TSTP Solution File: GRP124-4.004 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP124-4.004 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 16 22:26:00 EDT 2022
% Result : Unsatisfiable 0.18s 0.44s
% Output : Proof 0.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP124-4.004 : 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 : n027.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 15:09:17 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.
% 0.18/0.44 % SZS status Unsatisfiable
% 0.18/0.44 % SZS output start Proof
% 0.18/0.44 tff(product_type, type, (
% 0.18/0.44 product: ( $i * $i * $i ) > $o)).
% 0.18/0.44 tff(e_4_type, type, (
% 0.18/0.44 e_4: $i)).
% 0.18/0.44 tff(e_1_type, type, (
% 0.18/0.44 e_1: $i)).
% 0.18/0.44 tff(e_2_type, type, (
% 0.18/0.44 e_2: $i)).
% 0.18/0.44 tff(e_3_type, type, (
% 0.18/0.44 e_3: $i)).
% 0.18/0.44 tff(equalish_type, type, (
% 0.18/0.44 equalish: ( $i * $i ) > $o)).
% 0.18/0.44 tff(group_element_type, type, (
% 0.18/0.44 group_element: $i > $o)).
% 0.18/0.44 tff(1,assumption,(~product(e_4, e_3, e_1)), introduced(assumption)).
% 0.18/0.44 tff(2,assumption,(~product(e_1, e_3, e_4)), introduced(assumption)).
% 0.18/0.44 tff(3,plain,
% 0.18/0.44 (^[X: $i] : refl(product(X, X, X) <=> product(X, X, X))),
% 0.18/0.44 inference(bind,[status(th)],[])).
% 0.18/0.44 tff(4,plain,
% 0.18/0.44 (![X: $i] : product(X, X, X) <=> ![X: $i] : product(X, X, X)),
% 0.18/0.44 inference(quant_intro,[status(thm)],[3])).
% 0.18/0.44 tff(5,plain,
% 0.18/0.44 (![X: $i] : product(X, X, X) <=> ![X: $i] : product(X, X, X)),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(6,axiom,(![X: $i] : product(X, X, X)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product_idempotence')).
% 0.18/0.44 tff(7,plain,
% 0.18/0.44 (![X: $i] : product(X, X, X)),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.18/0.44 tff(8,plain,(
% 0.18/0.44 ![X: $i] : product(X, X, X)),
% 0.18/0.44 inference(skolemize,[status(sab)],[7])).
% 0.18/0.44 tff(9,plain,
% 0.18/0.44 (![X: $i] : product(X, X, X)),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.18/0.44 tff(10,plain,
% 0.18/0.44 ((~![X: $i] : product(X, X, X)) | product(e_4, e_4, e_4)),
% 0.18/0.44 inference(quant_inst,[status(thm)],[])).
% 0.18/0.44 tff(11,plain,
% 0.18/0.44 (product(e_4, e_4, e_4)),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[10, 9])).
% 0.18/0.44 tff(12,assumption,(product(e_4, e_3, e_4)), introduced(assumption)).
% 0.18/0.44 tff(13,plain,
% 0.18/0.44 (^[W: $i, Z: $i, Y: $i, X: $i] : refl((equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y))) <=> (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y))))),
% 0.18/0.44 inference(bind,[status(th)],[])).
% 0.18/0.44 tff(14,plain,
% 0.18/0.44 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.18/0.44 inference(quant_intro,[status(thm)],[13])).
% 0.18/0.44 tff(15,plain,
% 0.18/0.44 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(16,plain,
% 0.18/0.44 (^[W: $i, Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite(((~product(X, W, Y)) | (~product(X, Z, Y))) <=> ((~product(X, Z, Y)) | (~product(X, W, Y)))), ((((~product(X, W, Y)) | (~product(X, Z, Y))) | equalish(W, Z)) <=> (((~product(X, Z, Y)) | (~product(X, W, Y))) | equalish(W, Z)))), rewrite((((~product(X, Z, Y)) | (~product(X, W, Y))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))), ((((~product(X, W, Y)) | (~product(X, Z, Y))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))))),
% 0.18/0.44 inference(bind,[status(th)],[])).
% 0.18/0.44 tff(17,plain,
% 0.18/0.44 (![W: $i, Z: $i, Y: $i, X: $i] : (((~product(X, W, Y)) | (~product(X, Z, Y))) | equalish(W, Z)) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.18/0.44 inference(quant_intro,[status(thm)],[16])).
% 0.18/0.44 tff(18,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product(X, W, Y)) | (~product(X, Z, Y))) | equalish(W, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product_right_cancellation')).
% 0.18/0.44 tff(19,plain,
% 0.18/0.44 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.18/0.44 tff(20,plain,
% 0.18/0.44 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.18/0.44 tff(21,plain,(
% 0.18/0.44 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.18/0.44 inference(skolemize,[status(sab)],[20])).
% 0.18/0.44 tff(22,plain,
% 0.18/0.44 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.18/0.44 tff(23,plain,
% 0.18/0.44 ((~equalish(e_3, e_4)) <=> (~equalish(e_3, e_4))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(24,axiom,(~equalish(e_3, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_4')).
% 0.18/0.44 tff(25,plain,
% 0.18/0.44 (~equalish(e_3, e_4)),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.18/0.44 tff(26,plain,
% 0.18/0.44 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_3, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_3, e_4)))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(27,plain,
% 0.18/0.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_3, e_4)))),
% 0.18/0.44 inference(quant_inst,[status(thm)],[])).
% 0.18/0.44 tff(28,plain,
% 0.18/0.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_3, e_4))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.18/0.44 tff(29,plain,
% 0.18/0.44 ($false),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[28, 25, 22, 12, 11])).
% 0.18/0.44 tff(30,plain,(~product(e_4, e_3, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.44 tff(31,assumption,(~product(e_2, e_3, e_1)), introduced(assumption)).
% 0.18/0.44 tff(32,assumption,(product(e_1, e_3, e_1)), introduced(assumption)).
% 0.18/0.44 tff(33,plain,
% 0.18/0.44 ((~![X: $i] : product(X, X, X)) | product(e_1, e_1, e_1)),
% 0.18/0.44 inference(quant_inst,[status(thm)],[])).
% 0.18/0.44 tff(34,plain,
% 0.18/0.44 (product(e_1, e_1, e_1)),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[33, 9])).
% 0.18/0.44 tff(35,plain,
% 0.18/0.44 ((~equalish(e_3, e_1)) <=> (~equalish(e_3, e_1))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(36,axiom,(~equalish(e_3, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_1')).
% 0.18/0.44 tff(37,plain,
% 0.18/0.44 (~equalish(e_3, e_1)),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.18/0.44 tff(38,plain,
% 0.18/0.44 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_1)))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(39,plain,
% 0.18/0.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_1)))),
% 0.18/0.44 inference(quant_inst,[status(thm)],[])).
% 0.18/0.44 tff(40,plain,
% 0.18/0.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_1))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.18/0.44 tff(41,plain,
% 0.18/0.44 ($false),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[40, 37, 22, 34, 32])).
% 0.18/0.44 tff(42,plain,(~product(e_1, e_3, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.44 tff(43,assumption,(~product(e_1, e_3, e_2)), introduced(assumption)).
% 0.18/0.44 tff(44,assumption,(~product(e_1, e_3, e_1)), introduced(assumption)).
% 0.18/0.44 tff(45,plain,
% 0.18/0.44 (^[Y: $i, X: $i] : refl(((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | 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_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1)))),
% 0.18/0.44 inference(bind,[status(th)],[])).
% 0.18/0.44 tff(46,plain,
% 0.18/0.44 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | 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_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))),
% 0.18/0.44 inference(quant_intro,[status(thm)],[45])).
% 0.18/0.44 tff(47,plain,
% 0.18/0.44 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | 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_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(48,plain,
% 0.18/0.45 (^[Y: $i, X: $i] : trans(monotonicity(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)))), (((((((~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_4)) <=> (((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1)) | product(X, Y, e_4)))), rewrite((((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1)) | product(X, Y, e_4)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | 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)) | product(X, Y, e_4)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))))),
% 0.18/0.45 inference(bind,[status(th)],[])).
% 0.18/0.45 tff(49,plain,
% 0.18/0.45 (![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)) | product(X, Y, e_4)) <=> ![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))),
% 0.18/0.45 inference(quant_intro,[status(thm)],[48])).
% 0.18/0.45 tff(50,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)) | product(X, Y, e_4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product_total_function1')).
% 0.18/0.45 tff(51,plain,
% 0.18/0.45 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.18/0.45 tff(52,plain,
% 0.18/0.45 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.18/0.45 tff(53,plain,(
% 0.18/0.45 ![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))),
% 0.18/0.45 inference(skolemize,[status(sab)],[52])).
% 0.18/0.45 tff(54,plain,
% 0.18/0.45 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[53, 46])).
% 0.18/0.45 tff(55,plain,
% 0.18/0.45 (group_element(e_3) <=> group_element(e_3)),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(56,axiom,(group_element(e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_3')).
% 0.18/0.45 tff(57,plain,
% 0.18/0.45 (group_element(e_3)),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.18/0.45 tff(58,plain,
% 0.18/0.45 (group_element(e_1) <=> group_element(e_1)),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(59,axiom,(group_element(e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_1')).
% 0.18/0.45 tff(60,plain,
% 0.18/0.45 (group_element(e_1)),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.18/0.45 tff(61,plain,
% 0.18/0.45 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | (product(e_1, e_3, e_4) | product(e_1, e_3, e_2) | (~group_element(e_3)) | product(e_1, e_3, e_1) | (~group_element(e_1)) | product(e_1, e_3, e_3))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | product(e_1, e_3, e_4) | product(e_1, e_3, e_2) | (~group_element(e_3)) | product(e_1, e_3, e_1) | (~group_element(e_1)) | product(e_1, e_3, e_3))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(62,plain,
% 0.18/0.45 (((~group_element(e_3)) | (~group_element(e_1)) | product(e_1, e_3, e_4) | 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_4) | product(e_1, e_3, e_2) | (~group_element(e_3)) | product(e_1, e_3, e_1) | (~group_element(e_1)) | product(e_1, e_3, e_3))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(63,plain,
% 0.18/0.45 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | 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_4) | 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_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | (product(e_1, e_3, e_4) | product(e_1, e_3, e_2) | (~group_element(e_3)) | product(e_1, e_3, e_1) | (~group_element(e_1)) | product(e_1, e_3, e_3)))),
% 0.18/0.45 inference(monotonicity,[status(thm)],[62])).
% 0.18/0.45 tff(64,plain,
% 0.18/0.45 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | 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_4) | 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_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | product(e_1, e_3, e_4) | product(e_1, e_3, e_2) | (~group_element(e_3)) | product(e_1, e_3, e_1) | (~group_element(e_1)) | product(e_1, e_3, e_3))),
% 0.18/0.45 inference(transitivity,[status(thm)],[63, 61])).
% 0.18/0.45 tff(65,plain,
% 0.18/0.45 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | 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_4) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1))),
% 0.18/0.45 inference(quant_inst,[status(thm)],[])).
% 0.18/0.45 tff(66,plain,
% 0.18/0.45 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | product(e_1, e_3, e_4) | product(e_1, e_3, e_2) | (~group_element(e_3)) | product(e_1, e_3, e_1) | (~group_element(e_1)) | product(e_1, e_3, e_3)),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.18/0.45 tff(67,plain,
% 0.18/0.45 (product(e_1, e_3, e_4) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1) | product(e_1, e_3, e_3)),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[66, 60, 57, 54])).
% 0.18/0.45 tff(68,plain,
% 0.18/0.45 (product(e_1, e_3, e_3)),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[67, 44, 43, 2])).
% 0.18/0.45 tff(69,plain,
% 0.18/0.45 (^[Y: $i, X: $i] : refl((product(e_4, 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_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X))))),
% 0.18/0.45 inference(bind,[status(th)],[])).
% 0.18/0.45 tff(70,plain,
% 0.18/0.45 (![Y: $i, X: $i] : (product(e_4, X, Y) | 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_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))),
% 0.18/0.45 inference(quant_intro,[status(thm)],[69])).
% 0.18/0.45 tff(71,plain,
% 0.18/0.45 (![Y: $i, X: $i] : (product(e_4, X, Y) | 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_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(72,plain,
% 0.18/0.45 (^[Y: $i, X: $i] : trans(monotonicity(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))))), (((((((~group_element(X)) | (~group_element(Y))) | product(e_1, X, Y)) | product(e_2, X, Y)) | product(e_3, X, Y)) | product(e_4, 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_4, X, Y)))), rewrite(((product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X))) | product(e_4, X, Y)) <=> (product(e_4, 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_4, X, Y)) <=> (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))))),
% 0.18/0.45 inference(bind,[status(th)],[])).
% 0.18/0.45 tff(73,plain,
% 0.18/0.45 (![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)) | product(e_4, X, Y)) <=> ![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))),
% 0.18/0.45 inference(quant_intro,[status(thm)],[72])).
% 0.18/0.45 tff(74,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)) | product(e_4, X, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','row_surjectivity')).
% 0.18/0.45 tff(75,plain,
% 0.18/0.45 (![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.18/0.46 tff(76,plain,
% 0.18/0.46 (![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[75, 71])).
% 0.18/0.46 tff(77,plain,(
% 0.18/0.46 ![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))),
% 0.18/0.46 inference(skolemize,[status(sab)],[76])).
% 0.18/0.46 tff(78,plain,
% 0.18/0.46 (![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[77, 70])).
% 0.18/0.46 tff(79,plain,
% 0.18/0.46 (((~![Y: $i, X: $i] : (product(e_4, 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(e_3)) | product(e_2, e_3, e_1) | product(e_3, e_3, e_1) | product(e_4, e_3, e_1) | product(e_1, e_3, e_1) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (product(e_4, 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(e_3)) | product(e_2, e_3, e_1) | product(e_3, e_3, e_1) | product(e_4, e_3, e_1) | product(e_1, e_3, e_1) | (~group_element(e_1)))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(80,plain,
% 0.18/0.46 ((product(e_4, e_3, e_1) | 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))) <=> ((~group_element(e_3)) | product(e_2, e_3, e_1) | product(e_3, e_3, e_1) | product(e_4, e_3, e_1) | product(e_1, e_3, e_1) | (~group_element(e_1)))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(81,plain,
% 0.18/0.46 (((~![Y: $i, X: $i] : (product(e_4, 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_4, e_3, e_1) | 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_4, 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(e_3)) | product(e_2, e_3, e_1) | product(e_3, e_3, e_1) | product(e_4, e_3, e_1) | product(e_1, e_3, e_1) | (~group_element(e_1))))),
% 0.18/0.46 inference(monotonicity,[status(thm)],[80])).
% 0.18/0.46 tff(82,plain,
% 0.18/0.46 (((~![Y: $i, X: $i] : (product(e_4, 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_4, e_3, e_1) | 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_4, 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(e_3)) | product(e_2, e_3, e_1) | product(e_3, e_3, e_1) | product(e_4, e_3, e_1) | product(e_1, e_3, e_1) | (~group_element(e_1)))),
% 0.18/0.46 inference(transitivity,[status(thm)],[81, 79])).
