TSTP Solution File: GRP129-2.004 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP129-2.004 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n004.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 22:26:12 EDT 2022
% Result : Unsatisfiable 0.20s 0.45s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.12 % Problem : GRP129-2.004 : TPTP v8.1.0. Released v1.2.0.
% 0.09/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n004.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 14:59:19 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.
% 0.20/0.45 % SZS status Unsatisfiable
% 0.20/0.45 % SZS output start Proof
% 0.20/0.45 tff(product_type, type, (
% 0.20/0.45 product: ( $i * $i * $i ) > $o)).
% 0.20/0.45 tff(e_1_type, type, (
% 0.20/0.45 e_1: $i)).
% 0.20/0.45 tff(e_4_type, type, (
% 0.20/0.45 e_4: $i)).
% 0.20/0.45 tff(e_2_type, type, (
% 0.20/0.45 e_2: $i)).
% 0.20/0.45 tff(e_3_type, type, (
% 0.20/0.45 e_3: $i)).
% 0.20/0.45 tff(next_type, type, (
% 0.20/0.45 next: ( $i * $i ) > $o)).
% 0.20/0.45 tff(greater_type, type, (
% 0.20/0.45 greater: ( $i * $i ) > $o)).
% 0.20/0.45 tff(group_element_type, type, (
% 0.20/0.45 group_element: $i > $o)).
% 0.20/0.45 tff(equalish_type, type, (
% 0.20/0.45 equalish: ( $i * $i ) > $o)).
% 0.20/0.45 tff(1,assumption,(product(e_1, e_2, e_4)), introduced(assumption)).
% 0.20/0.45 tff(2,assumption,(~product(e_4, e_1, e_4)), introduced(assumption)).
% 0.20/0.45 tff(3,plain,
% 0.20/0.45 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : refl((product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1))) <=> (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(4,plain,
% 0.20/0.45 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.45 tff(5,plain,
% 0.20/0.45 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(6,plain,
% 0.20/0.45 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : trans(monotonicity(rewrite(((~product(Y, X, Z1)) | (~product(X, Z1, Z2))) <=> ((~product(X, Z1, Z2)) | (~product(Y, X, Z1)))), ((((~product(Y, X, Z1)) | (~product(X, Z1, Z2))) | product(Z1, Y, Z2)) <=> (((~product(X, Z1, Z2)) | (~product(Y, X, Z1))) | product(Z1, Y, Z2)))), rewrite((((~product(X, Z1, Z2)) | (~product(Y, X, Z1))) | product(Z1, Y, Z2)) <=> (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))), ((((~product(Y, X, Z1)) | (~product(X, Z1, Z2))) | product(Z1, Y, Z2)) <=> (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(7,plain,
% 0.20/0.45 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(Y, X, Z1)) | (~product(X, Z1, Z2))) | product(Z1, Y, Z2)) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[6])).
% 0.20/0.45 tff(8,axiom,(![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(Y, X, Z1)) | (~product(X, Z1, Z2))) | product(Z1, Y, Z2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qg3')).
% 0.20/0.45 tff(9,plain,
% 0.20/0.45 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.20/0.45 tff(10,plain,
% 0.20/0.45 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.20/0.45 tff(11,plain,(
% 0.20/0.45 ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))),
% 0.20/0.45 inference(skolemize,[status(sab)],[10])).
% 0.20/0.45 tff(12,plain,
% 0.20/0.45 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.20/0.45 tff(13,plain,
% 0.20/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_1, e_4) | (~product(e_2, e_4, e_4)) | (~product(e_1, e_2, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_4, e_1, e_4) | (~product(e_2, e_4, e_4)) | (~product(e_1, e_2, e_4)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(14,plain,
% 0.20/0.45 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_1, e_4) | (~product(e_2, e_4, e_4)) | (~product(e_1, e_2, e_4)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(15,plain,
% 0.20/0.45 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_4, e_1, e_4) | (~product(e_2, e_4, e_4)) | (~product(e_1, e_2, e_4))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.20/0.45 tff(16,plain,
% 0.20/0.45 (product(e_4, e_1, e_4) | (~product(e_2, e_4, e_4)) | (~product(e_1, e_2, e_4))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[15, 12])).
% 0.20/0.45 tff(17,plain,
% 0.20/0.45 (~product(e_2, e_4, e_4)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[16, 2, 1])).
% 0.20/0.45 tff(18,plain,
% 0.20/0.45 (^[Y: $i, X: $i, X1: $i] : refl(((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y))) <=> ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(19,plain,
% 0.20/0.45 (![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y))) <=> ![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[18])).
% 0.20/0.45 tff(20,plain,
% 0.20/0.45 (![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y))) <=> ![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(21,plain,
% 0.20/0.45 (^[Y: $i, X: $i, X1: $i] : trans(monotonicity(rewrite(((~product(X, e_1, Y)) | (~next(X, X1))) <=> ((~next(X, X1)) | (~product(X, e_1, Y)))), ((((~product(X, e_1, Y)) | (~next(X, X1))) | (~greater(Y, X1))) <=> (((~next(X, X1)) | (~product(X, e_1, Y))) | (~greater(Y, X1))))), rewrite((((~next(X, X1)) | (~product(X, e_1, Y))) | (~greater(Y, X1))) <=> ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))), ((((~product(X, e_1, Y)) | (~next(X, X1))) | (~greater(Y, X1))) <=> ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(22,plain,
% 0.20/0.45 (![Y: $i, X: $i, X1: $i] : (((~product(X, e_1, Y)) | (~next(X, X1))) | (~greater(Y, X1))) <=> ![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[21])).
% 0.20/0.45 tff(23,axiom,(![Y: $i, X: $i, X1: $i] : (((~product(X, e_1, Y)) | (~next(X, X1))) | (~greater(Y, X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','no_redundancy')).
% 0.20/0.45 tff(24,plain,
% 0.20/0.45 (![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.20/0.45 tff(25,plain,
% 0.20/0.45 (![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.20/0.45 tff(26,plain,(
% 0.20/0.45 ![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))),
% 0.20/0.45 inference(skolemize,[status(sab)],[25])).
% 0.20/0.45 tff(27,plain,
% 0.20/0.45 (![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.20/0.45 tff(28,plain,
% 0.20/0.45 (greater(e_4, e_3) <=> greater(e_4, e_3)),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(29,axiom,(greater(e_4, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_greater_e_3')).
