TSTP Solution File: GRP715+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP715+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n023.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 22:29:37 EDT 2022
% Result : Theorem 0.63s 0.68s
% Output : Proof 0.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP715+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n023.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 31 20:45:04 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.63/0.68 % SZS status Theorem
% 0.63/0.68 % SZS output start Proof
% 0.63/0.68 tff(tptp_fun_X0_0_type, type, (
% 0.63/0.68 tptp_fun_X0_0: $i)).
% 0.63/0.68 tff(mult_type, type, (
% 0.63/0.68 mult: ( $i * $i ) > $i)).
% 0.63/0.68 tff(op_a_type, type, (
% 0.63/0.68 op_a: $i)).
% 0.63/0.68 tff(op_b_type, type, (
% 0.63/0.68 op_b: $i)).
% 0.63/0.68 tff(unit_type, type, (
% 0.63/0.68 unit: $i)).
% 0.63/0.68 tff(1,plain,
% 0.63/0.68 (^[A: $i] : refl((mult(A, mult(op_a, op_b)) = A) <=> (mult(A, mult(op_a, op_b)) = A))),
% 0.63/0.68 inference(bind,[status(th)],[])).
% 0.63/0.68 tff(2,plain,
% 0.63/0.68 (![A: $i] : (mult(A, mult(op_a, op_b)) = A) <=> ![A: $i] : (mult(A, mult(op_a, op_b)) = A)),
% 0.63/0.68 inference(quant_intro,[status(thm)],[1])).
% 0.63/0.68 tff(3,plain,
% 0.63/0.68 (^[A: $i] : rewrite((mult(A, unit) = A) <=> (mult(A, mult(op_a, op_b)) = A))),
% 0.63/0.68 inference(bind,[status(th)],[])).
% 0.63/0.68 tff(4,plain,
% 0.63/0.68 (![A: $i] : (mult(A, unit) = A) <=> ![A: $i] : (mult(A, mult(op_a, op_b)) = A)),
% 0.63/0.68 inference(quant_intro,[status(thm)],[3])).
% 0.63/0.68 tff(5,plain,
% 0.63/0.68 (![A: $i] : (mult(A, unit) = A) <=> ![A: $i] : (mult(A, unit) = A)),
% 0.63/0.68 inference(rewrite,[status(thm)],[])).
% 0.63/0.68 tff(6,axiom,(![A: $i] : (mult(A, unit) = A)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','f08')).
% 0.63/0.68 tff(7,plain,
% 0.63/0.68 (![A: $i] : (mult(A, unit) = A)),
% 0.63/0.68 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.63/0.68 tff(8,plain,
% 0.63/0.68 (![A: $i] : (mult(A, mult(op_a, op_b)) = A)),
% 0.63/0.68 inference(modus_ponens,[status(thm)],[7, 4])).
% 0.63/0.68 tff(9,plain,(
% 0.63/0.68 ![A: $i] : (mult(A, mult(op_a, op_b)) = A)),
% 0.63/0.68 inference(skolemize,[status(sab)],[8])).
% 0.63/0.68 tff(10,plain,
% 0.63/0.68 (![A: $i] : (mult(A, mult(op_a, op_b)) = A)),
% 0.63/0.68 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.63/0.68 tff(11,plain,
% 0.63/0.68 ((~![A: $i] : (mult(A, mult(op_a, op_b)) = A)) | (mult(X0!0, mult(op_a, op_b)) = X0!0)),
% 0.63/0.68 inference(quant_inst,[status(thm)],[])).
% 0.63/0.68 tff(12,plain,
% 0.63/0.68 (mult(X0!0, mult(op_a, op_b)) = X0!0),
% 0.63/0.68 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.63/0.68 tff(13,plain,
% 0.63/0.68 (^[A: $i] : refl((mult(mult(op_a, op_b), A) = A) <=> (mult(mult(op_a, op_b), A) = A))),
% 0.63/0.68 inference(bind,[status(th)],[])).
% 0.63/0.68 tff(14,plain,
% 0.63/0.68 (![A: $i] : (mult(mult(op_a, op_b), A) = A) <=> ![A: $i] : (mult(mult(op_a, op_b), A) = A)),
% 0.63/0.68 inference(quant_intro,[status(thm)],[13])).
% 0.63/0.68 tff(15,plain,
% 0.63/0.68 (^[A: $i] : rewrite((mult(unit, A) = A) <=> (mult(mult(op_a, op_b), A) = A))),
% 0.63/0.68 inference(bind,[status(th)],[])).
% 0.63/0.68 tff(16,plain,
% 0.63/0.68 (![A: $i] : (mult(unit, A) = A) <=> ![A: $i] : (mult(mult(op_a, op_b), A) = A)),
% 0.63/0.68 inference(quant_intro,[status(thm)],[15])).
% 0.63/0.68 tff(17,plain,
% 0.63/0.68 (![A: $i] : (mult(unit, A) = A) <=> ![A: $i] : (mult(unit, A) = A)),
% 0.63/0.68 inference(rewrite,[status(thm)],[])).
% 0.63/0.68 tff(18,axiom,(![A: $i] : (mult(unit, A) = A)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','f09')).
% 0.63/0.68 tff(19,plain,
% 0.63/0.68 (![A: $i] : (mult(unit, A) = A)),
% 0.63/0.68 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.63/0.68 tff(20,plain,
% 0.63/0.68 (![A: $i] : (mult(mult(op_a, op_b), A) = A)),
% 0.63/0.68 inference(modus_ponens,[status(thm)],[19, 16])).
% 0.63/0.68 tff(21,plain,(
% 0.63/0.68 ![A: $i] : (mult(mult(op_a, op_b), A) = A)),
% 0.63/0.68 inference(skolemize,[status(sab)],[20])).
% 0.63/0.68 tff(22,plain,
% 0.63/0.68 (![A: $i] : (mult(mult(op_a, op_b), A) = A)),
% 0.63/0.68 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.63/0.68 tff(23,plain,
% 0.63/0.68 ((~![A: $i] : (mult(mult(op_a, op_b), A) = A)) | (mult(mult(op_a, op_b), mult(op_a, op_b)) = mult(op_a, op_b))),
% 0.63/0.68 inference(quant_inst,[status(thm)],[])).
% 0.63/0.68 tff(24,plain,
% 0.63/0.68 (mult(mult(op_a, op_b), mult(op_a, op_b)) = mult(op_a, op_b)),
% 0.63/0.68 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.63/0.68 tff(25,plain,
% 0.63/0.68 (mult(op_a, op_b) = mult(mult(op_a, op_b), mult(op_a, op_b))),
% 0.63/0.68 inference(symmetry,[status(thm)],[24])).
% 0.63/0.68 tff(26,plain,
% 0.63/0.68 (mult(X0!0, mult(op_a, op_b)) = mult(X0!0, mult(mult(op_a, op_b), mult(op_a, op_b)))),
% 0.63/0.68 inference(monotonicity,[status(thm)],[25])).
