TSTP Solution File: GRP008-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP008-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n010.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 22:25:24 EDT 2022
% Result : Unsatisfiable 0.83s 0.78s
% Output : Proof 0.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP008-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n010.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % 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 13:56:58 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.83/0.78 % SZS status Unsatisfiable
% 0.83/0.78 % SZS output start Proof
% 0.83/0.78 tff(product_type, type, (
% 0.83/0.78 product: ( $i * $i * $i ) > $o)).
% 0.83/0.78 tff(multiply_type, type, (
% 0.83/0.78 multiply: ( $i * $i ) > $i)).
% 0.83/0.78 tff(identity_type, type, (
% 0.83/0.78 identity: $i)).
% 0.83/0.78 tff(h_type, type, (
% 0.83/0.78 h: $i > $i)).
% 0.83/0.78 tff(j_type, type, (
% 0.83/0.78 j: $i > $i)).
% 0.83/0.78 tff(inverse_type, type, (
% 0.83/0.78 inverse: $i > $i)).
% 0.83/0.78 tff(q_type, type, (
% 0.83/0.78 q: $i > $o)).
% 0.83/0.78 tff(1,plain,
% 0.83/0.78 (^[Y: $i, X: $i] : refl(product(X, Y, multiply(X, Y)) <=> product(X, Y, multiply(X, Y)))),
% 0.83/0.78 inference(bind,[status(th)],[])).
% 0.83/0.78 tff(2,plain,
% 0.83/0.78 (![Y: $i, X: $i] : product(X, Y, multiply(X, Y)) <=> ![Y: $i, X: $i] : product(X, Y, multiply(X, Y))),
% 0.83/0.78 inference(quant_intro,[status(thm)],[1])).
% 0.83/0.78 tff(3,plain,
% 0.83/0.78 (![Y: $i, X: $i] : product(X, Y, multiply(X, Y)) <=> ![Y: $i, X: $i] : product(X, Y, multiply(X, Y))),
% 0.83/0.78 inference(rewrite,[status(thm)],[])).
% 0.83/0.78 tff(4,axiom,(![Y: $i, X: $i] : product(X, Y, multiply(X, Y))), file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax','total_function1')).
% 0.83/0.78 tff(5,plain,
% 0.83/0.78 (![Y: $i, X: $i] : product(X, Y, multiply(X, Y))),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.83/0.78 tff(6,plain,(
% 0.83/0.78 ![Y: $i, X: $i] : product(X, Y, multiply(X, Y))),
% 0.83/0.78 inference(skolemize,[status(sab)],[5])).
% 0.83/0.78 tff(7,plain,
% 0.83/0.78 (![Y: $i, X: $i] : product(X, Y, multiply(X, Y))),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.83/0.78 tff(8,plain,
% 0.83/0.78 ((~![Y: $i, X: $i] : product(X, Y, multiply(X, Y))) | product(h(identity), identity, multiply(h(identity), identity))),
% 0.83/0.78 inference(quant_inst,[status(thm)],[])).
% 0.83/0.78 tff(9,plain,
% 0.83/0.78 (product(h(identity), identity, multiply(h(identity), identity))),
% 0.83/0.78 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.83/0.78 tff(10,plain,
% 0.83/0.78 (^[X: $i] : refl(product(X, identity, X) <=> product(X, identity, X))),
% 0.83/0.78 inference(bind,[status(th)],[])).
% 0.83/0.78 tff(11,plain,
% 0.83/0.78 (![X: $i] : product(X, identity, X) <=> ![X: $i] : product(X, identity, X)),
% 0.83/0.78 inference(quant_intro,[status(thm)],[10])).
% 0.83/0.78 tff(12,plain,
% 0.83/0.78 (![X: $i] : product(X, identity, X) <=> ![X: $i] : product(X, identity, X)),
% 0.83/0.78 inference(rewrite,[status(thm)],[])).
% 0.83/0.78 tff(13,axiom,(![X: $i] : product(X, identity, X)), file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax','right_identity')).
% 0.83/0.78 tff(14,plain,
% 0.83/0.78 (![X: $i] : product(X, identity, X)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.83/0.78 tff(15,plain,(
% 0.83/0.78 ![X: $i] : product(X, identity, X)),
% 0.83/0.78 inference(skolemize,[status(sab)],[14])).
% 0.83/0.78 tff(16,plain,
% 0.83/0.78 (![X: $i] : product(X, identity, X)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.83/0.78 tff(17,plain,
% 0.83/0.78 ((~![X: $i] : product(X, identity, X)) | product(h(identity), identity, h(identity))),
% 0.83/0.78 inference(quant_inst,[status(thm)],[])).