% 0.20/0.45 tff(30,plain,
% 0.20/0.45 (greater(e_4, e_3)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.20/0.45 tff(31,plain,
% 0.20/0.45 (next(e_2, e_3) <=> next(e_2, e_3)),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(32,axiom,(next(e_2, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_then_e_3')).
% 0.20/0.45 tff(33,plain,
% 0.20/0.45 (next(e_2, e_3)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.20/0.45 tff(34,plain,
% 0.20/0.45 (((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_4, e_3)) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4)))) <=> ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_4, e_3)) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(35,plain,
% 0.20/0.45 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_4, e_3)) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(36,plain,
% 0.20/0.45 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_4, e_3)) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.20/0.45 tff(37,plain,
% 0.20/0.45 (~product(e_2, e_1, e_4)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[36, 33, 30, 27])).
% 0.20/0.45 tff(38,plain,
% 0.20/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_2, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_4) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_2, e_4)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(39,plain,
% 0.20/0.45 ((product(e_2, e_1, e_4) | (~product(e_1, e_2, e_4)) | (~product(e_1, e_1, e_2))) <=> (product(e_2, e_1, e_4) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_2, e_4)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(40,plain,
% 0.20/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_1, e_2, e_4)) | (~product(e_1, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_2, e_4))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[39])).
% 0.20/0.45 tff(41,plain,
% 0.20/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_1, e_2, e_4)) | (~product(e_1, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_4) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_2, e_4)))),
% 0.20/0.45 inference(transitivity,[status(thm)],[40, 38])).
% 0.20/0.45 tff(42,plain,
% 0.20/0.45 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_1, e_2, e_4)) | (~product(e_1, e_1, e_2)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(43,plain,
% 0.20/0.45 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_4) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_2, e_4))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.20/0.45 tff(44,plain,
% 0.20/0.45 (~product(e_1, e_1, e_2)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[43, 12, 37, 1])).
% 0.20/0.45 tff(45,plain,
% 0.20/0.45 (greater(e_4, e_2) <=> greater(e_4, e_2)),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(46,axiom,(greater(e_4, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_greater_e_2')).
% 0.20/0.45 tff(47,plain,
% 0.20/0.45 (greater(e_4, e_2)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.20/0.45 tff(48,plain,
% 0.20/0.45 (next(e_1, e_2) <=> next(e_1, e_2)),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(49,axiom,(next(e_1, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_then_e_2')).
% 0.20/0.45 tff(50,plain,
% 0.20/0.45 (next(e_1, e_2)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.20/0.45 tff(51,plain,
% 0.20/0.45 (((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_4, e_2)) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_4)))) <=> ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_4, e_2)) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_4)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(52,plain,
% 0.20/0.45 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_4, e_2)) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_4)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(53,plain,
% 0.20/0.45 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_4, e_2)) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_4))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.20/0.45 tff(54,plain,
% 0.20/0.45 (~product(e_1, e_1, e_4)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[53, 50, 47, 27])).
% 0.20/0.45 tff(55,plain,
% 0.20/0.45 (greater(e_3, e_2) <=> greater(e_3, e_2)),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(56,axiom,(greater(e_3, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_greater_e_2')).
% 0.20/0.45 tff(57,plain,
% 0.20/0.45 (greater(e_3, e_2)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.20/0.45 tff(58,plain,
% 0.20/0.45 (((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_3, e_2)) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_3)))) <=> ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_3, e_2)) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_3)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(59,plain,
% 0.20/0.45 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_3, e_2)) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_3)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(60,plain,
% 0.20/0.45 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_3, e_2)) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_3))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.20/0.45 tff(61,plain,
% 0.20/0.45 (~product(e_1, e_1, e_3)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[60, 50, 57, 27])).
% 0.20/0.45 tff(62,plain,
% 0.20/0.45 (^[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))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(63,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))) <=> ![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(quant_intro,[status(thm)],[62])).
% 0.20/0.45 tff(64,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))) <=> ![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(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(65,plain,
% 0.20/0.45 (^[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)))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(66,plain,
% 0.20/0.45 (![Y: $i, X: $i] : ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) | product(X, Y, e_4)) <=> ![Y: $i, X: $i] : (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(quant_intro,[status(thm)],[65])).
% 0.20/0.45 tff(67,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')).
% 0.20/0.45 tff(68,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)],[67, 66])).
% 0.20/0.45 tff(69,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)],[68, 64])).
% 0.20/0.45 tff(70,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(skolemize,[status(sab)],[69])).
% 0.20/0.45 tff(71,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)],[70, 63])).
% 0.20/0.45 tff(72,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(73,axiom,(group_element(e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_1')).
% 0.20/0.45 tff(74,plain,
% 0.20/0.45 (group_element(e_1)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.20/0.45 tff(75,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_1, e_3) | product(e_1, e_1, e_4) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~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)))) | product(e_1, e_1, e_3) | product(e_1, e_1, e_4) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(76,plain,
% 0.20/0.45 ((product(e_1, e_1, e_4) | product(e_1, e_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_1))) <=> (product(e_1, e_1, e_3) | product(e_1, e_1, e_4) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(77,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_1, e_4) | product(e_1, e_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1)) | (~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)))) | (product(e_1, e_1, e_3) | product(e_1, e_1, e_4) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[76])).
% 0.20/0.45 tff(78,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_1, e_4) | product(e_1, e_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1)) | (~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)))) | product(e_1, e_1, e_3) | product(e_1, e_1, e_4) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1)))),
% 0.20/0.46 inference(transitivity,[status(thm)],[77, 75])).
% 0.20/0.46 tff(79,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_1, e_1, e_4) | product(e_1, e_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_1)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(80,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_1, e_1, e_3) | product(e_1, e_1, e_4) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.20/0.46 tff(81,plain,
% 0.20/0.46 (product(e_1, e_1, e_2) | product(e_1, e_1, e_1)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[80, 74, 71, 61, 54])).
% 0.20/0.46 tff(82,plain,
% 0.20/0.46 (product(e_1, e_1, e_1)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[81, 44])).
% 0.20/0.46 tff(83,assumption,(product(e_4, e_1, e_1)), introduced(assumption)).
% 0.20/0.46 tff(84,assumption,(product(e_1, e_1, e_1)), introduced(assumption)).