% 0.18/0.46 tff(83,plain,
% 0.18/0.46 ((~![Y: $i, X: $i] : (product(e_4, 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_4, e_3, e_1) | 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)))),
% 0.18/0.46 inference(quant_inst,[status(thm)],[])).
% 0.18/0.46 tff(84,plain,
% 0.18/0.46 ((~![Y: $i, X: $i] : (product(e_4, 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(e_3)) | product(e_2, e_3, e_1) | product(e_3, e_3, e_1) | product(e_4, e_3, e_1) | product(e_1, e_3, e_1) | (~group_element(e_1))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.18/0.46 tff(85,plain,
% 0.18/0.46 (product(e_2, e_3, e_1) | product(e_3, e_3, e_1) | product(e_4, e_3, e_1) | product(e_1, e_3, e_1)),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[84, 78, 60, 57])).
% 0.18/0.46 tff(86,plain,
% 0.18/0.46 (product(e_3, e_3, e_1)),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[85, 44, 1, 31])).
% 0.18/0.46 tff(87,plain,
% 0.18/0.46 (^[Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : refl(((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2)) <=> ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2)))),
% 0.18/0.46 inference(bind,[status(th)],[])).
% 0.18/0.46 tff(88,plain,
% 0.18/0.46 (![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~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, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))),
% 0.18/0.46 inference(quant_intro,[status(thm)],[87])).
% 0.18/0.46 tff(89,plain,
% 0.18/0.46 (![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~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, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(90,plain,
% 0.18/0.46 (^[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, X1, Y1))) <=> ((~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)))), (((((~product(X1, Y1, Z1)) | (~product(X2, Y2, Z1))) | (~product(Z2, X1, Y1))) | (~product(Z2, X2, Y2))) <=> (((~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1))) | (~product(Z2, X2, Y2))))), rewrite((((~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1))) | (~product(Z2, X2, Y2))) <=> ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)))), (((((~product(X1, Y1, Z1)) | (~product(X2, Y2, Z1))) | (~product(Z2, X1, Y1))) | (~product(Z2, X2, Y2))) <=> ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1))))), ((((((~product(X1, Y1, Z1)) | (~product(X2, Y2, Z1))) | (~product(Z2, X1, Y1))) | (~product(Z2, X2, Y2))) | equalish(Y1, Y2)) <=> (((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1))) | equalish(Y1, Y2)))), rewrite((((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1))) | equalish(Y1, Y2)) <=> ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))), ((((((~product(X1, Y1, Z1)) | (~product(X2, Y2, Z1))) | (~product(Z2, X1, Y1))) | (~product(Z2, X2, Y2))) | equalish(Y1, Y2)) <=> ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))))),
% 0.18/0.46 inference(bind,[status(th)],[])).
% 0.18/0.46 tff(91,plain,
% 0.18/0.46 (![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : (((((~product(X1, Y1, Z1)) | (~product(X2, Y2, Z1))) | (~product(Z2, X1, Y1))) | (~product(Z2, X2, Y2))) | equalish(Y1, Y2)) <=> ![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))),
% 0.18/0.46 inference(quant_intro,[status(thm)],[90])).
% 0.18/0.46 tff(92,axiom,(![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : (((((~product(X1, Y1, Z1)) | (~product(X2, Y2, Z1))) | (~product(Z2, X1, Y1))) | (~product(Z2, X2, Y2))) | equalish(Y1, Y2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qg2_2')).
% 0.18/0.46 tff(93,plain,
% 0.18/0.46 (![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.18/0.46 tff(94,plain,
% 0.18/0.46 (![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[93, 89])).
% 0.18/0.46 tff(95,plain,(
% 0.18/0.46 ![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))),
% 0.18/0.46 inference(skolemize,[status(sab)],[94])).
% 0.18/0.46 tff(96,plain,
% 0.18/0.46 (![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[95, 88])).
% 0.18/0.46 tff(97,plain,
% 0.18/0.46 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~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, X2, Y2)) | (~product(Z2, X1, Y1)) | (~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)))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(98,plain,
% 0.18/0.46 (((~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)))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(99,plain,
% 0.18/0.46 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~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, X2, Y2)) | (~product(Z2, X1, Y1)) | (~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))))),
% 0.18/0.46 inference(monotonicity,[status(thm)],[98])).
% 0.18/0.46 tff(100,plain,
% 0.18/0.46 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~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, X2, Y2)) | (~product(Z2, X1, Y1)) | (~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)))),
% 0.18/0.46 inference(transitivity,[status(thm)],[99, 97])).
% 0.18/0.46 tff(101,plain,
% 0.18/0.46 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~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))),
% 0.18/0.46 inference(quant_inst,[status(thm)],[])).
% 0.18/0.46 tff(102,plain,
% 0.18/0.46 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_1))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.18/0.46 tff(103,plain,
% 0.18/0.46 ($false),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[102, 37, 96, 34, 86, 68])).
% 0.18/0.46 tff(104,plain,(product(e_1, e_3, e_1) | product(e_4, e_3, e_1) | product(e_2, e_3, e_1) | product(e_1, e_3, e_2) | product(e_1, e_3, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.46 tff(105,plain,
% 0.18/0.46 (product(e_4, e_3, e_1) | product(e_2, e_3, e_1) | product(e_1, e_3, e_2) | product(e_1, e_3, e_4)),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[104, 42])).
% 0.18/0.46 tff(106,plain,
% 0.18/0.46 (product(e_1, e_3, e_2)),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[105, 31, 1, 2])).
% 0.18/0.46 tff(107,assumption,(product(e_4, e_3, e_2)), introduced(assumption)).
% 0.18/0.47 tff(108,assumption,(product(e_1, e_3, e_2)), introduced(assumption)).
% 0.18/0.47 tff(109,plain,
% 0.18/0.47 (^[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))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(110,plain,
% 0.18/0.47 (![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)))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[109])).
% 0.18/0.47 tff(111,plain,
% 0.18/0.47 (![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)))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(112,plain,
% 0.18/0.47 (^[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)))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(113,plain,
% 0.18/0.47 (![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)))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[112])).
% 0.18/0.47 tff(114,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')).
% 0.18/0.47 tff(115,plain,
% 0.18/0.47 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.18/0.47 tff(116,plain,
% 0.18/0.47 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[115, 111])).
% 0.18/0.47 tff(117,plain,(
% 0.18/0.47 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.18/0.47 inference(skolemize,[status(sab)],[116])).
% 0.18/0.47 tff(118,plain,
% 0.18/0.47 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[117, 110])).
% 0.18/0.47 tff(119,plain,
% 0.18/0.47 ((~equalish(e_4, e_1)) <=> (~equalish(e_4, e_1))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(120,axiom,(~equalish(e_4, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_1')).
% 0.18/0.47 tff(121,plain,
% 0.18/0.47 (~equalish(e_4, e_1)),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.18/0.47 tff(122,plain,
% 0.18/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_1) | (~product(e_1, e_3, e_2)) | (~product(e_4, e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_1) | (~product(e_1, e_3, e_2)) | (~product(e_4, e_3, e_2)))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(123,plain,
% 0.18/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_1) | (~product(e_1, e_3, e_2)) | (~product(e_4, e_3, e_2)))),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(124,plain,
% 0.18/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_1) | (~product(e_1, e_3, e_2)) | (~product(e_4, e_3, e_2))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.18/0.47 tff(125,plain,
% 0.18/0.47 ($false),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[124, 121, 118, 108, 107])).
% 0.18/0.47 tff(126,plain,((~product(e_4, e_3, e_2)) | (~product(e_1, e_3, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.47 tff(127,plain,
% 0.18/0.47 (~product(e_4, e_3, e_2)),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[126, 106])).
% 0.18/0.47 tff(128,plain,
% 0.18/0.47 (group_element(e_4) <=> group_element(e_4)),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(129,axiom,(group_element(e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_4')).
% 0.18/0.47 tff(130,plain,
% 0.18/0.47 (group_element(e_4)),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.18/0.47 tff(131,plain,
% 0.18/0.47 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | (product(e_4, e_3, e_4) | (~group_element(e_4)) | product(e_4, e_3, e_2) | (~group_element(e_3)) | product(e_4, e_3, e_1) | product(e_4, e_3, e_3))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | product(e_4, e_3, e_4) | (~group_element(e_4)) | product(e_4, e_3, e_2) | (~group_element(e_3)) | product(e_4, e_3, e_1) | product(e_4, e_3, e_3))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(132,plain,
% 0.18/0.47 (((~group_element(e_3)) | (~group_element(e_4)) | product(e_4, e_3, e_4) | product(e_4, e_3, e_3) | product(e_4, e_3, e_2) | product(e_4, e_3, e_1)) <=> (product(e_4, e_3, e_4) | (~group_element(e_4)) | product(e_4, e_3, e_2) | (~group_element(e_3)) | product(e_4, e_3, e_1) | product(e_4, e_3, e_3))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(133,plain,
% 0.18/0.47 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | ((~group_element(e_3)) | (~group_element(e_4)) | product(e_4, e_3, e_4) | product(e_4, e_3, e_3) | product(e_4, e_3, e_2) | product(e_4, e_3, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | (product(e_4, e_3, e_4) | (~group_element(e_4)) | product(e_4, e_3, e_2) | (~group_element(e_3)) | product(e_4, e_3, e_1) | product(e_4, e_3, e_3)))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[132])).
% 0.18/0.47 tff(134,plain,
% 0.18/0.47 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | ((~group_element(e_3)) | (~group_element(e_4)) | product(e_4, e_3, e_4) | product(e_4, e_3, e_3) | product(e_4, e_3, e_2) | product(e_4, e_3, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | product(e_4, e_3, e_4) | (~group_element(e_4)) | product(e_4, e_3, e_2) | (~group_element(e_3)) | product(e_4, e_3, e_1) | product(e_4, e_3, e_3))),
% 0.18/0.47 inference(transitivity,[status(thm)],[133, 131])).
% 0.18/0.47 tff(135,plain,
% 0.18/0.47 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | ((~group_element(e_3)) | (~group_element(e_4)) | product(e_4, e_3, e_4) | product(e_4, e_3, e_3) | product(e_4, e_3, e_2) | product(e_4, e_3, e_1))),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(136,plain,
% 0.18/0.47 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | product(e_4, e_3, e_4) | (~group_element(e_4)) | product(e_4, e_3, e_2) | (~group_element(e_3)) | product(e_4, e_3, e_1) | product(e_4, e_3, e_3)),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.18/0.47 tff(137,plain,
% 0.18/0.47 (product(e_4, e_3, e_4) | product(e_4, e_3, e_2) | product(e_4, e_3, e_1) | product(e_4, e_3, e_3)),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[136, 57, 130, 54])).
% 0.18/0.47 tff(138,plain,
% 0.18/0.47 (product(e_4, e_3, e_3)),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[137, 127, 1, 30])).
% 0.18/0.47 tff(139,plain,
% 0.18/0.47 (product(e_2, e_3, e_1) | product(e_3, e_3, e_1) | product(e_4, e_3, e_1)),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[85, 42])).
% 0.18/0.47 tff(140,plain,
% 0.18/0.47 (product(e_3, e_3, e_1)),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[139, 31, 1])).
% 0.18/0.47 tff(141,assumption,(product(e_3, e_3, e_1)), introduced(assumption)).
% 0.18/0.47 tff(142,assumption,(product(e_3, e_3, e_4)), introduced(assumption)).
% 0.18/0.47 tff(143,plain,
% 0.18/0.47 (^[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))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(144,plain,
% 0.18/0.47 (![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)))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[143])).
% 0.18/0.47 tff(145,plain,
% 0.18/0.47 (![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)))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(146,plain,
% 0.18/0.47 (^[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)))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(147,plain,
% 0.18/0.47 (![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)))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[146])).
% 0.18/0.47 tff(148,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product(X, Y, W)) | (~product(X, Y, Z))) | equalish(W, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product_total_function2')).
% 0.18/0.47 tff(149,plain,
% 0.18/0.47 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.18/0.47 tff(150,plain,
% 0.18/0.47 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[149, 145])).
% 0.18/0.47 tff(151,plain,(
% 0.18/0.47 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))),
% 0.18/0.47 inference(skolemize,[status(sab)],[150])).
% 0.18/0.47 tff(152,plain,
% 0.18/0.47 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[151, 144])).
% 0.18/0.47 tff(153,plain,
% 0.18/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_4, e_1) | (~product(e_3, e_3, e_4)) | (~product(e_3, e_3, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | equalish(e_4, e_1) | (~product(e_3, e_3, e_4)) | (~product(e_3, e_3, e_1)))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(154,plain,
% 0.18/0.47 ((equalish(e_4, e_1) | (~product(e_3, e_3, e_1)) | (~product(e_3, e_3, e_4))) <=> (equalish(e_4, e_1) | (~product(e_3, e_3, e_4)) | (~product(e_3, e_3, e_1)))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(155,plain,
% 0.18/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_4, e_1) | (~product(e_3, e_3, e_1)) | (~product(e_3, e_3, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_4, e_1) | (~product(e_3, e_3, e_4)) | (~product(e_3, e_3, e_1))))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[154])).
% 0.18/0.47 tff(156,plain,
% 0.18/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_4, e_1) | (~product(e_3, e_3, e_1)) | (~product(e_3, e_3, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | equalish(e_4, e_1) | (~product(e_3, e_3, e_4)) | (~product(e_3, e_3, e_1)))),
% 0.18/0.47 inference(transitivity,[status(thm)],[155, 153])).
% 0.18/0.47 tff(157,plain,
% 0.18/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_4, e_1) | (~product(e_3, e_3, e_1)) | (~product(e_3, e_3, e_4)))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(158,plain,
% 0.18/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | equalish(e_4, e_1) | (~product(e_3, e_3, e_4)) | (~product(e_3, e_3, e_1))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.18/0.48 tff(159,plain,
% 0.18/0.48 ($false),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[158, 121, 152, 142, 141])).
% 0.18/0.48 tff(160,plain,((~product(e_3, e_3, e_4)) | (~product(e_3, e_3, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.48 tff(161,plain,
% 0.18/0.48 (~product(e_3, e_3, e_4)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[160, 140])).
