TSTP Solution File: GRP126-1.004 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP126-1.004 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n009.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 22:26:04 EDT 2022
% Result : Unsatisfiable 0.20s 0.42s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP126-1.004 : TPTP v8.1.0. Released v1.2.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n009.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Aug 31 14:55:20 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.20/0.42 % SZS status Unsatisfiable
% 0.20/0.42 % SZS output start Proof
% 0.20/0.42 tff(product_type, type, (
% 0.20/0.42 product: ( $i * $i * $i ) > $o)).
% 0.20/0.42 tff(e_3_type, type, (
% 0.20/0.42 e_3: $i)).
% 0.20/0.42 tff(e_1_type, type, (
% 0.20/0.42 e_1: $i)).
% 0.20/0.42 tff(e_2_type, type, (
% 0.20/0.42 e_2: $i)).
% 0.20/0.42 tff(equalish_type, type, (
% 0.20/0.42 equalish: ( $i * $i ) > $o)).
% 0.20/0.42 tff(e_4_type, type, (
% 0.20/0.42 e_4: $i)).
% 0.20/0.42 tff(group_element_type, type, (
% 0.20/0.42 group_element: $i > $o)).
% 0.20/0.42 tff(1,assumption,(product(e_2, e_1, e_1)), introduced(assumption)).
% 0.20/0.42 tff(2,plain,
% 0.20/0.42 (^[X: $i] : refl(product(X, X, X) <=> product(X, X, X))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(3,plain,
% 0.20/0.42 (![X: $i] : product(X, X, X) <=> ![X: $i] : product(X, X, X)),
% 0.20/0.42 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.42 tff(4,plain,
% 0.20/0.42 (![X: $i] : product(X, X, X) <=> ![X: $i] : product(X, X, X)),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(5,axiom,(![X: $i] : product(X, X, X)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product_idempotence')).
% 0.20/0.42 tff(6,plain,
% 0.20/0.42 (![X: $i] : product(X, X, X)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.42 tff(7,plain,(
% 0.20/0.42 ![X: $i] : product(X, X, X)),
% 0.20/0.42 inference(skolemize,[status(sab)],[6])).
% 0.20/0.42 tff(8,plain,
% 0.20/0.42 (![X: $i] : product(X, X, X)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.42 tff(9,plain,
% 0.20/0.42 ((~![X: $i] : product(X, X, X)) | product(e_1, e_1, e_1)),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(10,plain,
% 0.20/0.42 (product(e_1, e_1, e_1)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[9, 8])).
% 0.20/0.42 tff(11,plain,
% 0.20/0.42 (^[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))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(12,plain,
% 0.20/0.42 (![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)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[11])).
% 0.20/0.42 tff(13,plain,
% 0.20/0.42 (![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)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(14,plain,
% 0.20/0.42 (^[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)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(15,plain,
% 0.20/0.42 (![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)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[14])).
% 0.20/0.42 tff(16,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')).
% 0.20/0.42 tff(17,plain,
% 0.20/0.42 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.20/0.42 tff(18,plain,
% 0.20/0.42 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.20/0.42 tff(19,plain,(
% 0.20/0.42 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[18])).
% 0.20/0.42 tff(20,plain,
% 0.20/0.42 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.20/0.42 tff(21,plain,
% 0.20/0.42 ((~equalish(e_2, e_1)) <=> (~equalish(e_2, e_1))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(22,axiom,(~equalish(e_2, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_1')).
% 0.20/0.42 tff(23,plain,
% 0.20/0.42 (~equalish(e_2, e_1)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.20/0.42 tff(24,plain,
% 0.20/0.42 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(25,plain,
% 0.20/0.42 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(26,plain,
% 0.20/0.42 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.20/0.42 tff(27,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[26, 23, 20, 10, 1])).
% 0.20/0.42 tff(28,plain,(~product(e_2, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(29,assumption,(product(e_2, e_1, e_4)), introduced(assumption)).
% 0.20/0.42 tff(30,assumption,(product(e_3, e_1, e_3)), introduced(assumption)).
% 0.20/0.42 tff(31,plain,
% 0.20/0.42 ((~![X: $i] : product(X, X, X)) | product(e_3, e_3, e_3)),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(32,plain,
% 0.20/0.42 (product(e_3, e_3, e_3)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[31, 8])).
% 0.20/0.42 tff(33,plain,
% 0.20/0.42 (^[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))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(34,plain,
% 0.20/0.42 (![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)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[33])).
% 0.20/0.42 tff(35,plain,
% 0.20/0.42 (![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)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(36,plain,
% 0.20/0.42 (^[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)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(37,plain,
% 0.20/0.42 (![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)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[36])).
% 0.20/0.43 tff(38,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')).
% 0.20/0.43 tff(39,plain,
% 0.20/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.20/0.43 tff(40,plain,
% 0.20/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.20/0.43 tff(41,plain,(
% 0.20/0.43 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.43 inference(skolemize,[status(sab)],[40])).
% 0.20/0.43 tff(42,plain,
% 0.20/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[41, 34])).
% 0.20/0.43 tff(43,plain,
% 0.20/0.43 ((~equalish(e_1, e_3)) <=> (~equalish(e_1, e_3))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(44,axiom,(~equalish(e_1, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_3')).
% 0.20/0.43 tff(45,plain,
% 0.20/0.43 (~equalish(e_1, e_3)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.20/0.43 tff(46,plain,
% 0.20/0.43 (((~![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_3)) | (~product(e_3, e_1, e_3)))) <=> ((~![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_3)) | (~product(e_3, e_1, e_3)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(47,plain,
% 0.20/0.43 ((~![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_3)) | (~product(e_3, e_1, e_3)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(48,plain,
% 0.20/0.43 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_1, e_3))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.20/0.43 tff(49,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[48, 45, 42, 32, 30])).
% 0.20/0.43 tff(50,plain,(~product(e_3, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.43 tff(51,assumption,(~product(e_1, e_3, e_2)), introduced(assumption)).
% 0.20/0.43 tff(52,assumption,(product(e_1, e_3, e_1)), introduced(assumption)).
% 0.20/0.43 tff(53,plain,
% 0.20/0.43 ((~equalish(e_3, e_1)) <=> (~equalish(e_3, e_1))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(54,axiom,(~equalish(e_3, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_1')).
% 0.20/0.43 tff(55,plain,
% 0.20/0.43 (~equalish(e_3, e_1)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.20/0.43 tff(56,plain,
% 0.20/0.43 (((~![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)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(57,plain,
% 0.20/0.43 ((~![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)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(58,plain,
% 0.20/0.43 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_1))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.20/0.43 tff(59,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[58, 55, 42, 10, 52])).
% 0.20/0.43 tff(60,plain,(~product(e_1, e_3, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.43 tff(61,assumption,(product(e_3, e_1, e_4)), introduced(assumption)).
% 0.20/0.43 tff(62,assumption,(product(e_3, e_4, e_3)), introduced(assumption)).
