TSTP Solution File: GRP007-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP007-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n027.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 22:25:23 EDT 2022
% Result : Unsatisfiable 0.21s 0.44s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP007-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n027.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 31 14:18:32 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.36 Usage: tptp [options] [-file:]file
% 0.13/0.36 -h, -? prints this message.
% 0.13/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.36 -m, -model generate model.
% 0.13/0.36 -p, -proof generate proof.
% 0.13/0.36 -c, -core generate unsat core of named formulas.
% 0.13/0.36 -st, -statistics display statistics.
% 0.13/0.36 -t:timeout set timeout (in second).
% 0.13/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.36 -<param>:<value> configuration parameter and value.
% 0.13/0.36 -o:<output-file> file to place output in.
% 0.21/0.44 % SZS status Unsatisfiable
% 0.21/0.44 % SZS output start Proof
% 0.21/0.44 tff(product_type, type, (
% 0.21/0.44 product: ( $i * $i * $i ) > $o)).
% 0.21/0.44 tff(identity_type, type, (
% 0.21/0.44 identity: $i)).
% 0.21/0.44 tff(c_type, type, (
% 0.21/0.44 c: $i)).
% 0.21/0.44 tff(elem_0_type, type, (
% 0.21/0.44 elem_0: $i)).
% 0.21/0.44 tff(inverse_type, type, (
% 0.21/0.44 inverse: $i > $i)).
% 0.21/0.44 tff(1,plain,
% 0.21/0.44 (^[A: $i] : refl(product(A, c, A) <=> product(A, c, A))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(2,plain,
% 0.21/0.44 (![A: $i] : product(A, c, A) <=> ![A: $i] : product(A, c, A)),
% 0.21/0.44 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.44 tff(3,plain,
% 0.21/0.44 (![A: $i] : product(A, c, A) <=> ![A: $i] : product(A, c, A)),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(4,axiom,(![A: $i] : product(A, c, A)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','another_right_identity')).
% 0.21/0.44 tff(5,plain,
% 0.21/0.44 (![A: $i] : product(A, c, A)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.21/0.44 tff(6,plain,(
% 0.21/0.44 ![A: $i] : product(A, c, A)),
% 0.21/0.44 inference(skolemize,[status(sab)],[5])).
% 0.21/0.44 tff(7,plain,
% 0.21/0.44 (![A: $i] : product(A, c, A)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.21/0.44 tff(8,plain,
% 0.21/0.44 ((~![A: $i] : product(A, c, A)) | product(elem!0, c, elem!0)),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(9,plain,
% 0.21/0.44 (product(elem!0, c, elem!0)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.21/0.44 tff(10,plain,
% 0.21/0.44 (^[X: $i] : refl(product(inverse(X), X, identity) <=> product(inverse(X), X, identity))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(11,plain,
% 0.21/0.44 (![X: $i] : product(inverse(X), X, identity) <=> ![X: $i] : product(inverse(X), X, identity)),
% 0.21/0.44 inference(quant_intro,[status(thm)],[10])).
% 0.21/0.44 tff(12,plain,
% 0.21/0.44 (![X: $i] : product(inverse(X), X, identity) <=> ![X: $i] : product(inverse(X), X, identity)),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(13,axiom,(![X: $i] : product(inverse(X), X, identity)), file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax','left_inverse')).
% 0.21/0.44 tff(14,plain,
% 0.21/0.44 (![X: $i] : product(inverse(X), X, identity)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.21/0.44 tff(15,plain,(
% 0.21/0.44 ![X: $i] : product(inverse(X), X, identity)),
% 0.21/0.44 inference(skolemize,[status(sab)],[14])).
% 0.21/0.44 tff(16,plain,
% 0.21/0.44 (![X: $i] : product(inverse(X), X, identity)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.21/0.44 tff(17,plain,
% 0.21/0.44 ((~![X: $i] : product(inverse(X), X, identity)) | product(inverse(elem!0), elem!0, identity)),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(18,plain,
% 0.21/0.44 (product(inverse(elem!0), elem!0, identity)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.21/0.44 tff(19,plain,
% 0.21/0.44 (^[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))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(20,plain,
% 0.21/0.44 (![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)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[19])).
% 0.21/0.44 tff(21,plain,
% 0.21/0.44 (![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)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(22,plain,
% 0.21/0.44 (^[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)))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(23,plain,
% 0.21/0.44 (![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)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[22])).
% 0.21/0.44 tff(24,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')).
% 0.21/0.44 tff(25,plain,
% 0.21/0.44 (![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)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.21/0.44 tff(26,plain,
% 0.21/0.44 (![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)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.21/0.44 tff(27,plain,(
% 0.21/0.44 ![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)))),
% 0.21/0.44 inference(skolemize,[status(sab)],[26])).
% 0.21/0.44 tff(28,plain,
% 0.21/0.44 (![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)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.21/0.44 tff(29,plain,
% 0.21/0.44 (((~![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, c, identity) | (~product(elem!0, c, elem!0)) | (~product(inverse(elem!0), elem!0, 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, c, identity) | (~product(elem!0, c, elem!0)) | (~product(inverse(elem!0), elem!0, identity)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(30,plain,
% 0.21/0.44 ((product(identity, c, identity) | (~product(elem!0, c, elem!0)) | (~product(inverse(elem!0), elem!0, identity)) | (~product(inverse(elem!0), elem!0, identity))) <=> (product(identity, c, identity) | (~product(elem!0, c, elem!0)) | (~product(inverse(elem!0), elem!0, identity)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(31,plain,
% 0.21/0.44 (((~![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, c, identity) | (~product(elem!0, c, elem!0)) | (~product(inverse(elem!0), elem!0, identity)) | (~product(inverse(elem!0), elem!0, 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, c, identity) | (~product(elem!0, c, elem!0)) | (~product(inverse(elem!0), elem!0, identity))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[30])).