% 0.18/0.48 tff(162,plain,
% 0.18/0.48 (((~![Y: $i, X: $i] : (product(e_4, 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_4, e_3, e_4) | product(e_2, e_3, e_4) | product(e_3, e_3, e_4) | product(e_1, e_3, e_4) | (~group_element(e_4)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(e_4, 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_4, e_3, e_4) | product(e_2, e_3, e_4) | product(e_3, e_3, e_4) | product(e_1, e_3, e_4) | (~group_element(e_4)) | (~group_element(e_3)))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(163,plain,
% 0.18/0.48 ((product(e_4, e_3, e_4) | product(e_3, e_3, e_4) | product(e_2, e_3, e_4) | product(e_1, e_3, e_4) | (~group_element(e_4)) | (~group_element(e_3))) <=> (product(e_4, e_3, e_4) | product(e_2, e_3, e_4) | product(e_3, e_3, e_4) | product(e_1, e_3, e_4) | (~group_element(e_4)) | (~group_element(e_3)))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(164,plain,
% 0.18/0.48 (((~![Y: $i, X: $i] : (product(e_4, 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_4, e_3, e_4) | product(e_3, e_3, e_4) | product(e_2, e_3, e_4) | product(e_1, e_3, e_4) | (~group_element(e_4)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(e_4, 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_4, e_3, e_4) | product(e_2, e_3, e_4) | product(e_3, e_3, e_4) | product(e_1, e_3, e_4) | (~group_element(e_4)) | (~group_element(e_3))))),
% 0.18/0.48 inference(monotonicity,[status(thm)],[163])).
% 0.18/0.48 tff(165,plain,
% 0.18/0.48 (((~![Y: $i, X: $i] : (product(e_4, 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_4, e_3, e_4) | product(e_3, e_3, e_4) | product(e_2, e_3, e_4) | product(e_1, e_3, e_4) | (~group_element(e_4)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(e_4, 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_4, e_3, e_4) | product(e_2, e_3, e_4) | product(e_3, e_3, e_4) | product(e_1, e_3, e_4) | (~group_element(e_4)) | (~group_element(e_3)))),
% 0.18/0.48 inference(transitivity,[status(thm)],[164, 162])).
% 0.18/0.48 tff(166,plain,
% 0.18/0.48 ((~![Y: $i, X: $i] : (product(e_4, 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_4, e_3, e_4) | product(e_3, e_3, e_4) | product(e_2, e_3, e_4) | product(e_1, e_3, e_4) | (~group_element(e_4)) | (~group_element(e_3)))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(167,plain,
% 0.18/0.48 ((~![Y: $i, X: $i] : (product(e_4, 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_4, e_3, e_4) | product(e_2, e_3, e_4) | product(e_3, e_3, e_4) | product(e_1, e_3, e_4) | (~group_element(e_4)) | (~group_element(e_3))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.18/0.48 tff(168,plain,
% 0.18/0.48 (product(e_4, e_3, e_4) | product(e_2, e_3, e_4) | product(e_3, e_3, e_4) | product(e_1, e_3, e_4)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[167, 78, 57, 130])).
% 0.18/0.48 tff(169,plain,
% 0.18/0.48 (product(e_2, e_3, e_4)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[168, 161, 30, 2])).
% 0.18/0.48 tff(170,assumption,(product(e_4, e_2, e_3)), introduced(assumption)).
% 0.18/0.48 tff(171,assumption,(product(e_2, e_3, e_4)), introduced(assumption)).
% 0.18/0.48 tff(172,plain,
% 0.18/0.48 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_3, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_2, e_3)) | (~product(e_2, e_3, e_4)))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_3, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_2, e_3)) | (~product(e_2, e_3, e_4)))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(173,plain,
% 0.18/0.48 (((~product(e_4, e_4, e_4)) | (~product(e_4, e_2, e_3)) | (~product(e_4, e_4, e_4)) | (~product(e_2, e_3, e_4)) | equalish(e_3, e_4)) <=> (equalish(e_3, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_2, e_3)) | (~product(e_2, e_3, e_4)))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(174,plain,
% 0.18/0.48 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_4, e_4, e_4)) | (~product(e_4, e_2, e_3)) | (~product(e_4, e_4, e_4)) | (~product(e_2, e_3, e_4)) | equalish(e_3, e_4))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_3, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_2, e_3)) | (~product(e_2, e_3, e_4))))),
% 0.18/0.48 inference(monotonicity,[status(thm)],[173])).
% 0.18/0.48 tff(175,plain,
% 0.18/0.48 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_4, e_4, e_4)) | (~product(e_4, e_2, e_3)) | (~product(e_4, e_4, e_4)) | (~product(e_2, e_3, e_4)) | equalish(e_3, e_4))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_3, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_2, e_3)) | (~product(e_2, e_3, e_4)))),
% 0.18/0.48 inference(transitivity,[status(thm)],[174, 172])).
% 0.18/0.48 tff(176,plain,
% 0.18/0.48 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_4, e_4, e_4)) | (~product(e_4, e_2, e_3)) | (~product(e_4, e_4, e_4)) | (~product(e_2, e_3, e_4)) | equalish(e_3, e_4))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(177,plain,
% 0.18/0.48 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_3, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_2, e_3)) | (~product(e_2, e_3, e_4))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.18/0.48 tff(178,plain,
% 0.18/0.48 ($false),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[177, 25, 96, 171, 170, 11])).
% 0.18/0.48 tff(179,plain,((~product(e_4, e_2, e_3)) | (~product(e_2, e_3, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.48 tff(180,plain,
% 0.18/0.48 (~product(e_4, e_2, e_3)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[179, 169])).
% 0.18/0.48 tff(181,assumption,(product(e_4, e_2, e_4)), introduced(assumption)).
% 0.18/0.48 tff(182,plain,
% 0.18/0.48 ((~equalish(e_2, e_4)) <=> (~equalish(e_2, e_4))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(183,axiom,(~equalish(e_2, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_4')).
% 0.18/0.48 tff(184,plain,
% 0.18/0.48 (~equalish(e_2, e_4)),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[183, 182])).
% 0.18/0.48 tff(185,plain,
% 0.18/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_4) | (~product(e_4, e_2, e_4)) | (~product(e_4, e_4, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_4) | (~product(e_4, e_2, e_4)) | (~product(e_4, e_4, e_4)))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(186,plain,
% 0.18/0.49 ((equalish(e_2, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_2, e_4))) <=> (equalish(e_2, e_4) | (~product(e_4, e_2, e_4)) | (~product(e_4, e_4, e_4)))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(187,plain,
% 0.18/0.49 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_2, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_4) | (~product(e_4, e_2, e_4)) | (~product(e_4, e_4, e_4))))),
% 0.18/0.49 inference(monotonicity,[status(thm)],[186])).
% 0.18/0.49 tff(188,plain,
% 0.18/0.49 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_2, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_4) | (~product(e_4, e_2, e_4)) | (~product(e_4, e_4, e_4)))),
% 0.18/0.49 inference(transitivity,[status(thm)],[187, 185])).
% 0.18/0.49 tff(189,plain,
% 0.18/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_2, e_4)))),
% 0.18/0.49 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(190,plain,
% 0.18/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_4) | (~product(e_4, e_2, e_4)) | (~product(e_4, e_4, e_4))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[189, 188])).
% 0.18/0.49 tff(191,plain,
% 0.18/0.49 ($false),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[190, 184, 22, 181, 11])).
% 0.18/0.49 tff(192,plain,(~product(e_4, e_2, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.49 tff(193,plain,
% 0.18/0.49 ((~![X: $i] : product(X, X, X)) | product(e_2, e_2, e_2)),
% 0.18/0.49 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(194,plain,
% 0.18/0.49 (product(e_2, e_2, e_2)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[193, 9])).
% 0.18/0.49 tff(195,assumption,(product(e_4, e_2, e_2)), introduced(assumption)).
% 0.18/0.49 tff(196,plain,
% 0.18/0.49 ((~equalish(e_4, e_2)) <=> (~equalish(e_4, e_2))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(197,axiom,(~equalish(e_4, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_2')).
% 0.18/0.49 tff(198,plain,
% 0.18/0.49 (~equalish(e_4, e_2)),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[197, 196])).
% 0.18/0.49 tff(199,plain,
% 0.18/0.49 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_2) | (~product(e_4, 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_4, e_2) | (~product(e_4, e_2, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(200,plain,
% 0.18/0.49 ((equalish(e_4, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_4, e_2, e_2))) <=> (equalish(e_4, e_2) | (~product(e_4, e_2, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(201,plain,
% 0.18/0.49 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_4, 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_4, e_2) | (~product(e_4, e_2, e_2)) | (~product(e_2, e_2, e_2))))),
% 0.18/0.49 inference(monotonicity,[status(thm)],[200])).
% 0.18/0.49 tff(202,plain,
% 0.18/0.49 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_4, 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_4, e_2) | (~product(e_4, e_2, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.18/0.49 inference(transitivity,[status(thm)],[201, 199])).
% 0.18/0.49 tff(203,plain,
% 0.18/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_4, e_2, e_2)))),
% 0.18/0.49 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(204,plain,
% 0.18/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_2) | (~product(e_4, e_2, e_2)) | (~product(e_2, e_2, e_2))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[203, 202])).
% 0.18/0.49 tff(205,plain,
% 0.18/0.49 ($false),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[204, 198, 118, 195, 194])).
% 0.18/0.49 tff(206,plain,(~product(e_4, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.49 tff(207,plain,
% 0.18/0.49 (group_element(e_2) <=> group_element(e_2)),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(208,axiom,(group_element(e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_2')).
% 0.18/0.49 tff(209,plain,
% 0.18/0.49 (group_element(e_2)),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[208, 207])).
% 0.18/0.49 tff(210,plain,
% 0.18/0.49 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | (product(e_4, e_2, e_1) | (~group_element(e_2)) | product(e_4, e_2, e_4) | (~group_element(e_4)) | product(e_4, e_2, e_3) | product(e_4, e_2, e_2))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | product(e_4, e_2, e_1) | (~group_element(e_2)) | product(e_4, e_2, e_4) | (~group_element(e_4)) | product(e_4, e_2, e_3) | product(e_4, e_2, e_2))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(211,plain,
% 0.18/0.49 (((~group_element(e_2)) | (~group_element(e_4)) | product(e_4, e_2, e_4) | product(e_4, e_2, e_3) | product(e_4, e_2, e_2) | product(e_4, e_2, e_1)) <=> (product(e_4, e_2, e_1) | (~group_element(e_2)) | product(e_4, e_2, e_4) | (~group_element(e_4)) | product(e_4, e_2, e_3) | product(e_4, e_2, e_2))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(212,plain,
% 0.18/0.49 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | ((~group_element(e_2)) | (~group_element(e_4)) | product(e_4, e_2, e_4) | product(e_4, e_2, e_3) | product(e_4, e_2, e_2) | product(e_4, e_2, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | (product(e_4, e_2, e_1) | (~group_element(e_2)) | product(e_4, e_2, e_4) | (~group_element(e_4)) | product(e_4, e_2, e_3) | product(e_4, e_2, e_2)))),
% 0.18/0.49 inference(monotonicity,[status(thm)],[211])).
% 0.18/0.49 tff(213,plain,
% 0.18/0.49 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | ((~group_element(e_2)) | (~group_element(e_4)) | product(e_4, e_2, e_4) | product(e_4, e_2, e_3) | product(e_4, e_2, e_2) | product(e_4, e_2, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | product(e_4, e_2, e_1) | (~group_element(e_2)) | product(e_4, e_2, e_4) | (~group_element(e_4)) | product(e_4, e_2, e_3) | product(e_4, e_2, e_2))),
% 0.18/0.49 inference(transitivity,[status(thm)],[212, 210])).
% 0.18/0.49 tff(214,plain,
% 0.18/0.49 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | ((~group_element(e_2)) | (~group_element(e_4)) | product(e_4, e_2, e_4) | product(e_4, e_2, e_3) | product(e_4, e_2, e_2) | product(e_4, e_2, e_1))),
% 0.18/0.49 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(215,plain,
% 0.18/0.49 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | product(e_4, e_2, e_1) | (~group_element(e_2)) | product(e_4, e_2, e_4) | (~group_element(e_4)) | product(e_4, e_2, e_3) | product(e_4, e_2, e_2)),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[214, 213])).
% 0.18/0.50 tff(216,plain,
% 0.18/0.50 (product(e_4, e_2, e_1) | product(e_4, e_2, e_4) | product(e_4, e_2, e_3) | product(e_4, e_2, e_2)),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[215, 209, 130, 54])).
% 0.18/0.50 tff(217,plain,
% 0.18/0.50 (product(e_4, e_2, e_1) | product(e_4, e_2, e_3)),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[216, 206, 192])).
% 0.18/0.50 tff(218,plain,
% 0.18/0.50 (product(e_4, e_2, e_1)),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[217, 180])).
% 0.18/0.50 tff(219,plain,
% 0.18/0.50 ((~equalish(e_1, e_3)) <=> (~equalish(e_1, e_3))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(220,axiom,(~equalish(e_1, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_3')).
% 0.18/0.50 tff(221,plain,
% 0.18/0.50 (~equalish(e_1, e_3)),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[220, 219])).
% 0.18/0.50 tff(222,plain,
% 0.18/0.50 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_1, e_3) | (~product(e_4, e_2, e_1)) | (~product(e_3, e_3, e_1)) | (~product(e_4, e_3, e_3)) | (~product(e_2, e_1, e_1)))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_1, e_3) | (~product(e_4, e_2, e_1)) | (~product(e_3, e_3, e_1)) | (~product(e_4, e_3, e_3)) | (~product(e_2, e_1, e_1)))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(223,plain,
% 0.18/0.50 (((~product(e_4, e_3, e_3)) | (~product(e_4, e_2, e_1)) | (~product(e_3, e_3, e_1)) | (~product(e_2, e_1, e_1)) | equalish(e_1, e_3)) <=> (equalish(e_1, e_3) | (~product(e_4, e_2, e_1)) | (~product(e_3, e_3, e_1)) | (~product(e_4, e_3, e_3)) | (~product(e_2, e_1, e_1)))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(224,plain,
% 0.18/0.50 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_4, e_3, e_3)) | (~product(e_4, e_2, e_1)) | (~product(e_3, e_3, e_1)) | (~product(e_2, e_1, e_1)) | equalish(e_1, e_3))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_1, e_3) | (~product(e_4, e_2, e_1)) | (~product(e_3, e_3, e_1)) | (~product(e_4, e_3, e_3)) | (~product(e_2, e_1, e_1))))),
% 0.18/0.50 inference(monotonicity,[status(thm)],[223])).
% 0.18/0.50 tff(225,plain,
% 0.18/0.50 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_4, e_3, e_3)) | (~product(e_4, e_2, e_1)) | (~product(e_3, e_3, e_1)) | (~product(e_2, e_1, e_1)) | equalish(e_1, e_3))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_1, e_3) | (~product(e_4, e_2, e_1)) | (~product(e_3, e_3, e_1)) | (~product(e_4, e_3, e_3)) | (~product(e_2, e_1, e_1)))),
% 0.18/0.50 inference(transitivity,[status(thm)],[224, 222])).
% 0.18/0.50 tff(226,plain,
% 0.18/0.50 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_4, e_3, e_3)) | (~product(e_4, e_2, e_1)) | (~product(e_3, e_3, e_1)) | (~product(e_2, e_1, e_1)) | equalish(e_1, e_3))),
% 0.18/0.50 inference(quant_inst,[status(thm)],[])).
