(mult(a, b), unit)), mult(mult(i(b), i(b)), b)))) <=> (~(mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b)) = mult(mult(a, b), mult(i(b), ld(mult(a, b), unit)))))),
% 4.67/3.27 inference(monotonicity,[status(thm)],[853])).
% 4.67/3.27 tff(855,plain,
% 4.67/3.27 (~(mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b)) = mult(mult(a, b), mult(i(b), ld(mult(a, b), unit))))),
% 4.67/3.27 inference(modus_ponens,[status(thm)],[780, 854])).
% 4.67/3.27 tff(856,plain,
% 4.67/3.27 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(a, mult(b, mult(i(b), ld(mult(a, b), unit)))) = mult(mult(a, b), mult(i(b), ld(mult(a, b), unit)))) | (mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b)) = mult(mult(a, b), mult(i(b), ld(mult(a, b), unit)))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(a, mult(b, mult(i(b), ld(mult(a, b), unit)))) = mult(mult(a, b), mult(i(b), ld(mult(a, b), unit)))) | (mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b)) = mult(mult(a, b), mult(i(b), ld(mult(a, b), unit)))))),
% 4.77/3.27 inference(rewrite,[status(thm)],[])).
% 4.77/3.27 tff(857,plain,
% 4.77/3.27 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(a, mult(b, mult(i(b), ld(mult(a, b), unit)))) = mult(mult(a, b), mult(i(b), ld(mult(a, b), unit)))) | (mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b)) = mult(mult(a, b), mult(i(b), ld(mult(a, b), unit)))))),
% 4.77/3.27 inference(quant_inst,[status(thm)],[])).
% 4.77/3.27 tff(858,plain,
% 4.77/3.27 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(a, mult(b, mult(i(b), ld(mult(a, b), unit)))) = mult(mult(a, b), mult(i(b), ld(mult(a, b), unit)))) | (mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b)) = mult(mult(a, b), mult(i(b), ld(mult(a, b), unit))))),
% 4.77/3.27 inference(modus_ponens,[status(thm)],[857, 856])).
% 4.77/3.27 tff(859,plain,
% 4.77/3.27 ((mult(a, mult(b, mult(i(b), ld(mult(a, b), unit)))) = mult(mult(a, b), mult(i(b), ld(mult(a, b), unit)))) | (mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b)) = mult(mult(a, b), mult(i(b), ld(mult(a, b), unit))))),
% 4.77/3.27 inference(unit_resolution,[status(thm)],[858, 51])).
% 4.77/3.27 tff(860,plain,
% 4.77/3.27 (mult(a, mult(b, mult(i(b), ld(mult(a, b), unit)))) = mult(mult(a, b), mult(i(b), ld(mult(a, b), unit)))),
% 4.77/3.27 inference(unit_resolution,[status(thm)],[859, 855])).
% 4.77/3.27 tff(861,plain,
% 4.77/3.27 (mult(mult(a, b), mult(i(b), ld(mult(a, b), unit))) = mult(a, mult(b, mult(i(b), ld(mult(a, b), unit))))),
% 4.77/3.27 inference(symmetry,[status(thm)],[860])).
% 4.77/3.27 tff(862,plain,
% 4.77/3.27 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | ((mult(mult(a, b), mult(mult(mult(i(b), i(b)), b), ld(mult(a, b), unit))) = mult(mult(mult(a, b), ld(mult(a, b), unit)), mult(mult(i(b), i(b)), b))) | (mult(mult(a, b), mult(mult(mult(i(b), i(b)), b), ld(mult(a, b), unit))) = mult(mult(mult(a, b), mult(mult(i(b), i(b)), b)), ld(mult(a, b), unit))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | (mult(mult(a, b), mult(mult(mult(i(b), i(b)), b), ld(mult(a, b), unit))) = mult(mult(mult(a, b), ld(mult(a, b), unit)), mult(mult(i(b), i(b)), b))) | (mult(mult(a, b), mult(mult(mult(i(b), i(b)), b), ld(mult(a, b), unit))) = mult(mult(mult(a, b), mult(mult(i(b), i(b)), b)), ld(mult(a, b), unit))))),
% 4.77/3.27 inference(rewrite,[status(thm)],[])).
% 4.77/3.27 tff(863,plain,
% 4.77/3.27 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | ((mult(mult(a, b), mult(mult(mult(i(b), i(b)), b), ld(mult(a, b), unit))) = mult(mult(mult(a, b), ld(mult(a, b), unit)), mult(mult(i(b), i(b)), b))) | (mult(mult(a, b), mult(mult(mult(i(b), i(b)), b), ld(mult(a, b), unit))) = mult(mult(mult(a, b), mult(mult(i(b), i(b)), b)), ld(mult(a, b), unit))))),
% 4.77/3.27 inference(quant_inst,[status(thm)],[])).
% 4.77/3.27 tff(864,plain,
% 4.77/3.27 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | (mult(mult(a, b), mult(mult(mult(i(b), i(b)), b), ld(mult(a, b), unit))) = mult(mult(mult(a, b), ld(mult(a, b), unit)), mult(mult(i(b), i(b)), b))) | (mult(mult(a, b), mult(mult(mult(i(b), i(b)), b), ld(mult(a, b), unit))) = mult(mult(mult(a, b), mult(mult(i(b), i(b)), b)), ld(mult(a, b), unit)))),
% 4.77/3.27 inference(modus_ponens,[status(thm)],[863, 862])).
% 4.77/3.27 tff(865,plain,
% 4.77/3.27 ((mult(mult(a, b), mult(mult(mult(i(b), i(b)), b), ld(mult(a, b), unit))) = mult(mult(mult(a, b), ld(mult(a, b), unit)), mult(mult(i(b), i(b)), b))) | (mult(mult(a, b), mult(mult(mult(i(b), i(b)), b), ld(mult(a, b), unit))) = mult(mult(mult(a, b), mult(mult(i(b), i(b)), b)), ld(mult(a, b), unit)))),
% 4.77/3.27 inference(unit_resolution,[status(thm)],[864, 132])).
% 4.77/3.27 tff(866,plain,
% 4.77/3.27 (mult(mult(a, b), mult(mult(mult(i(b), i(b)), b), ld(mult(a, b), unit))) = mult(mult(mult(a, b), mult(mult(i(b), i(b)), b)), ld(mult(a, b), unit))),
% 4.77/3.27 inference(unit_resolution,[status(thm)],[865, 780])).
% 4.77/3.27 tff(867,plain,
% 4.77/3.27 (mult(mult(mult(a, b), mult(mult(i(b), i(b)), b)), ld(mult(a, b), unit)) = mult(mult(a, b), mult(mult(mult(i(b), i(b)), b), ld(mult(a, b), unit)))),
% 4.77/3.27 inference(symmetry,[status(thm)],[866])).
% 4.77/3.27 tff(868,plain,
% 4.77/3.27 (mult(mult(a, b), mult(mult(i(b), i(b)), b)) = mult(mult(a, b), i(b))),
% 4.77/3.27 inference(monotonicity,[status(thm)],[775])).
% 4.77/3.27 tff(869,plain,
% 4.77/3.27 (mult(mult(a, b), i(b)) = mult(mult(a, b), mult(mult(i(b), i(b)), b))),
% 4.77/3.27 inference(symmetry,[status(thm)],[868])).
% 4.77/3.27 tff(870,plain,
% 4.77/3.27 (mult(mult(mult(a, b), i(b)), ld(mult(a, b), unit)) = mult(mult(mult(a, b), mult(mult(i(b), i(b)), b)), ld(mult(a, b), unit))),
% 4.77/3.27 inference(monotonicity,[status(thm)],[869])).
% 4.77/3.27 tff(871,plain,
% 4.77/3.27 (mult(a, unit) = mult(a, mult(b, i(b)))),
% 4.77/3.27 inference(symmetry,[status(thm)],[31])).
% 4.77/3.27 tff(872,plain,
% 4.77/3.27 (a = mult(a, unit)),
% 4.77/3.27 inference(symmetry,[status(thm)],[10])).
% 4.77/3.27 tff(873,plain,
% 4.77/3.27 (a = mult(mult(a, b), i(b))),
% 4.77/3.27 inference(transitivity,[status(thm)],[872, 871, 230])).
% 4.77/3.27 tff(874,plain,
% 4.77/3.27 (mult(a, ld(mult(a, b), unit)) = mult(mult(mult(a, b), i(b)), ld(mult(a, b), unit))),
% 4.77/3.27 inference(monotonicity,[status(thm)],[873])).
% 4.77/3.27 tff(875,plain,
% 4.77/3.27 (mult(a, mult(mult(ld(mult(a, b), unit), b), i(b))) = mult(a, ld(mult(a, b), unit))),
% 4.77/3.27 inference(monotonicity,[status(thm)],[304])).
% 4.77/3.27 tff(876,plain,
% 4.77/3.27 (mult(a, mult(mult(ld(mult(a, b), unit), b), i(b))) = mult(mult(a, mult(ld(mult(a, b), unit), b)), i(b))),
% 4.77/3.27 inference(transitivity,[status(thm)],[875, 874, 870, 867, 801, 861, 847, 843, 470, 464, 404, 766])).
% 4.77/3.27 tff(877,plain,
% 4.77/3.27 ((mult(mult(a, i(b)), i(a)) = mult(a, mult(i(b), i(a)))) <=> (mult(a, mult(i(b), i(a))) = mult(mult(a, i(b)), i(a)))),
% 4.77/3.27 inference(commutativity,[status(thm)],[])).
% 4.77/3.27 tff(878,plain,
% 4.77/3.27 (mult(mult(a, i(a)), i(b)) = mult(a, mult(i(b), i(a)))),
% 4.77/3.27 inference(symmetry,[status(thm)],[464])).
% 4.77/3.27 tff(879,plain,
% 4.77/3.27 (mult(unit, i(b)) = mult(mult(a, i(a)), i(b))),
% 4.77/3.27 inference(symmetry,[status(thm)],[404])).
% 4.77/3.27 tff(880,plain,
% 4.77/3.27 (mult(mult(a, mult(ld(mult(a, b), unit), b)), i(b)) = mult(a, mult(i(b), i(a)))),
% 4.77/3.27 inference(transitivity,[status(thm)],[765, 879, 878])).
% 4.77/3.27 tff(881,plain,
% 4.77/3.27 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | ((mult(a, mult(i(a), i(b))) = mult(mult(a, i(a)), i(b))) | (mult(a, mult(i(a), i(b))) = mult(mult(a, i(b)), i(a))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | (mult(a, mult(i(a), i(b))) = mult(mult(a, i(a)), i(b))) | (mult(a, mult(i(a), i(b))) = mult(mult(a, i(b)), i(a))))),
% 4.77/3.27 inference(rewrite,[status(thm)],[])).
% 4.77/3.27 tff(882,plain,
% 4.77/3.27 (((mult(a, mult(i(a), i(b))) = mult(mult(a, i(b)), i(a))) | (mult(a, mult(i(a), i(b))) = mult(mult(a, i(a)), i(b)))) <=> ((mult(a, mult(i(a), i(b))) = mult(mult(a, i(a)), i(b))) | (mult(a, mult(i(a), i(b))) = mult(mult(a, i(b)), i(a))))),
% 4.77/3.27 inference(rewrite,[status(thm)],[])).
% 4.77/3.27 tff(883,plain,
% 4.77/3.27 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | ((mult(a, mult(i(a), i(b))) = mult(mult(a, i(b)), i(a))) | (mult(a, mult(i(a), i(b))) = mult(mult(a, i(a)), i(b))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | ((mult(a, mult(i(a), i(b))) = mult(mult(a, i(a)), i(b))) | (mult(a, mult(i(a), i(b))) = mult(mult(a, i(b)), i(a)))))),
% 4.77/3.27 inference(monotonicity,[status(thm)],[882])).
% 4.77/3.27 tff(884,plain,
% 4.77/3.27 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | ((mult(a, mult(i(a), i(b))) = mult(mult(a, i(b)), i(a))) | (mult(a, mult(i(a), i(b))) = mult(mult(a, i(a)), i(b))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | (mult(a, mult(i(a), i(b))) = mult(mult(a, i(a)), i(b))) | (mult(a, mult(i(a), i(b))) = mult(mult(a, i(b)), i(a))))),
% 4.77/3.27 inference(transitivity,[status(thm)],[883, 881])).
% 4.77/3.27 tff(885,plain,
% 4.77/3.27 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | ((mult(a, mult(i(a), i(b))) = mult(mult(a, i(b)), i(a))) | (mult(a, mult(i(a), i(b))) = mult(mult(a, i(a)), i(b))))),
% 4.77/3.28 inference(quant_inst,[status(thm)],[])).
% 4.77/3.28 tff(886,plain,
% 4.77/3.28 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | (mult(a, mult(i(a), i(b))) = mult(mult(a, i(a)), i(b))) | (mult(a, mult(i(a), i(b))) = mult(mult(a, i(b)), i(a)))),
% 4.77/3.28 inference(modus_ponens,[status(thm)],[885, 884])).
% 4.77/3.28 tff(887,plain,
% 4.77/3.28 ((mult(a, mult(i(a), i(b))) = mult(mult(a, i(a)), i(b))) | (mult(a, mult(i(a), i(b))) = mult(mult(a, i(b)), i(a)))),
% 4.77/3.28 inference(unit_resolution,[status(thm)],[886, 132])).
% 4.77/3.28 tff(888,plain,
% 4.77/3.28 (mult(a, mult(i(a), i(b))) = mult(mult(a, i(b)), i(a))),
% 4.77/3.28 inference(unit_resolution,[status(thm)],[887, 459])).
% 4.77/3.28 tff(889,plain,
% 4.77/3.28 (mult(i(a), i(b)) = mult(mult(ld(mult(a, b), unit), b), i(b))),
% 4.77/3.28 inference(monotonicity,[status(thm)],[467])).
% 4.77/3.28 tff(890,plain,
% 4.77/3.28 (mult(i(a), i(b)) = ld(mult(a, b), unit)),
% 4.77/3.28 inference(transitivity,[status(thm)],[889, 303, 300, 280])).
% 4.77/3.28 tff(891,plain,
% 4.77/3.28 (mult(a, mult(i(a), i(b))) = mult(a, ld(mult(a, b), unit))),
% 4.77/3.28 inference(monotonicity,[status(thm)],[890])).
% 4.77/3.28 tff(892,plain,
% 4.77/3.28 (mult(a, ld(mult(a, b), unit)) = mult(a, mult(i(a), i(b)))),
% 4.77/3.28 inference(symmetry,[status(thm)],[891])).
% 4.77/3.28 tff(893,plain,
% 4.77/3.28 (mult(a, mult(mult(ld(mult(a, b), unit), b), i(b))) = mult(mult(a, i(b)), i(a))),
% 4.77/3.28 inference(transitivity,[status(thm)],[875, 892, 888])).
% 4.77/3.28 tff(894,plain,
% 4.77/3.28 ((mult(a, mult(mult(ld(mult(a, b), unit), b), i(b))) = mult(mult(a, mult(ld(mult(a, b), unit), b)), i(b))) <=> (mult(mult(a, i(b)), i(a)) = mult(a, mult(i(b), i(a))))),
% 4.77/3.28 inference(monotonicity,[status(thm)],[893, 880])).
% 4.77/3.28 tff(895,plain,
% 4.77/3.28 ((mult(a, mult(mult(ld(mult(a, b), unit), b), i(b))) = mult(mult(a, mult(ld(mult(a, b), unit), b)), i(b))) <=> (mult(a, mult(i(b), i(a))) = mult(mult(a, i(b)), i(a)))),
% 4.77/3.28 inference(transitivity,[status(thm)],[894, 877])).
% 4.77/3.28 tff(896,plain,
% 4.77/3.28 ((mult(a, mult(i(b), i(a))) = mult(mult(a, i(b)), i(a))) <=> (mult(a, mult(mult(ld(mult(a, b), unit), b), i(b))) = mult(mult(a, mult(ld(mult(a, b), unit), b)), i(b)))),
% 4.77/3.28 inference(symmetry,[status(thm)],[895])).