% 0.20/0.43 tff(63,plain,
% 0.20/0.43 ((~equalish(e_4, e_3)) <=> (~equalish(e_4, e_3))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(64,axiom,(~equalish(e_4, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_3')).
% 0.20/0.43 tff(65,plain,
% 0.20/0.43 (~equalish(e_4, e_3)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.20/0.43 tff(66,plain,
% 0.20/0.43 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_3) | (~product(e_3, e_4, e_3)) | (~product(e_3, 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_4, e_3) | (~product(e_3, e_4, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(67,plain,
% 0.20/0.43 ((equalish(e_4, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_4, e_3))) <=> (equalish(e_4, e_3) | (~product(e_3, e_4, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(68,plain,
% 0.20/0.43 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_4, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_3) | (~product(e_3, e_4, e_3)) | (~product(e_3, e_3, e_3))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[67])).
% 0.20/0.43 tff(69,plain,
% 0.20/0.43 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_4, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_3) | (~product(e_3, e_4, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.20/0.43 inference(transitivity,[status(thm)],[68, 66])).
% 0.20/0.43 tff(70,plain,
% 0.20/0.43 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_4, e_3)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(71,plain,
% 0.20/0.43 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_3) | (~product(e_3, e_4, e_3)) | (~product(e_3, e_3, e_3))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.20/0.43 tff(72,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[71, 65, 42, 62, 32])).
% 0.20/0.43 tff(73,plain,(~product(e_3, e_4, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.43 tff(74,plain,
% 0.20/0.43 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : refl(((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1))) <=> ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(75,plain,
% 0.20/0.43 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[74])).
% 0.20/0.43 tff(76,plain,
% 0.20/0.43 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(77,plain,
% 0.20/0.43 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : rewrite((((~product(X, Y, Z1)) | (~product(Y, X, Z2))) | product(Z1, Z2, Y)) <=> ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(78,plain,
% 0.20/0.43 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(X, Y, Z1)) | (~product(Y, X, Z2))) | product(Z1, Z2, Y)) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[77])).
% 0.20/0.43 tff(79,axiom,(![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(X, Y, Z1)) | (~product(Y, X, Z2))) | product(Z1, Z2, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qg4')).
% 0.20/0.43 tff(80,plain,
% 0.20/0.43 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.20/0.43 tff(81,plain,
% 0.20/0.43 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[80, 76])).
% 0.20/0.43 tff(82,plain,(
% 0.20/0.43 ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))),
% 0.20/0.43 inference(skolemize,[status(sab)],[81])).
% 0.20/0.43 tff(83,plain,
% 0.20/0.43 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[82, 75])).
% 0.20/0.43 tff(84,plain,
% 0.20/0.43 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_3, e_4, e_3) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_3, e_4, e_3) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_3, e_3)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(85,plain,
% 0.20/0.43 (((~product(e_3, e_1, e_4)) | product(e_3, e_4, e_3) | (~product(e_1, e_3, e_3))) <=> (product(e_3, e_4, e_3) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_3, e_3)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(86,plain,
% 0.20/0.44 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_4)) | product(e_3, e_4, e_3) | (~product(e_1, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_3, e_4, e_3) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_3, e_3))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[85])).
% 0.20/0.44 tff(87,plain,
% 0.20/0.44 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_4)) | product(e_3, e_4, e_3) | (~product(e_1, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_3, e_4, e_3) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_3, e_3)))),
% 0.20/0.44 inference(transitivity,[status(thm)],[86, 84])).
% 0.20/0.44 tff(88,plain,
% 0.20/0.44 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_4)) | product(e_3, e_4, e_3) | (~product(e_1, e_3, e_3)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(89,plain,
% 0.20/0.44 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_3, e_4, e_3) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_3, e_3))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.20/0.44 tff(90,plain,
% 0.20/0.44 (~product(e_1, e_3, e_3)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[89, 83, 73, 61])).
% 0.20/0.44 tff(91,plain,
% 0.20/0.44 ((~![X: $i] : product(X, X, X)) | product(e_4, e_4, e_4)),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(92,plain,
% 0.20/0.44 (product(e_4, e_4, e_4)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[91, 8])).
% 0.20/0.44 tff(93,assumption,(product(e_3, e_4, e_4)), introduced(assumption)).
% 0.20/0.44 tff(94,plain,
% 0.20/0.44 ((~equalish(e_3, e_4)) <=> (~equalish(e_3, e_4))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(95,axiom,(~equalish(e_3, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_4')).
% 0.20/0.44 tff(96,plain,
% 0.20/0.44 (~equalish(e_3, e_4)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.20/0.44 tff(97,plain,
% 0.20/0.44 (((~![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_3, e_4, e_4)) | (~product(e_4, 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_3, e_4, e_4)) | (~product(e_4, e_4, e_4)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(98,plain,
% 0.20/0.44 ((equalish(e_3, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_3, e_4, e_4))) <=> (equalish(e_3, e_4) | (~product(e_3, e_4, e_4)) | (~product(e_4, e_4, e_4)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(99,plain,
% 0.20/0.44 (((~![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_3, e_4, e_4)) | (~product(e_4, e_4, e_4))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[98])).
% 0.20/0.44 tff(100,plain,
% 0.20/0.44 (((~![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_3, e_4, e_4)) | (~product(e_4, e_4, e_4)))),
% 0.20/0.44 inference(transitivity,[status(thm)],[99, 97])).
% 0.20/0.44 tff(101,plain,
% 0.20/0.44 ((~![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)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(102,plain,
% 0.20/0.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_4) | (~product(e_3, e_4, e_4)) | (~product(e_4, e_4, e_4))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.20/0.44 tff(103,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[102, 96, 20, 93, 92])).
% 0.20/0.44 tff(104,plain,(~product(e_3, e_4, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(105,plain,
% 0.20/0.44 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_3, e_4, e_4) | (~product(e_4, e_4, e_3)) | (~product(e_4, e_4, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_3, e_4, e_4) | (~product(e_4, e_4, e_3)) | (~product(e_4, e_4, e_4)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(106,plain,
% 0.20/0.44 (((~product(e_4, e_4, e_4)) | product(e_3, e_4, e_4) | (~product(e_4, e_4, e_3))) <=> (product(e_3, e_4, e_4) | (~product(e_4, e_4, e_3)) | (~product(e_4, e_4, e_4)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(107,plain,
% 0.20/0.44 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_4, e_4, e_4)) | product(e_3, e_4, e_4) | (~product(e_4, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_3, e_4, e_4) | (~product(e_4, e_4, e_3)) | (~product(e_4, e_4, e_4))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[106])).
% 0.20/0.44 tff(108,plain,
% 0.20/0.44 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_4, e_4, e_4)) | product(e_3, e_4, e_4) | (~product(e_4, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_3, e_4, e_4) | (~product(e_4, e_4, e_3)) | (~product(e_4, e_4, e_4)))),
% 0.20/0.44 inference(transitivity,[status(thm)],[107, 105])).