% 0.83/0.78 tff(18,plain,
% 0.83/0.78 (product(h(identity), identity, h(identity))),
% 0.83/0.78 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.83/0.78 tff(19,plain,
% 0.83/0.78 (^[W: $i, Z: $i, Y: $i, X: $i] : refl(((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z))) <=> ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z))))),
% 0.83/0.78 inference(bind,[status(th)],[])).
% 0.83/0.78 tff(20,plain,
% 0.83/0.78 (![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))),
% 0.83/0.78 inference(quant_intro,[status(thm)],[19])).
% 0.83/0.78 tff(21,plain,
% 0.83/0.78 (![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))),
% 0.83/0.78 inference(rewrite,[status(thm)],[])).
% 0.83/0.78 tff(22,plain,
% 0.83/0.78 (^[W: $i, Z: $i, Y: $i, X: $i] : rewrite((((~product(X, Y, Z)) | (~product(X, Y, W))) | (Z = W)) <=> ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z))))),
% 0.83/0.78 inference(bind,[status(th)],[])).
% 0.83/0.78 tff(23,plain,
% 0.83/0.78 (![W: $i, Z: $i, Y: $i, X: $i] : (((~product(X, Y, Z)) | (~product(X, Y, W))) | (Z = W)) <=> ![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))),
% 0.83/0.78 inference(quant_intro,[status(thm)],[22])).
% 0.83/0.78 tff(24,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product(X, Y, Z)) | (~product(X, Y, W))) | (Z = W))), file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax','total_function2')).
% 0.83/0.78 tff(25,plain,
% 0.83/0.78 (![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.83/0.78 tff(26,plain,
% 0.83/0.78 (![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.83/0.78 tff(27,plain,(
% 0.83/0.78 ![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))),
% 0.83/0.78 inference(skolemize,[status(sab)],[26])).
% 0.83/0.78 tff(28,plain,
% 0.83/0.78 (![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.83/0.78 tff(29,plain,
% 0.83/0.78 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | ((~product(h(identity), identity, multiply(h(identity), identity))) | (~product(h(identity), identity, h(identity))) | (h(identity) = multiply(h(identity), identity)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | (~product(h(identity), identity, multiply(h(identity), identity))) | (~product(h(identity), identity, h(identity))) | (h(identity) = multiply(h(identity), identity)))),
% 0.83/0.78 inference(rewrite,[status(thm)],[])).
% 0.83/0.78 tff(30,plain,
% 0.83/0.78 (((h(identity) = multiply(h(identity), identity)) | (~product(h(identity), identity, multiply(h(identity), identity))) | (~product(h(identity), identity, h(identity)))) <=> ((~product(h(identity), identity, multiply(h(identity), identity))) | (~product(h(identity), identity, h(identity))) | (h(identity) = multiply(h(identity), identity)))),
% 0.83/0.78 inference(rewrite,[status(thm)],[])).
% 0.83/0.78 tff(31,plain,
% 0.83/0.78 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | ((h(identity) = multiply(h(identity), identity)) | (~product(h(identity), identity, multiply(h(identity), identity))) | (~product(h(identity), identity, h(identity))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | ((~product(h(identity), identity, multiply(h(identity), identity))) | (~product(h(identity), identity, h(identity))) | (h(identity) = multiply(h(identity), identity))))),
% 0.83/0.78 inference(monotonicity,[status(thm)],[30])).
% 0.83/0.78 tff(32,plain,
% 0.83/0.78 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | ((h(identity) = multiply(h(identity), identity)) | (~product(h(identity), identity, multiply(h(identity), identity))) | (~product(h(identity), identity, h(identity))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | (~product(h(identity), identity, multiply(h(identity), identity))) | (~product(h(identity), identity, h(identity))) | (h(identity) = multiply(h(identity), identity)))),
% 0.83/0.78 inference(transitivity,[status(thm)],[31, 29])).
% 0.83/0.78 tff(33,plain,
% 0.83/0.78 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | ((h(identity) = multiply(h(identity), identity)) | (~product(h(identity), identity, multiply(h(identity), identity))) | (~product(h(identity), identity, h(identity))))),
% 0.83/0.78 inference(quant_inst,[status(thm)],[])).
% 0.83/0.78 tff(34,plain,
% 0.83/0.78 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | (~product(h(identity), identity, multiply(h(identity), identity))) | (~product(h(identity), identity, h(identity))) | (h(identity) = multiply(h(identity), identity))),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.83/0.78 tff(35,plain,
% 0.83/0.78 (h(identity) = multiply(h(identity), identity)),
% 0.83/0.78 inference(unit_resolution,[status(thm)],[34, 28, 18, 9])).