% 0.18/0.50 tff(227,plain,
% 0.18/0.50 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_1, e_3) | (~product(e_4, e_2, e_1)) | (~product(e_3, e_3, e_1)) | (~product(e_4, e_3, e_3)) | (~product(e_2, e_1, e_1))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[226, 225])).
% 0.18/0.50 tff(228,plain,
% 0.18/0.50 (~product(e_2, e_1, e_1)),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[227, 221, 96, 218, 140, 138])).
% 0.18/0.50 tff(229,assumption,(product(e_2, e_1, e_4)), introduced(assumption)).
% 0.18/0.50 tff(230,assumption,(product(e_4, e_2, e_1)), introduced(assumption)).
% 0.18/0.50 tff(231,plain,
% 0.18/0.50 ((~equalish(e_1, e_4)) <=> (~equalish(e_1, e_4))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(232,axiom,(~equalish(e_1, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_4')).
% 0.18/0.50 tff(233,plain,
% 0.18/0.50 (~equalish(e_1, e_4)),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[232, 231])).
% 0.18/0.50 tff(234,plain,
% 0.18/0.50 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_1, e_4) | (~product(e_4, e_2, e_1)) | (~product(e_4, e_4, e_4)) | (~product(e_2, e_1, e_4)))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_1, e_4) | (~product(e_4, e_2, e_1)) | (~product(e_4, e_4, e_4)) | (~product(e_2, e_1, e_4)))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(235,plain,
% 0.18/0.50 (((~product(e_4, e_4, e_4)) | (~product(e_4, e_2, e_1)) | (~product(e_4, e_4, e_4)) | (~product(e_2, e_1, e_4)) | equalish(e_1, e_4)) <=> (equalish(e_1, e_4) | (~product(e_4, e_2, e_1)) | (~product(e_4, e_4, e_4)) | (~product(e_2, e_1, e_4)))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(236,plain,
% 0.18/0.50 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_4, e_4, e_4)) | (~product(e_4, e_2, e_1)) | (~product(e_4, e_4, e_4)) | (~product(e_2, e_1, e_4)) | equalish(e_1, e_4))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_1, e_4) | (~product(e_4, e_2, e_1)) | (~product(e_4, e_4, e_4)) | (~product(e_2, e_1, e_4))))),
% 0.18/0.50 inference(monotonicity,[status(thm)],[235])).
% 0.18/0.50 tff(237,plain,
% 0.18/0.50 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_4, e_4, e_4)) | (~product(e_4, e_2, e_1)) | (~product(e_4, e_4, e_4)) | (~product(e_2, e_1, e_4)) | equalish(e_1, e_4))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_1, e_4) | (~product(e_4, e_2, e_1)) | (~product(e_4, e_4, e_4)) | (~product(e_2, e_1, e_4)))),
% 0.18/0.50 inference(transitivity,[status(thm)],[236, 234])).
% 0.18/0.50 tff(238,plain,
% 0.18/0.50 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_4, e_4, e_4)) | (~product(e_4, e_2, e_1)) | (~product(e_4, e_4, e_4)) | (~product(e_2, e_1, e_4)) | equalish(e_1, e_4))),
% 0.18/0.50 inference(quant_inst,[status(thm)],[])).
% 0.18/0.50 tff(239,plain,
% 0.18/0.50 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_1, e_4) | (~product(e_4, e_2, e_1)) | (~product(e_4, e_4, e_4)) | (~product(e_2, e_1, e_4))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[238, 237])).
% 0.18/0.50 tff(240,plain,
% 0.18/0.50 ($false),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[239, 233, 96, 230, 11, 229])).
% 0.18/0.50 tff(241,plain,((~product(e_4, e_2, e_1)) | (~product(e_2, e_1, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.50 tff(242,plain,
% 0.18/0.50 (~product(e_2, e_1, e_4)),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[241, 218])).
% 0.18/0.50 tff(243,assumption,(product(e_1, e_1, e_4)), introduced(assumption)).
% 0.18/0.50 tff(244,plain,
% 0.18/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_1, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_1, e_4)))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(245,plain,
% 0.18/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_1, e_4)))),
% 0.18/0.51 inference(quant_inst,[status(thm)],[])).
% 0.18/0.51 tff(246,plain,
% 0.18/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_1, e_4))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[245, 244])).
% 0.18/0.51 tff(247,plain,
% 0.18/0.51 ($false),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[246, 121, 152, 34, 243])).
% 0.18/0.51 tff(248,plain,(~product(e_1, e_1, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.51 tff(249,assumption,(product(e_4, e_1, e_4)), introduced(assumption)).
% 0.18/0.51 tff(250,plain,
% 0.18/0.51 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_1, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_1, e_4)))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(251,plain,
% 0.18/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_1, e_4)))),
% 0.18/0.51 inference(quant_inst,[status(thm)],[])).
% 0.18/0.51 tff(252,plain,
% 0.18/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_1, e_4))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[251, 250])).
% 0.18/0.51 tff(253,plain,
% 0.18/0.51 ($false),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[252, 233, 22, 11, 249])).
% 0.18/0.51 tff(254,plain,(~product(e_4, e_1, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.51 tff(255,plain,
% 0.18/0.51 (((~![Y: $i, X: $i] : (product(e_4, 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, e_1, e_4) | (~group_element(e_4)) | (~group_element(e_1)) | product(e_4, e_1, e_4) | product(e_1, e_1, e_4) | product(e_2, e_1, e_4))) <=> ((~![Y: $i, X: $i] : (product(e_4, 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, e_1, e_4) | (~group_element(e_4)) | (~group_element(e_1)) | product(e_4, e_1, e_4) | product(e_1, e_1, e_4) | product(e_2, e_1, e_4))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(256,plain,
% 0.18/0.51 ((product(e_4, e_1, e_4) | product(e_3, e_1, e_4) | product(e_2, e_1, e_4) | product(e_1, e_1, e_4) | (~group_element(e_4)) | (~group_element(e_1))) <=> (product(e_3, e_1, e_4) | (~group_element(e_4)) | (~group_element(e_1)) | product(e_4, e_1, e_4) | product(e_1, e_1, e_4) | product(e_2, e_1, e_4))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(257,plain,
% 0.18/0.51 (((~![Y: $i, X: $i] : (product(e_4, 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_4, e_1, e_4) | product(e_3, e_1, e_4) | product(e_2, e_1, e_4) | product(e_1, e_1, e_4) | (~group_element(e_4)) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (product(e_4, 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, e_1, e_4) | (~group_element(e_4)) | (~group_element(e_1)) | product(e_4, e_1, e_4) | product(e_1, e_1, e_4) | product(e_2, e_1, e_4)))),
% 0.18/0.51 inference(monotonicity,[status(thm)],[256])).
% 0.18/0.51 tff(258,plain,
% 0.18/0.51 (((~![Y: $i, X: $i] : (product(e_4, 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_4, e_1, e_4) | product(e_3, e_1, e_4) | product(e_2, e_1, e_4) | product(e_1, e_1, e_4) | (~group_element(e_4)) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (product(e_4, 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, e_1, e_4) | (~group_element(e_4)) | (~group_element(e_1)) | product(e_4, e_1, e_4) | product(e_1, e_1, e_4) | product(e_2, e_1, e_4))),
% 0.18/0.51 inference(transitivity,[status(thm)],[257, 255])).
% 0.18/0.51 tff(259,plain,
% 0.18/0.51 ((~![Y: $i, X: $i] : (product(e_4, 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_4, e_1, e_4) | product(e_3, e_1, e_4) | product(e_2, e_1, e_4) | product(e_1, e_1, e_4) | (~group_element(e_4)) | (~group_element(e_1)))),
% 0.18/0.51 inference(quant_inst,[status(thm)],[])).
% 0.18/0.51 tff(260,plain,
% 0.18/0.51 ((~![Y: $i, X: $i] : (product(e_4, 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, e_1, e_4) | (~group_element(e_4)) | (~group_element(e_1)) | product(e_4, e_1, e_4) | product(e_1, e_1, e_4) | product(e_2, e_1, e_4)),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[259, 258])).
% 0.18/0.51 tff(261,plain,
% 0.18/0.51 (product(e_3, e_1, e_4) | product(e_1, e_1, e_4) | product(e_2, e_1, e_4)),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[260, 78, 60, 130, 254])).
% 0.18/0.51 tff(262,plain,
% 0.18/0.51 (product(e_3, e_1, e_4) | product(e_2, e_1, e_4)),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[261, 248])).
% 0.18/0.51 tff(263,plain,
% 0.18/0.51 (product(e_3, e_1, e_4)),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[262, 242])).
% 0.18/0.51 tff(264,plain,
% 0.18/0.51 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_4, e_1) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_4, e_4)) | (~product(e_3, e_3, e_1)))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_4, e_1) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_4, e_4)) | (~product(e_3, e_3, e_1)))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(265,plain,
% 0.18/0.51 (((~product(e_3, e_3, e_1)) | (~product(e_3, e_1, e_4)) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_4, e_4)) | equalish(e_4, e_1)) <=> (equalish(e_4, e_1) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_4, e_4)) | (~product(e_3, e_3, e_1)))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(266,plain,
% 0.18/0.51 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_3, e_3, e_1)) | (~product(e_3, e_1, e_4)) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_4, e_4)) | equalish(e_4, e_1))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_4, e_1) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_4, e_4)) | (~product(e_3, e_3, e_1))))),
% 0.18/0.51 inference(monotonicity,[status(thm)],[265])).
% 0.18/0.51 tff(267,plain,
% 0.18/0.51 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_3, e_3, e_1)) | (~product(e_3, e_1, e_4)) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_4, e_4)) | equalish(e_4, e_1))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_4, e_1) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_4, e_4)) | (~product(e_3, e_3, e_1)))),
% 0.18/0.51 inference(transitivity,[status(thm)],[266, 264])).
% 0.18/0.51 tff(268,plain,
% 0.18/0.51 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_3, e_3, e_1)) | (~product(e_3, e_1, e_4)) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_4, e_4)) | equalish(e_4, e_1))),
% 0.18/0.51 inference(quant_inst,[status(thm)],[])).
% 0.18/0.51 tff(269,plain,
% 0.18/0.51 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_4, e_1) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_4, e_4)) | (~product(e_3, e_3, e_1))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[268, 267])).
% 0.18/0.51 tff(270,plain,
% 0.18/0.51 (~product(e_1, e_4, e_4)),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[269, 121, 96, 263, 140])).
% 0.18/0.51 tff(271,plain,
% 0.18/0.51 (^[Y: $i, X: $i] : refl(((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y)))),
% 0.18/0.51 inference(bind,[status(th)],[])).
% 0.18/0.51 tff(272,plain,
% 0.18/0.51 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | 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_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))),
% 0.18/0.51 inference(quant_intro,[status(thm)],[271])).
% 0.18/0.51 tff(273,plain,
% 0.18/0.51 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | 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_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(274,plain,
% 0.18/0.51 (^[Y: $i, X: $i] : trans(monotonicity(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)))), (((((((~group_element(X)) | (~group_element(Y))) | product(X, e_1, Y)) | product(X, e_2, Y)) | product(X, e_3, Y)) | product(X, e_4, Y)) <=> (((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y)) | product(X, e_4, Y)))), rewrite((((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y)) | product(X, e_4, Y)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | 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)) | product(X, e_4, Y)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))))),
% 0.18/0.51 inference(bind,[status(th)],[])).
% 0.18/0.51 tff(275,plain,
% 0.18/0.51 (![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)) | product(X, e_4, Y)) <=> ![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))),
% 0.18/0.52 inference(quant_intro,[status(thm)],[274])).
% 0.18/0.52 tff(276,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)) | product(X, e_4, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','column_surjectivity')).
% 0.18/0.52 tff(277,plain,
% 0.18/0.52 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[276, 275])).
% 0.18/0.52 tff(278,plain,
% 0.18/0.52 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[277, 273])).
% 0.18/0.52 tff(279,plain,(
% 0.18/0.52 ![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))),
% 0.18/0.52 inference(skolemize,[status(sab)],[278])).
% 0.18/0.52 tff(280,plain,
% 0.18/0.52 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[279, 272])).
% 0.18/0.52 tff(281,plain,
% 0.18/0.52 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | (product(e_1, e_3, e_4) | (~group_element(e_4)) | (~group_element(e_1)) | product(e_1, e_2, e_4) | product(e_1, e_1, e_4) | product(e_1, e_4, e_4))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | product(e_1, e_3, e_4) | (~group_element(e_4)) | (~group_element(e_1)) | product(e_1, e_2, e_4) | product(e_1, e_1, e_4) | product(e_1, e_4, e_4))),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(282,plain,
% 0.18/0.52 (((~group_element(e_4)) | (~group_element(e_1)) | product(e_1, e_4, e_4) | product(e_1, e_3, e_4) | product(e_1, e_2, e_4) | product(e_1, e_1, e_4)) <=> (product(e_1, e_3, e_4) | (~group_element(e_4)) | (~group_element(e_1)) | product(e_1, e_2, e_4) | product(e_1, e_1, e_4) | product(e_1, e_4, e_4))),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(283,plain,
% 0.18/0.52 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_4)) | (~group_element(e_1)) | product(e_1, e_4, e_4) | product(e_1, e_3, e_4) | product(e_1, e_2, e_4) | product(e_1, e_1, e_4))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | (product(e_1, e_3, e_4) | (~group_element(e_4)) | (~group_element(e_1)) | product(e_1, e_2, e_4) | product(e_1, e_1, e_4) | product(e_1, e_4, e_4)))),
% 0.18/0.52 inference(monotonicity,[status(thm)],[282])).
% 0.18/0.52 tff(284,plain,
% 0.18/0.52 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_4)) | (~group_element(e_1)) | product(e_1, e_4, e_4) | product(e_1, e_3, e_4) | product(e_1, e_2, e_4) | product(e_1, e_1, e_4))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | product(e_1, e_3, e_4) | (~group_element(e_4)) | (~group_element(e_1)) | product(e_1, e_2, e_4) | product(e_1, e_1, e_4) | product(e_1, e_4, e_4))),
% 0.18/0.52 inference(transitivity,[status(thm)],[283, 281])).
% 0.18/0.52 tff(285,plain,
% 0.18/0.52 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_4)) | (~group_element(e_1)) | product(e_1, e_4, e_4) | product(e_1, e_3, e_4) | product(e_1, e_2, e_4) | product(e_1, e_1, e_4))),
% 0.18/0.52 inference(quant_inst,[status(thm)],[])).
% 0.18/0.52 tff(286,plain,
% 0.18/0.52 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | product(e_1, e_3, e_4) | (~group_element(e_4)) | (~group_element(e_1)) | product(e_1, e_2, e_4) | product(e_1, e_1, e_4) | product(e_1, e_4, e_4)),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[285, 284])).
% 0.18/0.52 tff(287,plain,
% 0.18/0.52 (product(e_1, e_3, e_4) | product(e_1, e_2, e_4) | product(e_1, e_4, e_4)),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[286, 280, 60, 130, 248])).