% 0.20/0.44 tff(109,plain,
% 0.20/0.44 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_4, e_4, e_4)) | product(e_3, e_4, e_4) | (~product(e_4, e_4, e_3)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(110,plain,
% 0.20/0.44 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_3, e_4, e_4) | (~product(e_4, e_4, e_3)) | (~product(e_4, e_4, e_4))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.20/0.44 tff(111,plain,
% 0.20/0.44 (~product(e_4, e_4, e_3)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[110, 83, 104, 92])).
% 0.20/0.44 tff(112,plain,
% 0.20/0.44 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_4)) | product(e_4, e_4, e_3) | (~product(e_1, e_3, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_4)) | product(e_4, e_4, e_3) | (~product(e_1, e_3, e_4)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(113,plain,
% 0.20/0.44 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_4)) | product(e_4, e_4, e_3) | (~product(e_1, e_3, e_4)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(114,plain,
% 0.20/0.44 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_4)) | product(e_4, e_4, e_3) | (~product(e_1, e_3, e_4))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.20/0.44 tff(115,plain,
% 0.20/0.44 (~product(e_1, e_3, e_4)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[114, 83, 61, 111])).
% 0.20/0.44 tff(116,plain,
% 0.20/0.44 (^[Y: $i, X: $i] : refl((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) | (~group_element(Y)) | (~group_element(X))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(117,plain,
% 0.20/0.44 (![Y: $i, X: $i] : (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))) <=> ![Y: $i, X: $i] : (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)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[116])).
% 0.20/0.44 tff(118,plain,
% 0.20/0.44 (![Y: $i, X: $i] : (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))) <=> ![Y: $i, X: $i] : (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)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(119,plain,
% 0.20/0.44 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) <=> (product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))), (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) <=> ((product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_2)))), rewrite(((product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_2)) <=> (product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))), (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) <=> (product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))))), ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) <=> ((product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_3)))), rewrite(((product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_3)) <=> (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))), ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) <=> (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))))), (((((((~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)) <=> ((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)))), rewrite(((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_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))), (((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) | product(X, Y, e_4)) <=> (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)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(120,plain,
% 0.20/0.44 (![Y: $i, X: $i] : ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) | product(X, Y, e_4)) <=> ![Y: $i, X: $i] : (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)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[119])).
% 0.20/0.44 tff(121,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')).
% 0.20/0.44 tff(122,plain,
% 0.20/0.44 (![Y: $i, X: $i] : (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)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.20/0.44 tff(123,plain,
% 0.20/0.44 (![Y: $i, X: $i] : (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)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[122, 118])).
% 0.20/0.44 tff(124,plain,(
% 0.20/0.44 ![Y: $i, X: $i] : (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)))),
% 0.20/0.45 inference(skolemize,[status(sab)],[123])).
% 0.20/0.45 tff(125,plain,
% 0.20/0.45 (![Y: $i, X: $i] : (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)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[124, 117])).
% 0.20/0.45 tff(126,plain,
% 0.20/0.45 (group_element(e_3) <=> group_element(e_3)),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(127,axiom,(group_element(e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_3')).
% 0.20/0.45 tff(128,plain,
% 0.20/0.45 (group_element(e_3)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.20/0.45 tff(129,plain,
% 0.20/0.45 (group_element(e_1) <=> group_element(e_1)),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(130,axiom,(group_element(e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_1')).
% 0.20/0.45 tff(131,plain,
% 0.20/0.45 (group_element(e_1)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.20/0.45 tff(132,plain,
% 0.20/0.45 (((~![Y: $i, X: $i] : (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)))) | ((~group_element(e_3)) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | (~group_element(e_1)) | product(e_1, e_3, e_1))) <=> ((~![Y: $i, X: $i] : (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)))) | (~group_element(e_3)) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | (~group_element(e_1)) | product(e_1, e_3, e_1))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(133,plain,
% 0.20/0.45 ((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) | (~group_element(e_3)) | (~group_element(e_1))) <=> ((~group_element(e_3)) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | (~group_element(e_1)) | product(e_1, e_3, e_1))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(134,plain,
% 0.20/0.45 (((~![Y: $i, X: $i] : (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(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) | (~group_element(e_3)) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (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)))) | ((~group_element(e_3)) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | (~group_element(e_1)) | product(e_1, e_3, e_1)))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[133])).
% 0.20/0.45 tff(135,plain,
% 0.20/0.45 (((~![Y: $i, X: $i] : (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(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) | (~group_element(e_3)) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (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)))) | (~group_element(e_3)) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | (~group_element(e_1)) | product(e_1, e_3, e_1))),
% 0.20/0.45 inference(transitivity,[status(thm)],[134, 132])).
% 0.20/0.45 tff(136,plain,
% 0.20/0.45 ((~![Y: $i, X: $i] : (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(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) | (~group_element(e_3)) | (~group_element(e_1)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(137,plain,
% 0.20/0.45 ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_3)) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | (~group_element(e_1)) | product(e_1, e_3, e_1)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.20/0.45 tff(138,plain,
% 0.20/0.45 (product(e_1, e_3, e_4) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[137, 131, 128, 125])).
% 0.20/0.45 tff(139,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[138, 115, 90, 60, 51])).
% 0.20/0.45 tff(140,plain,((~product(e_3, e_1, e_4)) | product(e_1, e_3, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(141,plain,
% 0.20/0.45 (~product(e_3, e_1, e_4)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[140, 51])).
% 0.20/0.45 tff(142,assumption,(product(e_3, e_1, e_1)), introduced(assumption)).
% 0.20/0.45 tff(143,plain,
% 0.20/0.45 (((~![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_1, e_1)) | (~product(e_3, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_1, e_1)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(144,plain,
% 0.20/0.45 ((~![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_1, e_1)) | (~product(e_3, e_1, e_1)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(145,plain,
% 0.20/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_1, e_1))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.20/0.45 tff(146,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[145, 55, 20, 10, 142])).
% 0.20/0.45 tff(147,plain,(~product(e_3, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(148,plain,
% 0.20/0.45 (((~![Y: $i, X: $i] : (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)))) | ((~group_element(e_3)) | product(e_3, e_1, e_2) | (~group_element(e_1)) | product(e_3, e_1, e_3) | product(e_3, e_1, e_1) | product(e_3, e_1, e_4))) <=> ((~![Y: $i, X: $i] : (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)))) | (~group_element(e_3)) | product(e_3, e_1, e_2) | (~group_element(e_1)) | product(e_3, e_1, e_3) | product(e_3, e_1, e_1) | product(e_3, e_1, e_4))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(149,plain,
% 0.20/0.45 ((product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_3))) <=> ((~group_element(e_3)) | product(e_3, e_1, e_2) | (~group_element(e_1)) | product(e_3, e_1, e_3) | product(e_3, e_1, e_1) | product(e_3, e_1, e_4))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(150,plain,
% 0.20/0.45 (((~![Y: $i, X: $i] : (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(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (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)))) | ((~group_element(e_3)) | product(e_3, e_1, e_2) | (~group_element(e_1)) | product(e_3, e_1, e_3) | product(e_3, e_1, e_1) | product(e_3, e_1, e_4)))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[149])).