% 0.20/0.46 tff(85,plain,
% 0.20/0.46 (^[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))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(86,plain,
% 0.20/0.46 (![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)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[85])).
% 0.20/0.46 tff(87,plain,
% 0.20/0.46 (![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)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(88,plain,
% 0.20/0.46 (^[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)))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(89,plain,
% 0.20/0.46 (![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)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[88])).
% 0.20/0.46 tff(90,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')).
% 0.20/0.46 tff(91,plain,
% 0.20/0.46 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.20/0.46 tff(92,plain,
% 0.20/0.46 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[91, 87])).
% 0.20/0.46 tff(93,plain,(
% 0.20/0.46 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.46 inference(skolemize,[status(sab)],[92])).
% 0.20/0.46 tff(94,plain,
% 0.20/0.46 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[93, 86])).
% 0.20/0.46 tff(95,plain,
% 0.20/0.46 ((~equalish(e_4, e_1)) <=> (~equalish(e_4, e_1))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(96,axiom,(~equalish(e_4, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_1')).
% 0.20/0.46 tff(97,plain,
% 0.20/0.46 (~equalish(e_4, e_1)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.20/0.46 tff(98,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_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_4, 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_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_4, e_1, e_1)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(99,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_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_4, e_1, e_1)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(100,plain,
% 0.20/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_4, e_1, e_1))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.20/0.46 tff(101,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[100, 97, 94, 84, 83])).
% 0.20/0.46 tff(102,plain,((~product(e_4, e_1, e_1)) | (~product(e_1, e_1, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(103,plain,
% 0.20/0.46 (~product(e_4, e_1, e_1)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[102, 82])).
% 0.20/0.46 tff(104,assumption,(~product(e_2, e_1, e_3)), introduced(assumption)).
% 0.20/0.46 tff(105,assumption,(product(e_2, e_1, e_2)), introduced(assumption)).
% 0.20/0.46 tff(106,assumption,(~product(e_1, e_2, e_3)), introduced(assumption)).
% 0.20/0.46 tff(107,assumption,(product(e_2, e_2, e_2)), introduced(assumption)).
% 0.20/0.46 tff(108,plain,
% 0.20/0.46 (^[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))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(109,plain,
% 0.20/0.46 (![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)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[108])).
% 0.20/0.46 tff(110,plain,
% 0.20/0.46 (![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)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(111,plain,
% 0.20/0.46 (^[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)))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(112,plain,
% 0.20/0.46 (![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)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[111])).
% 0.20/0.46 tff(113,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')).
% 0.20/0.46 tff(114,plain,
% 0.20/0.46 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.20/0.46 tff(115,plain,
% 0.20/0.46 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[114, 110])).
% 0.20/0.46 tff(116,plain,(
% 0.20/0.46 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.46 inference(skolemize,[status(sab)],[115])).
% 0.20/0.46 tff(117,plain,
% 0.20/0.46 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[116, 109])).
% 0.20/0.46 tff(118,plain,
% 0.20/0.46 ((~equalish(e_2, e_1)) <=> (~equalish(e_2, e_1))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(119,axiom,(~equalish(e_2, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_1')).
% 0.20/0.46 tff(120,plain,
% 0.20/0.46 (~equalish(e_2, e_1)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.20/0.46 tff(121,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_2, e_1) | (~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_2, e_1) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(122,plain,
% 0.20/0.46 ((equalish(e_2, e_1) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_2))) <=> (equalish(e_2, e_1) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(123,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_2, e_1) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_1) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[122])).
% 0.20/0.46 tff(124,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_2, e_1) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.20/0.46 inference(transitivity,[status(thm)],[123, 121])).
% 0.20/0.46 tff(125,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_2, e_1) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(126,plain,
% 0.20/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.20/0.46 tff(127,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[126, 120, 117, 105, 107])).
% 0.20/0.46 tff(128,plain,((~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(129,plain,
% 0.20/0.46 (~product(e_2, e_2, e_2)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[128, 105])).
% 0.20/0.46 tff(130,assumption,(product(e_2, e_2, e_1)), introduced(assumption)).
% 0.20/0.46 tff(131,assumption,(product(e_2, e_1, e_1)), introduced(assumption)).
% 0.20/0.46 tff(132,plain,
% 0.20/0.46 ((~equalish(e_1, e_2)) <=> (~equalish(e_1, e_2))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(133,axiom,(~equalish(e_1, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_2')).
% 0.20/0.46 tff(134,plain,
% 0.20/0.46 (~equalish(e_1, e_2)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.20/0.46 tff(135,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_1, e_2) | (~product(e_2, e_1, e_1)) | (~product(e_2, e_2, e_1)))) <=> ((~![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_1, e_1)) | (~product(e_2, e_2, e_1)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(136,plain,
% 0.20/0.46 ((equalish(e_1, e_2) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_1, e_1))) <=> (equalish(e_1, e_2) | (~product(e_2, e_1, e_1)) | (~product(e_2, e_2, e_1)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(137,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_1, e_2) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_1, e_1)))) <=> ((~![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_1, e_1)) | (~product(e_2, e_2, e_1))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[136])).
% 0.20/0.46 tff(138,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_1, e_2) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_1, e_1)))) <=> ((~![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_1, e_1)) | (~product(e_2, e_2, e_1)))),
% 0.20/0.46 inference(transitivity,[status(thm)],[137, 135])).
% 0.20/0.46 tff(139,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_1, e_2) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_1, e_1)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(140,plain,
% 0.20/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_2) | (~product(e_2, e_1, e_1)) | (~product(e_2, e_2, e_1))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.20/0.46 tff(141,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[140, 134, 117, 131, 130])).
% 0.20/0.46 tff(142,plain,((~product(e_2, e_1, e_1)) | (~product(e_2, e_2, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(143,plain,
% 0.20/0.46 (~product(e_2, e_1, e_1)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[142, 130])).
% 0.20/0.46 tff(144,plain,
% 0.20/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_1) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_1) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_1)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(145,plain,
% 0.20/0.46 ((product(e_2, e_1, e_1) | (~product(e_2, e_2, e_1)) | (~product(e_1, e_2, e_2))) <=> (product(e_2, e_1, e_1) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_1)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(146,plain,
% 0.20/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_1) | (~product(e_2, e_2, e_1)) | (~product(e_1, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_1) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_1))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[145])).
