TSTP Solution File: GRP123-2.003 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP123-2.003 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n002.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 22:25:55 EDT 2022
% Result : Unsatisfiable 0.23s 0.43s
% Output : Proof 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : GRP123-2.003 : TPTP v8.1.0. Released v1.2.0.
% 0.08/0.15 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.15/0.37 % Computer : n002.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Wed Aug 31 15:01:59 EDT 2022
% 0.15/0.37 % CPUTime :
% 0.15/0.37 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.15/0.37 Usage: tptp [options] [-file:]file
% 0.15/0.37 -h, -? prints this message.
% 0.15/0.37 -smt2 print SMT-LIB2 benchmark.
% 0.15/0.37 -m, -model generate model.
% 0.15/0.37 -p, -proof generate proof.
% 0.15/0.37 -c, -core generate unsat core of named formulas.
% 0.15/0.37 -st, -statistics display statistics.
% 0.15/0.37 -t:timeout set timeout (in second).
% 0.15/0.37 -smt2status display status in smt2 format instead of SZS.
% 0.15/0.37 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.15/0.37 -<param>:<value> configuration parameter and value.
% 0.15/0.37 -o:<output-file> file to place output in.
% 0.23/0.43 % SZS status Unsatisfiable
% 0.23/0.43 % SZS output start Proof
% 0.23/0.43 tff(product_type, type, (
% 0.23/0.43 product: ( $i * $i * $i ) > $o)).
% 0.23/0.43 tff(e_3_type, type, (
% 0.23/0.43 e_3: $i)).
% 0.23/0.43 tff(e_2_type, type, (
% 0.23/0.43 e_2: $i)).
% 0.23/0.43 tff(equalish_type, type, (
% 0.23/0.43 equalish: ( $i * $i ) > $o)).
% 0.23/0.43 tff(e_1_type, type, (
% 0.23/0.43 e_1: $i)).
% 0.23/0.43 tff(group_element_type, type, (
% 0.23/0.43 group_element: $i > $o)).
% 0.23/0.43 tff(1,assumption,(product(e_3, e_2, e_2)), introduced(assumption)).
% 0.23/0.43 tff(2,assumption,(~product(e_2, e_2, e_2)), introduced(assumption)).
% 0.23/0.43 tff(3,plain,
% 0.23/0.43 (^[X: $i] : refl(product(X, X, X) <=> product(X, X, X))),
% 0.23/0.43 inference(bind,[status(th)],[])).
% 0.23/0.43 tff(4,plain,
% 0.23/0.43 (![X: $i] : product(X, X, X) <=> ![X: $i] : product(X, X, X)),
% 0.23/0.43 inference(quant_intro,[status(thm)],[3])).
% 0.23/0.43 tff(5,plain,
% 0.23/0.43 (![X: $i] : product(X, X, X) <=> ![X: $i] : product(X, X, X)),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(6,axiom,(![X: $i] : product(X, X, X)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product_idempotence')).
% 0.23/0.43 tff(7,plain,
% 0.23/0.43 (![X: $i] : product(X, X, X)),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.23/0.43 tff(8,plain,(
% 0.23/0.43 ![X: $i] : product(X, X, X)),
% 0.23/0.43 inference(skolemize,[status(sab)],[7])).
% 0.23/0.43 tff(9,plain,
% 0.23/0.43 (![X: $i] : product(X, X, X)),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.23/0.43 tff(10,plain,
% 0.23/0.43 ((~![X: $i] : product(X, X, X)) | product(e_2, e_2, e_2)),
% 0.23/0.43 inference(quant_inst,[status(thm)],[])).
% 0.23/0.43 tff(11,plain,
% 0.23/0.43 ($false),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[10, 9, 2])).