% 0.20/0.45 tff(151,plain,
% 0.20/0.45 (((~![Y: $i, X: $i] : (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(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (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)))) | (~group_element(e_3)) | product(e_3, e_1, e_2) | (~group_element(e_1)) | product(e_3, e_1, e_3) | product(e_3, e_1, e_1) | product(e_3, e_1, e_4))),
% 0.20/0.45 inference(transitivity,[status(thm)],[150, 148])).
% 0.20/0.45 tff(152,plain,
% 0.20/0.45 ((~![Y: $i, X: $i] : (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(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_3)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(153,plain,
% 0.20/0.45 ((~![Y: $i, X: $i] : (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)))) | (~group_element(e_3)) | product(e_3, e_1, e_2) | (~group_element(e_1)) | product(e_3, e_1, e_3) | product(e_3, e_1, e_1) | product(e_3, e_1, e_4)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.20/0.45 tff(154,plain,
% 0.20/0.45 (product(e_3, e_1, e_2) | product(e_3, e_1, e_3) | product(e_3, e_1, e_1) | product(e_3, e_1, e_4)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[153, 131, 128, 125])).
% 0.20/0.45 tff(155,plain,
% 0.20/0.45 (product(e_3, e_1, e_2) | product(e_3, e_1, e_4)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[154, 50, 147])).
% 0.20/0.45 tff(156,plain,
% 0.20/0.45 (product(e_3, e_1, e_2)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[155, 141])).
% 0.20/0.45 tff(157,assumption,(product(e_3, e_1, e_2)), introduced(assumption)).
% 0.20/0.45 tff(158,assumption,(product(e_3, e_4, e_2)), introduced(assumption)).
% 0.20/0.45 tff(159,plain,
% 0.20/0.45 ((~equalish(e_4, e_1)) <=> (~equalish(e_4, e_1))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(160,axiom,(~equalish(e_4, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_1')).
% 0.20/0.45 tff(161,plain,
% 0.20/0.45 (~equalish(e_4, e_1)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.20/0.45 tff(162,plain,
% 0.20/0.45 (((~![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_3, e_4, e_2)) | (~product(e_3, e_1, e_2)))) <=> ((~![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_3, e_4, e_2)) | (~product(e_3, e_1, e_2)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(163,plain,
% 0.20/0.46 ((equalish(e_4, e_1) | (~product(e_3, e_1, e_2)) | (~product(e_3, e_4, e_2))) <=> (equalish(e_4, e_1) | (~product(e_3, e_4, e_2)) | (~product(e_3, e_1, e_2)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(164,plain,
% 0.20/0.46 (((~![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_3, e_1, e_2)) | (~product(e_3, e_4, e_2)))) <=> ((~![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_3, e_4, e_2)) | (~product(e_3, e_1, e_2))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[163])).
% 0.20/0.46 tff(165,plain,
% 0.20/0.46 (((~![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_3, e_1, e_2)) | (~product(e_3, e_4, e_2)))) <=> ((~![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_3, e_4, e_2)) | (~product(e_3, e_1, e_2)))),
% 0.20/0.46 inference(transitivity,[status(thm)],[164, 162])).
% 0.20/0.46 tff(166,plain,
% 0.20/0.46 ((~![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_3, e_1, e_2)) | (~product(e_3, e_4, e_2)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(167,plain,
% 0.20/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_1) | (~product(e_3, e_4, e_2)) | (~product(e_3, e_1, e_2))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.20/0.46 tff(168,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[167, 161, 42, 158, 157])).
% 0.20/0.46 tff(169,plain,((~product(e_3, e_4, e_2)) | (~product(e_3, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(170,plain,
% 0.20/0.46 (~product(e_3, e_4, e_2)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[169, 156])).
% 0.20/0.46 tff(171,plain,
% 0.20/0.46 (group_element(e_4) <=> group_element(e_4)),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(172,axiom,(group_element(e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_4')).
% 0.20/0.46 tff(173,plain,
% 0.20/0.46 (group_element(e_4)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[172, 171])).
% 0.20/0.46 tff(174,plain,
% 0.20/0.46 (((~![Y: $i, X: $i] : (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)))) | ((~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) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : (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)))) | (~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) | (~group_element(e_4)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(175,plain,
% 0.20/0.46 ((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) | (~group_element(e_4)) | (~group_element(e_3))) <=> ((~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) | (~group_element(e_4)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(176,plain,
% 0.20/0.46 (((~![Y: $i, X: $i] : (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(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) | (~group_element(e_4)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (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)))) | ((~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) | (~group_element(e_4))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[175])).
% 0.20/0.46 tff(177,plain,
% 0.20/0.46 (((~![Y: $i, X: $i] : (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(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) | (~group_element(e_4)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (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)))) | (~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) | (~group_element(e_4)))),
% 0.20/0.46 inference(transitivity,[status(thm)],[176, 174])).
% 0.20/0.46 tff(178,plain,
% 0.20/0.46 ((~![Y: $i, X: $i] : (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(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) | (~group_element(e_4)) | (~group_element(e_3)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(179,plain,
% 0.20/0.46 ((~![Y: $i, X: $i] : (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)))) | (~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) | (~group_element(e_4))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.20/0.46 tff(180,plain,
% 0.20/0.46 (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)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[179, 128, 173, 125])).
% 0.20/0.46 tff(181,plain,
% 0.20/0.46 (product(e_3, e_4, e_4) | product(e_3, e_4, e_2) | product(e_3, e_4, e_1)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[180, 73])).
% 0.20/0.46 tff(182,plain,
% 0.20/0.46 (product(e_3, e_4, e_2) | product(e_3, e_4, e_1)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[181, 104])).
% 0.20/0.46 tff(183,plain,
% 0.20/0.46 (product(e_3, e_4, e_1)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[182, 170])).
% 0.20/0.46 tff(184,plain,
% 0.20/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_3) | (~product(e_3, e_4, e_1)) | (~product(e_4, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_3) | (~product(e_3, e_4, e_1)) | (~product(e_4, e_3, e_3)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(185,plain,
% 0.20/0.46 (((~product(e_3, e_4, e_1)) | product(e_3, e_1, e_3) | (~product(e_4, e_3, e_3))) <=> (product(e_3, e_1, e_3) | (~product(e_3, e_4, e_1)) | (~product(e_4, e_3, e_3)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(186,plain,
% 0.20/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_4, e_1)) | product(e_3, e_1, e_3) | (~product(e_4, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_3) | (~product(e_3, e_4, e_1)) | (~product(e_4, e_3, e_3))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[185])).