% 0.63/0.68 tff(27,plain,
% 0.63/0.68 (mult(X0!0, mult(mult(op_a, op_b), mult(op_a, op_b))) = mult(X0!0, mult(op_a, op_b))),
% 0.63/0.68 inference(symmetry,[status(thm)],[26])).
% 0.63/0.68 tff(28,plain,
% 0.63/0.68 ((~![A: $i] : (mult(mult(op_a, op_b), A) = A)) | (mult(mult(op_a, op_b), op_a) = op_a)),
% 0.63/0.68 inference(quant_inst,[status(thm)],[])).
% 0.63/0.68 tff(29,plain,
% 0.63/0.68 (mult(mult(op_a, op_b), op_a) = op_a),
% 0.63/0.68 inference(unit_resolution,[status(thm)],[28, 22])).
% 0.63/0.68 tff(30,plain,
% 0.63/0.68 (mult(mult(mult(op_a, op_b), mult(op_a, op_b)), op_a) = mult(mult(op_a, op_b), op_a)),
% 0.63/0.68 inference(monotonicity,[status(thm)],[24])).
% 0.63/0.68 tff(31,plain,
% 0.63/0.68 ((mult(op_b, op_a) = unit) <=> (mult(op_b, op_a) = mult(op_a, op_b))),
% 0.63/0.68 inference(rewrite,[status(thm)],[])).
% 0.63/0.68 tff(32,plain,
% 0.63/0.68 ((mult(op_b, op_a) = unit) <=> (mult(op_b, op_a) = unit)),
% 0.63/0.68 inference(rewrite,[status(thm)],[])).
% 0.63/0.68 tff(33,axiom,(mult(op_b, op_a) = unit), file('/export/starexec/sandbox/benchmark/theBenchmark.p','f11')).
% 0.63/0.68 tff(34,plain,
% 0.63/0.68 (mult(op_b, op_a) = unit),
% 0.63/0.68 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.63/0.68 tff(35,plain,
% 0.63/0.68 (mult(op_b, op_a) = mult(op_a, op_b)),
% 0.63/0.68 inference(modus_ponens,[status(thm)],[34, 31])).
% 0.63/0.68 tff(36,plain,
% 0.63/0.68 (mult(op_b, op_a) = mult(mult(op_a, op_b), mult(op_a, op_b))),
% 0.63/0.68 inference(transitivity,[status(thm)],[35, 25])).
% 0.63/0.68 tff(37,plain,
% 0.63/0.68 (mult(mult(op_b, op_a), op_a) = mult(mult(mult(op_a, op_b), mult(op_a, op_b)), op_a)),
% 0.63/0.68 inference(monotonicity,[status(thm)],[36])).
% 0.63/0.68 tff(38,plain,
% 0.63/0.68 (^[B: $i, A: $i] : refl((mult(A, mult(B, B)) = mult(mult(A, B), B)) <=> (mult(A, mult(B, B)) = mult(mult(A, B), B)))),
% 0.63/0.68 inference(bind,[status(th)],[])).
% 0.63/0.68 tff(39,plain,
% 0.63/0.68 (![B: $i, A: $i] : (mult(A, mult(B, B)) = mult(mult(A, B), B)) <=> ![B: $i, A: $i] : (mult(A, mult(B, B)) = mult(mult(A, B), B))),
% 0.63/0.68 inference(quant_intro,[status(thm)],[38])).
% 0.63/0.68 tff(40,plain,
% 0.63/0.68 (![B: $i, A: $i] : (mult(A, mult(B, B)) = mult(mult(A, B), B)) <=> ![B: $i, A: $i] : (mult(A, mult(B, B)) = mult(mult(A, B), B))),
% 0.63/0.68 inference(rewrite,[status(thm)],[])).
% 0.63/0.68 tff(41,axiom,(![B: $i, A: $i] : (mult(A, mult(B, B)) = mult(mult(A, B), B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','f07')).
% 0.63/0.68 tff(42,plain,
% 0.63/0.68 (![B: $i, A: $i] : (mult(A, mult(B, B)) = mult(mult(A, B), B))),
% 0.63/0.68 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.63/0.68 tff(43,plain,(
% 0.63/0.68 ![B: $i, A: $i] : (mult(A, mult(B, B)) = mult(mult(A, B), B))),
% 0.63/0.68 inference(skolemize,[status(sab)],[42])).
% 0.63/0.68 tff(44,plain,
% 0.63/0.68 (![B: $i, A: $i] : (mult(A, mult(B, B)) = mult(mult(A, B), B))),
% 0.63/0.68 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.63/0.68 tff(45,plain,
% 0.63/0.68 ((~![B: $i, A: $i] : (mult(A, mult(B, B)) = mult(mult(A, B), B))) | (mult(op_b, mult(op_a, op_a)) = mult(mult(op_b, op_a), op_a))),
% 0.63/0.68 inference(quant_inst,[status(thm)],[])).
% 0.63/0.68 tff(46,plain,
% 0.63/0.68 (mult(op_b, mult(op_a, op_a)) = mult(mult(op_b, op_a), op_a)),
% 0.63/0.68 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.63/0.68 tff(47,plain,
% 0.63/0.68 (mult(op_b, mult(op_a, op_a)) = op_a),
% 0.63/0.68 inference(transitivity,[status(thm)],[46, 37, 30, 29])).
% 0.63/0.68 tff(48,plain,
% 0.63/0.68 (mult(mult(op_b, mult(op_a, op_a)), op_b) = mult(op_a, op_b)),
% 0.63/0.68 inference(monotonicity,[status(thm)],[47])).
% 0.63/0.68 tff(49,plain,
% 0.63/0.68 (mult(op_a, op_b) = mult(mult(op_b, mult(op_a, op_a)), op_b)),
% 0.63/0.68 inference(symmetry,[status(thm)],[48])).
% 0.63/0.68 tff(50,plain,
% 0.63/0.68 (mult(mult(op_a, op_b), mult(op_a, op_b)) = mult(mult(op_b, mult(op_a, op_a)), op_b)),
% 0.63/0.68 inference(transitivity,[status(thm)],[24, 49])).
% 0.63/0.68 tff(51,plain,
% 0.63/0.68 (mult(X0!0, mult(mult(op_a, op_b), mult(op_a, op_b))) = mult(X0!0, mult(mult(op_b, mult(op_a, op_a)), op_b))),
% 0.63/0.68 inference(monotonicity,[status(thm)],[50])).
% 0.63/0.68 tff(52,plain,
% 0.63/0.68 (mult(X0!0, mult(mult(op_b, mult(op_a, op_a)), op_b)) = mult(X0!0, mult(mult(op_a, op_b), mult(op_a, op_b)))),
% 0.63/0.68 inference(symmetry,[status(thm)],[51])).