% 4.77/3.28 tff(897,plain,
% 4.77/3.28 ((~(mult(a, mult(i(b), i(a))) = mult(mult(a, i(b)), i(a)))) <=> (~(mult(a, mult(mult(ld(mult(a, b), unit), b), i(b))) = mult(mult(a, mult(ld(mult(a, b), unit), b)), i(b))))),
% 4.77/3.28 inference(monotonicity,[status(thm)],[896])).
% 4.77/3.28 tff(898,plain,
% 4.77/3.28 ((mult(a, mult(i(a), i(b))) = mult(mult(a, i(a)), i(b))) <=> (mult(mult(a, i(b)), i(a)) = mult(a, mult(i(b), i(a))))),
% 4.77/3.28 inference(monotonicity,[status(thm)],[888, 878])).
% 4.77/3.28 tff(899,plain,
% 4.77/3.28 ((mult(a, mult(i(a), i(b))) = mult(mult(a, i(a)), i(b))) <=> (mult(a, mult(i(b), i(a))) = mult(mult(a, i(b)), i(a)))),
% 4.77/3.28 inference(transitivity,[status(thm)],[898, 877])).
% 4.77/3.28 tff(900,plain,
% 4.77/3.28 ((~(mult(a, mult(i(a), i(b))) = mult(mult(a, i(a)), i(b)))) <=> (~(mult(a, mult(i(b), i(a))) = mult(mult(a, i(b)), i(a))))),
% 4.77/3.28 inference(monotonicity,[status(thm)],[899])).
% 4.77/3.28 tff(901,plain,
% 4.77/3.28 (~(mult(a, mult(i(b), i(a))) = mult(mult(a, i(b)), i(a)))),
% 4.77/3.28 inference(modus_ponens,[status(thm)],[459, 900])).
% 4.77/3.28 tff(902,plain,
% 4.77/3.28 (~(mult(a, mult(mult(ld(mult(a, b), unit), b), i(b))) = mult(mult(a, mult(ld(mult(a, b), unit), b)), i(b)))),
% 4.77/3.28 inference(modus_ponens,[status(thm)],[901, 897])).
% 4.77/3.28 tff(903,plain,
% 4.77/3.28 ($false),
% 4.77/3.28 inference(unit_resolution,[status(thm)],[902, 876])).
% 4.77/3.28 tff(904,plain,((mult(mult(a, b), mult(mult(mult(i(b), i(b)), b), ld(mult(a, b), unit))) = mult(mult(mult(a, b), ld(mult(a, b), unit)), mult(mult(i(b), i(b)), b))) | (~(mult(mult(unit, b), mult(i(b), ld(mult(a, b), unit))) = mult(mult(mult(unit, b), ld(mult(a, b), unit)), i(b)))) | (~(mult(mult(unit, b), mult(ld(mult(a, b), unit), i(b))) = mult(mult(mult(unit, b), i(b)), ld(mult(a, b), unit))))), inference(lemma,lemma(discharge,[]))).
% 4.77/3.28 tff(905,plain,
% 4.77/3.28 (mult(mult(a, b), mult(mult(mult(i(b), i(b)), b), ld(mult(a, b), unit))) = mult(mult(mult(a, b), ld(mult(a, b), unit)), mult(mult(i(b), i(b)), b))),
% 4.77/3.28 inference(unit_resolution,[status(thm)],[904, 759, 764])).
% 4.77/3.28 tff(906,plain,
% 4.77/3.28 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(a, b), mult(mult(a, b), mult(mult(i(b), ld(mult(a, b), unit)), b))) = mult(mult(i(b), ld(mult(a, b), unit)), b))),
% 4.77/3.28 inference(quant_inst,[status(thm)],[])).
% 4.77/3.28 tff(907,plain,
% 4.77/3.28 (ld(mult(a, b), mult(mult(a, b), mult(mult(i(b), ld(mult(a, b), unit)), b))) = mult(mult(i(b), ld(mult(a, b), unit)), b)),
% 4.77/3.28 inference(unit_resolution,[status(thm)],[906, 251])).
% 4.77/3.28 tff(908,assumption,(mult(mult(a, b), mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(mult(a, b), i(b)), mult(ld(mult(a, b), unit), b))), introduced(assumption)).
% 4.77/3.28 tff(909,plain,
% 4.77/3.28 (mult(mult(a, b), mult(mult(i(b), ld(mult(a, b), unit)), b)) = mult(mult(a, b), mult(i(b), mult(ld(mult(a, b), unit), b)))),
% 4.77/3.28 inference(monotonicity,[status(thm)],[336])).
% 4.77/3.28 tff(910,plain,
% 4.77/3.28 (mult(mult(a, b), mult(mult(i(b), ld(mult(a, b), unit)), b)) = unit),
% 4.77/3.28 inference(transitivity,[status(thm)],[909, 908, 233, 429, 257])).
% 4.77/3.28 tff(911,plain,
% 4.77/3.28 (ld(mult(a, b), mult(mult(a, b), mult(mult(i(b), ld(mult(a, b), unit)), b))) = ld(mult(a, b), unit)),
% 4.77/3.28 inference(monotonicity,[status(thm)],[910])).
% 4.77/3.28 tff(912,plain,
% 4.77/3.28 (ld(mult(a, b), unit) = ld(mult(a, b), mult(mult(a, b), mult(mult(i(b), ld(mult(a, b), unit)), b)))),
% 4.77/3.28 inference(symmetry,[status(thm)],[911])).
% 4.77/3.28 tff(913,plain,
% 4.77/3.28 (mult(i(b), mult(b, ld(mult(a, b), unit))) = mult(mult(i(b), ld(mult(a, b), unit)), b)),
% 4.77/3.28 inference(transitivity,[status(thm)],[409, 237, 235, 912, 907])).
% 4.77/3.28 tff(914,plain,
% 4.77/3.28 ($false),
% 4.77/3.28 inference(unit_resolution,[status(thm)],[826, 913])).
% 4.77/3.28 tff(915,plain,(~(mult(mult(a, b), mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(mult(a, b), i(b)), mult(ld(mult(a, b), unit), b)))), inference(lemma,lemma(discharge,[]))).
% 4.77/3.28 tff(916,plain,
% 4.77/3.28 (mult(a, mult(ld(mult(a, b), unit), b)) = mult(mult(mult(a, b), i(b)), mult(ld(mult(a, b), unit), b))),
% 4.77/3.28 inference(symmetry,[status(thm)],[233])).
% 4.77/3.28 tff(917,assumption,(mult(mult(a, b), mult(mult(mult(i(b), i(b)), b), ld(mult(a, b), unit))) = mult(mult(mult(a, b), ld(mult(a, b), unit)), mult(mult(i(b), i(b)), b))), introduced(assumption)).
% 4.77/3.28 tff(918,plain,
% 4.77/3.28 (mult(i(b), ld(mult(a, b), unit)) = mult(mult(mult(i(b), i(b)), b), ld(mult(a, b), unit))),
% 4.77/3.28 inference(symmetry,[status(thm)],[800])).
% 4.77/3.28 tff(919,plain,
% 4.77/3.28 (mult(mult(a, b), mult(i(b), ld(mult(a, b), unit))) = mult(mult(a, b), mult(mult(mult(i(b), i(b)), b), ld(mult(a, b), unit)))),
% 4.77/3.28 inference(monotonicity,[status(thm)],[918])).
% 4.77/3.28 tff(920,plain,
% 4.77/3.28 (mult(mult(a, b), mult(i(b), ld(mult(a, b), unit))) = i(b)),
% 4.77/3.28 inference(transitivity,[status(thm)],[919, 917, 787, 384, 122, 353, 43])).
% 4.77/3.28 tff(921,plain,
% 4.77/3.28 (mult(mult(mult(a, b), mult(i(b), ld(mult(a, b), unit))), b) = mult(i(b), b)),
% 4.77/3.28 inference(monotonicity,[status(thm)],[920])).
% 4.77/3.28 tff(922,plain,
% 4.77/3.28 (mult(mult(mult(a, b), mult(i(b), ld(mult(a, b), unit))), b) = mult(mult(mult(a, b), i(b)), mult(ld(mult(a, b), unit), b))),
% 4.77/3.28 inference(transitivity,[status(thm)],[921, 218, 213, 60, 19, 258, 431, 916])).
% 4.77/3.28 tff(923,plain,
% 4.77/3.28 ((mult(mult(a, b), mult(mult(i(b), ld(mult(a, b), unit)), b)) = mult(mult(mult(a, b), mult(i(b), ld(mult(a, b), unit))), b)) <=> (mult(mult(a, b), mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(mult(a, b), i(b)), mult(ld(mult(a, b), unit), b)))),
% 4.77/3.28 inference(monotonicity,[status(thm)],[909, 922])).
% 4.77/3.28 tff(924,plain,
% 4.77/3.28 ((mult(mult(a, b), mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(mult(a, b), i(b)), mult(ld(mult(a, b), unit), b))) <=> (mult(mult(a, b), mult(mult(i(b), ld(mult(a, b), unit)), b)) = mult(mult(mult(a, b), mult(i(b), ld(mult(a, b), unit))), b))),
% 4.77/3.28 inference(symmetry,[status(thm)],[923])).
% 4.77/3.28 tff(925,plain,
% 4.77/3.28 ((~(mult(mult(a, b), mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(mult(a, b), i(b)), mult(ld(mult(a, b), unit), b)))) <=> (~(mult(mult(a, b), mult(mult(i(b), ld(mult(a, b), unit)), b)) = mult(mult(mult(a, b), mult(i(b), ld(mult(a, b), unit))), b)))),
% 4.77/3.28 inference(monotonicity,[status(thm)],[924])).
% 4.77/3.28 tff(926,assumption,(~(mult(mult(a, b), mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(mult(a, b), i(b)), mult(ld(mult(a, b), unit), b)))), introduced(assumption)).
% 4.77/3.28 tff(927,plain,
% 4.77/3.28 (~(mult(mult(a, b), mult(mult(i(b), ld(mult(a, b), unit)), b)) = mult(mult(mult(a, b), mult(i(b), ld(mult(a, b), unit))), b))),
% 4.77/3.28 inference(modus_ponens,[status(thm)],[926, 925])).
% 4.77/3.28 tff(928,plain,
% 4.77/3.28 (mult(mult(mult(a, b), mult(i(b), ld(mult(a, b), unit))), b) = mult(a, mult(ld(mult(a, b), unit), b))),
% 4.77/3.28 inference(transitivity,[status(thm)],[921, 218, 213, 60, 19, 258, 431])).
% 4.77/3.28 tff(929,plain,
% 4.77/3.28 (mult(mult(mult(a, b), i(b)), mult(b, ld(mult(a, b), unit))) = mult(a, mult(b, ld(mult(a, b), unit)))),
% 4.77/3.28 inference(monotonicity,[status(thm)],[232])).
% 4.77/3.28 tff(930,plain,
% 4.77/3.28 (mult(mult(mult(a, b), i(b)), mult(b, ld(mult(a, b), unit))) = mult(mult(a, ld(mult(a, b), unit)), b)),
% 4.77/3.28 inference(transitivity,[status(thm)],[929, 439])).
% 4.77/3.28 tff(931,plain,
% 4.77/3.28 (mult(i(b), mult(b, ld(mult(a, b), unit))) = ld(mult(a, b), unit)),
% 4.77/3.28 inference(transitivity,[status(thm)],[409, 237, 235])).
% 4.77/3.28 tff(932,plain,
% 4.77/3.28 (mult(mult(a, b), mult(i(b), mult(b, ld(mult(a, b), unit)))) = mult(mult(a, b), ld(mult(a, b), unit))),
% 4.77/3.28 inference(monotonicity,[status(thm)],[931])).
% 4.77/3.28 tff(933,plain,
% 4.77/3.28 (mult(mult(a, b), mult(i(b), mult(b, ld(mult(a, b), unit)))) = mult(a, mult(ld(mult(a, b), unit), b))),
% 4.77/3.28 inference(transitivity,[status(thm)],[932, 431])).
% 4.77/3.28 tff(934,plain,
% 4.77/3.28 ((mult(mult(a, b), mult(i(b), mult(b, ld(mult(a, b), unit)))) = mult(mult(mult(a, b), i(b)), mult(b, ld(mult(a, b), unit)))) <=> (mult(a, mult(ld(mult(a, b), unit), b)) = mult(mult(a, ld(mult(a, b), unit)), b))),
% 4.77/3.28 inference(monotonicity,[status(thm)],[933, 930])).
% 4.77/3.28 tff(935,plain,
% 4.77/3.28 ((mult(a, mult(ld(mult(a, b), unit), b)) = mult(mult(a, ld(mult(a, b), unit)), b)) <=> (mult(mult(a, b), mult(i(b), mult(b, ld(mult(a, b), unit)))) = mult(mult(mult(a, b), i(b)), mult(b, ld(mult(a, b), unit))))),
% 4.77/3.28 inference(symmetry,[status(thm)],[934])).
% 4.77/3.28 tff(936,plain,
% 4.77/3.28 ((~(mult(a, mult(ld(mult(a, b), unit), b)) = mult(mult(a, ld(mult(a, b), unit)), b))) <=> (~(mult(mult(a, b), mult(i(b), mult(b, ld(mult(a, b), unit)))) = mult(mult(mult(a, b), i(b)), mult(b, ld(mult(a, b), unit)))))),
% 4.77/3.28 inference(monotonicity,[status(thm)],[935])).
% 4.77/3.28 tff(937,plain,
% 4.77/3.28 (~(mult(mult(a, b), mult(i(b), mult(b, ld(mult(a, b), unit)))) = mult(mult(mult(a, b), i(b)), mult(b, ld(mult(a, b), unit))))),
% 4.77/3.28 inference(modus_ponens,[status(thm)],[443, 936])).
% 4.77/3.28 tff(938,plain,
% 4.77/3.28 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(mult(a, b), mult(i(b), mult(b, ld(mult(a, b), unit)))) = mult(mult(mult(a, b), i(b)), mult(b, ld(mult(a, b), unit)))) | (mult(mult(a, b), mult(mult(b, ld(mult(a, b), unit)), i(b))) = mult(mult(mult(a, b), i(b)), mult(b, ld(mult(a, b), unit)))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(a, b), mult(i(b), mult(b, ld(mult(a, b), unit)))) = mult(mult(mult(a, b), i(b)), mult(b, ld(mult(a, b), unit)))) | (mult(mult(a, b), mult(mult(b, ld(mult(a, b), unit)), i(b))) = mult(mult(mult(a, b), i(b)), mult(b, ld(mult(a, b), unit)))))),
% 4.77/3.28 inference(rewrite,[status(thm)],[])).
% 4.77/3.28 tff(939,plain,
% 4.77/3.28 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(mult(a, b), mult(i(b), mult(b, ld(mult(a, b), unit)))) = mult(mult(mult(a, b), i(b)), mult(b, ld(mult(a, b), unit)))) | (mult(mult(a, b), mult(mult(b, ld(mult(a, b), unit)), i(b))) = mult(mult(mult(a, b), i(b)), mult(b, ld(mult(a, b), unit)))))),
% 4.77/3.28 inference(quant_inst,[status(thm)],[])).
% 4.77/3.28 tff(940,plain,
% 4.77/3.28 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(a, b), mult(i(b), mult(b, ld(mult(a, b), unit)))) = mult(mult(mult(a, b), i(b)), mult(b, ld(mult(a, b), unit)))) | (mult(mult(a, b), mult(mult(b, ld(mult(a, b), unit)), i(b))) = mult(mult(mult(a, b), i(b)), mult(b, ld(mult(a, b), unit))))),
% 4.77/3.28 inference(modus_ponens,[status(thm)],[939, 938])).