% 0.20/0.46 tff(147,plain,
% 0.20/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_1) | (~product(e_2, e_2, e_1)) | (~product(e_1, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_1) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_1)))),
% 0.20/0.46 inference(transitivity,[status(thm)],[146, 144])).
% 0.20/0.46 tff(148,plain,
% 0.20/0.46 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_1) | (~product(e_2, e_2, e_1)) | (~product(e_1, e_2, e_2)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(149,plain,
% 0.20/0.46 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_1) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_1))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.20/0.46 tff(150,plain,
% 0.20/0.46 (~product(e_1, e_2, e_2)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[149, 12, 143, 130])).
% 0.20/0.46 tff(151,plain,
% 0.20/0.46 (group_element(e_2) <=> group_element(e_2)),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(152,axiom,(group_element(e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_2')).
% 0.20/0.46 tff(153,plain,
% 0.20/0.46 (group_element(e_2)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.20/0.46 tff(154,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_2, e_1, e_4) | (~group_element(e_1)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, 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)))) | product(e_2, e_1, e_4) | (~group_element(e_1)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_2)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(155,plain,
% 0.20/0.47 ((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))) <=> (product(e_2, e_1, e_4) | (~group_element(e_1)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_2)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(156,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_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)))) | (product(e_2, e_1, e_4) | (~group_element(e_1)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_2))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[155])).
% 0.20/0.47 tff(157,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_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)))) | product(e_2, e_1, e_4) | (~group_element(e_1)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_2)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[156, 154])).
% 0.20/0.47 tff(158,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_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)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(159,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_1, e_4) | (~group_element(e_1)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_2))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.20/0.47 tff(160,plain,
% 0.20/0.47 (product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[159, 74, 153, 71, 37])).
% 0.20/0.47 tff(161,plain,
% 0.20/0.47 (product(e_2, e_1, e_2)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[160, 143, 104])).
% 0.20/0.47 tff(162,plain,
% 0.20/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_2) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_2, e_2) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_1, e_2)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(163,plain,
% 0.20/0.47 ((product(e_1, e_2, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_1))) <=> (product(e_1, e_2, e_2) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_1, e_2)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(164,plain,
% 0.20/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_2) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_1, e_2))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[163])).
% 0.20/0.47 tff(165,plain,
% 0.20/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_2, e_2) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_1, e_2)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[164, 162])).
% 0.20/0.47 tff(166,plain,
% 0.20/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_1)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(167,plain,
% 0.20/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_2, e_2) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_1, e_2))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.20/0.47 tff(168,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[167, 12, 161, 130, 150])).
% 0.20/0.47 tff(169,plain,((~product(e_2, e_2, e_1)) | product(e_2, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(170,plain,
% 0.20/0.47 (~product(e_2, e_2, e_1)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[169, 104])).
% 0.20/0.47 tff(171,assumption,(product(e_1, e_2, e_1)), introduced(assumption)).
% 0.20/0.47 tff(172,assumption,(~product(e_2, e_2, e_1)), introduced(assumption)).
% 0.20/0.47 tff(173,plain,
% 0.20/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_2, e_1)) | product(e_2, e_2, e_1) | (~product(e_2, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_2, e_1)) | product(e_2, e_2, e_1) | (~product(e_2, e_1, e_2)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(174,plain,
% 0.20/0.47 ((product(e_2, e_2, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_2, e_1, e_2))) <=> ((~product(e_1, e_2, e_1)) | product(e_2, e_2, e_1) | (~product(e_2, e_1, e_2)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(175,plain,
% 0.20/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_2, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_2, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_2, e_1)) | product(e_2, e_2, e_1) | (~product(e_2, e_1, e_2))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[174])).
% 0.20/0.47 tff(176,plain,
% 0.20/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_2, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_2, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_2, e_1)) | product(e_2, e_2, e_1) | (~product(e_2, e_1, e_2)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[175, 173])).
% 0.20/0.47 tff(177,plain,
% 0.20/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_2, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_2, e_1, e_2)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(178,plain,
% 0.20/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_2, e_1)) | product(e_2, e_2, e_1) | (~product(e_2, e_1, e_2))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[177, 176])).
% 0.20/0.47 tff(179,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[178, 12, 105, 172, 171])).
% 0.20/0.47 tff(180,plain,((~product(e_1, e_2, e_1)) | (~product(e_2, e_1, e_2)) | product(e_2, e_2, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(181,plain,
% 0.20/0.47 (~product(e_1, e_2, e_1)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[180, 105, 170])).
% 0.20/0.47 tff(182,assumption,(product(e_2, e_2, e_4)), introduced(assumption)).
% 0.20/0.47 tff(183,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_1) | (~product(e_2, e_2, e_4)) | (~product(e_1, e_2, 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_1) | (~product(e_2, e_2, e_4)) | (~product(e_1, e_2, e_4)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(184,plain,
% 0.20/0.47 ((equalish(e_2, e_1) | (~product(e_1, e_2, e_4)) | (~product(e_2, e_2, e_4))) <=> (equalish(e_2, e_1) | (~product(e_2, e_2, e_4)) | (~product(e_1, e_2, e_4)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(185,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_1) | (~product(e_1, e_2, e_4)) | (~product(e_2, e_2, 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_1) | (~product(e_2, e_2, e_4)) | (~product(e_1, e_2, e_4))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[184])).
% 0.20/0.47 tff(186,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_1) | (~product(e_1, e_2, e_4)) | (~product(e_2, e_2, 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_1) | (~product(e_2, e_2, e_4)) | (~product(e_1, e_2, e_4)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[185, 183])).
% 0.20/0.47 tff(187,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_1) | (~product(e_1, e_2, e_4)) | (~product(e_2, e_2, e_4)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(188,plain,
% 0.20/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_2, e_2, e_4)) | (~product(e_1, e_2, e_4))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[187, 186])).
% 0.20/0.47 tff(189,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[188, 120, 94, 182, 1])).
% 0.20/0.47 tff(190,plain,((~product(e_2, e_2, e_4)) | (~product(e_1, e_2, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(191,plain,
% 0.20/0.47 (~product(e_1, e_2, e_4)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[190, 182])).
% 0.20/0.47 tff(192,assumption,(~product(e_1, e_2, e_1)), introduced(assumption)).