% 0.83/0.78 tff(36,plain,
% 0.83/0.78 (multiply(h(identity), identity) = h(identity)),
% 0.83/0.78 inference(symmetry,[status(thm)],[35])).
% 0.83/0.78 tff(37,plain,
% 0.83/0.78 (product(identity, j(identity), multiply(h(identity), identity)) <=> product(identity, j(identity), h(identity))),
% 0.83/0.78 inference(monotonicity,[status(thm)],[36])).
% 0.83/0.78 tff(38,plain,
% 0.83/0.78 (product(identity, j(identity), h(identity)) <=> product(identity, j(identity), multiply(h(identity), identity))),
% 0.83/0.78 inference(symmetry,[status(thm)],[37])).
% 0.83/0.78 tff(39,plain,
% 0.83/0.78 ((~product(identity, j(identity), h(identity))) <=> (~product(identity, j(identity), multiply(h(identity), identity)))),
% 0.83/0.78 inference(monotonicity,[status(thm)],[38])).
% 0.83/0.78 tff(40,assumption,(~product(identity, j(identity), h(identity))), introduced(assumption)).
% 0.83/0.78 tff(41,plain,
% 0.83/0.78 (~product(identity, j(identity), multiply(h(identity), identity))),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.83/0.78 tff(42,plain,
% 0.83/0.78 (^[X: $i] : refl(product(inverse(X), X, identity) <=> product(inverse(X), X, identity))),
% 0.83/0.78 inference(bind,[status(th)],[])).
% 0.83/0.78 tff(43,plain,
% 0.83/0.78 (![X: $i] : product(inverse(X), X, identity) <=> ![X: $i] : product(inverse(X), X, identity)),
% 0.83/0.78 inference(quant_intro,[status(thm)],[42])).
% 0.83/0.78 tff(44,plain,
% 0.83/0.78 (![X: $i] : product(inverse(X), X, identity) <=> ![X: $i] : product(inverse(X), X, identity)),
% 0.83/0.78 inference(rewrite,[status(thm)],[])).
% 0.83/0.78 tff(45,axiom,(![X: $i] : product(inverse(X), X, identity)), file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax','left_inverse')).
% 0.83/0.78 tff(46,plain,
% 0.83/0.78 (![X: $i] : product(inverse(X), X, identity)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.83/0.78 tff(47,plain,(
% 0.83/0.78 ![X: $i] : product(inverse(X), X, identity)),
% 0.83/0.78 inference(skolemize,[status(sab)],[46])).
% 0.83/0.78 tff(48,plain,
% 0.83/0.78 (![X: $i] : product(inverse(X), X, identity)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.83/0.78 tff(49,plain,
% 0.83/0.78 ((~![X: $i] : product(inverse(X), X, identity)) | product(inverse(j(identity)), j(identity), identity)),
% 0.83/0.78 inference(quant_inst,[status(thm)],[])).
% 0.83/0.78 tff(50,plain,
% 0.83/0.78 (product(inverse(j(identity)), j(identity), identity)),
% 0.83/0.78 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.83/0.78 tff(51,plain,
% 0.83/0.78 (product(j(identity), identity, multiply(h(identity), identity)) <=> product(j(identity), identity, h(identity))),
% 0.83/0.78 inference(monotonicity,[status(thm)],[36])).
% 0.83/0.78 tff(52,plain,
% 0.83/0.78 (product(j(identity), identity, h(identity)) <=> product(j(identity), identity, multiply(h(identity), identity))),
% 0.83/0.78 inference(symmetry,[status(thm)],[51])).
% 0.83/0.78 tff(53,plain,
% 0.83/0.78 ((~q(identity)) <=> (~q(identity))),
% 0.83/0.78 inference(rewrite,[status(thm)],[])).
% 0.83/0.78 tff(54,axiom,(~q(identity)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_identity_is_q')).
% 0.83/0.78 tff(55,plain,
% 0.83/0.78 (~q(identity)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.83/0.78 tff(56,plain,
% 0.83/0.78 (^[A: $i] : refl((q(A) | product(A, j(A), h(A)) | product(j(A), A, h(A))) <=> (q(A) | product(A, j(A), h(A)) | product(j(A), A, h(A))))),
% 0.83/0.78 inference(bind,[status(th)],[])).
% 0.83/0.78 tff(57,plain,
% 0.83/0.78 (![A: $i] : (q(A) | product(A, j(A), h(A)) | product(j(A), A, h(A))) <=> ![A: $i] : (q(A) | product(A, j(A), h(A)) | product(j(A), A, h(A)))),
% 0.83/0.78 inference(quant_intro,[status(thm)],[56])).