% 4.77/3.28 tff(941,plain,
% 4.77/3.28 ((mult(mult(a, b), mult(i(b), mult(b, ld(mult(a, b), unit)))) = mult(mult(mult(a, b), i(b)), mult(b, ld(mult(a, b), unit)))) | (mult(mult(a, b), mult(mult(b, ld(mult(a, b), unit)), i(b))) = mult(mult(mult(a, b), i(b)), mult(b, ld(mult(a, b), unit))))),
% 4.77/3.28 inference(unit_resolution,[status(thm)],[940, 51])).
% 4.77/3.28 tff(942,plain,
% 4.77/3.28 (mult(mult(a, b), mult(mult(b, ld(mult(a, b), unit)), i(b))) = mult(mult(mult(a, b), i(b)), mult(b, ld(mult(a, b), unit)))),
% 4.77/3.28 inference(unit_resolution,[status(thm)],[941, 937])).
% 4.77/3.28 tff(943,plain,
% 4.77/3.28 (mult(mult(mult(unit, b), ld(mult(a, b), unit)), i(b)) = mult(mult(b, ld(mult(a, b), unit)), i(b))),
% 4.77/3.28 inference(monotonicity,[status(thm)],[748])).
% 4.77/3.28 tff(944,plain,
% 4.77/3.28 (mult(b, mult(i(b), ld(mult(a, b), unit))) = mult(mult(unit, b), mult(i(b), ld(mult(a, b), unit)))),
% 4.77/3.28 inference(monotonicity,[status(thm)],[771])).
% 4.77/3.28 tff(945,plain,
% 4.77/3.28 (mult(b, mult(i(b), ld(mult(a, b), unit))) = mult(mult(b, ld(mult(a, b), unit)), i(b))),
% 4.77/3.28 inference(transitivity,[status(thm)],[944, 839, 943])).
% 4.77/3.28 tff(946,plain,
% 4.77/3.28 (mult(mult(a, b), mult(b, mult(i(b), ld(mult(a, b), unit)))) = mult(mult(a, b), mult(mult(b, ld(mult(a, b), unit)), i(b)))),
% 4.77/3.28 inference(monotonicity,[status(thm)],[945])).
% 4.77/3.28 tff(947,plain,
% 4.77/3.28 (mult(mult(a, b), mult(b, mult(i(b), ld(mult(a, b), unit)))) = mult(mult(a, ld(mult(a, b), unit)), b)),
% 4.77/3.28 inference(transitivity,[status(thm)],[946, 942, 929, 439])).
% 4.77/3.28 tff(948,plain,
% 4.77/3.28 ((mult(mult(a, b), mult(b, mult(i(b), ld(mult(a, b), unit)))) = mult(mult(mult(a, b), mult(i(b), ld(mult(a, b), unit))), b)) <=> (mult(mult(a, ld(mult(a, b), unit)), b) = mult(a, mult(ld(mult(a, b), unit), b)))),
% 4.77/3.28 inference(monotonicity,[status(thm)],[947, 928])).
% 4.77/3.28 tff(949,plain,
% 4.77/3.28 ((mult(mult(a, b), mult(b, mult(i(b), ld(mult(a, b), unit)))) = mult(mult(mult(a, b), mult(i(b), ld(mult(a, b), unit))), b)) <=> (mult(a, mult(ld(mult(a, b), unit), b)) = mult(mult(a, ld(mult(a, b), unit)), b))),
% 4.77/3.28 inference(transitivity,[status(thm)],[948, 430])).
% 4.77/3.28 tff(950,plain,
% 4.77/3.28 ((mult(a, mult(ld(mult(a, b), unit), b)) = mult(mult(a, ld(mult(a, b), unit)), b)) <=> (mult(mult(a, b), mult(b, mult(i(b), ld(mult(a, b), unit)))) = mult(mult(mult(a, b), mult(i(b), ld(mult(a, b), unit))), b))),
% 4.77/3.28 inference(symmetry,[status(thm)],[949])).
% 4.77/3.28 tff(951,plain,
% 4.77/3.28 ((~(mult(a, mult(ld(mult(a, b), unit), b)) = mult(mult(a, ld(mult(a, b), unit)), b))) <=> (~(mult(mult(a, b), mult(b, mult(i(b), ld(mult(a, b), unit)))) = mult(mult(mult(a, b), mult(i(b), ld(mult(a, b), unit))), b)))),
% 4.77/3.28 inference(monotonicity,[status(thm)],[950])).
% 4.77/3.28 tff(952,plain,
% 4.77/3.28 (~(mult(mult(a, b), mult(b, mult(i(b), ld(mult(a, b), unit)))) = mult(mult(mult(a, b), mult(i(b), ld(mult(a, b), unit))), b))),
% 4.77/3.28 inference(modus_ponens,[status(thm)],[443, 951])).
% 4.77/3.28 tff(953,plain,
% 4.77/3.28 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(mult(a, b), mult(mult(i(b), ld(mult(a, b), unit)), b)) = mult(mult(mult(a, b), mult(i(b), ld(mult(a, b), unit))), b)) | (mult(mult(a, b), mult(b, mult(i(b), ld(mult(a, b), unit)))) = mult(mult(mult(a, b), mult(i(b), ld(mult(a, b), unit))), b)))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(a, b), mult(mult(i(b), ld(mult(a, b), unit)), b)) = mult(mult(mult(a, b), mult(i(b), ld(mult(a, b), unit))), b)) | (mult(mult(a, b), mult(b, mult(i(b), ld(mult(a, b), unit)))) = mult(mult(mult(a, b), mult(i(b), ld(mult(a, b), unit))), b)))),
% 4.77/3.28 inference(rewrite,[status(thm)],[])).
% 4.77/3.28 tff(954,plain,
% 4.77/3.28 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(mult(a, b), mult(mult(i(b), ld(mult(a, b), unit)), b)) = mult(mult(mult(a, b), mult(i(b), ld(mult(a, b), unit))), b)) | (mult(mult(a, b), mult(b, mult(i(b), ld(mult(a, b), unit)))) = mult(mult(mult(a, b), mult(i(b), ld(mult(a, b), unit))), b)))),
% 4.77/3.28 inference(quant_inst,[status(thm)],[])).
% 4.77/3.29 tff(955,plain,
% 4.77/3.29 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(a, b), mult(mult(i(b), ld(mult(a, b), unit)), b)) = mult(mult(mult(a, b), mult(i(b), ld(mult(a, b), unit))), b)) | (mult(mult(a, b), mult(b, mult(i(b), ld(mult(a, b), unit)))) = mult(mult(mult(a, b), mult(i(b), ld(mult(a, b), unit))), b))),
% 4.77/3.29 inference(modus_ponens,[status(thm)],[954, 953])).
% 4.77/3.29 tff(956,plain,
% 4.77/3.29 ((mult(mult(a, b), mult(mult(i(b), ld(mult(a, b), unit)), b)) = mult(mult(mult(a, b), mult(i(b), ld(mult(a, b), unit))), b)) | (mult(mult(a, b), mult(b, mult(i(b), ld(mult(a, b), unit)))) = mult(mult(mult(a, b), mult(i(b), ld(mult(a, b), unit))), b))),
% 4.77/3.29 inference(unit_resolution,[status(thm)],[955, 51])).
% 4.77/3.29 tff(957,plain,
% 4.77/3.29 ($false),
% 4.77/3.29 inference(unit_resolution,[status(thm)],[956, 952, 927])).
% 4.77/3.29 tff(958,plain,((~(mult(mult(a, b), mult(mult(mult(i(b), i(b)), b), ld(mult(a, b), unit))) = mult(mult(mult(a, b), ld(mult(a, b), unit)), mult(mult(i(b), i(b)), b)))) | (~(mult(mult(unit, b), mult(i(b), ld(mult(a, b), unit))) = mult(mult(mult(unit, b), ld(mult(a, b), unit)), i(b)))) | (mult(mult(a, b), mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(mult(a, b), i(b)), mult(ld(mult(a, b), unit), b)))), inference(lemma,lemma(discharge,[]))).
% 4.77/3.29 tff(959,plain,
% 4.77/3.29 ((~(mult(mult(a, b), mult(mult(mult(i(b), i(b)), b), ld(mult(a, b), unit))) = mult(mult(mult(a, b), ld(mult(a, b), unit)), mult(mult(i(b), i(b)), b)))) | (~(mult(mult(unit, b), mult(i(b), ld(mult(a, b), unit))) = mult(mult(mult(unit, b), ld(mult(a, b), unit)), i(b))))),
% 4.77/3.29 inference(unit_resolution,[status(thm)],[958, 915])).
% 4.77/3.29 tff(960,plain,
% 4.77/3.29 ($false),
% 4.77/3.29 inference(unit_resolution,[status(thm)],[959, 905, 759])).
% 4.77/3.29 tff(961,plain,(mult(mult(unit, b), mult(i(b), ld(mult(a, b), unit))) = mult(mult(mult(unit, b), i(b)), ld(mult(a, b), unit))), inference(lemma,lemma(discharge,[]))).
% 4.77/3.29 tff(962,plain,
% 4.77/3.29 (mult(b, mult(i(b), ld(mult(a, b), unit))) = ld(mult(a, b), unit)),
% 4.77/3.29 inference(transitivity,[status(thm)],[944, 961, 750, 235])).
% 4.77/3.29 tff(963,plain,
% 4.77/3.29 (mult(b, mult(b, mult(i(b), ld(mult(a, b), unit)))) = mult(b, ld(mult(a, b), unit))),
% 4.77/3.29 inference(monotonicity,[status(thm)],[962])).
% 4.77/3.29 tff(964,plain,
% 4.77/3.29 ((mult(mult(unit, b), ld(mult(a, b), unit)) = mult(unit, mult(ld(mult(a, b), unit), b))) <=> (mult(unit, mult(ld(mult(a, b), unit), b)) = mult(mult(unit, b), ld(mult(a, b), unit)))),
% 4.77/3.29 inference(commutativity,[status(thm)],[])).
% 4.77/3.29 tff(965,plain,
% 4.77/3.29 (mult(mult(b, mult(i(b), ld(mult(a, b), unit))), b) = mult(ld(mult(a, b), unit), b)),
% 4.77/3.29 inference(monotonicity,[status(thm)],[962])).
% 4.77/3.29 tff(966,plain,
% 4.77/3.29 (mult(mult(b, mult(i(b), ld(mult(a, b), unit))), b) = mult(unit, mult(ld(mult(a, b), unit), b))),
% 4.77/3.29 inference(transitivity,[status(thm)],[965, 522])).
% 4.77/3.29 tff(967,plain,
% 4.77/3.29 (mult(b, mult(b, mult(i(b), ld(mult(a, b), unit)))) = mult(mult(unit, b), ld(mult(a, b), unit))),
% 4.77/3.29 inference(transitivity,[status(thm)],[963, 749])).
% 4.77/3.29 tff(968,plain,
% 4.77/3.29 ((mult(b, mult(b, mult(i(b), ld(mult(a, b), unit)))) = mult(mult(b, mult(i(b), ld(mult(a, b), unit))), b)) <=> (mult(mult(unit, b), ld(mult(a, b), unit)) = mult(unit, mult(ld(mult(a, b), unit), b)))),
% 4.77/3.29 inference(monotonicity,[status(thm)],[967, 966])).
% 4.77/3.29 tff(969,plain,
% 4.77/3.29 ((mult(b, mult(b, mult(i(b), ld(mult(a, b), unit)))) = mult(mult(b, mult(i(b), ld(mult(a, b), unit))), b)) <=> (mult(unit, mult(ld(mult(a, b), unit), b)) = mult(mult(unit, b), ld(mult(a, b), unit)))),
% 4.77/3.29 inference(transitivity,[status(thm)],[968, 964])).
% 4.77/3.29 tff(970,plain,
% 4.77/3.29 ((mult(unit, mult(ld(mult(a, b), unit), b)) = mult(mult(unit, b), ld(mult(a, b), unit))) <=> (mult(b, mult(b, mult(i(b), ld(mult(a, b), unit)))) = mult(mult(b, mult(i(b), ld(mult(a, b), unit))), b))),
% 4.77/3.29 inference(symmetry,[status(thm)],[969])).
% 4.77/3.29 tff(971,plain,
% 4.77/3.29 (mult(b, mult(mult(ld(mult(a, b), unit), b), i(b))) = mult(b, ld(mult(a, b), unit))),
% 4.77/3.29 inference(monotonicity,[status(thm)],[304])).
% 4.77/3.29 tff(972,plain,
% 4.77/3.29 (mult(b, mult(mult(ld(mult(a, b), unit), b), i(b))) = mult(mult(unit, b), ld(mult(a, b), unit))),
% 4.77/3.29 inference(transitivity,[status(thm)],[971, 749])).
% 4.77/3.29 tff(973,plain,
% 4.77/3.29 ((mult(b, mult(mult(ld(mult(a, b), unit), b), i(b))) = mult(mult(b, i(b)), mult(ld(mult(a, b), unit), b))) <=> (mult(mult(unit, b), ld(mult(a, b), unit)) = mult(unit, mult(ld(mult(a, b), unit), b)))),
% 4.77/3.29 inference(monotonicity,[status(thm)],[972, 672])).
% 4.77/3.29 tff(974,plain,
% 4.77/3.29 ((mult(b, mult(mult(ld(mult(a, b), unit), b), i(b))) = mult(mult(b, i(b)), mult(ld(mult(a, b), unit), b))) <=> (mult(unit, mult(ld(mult(a, b), unit), b)) = mult(mult(unit, b), ld(mult(a, b), unit)))),
% 4.77/3.29 inference(transitivity,[status(thm)],[973, 964])).
% 4.77/3.29 tff(975,plain,
% 4.77/3.29 ((mult(b, mult(mult(ld(mult(a, b), unit), b), i(b))) = mult(mult(b, i(b)), mult(ld(mult(a, b), unit), b))) <=> (mult(b, mult(b, mult(i(b), ld(mult(a, b), unit)))) = mult(mult(b, mult(i(b), ld(mult(a, b), unit))), b))),
% 4.77/3.29 inference(transitivity,[status(thm)],[974, 970])).
% 4.77/3.29 tff(976,plain,
% 4.77/3.29 ((~(mult(b, mult(mult(ld(mult(a, b), unit), b), i(b))) = mult(mult(b, i(b)), mult(ld(mult(a, b), unit), b)))) <=> (~(mult(b, mult(b, mult(i(b), ld(mult(a, b), unit)))) = mult(mult(b, mult(i(b), ld(mult(a, b), unit))), b)))),
% 4.77/3.29 inference(monotonicity,[status(thm)],[975])).
% 4.77/3.29 tff(977,plain,
% 4.77/3.29 (~(mult(b, mult(b, mult(i(b), ld(mult(a, b), unit)))) = mult(mult(b, mult(i(b), ld(mult(a, b), unit))), b))),
% 4.77/3.29 inference(modus_ponens,[status(thm)],[681, 976])).
% 4.77/3.29 tff(978,plain,
% 4.77/3.29 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | ((mult(b, mult(b, mult(i(b), ld(mult(a, b), unit)))) = mult(mult(b, mult(i(b), ld(mult(a, b), unit))), b)) | (mult(b, mult(b, mult(i(b), ld(mult(a, b), unit)))) = mult(mult(b, b), mult(i(b), ld(mult(a, b), unit)))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | (mult(b, mult(b, mult(i(b), ld(mult(a, b), unit)))) = mult(mult(b, mult(i(b), ld(mult(a, b), unit))), b)) | (mult(b, mult(b, mult(i(b), ld(mult(a, b), unit)))) = mult(mult(b, b), mult(i(b), ld(mult(a, b), unit)))))),
% 4.77/3.29 inference(rewrite,[status(thm)],[])).
% 4.77/3.29 tff(979,plain,
% 4.77/3.29 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | ((mult(b, mult(b, mult(i(b), ld(mult(a, b), unit)))) = mult(mult(b, mult(i(b), ld(mult(a, b), unit))), b)) | (mult(b, mult(b, mult(i(b), ld(mult(a, b), unit)))) = mult(mult(b, b), mult(i(b), ld(mult(a, b), unit)))))),
% 4.77/3.29 inference(quant_inst,[status(thm)],[])).