% 0.18/0.52 tff(288,plain,
% 0.18/0.52 (product(e_1, e_2, e_4)),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[287, 270, 2])).
% 0.18/0.52 tff(289,plain,
% 0.18/0.52 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_4, e_1)) | (~product(e_1, e_2, e_4)))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_4, e_1)) | (~product(e_1, e_2, e_4)))),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(290,plain,
% 0.18/0.52 (((~product(e_1, e_1, e_1)) | (~product(e_1, e_2, e_4)) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_4, e_1)) | equalish(e_4, e_1)) <=> (equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_4, e_1)) | (~product(e_1, e_2, e_4)))),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(291,plain,
% 0.18/0.52 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_1, e_1, e_1)) | (~product(e_1, e_2, e_4)) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_4, e_1)) | equalish(e_4, e_1))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_4, e_1)) | (~product(e_1, e_2, e_4))))),
% 0.18/0.52 inference(monotonicity,[status(thm)],[290])).
% 0.18/0.52 tff(292,plain,
% 0.18/0.52 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_1, e_1, e_1)) | (~product(e_1, e_2, e_4)) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_4, e_1)) | equalish(e_4, e_1))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_4, e_1)) | (~product(e_1, e_2, e_4)))),
% 0.18/0.52 inference(transitivity,[status(thm)],[291, 289])).
% 0.18/0.52 tff(293,plain,
% 0.18/0.52 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_1, e_1, e_1)) | (~product(e_1, e_2, e_4)) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_4, e_1)) | equalish(e_4, e_1))),
% 0.18/0.52 inference(quant_inst,[status(thm)],[])).
% 0.18/0.52 tff(294,plain,
% 0.18/0.52 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_4, e_1)) | (~product(e_1, e_2, e_4))),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[293, 292])).
% 0.18/0.52 tff(295,plain,
% 0.18/0.52 (~product(e_2, e_4, e_1)),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[294, 121, 96, 34, 288])).
% 0.18/0.52 tff(296,plain,
% 0.18/0.52 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | 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) | product(e_2, e_4, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | 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) | product(e_2, e_4, e_1))),
% 0.18/0.53 inference(rewrite,[status(thm)],[])).
% 0.18/0.53 tff(297,plain,
% 0.18/0.53 (((~group_element(e_1)) | (~group_element(e_2)) | product(e_2, e_4, e_1) | 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) | product(e_2, e_4, e_1))),
% 0.18/0.53 inference(rewrite,[status(thm)],[])).
% 0.18/0.53 tff(298,plain,
% 0.18/0.53 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | 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_4, e_1) | 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_4, Y) | 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) | product(e_2, e_4, e_1)))),
% 0.18/0.53 inference(monotonicity,[status(thm)],[297])).
% 0.18/0.53 tff(299,plain,
% 0.18/0.53 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | 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_4, e_1) | 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_4, Y) | 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) | product(e_2, e_4, e_1))),
% 0.18/0.53 inference(transitivity,[status(thm)],[298, 296])).
% 0.18/0.53 tff(300,plain,
% 0.18/0.53 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | 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_4, e_1) | product(e_2, e_3, e_1) | product(e_2, e_2, e_1) | product(e_2, e_1, e_1))),
% 0.18/0.53 inference(quant_inst,[status(thm)],[])).
% 0.18/0.53 tff(301,plain,
% 0.18/0.53 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | 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) | product(e_2, e_4, e_1)),
% 0.18/0.53 inference(modus_ponens,[status(thm)],[300, 299])).
% 0.18/0.53 tff(302,plain,
% 0.18/0.53 (product(e_2, e_1, e_1) | product(e_2, e_2, e_1)),
% 0.18/0.53 inference(unit_resolution,[status(thm)],[301, 280, 60, 209, 31, 295])).
% 0.18/0.53 tff(303,plain,
% 0.18/0.53 (product(e_2, e_2, e_1)),
% 0.18/0.53 inference(unit_resolution,[status(thm)],[302, 228])).
% 0.18/0.53 tff(304,plain,
% 0.18/0.53 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_4) | (~product(e_4, e_2, e_1)) | (~product(e_2, e_2, 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_4) | (~product(e_4, e_2, e_1)) | (~product(e_2, e_2, e_1)))),
% 0.18/0.53 inference(rewrite,[status(thm)],[])).
% 0.18/0.53 tff(305,plain,
% 0.18/0.53 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_4) | (~product(e_4, e_2, e_1)) | (~product(e_2, e_2, e_1)))),
% 0.18/0.53 inference(quant_inst,[status(thm)],[])).
% 0.18/0.53 tff(306,plain,
% 0.18/0.53 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_4) | (~product(e_4, e_2, e_1)) | (~product(e_2, e_2, e_1))),
% 0.18/0.53 inference(modus_ponens,[status(thm)],[305, 304])).
% 0.18/0.53 tff(307,plain,
% 0.18/0.53 ($false),
% 0.18/0.53 inference(unit_resolution,[status(thm)],[306, 184, 118, 218, 303])).
% 0.18/0.53 tff(308,plain,(product(e_2, e_3, e_1) | product(e_4, e_3, e_1) | product(e_1, e_3, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.53 tff(309,plain,
% 0.18/0.53 (product(e_2, e_3, e_1)),
% 0.18/0.53 inference(unit_resolution,[status(thm)],[308, 2, 1])).
% 0.18/0.53 tff(310,assumption,(product(e_2, e_3, e_1)), introduced(assumption)).
% 0.18/0.53 tff(311,plain,
% 0.18/0.53 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_4, e_1) | (~product(e_2, e_3, e_1)) | (~product(e_2, e_3, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | equalish(e_4, e_1) | (~product(e_2, e_3, e_1)) | (~product(e_2, e_3, e_4)))),
% 0.18/0.53 inference(rewrite,[status(thm)],[])).
% 0.18/0.53 tff(312,plain,
% 0.18/0.53 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_4, e_1) | (~product(e_2, e_3, e_1)) | (~product(e_2, e_3, e_4)))),
% 0.18/0.53 inference(quant_inst,[status(thm)],[])).
% 0.18/0.53 tff(313,plain,
% 0.18/0.53 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | equalish(e_4, e_1) | (~product(e_2, e_3, e_1)) | (~product(e_2, e_3, e_4))),
% 0.18/0.53 inference(modus_ponens,[status(thm)],[312, 311])).
% 0.18/0.53 tff(314,plain,
% 0.18/0.53 ($false),
% 0.18/0.53 inference(unit_resolution,[status(thm)],[313, 121, 152, 171, 310])).
% 0.18/0.53 tff(315,plain,((~product(e_2, e_3, e_4)) | (~product(e_2, e_3, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.53 tff(316,plain,
% 0.18/0.53 (~product(e_2, e_3, e_4)),
% 0.18/0.53 inference(unit_resolution,[status(thm)],[315, 309])).
% 0.18/0.53 tff(317,plain,
% 0.18/0.53 (product(e_3, e_3, e_4)),
% 0.18/0.53 inference(unit_resolution,[status(thm)],[168, 316, 30, 2])).
% 0.18/0.53 tff(318,assumption,(product(e_3, e_1, e_4)), introduced(assumption)).
% 0.18/0.53 tff(319,plain,
% 0.18/0.53 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_3) | (~product(e_3, e_3, e_4)) | (~product(e_3, e_1, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_3) | (~product(e_3, e_3, e_4)) | (~product(e_3, e_1, e_4)))),
% 0.18/0.53 inference(rewrite,[status(thm)],[])).
% 0.18/0.53 tff(320,plain,
% 0.18/0.53 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_3) | (~product(e_3, e_3, e_4)) | (~product(e_3, e_1, e_4)))),
% 0.18/0.53 inference(quant_inst,[status(thm)],[])).
% 0.18/0.53 tff(321,plain,
% 0.18/0.53 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_3) | (~product(e_3, e_3, e_4)) | (~product(e_3, e_1, e_4))),
% 0.18/0.53 inference(modus_ponens,[status(thm)],[320, 319])).
% 0.18/0.53 tff(322,plain,
% 0.18/0.53 ($false),
% 0.18/0.53 inference(unit_resolution,[status(thm)],[321, 221, 22, 142, 318])).
% 0.18/0.53 tff(323,plain,((~product(e_3, e_1, e_4)) | (~product(e_3, e_3, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.53 tff(324,plain,
% 0.18/0.53 (~product(e_3, e_1, e_4)),
% 0.18/0.53 inference(unit_resolution,[status(thm)],[323, 317])).
% 0.18/0.53 tff(325,plain,
% 0.18/0.53 (product(e_2, e_1, e_4)),
% 0.18/0.53 inference(unit_resolution,[status(thm)],[262, 324])).
% 0.18/0.53 tff(326,plain,
% 0.18/0.53 (~product(e_4, e_2, e_1)),
% 0.18/0.53 inference(unit_resolution,[status(thm)],[241, 325])).
% 0.18/0.53 tff(327,plain,
% 0.18/0.53 (product(e_4, e_2, e_3)),
% 0.18/0.53 inference(unit_resolution,[status(thm)],[217, 326])).
% 0.18/0.53 tff(328,plain,
% 0.18/0.53 ((~equalish(e_4, e_3)) <=> (~equalish(e_4, e_3))),
% 0.18/0.53 inference(rewrite,[status(thm)],[])).
% 0.18/0.53 tff(329,axiom,(~equalish(e_4, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_3')).
% 0.18/0.53 tff(330,plain,
% 0.18/0.53 (~equalish(e_4, e_3)),
% 0.18/0.53 inference(modus_ponens,[status(thm)],[329, 328])).
% 0.18/0.53 tff(331,plain,
% 0.18/0.53 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_4, e_3) | (~product(e_4, e_4, e_1)) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_2, e_3)) | (~product(e_2, e_3, e_1)))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_4, e_3) | (~product(e_4, e_4, e_1)) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_2, e_3)) | (~product(e_2, e_3, e_1)))),
% 0.18/0.54 inference(rewrite,[status(thm)],[])).
% 0.18/0.54 tff(332,plain,
% 0.18/0.54 (((~product(e_4, e_2, e_3)) | (~product(e_4, e_4, e_4)) | (~product(e_2, e_3, e_1)) | (~product(e_4, e_4, e_1)) | equalish(e_4, e_3)) <=> (equalish(e_4, e_3) | (~product(e_4, e_4, e_1)) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_2, e_3)) | (~product(e_2, e_3, e_1)))),
% 0.18/0.54 inference(rewrite,[status(thm)],[])).
% 0.18/0.54 tff(333,plain,
% 0.18/0.54 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_4, e_2, e_3)) | (~product(e_4, e_4, e_4)) | (~product(e_2, e_3, e_1)) | (~product(e_4, e_4, e_1)) | equalish(e_4, e_3))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_4, e_3) | (~product(e_4, e_4, e_1)) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_2, e_3)) | (~product(e_2, e_3, e_1))))),
% 0.18/0.54 inference(monotonicity,[status(thm)],[332])).
% 0.18/0.54 tff(334,plain,
% 0.18/0.54 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_4, e_2, e_3)) | (~product(e_4, e_4, e_4)) | (~product(e_2, e_3, e_1)) | (~product(e_4, e_4, e_1)) | equalish(e_4, e_3))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_4, e_3) | (~product(e_4, e_4, e_1)) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_2, e_3)) | (~product(e_2, e_3, e_1)))),
% 0.18/0.54 inference(transitivity,[status(thm)],[333, 331])).
% 0.18/0.54 tff(335,plain,
% 0.18/0.54 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_4, e_2, e_3)) | (~product(e_4, e_4, e_4)) | (~product(e_2, e_3, e_1)) | (~product(e_4, e_4, e_1)) | equalish(e_4, e_3))),
% 0.18/0.54 inference(quant_inst,[status(thm)],[])).
% 0.18/0.54 tff(336,plain,
% 0.18/0.54 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_4, e_3) | (~product(e_4, e_4, e_1)) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_2, e_3)) | (~product(e_2, e_3, e_1))),
% 0.18/0.54 inference(modus_ponens,[status(thm)],[335, 334])).
% 0.18/0.54 tff(337,plain,
% 0.18/0.54 (~product(e_4, e_4, e_1)),
% 0.18/0.54 inference(unit_resolution,[status(thm)],[336, 330, 96, 170, 310, 11])).
% 0.18/0.54 tff(338,assumption,(~product(e_4, e_2, e_1)), introduced(assumption)).
% 0.18/0.54 tff(339,plain,
% 0.18/0.54 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | (product(e_4, e_2, e_1) | (~group_element(e_4)) | product(e_4, e_3, e_1) | (~group_element(e_1)) | product(e_4, e_1, e_1) | product(e_4, e_4, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | product(e_4, e_2, e_1) | (~group_element(e_4)) | product(e_4, e_3, e_1) | (~group_element(e_1)) | product(e_4, e_1, e_1) | product(e_4, e_4, e_1))),
% 0.18/0.54 inference(rewrite,[status(thm)],[])).
% 0.18/0.54 tff(340,plain,
% 0.18/0.54 (((~group_element(e_1)) | (~group_element(e_4)) | product(e_4, e_4, e_1) | product(e_4, e_3, e_1) | product(e_4, e_2, e_1) | product(e_4, e_1, e_1)) <=> (product(e_4, e_2, e_1) | (~group_element(e_4)) | product(e_4, e_3, e_1) | (~group_element(e_1)) | product(e_4, e_1, e_1) | product(e_4, e_4, e_1))),
% 0.18/0.54 inference(rewrite,[status(thm)],[])).
% 0.18/0.54 tff(341,plain,
% 0.18/0.54 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_1)) | (~group_element(e_4)) | product(e_4, e_4, e_1) | product(e_4, e_3, e_1) | product(e_4, e_2, e_1) | product(e_4, e_1, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | (product(e_4, e_2, e_1) | (~group_element(e_4)) | product(e_4, e_3, e_1) | (~group_element(e_1)) | product(e_4, e_1, e_1) | product(e_4, e_4, e_1)))),
% 0.18/0.54 inference(monotonicity,[status(thm)],[340])).
% 0.18/0.54 tff(342,plain,
% 0.18/0.54 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_1)) | (~group_element(e_4)) | product(e_4, e_4, e_1) | product(e_4, e_3, e_1) | product(e_4, e_2, e_1) | product(e_4, e_1, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | product(e_4, e_2, e_1) | (~group_element(e_4)) | product(e_4, e_3, e_1) | (~group_element(e_1)) | product(e_4, e_1, e_1) | product(e_4, e_4, e_1))),
% 0.18/0.54 inference(transitivity,[status(thm)],[341, 339])).
% 0.18/0.54 tff(343,plain,
% 0.18/0.54 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_1)) | (~group_element(e_4)) | product(e_4, e_4, e_1) | product(e_4, e_3, e_1) | product(e_4, e_2, e_1) | product(e_4, e_1, e_1))),
% 0.18/0.54 inference(quant_inst,[status(thm)],[])).