% 0.83/0.78 tff(58,plain,
% 0.83/0.78 (![A: $i] : (q(A) | product(A, j(A), h(A)) | product(j(A), A, h(A))) <=> ![A: $i] : (q(A) | product(A, j(A), h(A)) | product(j(A), A, h(A)))),
% 0.83/0.78 inference(rewrite,[status(thm)],[])).
% 0.83/0.78 tff(59,plain,
% 0.83/0.78 (^[A: $i] : rewrite(((product(j(A), A, h(A)) | product(A, j(A), h(A))) | q(A)) <=> (q(A) | product(A, j(A), h(A)) | product(j(A), A, h(A))))),
% 0.83/0.78 inference(bind,[status(th)],[])).
% 0.83/0.78 tff(60,plain,
% 0.83/0.78 (![A: $i] : ((product(j(A), A, h(A)) | product(A, j(A), h(A))) | q(A)) <=> ![A: $i] : (q(A) | product(A, j(A), h(A)) | product(j(A), A, h(A)))),
% 0.83/0.78 inference(quant_intro,[status(thm)],[59])).
% 0.83/0.78 tff(61,axiom,(![A: $i] : ((product(j(A), A, h(A)) | product(A, j(A), h(A))) | q(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','unknown_meaning3')).
% 0.83/0.78 tff(62,plain,
% 0.83/0.78 (![A: $i] : (q(A) | product(A, j(A), h(A)) | product(j(A), A, h(A)))),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.83/0.78 tff(63,plain,
% 0.83/0.78 (![A: $i] : (q(A) | product(A, j(A), h(A)) | product(j(A), A, h(A)))),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.83/0.78 tff(64,plain,(
% 0.83/0.78 ![A: $i] : (q(A) | product(A, j(A), h(A)) | product(j(A), A, h(A)))),
% 0.83/0.78 inference(skolemize,[status(sab)],[63])).
% 0.83/0.78 tff(65,plain,
% 0.83/0.78 (![A: $i] : (q(A) | product(A, j(A), h(A)) | product(j(A), A, h(A)))),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[64, 57])).
% 0.83/0.78 tff(66,plain,
% 0.83/0.78 (((~![A: $i] : (q(A) | product(A, j(A), h(A)) | product(j(A), A, h(A)))) | (q(identity) | product(identity, j(identity), h(identity)) | product(j(identity), identity, h(identity)))) <=> ((~![A: $i] : (q(A) | product(A, j(A), h(A)) | product(j(A), A, h(A)))) | q(identity) | product(identity, j(identity), h(identity)) | product(j(identity), identity, h(identity)))),
% 0.83/0.78 inference(rewrite,[status(thm)],[])).
% 0.83/0.78 tff(67,plain,
% 0.83/0.78 ((~![A: $i] : (q(A) | product(A, j(A), h(A)) | product(j(A), A, h(A)))) | (q(identity) | product(identity, j(identity), h(identity)) | product(j(identity), identity, h(identity)))),
% 0.83/0.78 inference(quant_inst,[status(thm)],[])).
% 0.83/0.78 tff(68,plain,
% 0.83/0.78 ((~![A: $i] : (q(A) | product(A, j(A), h(A)) | product(j(A), A, h(A)))) | q(identity) | product(identity, j(identity), h(identity)) | product(j(identity), identity, h(identity))),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.83/0.78 tff(69,plain,
% 0.83/0.78 (product(identity, j(identity), h(identity)) | product(j(identity), identity, h(identity))),
% 0.83/0.78 inference(unit_resolution,[status(thm)],[68, 65, 55])).
% 0.83/0.78 tff(70,plain,
% 0.83/0.78 (product(j(identity), identity, h(identity))),
% 0.83/0.78 inference(unit_resolution,[status(thm)],[69, 40])).
% 0.83/0.78 tff(71,plain,
% 0.83/0.78 (product(j(identity), identity, multiply(h(identity), identity))),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[70, 52])).
% 0.83/0.78 tff(72,plain,
% 0.83/0.78 (^[X: $i] : refl(product(X, inverse(X), identity) <=> product(X, inverse(X), identity))),
% 0.83/0.78 inference(bind,[status(th)],[])).
% 0.83/0.78 tff(73,plain,
% 0.83/0.78 (![X: $i] : product(X, inverse(X), identity) <=> ![X: $i] : product(X, inverse(X), identity)),
% 0.83/0.78 inference(quant_intro,[status(thm)],[72])).
% 0.83/0.78 tff(74,plain,
% 0.83/0.78 (![X: $i] : product(X, inverse(X), identity) <=> ![X: $i] : product(X, inverse(X), identity)),
% 0.83/0.78 inference(rewrite,[status(thm)],[])).
% 0.83/0.78 tff(75,axiom,(![X: $i] : product(X, inverse(X), identity)), file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax','right_inverse')).