% 0.20/0.46 tff(187,plain,
% 0.20/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_4, e_1)) | product(e_3, e_1, e_3) | (~product(e_4, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_3) | (~product(e_3, e_4, e_1)) | (~product(e_4, e_3, e_3)))),
% 0.20/0.46 inference(transitivity,[status(thm)],[186, 184])).
% 0.20/0.46 tff(188,plain,
% 0.20/0.46 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_4, e_1)) | product(e_3, e_1, e_3) | (~product(e_4, e_3, e_3)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(189,plain,
% 0.20/0.46 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_3) | (~product(e_3, e_4, e_1)) | (~product(e_4, e_3, e_3))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[188, 187])).
% 0.20/0.46 tff(190,plain,
% 0.20/0.46 (~product(e_4, e_3, e_3)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[189, 83, 183, 50])).
% 0.20/0.46 tff(191,plain,
% 0.20/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_3, e_3)) | product(e_4, e_3, e_3) | (~product(e_3, e_3, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_3, e_3, e_3)) | product(e_4, e_3, e_3) | (~product(e_3, e_3, e_4)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(192,plain,
% 0.20/0.46 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_3, e_3)) | product(e_4, e_3, e_3) | (~product(e_3, e_3, e_4)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(193,plain,
% 0.20/0.46 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_3, e_3, e_3)) | product(e_4, e_3, e_3) | (~product(e_3, e_3, e_4))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[192, 191])).
% 0.20/0.46 tff(194,plain,
% 0.20/0.46 (~product(e_3, e_3, e_4)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[193, 83, 32, 190])).
% 0.20/0.46 tff(195,assumption,(product(e_2, e_4, e_1)), introduced(assumption)).
% 0.20/0.46 tff(196,assumption,(product(e_3, e_4, e_1)), introduced(assumption)).
% 0.20/0.46 tff(197,plain,
% 0.20/0.46 ((~equalish(e_2, e_3)) <=> (~equalish(e_2, e_3))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(198,axiom,(~equalish(e_2, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_3')).
% 0.20/0.46 tff(199,plain,
% 0.20/0.46 (~equalish(e_2, e_3)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[198, 197])).
% 0.20/0.46 tff(200,plain,
% 0.20/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_3) | (~product(e_2, e_4, e_1)) | (~product(e_3, e_4, 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_3) | (~product(e_2, e_4, e_1)) | (~product(e_3, e_4, e_1)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(201,plain,
% 0.20/0.46 ((equalish(e_2, e_3) | (~product(e_3, e_4, e_1)) | (~product(e_2, e_4, e_1))) <=> (equalish(e_2, e_3) | (~product(e_2, e_4, e_1)) | (~product(e_3, e_4, e_1)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(202,plain,
% 0.20/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_3) | (~product(e_3, e_4, e_1)) | (~product(e_2, e_4, 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_3) | (~product(e_2, e_4, e_1)) | (~product(e_3, e_4, e_1))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[201])).
% 0.20/0.47 tff(203,plain,
% 0.20/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_3) | (~product(e_3, e_4, e_1)) | (~product(e_2, e_4, 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_3) | (~product(e_2, e_4, e_1)) | (~product(e_3, e_4, e_1)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[202, 200])).
% 0.20/0.47 tff(204,plain,
% 0.20/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_3) | (~product(e_3, e_4, e_1)) | (~product(e_2, e_4, e_1)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(205,plain,
% 0.20/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_3) | (~product(e_2, e_4, e_1)) | (~product(e_3, e_4, e_1))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[204, 203])).
% 0.20/0.47 tff(206,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[205, 199, 20, 196, 195])).
% 0.20/0.47 tff(207,plain,((~product(e_2, e_4, e_1)) | (~product(e_3, e_4, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(208,plain,
% 0.20/0.47 (~product(e_2, e_4, e_1)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[207, 183])).
% 0.20/0.47 tff(209,assumption,(product(e_2, e_4, e_2)), introduced(assumption)).
% 0.20/0.47 tff(210,plain,
% 0.20/0.47 ((~![X: $i] : product(X, X, X)) | product(e_2, e_2, e_2)),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(211,plain,
% 0.20/0.47 (product(e_2, e_2, e_2)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[210, 8])).
% 0.20/0.47 tff(212,plain,
% 0.20/0.47 ((~equalish(e_4, e_2)) <=> (~equalish(e_4, e_2))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(213,axiom,(~equalish(e_4, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_2')).
% 0.20/0.47 tff(214,plain,
% 0.20/0.47 (~equalish(e_4, e_2)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[213, 212])).
% 0.20/0.47 tff(215,plain,
% 0.20/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_4, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_4, e_2)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(216,plain,
% 0.20/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_4, e_2)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(217,plain,
% 0.20/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_4, e_2))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[216, 215])).
% 0.20/0.47 tff(218,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[217, 214, 42, 211, 209])).
% 0.20/0.47 tff(219,plain,(~product(e_2, e_4, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(220,assumption,(product(e_2, e_4, e_4)), introduced(assumption)).
% 0.20/0.47 tff(221,plain,
% 0.20/0.47 ((~equalish(e_2, e_4)) <=> (~equalish(e_2, e_4))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(222,axiom,(~equalish(e_2, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_4')).
% 0.20/0.47 tff(223,plain,
% 0.20/0.47 (~equalish(e_2, e_4)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[222, 221])).
% 0.20/0.47 tff(224,plain,
% 0.20/0.47 (((~![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_2, e_4, e_4)) | (~product(e_4, 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_2, e_4) | (~product(e_2, e_4, e_4)) | (~product(e_4, e_4, e_4)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(225,plain,
% 0.20/0.47 ((equalish(e_2, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_2, e_4, e_4))) <=> (equalish(e_2, e_4) | (~product(e_2, e_4, e_4)) | (~product(e_4, e_4, e_4)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(226,plain,
% 0.20/0.47 (((~![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_4, e_4)) | (~product(e_2, 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_2, e_4) | (~product(e_2, e_4, e_4)) | (~product(e_4, e_4, e_4))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[225])).
% 0.20/0.47 tff(227,plain,
% 0.20/0.47 (((~![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_4, e_4)) | (~product(e_2, 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_2, e_4) | (~product(e_2, e_4, e_4)) | (~product(e_4, e_4, e_4)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[226, 224])).
% 0.20/0.47 tff(228,plain,
% 0.20/0.47 ((~![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_4, e_4)) | (~product(e_2, e_4, e_4)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(229,plain,
% 0.20/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_4) | (~product(e_2, e_4, e_4)) | (~product(e_4, e_4, e_4))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[228, 227])).
% 0.20/0.47 tff(230,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[229, 223, 20, 220, 92])).
% 0.20/0.47 tff(231,plain,(~product(e_2, e_4, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(232,plain,
% 0.20/0.47 (group_element(e_2) <=> group_element(e_2)),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(233,axiom,(group_element(e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_2')).
% 0.20/0.47 tff(234,plain,
% 0.20/0.47 (group_element(e_2)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[233, 232])).
