TSTP Solution File: GRP123-4.003 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP123-4.003 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n022.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 22:25:56 EDT 2022
% Result : Unsatisfiable 0.18s 0.38s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP123-4.003 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.32 % Computer : n022.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Wed Aug 31 14:52:40 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.11/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.33 Usage: tptp [options] [-file:]file
% 0.11/0.33 -h, -? prints this message.
% 0.11/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.33 -m, -model generate model.
% 0.11/0.33 -p, -proof generate proof.
% 0.11/0.33 -c, -core generate unsat core of named formulas.
% 0.11/0.33 -st, -statistics display statistics.
% 0.11/0.33 -t:timeout set timeout (in second).
% 0.11/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.33 -<param>:<value> configuration parameter and value.
% 0.11/0.33 -o:<output-file> file to place output in.
% 0.18/0.38 % SZS status Unsatisfiable
% 0.18/0.38 % SZS output start Proof
% 0.18/0.38 tff(product_type, type, (
% 0.18/0.38 product: ( $i * $i * $i ) > $o)).
% 0.18/0.38 tff(e_2_type, type, (
% 0.18/0.38 e_2: $i)).
% 0.18/0.38 tff(e_1_type, type, (
% 0.18/0.38 e_1: $i)).
% 0.18/0.38 tff(e_3_type, type, (
% 0.18/0.38 e_3: $i)).
% 0.18/0.38 tff(equalish_type, type, (
% 0.18/0.38 equalish: ( $i * $i ) > $o)).
% 0.18/0.38 tff(group_element_type, type, (
% 0.18/0.38 group_element: $i > $o)).
% 0.18/0.38 tff(1,assumption,(~product(e_2, e_2, e_2)), introduced(assumption)).
% 0.18/0.38 tff(2,plain,
% 0.18/0.38 (^[X: $i] : refl(product(X, X, X) <=> product(X, X, X))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(3,plain,
% 0.18/0.38 (![X: $i] : product(X, X, X) <=> ![X: $i] : product(X, X, X)),
% 0.18/0.38 inference(quant_intro,[status(thm)],[2])).
% 0.18/0.38 tff(4,plain,
% 0.18/0.38 (![X: $i] : product(X, X, X) <=> ![X: $i] : product(X, X, X)),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(5,axiom,(![X: $i] : product(X, X, X)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','product_idempotence')).
% 0.18/0.38 tff(6,plain,
% 0.18/0.38 (![X: $i] : product(X, X, X)),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.18/0.38 tff(7,plain,(
% 0.18/0.38 ![X: $i] : product(X, X, X)),
% 0.18/0.39 inference(skolemize,[status(sab)],[6])).
% 0.18/0.39 tff(8,plain,
% 0.18/0.39 (![X: $i] : product(X, X, X)),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.18/0.39 tff(9,plain,
% 0.18/0.39 ((~![X: $i] : product(X, X, X)) | product(e_2, e_2, e_2)),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(10,plain,
% 0.18/0.39 ($false),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.18/0.39 tff(11,plain,(product(e_2, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.39 tff(12,assumption,(product(e_1, e_3, e_3)), introduced(assumption)).
% 0.18/0.39 tff(13,plain,
% 0.18/0.39 ((~![X: $i] : product(X, X, X)) | product(e_1, e_1, e_1)),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(14,plain,
% 0.18/0.39 (product(e_1, e_1, e_1)),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[13, 8])).
% 0.18/0.39 tff(15,assumption,(~product(e_3, e_3, e_1)), introduced(assumption)).
% 0.18/0.39 tff(16,assumption,(product(e_1, e_3, e_1)), introduced(assumption)).
% 0.18/0.39 tff(17,plain,
% 0.18/0.39 (^[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)))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(18,plain,
% 0.18/0.39 (![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))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[17])).
% 0.18/0.39 tff(19,plain,
% 0.18/0.39 (![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))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(20,plain,
% 0.18/0.39 (^[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))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(21,plain,
% 0.18/0.39 (![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))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[20])).
% 0.18/0.39 tff(22,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/sandbox/benchmark/theBenchmark.p','qg1_2')).
% 0.18/0.39 tff(23,plain,
% 0.18/0.39 (![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))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.18/0.39 tff(24,plain,
% 0.18/0.39 (![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))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.18/0.39 tff(25,plain,(
% 0.18/0.39 ![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))),
% 0.18/0.39 inference(skolemize,[status(sab)],[24])).
% 0.18/0.39 tff(26,plain,
% 0.18/0.39 (![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))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.18/0.39 tff(27,plain,
% 0.18/0.39 ((~equalish(e_1, e_3)) <=> (~equalish(e_1, e_3))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(28,axiom,(~equalish(e_1, e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_1_is_not_e_3')).