% 0.21/0.44 tff(32,plain,
% 0.21/0.44 (((~![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, c, identity) | (~product(elem!0, c, elem!0)) | (~product(inverse(elem!0), elem!0, identity)) | (~product(inverse(elem!0), elem!0, 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, c, identity) | (~product(elem!0, c, elem!0)) | (~product(inverse(elem!0), elem!0, identity)))),
% 0.21/0.44 inference(transitivity,[status(thm)],[31, 29])).
% 0.21/0.44 tff(33,plain,
% 0.21/0.44 ((~![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, c, identity) | (~product(elem!0, c, elem!0)) | (~product(inverse(elem!0), elem!0, identity)) | (~product(inverse(elem!0), elem!0, identity)))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(34,plain,
% 0.21/0.44 ((~![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, c, identity) | (~product(elem!0, c, elem!0)) | (~product(inverse(elem!0), elem!0, identity))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.21/0.44 tff(35,plain,
% 0.21/0.44 (product(identity, c, identity)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[34, 28, 18, 9])).
% 0.21/0.44 tff(36,plain,
% 0.21/0.44 (^[X: $i] : refl(product(identity, X, X) <=> product(identity, X, X))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(37,plain,
% 0.21/0.44 (![X: $i] : product(identity, X, X) <=> ![X: $i] : product(identity, X, X)),
% 0.21/0.44 inference(quant_intro,[status(thm)],[36])).
% 0.21/0.44 tff(38,plain,
% 0.21/0.44 (![X: $i] : product(identity, X, X) <=> ![X: $i] : product(identity, X, X)),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(39,axiom,(![X: $i] : product(identity, X, X)), file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax','left_identity')).
% 0.21/0.44 tff(40,plain,
% 0.21/0.44 (![X: $i] : product(identity, X, X)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.21/0.44 tff(41,plain,(
% 0.21/0.44 ![X: $i] : product(identity, X, X)),
% 0.21/0.44 inference(skolemize,[status(sab)],[40])).
% 0.21/0.44 tff(42,plain,
% 0.21/0.44 (![X: $i] : product(identity, X, X)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.21/0.44 tff(43,plain,
% 0.21/0.44 ((~![X: $i] : product(identity, X, X)) | product(identity, c, c)),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(44,plain,
% 0.21/0.44 (product(identity, c, c)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.21/0.44 tff(45,plain,
% 0.21/0.44 ((~(identity = c)) <=> (~(identity = c))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(46,axiom,(~(identity = c)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_identity_equals_c')).
% 0.21/0.44 tff(47,plain,
% 0.21/0.44 (~(identity = c)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.21/0.44 tff(48,plain,
% 0.21/0.44 (^[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))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(49,plain,
% 0.21/0.44 (![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)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[48])).
% 0.21/0.44 tff(50,plain,
% 0.21/0.44 (![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)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(51,plain,
% 0.21/0.44 (^[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))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(52,plain,
% 0.21/0.44 (![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)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[51])).
% 0.21/0.44 tff(53,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')).
% 0.21/0.44 tff(54,plain,
% 0.21/0.44 (![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.21/0.44 tff(55,plain,
% 0.21/0.44 (![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.21/0.44 tff(56,plain,(
% 0.21/0.44 ![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))),
% 0.21/0.44 inference(skolemize,[status(sab)],[55])).
% 0.21/0.44 tff(57,plain,
% 0.21/0.44 (![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[56, 49])).
% 0.21/0.44 tff(58,plain,
% 0.21/0.44 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | ((identity = c) | (~product(identity, c, identity)) | (~product(identity, c, c)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | (identity = c) | (~product(identity, c, identity)) | (~product(identity, c, c)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(59,plain,
% 0.21/0.45 (((identity = c) | (~product(identity, c, c)) | (~product(identity, c, identity))) <=> ((identity = c) | (~product(identity, c, identity)) | (~product(identity, c, c)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(60,plain,
% 0.21/0.45 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | ((identity = c) | (~product(identity, c, c)) | (~product(identity, c, identity)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | ((identity = c) | (~product(identity, c, identity)) | (~product(identity, c, c))))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[59])).
% 0.21/0.45 tff(61,plain,
% 0.21/0.45 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | ((identity = c) | (~product(identity, c, c)) | (~product(identity, c, identity)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | (identity = c) | (~product(identity, c, identity)) | (~product(identity, c, c)))),
% 0.21/0.45 inference(transitivity,[status(thm)],[60, 58])).
% 0.21/0.45 tff(62,plain,
% 0.21/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | ((identity = c) | (~product(identity, c, c)) | (~product(identity, c, identity)))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(63,plain,
% 0.21/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | (identity = c) | (~product(identity, c, identity)) | (~product(identity, c, c))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.21/0.45 tff(64,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[63, 57, 47, 44, 35])).
% 0.21/0.45 % SZS output end Proof
%------------------------------------------------------------------------------