% 0.20/0.47 tff(193,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_1)) | (~group_element(e_2)) | product(e_1, e_2, e_1) | product(e_1, e_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, 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_1)) | (~group_element(e_2)) | product(e_1, e_2, e_1) | product(e_1, e_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(194,plain,
% 0.20/0.47 ((product(e_1, e_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_1))) <=> ((~group_element(e_1)) | (~group_element(e_2)) | product(e_1, e_2, e_1) | product(e_1, e_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(195,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_1, e_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_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_1)) | (~group_element(e_2)) | product(e_1, e_2, e_1) | product(e_1, e_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2)))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[194])).
% 0.20/0.47 tff(196,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_1, e_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_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_1)) | (~group_element(e_2)) | product(e_1, e_2, e_1) | product(e_1, e_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2))),
% 0.20/0.47 inference(transitivity,[status(thm)],[195, 193])).
% 0.20/0.47 tff(197,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_1, e_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_1)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(198,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_1)) | (~group_element(e_2)) | product(e_1, e_2, e_1) | product(e_1, e_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[197, 196])).
% 0.20/0.47 tff(199,plain,
% 0.20/0.47 (product(e_1, e_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[198, 74, 153, 71, 192])).
% 0.20/0.47 tff(200,plain,
% 0.20/0.47 (product(e_1, e_2, e_2)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[199, 191, 106])).
% 0.20/0.47 tff(201,plain,
% 0.20/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_4) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_4)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(202,plain,
% 0.20/0.47 ((product(e_2, e_1, e_4) | (~product(e_2, e_2, e_4)) | (~product(e_1, e_2, e_2))) <=> (product(e_2, e_1, e_4) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_4)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(203,plain,
% 0.20/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_2, e_2, e_4)) | (~product(e_1, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_4))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[202])).
% 0.20/0.47 tff(204,plain,
% 0.20/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_2, e_2, e_4)) | (~product(e_1, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_4) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_4)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[203, 201])).
% 0.20/0.47 tff(205,plain,
% 0.20/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_2, e_2, e_4)) | (~product(e_1, e_2, e_2)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(206,plain,
% 0.20/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_4) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_4))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[205, 204])).
% 0.20/0.47 tff(207,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[206, 12, 37, 182, 200])).
% 0.20/0.47 tff(208,plain,((~product(e_2, e_2, e_4)) | product(e_1, e_2, e_3) | product(e_1, e_2, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(209,plain,
% 0.20/0.48 (~product(e_2, e_2, e_4)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[208, 106, 181])).
% 0.20/0.48 tff(210,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)) | product(e_2, e_2, e_2) | product(e_2, e_2, e_4) | product(e_2, e_2, e_1) | product(e_2, e_2, 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)) | product(e_2, e_2, e_2) | product(e_2, e_2, e_4) | product(e_2, e_2, e_1) | product(e_2, e_2, e_3))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(211,plain,
% 0.20/0.48 ((product(e_2, e_2, e_4) | product(e_2, e_2, e_3) | product(e_2, e_2, e_2) | product(e_2, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_2))) <=> ((~group_element(e_2)) | product(e_2, e_2, e_2) | product(e_2, e_2, e_4) | product(e_2, e_2, e_1) | product(e_2, e_2, e_3))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(212,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_2, e_4) | product(e_2, e_2, e_3) | product(e_2, e_2, e_2) | product(e_2, e_2, e_1) | (~group_element(e_2)) | (~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)) | product(e_2, e_2, e_2) | product(e_2, e_2, e_4) | product(e_2, e_2, e_1) | product(e_2, e_2, e_3)))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[211])).
% 0.20/0.48 tff(213,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_2, e_4) | product(e_2, e_2, e_3) | product(e_2, e_2, e_2) | product(e_2, e_2, e_1) | (~group_element(e_2)) | (~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)) | product(e_2, e_2, e_2) | product(e_2, e_2, e_4) | product(e_2, e_2, e_1) | product(e_2, e_2, e_3))),
% 0.20/0.48 inference(transitivity,[status(thm)],[212, 210])).
% 0.20/0.48 tff(214,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_2, e_4) | product(e_2, e_2, e_3) | product(e_2, e_2, e_2) | product(e_2, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_2)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(215,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)) | product(e_2, e_2, e_2) | product(e_2, e_2, e_4) | product(e_2, e_2, e_1) | product(e_2, e_2, e_3)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[214, 213])).
% 0.20/0.48 tff(216,plain,
% 0.20/0.48 (product(e_2, e_2, e_2) | product(e_2, e_2, e_4) | product(e_2, e_2, e_1) | product(e_2, e_2, e_3)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[215, 153, 71])).
% 0.20/0.48 tff(217,plain,
% 0.20/0.48 (product(e_2, e_2, e_3)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[216, 209, 170, 129])).
% 0.20/0.48 tff(218,plain,
% 0.20/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_3) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_3) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_3)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(219,plain,
% 0.20/0.48 ((product(e_2, e_1, e_3) | (~product(e_2, e_2, e_3)) | (~product(e_1, e_2, e_2))) <=> (product(e_2, e_1, e_3) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_3)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(220,plain,
% 0.20/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_3) | (~product(e_2, e_2, e_3)) | (~product(e_1, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_3) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_3))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[219])).
% 0.20/0.48 tff(221,plain,
% 0.20/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_3) | (~product(e_2, e_2, e_3)) | (~product(e_1, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_3) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_3)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[220, 218])).
% 0.20/0.48 tff(222,plain,
% 0.20/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_3) | (~product(e_2, e_2, e_3)) | (~product(e_1, e_2, e_2)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(223,plain,
% 0.20/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_3) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_3))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[222, 221])).
% 0.20/0.48 tff(224,plain,
% 0.20/0.48 (~product(e_1, e_2, e_2)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[223, 12, 104, 217])).
% 0.20/0.48 tff(225,plain,
% 0.20/0.48 (product(e_1, e_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[198, 74, 153, 71, 181])).
% 0.20/0.48 tff(226,plain,
% 0.20/0.48 (product(e_1, e_2, e_4)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[225, 224, 106])).