% 0.18/0.39 tff(29,plain,
% 0.18/0.39 (~equalish(e_1, e_3)),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.18/0.39 tff(30,plain,
% 0.18/0.39 (((~![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_3) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, 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_3) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_1)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(31,plain,
% 0.18/0.39 (((~product(e_1, e_3, e_1)) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_1)) | (~product(e_1, e_1, e_1)) | equalish(e_1, e_3)) <=> (equalish(e_1, e_3) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_1)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(32,plain,
% 0.18/0.39 (((~![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_3, e_1)) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_1)) | (~product(e_1, e_1, e_1)) | equalish(e_1, 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_1, e_3) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_1))))),
% 0.18/0.39 inference(monotonicity,[status(thm)],[31])).
% 0.18/0.39 tff(33,plain,
% 0.18/0.39 (((~![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_3, e_1)) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_1)) | (~product(e_1, e_1, e_1)) | equalish(e_1, 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_1, e_3) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_1)))),
% 0.18/0.39 inference(transitivity,[status(thm)],[32, 30])).
% 0.18/0.39 tff(34,plain,
% 0.18/0.39 ((~![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_3, e_1)) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_1)) | (~product(e_1, e_1, e_1)) | equalish(e_1, e_3))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(35,plain,
% 0.18/0.39 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_1, e_3) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_1))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.18/0.39 tff(36,plain,
% 0.18/0.39 ($false),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[35, 29, 26, 16, 14])).
% 0.18/0.39 tff(37,plain,(~product(e_1, e_3, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.39 tff(38,plain,
% 0.18/0.39 (group_element(e_3) <=> group_element(e_3)),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(39,axiom,(group_element(e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_3')).
% 0.18/0.39 tff(40,plain,
% 0.18/0.39 (group_element(e_3)),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.18/0.39 tff(41,plain,
% 0.18/0.39 (group_element(e_1) <=> group_element(e_1)),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(42,axiom,(group_element(e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_1')).
% 0.18/0.39 tff(43,plain,
% 0.18/0.39 (group_element(e_1)),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.18/0.39 tff(44,plain,
% 0.18/0.39 (^[Y: $i, X: $i] : refl((product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X))) <=> (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(45,plain,
% 0.18/0.39 (![Y: $i, X: $i] : (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X))) <=> ![Y: $i, X: $i] : (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[44])).
% 0.18/0.39 tff(46,plain,
% 0.18/0.39 (![Y: $i, X: $i] : (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X))) <=> ![Y: $i, X: $i] : (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(47,plain,
% 0.18/0.39 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~group_element(X)) | (~group_element(Y))) | product(e_1, X, Y)) <=> (product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))), (((((~group_element(X)) | (~group_element(Y))) | product(e_1, X, Y)) | product(e_2, X, Y)) <=> ((product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X))) | product(e_2, X, Y)))), rewrite(((product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X))) | product(e_2, X, Y)) <=> (product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))), (((((~group_element(X)) | (~group_element(Y))) | product(e_1, X, Y)) | product(e_2, X, Y)) <=> (product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X))))), ((((((~group_element(X)) | (~group_element(Y))) | product(e_1, X, Y)) | product(e_2, X, Y)) | product(e_3, X, Y)) <=> ((product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X))) | product(e_3, X, Y)))), rewrite(((product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X))) | product(e_3, X, Y)) <=> (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))), ((((((~group_element(X)) | (~group_element(Y))) | product(e_1, X, Y)) | product(e_2, X, Y)) | product(e_3, X, Y)) <=> (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(48,plain,
% 0.18/0.39 (![Y: $i, X: $i] : (((((~group_element(X)) | (~group_element(Y))) | product(e_1, X, Y)) | product(e_2, X, Y)) | product(e_3, X, Y)) <=> ![Y: $i, X: $i] : (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[47])).
% 0.18/0.39 tff(49,axiom,(![Y: $i, X: $i] : (((((~group_element(X)) | (~group_element(Y))) | product(e_1, X, Y)) | product(e_2, X, Y)) | product(e_3, X, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','row_surjectivity')).
% 0.18/0.39 tff(50,plain,
% 0.18/0.39 (![Y: $i, X: $i] : (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.18/0.39 tff(51,plain,
% 0.18/0.39 (![Y: $i, X: $i] : (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.18/0.39 tff(52,plain,(
% 0.18/0.39 ![Y: $i, X: $i] : (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))),
% 0.18/0.39 inference(skolemize,[status(sab)],[51])).
% 0.18/0.39 tff(53,plain,
% 0.18/0.39 (![Y: $i, X: $i] : (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[52, 45])).