% 0.63/0.68 tff(53,plain,
% 0.63/0.68 (^[C: $i, B: $i, A: $i] : refl((mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B))) <=> (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B))))),
% 0.63/0.68 inference(bind,[status(th)],[])).
% 0.63/0.68 tff(54,plain,
% 0.63/0.68 (![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B))) <=> ![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))),
% 0.63/0.68 inference(quant_intro,[status(thm)],[53])).
% 0.63/0.68 tff(55,plain,
% 0.63/0.68 (![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B))) <=> ![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))),
% 0.63/0.68 inference(rewrite,[status(thm)],[])).
% 0.63/0.68 tff(56,axiom,(![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','f06')).
% 0.63/0.69 tff(57,plain,
% 0.63/0.69 (![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))),
% 0.63/0.69 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.63/0.69 tff(58,plain,(
% 0.63/0.69 ![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))),
% 0.63/0.69 inference(skolemize,[status(sab)],[57])).
% 0.63/0.69 tff(59,plain,
% 0.63/0.69 (![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))),
% 0.63/0.69 inference(modus_ponens,[status(thm)],[58, 54])).
% 0.63/0.69 tff(60,plain,
% 0.63/0.69 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(X0!0, op_b), mult(op_a, op_a)), op_b) = mult(X0!0, mult(mult(op_b, mult(op_a, op_a)), op_b)))),
% 0.63/0.69 inference(quant_inst,[status(thm)],[])).
% 0.63/0.69 tff(61,plain,
% 0.63/0.69 (mult(mult(mult(X0!0, op_b), mult(op_a, op_a)), op_b) = mult(X0!0, mult(mult(op_b, mult(op_a, op_a)), op_b))),
% 0.63/0.69 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.63/0.69 tff(62,plain,
% 0.63/0.69 ((~![A: $i] : (mult(mult(op_a, op_b), A) = A)) | (mult(mult(op_a, op_b), op_b) = op_b)),
% 0.63/0.69 inference(quant_inst,[status(thm)],[])).
% 0.63/0.69 tff(63,plain,
% 0.63/0.69 (mult(mult(op_a, op_b), op_b) = op_b),
% 0.63/0.69 inference(unit_resolution,[status(thm)],[62, 22])).
% 0.63/0.69 tff(64,plain,
% 0.63/0.69 (mult(mult(op_b, op_a), op_b) = mult(mult(op_a, op_b), op_b)),
% 0.63/0.69 inference(monotonicity,[status(thm)],[35])).
% 0.63/0.69 tff(65,plain,
% 0.63/0.69 (mult(mult(op_b, op_a), op_b) = op_b),
% 0.63/0.69 inference(transitivity,[status(thm)],[64, 63])).
% 0.63/0.69 tff(66,plain,
% 0.63/0.69 (mult(X0!0, mult(mult(op_b, op_a), op_b)) = mult(X0!0, op_b)),
% 0.63/0.69 inference(monotonicity,[status(thm)],[65])).
% 0.63/0.69 tff(67,plain,
% 0.63/0.69 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(X0!0, op_b), op_a), op_b) = mult(X0!0, mult(mult(op_b, op_a), op_b)))),
% 0.63/0.69 inference(quant_inst,[status(thm)],[])).
% 0.63/0.69 tff(68,plain,
% 0.63/0.69 (mult(mult(mult(X0!0, op_b), op_a), op_b) = mult(X0!0, mult(mult(op_b, op_a), op_b))),
% 0.63/0.69 inference(unit_resolution,[status(thm)],[67, 59])).
% 0.63/0.69 tff(69,plain,
% 0.63/0.69 (mult(X0!0, mult(mult(op_b, op_a), op_b)) = mult(mult(mult(X0!0, op_b), op_a), op_b)),
% 0.63/0.69 inference(symmetry,[status(thm)],[68])).
% 0.63/0.69 tff(70,plain,
% 0.63/0.69 (mult(X0!0, op_b) = mult(X0!0, mult(mult(op_b, op_a), op_b))),
% 0.63/0.69 inference(symmetry,[status(thm)],[66])).
% 0.63/0.69 tff(71,plain,
% 0.63/0.69 (mult(X0!0, op_b) = mult(mult(mult(X0!0, op_b), op_a), op_b)),
% 0.63/0.69 inference(transitivity,[status(thm)],[70, 69])).
% 0.63/0.69 tff(72,plain,
% 0.63/0.69 (mult(mult(X0!0, op_b), op_a) = mult(mult(mult(mult(X0!0, op_b), op_a), op_b), op_a)),
% 0.63/0.69 inference(monotonicity,[status(thm)],[71])).
% 0.63/0.69 tff(73,plain,
% 0.63/0.69 (mult(mult(mult(mult(X0!0, op_b), op_a), op_b), op_a) = mult(mult(X0!0, op_b), op_a)),
% 0.63/0.69 inference(symmetry,[status(thm)],[72])).
% 0.63/0.69 tff(74,plain,
% 0.63/0.69 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(X0!0, op_b), op_a), op_b), op_a) = mult(mult(X0!0, op_b), mult(mult(op_a, op_b), op_a)))),
% 0.63/0.69 inference(quant_inst,[status(thm)],[])).
% 0.63/0.69 tff(75,plain,
% 0.63/0.69 (mult(mult(mult(mult(X0!0, op_b), op_a), op_b), op_a) = mult(mult(X0!0, op_b), mult(mult(op_a, op_b), op_a))),
% 0.63/0.69 inference(unit_resolution,[status(thm)],[74, 59])).
% 0.63/0.69 tff(76,plain,
% 0.63/0.69 (mult(mult(X0!0, op_b), mult(mult(op_a, op_b), op_a)) = mult(mult(mult(mult(X0!0, op_b), op_a), op_b), op_a)),
% 0.63/0.69 inference(symmetry,[status(thm)],[75])).
% 0.63/0.69 tff(77,plain,
% 0.63/0.69 (mult(mult(X0!0, op_b), mult(mult(op_a, op_b), op_a)) = mult(mult(X0!0, op_b), op_a)),
% 0.63/0.69 inference(transitivity,[status(thm)],[76, 73])).
% 0.63/0.69 tff(78,plain,
% 0.63/0.69 (mult(mult(mult(X0!0, op_b), mult(mult(op_a, op_b), op_a)), op_b) = mult(mult(mult(X0!0, op_b), op_a), op_b)),
% 0.63/0.69 inference(monotonicity,[status(thm)],[77])).
% 0.63/0.69 tff(79,plain,
% 0.63/0.69 (mult(mult(mult(X0!0, op_b), mult(mult(op_a, op_b), op_a)), op_b) = mult(X0!0, op_b)),
% 0.63/0.69 inference(transitivity,[status(thm)],[78, 68, 66])).