% 0.23/0.43 tff(12,plain,(product(e_2, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.23/0.43 tff(13,plain,
% 0.23/0.43 (^[W: $i, Z: $i, Y: $i, X: $i] : refl((equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X))) <=> (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X))))),
% 0.23/0.43 inference(bind,[status(th)],[])).
% 0.23/0.43 tff(14,plain,
% 0.23/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.23/0.43 inference(quant_intro,[status(thm)],[13])).
% 0.23/0.43 tff(15,plain,
% 0.23/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(16,plain,
% 0.23/0.43 (^[W: $i, Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite(((~product(W, Y, X)) | (~product(Z, Y, X))) <=> ((~product(Z, Y, X)) | (~product(W, Y, X)))), ((((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z)) <=> (((~product(Z, Y, X)) | (~product(W, Y, X))) | equalish(W, Z)))), rewrite((((~product(Z, Y, X)) | (~product(W, Y, X))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))), ((((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))))),
% 0.23/0.43 inference(bind,[status(th)],[])).
% 0.23/0.43 tff(17,plain,
% 0.23/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z)) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.23/0.43 inference(quant_intro,[status(thm)],[16])).
% 0.23/0.43 tff(18,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product_left_cancellation')).
% 0.23/0.43 tff(19,plain,
% 0.23/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.23/0.43 tff(20,plain,
% 0.23/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.23/0.43 tff(21,plain,(
% 0.23/0.43 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.23/0.43 inference(skolemize,[status(sab)],[20])).
% 0.23/0.43 tff(22,plain,
% 0.23/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.23/0.43 tff(23,plain,
% 0.23/0.43 ((~equalish(e_3, e_2)) <=> (~equalish(e_3, e_2))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(24,axiom,(~equalish(e_3, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_2')).
% 0.23/0.43 tff(25,plain,
% 0.23/0.43 (~equalish(e_3, e_2)),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.23/0.43 tff(26,plain,
% 0.23/0.43 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(27,plain,
% 0.23/0.43 ((equalish(e_3, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_3, e_2, e_2))) <=> (equalish(e_3, e_2) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(28,plain,
% 0.23/0.43 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_3, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_2, e_2))))),
% 0.23/0.43 inference(monotonicity,[status(thm)],[27])).
% 0.23/0.43 tff(29,plain,
% 0.23/0.43 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_3, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.23/0.43 inference(transitivity,[status(thm)],[28, 26])).
% 0.23/0.43 tff(30,plain,
% 0.23/0.43 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_3, e_2, e_2)))),
% 0.23/0.43 inference(quant_inst,[status(thm)],[])).
% 0.23/0.43 tff(31,plain,
% 0.23/0.43 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_2, e_2))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.23/0.43 tff(32,plain,
% 0.23/0.43 ($false),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[31, 25, 22, 12, 1])).
% 0.23/0.43 tff(33,plain,(~product(e_3, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.23/0.43 tff(34,assumption,(product(e_2, e_2, e_2)), introduced(assumption)).
% 0.23/0.43 tff(35,assumption,(product(e_1, e_2, e_2)), introduced(assumption)).
% 0.23/0.43 tff(36,plain,
% 0.23/0.43 ((~equalish(e_2, e_1)) <=> (~equalish(e_2, e_1))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(37,axiom,(~equalish(e_2, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_1')).
% 0.23/0.43 tff(38,plain,
% 0.23/0.43 (~equalish(e_2, e_1)),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.23/0.43 tff(39,plain,
% 0.23/0.43 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_2, e_2, e_2)) | (~product(e_1, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_2, e_2, e_2)) | (~product(e_1, e_2, e_2)))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(40,plain,
% 0.23/0.43 ((equalish(e_2, e_1) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_2))) <=> (equalish(e_2, e_1) | (~product(e_2, e_2, e_2)) | (~product(e_1, e_2, e_2)))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(41,plain,
% 0.23/0.43 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_2, e_2, e_2)) | (~product(e_1, e_2, e_2))))),
% 0.23/0.43 inference(monotonicity,[status(thm)],[40])).