% 0.20/0.47 tff(235,plain,
% 0.20/0.47 (((~![Y: $i, X: $i] : (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)))) | ((~group_element(e_4)) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | (~group_element(e_2)) | product(e_2, e_4, e_4) | product(e_2, e_4, e_3))) <=> ((~![Y: $i, X: $i] : (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)))) | (~group_element(e_4)) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | (~group_element(e_2)) | product(e_2, e_4, e_4) | product(e_2, e_4, e_3))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(236,plain,
% 0.20/0.47 ((product(e_2, e_4, e_4) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_2))) <=> ((~group_element(e_4)) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | (~group_element(e_2)) | product(e_2, e_4, e_4) | product(e_2, e_4, e_3))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(237,plain,
% 0.20/0.47 (((~![Y: $i, X: $i] : (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(e_2, e_4, e_4) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : (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)))) | ((~group_element(e_4)) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | (~group_element(e_2)) | product(e_2, e_4, e_4) | product(e_2, e_4, e_3)))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[236])).
% 0.20/0.47 tff(238,plain,
% 0.20/0.47 (((~![Y: $i, X: $i] : (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(e_2, e_4, e_4) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : (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)))) | (~group_element(e_4)) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | (~group_element(e_2)) | product(e_2, e_4, e_4) | product(e_2, e_4, e_3))),
% 0.20/0.47 inference(transitivity,[status(thm)],[237, 235])).
% 0.20/0.47 tff(239,plain,
% 0.20/0.47 ((~![Y: $i, X: $i] : (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(e_2, e_4, e_4) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_2)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(240,plain,
% 0.20/0.47 ((~![Y: $i, X: $i] : (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)))) | (~group_element(e_4)) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | (~group_element(e_2)) | product(e_2, e_4, e_4) | product(e_2, e_4, e_3)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[239, 238])).
% 0.20/0.47 tff(241,plain,
% 0.20/0.47 (product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | product(e_2, e_4, e_4) | product(e_2, e_4, e_3)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[240, 234, 173, 125])).
% 0.20/0.47 tff(242,plain,
% 0.20/0.47 (product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | product(e_2, e_4, e_3)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[241, 231])).
% 0.20/0.47 tff(243,plain,
% 0.20/0.47 (product(e_2, e_4, e_1) | product(e_2, e_4, e_3)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[242, 219])).
% 0.20/0.47 tff(244,plain,
% 0.20/0.47 (product(e_2, e_4, e_3)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[243, 208])).
% 0.20/0.47 tff(245,assumption,(product(e_4, e_2, e_1)), introduced(assumption)).
% 0.20/0.47 tff(246,assumption,(product(e_2, e_4, e_3)), introduced(assumption)).
% 0.20/0.47 tff(247,plain,
% 0.20/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_4, e_3)) | product(e_1, e_3, e_2) | (~product(e_4, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_2, e_4, e_3)) | product(e_1, e_3, e_2) | (~product(e_4, e_2, e_1)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(248,plain,
% 0.20/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_4, e_3)) | product(e_1, e_3, e_2) | (~product(e_4, e_2, e_1)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(249,plain,
% 0.20/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_2, e_4, e_3)) | product(e_1, e_3, e_2) | (~product(e_4, e_2, e_1))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[248, 247])).
% 0.20/0.47 tff(250,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[249, 83, 246, 51, 245])).
% 0.20/0.47 tff(251,plain,(product(e_1, e_3, e_2) | (~product(e_2, e_4, e_3)) | (~product(e_4, e_2, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(252,plain,
% 0.20/0.47 (~product(e_4, e_2, e_1)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[251, 244, 51])).
% 0.20/0.47 tff(253,assumption,(product(e_4, e_2, e_4)), introduced(assumption)).
% 0.20/0.47 tff(254,plain,
% 0.20/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_3, e_4, e_4) | (~product(e_2, e_4, e_3)) | (~product(e_4, e_2, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_3, e_4, e_4) | (~product(e_2, e_4, e_3)) | (~product(e_4, e_2, e_4)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(255,plain,
% 0.20/0.47 (((~product(e_4, e_2, e_4)) | product(e_3, e_4, e_4) | (~product(e_2, e_4, e_3))) <=> (product(e_3, e_4, e_4) | (~product(e_2, e_4, e_3)) | (~product(e_4, e_2, e_4)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(256,plain,
% 0.20/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_4, e_2, e_4)) | product(e_3, e_4, e_4) | (~product(e_2, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_3, e_4, e_4) | (~product(e_2, e_4, e_3)) | (~product(e_4, e_2, e_4))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[255])).
% 0.20/0.47 tff(257,plain,
% 0.20/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_4, e_2, e_4)) | product(e_3, e_4, e_4) | (~product(e_2, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_3, e_4, e_4) | (~product(e_2, e_4, e_3)) | (~product(e_4, e_2, e_4)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[256, 254])).
% 0.20/0.47 tff(258,plain,
% 0.20/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_4, e_2, e_4)) | product(e_3, e_4, e_4) | (~product(e_2, e_4, e_3)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(259,plain,
% 0.20/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_3, e_4, e_4) | (~product(e_2, e_4, e_3)) | (~product(e_4, e_2, e_4))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[258, 257])).
% 0.20/0.47 tff(260,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[259, 83, 104, 246, 253])).
% 0.20/0.47 tff(261,plain,((~product(e_4, e_2, e_4)) | (~product(e_2, e_4, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(262,plain,
% 0.20/0.47 (~product(e_4, e_2, e_4)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[261, 244])).
% 0.20/0.47 tff(263,assumption,(product(e_4, e_2, e_2)), introduced(assumption)).
% 0.20/0.47 tff(264,plain,
% 0.20/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_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_2, e_2, e_2)) | (~product(e_4, e_2, e_2)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(265,plain,
% 0.20/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_4, e_2, e_2)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(266,plain,
% 0.20/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_4, e_2, e_2))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[265, 264])).
% 0.20/0.47 tff(267,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[266, 214, 20, 211, 263])).
% 0.20/0.47 tff(268,plain,(~product(e_4, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(269,plain,
% 0.20/0.47 (((~![Y: $i, X: $i] : (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)))) | ((~group_element(e_4)) | (~group_element(e_2)) | 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] : (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)))) | (~group_element(e_4)) | (~group_element(e_2)) | 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))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(270,plain,
% 0.20/0.47 ((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) | (~group_element(e_2)) | (~group_element(e_4))) <=> ((~group_element(e_4)) | (~group_element(e_2)) | 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))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(271,plain,
% 0.20/0.47 (((~![Y: $i, X: $i] : (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(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) | (~group_element(e_2)) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : (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)))) | ((~group_element(e_4)) | (~group_element(e_2)) | 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)))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[270])).
% 0.20/0.48 tff(272,plain,
% 0.20/0.48 (((~![Y: $i, X: $i] : (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(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) | (~group_element(e_2)) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : (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)))) | (~group_element(e_4)) | (~group_element(e_2)) | 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))),
% 0.20/0.48 inference(transitivity,[status(thm)],[271, 269])).