% 0.18/0.39 tff(54,plain,
% 0.18/0.39 (((~![Y: $i, X: $i] : (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_3, e_1) | product(e_1, e_3, e_1) | product(e_2, e_3, e_1) | (~group_element(e_1)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | product(e_3, e_3, e_1) | product(e_1, e_3, e_1) | product(e_2, e_3, e_1) | (~group_element(e_1)) | (~group_element(e_3)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(55,plain,
% 0.18/0.39 ((product(e_3, e_3, e_1) | product(e_2, e_3, e_1) | product(e_1, e_3, e_1) | (~group_element(e_1)) | (~group_element(e_3))) <=> (product(e_3, e_3, e_1) | product(e_1, e_3, e_1) | product(e_2, e_3, e_1) | (~group_element(e_1)) | (~group_element(e_3)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(56,plain,
% 0.18/0.39 (((~![Y: $i, X: $i] : (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_3, e_1) | product(e_2, e_3, e_1) | product(e_1, e_3, e_1) | (~group_element(e_1)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_3, e_1) | product(e_1, e_3, e_1) | product(e_2, e_3, e_1) | (~group_element(e_1)) | (~group_element(e_3))))),
% 0.18/0.39 inference(monotonicity,[status(thm)],[55])).
% 0.18/0.39 tff(57,plain,
% 0.18/0.39 (((~![Y: $i, X: $i] : (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_3, e_1) | product(e_2, e_3, e_1) | product(e_1, e_3, e_1) | (~group_element(e_1)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | product(e_3, e_3, e_1) | product(e_1, e_3, e_1) | product(e_2, e_3, e_1) | (~group_element(e_1)) | (~group_element(e_3)))),
% 0.18/0.39 inference(transitivity,[status(thm)],[56, 54])).
% 0.18/0.39 tff(58,plain,
% 0.18/0.39 ((~![Y: $i, X: $i] : (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_3, e_1) | product(e_2, e_3, e_1) | product(e_1, e_3, e_1) | (~group_element(e_1)) | (~group_element(e_3)))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(59,plain,
% 0.18/0.40 ((~![Y: $i, X: $i] : (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | product(e_3, e_3, e_1) | product(e_1, e_3, e_1) | product(e_2, e_3, e_1) | (~group_element(e_1)) | (~group_element(e_3))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.18/0.40 tff(60,plain,
% 0.18/0.40 (product(e_3, e_3, e_1) | product(e_1, e_3, e_1) | product(e_2, e_3, e_1)),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[59, 53, 43, 40])).
% 0.18/0.40 tff(61,plain,
% 0.18/0.40 (product(e_3, e_3, e_1) | product(e_2, e_3, e_1)),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[60, 37])).
% 0.18/0.40 tff(62,plain,
% 0.18/0.40 (product(e_2, e_3, e_1)),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[61, 15])).
% 0.18/0.40 tff(63,assumption,(product(e_1, e_3, e_2)), introduced(assumption)).
% 0.18/0.40 tff(64,assumption,(product(e_2, e_3, e_1)), introduced(assumption)).
% 0.18/0.40 tff(65,plain,
% 0.18/0.40 ((~equalish(e_3, e_1)) <=> (~equalish(e_3, e_1))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(66,axiom,(~equalish(e_3, e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_3_is_not_e_1')).
% 0.18/0.40 tff(67,plain,
% 0.18/0.40 (~equalish(e_3, e_1)),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.18/0.40 tff(68,plain,
% 0.18/0.40 (((~![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_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_2)) | (~product(e_2, e_3, 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_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_2)) | (~product(e_2, e_3, e_1)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(69,plain,
% 0.18/0.40 (((~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_2)) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_3, e_1)) | equalish(e_3, e_1)) <=> (equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_2)) | (~product(e_2, e_3, e_1)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(70,plain,
% 0.18/0.40 (((~![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_3, e_2)) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_3, e_1)) | equalish(e_3, 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_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_2)) | (~product(e_2, e_3, e_1))))),
% 0.18/0.40 inference(monotonicity,[status(thm)],[69])).
% 0.18/0.40 tff(71,plain,
% 0.18/0.40 (((~![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_3, e_2)) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_3, e_1)) | equalish(e_3, 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_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_2)) | (~product(e_2, e_3, e_1)))),
% 0.18/0.40 inference(transitivity,[status(thm)],[70, 68])).
% 0.18/0.40 tff(72,plain,
% 0.18/0.40 ((~![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_3, e_2)) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_3, e_1)) | equalish(e_3, e_1))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(73,plain,
% 0.18/0.40 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_2)) | (~product(e_2, e_3, e_1))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.18/0.40 tff(74,plain,
% 0.18/0.40 ($false),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[73, 67, 26, 64, 14, 63])).
% 0.18/0.40 tff(75,plain,((~product(e_1, e_3, e_2)) | (~product(e_2, e_3, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.40 tff(76,plain,
% 0.18/0.40 (~product(e_1, e_3, e_2)),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[75, 62])).
% 0.18/0.40 tff(77,plain,
% 0.18/0.40 (^[Y: $i, X: $i] : refl(((~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)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1)))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(78,plain,
% 0.18/0.40 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1)) <=> ![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[77])).