% 0.23/0.43 tff(42,plain,
% 0.23/0.43 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_2, e_2, e_2)) | (~product(e_1, e_2, e_2)))),
% 0.23/0.44 inference(transitivity,[status(thm)],[41, 39])).
% 0.23/0.44 tff(43,plain,
% 0.23/0.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.23/0.44 inference(quant_inst,[status(thm)],[])).
% 0.23/0.44 tff(44,plain,
% 0.23/0.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_2, e_2, e_2)) | (~product(e_1, e_2, e_2))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.23/0.44 tff(45,plain,
% 0.23/0.44 ($false),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[44, 38, 22, 35, 34])).
% 0.23/0.44 tff(46,plain,((~product(e_2, e_2, e_2)) | (~product(e_1, e_2, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.23/0.44 tff(47,plain,
% 0.23/0.44 (~product(e_1, e_2, e_2)),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[46, 12])).
% 0.23/0.44 tff(48,assumption,(product(e_1, e_2, e_1)), introduced(assumption)).
% 0.23/0.44 tff(49,plain,
% 0.23/0.44 ((~![X: $i] : product(X, X, X)) | product(e_1, e_1, e_1)),
% 0.23/0.44 inference(quant_inst,[status(thm)],[])).
% 0.23/0.44 tff(50,plain,
% 0.23/0.44 (product(e_1, e_1, e_1)),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[49, 9])).
% 0.23/0.44 tff(51,plain,
% 0.23/0.44 (^[Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : refl(((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2)) <=> ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2)))),
% 0.23/0.44 inference(bind,[status(th)],[])).
% 0.23/0.44 tff(52,plain,
% 0.23/0.44 (![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2)) <=> ![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))),
% 0.23/0.44 inference(quant_intro,[status(thm)],[51])).
% 0.23/0.44 tff(53,plain,
% 0.23/0.44 (![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2)) <=> ![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(54,plain,
% 0.23/0.44 (^[Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~product(X1, Y1, Z1)) | (~product(X2, Y2, Z1))) | (~product(Z2, Y1, X1))) <=> ((~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)))), (((((~product(X1, Y1, Z1)) | (~product(X2, Y2, Z1))) | (~product(Z2, Y1, X1))) | (~product(Z2, Y2, X2))) <=> (((~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1))) | (~product(Z2, Y2, X2))))), rewrite((((~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1))) | (~product(Z2, Y2, X2))) <=> ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)))), (((((~product(X1, Y1, Z1)) | (~product(X2, Y2, Z1))) | (~product(Z2, Y1, X1))) | (~product(Z2, Y2, X2))) <=> ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1))))), ((((((~product(X1, Y1, Z1)) | (~product(X2, Y2, Z1))) | (~product(Z2, Y1, X1))) | (~product(Z2, Y2, X2))) | equalish(Y1, Y2)) <=> (((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1))) | equalish(Y1, Y2)))), rewrite((((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1))) | equalish(Y1, Y2)) <=> ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))), ((((((~product(X1, Y1, Z1)) | (~product(X2, Y2, Z1))) | (~product(Z2, Y1, X1))) | (~product(Z2, Y2, X2))) | equalish(Y1, Y2)) <=> ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))))),
% 0.23/0.44 inference(bind,[status(th)],[])).
% 0.23/0.44 tff(55,plain,
% 0.23/0.44 (![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : (((((~product(X1, Y1, Z1)) | (~product(X2, Y2, Z1))) | (~product(Z2, Y1, X1))) | (~product(Z2, Y2, X2))) | equalish(Y1, Y2)) <=> ![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))),
% 0.23/0.44 inference(quant_intro,[status(thm)],[54])).
% 0.23/0.44 tff(56,axiom,(![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : (((((~product(X1, Y1, Z1)) | (~product(X2, Y2, Z1))) | (~product(Z2, Y1, X1))) | (~product(Z2, Y2, X2))) | equalish(Y1, Y2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qg1_2')).