% 0.18/0.54 tff(344,plain,
% 0.18/0.54 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | product(e_4, e_2, e_1) | (~group_element(e_4)) | product(e_4, e_3, e_1) | (~group_element(e_1)) | product(e_4, e_1, e_1) | product(e_4, e_4, e_1)),
% 0.18/0.54 inference(modus_ponens,[status(thm)],[343, 342])).
% 0.18/0.54 tff(345,plain,
% 0.18/0.54 (product(e_4, e_1, e_1)),
% 0.18/0.54 inference(unit_resolution,[status(thm)],[344, 280, 60, 130, 338, 1, 337])).
% 0.18/0.54 tff(346,plain,
% 0.18/0.54 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~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_4, e_2, e_3)) | (~product(e_4, e_1, e_1)) | (~product(e_2, e_3, e_1)))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~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_4, e_2, e_3)) | (~product(e_4, e_1, e_1)) | (~product(e_2, e_3, e_1)))),
% 0.18/0.54 inference(rewrite,[status(thm)],[])).
% 0.18/0.54 tff(347,plain,
% 0.18/0.54 (((~product(e_4, e_2, e_3)) | (~product(e_4, e_1, e_1)) | (~product(e_2, 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_4, e_2, e_3)) | (~product(e_4, e_1, e_1)) | (~product(e_2, e_3, e_1)))),
% 0.18/0.54 inference(rewrite,[status(thm)],[])).
% 0.18/0.54 tff(348,plain,
% 0.18/0.54 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_4, e_2, e_3)) | (~product(e_4, e_1, e_1)) | (~product(e_2, 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, X2, Y2)) | (~product(Z2, X1, Y1)) | (~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_4, e_2, e_3)) | (~product(e_4, e_1, e_1)) | (~product(e_2, e_3, e_1))))),
% 0.18/0.54 inference(monotonicity,[status(thm)],[347])).
% 0.18/0.54 tff(349,plain,
% 0.18/0.54 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_4, e_2, e_3)) | (~product(e_4, e_1, e_1)) | (~product(e_2, 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, X2, Y2)) | (~product(Z2, X1, Y1)) | (~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_4, e_2, e_3)) | (~product(e_4, e_1, e_1)) | (~product(e_2, e_3, e_1)))),
% 0.18/0.54 inference(transitivity,[status(thm)],[348, 346])).
% 0.18/0.54 tff(350,plain,
% 0.18/0.54 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_4, e_2, e_3)) | (~product(e_4, e_1, e_1)) | (~product(e_2, e_3, e_1)) | (~product(e_1, e_1, e_1)) | equalish(e_1, e_3))),
% 0.18/0.54 inference(quant_inst,[status(thm)],[])).
% 0.18/0.54 tff(351,plain,
% 0.18/0.54 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_1, e_3) | (~product(e_1, e_1, e_1)) | (~product(e_4, e_2, e_3)) | (~product(e_4, e_1, e_1)) | (~product(e_2, e_3, e_1))),
% 0.18/0.55 inference(modus_ponens,[status(thm)],[350, 349])).
% 0.18/0.55 tff(352,plain,
% 0.18/0.55 ($false),
% 0.18/0.55 inference(unit_resolution,[status(thm)],[351, 221, 96, 170, 34, 310, 345])).
% 0.18/0.55 tff(353,plain,((~product(e_4, e_2, e_3)) | (~product(e_2, e_3, e_1)) | product(e_4, e_2, e_1) | product(e_4, e_3, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.55 tff(354,plain,
% 0.18/0.55 ($false),
% 0.18/0.55 inference(unit_resolution,[status(thm)],[353, 327, 326, 309, 1])).
% 0.18/0.55 tff(355,plain,(product(e_1, e_3, e_4) | product(e_4, e_3, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.55 tff(356,plain,
% 0.18/0.55 (product(e_1, e_3, e_4)),
% 0.18/0.55 inference(unit_resolution,[status(thm)],[355, 1])).
% 0.18/0.55 tff(357,plain,
% 0.18/0.55 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_4, e_1)) | (~product(e_1, e_3, e_4)))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_4, e_1)) | (~product(e_1, e_3, e_4)))),
% 0.18/0.55 inference(rewrite,[status(thm)],[])).
% 0.18/0.55 tff(358,plain,
% 0.18/0.55 (((~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_4)) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_4, e_1)) | equalish(e_4, e_1)) <=> (equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_4, e_1)) | (~product(e_1, e_3, e_4)))),
% 0.18/0.55 inference(rewrite,[status(thm)],[])).
% 0.18/0.55 tff(359,plain,
% 0.18/0.55 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_4)) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_4, e_1)) | equalish(e_4, e_1))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_4, e_1)) | (~product(e_1, e_3, e_4))))),
% 0.18/0.55 inference(monotonicity,[status(thm)],[358])).
% 0.18/0.55 tff(360,plain,
% 0.18/0.55 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_4)) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_4, e_1)) | equalish(e_4, e_1))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_4, e_1)) | (~product(e_1, e_3, e_4)))),
% 0.18/0.55 inference(transitivity,[status(thm)],[359, 357])).
% 0.18/0.55 tff(361,plain,
% 0.18/0.55 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_4)) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_4, e_1)) | equalish(e_4, e_1))),
% 0.18/0.55 inference(quant_inst,[status(thm)],[])).
% 0.18/0.55 tff(362,plain,
% 0.18/0.55 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_4, e_1)) | (~product(e_1, e_3, e_4))),
% 0.18/0.55 inference(modus_ponens,[status(thm)],[361, 360])).
% 0.18/0.55 tff(363,plain,
% 0.18/0.55 (~product(e_3, e_4, e_1)),
% 0.18/0.55 inference(unit_resolution,[status(thm)],[362, 121, 96, 356, 34])).
% 0.18/0.55 tff(364,assumption,(product(e_4, e_3, e_3)), introduced(assumption)).
% 0.18/0.55 tff(365,plain,
% 0.18/0.55 ((~equalish(e_3, e_2)) <=> (~equalish(e_3, e_2))),
% 0.18/0.55 inference(rewrite,[status(thm)],[])).
% 0.18/0.55 tff(366,axiom,(~equalish(e_3, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_2')).
% 0.18/0.55 tff(367,plain,
% 0.18/0.55 (~equalish(e_3, e_2)),
% 0.18/0.55 inference(modus_ponens,[status(thm)],[366, 365])).
% 0.18/0.55 tff(368,plain,
% 0.18/0.55 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_4, e_2, e_3)) | (~product(e_4, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_4, e_2, e_3)) | (~product(e_4, e_3, e_3)))),
% 0.18/0.55 inference(rewrite,[status(thm)],[])).
% 0.18/0.55 tff(369,plain,
% 0.18/0.55 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_4, e_2, e_3)) | (~product(e_4, e_3, e_3)))),
% 0.18/0.55 inference(quant_inst,[status(thm)],[])).
% 0.18/0.55 tff(370,plain,
% 0.18/0.55 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_4, e_2, e_3)) | (~product(e_4, e_3, e_3))),
% 0.18/0.55 inference(modus_ponens,[status(thm)],[369, 368])).
% 0.18/0.55 tff(371,plain,
% 0.18/0.55 ($false),
% 0.18/0.55 inference(unit_resolution,[status(thm)],[370, 367, 22, 170, 364])).
% 0.18/0.55 tff(372,plain,((~product(e_4, e_3, e_3)) | (~product(e_4, e_2, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.55 tff(373,plain,
% 0.18/0.55 (~product(e_4, e_3, e_3)),
% 0.18/0.55 inference(unit_resolution,[status(thm)],[372, 170])).
% 0.18/0.55 tff(374,plain,
% 0.18/0.55 (product(e_4, e_3, e_2) | product(e_4, e_3, e_1) | product(e_4, e_3, e_3)),
% 0.18/0.55 inference(unit_resolution,[status(thm)],[137, 30])).
% 0.18/0.55 tff(375,plain,
% 0.18/0.55 (product(e_4, e_3, e_2)),
% 0.18/0.55 inference(unit_resolution,[status(thm)],[374, 373, 1])).
% 0.18/0.55 tff(376,plain,
% 0.18/0.55 (~product(e_1, e_3, e_2)),
% 0.18/0.55 inference(unit_resolution,[status(thm)],[126, 375])).
% 0.18/0.55 tff(377,assumption,(product(e_1, e_4, e_4)), introduced(assumption)).
% 0.18/0.55 tff(378,plain,
% 0.18/0.55 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_1, e_4, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_1, e_4, e_4)))),
% 0.18/0.55 inference(rewrite,[status(thm)],[])).
% 0.18/0.55 tff(379,plain,
% 0.18/0.55 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_1, e_4, e_4)))),
% 0.18/0.55 inference(quant_inst,[status(thm)],[])).
% 0.18/0.55 tff(380,plain,
% 0.18/0.55 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_1, e_4, e_4))),
% 0.18/0.55 inference(modus_ponens,[status(thm)],[379, 378])).
% 0.18/0.55 tff(381,plain,
% 0.18/0.55 ($false),
% 0.18/0.55 inference(unit_resolution,[status(thm)],[380, 233, 118, 11, 377])).
% 0.18/0.55 tff(382,plain,(~product(e_1, e_4, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.55 tff(383,assumption,(~product(e_1, e_4, e_2)), introduced(assumption)).
% 0.18/0.55 tff(384,assumption,(product(e_1, e_4, e_1)), introduced(assumption)).
% 0.18/0.55 tff(385,plain,
% 0.18/0.55 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_4, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_4, e_1)))),
% 0.45/0.55 inference(rewrite,[status(thm)],[])).
% 0.45/0.55 tff(386,plain,
% 0.45/0.55 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_4, e_1)))),
% 0.45/0.55 inference(quant_inst,[status(thm)],[])).
% 0.45/0.55 tff(387,plain,
% 0.45/0.55 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_4, e_1))),
% 0.45/0.55 inference(modus_ponens,[status(thm)],[386, 385])).
% 0.45/0.55 tff(388,plain,
% 0.45/0.55 ($false),
% 0.45/0.55 inference(unit_resolution,[status(thm)],[387, 121, 22, 34, 384])).
% 0.45/0.55 tff(389,plain,(~product(e_1, e_4, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.45/0.55 tff(390,plain,
% 0.45/0.55 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | ((~group_element(e_4)) | (~group_element(e_1)) | product(e_1, e_4, e_1) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_4))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | (~group_element(e_4)) | (~group_element(e_1)) | product(e_1, e_4, e_1) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_4))),
% 0.45/0.55 inference(rewrite,[status(thm)],[])).
% 0.45/0.55 tff(391,plain,
% 0.45/0.55 (((~group_element(e_4)) | (~group_element(e_1)) | product(e_1, e_4, e_4) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_1)) <=> ((~group_element(e_4)) | (~group_element(e_1)) | product(e_1, e_4, e_1) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_4))),
% 0.45/0.55 inference(rewrite,[status(thm)],[])).
% 0.45/0.55 tff(392,plain,
% 0.45/0.55 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | ((~group_element(e_4)) | (~group_element(e_1)) | product(e_1, e_4, e_4) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | ((~group_element(e_4)) | (~group_element(e_1)) | product(e_1, e_4, e_1) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_4)))),
% 0.45/0.55 inference(monotonicity,[status(thm)],[391])).
% 0.45/0.55 tff(393,plain,
% 0.45/0.55 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | ((~group_element(e_4)) | (~group_element(e_1)) | product(e_1, e_4, e_4) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | (~group_element(e_4)) | (~group_element(e_1)) | product(e_1, e_4, e_1) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_4))),
% 0.45/0.55 inference(transitivity,[status(thm)],[392, 390])).
% 0.45/0.55 tff(394,plain,
% 0.45/0.55 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | ((~group_element(e_4)) | (~group_element(e_1)) | product(e_1, e_4, e_4) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_1))),
% 0.45/0.55 inference(quant_inst,[status(thm)],[])).
% 0.45/0.55 tff(395,plain,
% 0.45/0.55 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | (~group_element(e_4)) | (~group_element(e_1)) | product(e_1, e_4, e_1) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_4)),
% 0.45/0.56 inference(modus_ponens,[status(thm)],[394, 393])).
% 0.45/0.56 tff(396,plain,
% 0.45/0.56 (product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_4)),
% 0.45/0.56 inference(unit_resolution,[status(thm)],[395, 60, 130, 54, 389])).
% 0.45/0.56 tff(397,plain,
% 0.45/0.56 (product(e_1, e_4, e_3)),
% 0.45/0.56 inference(unit_resolution,[status(thm)],[396, 383, 382])).
% 0.45/0.56 tff(398,assumption,(product(e_1, e_3, e_4)), introduced(assumption)).
% 0.45/0.56 tff(399,plain,
% 0.45/0.56 (~product(e_3, e_4, e_1)),
% 0.45/0.56 inference(unit_resolution,[status(thm)],[362, 121, 96, 398, 34])).
% 0.45/0.56 tff(400,assumption,(product(e_3, e_4, e_2)), introduced(assumption)).
% 0.45/0.56 tff(401,plain,
% 0.45/0.56 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_1, e_4) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_1, e_2)) | (~product(e_3, e_4, e_2)) | (~product(e_1, e_3, e_4)))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_1, e_4) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_1, e_2)) | (~product(e_3, e_4, e_2)) | (~product(e_1, e_3, e_4)))),
% 0.45/0.56 inference(rewrite,[status(thm)],[])).
% 0.45/0.56 tff(402,plain,
% 0.45/0.56 (((~product(e_1, e_3, e_4)) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_4, e_2)) | (~product(e_1, e_1, e_2)) | equalish(e_1, e_4)) <=> (equalish(e_1, e_4) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_1, e_2)) | (~product(e_3, e_4, e_2)) | (~product(e_1, e_3, e_4)))),
% 0.45/0.56 inference(rewrite,[status(thm)],[])).
% 0.45/0.56 tff(403,plain,
% 0.45/0.56 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_1, e_3, e_4)) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_4, e_2)) | (~product(e_1, e_1, e_2)) | equalish(e_1, e_4))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_1, e_4) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_1, e_2)) | (~product(e_3, e_4, e_2)) | (~product(e_1, e_3, e_4))))),
% 0.45/0.56 inference(monotonicity,[status(thm)],[402])).
% 0.45/0.56 tff(404,plain,
% 0.45/0.56 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_1, e_3, e_4)) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_4, e_2)) | (~product(e_1, e_1, e_2)) | equalish(e_1, e_4))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_1, e_4) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_1, e_2)) | (~product(e_3, e_4, e_2)) | (~product(e_1, e_3, e_4)))),
% 0.45/0.56 inference(transitivity,[status(thm)],[403, 401])).
% 0.45/0.56 tff(405,plain,
% 0.45/0.56 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_1, e_3, e_4)) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_4, e_2)) | (~product(e_1, e_1, e_2)) | equalish(e_1, e_4))),
% 0.45/0.56 inference(quant_inst,[status(thm)],[])).
% 0.45/0.56 tff(406,plain,
% 0.45/0.56 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_1, e_4) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_1, e_2)) | (~product(e_3, e_4, e_2)) | (~product(e_1, e_3, e_4))),
% 0.45/0.56 inference(modus_ponens,[status(thm)],[405, 404])).