% 0.18/0.40 tff(79,plain,
% 0.18/0.40 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1)) <=> ![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(80,plain,
% 0.18/0.40 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_1))), (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) <=> (((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_1)) | product(X, Y, e_2)))), rewrite((((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_1)) | product(X, Y, e_2)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_2) | product(X, Y, e_1))), (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_2) | product(X, Y, e_1)))), ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) <=> (((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_2) | product(X, Y, e_1)) | product(X, Y, e_3)))), rewrite((((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_2) | product(X, Y, e_1)) | product(X, Y, e_3)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))), ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(81,plain,
% 0.18/0.40 (![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] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[80])).
% 0.18/0.40 tff(82,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/sandbox/benchmark/theBenchmark.p','product_total_function1')).
% 0.18/0.40 tff(83,plain,
% 0.18/0.40 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.18/0.40 tff(84,plain,
% 0.18/0.40 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[83, 79])).
% 0.18/0.40 tff(85,plain,(
% 0.18/0.40 ![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))),
% 0.18/0.41 inference(skolemize,[status(sab)],[84])).
% 0.18/0.41 tff(86,plain,
% 0.18/0.41 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[85, 78])).
% 0.18/0.41 tff(87,plain,
% 0.18/0.41 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | (product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1) | (~group_element(e_1)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1) | (~group_element(e_1)) | (~group_element(e_3)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(88,plain,
% 0.18/0.41 (((~group_element(e_3)) | (~group_element(e_1)) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1)) <=> (product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1) | (~group_element(e_1)) | (~group_element(e_3)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(89,plain,
% 0.18/0.41 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | ((~group_element(e_3)) | (~group_element(e_1)) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | (product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1) | (~group_element(e_1)) | (~group_element(e_3))))),
% 0.18/0.41 inference(monotonicity,[status(thm)],[88])).
% 0.18/0.41 tff(90,plain,
% 0.18/0.41 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | ((~group_element(e_3)) | (~group_element(e_1)) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1) | (~group_element(e_1)) | (~group_element(e_3)))),
% 0.18/0.41 inference(transitivity,[status(thm)],[89, 87])).
% 0.18/0.41 tff(91,plain,
% 0.18/0.41 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | ((~group_element(e_3)) | (~group_element(e_1)) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(92,plain,
% 0.18/0.41 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1) | (~group_element(e_1)) | (~group_element(e_3))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.18/0.41 tff(93,plain,
% 0.18/0.41 (product(e_1, e_3, e_3) | product(e_1, e_3, e_2)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[92, 43, 40, 86, 37])).
% 0.18/0.41 tff(94,plain,
% 0.18/0.41 (product(e_1, e_3, e_3)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[93, 76])).
% 0.18/0.41 tff(95,assumption,(~product(e_3, e_3, e_2)), introduced(assumption)).
% 0.18/0.41 tff(96,plain,
% 0.18/0.41 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | (product(e_3, e_3, e_2) | product(e_3, e_3, e_1) | (~group_element(e_3)) | product(e_3, e_3, e_3))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | product(e_3, e_3, e_2) | product(e_3, e_3, e_1) | (~group_element(e_3)) | product(e_3, e_3, e_3))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(97,plain,
% 0.18/0.41 (((~group_element(e_3)) | (~group_element(e_3)) | product(e_3, e_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_1)) <=> (product(e_3, e_3, e_2) | product(e_3, e_3, e_1) | (~group_element(e_3)) | product(e_3, e_3, e_3))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(98,plain,
% 0.18/0.41 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | ((~group_element(e_3)) | (~group_element(e_3)) | product(e_3, e_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | (product(e_3, e_3, e_2) | product(e_3, e_3, e_1) | (~group_element(e_3)) | product(e_3, e_3, e_3)))),
% 0.18/0.41 inference(monotonicity,[status(thm)],[97])).
% 0.18/0.41 tff(99,plain,
% 0.18/0.41 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | ((~group_element(e_3)) | (~group_element(e_3)) | product(e_3, e_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | product(e_3, e_3, e_2) | product(e_3, e_3, e_1) | (~group_element(e_3)) | product(e_3, e_3, e_3))),
% 0.18/0.41 inference(transitivity,[status(thm)],[98, 96])).
% 0.18/0.41 tff(100,plain,
% 0.18/0.41 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | ((~group_element(e_3)) | (~group_element(e_3)) | product(e_3, e_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_1))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(101,plain,
% 0.18/0.41 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | product(e_3, e_3, e_2) | product(e_3, e_3, e_1) | (~group_element(e_3)) | product(e_3, e_3, e_3)),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.18/0.41 tff(102,plain,
% 0.18/0.41 (product(e_3, e_3, e_3)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[101, 40, 86, 15, 95])).