% 0.23/0.44 tff(57,plain,
% 0.23/0.44 (![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.23/0.44 tff(58,plain,
% 0.23/0.44 (![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.23/0.44 tff(59,plain,(
% 0.23/0.44 ![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))),
% 0.23/0.44 inference(skolemize,[status(sab)],[58])).
% 0.23/0.44 tff(60,plain,
% 0.23/0.44 (![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[59, 52])).
% 0.23/0.44 tff(61,plain,
% 0.23/0.44 ((~equalish(e_1, e_2)) <=> (~equalish(e_1, e_2))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(62,axiom,(~equalish(e_1, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_2')).
% 0.23/0.44 tff(63,plain,
% 0.23/0.44 (~equalish(e_1, e_2)),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.23/0.44 tff(64,plain,
% 0.23/0.44 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_1, e_2) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_2, e_1)))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_1, e_2) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_2, e_1)))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(65,plain,
% 0.23/0.44 (((~product(e_1, e_2, e_1)) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_1, e_1)) | equalish(e_1, e_2)) <=> (equalish(e_1, e_2) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_2, e_1)))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(66,plain,
% 0.23/0.44 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_1, e_2, e_1)) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_1, e_1)) | equalish(e_1, e_2))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_1, e_2) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_2, e_1))))),
% 0.23/0.44 inference(monotonicity,[status(thm)],[65])).
% 0.23/0.44 tff(67,plain,
% 0.23/0.44 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_1, e_2, e_1)) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_1, e_1)) | equalish(e_1, e_2))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_1, e_2) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_2, e_1)))),
% 0.23/0.44 inference(transitivity,[status(thm)],[66, 64])).
% 0.23/0.44 tff(68,plain,
% 0.23/0.44 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_1, e_2, e_1)) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_1, e_1)) | equalish(e_1, e_2))),
% 0.23/0.44 inference(quant_inst,[status(thm)],[])).
% 0.23/0.44 tff(69,plain,
% 0.23/0.44 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_1, e_2) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_2, e_1))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.23/0.44 tff(70,plain,
% 0.23/0.44 ($false),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[69, 63, 60, 50, 48])).
% 0.23/0.44 tff(71,plain,(~product(e_1, e_2, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.23/0.44 tff(72,plain,
% 0.23/0.44 (^[Y: $i, X: $i] : refl((product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) <=> (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))))),
% 0.23/0.44 inference(bind,[status(th)],[])).
% 0.23/0.44 tff(73,plain,
% 0.23/0.44 (![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) <=> ![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.23/0.44 inference(quant_intro,[status(thm)],[72])).
% 0.23/0.44 tff(74,plain,
% 0.23/0.44 (![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) <=> ![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(75,plain,
% 0.23/0.44 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) <=> (product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))), (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) <=> ((product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_2)))), rewrite(((product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_2)) <=> (product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))), (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) <=> (product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))))), ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) <=> ((product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_3)))), rewrite(((product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_3)) <=> (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))), ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) <=> (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))))),
% 0.23/0.44 inference(bind,[status(th)],[])).
% 0.23/0.44 tff(76,plain,
% 0.23/0.44 (![Y: $i, X: $i] : (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) <=> ![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.23/0.44 inference(quant_intro,[status(thm)],[75])).
% 0.23/0.44 tff(77,axiom,(![Y: $i, X: $i] : (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product_total_function1')).
% 0.23/0.44 tff(78,plain,
% 0.23/0.44 (![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.23/0.45 tff(79,plain,
% 0.23/0.45 (![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[78, 74])).
% 0.23/0.45 tff(80,plain,(
% 0.23/0.45 ![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.23/0.45 inference(skolemize,[status(sab)],[79])).
% 0.23/0.45 tff(81,plain,
% 0.23/0.45 (![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[80, 73])).