% 0.63/0.69 tff(80,plain,
% 0.63/0.69 (mult(mult(mult(mult(X0!0, op_b), mult(mult(op_a, op_b), op_a)), op_b), mult(op_a, op_a)) = mult(mult(X0!0, op_b), mult(op_a, op_a))),
% 0.63/0.69 inference(monotonicity,[status(thm)],[79])).
% 0.63/0.69 tff(81,plain,
% 0.63/0.69 (mult(mult(X0!0, op_b), mult(op_a, op_a)) = mult(mult(mult(mult(X0!0, op_b), mult(mult(op_a, op_b), op_a)), op_b), mult(op_a, op_a))),
% 0.63/0.69 inference(symmetry,[status(thm)],[80])).
% 0.63/0.69 tff(82,plain,
% 0.63/0.69 (mult(mult(mult(X0!0, op_b), mult(op_a, op_a)), op_b) = mult(mult(mult(mult(mult(X0!0, op_b), mult(mult(op_a, op_b), op_a)), op_b), mult(op_a, op_a)), op_b)),
% 0.63/0.69 inference(monotonicity,[status(thm)],[81])).
% 0.63/0.69 tff(83,plain,
% 0.63/0.69 (mult(mult(mult(mult(mult(X0!0, op_b), mult(mult(op_a, op_b), op_a)), op_b), mult(op_a, op_a)), op_b) = mult(mult(mult(X0!0, op_b), mult(op_a, op_a)), op_b)),
% 0.63/0.69 inference(symmetry,[status(thm)],[82])).
% 0.63/0.69 tff(84,plain,
% 0.63/0.69 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(mult(X0!0, op_b), mult(mult(op_a, op_b), op_a)), op_b), mult(op_a, op_a)), op_b) = mult(mult(mult(X0!0, op_b), mult(mult(op_a, op_b), op_a)), mult(mult(op_b, mult(op_a, op_a)), op_b)))),
% 0.63/0.69 inference(quant_inst,[status(thm)],[])).
% 0.63/0.69 tff(85,plain,
% 0.63/0.69 (mult(mult(mult(mult(mult(X0!0, op_b), mult(mult(op_a, op_b), op_a)), op_b), mult(op_a, op_a)), op_b) = mult(mult(mult(X0!0, op_b), mult(mult(op_a, op_b), op_a)), mult(mult(op_b, mult(op_a, op_a)), op_b))),
% 0.63/0.69 inference(unit_resolution,[status(thm)],[84, 59])).
% 0.63/0.69 tff(86,plain,
% 0.63/0.69 (mult(mult(mult(X0!0, op_b), mult(mult(op_a, op_b), op_a)), mult(mult(op_b, mult(op_a, op_a)), op_b)) = mult(mult(mult(mult(mult(X0!0, op_b), mult(mult(op_a, op_b), op_a)), op_b), mult(op_a, op_a)), op_b)),
% 0.63/0.69 inference(symmetry,[status(thm)],[85])).
% 0.63/0.69 tff(87,plain,
% 0.63/0.69 (mult(mult(op_b, mult(op_a, op_a)), op_b) = mult(mult(op_a, op_b), mult(op_a, op_b))),
% 0.63/0.69 inference(transitivity,[status(thm)],[48, 25])).
% 0.63/0.69 tff(88,plain,
% 0.63/0.69 (mult(mult(mult(X0!0, op_b), mult(mult(op_a, op_b), op_a)), mult(mult(op_b, mult(op_a, op_a)), op_b)) = mult(mult(mult(X0!0, op_b), mult(mult(op_a, op_b), op_a)), mult(mult(op_a, op_b), mult(op_a, op_b)))),
% 0.63/0.69 inference(monotonicity,[status(thm)],[87])).
% 0.63/0.69 tff(89,plain,
% 0.63/0.69 (mult(mult(mult(X0!0, op_b), mult(mult(op_a, op_b), op_a)), mult(mult(op_a, op_b), mult(op_a, op_b))) = mult(mult(mult(X0!0, op_b), mult(mult(op_a, op_b), op_a)), mult(mult(op_b, mult(op_a, op_a)), op_b))),
% 0.63/0.69 inference(symmetry,[status(thm)],[88])).
% 0.63/0.69 tff(90,plain,
% 0.63/0.69 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(X0!0, op_b), mult(mult(op_a, op_b), mult(op_a, op_b))), op_a), mult(mult(op_a, op_b), mult(op_a, op_b))) = mult(mult(X0!0, op_b), mult(mult(mult(mult(op_a, op_b), mult(op_a, op_b)), op_a), mult(mult(op_a, op_b), mult(op_a, op_b)))))),
% 0.63/0.69 inference(quant_inst,[status(thm)],[])).
% 0.63/0.69 tff(91,plain,
% 0.63/0.69 (mult(mult(mult(mult(X0!0, op_b), mult(mult(op_a, op_b), mult(op_a, op_b))), op_a), mult(mult(op_a, op_b), mult(op_a, op_b))) = mult(mult(X0!0, op_b), mult(mult(mult(mult(op_a, op_b), mult(op_a, op_b)), op_a), mult(mult(op_a, op_b), mult(op_a, op_b))))),
% 0.63/0.69 inference(unit_resolution,[status(thm)],[90, 59])).
% 0.63/0.69 tff(92,plain,
% 0.63/0.69 (mult(mult(X0!0, op_b), mult(mult(mult(mult(op_a, op_b), mult(op_a, op_b)), op_a), mult(mult(op_a, op_b), mult(op_a, op_b)))) = mult(mult(mult(mult(X0!0, op_b), mult(mult(op_a, op_b), mult(op_a, op_b))), op_a), mult(mult(op_a, op_b), mult(op_a, op_b)))),
% 0.63/0.69 inference(symmetry,[status(thm)],[91])).
% 0.63/0.69 tff(93,plain,
% 0.63/0.69 ((~![A: $i] : (mult(A, mult(op_a, op_b)) = A)) | (mult(op_a, mult(op_a, op_b)) = op_a)),
% 0.63/0.69 inference(quant_inst,[status(thm)],[])).
% 0.63/0.69 tff(94,plain,
% 0.63/0.69 (mult(op_a, mult(op_a, op_b)) = op_a),
% 0.63/0.69 inference(unit_resolution,[status(thm)],[93, 10])).
% 0.63/0.69 tff(95,plain,
% 0.63/0.69 (mult(mult(op_a, mult(op_a, op_b)), mult(op_a, op_b)) = mult(op_a, mult(op_a, op_b))),
% 0.63/0.69 inference(monotonicity,[status(thm)],[94])).
% 0.63/0.69 tff(96,plain,
% 0.63/0.69 ((~![B: $i, A: $i] : (mult(A, mult(B, B)) = mult(mult(A, B), B))) | (mult(op_a, mult(mult(op_a, op_b), mult(op_a, op_b))) = mult(mult(op_a, mult(op_a, op_b)), mult(op_a, op_b)))),
% 0.63/0.69 inference(quant_inst,[status(thm)],[])).