% 0.83/0.78 tff(76,plain,
% 0.83/0.78 (![X: $i] : product(X, inverse(X), identity)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.83/0.78 tff(77,plain,(
% 0.83/0.78 ![X: $i] : product(X, inverse(X), identity)),
% 0.83/0.78 inference(skolemize,[status(sab)],[76])).
% 0.83/0.78 tff(78,plain,
% 0.83/0.78 (![X: $i] : product(X, inverse(X), identity)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[77, 73])).
% 0.83/0.78 tff(79,plain,
% 0.83/0.78 ((~![X: $i] : product(X, inverse(X), identity)) | product(j(identity), inverse(j(identity)), identity)),
% 0.83/0.78 inference(quant_inst,[status(thm)],[])).
% 0.83/0.78 tff(80,plain,
% 0.83/0.78 (product(j(identity), inverse(j(identity)), identity)),
% 0.83/0.78 inference(unit_resolution,[status(thm)],[79, 78])).
% 0.83/0.78 tff(81,plain,
% 0.83/0.78 (^[W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : refl((product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W))) <=> (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W))))),
% 0.83/0.78 inference(bind,[status(th)],[])).
% 0.83/0.78 tff(82,plain,
% 0.83/0.78 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W))) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))),
% 0.83/0.78 inference(quant_intro,[status(thm)],[81])).
% 0.83/0.78 tff(83,plain,
% 0.83/0.78 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W))) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))),
% 0.83/0.78 inference(rewrite,[status(thm)],[])).
% 0.83/0.78 tff(84,plain,
% 0.83/0.78 (^[W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : trans(monotonicity(rewrite((((~product(X, Y, U)) | (~product(Y, Z, V))) | (~product(X, V, W))) <=> ((~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))), (((((~product(X, Y, U)) | (~product(Y, Z, V))) | (~product(X, V, W))) | product(U, Z, W)) <=> (((~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W))) | product(U, Z, W)))), rewrite((((~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W))) | product(U, Z, W)) <=> (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))), (((((~product(X, Y, U)) | (~product(Y, Z, V))) | (~product(X, V, W))) | product(U, Z, W)) <=> (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))))),
% 0.83/0.78 inference(bind,[status(th)],[])).
% 0.83/0.78 tff(85,plain,
% 0.83/0.78 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((((~product(X, Y, U)) | (~product(Y, Z, V))) | (~product(X, V, W))) | product(U, Z, W)) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))),
% 0.83/0.78 inference(quant_intro,[status(thm)],[84])).
% 0.83/0.78 tff(86,axiom,(![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((((~product(X, Y, U)) | (~product(Y, Z, V))) | (~product(X, V, W))) | product(U, Z, W))), file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax','associativity2')).
% 0.83/0.78 tff(87,plain,
% 0.83/0.78 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.83/0.78 tff(88,plain,
% 0.83/0.78 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[87, 83])).
% 0.83/0.78 tff(89,plain,(
% 0.83/0.78 ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))),
% 0.83/0.78 inference(skolemize,[status(sab)],[88])).
% 0.83/0.78 tff(90,plain,
% 0.83/0.78 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[89, 82])).
% 0.83/0.78 tff(91,plain,
% 0.83/0.78 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | (product(identity, j(identity), multiply(h(identity), identity)) | (~product(j(identity), identity, multiply(h(identity), identity))) | (~product(j(identity), inverse(j(identity)), identity)) | (~product(inverse(j(identity)), j(identity), identity)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | product(identity, j(identity), multiply(h(identity), identity)) | (~product(j(identity), identity, multiply(h(identity), identity))) | (~product(j(identity), inverse(j(identity)), identity)) | (~product(inverse(j(identity)), j(identity), identity)))),
% 0.83/0.78 inference(rewrite,[status(thm)],[])).
% 0.83/0.78 tff(92,plain,
% 0.83/0.78 ((product(identity, j(identity), multiply(h(identity), identity)) | (~product(inverse(j(identity)), j(identity), identity)) | (~product(j(identity), inverse(j(identity)), identity)) | (~product(j(identity), identity, multiply(h(identity), identity)))) <=> (product(identity, j(identity), multiply(h(identity), identity)) | (~product(j(identity), identity, multiply(h(identity), identity))) | (~product(j(identity), inverse(j(identity)), identity)) | (~product(inverse(j(identity)), j(identity), identity)))),
% 0.83/0.78 inference(rewrite,[status(thm)],[])).