% 0.23/0.45 tff(82,plain,
% 0.23/0.45 (group_element(e_2) <=> group_element(e_2)),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(83,axiom,(group_element(e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_2')).
% 0.23/0.45 tff(84,plain,
% 0.23/0.45 (group_element(e_2)),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.23/0.45 tff(85,plain,
% 0.23/0.45 (group_element(e_1) <=> group_element(e_1)),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(86,axiom,(group_element(e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_1')).
% 0.23/0.45 tff(87,plain,
% 0.23/0.45 (group_element(e_1)),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.23/0.45 tff(88,plain,
% 0.23/0.45 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_1)) | (~group_element(e_2)) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | (~group_element(e_2)) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1))),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(89,plain,
% 0.23/0.45 ((product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_1))) <=> ((~group_element(e_1)) | (~group_element(e_2)) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1))),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(90,plain,
% 0.23/0.45 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_1)) | (~group_element(e_2)) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1)))),
% 0.23/0.45 inference(monotonicity,[status(thm)],[89])).
% 0.23/0.45 tff(91,plain,
% 0.23/0.45 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | (~group_element(e_2)) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1))),
% 0.23/0.45 inference(transitivity,[status(thm)],[90, 88])).
% 0.23/0.45 tff(92,plain,
% 0.23/0.45 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_1)))),
% 0.23/0.45 inference(quant_inst,[status(thm)],[])).
% 0.23/0.45 tff(93,plain,
% 0.23/0.45 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | (~group_element(e_2)) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1)),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.23/0.45 tff(94,plain,
% 0.23/0.45 (product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1)),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[93, 87, 84, 81])).
% 0.23/0.45 tff(95,plain,
% 0.23/0.45 (product(e_1, e_2, e_3) | product(e_1, e_2, e_2)),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[94, 71])).
% 0.23/0.45 tff(96,plain,
% 0.23/0.45 (product(e_1, e_2, e_3)),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[95, 47])).
% 0.23/0.45 tff(97,plain,
% 0.23/0.45 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_2, e_1)) | (~product(e_1, e_2, e_3)))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_2, e_1)) | (~product(e_1, e_2, e_3)))),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(98,plain,
% 0.23/0.45 (((~product(e_1, e_1, e_1)) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_2, e_1)) | equalish(e_2, e_1)) <=> (equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_2, e_1)) | (~product(e_1, e_2, e_3)))),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(99,plain,
% 0.23/0.45 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_1, e_1, e_1)) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_2, e_1)) | equalish(e_2, e_1))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_2, e_1)) | (~product(e_1, e_2, e_3))))),
% 0.23/0.45 inference(monotonicity,[status(thm)],[98])).
% 0.23/0.45 tff(100,plain,
% 0.23/0.45 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_1, e_1, e_1)) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_2, e_1)) | equalish(e_2, e_1))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_2, e_1)) | (~product(e_1, e_2, e_3)))),
% 0.23/0.45 inference(transitivity,[status(thm)],[99, 97])).
% 0.23/0.45 tff(101,plain,
% 0.23/0.45 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_1, e_1, e_1)) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_2, e_1)) | equalish(e_2, e_1))),
% 0.23/0.45 inference(quant_inst,[status(thm)],[])).
% 0.23/0.45 tff(102,plain,
% 0.23/0.45 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_2, e_1)) | (~product(e_1, e_2, e_3))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.23/0.45 tff(103,plain,
% 0.23/0.45 (~product(e_3, e_2, e_1)),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[102, 38, 60, 50, 96])).
% 0.23/0.45 tff(104,plain,
% 0.23/0.45 (group_element(e_3) <=> group_element(e_3)),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(105,axiom,(group_element(e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_3')).