% 0.20/0.48 tff(273,plain,
% 0.20/0.48 ((~![Y: $i, X: $i] : (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(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) | (~group_element(e_2)) | (~group_element(e_4)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(274,plain,
% 0.20/0.48 ((~![Y: $i, X: $i] : (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)))) | (~group_element(e_4)) | (~group_element(e_2)) | 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)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[273, 272])).
% 0.20/0.48 tff(275,plain,
% 0.20/0.48 (product(e_4, e_2, e_4) | product(e_4, e_2, e_3) | product(e_4, e_2, e_1)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[274, 234, 173, 125, 268])).
% 0.20/0.48 tff(276,plain,
% 0.20/0.48 (product(e_4, e_2, e_3)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[275, 262, 252])).
% 0.20/0.48 tff(277,plain,
% 0.20/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_4, e_3)) | product(e_3, e_3, e_4) | (~product(e_4, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_2, e_4, e_3)) | product(e_3, e_3, e_4) | (~product(e_4, e_2, e_3)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(278,plain,
% 0.20/0.48 (((~product(e_4, e_2, e_3)) | product(e_3, e_3, e_4) | (~product(e_2, e_4, e_3))) <=> ((~product(e_2, e_4, e_3)) | product(e_3, e_3, e_4) | (~product(e_4, e_2, e_3)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(279,plain,
% 0.20/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_4, e_2, e_3)) | product(e_3, e_3, e_4) | (~product(e_2, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_4, e_3)) | product(e_3, e_3, e_4) | (~product(e_4, e_2, e_3))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[278])).
% 0.20/0.48 tff(280,plain,
% 0.20/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_4, e_2, e_3)) | product(e_3, e_3, e_4) | (~product(e_2, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_2, e_4, e_3)) | product(e_3, e_3, e_4) | (~product(e_4, e_2, e_3)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[279, 277])).
% 0.20/0.48 tff(281,plain,
% 0.20/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_4, e_2, e_3)) | product(e_3, e_3, e_4) | (~product(e_2, e_4, e_3)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(282,plain,
% 0.20/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_2, e_4, e_3)) | product(e_3, e_3, e_4) | (~product(e_4, e_2, e_3))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[281, 280])).
% 0.20/0.48 tff(283,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[282, 83, 244, 276, 194])).
% 0.20/0.48 tff(284,plain,(product(e_1, e_3, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(285,assumption,(product(e_1, e_2, e_2)), introduced(assumption)).
% 0.20/0.48 tff(286,plain,
% 0.20/0.48 ((~equalish(e_1, e_2)) <=> (~equalish(e_1, e_2))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(287,axiom,(~equalish(e_1, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_2')).
% 0.20/0.48 tff(288,plain,
% 0.20/0.48 (~equalish(e_1, e_2)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[287, 286])).
% 0.20/0.48 tff(289,plain,
% 0.20/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_1, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_1, e_2, e_2)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(290,plain,
% 0.20/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_1, e_2, e_2)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(291,plain,
% 0.20/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_1, e_2, e_2))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[290, 289])).
% 0.20/0.48 tff(292,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[291, 288, 20, 211, 285])).
% 0.20/0.48 tff(293,plain,(~product(e_1, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(294,plain,
% 0.20/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_2, e_2)) | product(e_1, e_2, e_2) | (~product(e_2, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_2, e_2, e_2)) | product(e_1, e_2, e_2) | (~product(e_2, e_2, e_1)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(295,plain,
% 0.20/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_2, e_2)) | product(e_1, e_2, e_2) | (~product(e_2, e_2, e_1)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(296,plain,
% 0.20/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_2, e_2, e_2)) | product(e_1, e_2, e_2) | (~product(e_2, e_2, e_1))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[295, 294])).
% 0.20/0.48 tff(297,plain,
% 0.20/0.48 (~product(e_2, e_2, e_1)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[296, 83, 211, 293])).
% 0.20/0.48 tff(298,assumption,(product(e_1, e_3, e_2)), introduced(assumption)).
% 0.20/0.48 tff(299,plain,
% 0.20/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_2)) | product(e_2, e_2, e_1) | (~product(e_3, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_1, e_3, e_2)) | product(e_2, e_2, e_1) | (~product(e_3, e_1, e_2)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(300,plain,
% 0.20/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_2)) | product(e_2, e_2, e_1) | (~product(e_3, e_1, e_2)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(301,plain,
% 0.20/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_1, e_3, e_2)) | product(e_2, e_2, e_1) | (~product(e_3, e_1, e_2))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[300, 299])).
% 0.20/0.48 tff(302,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[301, 83, 298, 157, 297])).
% 0.20/0.48 tff(303,plain,((~product(e_1, e_3, e_2)) | (~product(e_3, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(304,plain,
% 0.20/0.48 (~product(e_3, e_1, e_2)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[303, 284])).
% 0.20/0.48 tff(305,plain,
% 0.20/0.48 (product(e_3, e_1, e_4)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[155, 304])).
% 0.20/0.48 tff(306,plain,
% 0.20/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_3) | (~product(e_3, e_1, e_4)) | (~product(e_2, e_1, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_3) | (~product(e_3, e_1, e_4)) | (~product(e_2, e_1, e_4)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(307,plain,
% 0.20/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_3) | (~product(e_3, e_1, e_4)) | (~product(e_2, e_1, e_4)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(308,plain,
% 0.20/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_3) | (~product(e_3, e_1, e_4)) | (~product(e_2, e_1, e_4))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[307, 306])).
% 0.20/0.48 tff(309,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[308, 199, 20, 305, 29])).
% 0.20/0.48 tff(310,plain,(~product(e_2, e_1, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(311,assumption,(product(e_2, e_1, e_2)), introduced(assumption)).
% 0.20/0.48 tff(312,plain,
% 0.20/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(313,plain,
% 0.20/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(314,plain,
% 0.20/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[313, 312])).
% 0.20/0.48 tff(315,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[314, 288, 42, 211, 311])).
% 0.20/0.48 tff(316,plain,(~product(e_2, e_1, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(317,plain,
% 0.20/0.48 (((~![Y: $i, X: $i] : (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)))) | ((~group_element(e_2)) | (~group_element(e_1)) | product(e_2, e_1, e_4) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | product(e_2, e_1, e_3))) <=> ((~![Y: $i, X: $i] : (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)))) | (~group_element(e_2)) | (~group_element(e_1)) | product(e_2, e_1, e_4) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | product(e_2, e_1, e_3))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(318,plain,
% 0.20/0.48 ((product(e_2, e_1, e_4) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_2))) <=> ((~group_element(e_2)) | (~group_element(e_1)) | product(e_2, e_1, e_4) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | product(e_2, e_1, e_3))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(319,plain,
% 0.20/0.48 (((~![Y: $i, X: $i] : (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(e_2, e_1, e_4) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : (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)))) | ((~group_element(e_2)) | (~group_element(e_1)) | product(e_2, e_1, e_4) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | product(e_2, e_1, e_3)))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[318])).