% 0.83/0.78 tff(93,plain,
% 0.83/0.78 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | (product(identity, j(identity), multiply(h(identity), identity)) | (~product(inverse(j(identity)), j(identity), identity)) | (~product(j(identity), inverse(j(identity)), identity)) | (~product(j(identity), identity, multiply(h(identity), identity))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | (product(identity, j(identity), multiply(h(identity), identity)) | (~product(j(identity), identity, multiply(h(identity), identity))) | (~product(j(identity), inverse(j(identity)), identity)) | (~product(inverse(j(identity)), j(identity), identity))))),
% 0.83/0.78 inference(monotonicity,[status(thm)],[92])).
% 0.83/0.78 tff(94,plain,
% 0.83/0.78 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | (product(identity, j(identity), multiply(h(identity), identity)) | (~product(inverse(j(identity)), j(identity), identity)) | (~product(j(identity), inverse(j(identity)), identity)) | (~product(j(identity), identity, multiply(h(identity), identity))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | product(identity, j(identity), multiply(h(identity), identity)) | (~product(j(identity), identity, multiply(h(identity), identity))) | (~product(j(identity), inverse(j(identity)), identity)) | (~product(inverse(j(identity)), j(identity), identity)))),
% 0.83/0.78 inference(transitivity,[status(thm)],[93, 91])).
% 0.83/0.78 tff(95,plain,
% 0.83/0.78 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | (product(identity, j(identity), multiply(h(identity), identity)) | (~product(inverse(j(identity)), j(identity), identity)) | (~product(j(identity), inverse(j(identity)), identity)) | (~product(j(identity), identity, multiply(h(identity), identity))))),
% 0.83/0.78 inference(quant_inst,[status(thm)],[])).
% 0.83/0.78 tff(96,plain,
% 0.83/0.78 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | product(identity, j(identity), multiply(h(identity), identity)) | (~product(j(identity), identity, multiply(h(identity), identity))) | (~product(j(identity), inverse(j(identity)), identity)) | (~product(inverse(j(identity)), j(identity), identity))),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.83/0.78 tff(97,plain,
% 0.83/0.78 (product(identity, j(identity), multiply(h(identity), identity))),
% 0.83/0.78 inference(unit_resolution,[status(thm)],[96, 90, 80, 71, 50])).
% 0.83/0.78 tff(98,plain,
% 0.83/0.78 ($false),
% 0.83/0.78 inference(unit_resolution,[status(thm)],[97, 41])).
% 0.83/0.78 tff(99,plain,(product(identity, j(identity), h(identity))), inference(lemma,lemma(discharge,[]))).
% 0.83/0.78 tff(100,plain,
% 0.83/0.78 (product(identity, j(identity), multiply(h(identity), identity))),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[99, 38])).
% 0.83/0.78 tff(101,plain,
% 0.83/0.78 ((~product(j(identity), identity, h(identity))) <=> (~product(j(identity), identity, multiply(h(identity), identity)))),
% 0.83/0.78 inference(monotonicity,[status(thm)],[52])).
% 0.83/0.78 tff(102,plain,
% 0.83/0.78 (^[A: $i] : refl((q(A) | (~product(A, j(A), h(A))) | (~product(j(A), A, h(A)))) <=> (q(A) | (~product(A, j(A), h(A))) | (~product(j(A), A, h(A)))))),
% 0.83/0.78 inference(bind,[status(th)],[])).
% 0.83/0.78 tff(103,plain,
% 0.83/0.78 (![A: $i] : (q(A) | (~product(A, j(A), h(A))) | (~product(j(A), A, h(A)))) <=> ![A: $i] : (q(A) | (~product(A, j(A), h(A))) | (~product(j(A), A, h(A))))),
% 0.83/0.78 inference(quant_intro,[status(thm)],[102])).
% 0.83/0.78 tff(104,plain,
% 0.83/0.78 (![A: $i] : (q(A) | (~product(A, j(A), h(A))) | (~product(j(A), A, h(A)))) <=> ![A: $i] : (q(A) | (~product(A, j(A), h(A))) | (~product(j(A), A, h(A))))),
% 0.83/0.78 inference(rewrite,[status(thm)],[])).
% 0.83/0.78 tff(105,plain,
% 0.83/0.78 (^[A: $i] : rewrite((((~product(j(A), A, h(A))) | (~product(A, j(A), h(A)))) | q(A)) <=> (q(A) | (~product(A, j(A), h(A))) | (~product(j(A), A, h(A)))))),
% 0.83/0.78 inference(bind,[status(th)],[])).
% 0.83/0.78 tff(106,plain,
% 0.83/0.78 (![A: $i] : (((~product(j(A), A, h(A))) | (~product(A, j(A), h(A)))) | q(A)) <=> ![A: $i] : (q(A) | (~product(A, j(A), h(A))) | (~product(j(A), A, h(A))))),
% 0.83/0.78 inference(quant_intro,[status(thm)],[105])).