% 0.18/0.41 tff(103,plain,
% 0.18/0.41 (^[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))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(104,plain,
% 0.18/0.41 (![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)))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[103])).
% 0.18/0.41 tff(105,plain,
% 0.18/0.41 (![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)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(106,plain,
% 0.18/0.41 (^[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)))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(107,plain,
% 0.18/0.41 (![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)))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[106])).
% 0.18/0.41 tff(108,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','product_left_cancellation')).
% 0.18/0.41 tff(109,plain,
% 0.18/0.41 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.18/0.41 tff(110,plain,
% 0.18/0.41 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[109, 105])).
% 0.18/0.41 tff(111,plain,(
% 0.18/0.41 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.18/0.41 inference(skolemize,[status(sab)],[110])).
% 0.18/0.41 tff(112,plain,
% 0.18/0.41 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[111, 104])).
% 0.18/0.41 tff(113,plain,
% 0.18/0.41 (((~![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_3, e_3)) | (~product(e_3, e_3, 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_1, e_3, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(114,plain,
% 0.18/0.41 ((~![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_3, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(115,plain,
% 0.18/0.41 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_3))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.18/0.41 tff(116,plain,
% 0.18/0.41 ($false),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[115, 67, 112, 12, 102])).
% 0.18/0.41 tff(117,plain,((~product(e_1, e_3, e_3)) | product(e_3, e_3, e_1) | product(e_3, e_3, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.41 tff(118,plain,
% 0.18/0.41 (~product(e_1, e_3, e_3)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[117, 15, 95])).
% 0.18/0.41 tff(119,plain,
% 0.18/0.41 (product(e_1, e_3, e_2)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[93, 118])).
% 0.18/0.41 tff(120,plain,
% 0.18/0.41 ($false),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[73, 67, 26, 62, 14, 119])).
% 0.18/0.41 tff(121,plain,(product(e_3, e_3, e_1) | product(e_3, e_3, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.41 tff(122,plain,
% 0.18/0.41 (product(e_3, e_3, e_2)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[121, 15])).
% 0.18/0.41 tff(123,plain,
% 0.18/0.41 (((~![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_3) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_2)) | (~product(e_1, 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_3) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_2)) | (~product(e_1, e_1, e_2)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(124,plain,
% 0.18/0.41 (((~product(e_1, e_3, e_3)) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_3, e_2)) | (~product(e_1, e_1, e_2)) | equalish(e_1, e_3)) <=> (equalish(e_1, e_3) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_2)) | (~product(e_1, e_1, e_2)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(125,plain,
% 0.18/0.41 (((~![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_3, e_3)) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_3, e_2)) | (~product(e_1, e_1, e_2)) | equalish(e_1, 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_1, e_3) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_2)) | (~product(e_1, e_1, e_2))))),
% 0.18/0.41 inference(monotonicity,[status(thm)],[124])).
% 0.18/0.41 tff(126,plain,
% 0.18/0.41 (((~![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_3, e_3)) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_3, e_2)) | (~product(e_1, e_1, e_2)) | equalish(e_1, 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_1, e_3) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_2)) | (~product(e_1, e_1, e_2)))),
% 0.18/0.42 inference(transitivity,[status(thm)],[125, 123])).
% 0.18/0.42 tff(127,plain,
% 0.18/0.42 ((~![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_3, e_3)) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_3, e_2)) | (~product(e_1, e_1, e_2)) | equalish(e_1, e_3))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(128,plain,
% 0.18/0.42 ((~![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_3) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_2)) | (~product(e_1, e_1, e_2))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.18/0.42 tff(129,plain,
% 0.18/0.42 (~product(e_1, e_1, e_2)),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[128, 29, 26, 122, 14, 94])).
% 0.18/0.42 tff(130,plain,
% 0.18/0.42 (group_element(e_2) <=> group_element(e_2)),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(131,axiom,(group_element(e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_2')).
% 0.18/0.42 tff(132,plain,
% 0.18/0.42 (group_element(e_2)),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.18/0.42 tff(133,plain,
% 0.18/0.42 (^[Y: $i, X: $i] : refl(((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y)))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(134,plain,
% 0.18/0.42 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y)) <=> ![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[133])).