% 4.77/3.29 tff(980,plain,
% 4.77/3.29 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | (mult(b, mult(b, mult(i(b), ld(mult(a, b), unit)))) = mult(mult(b, mult(i(b), ld(mult(a, b), unit))), b)) | (mult(b, mult(b, mult(i(b), ld(mult(a, b), unit)))) = mult(mult(b, b), mult(i(b), ld(mult(a, b), unit))))),
% 4.77/3.29 inference(modus_ponens,[status(thm)],[979, 978])).
% 4.77/3.29 tff(981,plain,
% 4.77/3.29 ((mult(b, mult(b, mult(i(b), ld(mult(a, b), unit)))) = mult(mult(b, mult(i(b), ld(mult(a, b), unit))), b)) | (mult(b, mult(b, mult(i(b), ld(mult(a, b), unit)))) = mult(mult(b, b), mult(i(b), ld(mult(a, b), unit))))),
% 4.77/3.29 inference(unit_resolution,[status(thm)],[980, 132])).
% 4.77/3.29 tff(982,plain,
% 4.77/3.29 (mult(b, mult(b, mult(i(b), ld(mult(a, b), unit)))) = mult(mult(b, b), mult(i(b), ld(mult(a, b), unit)))),
% 4.77/3.29 inference(unit_resolution,[status(thm)],[981, 977])).
% 4.77/3.29 tff(983,plain,
% 4.77/3.29 (mult(mult(b, b), mult(i(b), ld(mult(a, b), unit))) = mult(b, mult(b, mult(i(b), ld(mult(a, b), unit))))),
% 4.77/3.29 inference(symmetry,[status(thm)],[982])).
% 4.77/3.29 tff(984,plain,
% 4.77/3.29 (mult(mult(b, b), mult(i(b), ld(mult(a, b), unit))) = mult(mult(unit, b), ld(mult(a, b), unit))),
% 4.77/3.29 inference(transitivity,[status(thm)],[983, 963, 749])).
% 4.77/3.29 tff(985,plain,
% 4.77/3.29 (mult(b, mult(mult(i(b), ld(mult(a, b), unit)), b)) = mult(unit, mult(ld(mult(a, b), unit), b))),
% 4.77/3.29 inference(transitivity,[status(thm)],[740, 686, 672])).
% 4.77/3.29 tff(986,plain,
% 4.77/3.29 ((mult(b, mult(mult(i(b), ld(mult(a, b), unit)), b)) = mult(mult(b, b), mult(i(b), ld(mult(a, b), unit)))) <=> (mult(unit, mult(ld(mult(a, b), unit), b)) = mult(mult(unit, b), ld(mult(a, b), unit)))),
% 4.77/3.29 inference(monotonicity,[status(thm)],[985, 984])).
% 4.77/3.29 tff(987,plain,
% 4.77/3.29 ((mult(unit, mult(ld(mult(a, b), unit), b)) = mult(mult(unit, b), ld(mult(a, b), unit))) <=> (mult(b, mult(mult(i(b), ld(mult(a, b), unit)), b)) = mult(mult(b, b), mult(i(b), ld(mult(a, b), unit))))),
% 4.77/3.29 inference(symmetry,[status(thm)],[986])).
% 4.77/3.29 tff(988,plain,
% 4.77/3.29 ((mult(unit, mult(ld(mult(a, b), unit), b)) = mult(mult(unit, b), ld(mult(a, b), unit))) <=> (mult(mult(b, b), mult(mult(mult(i(b), ld(mult(a, b), unit)), b), i(b))) = mult(mult(mult(b, b), i(b)), mult(mult(i(b), ld(mult(a, b), unit)), b)))),
% 4.77/3.29 inference(transitivity,[status(thm)],[987, 747])).
% 4.77/3.29 tff(989,plain,
% 4.77/3.29 ((~(mult(unit, mult(ld(mult(a, b), unit), b)) = mult(mult(unit, b), ld(mult(a, b), unit)))) <=> (~(mult(mult(b, b), mult(mult(mult(i(b), ld(mult(a, b), unit)), b), i(b))) = mult(mult(mult(b, b), i(b)), mult(mult(i(b), ld(mult(a, b), unit)), b))))),
% 4.77/3.29 inference(monotonicity,[status(thm)],[988])).
% 4.77/3.29 tff(990,plain,
% 4.77/3.29 ((~(mult(b, mult(mult(ld(mult(a, b), unit), b), i(b))) = mult(mult(b, i(b)), mult(ld(mult(a, b), unit), b)))) <=> (~(mult(unit, mult(ld(mult(a, b), unit), b)) = mult(mult(unit, b), ld(mult(a, b), unit))))),
% 4.77/3.29 inference(monotonicity,[status(thm)],[974])).
% 4.77/3.29 tff(991,plain,
% 4.77/3.29 (~(mult(unit, mult(ld(mult(a, b), unit), b)) = mult(mult(unit, b), ld(mult(a, b), unit)))),
% 4.77/3.29 inference(modus_ponens,[status(thm)],[681, 990])).
% 4.77/3.29 tff(992,plain,
% 4.77/3.29 (~(mult(mult(b, b), mult(mult(mult(i(b), ld(mult(a, b), unit)), b), i(b))) = mult(mult(mult(b, b), i(b)), mult(mult(i(b), ld(mult(a, b), unit)), b)))),
% 4.77/3.29 inference(modus_ponens,[status(thm)],[991, 989])).
% 4.77/3.29 tff(993,plain,
% 4.77/3.29 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(mult(b, b), mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b))) = mult(mult(mult(b, b), i(b)), mult(mult(i(b), ld(mult(a, b), unit)), b))) | (mult(mult(b, b), mult(mult(mult(i(b), ld(mult(a, b), unit)), b), i(b))) = mult(mult(mult(b, b), i(b)), mult(mult(i(b), ld(mult(a, b), unit)), b))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(b, b), mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b))) = mult(mult(mult(b, b), i(b)), mult(mult(i(b), ld(mult(a, b), unit)), b))) | (mult(mult(b, b), mult(mult(mult(i(b), ld(mult(a, b), unit)), b), i(b))) = mult(mult(mult(b, b), i(b)), mult(mult(i(b), ld(mult(a, b), unit)), b))))),
% 4.77/3.29 inference(rewrite,[status(thm)],[])).
% 4.77/3.29 tff(994,plain,
% 4.77/3.29 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(mult(b, b), mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b))) = mult(mult(mult(b, b), i(b)), mult(mult(i(b), ld(mult(a, b), unit)), b))) | (mult(mult(b, b), mult(mult(mult(i(b), ld(mult(a, b), unit)), b), i(b))) = mult(mult(mult(b, b), i(b)), mult(mult(i(b), ld(mult(a, b), unit)), b))))),
% 4.77/3.29 inference(quant_inst,[status(thm)],[])).
% 4.77/3.29 tff(995,plain,
% 4.77/3.29 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(b, b), mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b))) = mult(mult(mult(b, b), i(b)), mult(mult(i(b), ld(mult(a, b), unit)), b))) | (mult(mult(b, b), mult(mult(mult(i(b), ld(mult(a, b), unit)), b), i(b))) = mult(mult(mult(b, b), i(b)), mult(mult(i(b), ld(mult(a, b), unit)), b)))),
% 4.77/3.29 inference(modus_ponens,[status(thm)],[994, 993])).
% 4.77/3.29 tff(996,plain,
% 4.77/3.29 ((mult(mult(b, b), mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b))) = mult(mult(mult(b, b), i(b)), mult(mult(i(b), ld(mult(a, b), unit)), b))) | (mult(mult(b, b), mult(mult(mult(i(b), ld(mult(a, b), unit)), b), i(b))) = mult(mult(mult(b, b), i(b)), mult(mult(i(b), ld(mult(a, b), unit)), b)))),
% 4.77/3.29 inference(unit_resolution,[status(thm)],[995, 51])).
% 4.77/3.29 tff(997,plain,
% 4.77/3.29 (mult(mult(b, b), mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b))) = mult(mult(mult(b, b), i(b)), mult(mult(i(b), ld(mult(a, b), unit)), b))),
% 4.77/3.29 inference(unit_resolution,[status(thm)],[996, 992])).
% 4.77/3.29 tff(998,plain,
% 4.77/3.29 (mult(mult(b, b), mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b))) = mult(ld(mult(a, b), unit), b)),
% 4.77/3.29 inference(transitivity,[status(thm)],[997, 738, 686, 672, 495])).
% 4.77/3.29 tff(999,plain,
% 4.77/3.29 (mult(mult(mult(b, b), mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b))), a) = mult(mult(ld(mult(a, b), unit), b), a)),
% 4.77/3.29 inference(monotonicity,[status(thm)],[998])).
% 4.77/3.29 tff(1000,plain,
% 4.77/3.29 (mult(mult(mult(b, b), mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b))), a) = mult(mult(unit, mult(ld(mult(a, b), unit), b)), a)),
% 4.77/3.29 inference(transitivity,[status(thm)],[999, 671])).
% 4.77/3.29 tff(1001,plain,
% 4.77/3.29 (mult(unit, mult(a, mult(ld(mult(a, b), unit), b))) = mult(unit, unit)),
% 4.77/3.29 inference(monotonicity,[status(thm)],[474])).
% 4.77/3.29 tff(1002,plain,
% 4.77/3.29 (mult(unit, unit) = mult(unit, mult(a, mult(ld(mult(a, b), unit), b)))),
% 4.77/3.29 inference(symmetry,[status(thm)],[1001])).
% 4.77/3.29 tff(1003,plain,
% 4.77/3.29 (unit = mult(unit, unit)),
% 4.77/3.29 inference(symmetry,[status(thm)],[69])).
% 4.77/3.29 tff(1004,plain,
% 4.77/3.29 (mult(mult(b, b), mult(mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)), a)) = mult(unit, mult(a, mult(ld(mult(a, b), unit), b)))),
% 4.77/3.29 inference(transitivity,[status(thm)],[669, 399, 386, 19, 1003, 1002])).
% 4.77/3.29 tff(1005,plain,
% 4.77/3.29 ((mult(mult(b, b), mult(mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)), a)) = mult(mult(mult(b, b), mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b))), a)) <=> (mult(unit, mult(a, mult(ld(mult(a, b), unit), b))) = mult(mult(unit, mult(ld(mult(a, b), unit), b)), a))),
% 4.77/3.29 inference(monotonicity,[status(thm)],[1004, 1000])).
% 4.77/3.29 tff(1006,plain,
% 4.77/3.29 ((mult(unit, mult(a, mult(ld(mult(a, b), unit), b))) = mult(mult(unit, mult(ld(mult(a, b), unit), b)), a)) <=> (mult(mult(b, b), mult(mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)), a)) = mult(mult(mult(b, b), mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b))), a))),
% 4.77/3.29 inference(symmetry,[status(thm)],[1005])).
% 4.77/3.29 tff(1007,plain,
% 4.77/3.29 (mult(mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b)), i(b)) = mult(i(b), i(b))),
% 4.77/3.29 inference(monotonicity,[status(thm)],[472])).
% 4.77/3.29 tff(1008,assumption,(mult(a, mult(mult(mult(i(b), ld(mult(a, b), unit)), b), i(b))) = mult(mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b)), i(b))), introduced(assumption)).
% 4.77/3.29 tff(1009,plain,
% 4.77/3.29 (mult(a, mult(i(b), ld(mult(a, b), unit))) = mult(a, mult(mult(mult(i(b), ld(mult(a, b), unit)), b), i(b)))),
% 4.77/3.29 inference(monotonicity,[status(thm)],[836])).
% 4.77/3.29 tff(1010,plain,
% 4.77/3.29 (mult(a, mult(i(b), ld(mult(a, b), unit))) = mult(i(b), i(b))),
% 4.77/3.29 inference(transitivity,[status(thm)],[1009, 1008, 1007])).
% 4.77/3.29 tff(1011,plain,
% 4.77/3.29 (mult(mult(a, mult(i(b), ld(mult(a, b), unit))), b) = mult(mult(i(b), i(b)), b)),
% 4.77/3.29 inference(monotonicity,[status(thm)],[1010])).
% 4.77/3.29 tff(1012,plain,
% 4.77/3.29 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(a, i(b)), mult(mult(a, i(b)), mult(ld(mult(a, b), unit), b))) = mult(ld(mult(a, b), unit), b))),
% 4.77/3.29 inference(quant_inst,[status(thm)],[])).
% 4.77/3.29 tff(1013,plain,
% 4.77/3.29 (ld(mult(a, i(b)), mult(mult(a, i(b)), mult(ld(mult(a, b), unit), b))) = mult(ld(mult(a, b), unit), b)),
% 4.77/3.29 inference(unit_resolution,[status(thm)],[1012, 251])).
% 4.77/3.29 tff(1014,plain,
% 4.77/3.29 (mult(mult(a, i(b)), mult(ld(mult(a, b), unit), b)) = mult(mult(a, i(b)), i(a))),
% 4.77/3.29 inference(monotonicity,[status(thm)],[528])).
% 4.77/3.29 tff(1015,plain,
% 4.77/3.29 (mult(mult(a, i(b)), i(a)) = mult(mult(a, i(b)), mult(ld(mult(a, b), unit), b))),
% 4.77/3.29 inference(symmetry,[status(thm)],[1014])).
% 4.77/3.29 tff(1016,plain,
% 4.77/3.29 (mult(mult(mult(a, b), i(b)), ld(mult(a, b), unit)) = mult(a, ld(mult(a, b), unit))),
% 4.77/3.29 inference(symmetry,[status(thm)],[874])).
% 4.77/3.29 tff(1017,plain,
% 4.77/3.29 (mult(mult(mult(a, b), mult(mult(i(b), i(b)), b)), ld(mult(a, b), unit)) = mult(mult(mult(a, b), i(b)), ld(mult(a, b), unit))),
% 4.77/3.29 inference(monotonicity,[status(thm)],[868])).
% 4.77/3.29 tff(1018,assumption,(mult(mult(a, b), mult(mult(mult(i(b), i(b)), b), ld(mult(a, b), unit))) = mult(mult(mult(a, b), mult(mult(i(b), i(b)), b)), ld(mult(a, b), unit))), introduced(assumption)).
% 4.77/3.29 tff(1019,plain,
% 4.77/3.29 (mult(mult(a, b), mult(i(b), ld(mult(a, b), unit))) = mult(a, ld(mult(a, b), unit))),
% 4.80/3.30 inference(transitivity,[status(thm)],[919, 1018, 1017, 1016])).
% 4.80/3.30 tff(1020,plain,
% 4.80/3.30 (mult(mult(mult(a, b), mult(i(b), ld(mult(a, b), unit))), b) = mult(mult(a, ld(mult(a, b), unit)), b)),
% 4.80/3.30 inference(monotonicity,[status(thm)],[1019])).
% 4.80/3.30 tff(1021,assumption,(mult(mult(unit, b), mult(i(b), ld(mult(a, b), unit))) = mult(mult(mult(unit, b), i(b)), ld(mult(a, b), unit))), introduced(assumption)).
% 4.80/3.30 tff(1022,plain,
% 4.80/3.30 (mult(b, mult(i(b), ld(mult(a, b), unit))) = ld(mult(a, b), unit)),
% 4.80/3.30 inference(transitivity,[status(thm)],[944, 1021, 750, 235])).
% 4.80/3.30 tff(1023,plain,
% 4.80/3.30 (mult(mult(a, b), mult(b, mult(i(b), ld(mult(a, b), unit)))) = mult(mult(a, b), ld(mult(a, b), unit))),
% 4.80/3.30 inference(monotonicity,[status(thm)],[1022])).
% 4.80/3.30 tff(1024,plain,
% 4.80/3.30 (mult(mult(a, b), mult(b, mult(i(b), ld(mult(a, b), unit)))) = mult(a, mult(ld(mult(a, b), unit), b))),
% 4.80/3.30 inference(transitivity,[status(thm)],[1023, 431])).