% 0.20/0.48 tff(320,plain,
% 0.20/0.48 (((~![Y: $i, X: $i] : (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(e_2, e_1, e_4) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : (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)))) | (~group_element(e_2)) | (~group_element(e_1)) | product(e_2, e_1, e_4) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | product(e_2, e_1, e_3))),
% 0.20/0.48 inference(transitivity,[status(thm)],[319, 317])).
% 0.20/0.48 tff(321,plain,
% 0.20/0.48 ((~![Y: $i, X: $i] : (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(e_2, e_1, e_4) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_2)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(322,plain,
% 0.20/0.48 ((~![Y: $i, X: $i] : (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)))) | (~group_element(e_2)) | (~group_element(e_1)) | product(e_2, e_1, e_4) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | product(e_2, e_1, e_3)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[321, 320])).
% 0.20/0.48 tff(323,plain,
% 0.20/0.48 (product(e_2, e_1, e_4) | product(e_2, e_1, e_1) | product(e_2, e_1, e_3)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[322, 131, 234, 125, 316])).
% 0.20/0.48 tff(324,plain,
% 0.20/0.48 (product(e_2, e_1, e_1) | product(e_2, e_1, e_3)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[323, 310])).
% 0.20/0.48 tff(325,plain,
% 0.20/0.48 (product(e_2, e_1, e_3)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[324, 28])).
% 0.20/0.48 tff(326,plain,
% 0.20/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_1, e_1)) | product(e_2, e_1, e_1) | (~product(e_1, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_1, e_1, e_1)) | product(e_2, e_1, e_1) | (~product(e_1, e_1, e_2)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(327,plain,
% 0.20/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_1, e_1)) | product(e_2, e_1, e_1) | (~product(e_1, e_1, e_2)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(328,plain,
% 0.20/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_1, e_1, e_1)) | product(e_2, e_1, e_1) | (~product(e_1, e_1, e_2))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[327, 326])).
% 0.20/0.48 tff(329,plain,
% 0.20/0.48 (~product(e_1, e_1, e_2)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[328, 83, 10, 28])).
% 0.20/0.48 tff(330,assumption,(~product(e_4, e_2, e_1)), introduced(assumption)).
% 0.20/0.48 tff(331,plain,
% 0.20/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_4)) | product(e_4, e_2, e_1) | (~product(e_1, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_4)) | product(e_4, e_2, e_1) | (~product(e_1, e_3, e_2)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(332,plain,
% 0.20/0.48 (((~product(e_1, e_3, e_2)) | product(e_4, e_2, e_1) | (~product(e_3, e_1, e_4))) <=> ((~product(e_3, e_1, e_4)) | product(e_4, e_2, e_1) | (~product(e_1, e_3, e_2)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(333,plain,
% 0.20/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_2)) | product(e_4, e_2, e_1) | (~product(e_3, e_1, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_4)) | product(e_4, e_2, e_1) | (~product(e_1, e_3, e_2))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[332])).
% 0.20/0.49 tff(334,plain,
% 0.20/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_2)) | product(e_4, e_2, e_1) | (~product(e_3, e_1, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_4)) | product(e_4, e_2, e_1) | (~product(e_1, e_3, e_2)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[333, 331])).
% 0.20/0.49 tff(335,plain,
% 0.20/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_2)) | product(e_4, e_2, e_1) | (~product(e_3, e_1, e_4)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(336,plain,
% 0.20/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_4)) | product(e_4, e_2, e_1) | (~product(e_1, e_3, e_2))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[335, 334])).
% 0.20/0.49 tff(337,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[336, 83, 284, 305, 330])).
% 0.20/0.49 tff(338,plain,(product(e_4, e_2, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(339,plain,
% 0.20/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_4, e_1)) | (~product(e_4, e_2, e_1)) | product(e_1, e_1, e_2))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_2, e_4, e_1)) | (~product(e_4, e_2, e_1)) | product(e_1, e_1, e_2))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(340,plain,
% 0.20/0.49 (((~product(e_2, e_4, e_1)) | product(e_1, e_1, e_2) | (~product(e_4, e_2, e_1))) <=> ((~product(e_2, e_4, e_1)) | (~product(e_4, e_2, e_1)) | product(e_1, e_1, e_2))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(341,plain,
% 0.20/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_4, e_1)) | product(e_1, e_1, e_2) | (~product(e_4, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_4, e_1)) | (~product(e_4, e_2, e_1)) | product(e_1, e_1, e_2)))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[340])).
% 0.20/0.49 tff(342,plain,
% 0.20/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_4, e_1)) | product(e_1, e_1, e_2) | (~product(e_4, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_2, e_4, e_1)) | (~product(e_4, e_2, e_1)) | product(e_1, e_1, e_2))),
% 0.20/0.49 inference(transitivity,[status(thm)],[341, 339])).
% 0.20/0.49 tff(343,plain,
% 0.20/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_4, e_1)) | product(e_1, e_1, e_2) | (~product(e_4, e_2, e_1)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(344,plain,
% 0.20/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_2, e_4, e_1)) | (~product(e_4, e_2, e_1)) | product(e_1, e_1, e_2)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[343, 342])).
% 0.20/0.49 tff(345,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[344, 83, 195, 338, 329])).
% 0.20/0.49 tff(346,plain,(~product(e_2, e_4, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(347,plain,
% 0.20/0.49 (product(e_2, e_4, e_3)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[243, 346])).
% 0.20/0.49 tff(348,plain,
% 0.20/0.49 (((~![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_2, e_4, e_3)) | (~product(e_2, e_1, e_3)))) <=> ((~![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_2, e_4, e_3)) | (~product(e_2, e_1, e_3)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(349,plain,
% 0.20/0.49 ((equalish(e_4, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_4, e_3))) <=> (equalish(e_4, e_1) | (~product(e_2, e_4, e_3)) | (~product(e_2, e_1, e_3)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(350,plain,
% 0.20/0.49 (((~![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_2, e_1, e_3)) | (~product(e_2, e_4, e_3)))) <=> ((~![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_2, e_4, e_3)) | (~product(e_2, e_1, e_3))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[349])).
% 0.20/0.49 tff(351,plain,
% 0.20/0.49 (((~![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_2, e_1, e_3)) | (~product(e_2, e_4, e_3)))) <=> ((~![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_2, e_4, e_3)) | (~product(e_2, e_1, e_3)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[350, 348])).
% 0.20/0.49 tff(352,plain,
% 0.20/0.49 ((~![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_2, e_1, e_3)) | (~product(e_2, e_4, e_3)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(353,plain,
% 0.20/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_1) | (~product(e_2, e_4, e_3)) | (~product(e_2, e_1, e_3))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[352, 351])).
% 0.20/0.49 tff(354,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[353, 161, 42, 347, 325])).
% 0.20/0.49 % SZS output end Proof
%------------------------------------------------------------------------------