% 0.18/0.42 tff(135,plain,
% 0.18/0.42 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y)) <=> ![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(136,plain,
% 0.18/0.42 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~group_element(X)) | (~group_element(Y))) | product(X, e_1, Y)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, e_1, Y))), (((((~group_element(X)) | (~group_element(Y))) | product(X, e_1, Y)) | product(X, e_2, Y)) <=> (((~group_element(Y)) | (~group_element(X)) | product(X, e_1, Y)) | product(X, e_2, Y)))), rewrite((((~group_element(Y)) | (~group_element(X)) | product(X, e_1, Y)) | product(X, e_2, Y)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, e_2, Y) | product(X, e_1, Y))), (((((~group_element(X)) | (~group_element(Y))) | product(X, e_1, Y)) | product(X, e_2, Y)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, e_2, Y) | product(X, e_1, Y)))), ((((((~group_element(X)) | (~group_element(Y))) | product(X, e_1, Y)) | product(X, e_2, Y)) | product(X, e_3, Y)) <=> (((~group_element(Y)) | (~group_element(X)) | product(X, e_2, Y) | product(X, e_1, Y)) | product(X, e_3, Y)))), rewrite((((~group_element(Y)) | (~group_element(X)) | product(X, e_2, Y) | product(X, e_1, Y)) | product(X, e_3, Y)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))), ((((((~group_element(X)) | (~group_element(Y))) | product(X, e_1, Y)) | product(X, e_2, Y)) | product(X, e_3, Y)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(137,plain,
% 0.18/0.42 (![Y: $i, X: $i] : (((((~group_element(X)) | (~group_element(Y))) | product(X, e_1, Y)) | product(X, e_2, Y)) | product(X, e_3, Y)) <=> ![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[136])).
% 0.18/0.42 tff(138,axiom,(![Y: $i, X: $i] : (((((~group_element(X)) | (~group_element(Y))) | product(X, e_1, Y)) | product(X, e_2, Y)) | product(X, e_3, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','column_surjectivity')).
% 0.18/0.42 tff(139,plain,
% 0.18/0.42 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.18/0.42 tff(140,plain,
% 0.18/0.42 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[139, 135])).
% 0.18/0.42 tff(141,plain,(
% 0.18/0.42 ![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))),
% 0.18/0.42 inference(skolemize,[status(sab)],[140])).
% 0.18/0.42 tff(142,plain,
% 0.18/0.42 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[141, 134])).
% 0.18/0.42 tff(143,plain,
% 0.18/0.42 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_2)) | product(e_1, e_3, e_2) | (~group_element(e_1)) | product(e_1, e_1, e_2) | product(e_1, e_2, e_2))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | (~group_element(e_2)) | product(e_1, e_3, e_2) | (~group_element(e_1)) | product(e_1, e_1, e_2) | product(e_1, e_2, e_2))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(144,plain,
% 0.18/0.42 (((~group_element(e_2)) | (~group_element(e_1)) | product(e_1, e_3, e_2) | product(e_1, e_2, e_2) | product(e_1, e_1, e_2)) <=> ((~group_element(e_2)) | product(e_1, e_3, e_2) | (~group_element(e_1)) | product(e_1, e_1, e_2) | product(e_1, e_2, e_2))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(145,plain,
% 0.18/0.42 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_2)) | (~group_element(e_1)) | product(e_1, e_3, e_2) | product(e_1, e_2, e_2) | product(e_1, e_1, e_2))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_2)) | product(e_1, e_3, e_2) | (~group_element(e_1)) | product(e_1, e_1, e_2) | product(e_1, e_2, e_2)))),
% 0.18/0.42 inference(monotonicity,[status(thm)],[144])).
% 0.18/0.42 tff(146,plain,
% 0.18/0.42 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_2)) | (~group_element(e_1)) | product(e_1, e_3, e_2) | product(e_1, e_2, e_2) | product(e_1, e_1, e_2))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | (~group_element(e_2)) | product(e_1, e_3, e_2) | (~group_element(e_1)) | product(e_1, e_1, e_2) | product(e_1, e_2, e_2))),
% 0.18/0.42 inference(transitivity,[status(thm)],[145, 143])).
% 0.18/0.42 tff(147,plain,
% 0.18/0.42 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_2)) | (~group_element(e_1)) | product(e_1, e_3, e_2) | product(e_1, e_2, e_2) | product(e_1, e_1, e_2))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(148,plain,
% 0.18/0.42 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | (~group_element(e_2)) | product(e_1, e_3, e_2) | (~group_element(e_1)) | product(e_1, e_1, e_2) | product(e_1, e_2, e_2)),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.18/0.42 tff(149,plain,
% 0.18/0.42 (product(e_1, e_2, e_2)),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[148, 142, 43, 132, 76, 129])).
% 0.18/0.42 tff(150,plain,
% 0.18/0.42 ((~equalish(e_2, e_3)) <=> (~equalish(e_2, e_3))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(151,axiom,(~equalish(e_2, e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_is_not_e_3')).
% 0.18/0.42 tff(152,plain,
% 0.18/0.42 (~equalish(e_2, e_3)),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.18/0.42 tff(153,plain,
% 0.18/0.42 (((~![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_3) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_2)) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, 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_2, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_2)) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(154,plain,
% 0.18/0.42 (((~product(e_1, e_3, e_3)) | (~product(e_1, e_2, e_2)) | (~product(e_3, e_3, e_2)) | (~product(e_2, e_2, e_2)) | equalish(e_2, e_3)) <=> (equalish(e_2, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_2)) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(155,plain,
% 0.18/0.42 (((~![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_3, e_3)) | (~product(e_1, e_2, e_2)) | (~product(e_3, e_3, e_2)) | (~product(e_2, e_2, e_2)) | equalish(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_3) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_2)) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_2))))),
% 0.18/0.42 inference(monotonicity,[status(thm)],[154])).