% 4.80/3.30 tff(1025,plain,
% 4.80/3.30 ((mult(mult(a, b), mult(b, mult(i(b), ld(mult(a, b), unit)))) = mult(mult(mult(a, b), mult(i(b), ld(mult(a, b), unit))), b)) <=> (mult(a, mult(ld(mult(a, b), unit), b)) = mult(mult(a, ld(mult(a, b), unit)), b))),
% 4.80/3.30 inference(monotonicity,[status(thm)],[1024, 1020])).
% 4.80/3.30 tff(1026,plain,
% 4.80/3.30 ((mult(a, mult(ld(mult(a, b), unit), b)) = mult(mult(a, ld(mult(a, b), unit)), b)) <=> (mult(mult(a, b), mult(b, mult(i(b), ld(mult(a, b), unit)))) = mult(mult(mult(a, b), mult(i(b), ld(mult(a, b), unit))), b))),
% 4.80/3.30 inference(symmetry,[status(thm)],[1025])).
% 4.80/3.30 tff(1027,plain,
% 4.80/3.30 ((~(mult(a, mult(ld(mult(a, b), unit), b)) = mult(mult(a, ld(mult(a, b), unit)), b))) <=> (~(mult(mult(a, b), mult(b, mult(i(b), ld(mult(a, b), unit)))) = mult(mult(mult(a, b), mult(i(b), ld(mult(a, b), unit))), b)))),
% 4.80/3.30 inference(monotonicity,[status(thm)],[1026])).
% 4.80/3.30 tff(1028,plain,
% 4.80/3.30 (~(mult(mult(a, b), mult(b, mult(i(b), ld(mult(a, b), unit)))) = mult(mult(mult(a, b), mult(i(b), ld(mult(a, b), unit))), b))),
% 4.80/3.30 inference(modus_ponens,[status(thm)],[443, 1027])).
% 4.80/3.30 tff(1029,plain,
% 4.80/3.30 (mult(mult(a, b), mult(mult(i(b), ld(mult(a, b), unit)), b)) = mult(mult(mult(a, b), mult(i(b), ld(mult(a, b), unit))), b)),
% 4.80/3.30 inference(unit_resolution,[status(thm)],[956, 1028])).
% 4.80/3.30 tff(1030,plain,
% 4.80/3.30 (mult(mult(mult(a, b), mult(i(b), ld(mult(a, b), unit))), b) = mult(mult(a, b), mult(mult(i(b), ld(mult(a, b), unit)), b))),
% 4.80/3.30 inference(symmetry,[status(thm)],[1029])).
% 4.80/3.30 tff(1031,plain,
% 4.80/3.30 (mult(mult(a, ld(mult(a, b), unit)), b) = mult(mult(mult(a, b), mult(i(b), ld(mult(a, b), unit))), b)),
% 4.80/3.30 inference(symmetry,[status(thm)],[1020])).
% 4.80/3.30 tff(1032,plain,
% 4.80/3.30 (mult(mult(a, b), mult(mult(b, ld(mult(a, b), unit)), i(b))) = mult(mult(a, b), mult(mult(i(b), ld(mult(a, b), unit)), b))),
% 4.80/3.30 inference(transitivity,[status(thm)],[942, 929, 439, 1031, 1030])).
% 4.80/3.30 tff(1033,plain,
% 4.80/3.30 (ld(mult(a, b), mult(mult(a, b), mult(mult(b, ld(mult(a, b), unit)), i(b)))) = ld(mult(a, b), mult(mult(a, b), mult(mult(i(b), ld(mult(a, b), unit)), b)))),
% 4.80/3.30 inference(monotonicity,[status(thm)],[1032])).
% 4.80/3.30 tff(1034,plain,
% 4.80/3.30 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(a, b), mult(mult(a, b), mult(mult(b, ld(mult(a, b), unit)), i(b)))) = mult(mult(b, ld(mult(a, b), unit)), i(b)))),
% 4.80/3.30 inference(quant_inst,[status(thm)],[])).
% 4.80/3.30 tff(1035,plain,
% 4.80/3.30 (ld(mult(a, b), mult(mult(a, b), mult(mult(b, ld(mult(a, b), unit)), i(b)))) = mult(mult(b, ld(mult(a, b), unit)), i(b))),
% 4.80/3.30 inference(unit_resolution,[status(thm)],[1034, 251])).
% 4.80/3.30 tff(1036,plain,
% 4.80/3.30 (mult(mult(b, ld(mult(a, b), unit)), i(b)) = ld(mult(a, b), mult(mult(a, b), mult(mult(b, ld(mult(a, b), unit)), i(b))))),
% 4.80/3.30 inference(symmetry,[status(thm)],[1035])).
% 4.80/3.30 tff(1037,plain,
% 4.80/3.30 (mult(mult(b, ld(mult(a, b), unit)), i(b)) = mult(mult(i(b), ld(mult(a, b), unit)), b)),
% 4.80/3.30 inference(transitivity,[status(thm)],[1036, 1033, 907])).
% 4.80/3.30 tff(1038,plain,
% 4.80/3.30 (mult(mult(mult(b, ld(mult(a, b), unit)), i(b)), i(b)) = mult(mult(mult(i(b), ld(mult(a, b), unit)), b), i(b))),
% 4.80/3.30 inference(monotonicity,[status(thm)],[1037])).
% 4.80/3.30 tff(1039,plain,
% 4.80/3.30 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(b, ld(mult(a, b), unit)), mult(i(b), i(b))) = mult(mult(mult(b, ld(mult(a, b), unit)), i(b)), i(b)))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(b, ld(mult(a, b), unit)), mult(i(b), i(b))) = mult(mult(mult(b, ld(mult(a, b), unit)), i(b)), i(b))))),
% 4.80/3.30 inference(rewrite,[status(thm)],[])).
% 4.80/3.30 tff(1040,plain,
% 4.80/3.30 (((mult(mult(b, ld(mult(a, b), unit)), mult(i(b), i(b))) = mult(mult(mult(b, ld(mult(a, b), unit)), i(b)), i(b))) | (mult(mult(b, ld(mult(a, b), unit)), mult(i(b), i(b))) = mult(mult(mult(b, ld(mult(a, b), unit)), i(b)), i(b)))) <=> (mult(mult(b, ld(mult(a, b), unit)), mult(i(b), i(b))) = mult(mult(mult(b, ld(mult(a, b), unit)), i(b)), i(b)))),
% 4.80/3.30 inference(rewrite,[status(thm)],[])).
% 4.80/3.30 tff(1041,plain,
% 4.80/3.30 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(mult(b, ld(mult(a, b), unit)), mult(i(b), i(b))) = mult(mult(mult(b, ld(mult(a, b), unit)), i(b)), i(b))) | (mult(mult(b, ld(mult(a, b), unit)), mult(i(b), i(b))) = mult(mult(mult(b, ld(mult(a, b), unit)), i(b)), i(b))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(b, ld(mult(a, b), unit)), mult(i(b), i(b))) = mult(mult(mult(b, ld(mult(a, b), unit)), i(b)), i(b))))),
% 4.80/3.30 inference(monotonicity,[status(thm)],[1040])).
% 4.80/3.30 tff(1042,plain,
% 4.80/3.30 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(mult(b, ld(mult(a, b), unit)), mult(i(b), i(b))) = mult(mult(mult(b, ld(mult(a, b), unit)), i(b)), i(b))) | (mult(mult(b, ld(mult(a, b), unit)), mult(i(b), i(b))) = mult(mult(mult(b, ld(mult(a, b), unit)), i(b)), i(b))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(b, ld(mult(a, b), unit)), mult(i(b), i(b))) = mult(mult(mult(b, ld(mult(a, b), unit)), i(b)), i(b))))),
% 4.80/3.30 inference(transitivity,[status(thm)],[1041, 1039])).
% 4.80/3.30 tff(1043,plain,
% 4.80/3.30 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(mult(b, ld(mult(a, b), unit)), mult(i(b), i(b))) = mult(mult(mult(b, ld(mult(a, b), unit)), i(b)), i(b))) | (mult(mult(b, ld(mult(a, b), unit)), mult(i(b), i(b))) = mult(mult(mult(b, ld(mult(a, b), unit)), i(b)), i(b))))),
% 4.80/3.30 inference(quant_inst,[status(thm)],[])).
% 4.80/3.30 tff(1044,plain,
% 4.80/3.30 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(b, ld(mult(a, b), unit)), mult(i(b), i(b))) = mult(mult(mult(b, ld(mult(a, b), unit)), i(b)), i(b)))),
% 4.80/3.30 inference(modus_ponens,[status(thm)],[1043, 1042])).
% 4.80/3.30 tff(1045,plain,
% 4.80/3.30 (mult(mult(b, ld(mult(a, b), unit)), mult(i(b), i(b))) = mult(mult(mult(b, ld(mult(a, b), unit)), i(b)), i(b))),
% 4.80/3.30 inference(unit_resolution,[status(thm)],[1044, 51])).
% 4.80/3.30 tff(1046,plain,
% 4.80/3.30 (mult(mult(b, ld(mult(a, b), unit)), mult(i(b), i(b))) = mult(i(b), ld(mult(a, b), unit))),
% 4.80/3.30 inference(transitivity,[status(thm)],[1045, 1038, 618, 606, 605, 604, 598, 586])).
% 4.80/3.30 tff(1047,plain,
% 4.80/3.30 (mult(mult(a, b), mult(mult(b, ld(mult(a, b), unit)), mult(i(b), i(b)))) = mult(mult(a, b), mult(i(b), ld(mult(a, b), unit)))),
% 4.80/3.30 inference(monotonicity,[status(thm)],[1046])).
% 4.80/3.30 tff(1048,plain,
% 4.80/3.30 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | ((mult(mult(a, b), mult(i(b), mult(b, ld(mult(a, b), unit)))) = mult(mult(mult(a, b), mult(b, ld(mult(a, b), unit))), i(b))) | (mult(mult(a, b), mult(i(b), mult(b, ld(mult(a, b), unit)))) = mult(mult(mult(a, b), i(b)), mult(b, ld(mult(a, b), unit)))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | (mult(mult(a, b), mult(i(b), mult(b, ld(mult(a, b), unit)))) = mult(mult(mult(a, b), mult(b, ld(mult(a, b), unit))), i(b))) | (mult(mult(a, b), mult(i(b), mult(b, ld(mult(a, b), unit)))) = mult(mult(mult(a, b), i(b)), mult(b, ld(mult(a, b), unit)))))),
% 4.80/3.30 inference(rewrite,[status(thm)],[])).
% 4.80/3.30 tff(1049,plain,
% 4.80/3.30 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | ((mult(mult(a, b), mult(i(b), mult(b, ld(mult(a, b), unit)))) = mult(mult(mult(a, b), mult(b, ld(mult(a, b), unit))), i(b))) | (mult(mult(a, b), mult(i(b), mult(b, ld(mult(a, b), unit)))) = mult(mult(mult(a, b), i(b)), mult(b, ld(mult(a, b), unit)))))),
% 4.80/3.30 inference(quant_inst,[status(thm)],[])).
% 4.80/3.30 tff(1050,plain,
% 4.80/3.30 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | (mult(mult(a, b), mult(i(b), mult(b, ld(mult(a, b), unit)))) = mult(mult(mult(a, b), mult(b, ld(mult(a, b), unit))), i(b))) | (mult(mult(a, b), mult(i(b), mult(b, ld(mult(a, b), unit)))) = mult(mult(mult(a, b), i(b)), mult(b, ld(mult(a, b), unit))))),
% 4.80/3.30 inference(modus_ponens,[status(thm)],[1049, 1048])).
% 4.80/3.30 tff(1051,plain,
% 4.80/3.30 ((mult(mult(a, b), mult(i(b), mult(b, ld(mult(a, b), unit)))) = mult(mult(mult(a, b), mult(b, ld(mult(a, b), unit))), i(b))) | (mult(mult(a, b), mult(i(b), mult(b, ld(mult(a, b), unit)))) = mult(mult(mult(a, b), i(b)), mult(b, ld(mult(a, b), unit))))),
% 4.80/3.30 inference(unit_resolution,[status(thm)],[1050, 132])).
% 4.80/3.30 tff(1052,plain,
% 4.80/3.30 (mult(mult(a, b), mult(i(b), mult(b, ld(mult(a, b), unit)))) = mult(mult(mult(a, b), mult(b, ld(mult(a, b), unit))), i(b))),
% 4.80/3.30 inference(unit_resolution,[status(thm)],[1051, 937])).
% 4.80/3.30 tff(1053,plain,
% 4.80/3.30 (mult(mult(mult(a, b), mult(b, ld(mult(a, b), unit))), i(b)) = mult(mult(a, b), mult(i(b), mult(b, ld(mult(a, b), unit))))),
% 4.80/3.30 inference(symmetry,[status(thm)],[1052])).
% 4.80/3.30 tff(1054,plain,
% 4.80/3.30 (mult(mult(mult(a, b), mult(b, ld(mult(a, b), unit))), i(b)) = unit),
% 4.80/3.30 inference(transitivity,[status(thm)],[1053, 932, 257])).
% 4.80/3.30 tff(1055,plain,
% 4.80/3.30 (mult(mult(mult(mult(a, b), mult(b, ld(mult(a, b), unit))), i(b)), i(b)) = mult(unit, i(b))),
% 4.80/3.30 inference(monotonicity,[status(thm)],[1054])).
% 4.80/3.30 tff(1056,plain,
% 4.80/3.30 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(mult(a, b), mult(b, ld(mult(a, b), unit))), mult(i(b), i(b))) = mult(mult(mult(mult(a, b), mult(b, ld(mult(a, b), unit))), i(b)), i(b)))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(mult(a, b), mult(b, ld(mult(a, b), unit))), mult(i(b), i(b))) = mult(mult(mult(mult(a, b), mult(b, ld(mult(a, b), unit))), i(b)), i(b))))),
% 4.80/3.30 inference(rewrite,[status(thm)],[])).
% 4.80/3.30 tff(1057,plain,
% 4.80/3.30 (((mult(mult(mult(a, b), mult(b, ld(mult(a, b), unit))), mult(i(b), i(b))) = mult(mult(mult(mult(a, b), mult(b, ld(mult(a, b), unit))), i(b)), i(b))) | (mult(mult(mult(a, b), mult(b, ld(mult(a, b), unit))), mult(i(b), i(b))) = mult(mult(mult(mult(a, b), mult(b, ld(mult(a, b), unit))), i(b)), i(b)))) <=> (mult(mult(mult(a, b), mult(b, ld(mult(a, b), unit))), mult(i(b), i(b))) = mult(mult(mult(mult(a, b), mult(b, ld(mult(a, b), unit))), i(b)), i(b)))),
% 4.80/3.30 inference(rewrite,[status(thm)],[])).
% 4.80/3.30 tff(1058,plain,
% 4.80/3.30 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(mult(mult(a, b), mult(b, ld(mult(a, b), unit))), mult(i(b), i(b))) = mult(mult(mult(mult(a, b), mult(b, ld(mult(a, b), unit))), i(b)), i(b))) | (mult(mult(mult(a, b), mult(b, ld(mult(a, b), unit))), mult(i(b), i(b))) = mult(mult(mult(mult(a, b), mult(b, ld(mult(a, b), unit))), i(b)), i(b))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(mult(a, b), mult(b, ld(mult(a, b), unit))), mult(i(b), i(b))) = mult(mult(mult(mult(a, b), mult(b, ld(mult(a, b), unit))), i(b)), i(b))))),
% 4.80/3.30 inference(monotonicity,[status(thm)],[1057])).
% 4.80/3.31 tff(1059,plain,
% 4.80/3.31 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(mult(mult(a, b), mult(b, ld(mult(a, b), unit))), mult(i(b), i(b))) = mult(mult(mult(mult(a, b), mult(b, ld(mult(a, b), unit))), i(b)), i(b))) | (mult(mult(mult(a, b), mult(b, ld(mult(a, b), unit))), mult(i(b), i(b))) = mult(mult(mult(mult(a, b), mult(b, ld(mult(a, b), unit))), i(b)), i(b))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(mult(a, b), mult(b, ld(mult(a, b), unit))), mult(i(b), i(b))) = mult(mult(mult(mult(a, b), mult(b, ld(mult(a, b), unit))), i(b)), i(b))))),
% 4.80/3.31 inference(transitivity,[status(thm)],[1058, 1056])).