% 0.20/0.48 tff(227,plain,
% 0.20/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_2, e_4) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_2, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_2, e_4) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_2, e_4)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(228,plain,
% 0.20/0.48 ((product(e_2, e_2, e_4) | (~product(e_1, e_2, e_4)) | (~product(e_2, e_1, e_2))) <=> (product(e_2, e_2, e_4) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_2, e_4)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(229,plain,
% 0.20/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_2, e_4) | (~product(e_1, e_2, e_4)) | (~product(e_2, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_2, e_4) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_2, e_4))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[228])).
% 0.20/0.48 tff(230,plain,
% 0.20/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_2, e_4) | (~product(e_1, e_2, e_4)) | (~product(e_2, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_2, e_4) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_2, e_4)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[229, 227])).
% 0.20/0.48 tff(231,plain,
% 0.20/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_2, e_4) | (~product(e_1, e_2, e_4)) | (~product(e_2, e_1, e_2)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(232,plain,
% 0.20/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_2, e_4) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_2, e_4))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[231, 230])).
% 0.20/0.48 tff(233,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[232, 12, 105, 209, 226])).
% 0.20/0.48 tff(234,plain,(product(e_1, e_2, e_3) | (~product(e_2, e_1, e_2)) | product(e_2, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(235,plain,
% 0.20/0.48 (product(e_1, e_2, e_3)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[234, 105, 104])).
% 0.20/0.48 tff(236,assumption,(product(e_1, e_2, e_3)), introduced(assumption)).
% 0.20/0.48 tff(237,assumption,(product(e_2, e_2, e_3)), introduced(assumption)).
% 0.20/0.48 tff(238,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_1) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_2, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_2, e_3)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(239,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_1) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_2, e_3)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(240,plain,
% 0.20/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_2, e_3))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[239, 238])).
% 0.20/0.48 tff(241,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[240, 120, 94, 237, 236])).
% 0.20/0.48 tff(242,plain,((~product(e_2, e_2, e_3)) | (~product(e_1, e_2, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(243,plain,
% 0.20/0.48 (~product(e_2, e_2, e_3)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[242, 235])).
% 0.20/0.48 tff(244,plain,
% 0.20/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_2, e_3) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_2, e_3) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_2, e_3)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(245,plain,
% 0.20/0.48 ((product(e_2, e_2, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_1, e_2))) <=> (product(e_2, e_2, e_3) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_2, e_3)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(246,plain,
% 0.20/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_2, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_2, e_3) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_2, e_3))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[245])).
% 0.20/0.48 tff(247,plain,
% 0.20/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_2, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_2, e_3) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_2, e_3)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[246, 244])).
% 0.20/0.48 tff(248,plain,
% 0.20/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_2, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_1, e_2)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(249,plain,
% 0.20/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_2, e_3) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_2, e_3))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[248, 247])).
% 0.20/0.48 tff(250,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[249, 12, 105, 243, 235])).
% 0.20/0.48 tff(251,plain,((~product(e_2, e_1, e_2)) | product(e_2, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(252,plain,
% 0.20/0.48 (~product(e_2, e_1, e_2)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[251, 104])).
% 0.20/0.48 tff(253,plain,
% 0.20/0.48 (product(e_2, e_1, e_1)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[160, 252, 104])).
% 0.20/0.48 tff(254,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_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_1, e_2) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(255,plain,
% 0.20/0.48 ((equalish(e_1, e_2) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_1))) <=> (equalish(e_1, e_2) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(256,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_1, e_1)) | (~product(e_1, 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_1, e_2) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[255])).
% 0.20/0.48 tff(257,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_1, e_1)) | (~product(e_1, 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_1, e_2) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[256, 254])).
% 0.20/0.48 tff(258,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_1, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(259,plain,
% 0.20/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_2) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[258, 257])).
% 0.20/0.48 tff(260,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[259, 134, 94, 84, 131])).
% 0.20/0.48 tff(261,plain,((~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(262,plain,
% 0.20/0.48 (~product(e_1, e_1, e_1)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[261, 253])).
% 0.20/0.48 tff(263,plain,
% 0.20/0.48 (product(e_1, e_1, e_2)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[81, 262])).
% 0.20/0.48 tff(264,assumption,(~product(e_1, e_2, e_2)), introduced(assumption)).
% 0.20/0.48 tff(265,assumption,(product(e_1, e_1, e_2)), introduced(assumption)).
% 0.20/0.48 tff(266,plain,
% 0.20/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_2) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_2, e_2) | (~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(267,plain,
% 0.20/0.48 ((product(e_1, e_2, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_2, e_1, e_1))) <=> (product(e_1, e_2, e_2) | (~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(268,plain,
% 0.20/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_2, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_2) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_2))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[267])).
% 0.20/0.48 tff(269,plain,
% 0.20/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_2, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_2, e_2) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_2)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[268, 266])).
% 0.20/0.49 tff(270,plain,
% 0.20/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_2, e_1, e_1)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(271,plain,
% 0.20/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_2, e_2) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_2))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[270, 269])).
% 0.20/0.49 tff(272,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[271, 12, 265, 131, 264])).
% 0.20/0.49 tff(273,plain,((~product(e_1, e_1, e_2)) | (~product(e_2, e_1, e_1)) | product(e_1, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(274,plain,
% 0.20/0.49 (product(e_1, e_2, e_2)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[273, 263, 253])).
% 0.20/0.49 tff(275,plain,
% 0.20/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_2) | (~product(e_1, e_2, e_2)) | (~product(e_1, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_2) | (~product(e_1, e_2, e_2)) | (~product(e_1, e_1, e_2)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(276,plain,
% 0.20/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_2) | (~product(e_1, e_2, e_2)) | (~product(e_1, e_1, e_2)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(277,plain,
% 0.20/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_2) | (~product(e_1, e_2, e_2)) | (~product(e_1, e_1, e_2))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[276, 275])).
% 0.20/0.49 tff(278,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[277, 12, 263, 252, 274])).
% 0.20/0.49 tff(279,plain,(product(e_2, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(280,assumption,(product(e_4, e_1, e_3)), introduced(assumption)).
% 0.20/0.49 tff(281,assumption,(product(e_2, e_1, e_3)), introduced(assumption)).
% 0.20/0.49 tff(282,plain,
% 0.20/0.49 ((~equalish(e_4, e_2)) <=> (~equalish(e_4, e_2))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(283,axiom,(~equalish(e_4, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_2')).