% 0.63/0.69 tff(97,plain,
% 0.63/0.69 (mult(op_a, mult(mult(op_a, op_b), mult(op_a, op_b))) = mult(mult(op_a, mult(op_a, op_b)), mult(op_a, op_b))),
% 0.63/0.69 inference(unit_resolution,[status(thm)],[96, 44])).
% 0.63/0.69 tff(98,plain,
% 0.63/0.69 (mult(mult(mult(op_a, op_b), mult(op_a, op_b)), op_a) = op_a),
% 0.63/0.69 inference(transitivity,[status(thm)],[30, 29])).
% 0.63/0.69 tff(99,plain,
% 0.63/0.69 (mult(mult(mult(mult(op_a, op_b), mult(op_a, op_b)), op_a), mult(mult(op_a, op_b), mult(op_a, op_b))) = mult(op_a, mult(mult(op_a, op_b), mult(op_a, op_b)))),
% 0.63/0.69 inference(monotonicity,[status(thm)],[98])).
% 0.63/0.69 tff(100,plain,
% 0.63/0.69 (mult(mult(mult(mult(op_a, op_b), mult(op_a, op_b)), op_a), mult(mult(op_a, op_b), mult(op_a, op_b))) = op_a),
% 0.63/0.69 inference(transitivity,[status(thm)],[99, 97, 95, 94])).
% 0.63/0.69 tff(101,plain,
% 0.63/0.69 (mult(mult(X0!0, op_b), mult(mult(mult(mult(op_a, op_b), mult(op_a, op_b)), op_a), mult(mult(op_a, op_b), mult(op_a, op_b)))) = mult(mult(X0!0, op_b), op_a)),
% 0.63/0.69 inference(monotonicity,[status(thm)],[100])).
% 0.63/0.69 tff(102,plain,
% 0.63/0.69 (mult(mult(X0!0, op_b), op_a) = mult(mult(X0!0, op_b), mult(mult(mult(mult(op_a, op_b), mult(op_a, op_b)), op_a), mult(mult(op_a, op_b), mult(op_a, op_b))))),
% 0.63/0.69 inference(symmetry,[status(thm)],[101])).
% 0.63/0.69 tff(103,plain,
% 0.63/0.69 (mult(mult(X0!0, op_b), mult(mult(op_a, op_b), op_a)) = mult(mult(mult(mult(X0!0, op_b), mult(mult(op_a, op_b), mult(op_a, op_b))), op_a), mult(mult(op_a, op_b), mult(op_a, op_b)))),
% 0.63/0.69 inference(transitivity,[status(thm)],[76, 73, 102, 92])).
% 0.63/0.69 tff(104,plain,
% 0.63/0.69 (mult(mult(mult(X0!0, op_b), mult(mult(op_a, op_b), op_a)), mult(mult(op_a, op_b), mult(op_a, op_b))) = mult(mult(mult(mult(mult(X0!0, op_b), mult(mult(op_a, op_b), mult(op_a, op_b))), op_a), mult(mult(op_a, op_b), mult(op_a, op_b))), mult(mult(op_a, op_b), mult(op_a, op_b)))),
% 0.63/0.69 inference(monotonicity,[status(thm)],[103])).
% 0.63/0.69 tff(105,plain,
% 0.63/0.69 (mult(mult(mult(mult(mult(X0!0, op_b), mult(mult(op_a, op_b), mult(op_a, op_b))), op_a), mult(mult(op_a, op_b), mult(op_a, op_b))), mult(mult(op_a, op_b), mult(op_a, op_b))) = mult(mult(mult(X0!0, op_b), mult(mult(op_a, op_b), op_a)), mult(mult(op_a, op_b), mult(op_a, op_b)))),
% 0.63/0.69 inference(symmetry,[status(thm)],[104])).
% 0.63/0.69 tff(106,plain,
% 0.63/0.69 ((~![B: $i, A: $i] : (mult(A, mult(B, B)) = mult(mult(A, B), B))) | (mult(mult(mult(mult(X0!0, op_b), mult(mult(op_a, op_b), mult(op_a, op_b))), op_a), mult(mult(mult(op_a, op_b), mult(op_a, op_b)), mult(mult(op_a, op_b), mult(op_a, op_b)))) = mult(mult(mult(mult(mult(X0!0, op_b), mult(mult(op_a, op_b), mult(op_a, op_b))), op_a), mult(mult(op_a, op_b), mult(op_a, op_b))), mult(mult(op_a, op_b), mult(op_a, op_b))))),
% 0.63/0.69 inference(quant_inst,[status(thm)],[])).
% 0.63/0.69 tff(107,plain,
% 0.63/0.69 (mult(mult(mult(mult(X0!0, op_b), mult(mult(op_a, op_b), mult(op_a, op_b))), op_a), mult(mult(mult(op_a, op_b), mult(op_a, op_b)), mult(mult(op_a, op_b), mult(op_a, op_b)))) = mult(mult(mult(mult(mult(X0!0, op_b), mult(mult(op_a, op_b), mult(op_a, op_b))), op_a), mult(mult(op_a, op_b), mult(op_a, op_b))), mult(mult(op_a, op_b), mult(op_a, op_b)))),
% 0.63/0.69 inference(unit_resolution,[status(thm)],[106, 44])).
% 0.63/0.69 tff(108,plain,
% 0.63/0.69 (mult(mult(mult(op_a, op_b), mult(op_a, op_b)), mult(mult(op_a, op_b), mult(op_a, op_b))) = mult(mult(op_a, op_b), mult(op_a, op_b))),
% 0.63/0.69 inference(monotonicity,[status(thm)],[24, 24])).
% 0.63/0.69 tff(109,plain,
% 0.63/0.69 (mult(mult(mult(mult(X0!0, op_b), mult(mult(op_a, op_b), mult(op_a, op_b))), op_a), mult(mult(mult(op_a, op_b), mult(op_a, op_b)), mult(mult(op_a, op_b), mult(op_a, op_b)))) = mult(mult(mult(mult(X0!0, op_b), mult(mult(op_a, op_b), mult(op_a, op_b))), op_a), mult(mult(op_a, op_b), mult(op_a, op_b)))),
% 0.63/0.69 inference(monotonicity,[status(thm)],[108])).
% 0.63/0.69 tff(110,plain,
% 0.63/0.69 (mult(mult(mult(mult(X0!0, op_b), mult(mult(op_a, op_b), mult(op_a, op_b))), op_a), mult(mult(op_a, op_b), mult(op_a, op_b))) = mult(mult(mult(mult(X0!0, op_b), mult(mult(op_a, op_b), mult(op_a, op_b))), op_a), mult(mult(mult(op_a, op_b), mult(op_a, op_b)), mult(mult(op_a, op_b), mult(op_a, op_b))))),
% 0.63/0.69 inference(symmetry,[status(thm)],[109])).