% 0.45/0.56 tff(407,plain,
% 0.45/0.56 (~product(e_1, e_1, e_2)),
% 0.45/0.56 inference(unit_resolution,[status(thm)],[406, 233, 96, 398, 34, 400])).
% 0.45/0.56 tff(408,plain,
% 0.45/0.56 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | 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_4, e_2) | product(e_1, e_2, e_2))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | 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_4, e_2) | product(e_1, e_2, e_2))),
% 0.45/0.56 inference(rewrite,[status(thm)],[])).
% 0.45/0.56 tff(409,plain,
% 0.45/0.56 (((~group_element(e_2)) | (~group_element(e_1)) | product(e_1, e_4, e_2) | 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_4, e_2) | product(e_1, e_2, e_2))),
% 0.45/0.56 inference(rewrite,[status(thm)],[])).
% 0.45/0.56 tff(410,plain,
% 0.45/0.56 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | 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_4, e_2) | 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_4, Y) | 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_4, e_2) | product(e_1, e_2, e_2)))),
% 0.45/0.56 inference(monotonicity,[status(thm)],[409])).
% 0.45/0.56 tff(411,plain,
% 0.45/0.56 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | 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_4, e_2) | 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_4, Y) | 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_4, e_2) | product(e_1, e_2, e_2))),
% 0.45/0.56 inference(transitivity,[status(thm)],[410, 408])).
% 0.45/0.56 tff(412,plain,
% 0.45/0.56 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | 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_4, e_2) | product(e_1, e_3, e_2) | product(e_1, e_2, e_2) | product(e_1, e_1, e_2))),
% 0.45/0.56 inference(quant_inst,[status(thm)],[])).
% 0.45/0.56 tff(413,plain,
% 0.45/0.56 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | 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_4, e_2) | product(e_1, e_2, e_2)),
% 0.45/0.56 inference(modus_ponens,[status(thm)],[412, 411])).
% 0.45/0.56 tff(414,plain,
% 0.45/0.56 (product(e_1, e_3, e_2) | product(e_1, e_1, e_2) | product(e_1, e_4, e_2) | product(e_1, e_2, e_2)),
% 0.45/0.56 inference(unit_resolution,[status(thm)],[413, 280, 60, 209])).
% 0.45/0.56 tff(415,plain,
% 0.45/0.56 (product(e_1, e_2, e_2)),
% 0.45/0.56 inference(unit_resolution,[status(thm)],[414, 407, 383, 43])).
% 0.45/0.56 tff(416,plain,
% 0.45/0.56 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_2, e_4) | (~product(e_2, e_2, e_2)) | (~product(e_3, e_4, e_2)) | (~product(e_1, e_3, e_4)) | (~product(e_1, e_2, e_2)))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_2, e_4) | (~product(e_2, e_2, e_2)) | (~product(e_3, e_4, e_2)) | (~product(e_1, e_3, e_4)) | (~product(e_1, e_2, e_2)))),
% 0.45/0.56 inference(rewrite,[status(thm)],[])).
% 0.45/0.56 tff(417,plain,
% 0.45/0.56 (((~product(e_1, e_3, e_4)) | (~product(e_1, e_2, e_2)) | (~product(e_3, e_4, e_2)) | (~product(e_2, e_2, e_2)) | equalish(e_2, e_4)) <=> (equalish(e_2, e_4) | (~product(e_2, e_2, e_2)) | (~product(e_3, e_4, e_2)) | (~product(e_1, e_3, e_4)) | (~product(e_1, e_2, e_2)))),
% 0.46/0.57 inference(rewrite,[status(thm)],[])).
% 0.46/0.57 tff(418,plain,
% 0.46/0.57 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_1, e_3, e_4)) | (~product(e_1, e_2, e_2)) | (~product(e_3, e_4, e_2)) | (~product(e_2, e_2, e_2)) | equalish(e_2, e_4))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_2, e_4) | (~product(e_2, e_2, e_2)) | (~product(e_3, e_4, e_2)) | (~product(e_1, e_3, e_4)) | (~product(e_1, e_2, e_2))))),
% 0.46/0.57 inference(monotonicity,[status(thm)],[417])).
% 0.46/0.57 tff(419,plain,
% 0.46/0.57 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_1, e_3, e_4)) | (~product(e_1, e_2, e_2)) | (~product(e_3, e_4, e_2)) | (~product(e_2, e_2, e_2)) | equalish(e_2, e_4))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_2, e_4) | (~product(e_2, e_2, e_2)) | (~product(e_3, e_4, e_2)) | (~product(e_1, e_3, e_4)) | (~product(e_1, e_2, e_2)))),
% 0.46/0.57 inference(transitivity,[status(thm)],[418, 416])).
% 0.46/0.57 tff(420,plain,
% 0.46/0.57 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_1, e_3, e_4)) | (~product(e_1, e_2, e_2)) | (~product(e_3, e_4, e_2)) | (~product(e_2, e_2, e_2)) | equalish(e_2, e_4))),
% 0.46/0.57 inference(quant_inst,[status(thm)],[])).
% 0.46/0.57 tff(421,plain,
% 0.46/0.57 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_2, e_4) | (~product(e_2, e_2, e_2)) | (~product(e_3, e_4, e_2)) | (~product(e_1, e_3, e_4)) | (~product(e_1, e_2, e_2))),
% 0.46/0.57 inference(modus_ponens,[status(thm)],[420, 419])).
% 0.46/0.57 tff(422,plain,
% 0.46/0.57 ($false),
% 0.46/0.57 inference(unit_resolution,[status(thm)],[421, 184, 96, 398, 415, 194, 400])).
% 0.46/0.57 tff(423,plain,((~product(e_3, e_4, e_2)) | (~product(e_1, e_3, e_4)) | product(e_1, e_4, e_2) | product(e_1, e_3, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.46/0.57 tff(424,plain,
% 0.46/0.57 (~product(e_3, e_4, e_2)),
% 0.46/0.57 inference(unit_resolution,[status(thm)],[423, 383, 398, 43])).
% 0.46/0.57 tff(425,assumption,(product(e_3, e_4, e_4)), introduced(assumption)).
% 0.46/0.57 tff(426,plain,
% 0.46/0.57 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_3, e_4, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_3, e_4, e_4)))),
% 0.46/0.57 inference(rewrite,[status(thm)],[])).
% 0.46/0.57 tff(427,plain,
% 0.46/0.57 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_3, e_4, e_4)))),
% 0.46/0.57 inference(quant_inst,[status(thm)],[])).
% 0.46/0.57 tff(428,plain,
% 0.46/0.57 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_3, e_4, e_4))),
% 0.46/0.57 inference(modus_ponens,[status(thm)],[427, 426])).
% 0.46/0.57 tff(429,plain,
% 0.46/0.57 ($false),
% 0.46/0.57 inference(unit_resolution,[status(thm)],[428, 25, 118, 425, 11])).
% 0.46/0.57 tff(430,plain,(~product(e_3, e_4, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.46/0.57 tff(431,plain,
% 0.46/0.57 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | (product(e_3, e_4, e_4) | (~group_element(e_4)) | (~group_element(e_3)) | product(e_3, e_4, e_1) | product(e_3, e_4, e_2) | product(e_3, e_4, e_3))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | product(e_3, e_4, e_4) | (~group_element(e_4)) | (~group_element(e_3)) | product(e_3, e_4, e_1) | product(e_3, e_4, e_2) | product(e_3, e_4, e_3))),
% 0.46/0.57 inference(rewrite,[status(thm)],[])).
% 0.46/0.57 tff(432,plain,
% 0.46/0.57 (((~group_element(e_4)) | (~group_element(e_3)) | product(e_3, e_4, e_4) | product(e_3, e_4, e_3) | product(e_3, e_4, e_2) | product(e_3, e_4, e_1)) <=> (product(e_3, e_4, e_4) | (~group_element(e_4)) | (~group_element(e_3)) | product(e_3, e_4, e_1) | product(e_3, e_4, e_2) | product(e_3, e_4, e_3))),
% 0.46/0.57 inference(rewrite,[status(thm)],[])).
% 0.46/0.57 tff(433,plain,
% 0.46/0.57 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | ((~group_element(e_4)) | (~group_element(e_3)) | product(e_3, e_4, e_4) | product(e_3, e_4, e_3) | product(e_3, e_4, e_2) | product(e_3, e_4, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | (product(e_3, e_4, e_4) | (~group_element(e_4)) | (~group_element(e_3)) | product(e_3, e_4, e_1) | product(e_3, e_4, e_2) | product(e_3, e_4, e_3)))),
% 0.46/0.57 inference(monotonicity,[status(thm)],[432])).
% 0.46/0.57 tff(434,plain,
% 0.46/0.57 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | ((~group_element(e_4)) | (~group_element(e_3)) | product(e_3, e_4, e_4) | product(e_3, e_4, e_3) | product(e_3, e_4, e_2) | product(e_3, e_4, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | product(e_3, e_4, e_4) | (~group_element(e_4)) | (~group_element(e_3)) | product(e_3, e_4, e_1) | product(e_3, e_4, e_2) | product(e_3, e_4, e_3))),
% 0.46/0.57 inference(transitivity,[status(thm)],[433, 431])).
% 0.46/0.57 tff(435,plain,
% 0.46/0.57 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | ((~group_element(e_4)) | (~group_element(e_3)) | product(e_3, e_4, e_4) | product(e_3, e_4, e_3) | product(e_3, e_4, e_2) | product(e_3, e_4, e_1))),
% 0.46/0.57 inference(quant_inst,[status(thm)],[])).
% 0.46/0.57 tff(436,plain,
% 0.46/0.57 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | product(e_3, e_4, e_4) | (~group_element(e_4)) | (~group_element(e_3)) | product(e_3, e_4, e_1) | product(e_3, e_4, e_2) | product(e_3, e_4, e_3)),
% 0.46/0.57 inference(modus_ponens,[status(thm)],[435, 434])).
% 0.46/0.57 tff(437,plain,
% 0.46/0.57 (product(e_3, e_4, e_1) | product(e_3, e_4, e_2) | product(e_3, e_4, e_3)),
% 0.46/0.57 inference(unit_resolution,[status(thm)],[436, 57, 130, 54, 430])).
% 0.46/0.57 tff(438,plain,
% 0.46/0.57 (product(e_3, e_4, e_3)),
% 0.46/0.57 inference(unit_resolution,[status(thm)],[437, 424, 399])).
% 0.46/0.57 tff(439,plain,
% 0.46/0.57 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_3, e_4, e_3)) | (~product(e_1, e_4, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_3, e_4, e_3)) | (~product(e_1, e_4, e_3)))),
% 0.46/0.57 inference(rewrite,[status(thm)],[])).
% 0.46/0.57 tff(440,plain,
% 0.46/0.57 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_3, e_4, e_3)) | (~product(e_1, e_4, e_3)))),
% 0.46/0.57 inference(quant_inst,[status(thm)],[])).
% 0.46/0.57 tff(441,plain,
% 0.46/0.57 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_3, e_4, e_3)) | (~product(e_1, e_4, e_3))),
% 0.46/0.57 inference(modus_ponens,[status(thm)],[440, 439])).
% 0.46/0.57 tff(442,plain,
% 0.46/0.58 ($false),
% 0.46/0.58 inference(unit_resolution,[status(thm)],[441, 221, 118, 438, 397])).
% 0.46/0.58 tff(443,plain,(product(e_1, e_4, e_2) | (~product(e_1, e_3, e_4)) | product(e_1, e_3, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.46/0.58 tff(444,plain,
% 0.46/0.58 (product(e_1, e_4, e_2)),
% 0.46/0.58 inference(unit_resolution,[status(thm)],[443, 376, 356])).
% 0.46/0.58 tff(445,plain,
% 0.46/0.58 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_4, e_2) | (~product(e_4, e_2, e_3)) | (~product(e_1, e_4, e_2)) | (~product(e_1, e_3, e_4)) | (~product(e_3, e_4, e_3)))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_4, e_2) | (~product(e_4, e_2, e_3)) | (~product(e_1, e_4, e_2)) | (~product(e_1, e_3, e_4)) | (~product(e_3, e_4, e_3)))),
% 0.46/0.58 inference(rewrite,[status(thm)],[])).
% 0.46/0.58 tff(446,plain,
% 0.46/0.58 (((~product(e_1, e_4, e_2)) | (~product(e_1, e_3, e_4)) | (~product(e_4, e_2, e_3)) | (~product(e_3, e_4, e_3)) | equalish(e_4, e_2)) <=> (equalish(e_4, e_2) | (~product(e_4, e_2, e_3)) | (~product(e_1, e_4, e_2)) | (~product(e_1, e_3, e_4)) | (~product(e_3, e_4, e_3)))),
% 0.46/0.58 inference(rewrite,[status(thm)],[])).
% 0.46/0.58 tff(447,plain,
% 0.46/0.58 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_1, e_4, e_2)) | (~product(e_1, e_3, e_4)) | (~product(e_4, e_2, e_3)) | (~product(e_3, e_4, e_3)) | equalish(e_4, e_2))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_4, e_2) | (~product(e_4, e_2, e_3)) | (~product(e_1, e_4, e_2)) | (~product(e_1, e_3, e_4)) | (~product(e_3, e_4, e_3))))),
% 0.46/0.58 inference(monotonicity,[status(thm)],[446])).
% 0.46/0.58 tff(448,plain,
% 0.46/0.58 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_1, e_4, e_2)) | (~product(e_1, e_3, e_4)) | (~product(e_4, e_2, e_3)) | (~product(e_3, e_4, e_3)) | equalish(e_4, e_2))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_4, e_2) | (~product(e_4, e_2, e_3)) | (~product(e_1, e_4, e_2)) | (~product(e_1, e_3, e_4)) | (~product(e_3, e_4, e_3)))),
% 0.46/0.58 inference(transitivity,[status(thm)],[447, 445])).
% 0.46/0.58 tff(449,plain,
% 0.46/0.58 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_1, e_4, e_2)) | (~product(e_1, e_3, e_4)) | (~product(e_4, e_2, e_3)) | (~product(e_3, e_4, e_3)) | equalish(e_4, e_2))),
% 0.46/0.58 inference(quant_inst,[status(thm)],[])).
% 0.46/0.58 tff(450,plain,
% 0.46/0.58 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_4, e_2) | (~product(e_4, e_2, e_3)) | (~product(e_1, e_4, e_2)) | (~product(e_1, e_3, e_4)) | (~product(e_3, e_4, e_3))),
% 0.46/0.58 inference(modus_ponens,[status(thm)],[449, 448])).
% 0.46/0.58 tff(451,plain,
% 0.46/0.58 (~product(e_3, e_4, e_3)),
% 0.46/0.58 inference(unit_resolution,[status(thm)],[450, 198, 96, 356, 170, 444])).