% 0.20/0.49 tff(284,plain,
% 0.20/0.49 (~equalish(e_4, e_2)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[283, 282])).
% 0.20/0.49 tff(285,plain,
% 0.20/0.49 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_4, e_1, e_3)))) <=> ((~![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_1, e_3)) | (~product(e_4, e_1, e_3)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(286,plain,
% 0.20/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_4, e_1, e_3)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(287,plain,
% 0.20/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_4, e_1, e_3))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[286, 285])).
% 0.20/0.49 tff(288,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[287, 284, 94, 281, 280])).
% 0.20/0.49 tff(289,plain,((~product(e_4, e_1, e_3)) | (~product(e_2, e_1, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(290,plain,
% 0.20/0.49 (~product(e_4, e_1, e_3)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[289, 279])).
% 0.20/0.49 tff(291,plain,
% 0.20/0.49 (group_element(e_4) <=> group_element(e_4)),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(292,axiom,(group_element(e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_4')).
% 0.20/0.49 tff(293,plain,
% 0.20/0.49 (group_element(e_4)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[292, 291])).
% 0.20/0.49 tff(294,plain,
% 0.20/0.49 (((~![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_1)) | (~group_element(e_4)) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_4) | product(e_4, e_1, 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_1)) | (~group_element(e_4)) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_4) | product(e_4, e_1, e_1))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(295,plain,
% 0.20/0.49 ((product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_4))) <=> ((~group_element(e_1)) | (~group_element(e_4)) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_4) | product(e_4, e_1, e_1))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(296,plain,
% 0.20/0.49 (((~![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_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | (~group_element(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_1)) | (~group_element(e_4)) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_4) | product(e_4, e_1, e_1)))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[295])).
% 0.20/0.49 tff(297,plain,
% 0.20/0.49 (((~![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_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | (~group_element(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_1)) | (~group_element(e_4)) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_4) | product(e_4, e_1, e_1))),
% 0.20/0.49 inference(transitivity,[status(thm)],[296, 294])).
% 0.20/0.49 tff(298,plain,
% 0.20/0.49 ((~![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_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_4)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(299,plain,
% 0.20/0.49 ((~![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_1)) | (~group_element(e_4)) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_4) | product(e_4, e_1, e_1)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[298, 297])).
% 0.20/0.49 tff(300,plain,
% 0.20/0.49 (product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_4) | product(e_4, e_1, e_1)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[299, 74, 293, 71])).
% 0.20/0.49 tff(301,plain,
% 0.20/0.49 (product(e_4, e_1, e_2) | product(e_4, e_1, e_4) | product(e_4, e_1, e_1)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[300, 290])).
% 0.20/0.49 tff(302,plain,
% 0.20/0.49 (product(e_4, e_1, e_2)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[301, 2, 103])).
% 0.20/0.49 tff(303,plain,
% 0.20/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_4, e_4) | (~product(e_4, e_1, e_2)) | (~product(e_1, e_2, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_4, e_4) | (~product(e_4, e_1, e_2)) | (~product(e_1, e_2, e_4)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(304,plain,
% 0.20/0.49 ((product(e_2, e_4, e_4) | (~product(e_1, e_2, e_4)) | (~product(e_4, e_1, e_2))) <=> (product(e_2, e_4, e_4) | (~product(e_4, e_1, e_2)) | (~product(e_1, e_2, e_4)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(305,plain,
% 0.20/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_4, e_4) | (~product(e_1, e_2, e_4)) | (~product(e_4, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_4, e_4) | (~product(e_4, e_1, e_2)) | (~product(e_1, e_2, e_4))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[304])).
% 0.20/0.49 tff(306,plain,
% 0.20/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_4, e_4) | (~product(e_1, e_2, e_4)) | (~product(e_4, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_4, e_4) | (~product(e_4, e_1, e_2)) | (~product(e_1, e_2, e_4)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[305, 303])).
% 0.20/0.49 tff(307,plain,
% 0.20/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_4, e_4) | (~product(e_1, e_2, e_4)) | (~product(e_4, e_1, e_2)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(308,plain,
% 0.20/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_4, e_4) | (~product(e_4, e_1, e_2)) | (~product(e_1, e_2, e_4))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[307, 306])).
% 0.20/0.49 tff(309,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[308, 12, 302, 1, 17])).
% 0.20/0.49 tff(310,plain,(product(e_4, e_1, e_4) | (~product(e_1, e_2, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(311,plain,
% 0.20/0.49 (product(e_4, e_1, e_4)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[310, 1])).
% 0.20/0.49 tff(312,plain,
% 0.20/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_4) | (~product(e_1, e_4, e_1)) | (~product(e_4, e_1, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_4) | (~product(e_1, e_4, e_1)) | (~product(e_4, e_1, e_4)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(313,plain,
% 0.20/0.49 ((product(e_1, e_1, e_4) | (~product(e_4, e_1, e_4)) | (~product(e_1, e_4, e_1))) <=> (product(e_1, e_1, e_4) | (~product(e_1, e_4, e_1)) | (~product(e_4, e_1, e_4)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(314,plain,
% 0.20/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_4) | (~product(e_4, e_1, e_4)) | (~product(e_1, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_4) | (~product(e_1, e_4, e_1)) | (~product(e_4, e_1, e_4))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[313])).
% 0.20/0.49 tff(315,plain,
% 0.20/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_4) | (~product(e_4, e_1, e_4)) | (~product(e_1, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_4) | (~product(e_1, e_4, e_1)) | (~product(e_4, e_1, e_4)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[314, 312])).
% 0.20/0.49 tff(316,plain,
% 0.20/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_4) | (~product(e_4, e_1, e_4)) | (~product(e_1, e_4, e_1)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(317,plain,
% 0.20/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_4) | (~product(e_1, e_4, e_1)) | (~product(e_4, e_1, e_4))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[316, 315])).
% 0.20/0.49 tff(318,plain,
% 0.20/0.49 (~product(e_1, e_4, e_1)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[317, 12, 54, 311])).
% 0.20/0.49 tff(319,assumption,(product(e_1, e_4, e_4)), introduced(assumption)).
% 0.20/0.49 tff(320,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_2) | (~product(e_1, e_2, e_4)) | (~product(e_1, e_4, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_2) | (~product(e_1, e_2, e_4)) | (~product(e_1, e_4, e_4)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(321,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_2) | (~product(e_1, e_2, e_4)) | (~product(e_1, e_4, e_4)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(322,plain,
% 0.20/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_2) | (~product(e_1, e_2, e_4)) | (~product(e_1, e_4, e_4))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[321, 320])).