% 0.83/0.78 tff(107,axiom,(![A: $i] : (((~product(j(A), A, h(A))) | (~product(A, j(A), h(A)))) | q(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','unknown_meaning4')).
% 0.83/0.78 tff(108,plain,
% 0.83/0.78 (![A: $i] : (q(A) | (~product(A, j(A), h(A))) | (~product(j(A), A, h(A))))),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.83/0.78 tff(109,plain,
% 0.83/0.78 (![A: $i] : (q(A) | (~product(A, j(A), h(A))) | (~product(j(A), A, h(A))))),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[108, 104])).
% 0.83/0.78 tff(110,plain,(
% 0.83/0.78 ![A: $i] : (q(A) | (~product(A, j(A), h(A))) | (~product(j(A), A, h(A))))),
% 0.83/0.78 inference(skolemize,[status(sab)],[109])).
% 0.83/0.78 tff(111,plain,
% 0.83/0.78 (![A: $i] : (q(A) | (~product(A, j(A), h(A))) | (~product(j(A), A, h(A))))),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[110, 103])).
% 0.83/0.79 tff(112,plain,
% 0.83/0.79 (((~![A: $i] : (q(A) | (~product(A, j(A), h(A))) | (~product(j(A), A, h(A))))) | (q(identity) | (~product(identity, j(identity), h(identity))) | (~product(j(identity), identity, h(identity))))) <=> ((~![A: $i] : (q(A) | (~product(A, j(A), h(A))) | (~product(j(A), A, h(A))))) | q(identity) | (~product(identity, j(identity), h(identity))) | (~product(j(identity), identity, h(identity))))),
% 0.83/0.79 inference(rewrite,[status(thm)],[])).
% 0.83/0.79 tff(113,plain,
% 0.83/0.79 ((~![A: $i] : (q(A) | (~product(A, j(A), h(A))) | (~product(j(A), A, h(A))))) | (q(identity) | (~product(identity, j(identity), h(identity))) | (~product(j(identity), identity, h(identity))))),
% 0.83/0.79 inference(quant_inst,[status(thm)],[])).
% 0.83/0.79 tff(114,plain,
% 0.83/0.79 ((~![A: $i] : (q(A) | (~product(A, j(A), h(A))) | (~product(j(A), A, h(A))))) | q(identity) | (~product(identity, j(identity), h(identity))) | (~product(j(identity), identity, h(identity)))),
% 0.83/0.79 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.83/0.79 tff(115,plain,
% 0.83/0.79 ((~product(identity, j(identity), h(identity))) | (~product(j(identity), identity, h(identity)))),
% 0.83/0.79 inference(unit_resolution,[status(thm)],[114, 111, 55])).
% 0.83/0.79 tff(116,plain,
% 0.83/0.79 (~product(j(identity), identity, h(identity))),
% 0.83/0.79 inference(unit_resolution,[status(thm)],[115, 99])).
% 0.83/0.79 tff(117,plain,
% 0.83/0.79 (~product(j(identity), identity, multiply(h(identity), identity))),
% 0.83/0.79 inference(modus_ponens,[status(thm)],[116, 101])).
% 0.83/0.79 tff(118,plain,
% 0.83/0.79 (^[W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : refl((product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U))) <=> (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U))))),
% 0.83/0.79 inference(bind,[status(th)],[])).
% 0.83/0.79 tff(119,plain,
% 0.83/0.79 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U))) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))),
% 0.83/0.79 inference(quant_intro,[status(thm)],[118])).
% 0.83/0.79 tff(120,plain,
% 0.83/0.79 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U))) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))),
% 0.83/0.79 inference(rewrite,[status(thm)],[])).
% 0.83/0.79 tff(121,plain,
% 0.83/0.79 (^[W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : trans(monotonicity(rewrite((((~product(X, Y, U)) | (~product(Y, Z, V))) | (~product(U, Z, W))) <=> ((~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))), (((((~product(X, Y, U)) | (~product(Y, Z, V))) | (~product(U, Z, W))) | product(X, V, W)) <=> (((~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U))) | product(X, V, W)))), rewrite((((~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U))) | product(X, V, W)) <=> (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))), (((((~product(X, Y, U)) | (~product(Y, Z, V))) | (~product(U, Z, W))) | product(X, V, W)) <=> (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))))),
% 0.83/0.79 inference(bind,[status(th)],[])).
% 0.83/0.79 tff(122,plain,
% 0.83/0.79 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((((~product(X, Y, U)) | (~product(Y, Z, V))) | (~product(U, Z, W))) | product(X, V, W)) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))),
% 0.83/0.79 inference(quant_intro,[status(thm)],[121])).