% 4.80/3.31 tff(1060,plain,
% 4.80/3.31 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(mult(mult(a, b), mult(b, ld(mult(a, b), unit))), mult(i(b), i(b))) = mult(mult(mult(mult(a, b), mult(b, ld(mult(a, b), unit))), i(b)), i(b))) | (mult(mult(mult(a, b), mult(b, ld(mult(a, b), unit))), mult(i(b), i(b))) = mult(mult(mult(mult(a, b), mult(b, ld(mult(a, b), unit))), i(b)), i(b))))),
% 4.80/3.31 inference(quant_inst,[status(thm)],[])).
% 4.80/3.31 tff(1061,plain,
% 4.80/3.31 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(mult(a, b), mult(b, ld(mult(a, b), unit))), mult(i(b), i(b))) = mult(mult(mult(mult(a, b), mult(b, ld(mult(a, b), unit))), i(b)), i(b)))),
% 4.80/3.31 inference(modus_ponens,[status(thm)],[1060, 1059])).
% 4.80/3.31 tff(1062,plain,
% 4.80/3.31 (mult(mult(mult(a, b), mult(b, ld(mult(a, b), unit))), mult(i(b), i(b))) = mult(mult(mult(mult(a, b), mult(b, ld(mult(a, b), unit))), i(b)), i(b))),
% 4.80/3.31 inference(unit_resolution,[status(thm)],[1061, 51])).
% 4.80/3.31 tff(1063,plain,
% 4.80/3.31 (mult(mult(mult(a, b), mult(b, ld(mult(a, b), unit))), mult(i(b), i(b))) = mult(mult(a, mult(ld(mult(a, b), unit), b)), i(b))),
% 4.80/3.31 inference(transitivity,[status(thm)],[1062, 1055, 766])).
% 4.80/3.31 tff(1064,plain,
% 4.80/3.31 (mult(a, ld(mult(a, b), unit)) = mult(a, mult(mult(ld(mult(a, b), unit), b), i(b)))),
% 4.80/3.31 inference(symmetry,[status(thm)],[875])).
% 4.80/3.31 tff(1065,plain,
% 4.80/3.31 (mult(mult(a, b), mult(mult(b, ld(mult(a, b), unit)), mult(i(b), i(b)))) = mult(a, mult(mult(ld(mult(a, b), unit), b), i(b)))),
% 4.80/3.31 inference(transitivity,[status(thm)],[1047, 919, 1018, 1017, 1016, 1064])).
% 4.80/3.31 tff(1066,plain,
% 4.80/3.31 ((mult(mult(a, b), mult(mult(b, ld(mult(a, b), unit)), mult(i(b), i(b)))) = mult(mult(mult(a, b), mult(b, ld(mult(a, b), unit))), mult(i(b), i(b)))) <=> (mult(a, mult(mult(ld(mult(a, b), unit), b), i(b))) = mult(mult(a, mult(ld(mult(a, b), unit), b)), i(b)))),
% 4.80/3.31 inference(monotonicity,[status(thm)],[1065, 1063])).
% 4.80/3.31 tff(1067,plain,
% 4.80/3.31 ((mult(a, mult(mult(ld(mult(a, b), unit), b), i(b))) = mult(mult(a, mult(ld(mult(a, b), unit), b)), i(b))) <=> (mult(mult(a, b), mult(mult(b, ld(mult(a, b), unit)), mult(i(b), i(b)))) = mult(mult(mult(a, b), mult(b, ld(mult(a, b), unit))), mult(i(b), i(b))))),
% 4.80/3.31 inference(symmetry,[status(thm)],[1066])).
% 4.80/3.31 tff(1068,plain,
% 4.80/3.31 ((~(mult(a, mult(mult(ld(mult(a, b), unit), b), i(b))) = mult(mult(a, mult(ld(mult(a, b), unit), b)), i(b)))) <=> (~(mult(mult(a, b), mult(mult(b, ld(mult(a, b), unit)), mult(i(b), i(b)))) = mult(mult(mult(a, b), mult(b, ld(mult(a, b), unit))), mult(i(b), i(b)))))),
% 4.80/3.31 inference(monotonicity,[status(thm)],[1067])).
% 4.80/3.31 tff(1069,plain,
% 4.80/3.31 (~(mult(mult(a, b), mult(mult(b, ld(mult(a, b), unit)), mult(i(b), i(b)))) = mult(mult(mult(a, b), mult(b, ld(mult(a, b), unit))), mult(i(b), i(b))))),
% 4.80/3.31 inference(modus_ponens,[status(thm)],[902, 1068])).
% 4.80/3.31 tff(1070,plain,
% 4.80/3.31 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | ((mult(mult(a, b), mult(mult(b, ld(mult(a, b), unit)), mult(i(b), i(b)))) = mult(mult(mult(a, b), mult(i(b), i(b))), mult(b, ld(mult(a, b), unit)))) | (mult(mult(a, b), mult(mult(b, ld(mult(a, b), unit)), mult(i(b), i(b)))) = mult(mult(mult(a, b), mult(b, ld(mult(a, b), unit))), mult(i(b), i(b)))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | (mult(mult(a, b), mult(mult(b, ld(mult(a, b), unit)), mult(i(b), i(b)))) = mult(mult(mult(a, b), mult(i(b), i(b))), mult(b, ld(mult(a, b), unit)))) | (mult(mult(a, b), mult(mult(b, ld(mult(a, b), unit)), mult(i(b), i(b)))) = mult(mult(mult(a, b), mult(b, ld(mult(a, b), unit))), mult(i(b), i(b)))))),
% 4.80/3.31 inference(rewrite,[status(thm)],[])).
% 4.80/3.31 tff(1071,plain,
% 4.80/3.31 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | ((mult(mult(a, b), mult(mult(b, ld(mult(a, b), unit)), mult(i(b), i(b)))) = mult(mult(mult(a, b), mult(i(b), i(b))), mult(b, ld(mult(a, b), unit)))) | (mult(mult(a, b), mult(mult(b, ld(mult(a, b), unit)), mult(i(b), i(b)))) = mult(mult(mult(a, b), mult(b, ld(mult(a, b), unit))), mult(i(b), i(b)))))),
% 4.80/3.31 inference(quant_inst,[status(thm)],[])).
% 4.80/3.31 tff(1072,plain,
% 4.80/3.31 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | (mult(mult(a, b), mult(mult(b, ld(mult(a, b), unit)), mult(i(b), i(b)))) = mult(mult(mult(a, b), mult(i(b), i(b))), mult(b, ld(mult(a, b), unit)))) | (mult(mult(a, b), mult(mult(b, ld(mult(a, b), unit)), mult(i(b), i(b)))) = mult(mult(mult(a, b), mult(b, ld(mult(a, b), unit))), mult(i(b), i(b))))),
% 4.80/3.31 inference(modus_ponens,[status(thm)],[1071, 1070])).
% 4.80/3.31 tff(1073,plain,
% 4.80/3.31 ((mult(mult(a, b), mult(mult(b, ld(mult(a, b), unit)), mult(i(b), i(b)))) = mult(mult(mult(a, b), mult(i(b), i(b))), mult(b, ld(mult(a, b), unit)))) | (mult(mult(a, b), mult(mult(b, ld(mult(a, b), unit)), mult(i(b), i(b)))) = mult(mult(mult(a, b), mult(b, ld(mult(a, b), unit))), mult(i(b), i(b))))),
% 4.80/3.31 inference(unit_resolution,[status(thm)],[1072, 132])).
% 4.80/3.31 tff(1074,plain,
% 4.80/3.31 (mult(mult(a, b), mult(mult(b, ld(mult(a, b), unit)), mult(i(b), i(b)))) = mult(mult(mult(a, b), mult(i(b), i(b))), mult(b, ld(mult(a, b), unit)))),
% 4.80/3.31 inference(unit_resolution,[status(thm)],[1073, 1069])).
% 4.80/3.31 tff(1075,plain,
% 4.80/3.31 (mult(mult(mult(a, b), mult(i(b), i(b))), mult(b, ld(mult(a, b), unit))) = mult(mult(a, b), mult(mult(b, ld(mult(a, b), unit)), mult(i(b), i(b))))),
% 4.80/3.31 inference(symmetry,[status(thm)],[1074])).
% 4.80/3.31 tff(1076,plain,
% 4.80/3.31 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(a, b), mult(i(b), i(b))) = mult(mult(mult(a, b), i(b)), i(b)))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(a, b), mult(i(b), i(b))) = mult(mult(mult(a, b), i(b)), i(b))))),
% 4.80/3.31 inference(rewrite,[status(thm)],[])).
% 4.80/3.31 tff(1077,plain,
% 4.80/3.31 (((mult(mult(a, b), mult(i(b), i(b))) = mult(mult(mult(a, b), i(b)), i(b))) | (mult(mult(a, b), mult(i(b), i(b))) = mult(mult(mult(a, b), i(b)), i(b)))) <=> (mult(mult(a, b), mult(i(b), i(b))) = mult(mult(mult(a, b), i(b)), i(b)))),
% 4.80/3.31 inference(rewrite,[status(thm)],[])).
% 4.80/3.31 tff(1078,plain,
% 4.80/3.31 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(mult(a, b), mult(i(b), i(b))) = mult(mult(mult(a, b), i(b)), i(b))) | (mult(mult(a, b), mult(i(b), i(b))) = mult(mult(mult(a, b), i(b)), i(b))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(a, b), mult(i(b), i(b))) = mult(mult(mult(a, b), i(b)), i(b))))),
% 4.80/3.31 inference(monotonicity,[status(thm)],[1077])).
% 4.80/3.31 tff(1079,plain,
% 4.80/3.31 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(mult(a, b), mult(i(b), i(b))) = mult(mult(mult(a, b), i(b)), i(b))) | (mult(mult(a, b), mult(i(b), i(b))) = mult(mult(mult(a, b), i(b)), i(b))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(a, b), mult(i(b), i(b))) = mult(mult(mult(a, b), i(b)), i(b))))),
% 4.80/3.31 inference(transitivity,[status(thm)],[1078, 1076])).
% 4.80/3.31 tff(1080,plain,
% 4.80/3.31 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(mult(a, b), mult(i(b), i(b))) = mult(mult(mult(a, b), i(b)), i(b))) | (mult(mult(a, b), mult(i(b), i(b))) = mult(mult(mult(a, b), i(b)), i(b))))),
% 4.80/3.31 inference(quant_inst,[status(thm)],[])).
% 4.80/3.31 tff(1081,plain,
% 4.80/3.31 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(a, b), mult(i(b), i(b))) = mult(mult(mult(a, b), i(b)), i(b)))),
% 4.80/3.31 inference(modus_ponens,[status(thm)],[1080, 1079])).
% 4.80/3.31 tff(1082,plain,
% 4.80/3.31 (mult(mult(a, b), mult(i(b), i(b))) = mult(mult(mult(a, b), i(b)), i(b))),
% 4.80/3.31 inference(unit_resolution,[status(thm)],[1081, 51])).
% 4.80/3.31 tff(1083,plain,
% 4.80/3.31 (mult(mult(mult(a, b), i(b)), i(b)) = mult(mult(a, b), mult(i(b), i(b)))),
% 4.80/3.31 inference(symmetry,[status(thm)],[1082])).
% 4.80/3.31 tff(1084,plain,
% 4.80/3.31 (mult(mult(mult(a, b), i(b)), i(b)) = mult(a, i(b))),
% 4.80/3.31 inference(monotonicity,[status(thm)],[232])).
% 4.80/3.31 tff(1085,plain,
% 4.80/3.31 (mult(a, i(b)) = mult(mult(mult(a, b), i(b)), i(b))),
% 4.80/3.31 inference(symmetry,[status(thm)],[1084])).
% 4.80/3.31 tff(1086,plain,
% 4.80/3.31 (mult(a, i(b)) = mult(mult(a, b), mult(i(b), i(b)))),
% 4.80/3.31 inference(transitivity,[status(thm)],[1085, 1083])).
% 4.80/3.31 tff(1087,plain,
% 4.80/3.31 (mult(mult(a, i(b)), mult(b, ld(mult(a, b), unit))) = mult(mult(mult(a, b), mult(i(b), i(b))), mult(b, ld(mult(a, b), unit)))),
% 4.80/3.31 inference(monotonicity,[status(thm)],[1086])).
% 4.80/3.31 tff(1088,plain,
% 4.80/3.31 (mult(mult(a, i(b)), mult(b, ld(mult(a, b), unit))) = mult(mult(a, i(b)), mult(ld(mult(a, b), unit), b))),
% 4.80/3.31 inference(transitivity,[status(thm)],[1087, 1075, 1047, 919, 1018, 1017, 1016, 892, 888, 1015])).
% 4.80/3.31 tff(1089,plain,
% 4.80/3.31 (ld(mult(a, i(b)), mult(mult(a, i(b)), mult(b, ld(mult(a, b), unit)))) = ld(mult(a, i(b)), mult(mult(a, i(b)), mult(ld(mult(a, b), unit), b)))),
% 4.80/3.31 inference(monotonicity,[status(thm)],[1088])).
% 4.80/3.31 tff(1090,plain,
% 4.80/3.31 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(a, i(b)), mult(mult(a, i(b)), mult(b, ld(mult(a, b), unit)))) = mult(b, ld(mult(a, b), unit)))),
% 4.80/3.31 inference(quant_inst,[status(thm)],[])).
% 4.80/3.31 tff(1091,plain,
% 4.80/3.31 (ld(mult(a, i(b)), mult(mult(a, i(b)), mult(b, ld(mult(a, b), unit)))) = mult(b, ld(mult(a, b), unit))),
% 4.80/3.31 inference(unit_resolution,[status(thm)],[1090, 251])).
% 4.80/3.31 tff(1092,plain,
% 4.80/3.31 (mult(b, ld(mult(a, b), unit)) = ld(mult(a, i(b)), mult(mult(a, i(b)), mult(b, ld(mult(a, b), unit))))),
% 4.80/3.31 inference(symmetry,[status(thm)],[1091])).
% 4.80/3.31 tff(1093,plain,
% 4.80/3.31 (mult(b, ld(mult(a, b), unit)) = mult(ld(mult(a, b), unit), b)),
% 4.80/3.31 inference(transitivity,[status(thm)],[1092, 1089, 1013])).
% 4.80/3.31 tff(1094,plain,
% 4.80/3.31 (mult(a, mult(b, ld(mult(a, b), unit))) = mult(a, mult(ld(mult(a, b), unit), b))),
% 4.80/3.31 inference(monotonicity,[status(thm)],[1093])).
% 4.80/3.31 tff(1095,plain,
% 4.80/3.31 (mult(a, mult(ld(mult(a, b), unit), b)) = mult(a, mult(b, ld(mult(a, b), unit)))),
% 4.80/3.31 inference(symmetry,[status(thm)],[1094])).
% 4.80/3.31 tff(1096,plain,
% 4.80/3.31 (mult(a, mult(ld(mult(a, b), unit), b)) = mult(mult(a, ld(mult(a, b), unit)), b)),
% 4.80/3.31 inference(transitivity,[status(thm)],[1095, 439])).
% 4.80/3.31 tff(1097,plain,
% 4.80/3.31 ($false),
% 4.80/3.31 inference(unit_resolution,[status(thm)],[443, 1096])).
% 4.80/3.31 tff(1098,plain,((~(mult(mult(a, b), mult(mult(mult(i(b), i(b)), b), ld(mult(a, b), unit))) = mult(mult(mult(a, b), mult(mult(i(b), i(b)), b)), ld(mult(a, b), unit)))) | (~(mult(mult(unit, b), mult(i(b), ld(mult(a, b), unit))) = mult(mult(mult(unit, b), i(b)), ld(mult(a, b), unit))))), inference(lemma,lemma(discharge,[]))).