% 0.63/0.69 tff(111,plain,
% 0.63/0.69 (mult(mult(X0!0, op_b), op_a) = X0!0),
% 0.63/0.69 inference(transitivity,[status(thm)],[102, 92, 110, 107, 105, 89, 86, 83, 61, 52, 27, 12])).
% 0.63/0.69 tff(112,plain,
% 0.63/0.69 ((~![B: $i, A: $i] : (mult(A, mult(B, B)) = mult(mult(A, B), B))) | (mult(mult(X0!0, op_b), mult(op_a, op_a)) = mult(mult(mult(X0!0, op_b), op_a), op_a))),
% 0.72/0.69 inference(quant_inst,[status(thm)],[])).
% 0.72/0.69 tff(113,plain,
% 0.72/0.69 (mult(mult(X0!0, op_b), mult(op_a, op_a)) = mult(mult(mult(X0!0, op_b), op_a), op_a)),
% 0.72/0.69 inference(unit_resolution,[status(thm)],[112, 44])).
% 0.72/0.69 tff(114,plain,
% 0.72/0.69 (mult(mult(mult(X0!0, op_b), op_a), op_a) = mult(mult(X0!0, op_b), mult(op_a, op_a))),
% 0.72/0.69 inference(symmetry,[status(thm)],[113])).
% 0.72/0.69 tff(115,plain,
% 0.72/0.69 (mult(mult(mult(X0!0, op_b), mult(mult(op_a, op_b), op_a)), op_a) = mult(mult(mult(X0!0, op_b), op_a), op_a)),
% 0.72/0.69 inference(monotonicity,[status(thm)],[77])).
% 0.72/0.69 tff(116,plain,
% 0.72/0.69 (mult(op_a, mult(mult(op_b, mult(op_a, op_a)), op_b)) = mult(op_a, mult(mult(op_a, op_b), mult(op_a, op_b)))),
% 0.72/0.69 inference(monotonicity,[status(thm)],[87])).
% 0.72/0.69 tff(117,plain,
% 0.72/0.69 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(op_a, op_b), mult(op_a, op_a)), op_b) = mult(op_a, mult(mult(op_b, mult(op_a, op_a)), op_b)))),
% 0.72/0.69 inference(quant_inst,[status(thm)],[])).
% 0.72/0.69 tff(118,plain,
% 0.72/0.69 (mult(mult(mult(op_a, op_b), mult(op_a, op_a)), op_b) = mult(op_a, mult(mult(op_b, mult(op_a, op_a)), op_b))),
% 0.72/0.69 inference(unit_resolution,[status(thm)],[117, 59])).
% 0.72/0.69 tff(119,plain,
% 0.72/0.69 (mult(mult(op_a, op_b), mult(op_a, op_a)) = mult(mult(mult(op_a, op_b), mult(op_a, op_b)), mult(op_a, op_a))),
% 0.72/0.69 inference(monotonicity,[status(thm)],[25])).
% 0.72/0.69 tff(120,plain,
% 0.72/0.69 (mult(mult(mult(op_a, op_b), mult(op_a, op_b)), mult(op_a, op_a)) = mult(mult(op_a, op_b), mult(op_a, op_a))),
% 0.72/0.69 inference(symmetry,[status(thm)],[119])).
% 0.72/0.69 tff(121,plain,
% 0.72/0.69 ((~![B: $i, A: $i] : (mult(A, mult(B, B)) = mult(mult(A, B), B))) | (mult(mult(mult(op_a, op_b), mult(op_a, op_b)), mult(op_a, op_a)) = mult(mult(mult(mult(op_a, op_b), mult(op_a, op_b)), op_a), op_a))),
% 0.72/0.69 inference(quant_inst,[status(thm)],[])).
% 0.72/0.69 tff(122,plain,
% 0.72/0.69 (mult(mult(mult(op_a, op_b), mult(op_a, op_b)), mult(op_a, op_a)) = mult(mult(mult(mult(op_a, op_b), mult(op_a, op_b)), op_a), op_a)),
% 0.72/0.69 inference(unit_resolution,[status(thm)],[121, 44])).
% 0.72/0.69 tff(123,plain,
% 0.72/0.69 (mult(mult(mult(mult(op_a, op_b), mult(op_a, op_b)), op_a), op_a) = mult(mult(mult(op_a, op_b), mult(op_a, op_b)), mult(op_a, op_a))),
% 0.72/0.69 inference(symmetry,[status(thm)],[122])).
% 0.72/0.69 tff(124,plain,
% 0.72/0.69 (mult(mult(mult(mult(op_a, op_b), mult(op_a, op_b)), op_a), op_a) = mult(op_a, op_a)),
% 0.72/0.69 inference(monotonicity,[status(thm)],[98])).
% 0.72/0.69 tff(125,plain,
% 0.72/0.69 (mult(op_a, op_a) = mult(mult(mult(mult(op_a, op_b), mult(op_a, op_b)), op_a), op_a)),
% 0.72/0.69 inference(symmetry,[status(thm)],[124])).
% 0.72/0.69 tff(126,plain,
% 0.72/0.69 (mult(op_a, op_a) = mult(mult(op_a, op_b), mult(op_a, op_a))),
% 0.72/0.69 inference(transitivity,[status(thm)],[125, 123, 120])).
% 0.72/0.69 tff(127,plain,
% 0.72/0.69 (mult(mult(op_a, op_a), op_b) = mult(mult(mult(op_a, op_b), mult(op_a, op_a)), op_b)),
% 0.72/0.69 inference(monotonicity,[status(thm)],[126])).
% 0.72/0.69 tff(128,plain,
% 0.72/0.69 (mult(mult(op_b, op_a), op_a) = op_a),
% 0.72/0.69 inference(transitivity,[status(thm)],[37, 30, 29])).
% 0.72/0.69 tff(129,plain,
% 0.72/0.69 (mult(mult(mult(op_b, op_a), op_a), op_a) = mult(op_a, op_a)),
% 0.72/0.69 inference(monotonicity,[status(thm)],[128])).
% 0.72/0.69 tff(130,plain,
% 0.72/0.69 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(op_b, op_a), op_a), op_a) = mult(op_b, mult(mult(op_a, op_a), op_a)))),
% 0.72/0.69 inference(quant_inst,[status(thm)],[])).
% 0.72/0.69 tff(131,plain,
% 0.72/0.69 (mult(mult(mult(op_b, op_a), op_a), op_a) = mult(op_b, mult(mult(op_a, op_a), op_a))),
% 0.72/0.69 inference(unit_resolution,[status(thm)],[130, 59])).
% 0.72/0.69 tff(132,plain,
% 0.72/0.69 (mult(op_b, mult(mult(op_a, op_a), op_a)) = mult(mult(mult(op_b, op_a), op_a), op_a)),
% 0.72/0.69 inference(symmetry,[status(thm)],[131])).