% 0.83/0.79 tff(123,axiom,(![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((((~product(X, Y, U)) | (~product(Y, Z, V))) | (~product(U, Z, W))) | product(X, V, W))), file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax','associativity1')).
% 0.83/0.79 tff(124,plain,
% 0.83/0.79 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))),
% 0.83/0.79 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.83/0.79 tff(125,plain,
% 0.83/0.79 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))),
% 0.83/0.79 inference(modus_ponens,[status(thm)],[124, 120])).
% 0.83/0.79 tff(126,plain,(
% 0.83/0.79 ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))),
% 0.83/0.79 inference(skolemize,[status(sab)],[125])).
% 0.83/0.79 tff(127,plain,
% 0.83/0.79 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))),
% 0.83/0.79 inference(modus_ponens,[status(thm)],[126, 119])).
% 0.83/0.79 tff(128,plain,
% 0.83/0.79 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | (product(j(identity), identity, multiply(h(identity), identity)) | (~product(identity, j(identity), multiply(h(identity), identity))) | (~product(j(identity), inverse(j(identity)), identity)) | (~product(inverse(j(identity)), j(identity), identity)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | product(j(identity), identity, multiply(h(identity), identity)) | (~product(identity, j(identity), multiply(h(identity), identity))) | (~product(j(identity), inverse(j(identity)), identity)) | (~product(inverse(j(identity)), j(identity), identity)))),
% 0.83/0.79 inference(rewrite,[status(thm)],[])).
% 0.83/0.79 tff(129,plain,
% 0.83/0.79 ((product(j(identity), identity, multiply(h(identity), identity)) | (~product(identity, j(identity), multiply(h(identity), identity))) | (~product(inverse(j(identity)), j(identity), identity)) | (~product(j(identity), inverse(j(identity)), identity))) <=> (product(j(identity), identity, multiply(h(identity), identity)) | (~product(identity, j(identity), multiply(h(identity), identity))) | (~product(j(identity), inverse(j(identity)), identity)) | (~product(inverse(j(identity)), j(identity), identity)))),
% 0.83/0.79 inference(rewrite,[status(thm)],[])).
% 0.83/0.79 tff(130,plain,
% 0.83/0.79 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | (product(j(identity), identity, multiply(h(identity), identity)) | (~product(identity, j(identity), multiply(h(identity), identity))) | (~product(inverse(j(identity)), j(identity), identity)) | (~product(j(identity), inverse(j(identity)), identity)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | (product(j(identity), identity, multiply(h(identity), identity)) | (~product(identity, j(identity), multiply(h(identity), identity))) | (~product(j(identity), inverse(j(identity)), identity)) | (~product(inverse(j(identity)), j(identity), identity))))),
% 0.83/0.79 inference(monotonicity,[status(thm)],[129])).
% 0.83/0.79 tff(131,plain,
% 0.83/0.79 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | (product(j(identity), identity, multiply(h(identity), identity)) | (~product(identity, j(identity), multiply(h(identity), identity))) | (~product(inverse(j(identity)), j(identity), identity)) | (~product(j(identity), inverse(j(identity)), identity)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | product(j(identity), identity, multiply(h(identity), identity)) | (~product(identity, j(identity), multiply(h(identity), identity))) | (~product(j(identity), inverse(j(identity)), identity)) | (~product(inverse(j(identity)), j(identity), identity)))),
% 0.83/0.79 inference(transitivity,[status(thm)],[130, 128])).
% 0.83/0.79 tff(132,plain,
% 0.83/0.79 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | (product(j(identity), identity, multiply(h(identity), identity)) | (~product(identity, j(identity), multiply(h(identity), identity))) | (~product(inverse(j(identity)), j(identity), identity)) | (~product(j(identity), inverse(j(identity)), identity)))),
% 0.83/0.79 inference(quant_inst,[status(thm)],[])).
% 0.83/0.79 tff(133,plain,
% 0.83/0.79 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | product(j(identity), identity, multiply(h(identity), identity)) | (~product(identity, j(identity), multiply(h(identity), identity))) | (~product(j(identity), inverse(j(identity)), identity)) | (~product(inverse(j(identity)), j(identity), identity))),
% 0.83/0.79 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.83/0.79 tff(134,plain,
% 0.83/0.79 (~product(identity, j(identity), multiply(h(identity), identity))),
% 0.83/0.79 inference(unit_resolution,[status(thm)],[133, 127, 80, 117, 50])).
% 0.83/0.79 tff(135,plain,
% 0.83/0.79 ($false),
% 0.83/0.79 inference(unit_resolution,[status(thm)],[134, 100])).
% 0.83/0.79 % SZS output end Proof
%------------------------------------------------------------------------------