% 4.80/3.31 tff(1099,plain,
% 4.80/3.31 (~(mult(mult(a, b), mult(mult(mult(i(b), i(b)), b), ld(mult(a, b), unit))) = mult(mult(mult(a, b), mult(mult(i(b), i(b)), b)), ld(mult(a, b), unit)))),
% 4.80/3.31 inference(unit_resolution,[status(thm)],[1098, 961])).
% 4.80/3.31 tff(1100,plain,
% 4.80/3.31 (mult(mult(a, b), mult(mult(mult(i(b), i(b)), b), ld(mult(a, b), unit))) = mult(mult(mult(a, b), ld(mult(a, b), unit)), mult(mult(i(b), i(b)), b))),
% 4.80/3.31 inference(unit_resolution,[status(thm)],[865, 1099])).
% 4.80/3.31 tff(1101,plain,
% 4.80/3.31 (mult(mult(a, b), mult(i(b), ld(mult(a, b), unit))) = mult(mult(a, mult(ld(mult(a, b), unit), b)), i(b))),
% 4.80/3.31 inference(transitivity,[status(thm)],[919, 1100, 787, 384, 122, 353, 766])).
% 4.80/3.31 tff(1102,plain,
% 4.80/3.31 (mult(mult(unit, b), mult(i(b), ld(mult(a, b), unit))) = mult(b, mult(i(b), ld(mult(a, b), unit)))),
% 4.80/3.31 inference(symmetry,[status(thm)],[944])).
% 4.80/3.31 tff(1103,plain,
% 4.80/3.31 (mult(mult(mult(unit, b), i(b)), ld(mult(a, b), unit)) = mult(mult(unit, b), mult(i(b), ld(mult(a, b), unit)))),
% 4.80/3.31 inference(symmetry,[status(thm)],[961])).
% 4.80/3.31 tff(1104,plain,
% 4.80/3.31 (mult(unit, ld(mult(a, b), unit)) = mult(mult(mult(unit, b), i(b)), ld(mult(a, b), unit))),
% 4.80/3.31 inference(symmetry,[status(thm)],[750])).
% 4.80/3.31 tff(1105,plain,
% 4.80/3.31 (ld(mult(a, b), unit) = mult(b, mult(i(b), ld(mult(a, b), unit)))),
% 4.80/3.31 inference(transitivity,[status(thm)],[268, 1104, 1103, 1102])).
% 4.80/3.31 tff(1106,plain,
% 4.80/3.31 (mult(a, ld(mult(a, b), unit)) = mult(a, mult(b, mult(i(b), ld(mult(a, b), unit))))),
% 4.80/3.31 inference(monotonicity,[status(thm)],[1105])).
% 4.80/3.31 tff(1107,plain,
% 4.80/3.31 (mult(a, mult(b, mult(i(b), ld(mult(a, b), unit)))) = mult(a, ld(mult(a, b), unit))),
% 4.80/3.31 inference(symmetry,[status(thm)],[1106])).
% 4.80/3.31 tff(1108,plain,
% 4.80/3.31 (mult(a, mult(b, mult(i(b), ld(mult(a, b), unit)))) = mult(a, mult(mult(ld(mult(a, b), unit), b), i(b)))),
% 4.80/3.31 inference(transitivity,[status(thm)],[1107, 1064])).
% 4.80/3.31 tff(1109,plain,
% 4.80/3.31 ((mult(a, mult(b, mult(i(b), ld(mult(a, b), unit)))) = mult(mult(a, b), mult(i(b), ld(mult(a, b), unit)))) <=> (mult(a, mult(mult(ld(mult(a, b), unit), b), i(b))) = mult(mult(a, mult(ld(mult(a, b), unit), b)), i(b)))),
% 4.80/3.31 inference(monotonicity,[status(thm)],[1108, 1101])).
% 4.80/3.31 tff(1110,plain,
% 4.80/3.31 ((mult(a, mult(mult(ld(mult(a, b), unit), b), i(b))) = mult(mult(a, mult(ld(mult(a, b), unit), b)), i(b))) <=> (mult(a, mult(b, mult(i(b), ld(mult(a, b), unit)))) = mult(mult(a, b), mult(i(b), ld(mult(a, b), unit))))),
% 4.80/3.31 inference(symmetry,[status(thm)],[1109])).
% 4.80/3.31 tff(1111,plain,
% 4.80/3.31 ((~(mult(a, mult(mult(ld(mult(a, b), unit), b), i(b))) = mult(mult(a, mult(ld(mult(a, b), unit), b)), i(b)))) <=> (~(mult(a, mult(b, mult(i(b), ld(mult(a, b), unit)))) = mult(mult(a, b), mult(i(b), ld(mult(a, b), unit)))))),
% 4.80/3.31 inference(monotonicity,[status(thm)],[1110])).
% 4.80/3.31 tff(1112,plain,
% 4.80/3.31 (~(mult(a, mult(b, mult(i(b), ld(mult(a, b), unit)))) = mult(mult(a, b), mult(i(b), ld(mult(a, b), unit))))),
% 4.80/3.31 inference(modus_ponens,[status(thm)],[902, 1111])).
% 4.80/3.31 tff(1113,plain,
% 4.80/3.31 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | ((mult(a, mult(b, mult(i(b), ld(mult(a, b), unit)))) = mult(mult(a, b), mult(i(b), ld(mult(a, b), unit)))) | (mult(a, mult(b, mult(i(b), ld(mult(a, b), unit)))) = mult(mult(a, mult(i(b), ld(mult(a, b), unit))), b)))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | (mult(a, mult(b, mult(i(b), ld(mult(a, b), unit)))) = mult(mult(a, b), mult(i(b), ld(mult(a, b), unit)))) | (mult(a, mult(b, mult(i(b), ld(mult(a, b), unit)))) = mult(mult(a, mult(i(b), ld(mult(a, b), unit))), b)))),
% 4.80/3.31 inference(rewrite,[status(thm)],[])).
% 4.80/3.31 tff(1114,plain,
% 4.80/3.31 (((mult(a, mult(b, mult(i(b), ld(mult(a, b), unit)))) = mult(mult(a, mult(i(b), ld(mult(a, b), unit))), b)) | (mult(a, mult(b, mult(i(b), ld(mult(a, b), unit)))) = mult(mult(a, b), mult(i(b), ld(mult(a, b), unit))))) <=> ((mult(a, mult(b, mult(i(b), ld(mult(a, b), unit)))) = mult(mult(a, b), mult(i(b), ld(mult(a, b), unit)))) | (mult(a, mult(b, mult(i(b), ld(mult(a, b), unit)))) = mult(mult(a, mult(i(b), ld(mult(a, b), unit))), b)))),
% 4.80/3.31 inference(rewrite,[status(thm)],[])).
% 4.80/3.31 tff(1115,plain,
% 4.80/3.31 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | ((mult(a, mult(b, mult(i(b), ld(mult(a, b), unit)))) = mult(mult(a, mult(i(b), ld(mult(a, b), unit))), b)) | (mult(a, mult(b, mult(i(b), ld(mult(a, b), unit)))) = mult(mult(a, b), mult(i(b), ld(mult(a, b), unit)))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | ((mult(a, mult(b, mult(i(b), ld(mult(a, b), unit)))) = mult(mult(a, b), mult(i(b), ld(mult(a, b), unit)))) | (mult(a, mult(b, mult(i(b), ld(mult(a, b), unit)))) = mult(mult(a, mult(i(b), ld(mult(a, b), unit))), b))))),
% 4.80/3.32 inference(monotonicity,[status(thm)],[1114])).
% 4.80/3.32 tff(1116,plain,
% 4.80/3.32 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | ((mult(a, mult(b, mult(i(b), ld(mult(a, b), unit)))) = mult(mult(a, mult(i(b), ld(mult(a, b), unit))), b)) | (mult(a, mult(b, mult(i(b), ld(mult(a, b), unit)))) = mult(mult(a, b), mult(i(b), ld(mult(a, b), unit)))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | (mult(a, mult(b, mult(i(b), ld(mult(a, b), unit)))) = mult(mult(a, b), mult(i(b), ld(mult(a, b), unit)))) | (mult(a, mult(b, mult(i(b), ld(mult(a, b), unit)))) = mult(mult(a, mult(i(b), ld(mult(a, b), unit))), b)))),
% 4.80/3.32 inference(transitivity,[status(thm)],[1115, 1113])).
% 4.80/3.32 tff(1117,plain,
% 4.80/3.32 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | ((mult(a, mult(b, mult(i(b), ld(mult(a, b), unit)))) = mult(mult(a, mult(i(b), ld(mult(a, b), unit))), b)) | (mult(a, mult(b, mult(i(b), ld(mult(a, b), unit)))) = mult(mult(a, b), mult(i(b), ld(mult(a, b), unit)))))),
% 4.80/3.32 inference(quant_inst,[status(thm)],[])).
% 4.80/3.32 tff(1118,plain,
% 4.80/3.32 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, C), B)) | (mult(A, mult(B, C)) = mult(mult(A, B), C)))) | (mult(a, mult(b, mult(i(b), ld(mult(a, b), unit)))) = mult(mult(a, b), mult(i(b), ld(mult(a, b), unit)))) | (mult(a, mult(b, mult(i(b), ld(mult(a, b), unit)))) = mult(mult(a, mult(i(b), ld(mult(a, b), unit))), b))),
% 4.80/3.32 inference(modus_ponens,[status(thm)],[1117, 1116])).
% 4.80/3.32 tff(1119,plain,
% 4.80/3.32 (mult(a, mult(b, mult(i(b), ld(mult(a, b), unit)))) = mult(mult(a, mult(i(b), ld(mult(a, b), unit))), b)),
% 4.80/3.32 inference(unit_resolution,[status(thm)],[1118, 132, 1112])).
% 4.80/3.32 tff(1120,plain,
% 4.80/3.32 (mult(a, mult(mult(ld(mult(a, b), unit), b), i(b))) = mult(mult(a, mult(ld(mult(a, b), unit), b)), i(b))),
% 4.80/3.32 inference(transitivity,[status(thm)],[875, 1106, 1119, 1011, 197, 384, 122, 353, 766])).
% 4.80/3.32 tff(1121,plain,
% 4.80/3.32 ($false),
% 4.80/3.32 inference(unit_resolution,[status(thm)],[902, 1120])).
% 4.80/3.32 tff(1122,plain,(~(mult(a, mult(mult(mult(i(b), ld(mult(a, b), unit)), b), i(b))) = mult(mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b)), i(b)))), inference(lemma,lemma(discharge,[]))).
% 4.80/3.32 tff(1123,plain,
% 4.80/3.32 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(a, mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b))) = mult(mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b)), i(b))) | (mult(a, mult(mult(mult(i(b), ld(mult(a, b), unit)), b), i(b))) = mult(mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b)), i(b))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(a, mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b))) = mult(mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b)), i(b))) | (mult(a, mult(mult(mult(i(b), ld(mult(a, b), unit)), b), i(b))) = mult(mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b)), i(b))))),
% 4.80/3.32 inference(rewrite,[status(thm)],[])).
% 4.80/3.32 tff(1124,plain,
% 4.80/3.32 (((mult(a, mult(mult(mult(i(b), ld(mult(a, b), unit)), b), i(b))) = mult(mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b)), i(b))) | (mult(a, mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b))) = mult(mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b)), i(b)))) <=> ((mult(a, mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b))) = mult(mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b)), i(b))) | (mult(a, mult(mult(mult(i(b), ld(mult(a, b), unit)), b), i(b))) = mult(mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b)), i(b))))),
% 4.80/3.32 inference(rewrite,[status(thm)],[])).
% 4.80/3.32 tff(1125,plain,
% 4.80/3.32 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(a, mult(mult(mult(i(b), ld(mult(a, b), unit)), b), i(b))) = mult(mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b)), i(b))) | (mult(a, mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b))) = mult(mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b)), i(b))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(a, mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b))) = mult(mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b)), i(b))) | (mult(a, mult(mult(mult(i(b), ld(mult(a, b), unit)), b), i(b))) = mult(mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b)), i(b)))))),
% 4.80/3.32 inference(monotonicity,[status(thm)],[1124])).
% 4.80/3.32 tff(1126,plain,
% 4.80/3.32 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(a, mult(mult(mult(i(b), ld(mult(a, b), unit)), b), i(b))) = mult(mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b)), i(b))) | (mult(a, mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b))) = mult(mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b)), i(b))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(a, mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b))) = mult(mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b)), i(b))) | (mult(a, mult(mult(mult(i(b), ld(mult(a, b), unit)), b), i(b))) = mult(mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b)), i(b))))),
% 4.80/3.32 inference(transitivity,[status(thm)],[1125, 1123])).
% 4.80/3.32 tff(1127,plain,
% 4.80/3.32 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(a, mult(mult(mult(i(b), ld(mult(a, b), unit)), b), i(b))) = mult(mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b)), i(b))) | (mult(a, mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b))) = mult(mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b)), i(b))))),
% 4.80/3.32 inference(quant_inst,[status(thm)],[])).
% 4.80/3.32 tff(1128,plain,
% 4.80/3.32 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(a, mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b))) = mult(mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b)), i(b))) | (mult(a, mult(mult(mult(i(b), ld(mult(a, b), unit)), b), i(b))) = mult(mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b)), i(b)))),
% 4.80/3.32 inference(modus_ponens,[status(thm)],[1127, 1126])).
% 4.80/3.32 tff(1129,plain,
% 4.80/3.32 ((mult(a, mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b))) = mult(mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b)), i(b))) | (mult(a, mult(mult(mult(i(b), ld(mult(a, b), unit)), b), i(b))) = mult(mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b)), i(b)))),
% 4.80/3.32 inference(unit_resolution,[status(thm)],[1128, 51])).
% 4.80/3.32 tff(1130,plain,
% 4.80/3.32 (mult(a, mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b))) = mult(mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b)), i(b))),
% 4.80/3.32 inference(unit_resolution,[status(thm)],[1129, 1122])).
% 4.80/3.32 tff(1131,plain,
% 4.80/3.32 (mult(a, mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b))) = mult(i(b), i(b))),
% 4.80/3.32 inference(transitivity,[status(thm)],[1130, 1007])).
% 4.80/3.32 tff(1132,plain,
% 4.80/3.32 (mult(mult(b, b), mult(a, mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)))) = mult(mult(b, b), mult(i(b), i(b)))),
% 4.80/3.32 inference(monotonicity,[status(thm)],[1131])).
% 4.80/3.32 tff(1133,plain,
% 4.80/3.32 (mult(mult(b, b), mult(a, mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)))) = mult(unit, mult(a, mult(ld(mult(a, b), unit), b)))),
% 4.80/3.32 inference(transitivity,[status(thm)],[1132, 399, 386, 19, 1003, 1002])).
% 4.80/3.32 tff(1134,plain,
% 4.80/3.32 ((mult(mult(b, b), mult(a, mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)))) = mult(mult(mult(b, b), mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b))), a)) <=> (mult(unit, mult(a, mult(ld(mult(a, b), unit), b))) = mult(mult(unit, mult(ld(mult(a, b), unit), b)), a))),
% 4.80/3.32 inference(monotonicity,[status(thm)],[1133, 1000])).
% 4.80/3.32 tff(1135,plain,
% 4.80/3.32 ((mult(mult(b, b), mult(a, mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)))) = mult(mult(mult(b, b), mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b))), a)) <=> (mult(mult(b, b), mult(mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)), a)) = mult(mult(mult(b, b), mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b))), a))),
% 4.80/3.32 inference(transitivity,[status(thm)],[1134, 1006])).
% 4.80/3.32 tff(1136,assumption,(~(mult(mult(b, b), mult(mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)), a)) = mult(mult(mult(b, b), mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b))), a))), introduced(assumption)).