% 0.46/0.58 tff(452,plain,
% 0.46/0.58 (product(e_3, e_4, e_2)),
% 0.46/0.58 inference(unit_resolution,[status(thm)],[437, 451, 363])).
% 0.46/0.58 tff(453,plain,
% 0.46/0.58 (((~![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_4, e_2)) | (~product(e_3, e_4, 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_1) | (~product(e_1, e_4, e_2)) | (~product(e_3, e_4, e_2)))),
% 0.46/0.58 inference(rewrite,[status(thm)],[])).
% 0.46/0.58 tff(454,plain,
% 0.46/0.58 ((~![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_4, e_2)) | (~product(e_3, e_4, e_2)))),
% 0.46/0.58 inference(quant_inst,[status(thm)],[])).
% 0.46/0.58 tff(455,plain,
% 0.46/0.58 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_1, e_4, e_2)) | (~product(e_3, e_4, e_2))),
% 0.46/0.58 inference(modus_ponens,[status(thm)],[454, 453])).
% 0.46/0.58 tff(456,plain,
% 0.46/0.58 ($false),
% 0.46/0.58 inference(unit_resolution,[status(thm)],[455, 37, 118, 444, 452])).
% 0.46/0.58 tff(457,plain,((~product(e_4, e_2, e_3)) | product(e_4, e_3, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.46/0.58 tff(458,plain,
% 0.46/0.58 (~product(e_4, e_2, e_3)),
% 0.46/0.58 inference(unit_resolution,[status(thm)],[457, 1])).
% 0.46/0.58 tff(459,plain,
% 0.46/0.58 (product(e_4, e_2, e_1)),
% 0.46/0.58 inference(unit_resolution,[status(thm)],[217, 458])).
% 0.46/0.58 tff(460,assumption,(product(e_1, e_4, e_2)), introduced(assumption)).
% 0.46/0.58 tff(461,plain,
% 0.46/0.58 ((~equalish(e_2, e_1)) <=> (~equalish(e_2, e_1))),
% 0.46/0.58 inference(rewrite,[status(thm)],[])).
% 0.46/0.58 tff(462,axiom,(~equalish(e_2, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_1')).
% 0.46/0.58 tff(463,plain,
% 0.46/0.58 (~equalish(e_2, e_1)),
% 0.46/0.58 inference(modus_ponens,[status(thm)],[462, 461])).
% 0.46/0.58 tff(464,plain,
% 0.46/0.58 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_2, e_1) | (~product(e_4, e_2, e_1)) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_4, e_2)))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_2, e_1) | (~product(e_4, e_2, e_1)) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_4, e_2)))),
% 0.46/0.58 inference(rewrite,[status(thm)],[])).
% 0.46/0.58 tff(465,plain,
% 0.46/0.58 (((~product(e_1, e_1, e_1)) | (~product(e_1, e_4, e_2)) | (~product(e_1, e_1, e_1)) | (~product(e_4, e_2, e_1)) | equalish(e_2, e_1)) <=> (equalish(e_2, e_1) | (~product(e_4, e_2, e_1)) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_4, e_2)))),
% 0.46/0.58 inference(rewrite,[status(thm)],[])).
% 0.46/0.58 tff(466,plain,
% 0.46/0.58 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_1, e_1, e_1)) | (~product(e_1, e_4, e_2)) | (~product(e_1, e_1, e_1)) | (~product(e_4, e_2, e_1)) | equalish(e_2, e_1))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_2, e_1) | (~product(e_4, e_2, e_1)) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_4, e_2))))),
% 0.46/0.58 inference(monotonicity,[status(thm)],[465])).
% 0.46/0.58 tff(467,plain,
% 0.46/0.58 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_1, e_1, e_1)) | (~product(e_1, e_4, e_2)) | (~product(e_1, e_1, e_1)) | (~product(e_4, e_2, e_1)) | equalish(e_2, e_1))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_2, e_1) | (~product(e_4, e_2, e_1)) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_4, e_2)))),
% 0.46/0.58 inference(transitivity,[status(thm)],[466, 464])).
% 0.46/0.58 tff(468,plain,
% 0.46/0.58 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_1, e_1, e_1)) | (~product(e_1, e_4, e_2)) | (~product(e_1, e_1, e_1)) | (~product(e_4, e_2, e_1)) | equalish(e_2, e_1))),
% 0.46/0.58 inference(quant_inst,[status(thm)],[])).
% 0.46/0.58 tff(469,plain,
% 0.46/0.58 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_2, e_1) | (~product(e_4, e_2, e_1)) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_4, e_2))),
% 0.46/0.59 inference(modus_ponens,[status(thm)],[468, 467])).
% 0.46/0.59 tff(470,plain,
% 0.46/0.59 ($false),
% 0.46/0.59 inference(unit_resolution,[status(thm)],[469, 463, 96, 230, 34, 460])).
% 0.46/0.59 tff(471,plain,((~product(e_1, e_4, e_2)) | (~product(e_4, e_2, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.46/0.59 tff(472,plain,
% 0.46/0.59 (~product(e_1, e_4, e_2)),
% 0.46/0.59 inference(unit_resolution,[status(thm)],[471, 459])).
% 0.46/0.59 tff(473,plain,
% 0.46/0.59 (product(e_1, e_3, e_2)),
% 0.46/0.59 inference(unit_resolution,[status(thm)],[443, 472, 356])).
% 0.46/0.59 tff(474,plain,
% 0.46/0.59 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_2, e_4) | (~product(e_1, e_3, e_4)) | (~product(e_1, e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | equalish(e_2, e_4) | (~product(e_1, e_3, e_4)) | (~product(e_1, e_3, e_2)))),
% 0.46/0.59 inference(rewrite,[status(thm)],[])).
% 0.46/0.59 tff(475,plain,
% 0.46/0.59 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_2, e_4) | (~product(e_1, e_3, e_4)) | (~product(e_1, e_3, e_2)))),
% 0.46/0.59 inference(quant_inst,[status(thm)],[])).
% 0.46/0.59 tff(476,plain,
% 0.46/0.59 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | equalish(e_2, e_4) | (~product(e_1, e_3, e_4)) | (~product(e_1, e_3, e_2))),
% 0.46/0.59 inference(modus_ponens,[status(thm)],[475, 474])).
% 0.46/0.59 tff(477,plain,
% 0.46/0.59 ($false),
% 0.46/0.59 inference(unit_resolution,[status(thm)],[476, 184, 152, 356, 473])).
% 0.46/0.59 tff(478,plain,(product(e_4, e_3, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.46/0.59 tff(479,assumption,(product(e_4, e_3, e_1)), introduced(assumption)).
% 0.46/0.59 tff(480,plain,
% 0.46/0.59 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_1, e_4) | (~product(e_4, e_3, e_1)) | (~product(e_4, e_4, e_4)) | (~product(e_3, e_1, e_4)))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_1, e_4) | (~product(e_4, e_3, e_1)) | (~product(e_4, e_4, e_4)) | (~product(e_3, e_1, e_4)))),
% 0.46/0.59 inference(rewrite,[status(thm)],[])).
% 0.46/0.59 tff(481,plain,
% 0.46/0.59 (((~product(e_4, e_4, e_4)) | (~product(e_4, e_3, e_1)) | (~product(e_4, e_4, e_4)) | (~product(e_3, e_1, e_4)) | equalish(e_1, e_4)) <=> (equalish(e_1, e_4) | (~product(e_4, e_3, e_1)) | (~product(e_4, e_4, e_4)) | (~product(e_3, e_1, e_4)))),
% 0.46/0.59 inference(rewrite,[status(thm)],[])).
% 0.46/0.59 tff(482,plain,
% 0.46/0.59 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_4, e_4, e_4)) | (~product(e_4, e_3, e_1)) | (~product(e_4, e_4, e_4)) | (~product(e_3, e_1, e_4)) | equalish(e_1, e_4))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_1, e_4) | (~product(e_4, e_3, e_1)) | (~product(e_4, e_4, e_4)) | (~product(e_3, e_1, e_4))))),
% 0.46/0.59 inference(monotonicity,[status(thm)],[481])).
% 0.46/0.59 tff(483,plain,
% 0.46/0.59 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_4, e_4, e_4)) | (~product(e_4, e_3, e_1)) | (~product(e_4, e_4, e_4)) | (~product(e_3, e_1, e_4)) | equalish(e_1, e_4))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_1, e_4) | (~product(e_4, e_3, e_1)) | (~product(e_4, e_4, e_4)) | (~product(e_3, e_1, e_4)))),
% 0.46/0.59 inference(transitivity,[status(thm)],[482, 480])).
% 0.46/0.59 tff(484,plain,
% 0.46/0.59 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_4, e_4, e_4)) | (~product(e_4, e_3, e_1)) | (~product(e_4, e_4, e_4)) | (~product(e_3, e_1, e_4)) | equalish(e_1, e_4))),
% 0.46/0.59 inference(quant_inst,[status(thm)],[])).
% 0.46/0.59 tff(485,plain,
% 0.46/0.59 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_1, e_4) | (~product(e_4, e_3, e_1)) | (~product(e_4, e_4, e_4)) | (~product(e_3, e_1, e_4))),
% 0.46/0.59 inference(modus_ponens,[status(thm)],[484, 483])).
% 0.46/0.59 tff(486,plain,
% 0.46/0.59 ($false),
% 0.46/0.59 inference(unit_resolution,[status(thm)],[485, 233, 96, 318, 479, 11])).
% 0.46/0.59 tff(487,plain,((~product(e_4, e_3, e_1)) | (~product(e_3, e_1, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.46/0.59 tff(488,plain,
% 0.46/0.59 (~product(e_3, e_1, e_4)),
% 0.46/0.59 inference(unit_resolution,[status(thm)],[487, 478])).
% 0.46/0.59 tff(489,plain,
% 0.46/0.59 (product(e_2, e_1, e_4)),
% 0.46/0.59 inference(unit_resolution,[status(thm)],[262, 488])).
% 0.46/0.59 tff(490,assumption,(product(e_1, e_4, e_3)), introduced(assumption)).
% 0.46/0.59 tff(491,plain,
% 0.46/0.59 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~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_4, e_3, e_1)) | (~product(e_1, e_4, e_3)))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~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_4, e_3, e_1)) | (~product(e_1, e_4, e_3)))),
% 0.46/0.59 inference(rewrite,[status(thm)],[])).
% 0.46/0.59 tff(492,plain,
% 0.46/0.59 (((~product(e_1, e_1, e_1)) | (~product(e_1, e_4, e_3)) | (~product(e_1, e_1, e_1)) | (~product(e_4, e_3, e_1)) | equalish(e_3, e_1)) <=> (equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_4, e_3, e_1)) | (~product(e_1, e_4, e_3)))),
% 0.46/0.59 inference(rewrite,[status(thm)],[])).
% 0.46/0.59 tff(493,plain,
% 0.46/0.59 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_1, e_1, e_1)) | (~product(e_1, e_4, e_3)) | (~product(e_1, e_1, e_1)) | (~product(e_4, e_3, e_1)) | equalish(e_3, e_1))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~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_4, e_3, e_1)) | (~product(e_1, e_4, e_3))))),
% 0.46/0.59 inference(monotonicity,[status(thm)],[492])).
% 0.46/0.59 tff(494,plain,
% 0.46/0.59 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_1, e_1, e_1)) | (~product(e_1, e_4, e_3)) | (~product(e_1, e_1, e_1)) | (~product(e_4, e_3, e_1)) | equalish(e_3, e_1))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~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_4, e_3, e_1)) | (~product(e_1, e_4, e_3)))),
% 0.46/0.59 inference(transitivity,[status(thm)],[493, 491])).
% 0.46/0.59 tff(495,plain,
% 0.46/0.59 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_1, e_1, e_1)) | (~product(e_1, e_4, e_3)) | (~product(e_1, e_1, e_1)) | (~product(e_4, e_3, e_1)) | equalish(e_3, e_1))),
% 0.46/0.59 inference(quant_inst,[status(thm)],[])).
% 0.46/0.59 tff(496,plain,
% 0.46/0.59 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_4, e_3, e_1)) | (~product(e_1, e_4, e_3))),
% 0.46/0.60 inference(modus_ponens,[status(thm)],[495, 494])).
% 0.46/0.60 tff(497,plain,
% 0.46/0.60 ($false),
% 0.46/0.60 inference(unit_resolution,[status(thm)],[496, 37, 96, 34, 479, 490])).
% 0.46/0.60 tff(498,plain,((~product(e_1, e_4, e_3)) | (~product(e_4, e_3, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.46/0.60 tff(499,plain,
% 0.46/0.60 (~product(e_1, e_4, e_3)),
% 0.46/0.60 inference(unit_resolution,[status(thm)],[498, 478])).
% 0.46/0.60 tff(500,plain,
% 0.46/0.60 (product(e_1, e_4, e_2)),
% 0.46/0.60 inference(unit_resolution,[status(thm)],[396, 499, 382])).
% 0.46/0.60 tff(501,plain,
% 0.46/0.60 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_4, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_4)) | (~product(e_1, e_4, e_2)))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_4, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_4)) | (~product(e_1, e_4, e_2)))),
% 0.46/0.60 inference(rewrite,[status(thm)],[])).
% 0.46/0.60 tff(502,plain,
% 0.46/0.60 (((~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_4)) | (~product(e_2, e_2, e_2)) | (~product(e_1, e_4, e_2)) | equalish(e_4, e_2)) <=> (equalish(e_4, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_4)) | (~product(e_1, e_4, e_2)))),
% 0.46/0.60 inference(rewrite,[status(thm)],[])).
% 0.46/0.60 tff(503,plain,
% 0.46/0.60 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_4)) | (~product(e_2, e_2, e_2)) | (~product(e_1, e_4, e_2)) | equalish(e_4, e_2))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_4, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_4)) | (~product(e_1, e_4, e_2))))),
% 0.46/0.60 inference(monotonicity,[status(thm)],[502])).
% 0.46/0.60 tff(504,plain,
% 0.46/0.60 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_4)) | (~product(e_2, e_2, e_2)) | (~product(e_1, e_4, e_2)) | equalish(e_4, e_2))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_4, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_4)) | (~product(e_1, e_4, e_2)))),
% 0.46/0.60 inference(transitivity,[status(thm)],[503, 501])).
% 0.46/0.60 tff(505,plain,
% 0.46/0.60 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_4)) | (~product(e_2, e_2, e_2)) | (~product(e_1, e_4, e_2)) | equalish(e_4, e_2))),
% 0.46/0.60 inference(quant_inst,[status(thm)],[])).
% 0.46/0.60 tff(506,plain,
% 0.46/0.60 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_4, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_4)) | (~product(e_1, e_4, e_2))),
% 0.46/0.60 inference(modus_ponens,[status(thm)],[505, 504])).
% 0.46/0.60 tff(507,plain,
% 0.46/0.60 ($false),
% 0.46/0.60 inference(unit_resolution,[status(thm)],[506, 198, 96, 500, 194, 489])).
% 0.46/0.60 % SZS output end Proof
%------------------------------------------------------------------------------