% 0.72/0.69 tff(133,plain,
% 0.72/0.69 (mult(op_b, mult(mult(op_a, op_a), op_a)) = mult(op_a, op_a)),
% 0.72/0.69 inference(transitivity,[status(thm)],[132, 129])).
% 0.72/0.69 tff(134,plain,
% 0.72/0.69 (mult(mult(op_b, mult(mult(op_a, op_a), op_a)), op_b) = mult(mult(op_a, op_a), op_b)),
% 0.72/0.69 inference(monotonicity,[status(thm)],[133])).
% 0.72/0.69 tff(135,plain,
% 0.72/0.69 (mult(mult(op_b, mult(mult(op_a, op_a), op_a)), op_b) = op_a),
% 0.72/0.70 inference(transitivity,[status(thm)],[134, 127, 118, 116, 97, 95, 94])).
% 0.72/0.70 tff(136,plain,
% 0.72/0.70 (mult(mult(mult(X0!0, op_b), mult(mult(op_a, op_b), op_a)), mult(mult(op_b, mult(mult(op_a, op_a), op_a)), op_b)) = mult(mult(mult(X0!0, op_b), mult(mult(op_a, op_b), op_a)), op_a)),
% 0.72/0.70 inference(monotonicity,[status(thm)],[135])).
% 0.72/0.70 tff(137,plain,
% 0.72/0.70 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(mult(X0!0, op_b), mult(mult(op_a, op_b), op_a)), op_b), mult(mult(op_a, op_a), op_a)), op_b) = mult(mult(mult(X0!0, op_b), mult(mult(op_a, op_b), op_a)), mult(mult(op_b, mult(mult(op_a, op_a), op_a)), op_b)))),
% 0.72/0.70 inference(quant_inst,[status(thm)],[])).
% 0.72/0.70 tff(138,plain,
% 0.72/0.70 (mult(mult(mult(mult(mult(X0!0, op_b), mult(mult(op_a, op_b), op_a)), op_b), mult(mult(op_a, op_a), op_a)), op_b) = mult(mult(mult(X0!0, op_b), mult(mult(op_a, op_b), op_a)), mult(mult(op_b, mult(mult(op_a, op_a), op_a)), op_b))),
% 0.72/0.70 inference(unit_resolution,[status(thm)],[137, 59])).
% 0.72/0.70 tff(139,plain,
% 0.72/0.70 (mult(mult(mult(mult(X0!0, op_b), mult(mult(op_a, op_b), op_a)), op_b), mult(mult(op_a, op_a), op_a)) = mult(mult(X0!0, op_b), mult(mult(op_a, op_a), op_a))),
% 0.72/0.70 inference(monotonicity,[status(thm)],[79])).
% 0.72/0.70 tff(140,plain,
% 0.72/0.70 (mult(mult(X0!0, op_b), mult(mult(op_a, op_a), op_a)) = mult(mult(mult(mult(X0!0, op_b), mult(mult(op_a, op_b), op_a)), op_b), mult(mult(op_a, op_a), op_a))),
% 0.72/0.70 inference(symmetry,[status(thm)],[139])).
% 0.72/0.70 tff(141,plain,
% 0.72/0.70 (mult(mult(mult(X0!0, op_b), mult(mult(op_a, op_a), op_a)), op_b) = mult(mult(mult(mult(mult(X0!0, op_b), mult(mult(op_a, op_b), op_a)), op_b), mult(mult(op_a, op_a), op_a)), op_b)),
% 0.72/0.70 inference(monotonicity,[status(thm)],[140])).
% 0.72/0.70 tff(142,plain,
% 0.72/0.70 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(X0!0, op_b), mult(mult(op_a, op_a), op_a)), op_b) = mult(X0!0, mult(mult(op_b, mult(mult(op_a, op_a), op_a)), op_b)))),
% 0.72/0.70 inference(quant_inst,[status(thm)],[])).
% 0.72/0.70 tff(143,plain,
% 0.72/0.70 (mult(mult(mult(X0!0, op_b), mult(mult(op_a, op_a), op_a)), op_b) = mult(X0!0, mult(mult(op_b, mult(mult(op_a, op_a), op_a)), op_b))),
% 0.72/0.70 inference(unit_resolution,[status(thm)],[142, 59])).
% 0.72/0.70 tff(144,plain,
% 0.72/0.70 (mult(X0!0, mult(mult(op_b, mult(mult(op_a, op_a), op_a)), op_b)) = mult(mult(mult(X0!0, op_b), mult(mult(op_a, op_a), op_a)), op_b)),
% 0.72/0.70 inference(symmetry,[status(thm)],[143])).
% 0.72/0.70 tff(145,plain,
% 0.72/0.70 (mult(mult(op_a, op_a), op_b) = mult(mult(op_b, mult(mult(op_a, op_a), op_a)), op_b)),
% 0.72/0.70 inference(symmetry,[status(thm)],[134])).
% 0.72/0.70 tff(146,plain,
% 0.72/0.70 (mult(mult(mult(op_a, op_b), mult(op_a, op_a)), op_b) = mult(mult(op_a, op_a), op_b)),
% 0.72/0.70 inference(symmetry,[status(thm)],[127])).
% 0.72/0.70 tff(147,plain,
% 0.72/0.70 (mult(op_a, mult(mult(op_b, mult(op_a, op_a)), op_b)) = mult(mult(mult(op_a, op_b), mult(op_a, op_a)), op_b)),
% 0.72/0.70 inference(symmetry,[status(thm)],[118])).
% 0.72/0.70 tff(148,plain,
% 0.72/0.70 (mult(op_a, mult(mult(op_a, op_b), mult(op_a, op_b))) = mult(op_a, mult(mult(op_b, mult(op_a, op_a)), op_b))),
% 0.72/0.70 inference(symmetry,[status(thm)],[116])).
% 0.72/0.70 tff(149,plain,
% 0.72/0.70 (mult(mult(op_a, mult(op_a, op_b)), mult(op_a, op_b)) = mult(op_a, mult(mult(op_a, op_b), mult(op_a, op_b)))),
% 0.72/0.70 inference(symmetry,[status(thm)],[97])).
% 0.72/0.70 tff(150,plain,
% 0.72/0.70 (mult(op_a, mult(op_a, op_b)) = mult(mult(op_a, mult(op_a, op_b)), mult(op_a, op_b))),
% 0.72/0.70 inference(symmetry,[status(thm)],[95])).
% 0.72/0.70 tff(151,plain,
% 0.72/0.70 (op_a = mult(op_a, mult(op_a, op_b))),
% 0.72/0.70 inference(symmetry,[status(thm)],[94])).
% 0.72/0.70 tff(152,plain,
% 0.72/0.70 (op_a = mult(mult(op_b, mult(mult(op_a, op_a), op_a)), op_b)),
% 0.72/0.70 inference(transitivity,[status(thm)],[151, 150, 149, 148, 147, 146, 145])).