% 0.18/0.42 tff(156,plain,
% 0.18/0.42 (((~![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_3, e_3)) | (~product(e_1, e_2, e_2)) | (~product(e_3, e_3, e_2)) | (~product(e_2, e_2, e_2)) | equalish(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_3) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_2)) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.18/0.42 inference(transitivity,[status(thm)],[155, 153])).
% 0.18/0.42 tff(157,plain,
% 0.18/0.42 ((~![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_3, e_3)) | (~product(e_1, e_2, e_2)) | (~product(e_3, e_3, e_2)) | (~product(e_2, e_2, e_2)) | equalish(e_2, e_3))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(158,plain,
% 0.18/0.42 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_2, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_2)) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_2))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.18/0.42 tff(159,plain,
% 0.18/0.42 ($false),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[158, 152, 26, 122, 94, 11, 149])).
% 0.18/0.42 tff(160,plain,(product(e_3, e_3, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.42 tff(161,plain,
% 0.18/0.42 (((~![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_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, 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_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_1)))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(162,plain,
% 0.18/0.43 (((~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_3)) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_3, e_1)) | equalish(e_3, e_1)) <=> (equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_1)))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(163,plain,
% 0.18/0.43 (((~![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_3, e_3)) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_3, e_1)) | equalish(e_3, 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_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_1))))),
% 0.18/0.43 inference(monotonicity,[status(thm)],[162])).
% 0.18/0.43 tff(164,plain,
% 0.18/0.43 (((~![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_3, e_3)) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_3, e_1)) | equalish(e_3, 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_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_1)))),
% 0.18/0.43 inference(transitivity,[status(thm)],[163, 161])).
% 0.18/0.43 tff(165,plain,
% 0.18/0.43 ((~![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_3, e_3)) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_3, e_1)) | equalish(e_3, e_1))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(166,plain,
% 0.18/0.43 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_1))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[165, 164])).
% 0.18/0.43 tff(167,plain,
% 0.18/0.43 ($false),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[166, 67, 26, 160, 14, 12])).
% 0.18/0.43 tff(168,plain,(~product(e_1, e_3, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.43 tff(169,plain,
% 0.18/0.43 (product(e_1, e_3, e_2)),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[93, 168])).
% 0.18/0.43 tff(170,plain,
% 0.18/0.43 (~product(e_2, e_3, e_1)),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[75, 169])).
% 0.18/0.43 tff(171,assumption,(product(e_2, e_1, e_1)), introduced(assumption)).
% 0.18/0.43 tff(172,plain,
% 0.18/0.43 ((~equalish(e_2, e_1)) <=> (~equalish(e_2, e_1))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(173,axiom,(~equalish(e_2, e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_is_not_e_1')).
% 0.18/0.43 tff(174,plain,
% 0.18/0.43 (~equalish(e_2, e_1)),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.18/0.43 tff(175,plain,
% 0.18/0.43 (((~![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_1, e_1)) | (~product(e_2, e_1, e_1)))) <=> ((~![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_1, e_1)) | (~product(e_2, e_1, e_1)))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(176,plain,
% 0.18/0.43 ((~![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_1, e_1)) | (~product(e_2, e_1, e_1)))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(177,plain,
% 0.18/0.43 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.18/0.43 tff(178,plain,
% 0.18/0.43 ($false),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[177, 174, 112, 14, 171])).
% 0.18/0.43 tff(179,plain,(~product(e_2, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.43 tff(180,plain,
% 0.18/0.43 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_2)) | product(e_2, e_3, e_1) | (~group_element(e_1)) | product(e_2, e_1, e_1) | product(e_2, e_2, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | (~group_element(e_2)) | product(e_2, e_3, e_1) | (~group_element(e_1)) | product(e_2, e_1, e_1) | product(e_2, e_2, e_1))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(181,plain,
% 0.18/0.43 (((~group_element(e_1)) | (~group_element(e_2)) | product(e_2, e_3, e_1) | product(e_2, e_2, e_1) | product(e_2, e_1, e_1)) <=> ((~group_element(e_2)) | product(e_2, e_3, e_1) | (~group_element(e_1)) | product(e_2, e_1, e_1) | product(e_2, e_2, e_1))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(182,plain,
% 0.18/0.43 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_1)) | (~group_element(e_2)) | product(e_2, e_3, e_1) | product(e_2, e_2, e_1) | product(e_2, e_1, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_2)) | product(e_2, e_3, e_1) | (~group_element(e_1)) | product(e_2, e_1, e_1) | product(e_2, e_2, e_1)))),
% 0.18/0.43 inference(monotonicity,[status(thm)],[181])).