% 4.80/3.32 tff(1137,plain,
% 4.80/3.32 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(mult(b, b), mult(mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)), a)) = mult(mult(mult(b, b), mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b))), a)) | (mult(mult(b, b), mult(a, mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)))) = mult(mult(mult(b, b), mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b))), a)))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(b, b), mult(mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)), a)) = mult(mult(mult(b, b), mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b))), a)) | (mult(mult(b, b), mult(a, mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)))) = mult(mult(mult(b, b), mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b))), a)))),
% 4.80/3.32 inference(rewrite,[status(thm)],[])).
% 4.80/3.32 tff(1138,plain,
% 4.80/3.32 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(mult(b, b), mult(mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)), a)) = mult(mult(mult(b, b), mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b))), a)) | (mult(mult(b, b), mult(a, mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)))) = mult(mult(mult(b, b), mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b))), a)))),
% 4.80/3.32 inference(quant_inst,[status(thm)],[])).
% 4.80/3.32 tff(1139,plain,
% 4.80/3.32 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(b, b), mult(mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)), a)) = mult(mult(mult(b, b), mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b))), a)) | (mult(mult(b, b), mult(a, mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)))) = mult(mult(mult(b, b), mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b))), a))),
% 4.80/3.32 inference(modus_ponens,[status(thm)],[1138, 1137])).
% 4.80/3.32 tff(1140,plain,
% 4.80/3.32 ((mult(mult(b, b), mult(mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)), a)) = mult(mult(mult(b, b), mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b))), a)) | (mult(mult(b, b), mult(a, mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)))) = mult(mult(mult(b, b), mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b))), a))),
% 4.80/3.32 inference(unit_resolution,[status(thm)],[1139, 51])).
% 4.80/3.32 tff(1141,plain,
% 4.80/3.32 (mult(mult(b, b), mult(a, mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)))) = mult(mult(mult(b, b), mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b))), a)),
% 4.80/3.32 inference(unit_resolution,[status(thm)],[1140, 1136])).
% 4.80/3.32 tff(1142,plain,
% 4.80/3.32 (mult(mult(b, b), mult(mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)), a)) = mult(mult(mult(b, b), mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b))), a)),
% 4.80/3.32 inference(modus_ponens,[status(thm)],[1141, 1135])).
% 4.80/3.32 tff(1143,plain,
% 4.80/3.32 ($false),
% 4.80/3.32 inference(unit_resolution,[status(thm)],[1136, 1142])).
% 4.80/3.32 tff(1144,plain,(mult(mult(b, b), mult(mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)), a)) = mult(mult(mult(b, b), mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b))), a)), inference(lemma,lemma(discharge,[]))).
% 4.80/3.32 tff(1145,plain,
% 4.80/3.32 (mult(mult(mult(b, b), mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b))), a) = mult(mult(b, b), mult(mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)), a))),
% 4.80/3.32 inference(symmetry,[status(thm)],[1144])).
% 4.82/3.32 tff(1146,plain,
% 4.82/3.32 (mult(mult(mult(b, b), i(b)), mult(mult(i(b), ld(mult(a, b), unit)), b)) = mult(mult(b, b), mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)))),
% 4.82/3.32 inference(symmetry,[status(thm)],[997])).
% 4.82/3.32 tff(1147,plain,
% 4.82/3.32 (mult(b, mult(i(b), mult(ld(mult(a, b), unit), b))) = mult(mult(mult(b, b), i(b)), mult(mult(i(b), ld(mult(a, b), unit)), b))),
% 4.82/3.32 inference(symmetry,[status(thm)],[738])).
% 4.82/3.32 tff(1148,plain,
% 4.82/3.32 (mult(mult(b, i(b)), mult(ld(mult(a, b), unit), b)) = mult(b, mult(i(b), mult(ld(mult(a, b), unit), b)))),
% 4.82/3.32 inference(symmetry,[status(thm)],[686])).
% 4.82/3.32 tff(1149,plain,
% 4.82/3.32 (mult(unit, mult(ld(mult(a, b), unit), b)) = mult(mult(b, i(b)), mult(ld(mult(a, b), unit), b))),
% 4.82/3.32 inference(symmetry,[status(thm)],[672])).
% 4.82/3.32 tff(1150,plain,
% 4.82/3.32 (mult(ld(mult(a, b), unit), b) = mult(mult(b, b), mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b)))),
% 4.82/3.32 inference(transitivity,[status(thm)],[522, 1149, 1148, 1147, 1146])).
% 4.82/3.32 tff(1151,plain,
% 4.82/3.32 (mult(mult(ld(mult(a, b), unit), b), a) = mult(mult(mult(b, b), mult(i(b), mult(mult(i(b), ld(mult(a, b), unit)), b))), a)),
% 4.82/3.32 inference(monotonicity,[status(thm)],[1150])).
% 4.82/3.32 tff(1152,plain,
% 4.82/3.32 (mult(mult(ld(mult(a, b), unit), b), a) = unit),
% 4.82/3.32 inference(transitivity,[status(thm)],[1151, 1145, 669, 399, 386, 19])).
% 4.82/3.32 tff(1153,plain,
% 4.82/3.32 (mult(mult(mult(ld(mult(a, b), unit), b), a), mult(mult(i(b), ld(mult(a, b), unit)), b)) = mult(unit, mult(mult(i(b), ld(mult(a, b), unit)), b))),
% 4.82/3.32 inference(monotonicity,[status(thm)],[1152])).
% 4.82/3.32 tff(1154,plain,
% 4.82/3.32 (mult(mult(mult(ld(mult(a, b), unit), b), a), mult(mult(i(b), ld(mult(a, b), unit)), b)) = mult(mult(i(b), ld(mult(a, b), unit)), b)),
% 4.82/3.32 inference(transitivity,[status(thm)],[1153, 337, 335, 322, 321])).
% 4.82/3.32 tff(1155,plain,
% 4.82/3.32 (mult(mult(ld(mult(a, b), unit), b), mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b))) = mult(mult(ld(mult(a, b), unit), b), i(b))),
% 4.82/3.32 inference(monotonicity,[status(thm)],[472])).
% 4.82/3.32 tff(1156,plain,
% 4.82/3.32 (mult(mult(ld(mult(a, b), unit), b), mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b))) = mult(i(b), mult(b, ld(mult(a, b), unit)))),
% 4.82/3.32 inference(transitivity,[status(thm)],[1155, 303, 300, 280, 268, 267, 769])).
% 4.82/3.32 tff(1157,plain,
% 4.82/3.32 ((mult(mult(ld(mult(a, b), unit), b), mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b))) = mult(mult(mult(ld(mult(a, b), unit), b), a), mult(mult(i(b), ld(mult(a, b), unit)), b))) <=> (mult(i(b), mult(b, ld(mult(a, b), unit))) = mult(mult(i(b), ld(mult(a, b), unit)), b))),
% 4.82/3.32 inference(monotonicity,[status(thm)],[1156, 1154])).
% 4.82/3.32 tff(1158,plain,
% 4.82/3.32 ((mult(i(b), mult(b, ld(mult(a, b), unit))) = mult(mult(i(b), ld(mult(a, b), unit)), b)) <=> (mult(mult(ld(mult(a, b), unit), b), mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b))) = mult(mult(mult(ld(mult(a, b), unit), b), a), mult(mult(i(b), ld(mult(a, b), unit)), b)))),
% 4.82/3.32 inference(symmetry,[status(thm)],[1157])).
% 4.82/3.32 tff(1159,plain,
% 4.82/3.32 ((~(mult(i(b), mult(b, ld(mult(a, b), unit))) = mult(mult(i(b), ld(mult(a, b), unit)), b))) <=> (~(mult(mult(ld(mult(a, b), unit), b), mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b))) = mult(mult(mult(ld(mult(a, b), unit), b), a), mult(mult(i(b), ld(mult(a, b), unit)), b))))),
% 4.82/3.32 inference(monotonicity,[status(thm)],[1158])).
% 4.82/3.32 tff(1160,plain,
% 4.82/3.32 (~(mult(mult(ld(mult(a, b), unit), b), mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b))) = mult(mult(mult(ld(mult(a, b), unit), b), a), mult(mult(i(b), ld(mult(a, b), unit)), b)))),
% 4.82/3.32 inference(modus_ponens,[status(thm)],[826, 1159])).
% 4.82/3.32 tff(1161,plain,
% 4.82/3.32 (mult(mult(ld(mult(a, b), unit), b), i(b)) = mult(mult(ld(mult(a, b), unit), b), mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b)))),
% 4.82/3.32 inference(symmetry,[status(thm)],[1155])).
% 4.82/3.32 tff(1162,plain,
% 4.82/3.32 (mult(mult(i(b), mult(ld(mult(a, b), unit), b)), a) = mult(i(b), mult(a, mult(ld(mult(a, b), unit), b)))),
% 4.82/3.32 inference(symmetry,[status(thm)],[567])).
% 4.82/3.32 tff(1163,plain,
% 4.82/3.32 (mult(mult(mult(i(b), ld(mult(a, b), unit)), b), a) = i(b)),
% 4.82/3.32 inference(transitivity,[status(thm)],[648, 1162, 475, 359])).
% 4.82/3.32 tff(1164,plain,
% 4.82/3.32 (mult(mult(ld(mult(a, b), unit), b), mult(mult(mult(i(b), ld(mult(a, b), unit)), b), a)) = mult(mult(ld(mult(a, b), unit), b), i(b))),
% 4.82/3.33 inference(monotonicity,[status(thm)],[1163])).
% 4.82/3.33 tff(1165,plain,
% 4.82/3.33 (mult(mult(ld(mult(a, b), unit), b), mult(mult(mult(i(b), ld(mult(a, b), unit)), b), a)) = mult(mult(ld(mult(a, b), unit), b), mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b)))),
% 4.82/3.33 inference(transitivity,[status(thm)],[1164, 1161])).
% 4.82/3.33 tff(1166,plain,
% 4.82/3.33 ((mult(mult(ld(mult(a, b), unit), b), mult(mult(mult(i(b), ld(mult(a, b), unit)), b), a)) = mult(mult(mult(ld(mult(a, b), unit), b), a), mult(mult(i(b), ld(mult(a, b), unit)), b))) <=> (mult(mult(ld(mult(a, b), unit), b), mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b))) = mult(mult(mult(ld(mult(a, b), unit), b), a), mult(mult(i(b), ld(mult(a, b), unit)), b)))),
% 4.82/3.33 inference(monotonicity,[status(thm)],[1165])).
% 4.82/3.33 tff(1167,plain,
% 4.82/3.33 ((mult(mult(ld(mult(a, b), unit), b), mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b))) = mult(mult(mult(ld(mult(a, b), unit), b), a), mult(mult(i(b), ld(mult(a, b), unit)), b))) <=> (mult(mult(ld(mult(a, b), unit), b), mult(mult(mult(i(b), ld(mult(a, b), unit)), b), a)) = mult(mult(mult(ld(mult(a, b), unit), b), a), mult(mult(i(b), ld(mult(a, b), unit)), b)))),
% 4.82/3.33 inference(symmetry,[status(thm)],[1166])).
% 4.82/3.33 tff(1168,plain,
% 4.82/3.33 ((mult(i(b), mult(b, ld(mult(a, b), unit))) = mult(mult(i(b), ld(mult(a, b), unit)), b)) <=> (mult(mult(ld(mult(a, b), unit), b), mult(mult(mult(i(b), ld(mult(a, b), unit)), b), a)) = mult(mult(mult(ld(mult(a, b), unit), b), a), mult(mult(i(b), ld(mult(a, b), unit)), b)))),
% 4.82/3.33 inference(transitivity,[status(thm)],[1158, 1167])).
% 4.82/3.33 tff(1169,plain,
% 4.82/3.33 ((~(mult(i(b), mult(b, ld(mult(a, b), unit))) = mult(mult(i(b), ld(mult(a, b), unit)), b))) <=> (~(mult(mult(ld(mult(a, b), unit), b), mult(mult(mult(i(b), ld(mult(a, b), unit)), b), a)) = mult(mult(mult(ld(mult(a, b), unit), b), a), mult(mult(i(b), ld(mult(a, b), unit)), b))))),
% 4.82/3.33 inference(monotonicity,[status(thm)],[1168])).
% 4.82/3.33 tff(1170,plain,
% 4.82/3.33 (~(mult(mult(ld(mult(a, b), unit), b), mult(mult(mult(i(b), ld(mult(a, b), unit)), b), a)) = mult(mult(mult(ld(mult(a, b), unit), b), a), mult(mult(i(b), ld(mult(a, b), unit)), b)))),
% 4.82/3.33 inference(modus_ponens,[status(thm)],[826, 1169])).
% 4.82/3.33 tff(1171,plain,
% 4.82/3.33 (((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(mult(ld(mult(a, b), unit), b), mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b))) = mult(mult(mult(ld(mult(a, b), unit), b), a), mult(mult(i(b), ld(mult(a, b), unit)), b))) | (mult(mult(ld(mult(a, b), unit), b), mult(mult(mult(i(b), ld(mult(a, b), unit)), b), a)) = mult(mult(mult(ld(mult(a, b), unit), b), a), mult(mult(i(b), ld(mult(a, b), unit)), b))))) <=> ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(ld(mult(a, b), unit), b), mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b))) = mult(mult(mult(ld(mult(a, b), unit), b), a), mult(mult(i(b), ld(mult(a, b), unit)), b))) | (mult(mult(ld(mult(a, b), unit), b), mult(mult(mult(i(b), ld(mult(a, b), unit)), b), a)) = mult(mult(mult(ld(mult(a, b), unit), b), a), mult(mult(i(b), ld(mult(a, b), unit)), b))))),
% 4.82/3.33 inference(rewrite,[status(thm)],[])).
% 4.82/3.33 tff(1172,plain,
% 4.82/3.33 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | ((mult(mult(ld(mult(a, b), unit), b), mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b))) = mult(mult(mult(ld(mult(a, b), unit), b), a), mult(mult(i(b), ld(mult(a, b), unit)), b))) | (mult(mult(ld(mult(a, b), unit), b), mult(mult(mult(i(b), ld(mult(a, b), unit)), b), a)) = mult(mult(mult(ld(mult(a, b), unit), b), a), mult(mult(i(b), ld(mult(a, b), unit)), b))))),
% 4.82/3.33 inference(quant_inst,[status(thm)],[])).
% 4.82/3.33 tff(1173,plain,
% 4.82/3.33 ((~![B: $i, A: $i, C: $i] : ((mult(A, mult(B, C)) = mult(mult(A, B), C)) | (mult(A, mult(C, B)) = mult(mult(A, B), C)))) | (mult(mult(ld(mult(a, b), unit), b), mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b))) = mult(mult(mult(ld(mult(a, b), unit), b), a), mult(mult(i(b), ld(mult(a, b), unit)), b))) | (mult(mult(ld(mult(a, b), unit), b), mult(mult(mult(i(b), ld(mult(a, b), unit)), b), a)) = mult(mult(mult(ld(mult(a, b), unit), b), a), mult(mult(i(b), ld(mult(a, b), unit)), b)))),
% 4.82/3.33 inference(modus_ponens,[status(thm)],[1172, 1171])).
% 4.82/3.33 tff(1174,plain,
% 4.82/3.33 ((mult(mult(ld(mult(a, b), unit), b), mult(a, mult(mult(i(b), ld(mult(a, b), unit)), b))) = mult(mult(mult(ld(mult(a, b), unit), b), a), mult(mult(i(b), ld(mult(a, b), unit)), b))) | (mult(mult(ld(mult(a, b), unit), b), mult(mult(mult(i(b), ld(mult(a, b), unit)), b), a)) = mult(mult(mult(ld(mult(a, b), unit), b), a), mult(mult(i(b), ld(mult(a, b), unit)), b)))),
% 4.82/3.33 inference(unit_resolution,[status(thm)],[1173, 51])).
% 4.82/3.33 tff(1175,plain,
% 4.82/3.33 ($false),
% 4.82/3.33 inference(unit_resolution,[status(thm)],[1174, 1170, 1160])).
% 4.82/3.33 % SZS output end Proof
%------------------------------------------------------------------------------