% 0.23/0.45 tff(106,plain,
% 0.23/0.45 (group_element(e_3)),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.23/0.45 tff(107,plain,
% 0.23/0.45 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_2)) | product(e_3, e_2, e_3) | product(e_3, e_2, e_1) | (~group_element(e_3)) | product(e_3, e_2, e_2))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_2)) | product(e_3, e_2, e_3) | product(e_3, e_2, e_1) | (~group_element(e_3)) | product(e_3, e_2, e_2))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(108,plain,
% 0.23/0.46 ((product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_3))) <=> ((~group_element(e_2)) | product(e_3, e_2, e_3) | product(e_3, e_2, e_1) | (~group_element(e_3)) | product(e_3, e_2, e_2))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(109,plain,
% 0.23/0.46 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_2)) | product(e_3, e_2, e_3) | product(e_3, e_2, e_1) | (~group_element(e_3)) | product(e_3, e_2, e_2)))),
% 0.23/0.46 inference(monotonicity,[status(thm)],[108])).
% 0.23/0.46 tff(110,plain,
% 0.23/0.46 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_2)) | product(e_3, e_2, e_3) | product(e_3, e_2, e_1) | (~group_element(e_3)) | product(e_3, e_2, e_2))),
% 0.23/0.46 inference(transitivity,[status(thm)],[109, 107])).
% 0.23/0.46 tff(111,plain,
% 0.23/0.46 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_3)))),
% 0.23/0.46 inference(quant_inst,[status(thm)],[])).
% 0.23/0.46 tff(112,plain,
% 0.23/0.46 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_2)) | product(e_3, e_2, e_3) | product(e_3, e_2, e_1) | (~group_element(e_3)) | product(e_3, e_2, e_2)),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.23/0.46 tff(113,plain,
% 0.23/0.46 (product(e_3, e_2, e_3) | product(e_3, e_2, e_2)),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[112, 84, 106, 81, 103])).
% 0.23/0.46 tff(114,plain,
% 0.23/0.46 (product(e_3, e_2, e_3)),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[113, 33])).
% 0.23/0.46 tff(115,plain,
% 0.23/0.46 ((~equalish(e_3, e_1)) <=> (~equalish(e_3, e_1))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(116,axiom,(~equalish(e_3, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_1')).
% 0.23/0.46 tff(117,plain,
% 0.23/0.46 (~equalish(e_3, e_1)),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.23/0.46 tff(118,plain,
% 0.23/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_3, e_2, e_3)) | (~product(e_1, e_2, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_3, e_2, e_3)) | (~product(e_1, e_2, e_3)))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(119,plain,
% 0.23/0.46 ((equalish(e_3, e_1) | (~product(e_1, e_2, e_3)) | (~product(e_3, e_2, e_3))) <=> (equalish(e_3, e_1) | (~product(e_3, e_2, e_3)) | (~product(e_1, e_2, e_3)))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(120,plain,
% 0.23/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_1, e_2, e_3)) | (~product(e_3, e_2, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_3, e_2, e_3)) | (~product(e_1, e_2, e_3))))),
% 0.23/0.46 inference(monotonicity,[status(thm)],[119])).
% 0.23/0.46 tff(121,plain,
% 0.23/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_1, e_2, e_3)) | (~product(e_3, e_2, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_3, e_2, e_3)) | (~product(e_1, e_2, e_3)))),
% 0.23/0.46 inference(transitivity,[status(thm)],[120, 118])).
% 0.23/0.46 tff(122,plain,
% 0.23/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_1, e_2, e_3)) | (~product(e_3, e_2, e_3)))),
% 0.23/0.46 inference(quant_inst,[status(thm)],[])).
% 0.23/0.46 tff(123,plain,
% 0.23/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_3, e_2, e_3)) | (~product(e_1, e_2, e_3))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.23/0.46 tff(124,plain,
% 0.23/0.46 ($false),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[123, 117, 22, 96, 114])).
% 0.23/0.46 % SZS output end Proof
%------------------------------------------------------------------------------