% 0.72/0.70 tff(153,plain,
% 0.72/0.70 (mult(X0!0, op_a) = mult(X0!0, mult(mult(op_b, mult(mult(op_a, op_a), op_a)), op_b))),
% 0.72/0.70 inference(monotonicity,[status(thm)],[152])).
% 0.72/0.70 tff(154,plain,
% 0.72/0.70 (mult(X0!0, op_a) = mult(mult(X0!0, op_b), mult(op_a, op_a))),
% 0.72/0.70 inference(transitivity,[status(thm)],[153, 144, 141, 138, 136, 115, 114])).
% 0.72/0.70 tff(155,plain,
% 0.72/0.70 (mult(mult(X0!0, op_a), op_b) = mult(mult(mult(X0!0, op_b), mult(op_a, op_a)), op_b)),
% 0.72/0.70 inference(monotonicity,[status(thm)],[154])).
% 0.72/0.70 tff(156,plain,
% 0.72/0.70 (mult(mult(X0!0, op_a), op_b) = X0!0),
% 0.72/0.70 inference(transitivity,[status(thm)],[155, 61, 52, 27, 12])).
% 0.72/0.70 tff(157,plain,
% 0.72/0.70 ((~(~((~(mult(mult(X0!0, op_a), op_b) = X0!0)) | (~(mult(mult(X0!0, op_b), op_a) = X0!0))))) <=> ((~(mult(mult(X0!0, op_a), op_b) = X0!0)) | (~(mult(mult(X0!0, op_b), op_a) = X0!0)))),
% 0.72/0.70 inference(rewrite,[status(thm)],[])).
% 0.72/0.70 tff(158,plain,
% 0.72/0.70 (((mult(mult(X0!0, op_a), op_b) = X0!0) & (mult(mult(X0!0, op_b), op_a) = X0!0)) <=> (~((~(mult(mult(X0!0, op_a), op_b) = X0!0)) | (~(mult(mult(X0!0, op_b), op_a) = X0!0))))),
% 0.72/0.70 inference(rewrite,[status(thm)],[])).
% 0.72/0.70 tff(159,plain,
% 0.72/0.70 ((~((mult(mult(X0!0, op_a), op_b) = X0!0) & (mult(mult(X0!0, op_b), op_a) = X0!0))) <=> (~(~((~(mult(mult(X0!0, op_a), op_b) = X0!0)) | (~(mult(mult(X0!0, op_b), op_a) = X0!0)))))),
% 0.72/0.70 inference(monotonicity,[status(thm)],[158])).
% 0.72/0.70 tff(160,plain,
% 0.72/0.70 ((~((mult(mult(X0!0, op_a), op_b) = X0!0) & (mult(mult(X0!0, op_b), op_a) = X0!0))) <=> ((~(mult(mult(X0!0, op_a), op_b) = X0!0)) | (~(mult(mult(X0!0, op_b), op_a) = X0!0)))),
% 0.72/0.70 inference(transitivity,[status(thm)],[159, 157])).
% 0.72/0.70 tff(161,plain,
% 0.72/0.70 ((~![X0: $i] : ((mult(mult(X0, op_a), op_b) = X0) & (mult(mult(X0, op_b), op_a) = X0))) <=> (~![X0: $i] : ((mult(mult(X0, op_a), op_b) = X0) & (mult(mult(X0, op_b), op_a) = X0)))),
% 0.72/0.70 inference(rewrite,[status(thm)],[])).
% 0.72/0.70 tff(162,axiom,(~![X0: $i] : ((mult(mult(X0, op_a), op_b) = X0) & (mult(mult(X0, op_b), op_a) = X0))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','goals')).
% 0.72/0.70 tff(163,plain,
% 0.72/0.70 (~![X0: $i] : ((mult(mult(X0, op_a), op_b) = X0) & (mult(mult(X0, op_b), op_a) = X0))),
% 0.72/0.70 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.72/0.70 tff(164,plain,
% 0.72/0.70 (~![X0: $i] : ((mult(mult(X0, op_a), op_b) = X0) & (mult(mult(X0, op_b), op_a) = X0))),
% 0.72/0.70 inference(modus_ponens,[status(thm)],[163, 161])).
% 0.72/0.70 tff(165,plain,
% 0.72/0.70 (~![X0: $i] : ((mult(mult(X0, op_a), op_b) = X0) & (mult(mult(X0, op_b), op_a) = X0))),
% 0.72/0.70 inference(modus_ponens,[status(thm)],[164, 161])).
% 0.72/0.70 tff(166,plain,
% 0.72/0.70 (~![X0: $i] : ((mult(mult(X0, op_a), op_b) = X0) & (mult(mult(X0, op_b), op_a) = X0))),
% 0.72/0.70 inference(modus_ponens,[status(thm)],[165, 161])).
% 0.72/0.70 tff(167,plain,
% 0.72/0.70 (~![X0: $i] : ((mult(mult(X0, op_a), op_b) = X0) & (mult(mult(X0, op_b), op_a) = X0))),
% 0.72/0.70 inference(modus_ponens,[status(thm)],[166, 161])).
% 0.72/0.70 tff(168,plain,
% 0.72/0.70 (~![X0: $i] : ((mult(mult(X0, op_a), op_b) = X0) & (mult(mult(X0, op_b), op_a) = X0))),
% 0.72/0.70 inference(modus_ponens,[status(thm)],[167, 161])).
% 0.72/0.70 tff(169,plain,
% 0.72/0.70 (~![X0: $i] : ((mult(mult(X0, op_a), op_b) = X0) & (mult(mult(X0, op_b), op_a) = X0))),
% 0.72/0.70 inference(modus_ponens,[status(thm)],[168, 161])).
% 0.72/0.70 tff(170,plain,
% 0.72/0.70 (~![X0: $i] : ((mult(mult(X0, op_a), op_b) = X0) & (mult(mult(X0, op_b), op_a) = X0))),
% 0.72/0.70 inference(modus_ponens,[status(thm)],[169, 161])).
% 0.72/0.70 tff(171,plain,(
% 0.72/0.70 ~((mult(mult(X0!0, op_a), op_b) = X0!0) & (mult(mult(X0!0, op_b), op_a) = X0!0))),
% 0.72/0.70 inference(skolemize,[status(sab)],[170])).
% 0.72/0.70 tff(172,plain,
% 0.72/0.70 ((~(mult(mult(X0!0, op_a), op_b) = X0!0)) | (~(mult(mult(X0!0, op_b), op_a) = X0!0))),
% 0.72/0.70 inference(modus_ponens,[status(thm)],[171, 160])).
% 0.72/0.70 tff(173,plain,
% 0.72/0.70 ($false),
% 0.72/0.70 inference(unit_resolution,[status(thm)],[172, 156, 111])).
% 0.72/0.70 % SZS output end Proof
%------------------------------------------------------------------------------