% 0.18/0.43 tff(183,plain,
% 0.18/0.43 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_1)) | (~group_element(e_2)) | product(e_2, e_3, e_1) | product(e_2, e_2, e_1) | product(e_2, e_1, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | (~group_element(e_2)) | product(e_2, e_3, e_1) | (~group_element(e_1)) | product(e_2, e_1, e_1) | product(e_2, e_2, e_1))),
% 0.18/0.43 inference(transitivity,[status(thm)],[182, 180])).
% 0.18/0.43 tff(184,plain,
% 0.18/0.43 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_1)) | (~group_element(e_2)) | product(e_2, e_3, e_1) | product(e_2, e_2, e_1) | product(e_2, e_1, e_1))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(185,plain,
% 0.18/0.43 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | (~group_element(e_2)) | product(e_2, e_3, e_1) | (~group_element(e_1)) | product(e_2, e_1, e_1) | product(e_2, e_2, e_1)),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[184, 183])).
% 0.18/0.43 tff(186,plain,
% 0.18/0.43 (product(e_2, e_3, e_1) | product(e_2, e_2, e_1)),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[185, 142, 43, 132, 179])).
% 0.18/0.43 tff(187,plain,
% 0.18/0.43 (product(e_2, e_2, e_1)),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[186, 170])).
% 0.18/0.43 tff(188,plain,
% 0.18/0.43 (^[W: $i, Z: $i, Y: $i, X: $i] : refl((equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W))) <=> (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(189,plain,
% 0.18/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[188])).
% 0.18/0.43 tff(190,plain,
% 0.18/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(191,plain,
% 0.18/0.43 (^[W: $i, Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite(((~product(X, Y, W)) | (~product(X, Y, Z))) <=> ((~product(X, Y, Z)) | (~product(X, Y, W)))), ((((~product(X, Y, W)) | (~product(X, Y, Z))) | equalish(W, Z)) <=> (((~product(X, Y, Z)) | (~product(X, Y, W))) | equalish(W, Z)))), rewrite((((~product(X, Y, Z)) | (~product(X, Y, W))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))), ((((~product(X, Y, W)) | (~product(X, Y, Z))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))))),
% 0.18/0.44 inference(bind,[status(th)],[])).
% 0.18/0.44 tff(192,plain,
% 0.18/0.44 (![W: $i, Z: $i, Y: $i, X: $i] : (((~product(X, Y, W)) | (~product(X, Y, Z))) | equalish(W, Z)) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))),
% 0.18/0.44 inference(quant_intro,[status(thm)],[191])).
% 0.18/0.44 tff(193,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product(X, Y, W)) | (~product(X, Y, Z))) | equalish(W, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','product_total_function2')).
% 0.18/0.44 tff(194,plain,
% 0.18/0.44 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[193, 192])).
% 0.18/0.44 tff(195,plain,
% 0.18/0.44 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[194, 190])).
% 0.18/0.44 tff(196,plain,(
% 0.18/0.44 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))),
% 0.18/0.44 inference(skolemize,[status(sab)],[195])).
% 0.18/0.44 tff(197,plain,
% 0.18/0.44 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[196, 189])).
% 0.18/0.44 tff(198,plain,
% 0.18/0.44 ((~equalish(e_1, e_2)) <=> (~equalish(e_1, e_2))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(199,axiom,(~equalish(e_1, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_1_is_not_e_2')).
% 0.18/0.44 tff(200,plain,
% 0.18/0.44 (~equalish(e_1, e_2)),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[199, 198])).
% 0.18/0.44 tff(201,plain,
% 0.18/0.44 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | equalish(e_1, e_2) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_2, e_2)))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(202,plain,
% 0.18/0.44 ((equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_2, e_1))) <=> (equalish(e_1, e_2) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_2, e_2)))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(203,plain,
% 0.18/0.44 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_2, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_2, e_2))))),
% 0.18/0.44 inference(monotonicity,[status(thm)],[202])).
% 0.18/0.44 tff(204,plain,
% 0.18/0.44 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_2, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | equalish(e_1, e_2) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_2, e_2)))),
% 0.18/0.44 inference(transitivity,[status(thm)],[203, 201])).
% 0.18/0.44 tff(205,plain,
% 0.18/0.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_2, e_1)))),
% 0.18/0.44 inference(quant_inst,[status(thm)],[])).
% 0.18/0.44 tff(206,plain,
% 0.18/0.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | equalish(e_1, e_2) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_2, e_2))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[205, 204])).
% 0.18/0.44 tff(207,plain,
% 0.18/0.44 ($false),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[206, 200, 197, 187, 11])).
% 0.18/0.44 % SZS output end Proof
%------------------------------------------------------------------------------