% 0.20/0.49 tff(323,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[322, 284, 117, 1, 319])).
% 0.20/0.49 tff(324,plain,((~product(e_1, e_4, e_4)) | (~product(e_1, e_2, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(325,plain,
% 0.20/0.49 (~product(e_1, e_4, e_4)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[324, 1])).
% 0.20/0.49 tff(326,assumption,(product(e_4, e_1, e_4)), introduced(assumption)).
% 0.20/0.49 tff(327,assumption,(product(e_1, e_4, e_2)), introduced(assumption)).
% 0.20/0.49 tff(328,assumption,(~product(e_4, e_4, e_2)), introduced(assumption)).
% 0.20/0.49 tff(329,plain,
% 0.20/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_4, e_2)) | product(e_4, e_4, e_2) | (~product(e_4, e_1, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_4, e_2)) | product(e_4, e_4, e_2) | (~product(e_4, e_1, e_4)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(330,plain,
% 0.20/0.49 ((product(e_4, e_4, e_2) | (~product(e_1, e_4, e_2)) | (~product(e_4, e_1, e_4))) <=> ((~product(e_1, e_4, e_2)) | product(e_4, e_4, e_2) | (~product(e_4, e_1, e_4)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(331,plain,
% 0.20/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_4, e_2) | (~product(e_1, e_4, e_2)) | (~product(e_4, e_1, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_4, e_2)) | product(e_4, e_4, e_2) | (~product(e_4, e_1, e_4))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[330])).
% 0.20/0.49 tff(332,plain,
% 0.20/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_4, e_2) | (~product(e_1, e_4, e_2)) | (~product(e_4, e_1, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_4, e_2)) | product(e_4, e_4, e_2) | (~product(e_4, e_1, e_4)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[331, 329])).
% 0.20/0.49 tff(333,plain,
% 0.20/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_4, e_2) | (~product(e_1, e_4, e_2)) | (~product(e_4, e_1, e_4)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(334,plain,
% 0.20/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_4, e_2)) | product(e_4, e_4, e_2) | (~product(e_4, e_1, e_4))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[333, 332])).
% 0.20/0.49 tff(335,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[334, 12, 326, 328, 327])).
% 0.20/0.49 tff(336,plain,((~product(e_1, e_4, e_2)) | (~product(e_4, e_1, e_4)) | product(e_4, e_4, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(337,plain,
% 0.20/0.49 (product(e_4, e_4, e_2)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[336, 327, 326])).
% 0.20/0.49 tff(338,plain,
% 0.20/0.49 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_1) | (~product(e_1, e_4, e_2)) | (~product(e_4, e_4, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_1) | (~product(e_1, e_4, e_2)) | (~product(e_4, e_4, e_2)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(339,plain,
% 0.20/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_1) | (~product(e_1, e_4, e_2)) | (~product(e_4, e_4, e_2)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(340,plain,
% 0.20/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_1) | (~product(e_1, e_4, e_2)) | (~product(e_4, e_4, e_2))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[339, 338])).
% 0.20/0.50 tff(341,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[340, 97, 94, 327, 337])).
% 0.20/0.50 tff(342,plain,((~product(e_1, e_4, e_2)) | (~product(e_4, e_1, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(343,plain,
% 0.20/0.50 (~product(e_1, e_4, e_2)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[342, 311])).
% 0.20/0.50 tff(344,assumption,(~product(e_1, e_4, e_1)), introduced(assumption)).
% 0.20/0.50 tff(345,assumption,(~product(e_1, e_4, e_2)), introduced(assumption)).
% 0.20/0.50 tff(346,assumption,(~product(e_1, e_4, e_4)), introduced(assumption)).
% 0.20/0.50 tff(347,assumption,(~product(e_1, e_4, e_3)), introduced(assumption)).
% 0.20/0.50 tff(348,plain,
% 0.20/0.50 (((~![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_1)) | (~group_element(e_4)) | product(e_1, e_4, e_1) | product(e_1, e_4, e_2) | product(e_1, e_4, e_4) | product(e_1, 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_1)) | (~group_element(e_4)) | product(e_1, e_4, e_1) | product(e_1, e_4, e_2) | product(e_1, e_4, e_4) | product(e_1, e_4, e_3))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(349,plain,
% 0.20/0.50 ((product(e_1, e_4, e_4) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_1))) <=> ((~group_element(e_1)) | (~group_element(e_4)) | product(e_1, e_4, e_1) | product(e_1, e_4, e_2) | product(e_1, e_4, e_4) | product(e_1, e_4, e_3))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(350,plain,
% 0.20/0.50 (((~![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_4, e_4) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_1)))) <=> ((~![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_1)) | (~group_element(e_4)) | product(e_1, e_4, e_1) | product(e_1, e_4, e_2) | product(e_1, e_4, e_4) | product(e_1, e_4, e_3)))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[349])).
% 0.20/0.50 tff(351,plain,
% 0.20/0.50 (((~![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_4, e_4) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_1)))) <=> ((~![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_1)) | (~group_element(e_4)) | product(e_1, e_4, e_1) | product(e_1, e_4, e_2) | product(e_1, e_4, e_4) | product(e_1, e_4, e_3))),
% 0.20/0.50 inference(transitivity,[status(thm)],[350, 348])).
% 0.20/0.50 tff(352,plain,
% 0.20/0.50 ((~![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_4, e_4) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_1)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(353,plain,
% 0.20/0.50 ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | (~group_element(e_4)) | product(e_1, e_4, e_1) | product(e_1, e_4, e_2) | product(e_1, e_4, e_4) | product(e_1, e_4, e_3)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[352, 351])).
% 0.20/0.50 tff(354,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[353, 74, 293, 71, 347, 346, 345, 344])).
% 0.20/0.50 tff(355,plain,(product(e_1, e_4, e_1) | product(e_1, e_4, e_3) | product(e_1, e_4, e_4) | product(e_1, e_4, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(356,plain,
% 0.20/0.50 (product(e_1, e_4, e_3)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[355, 343, 325, 318])).
% 0.20/0.50 tff(357,assumption,(~product(e_4, e_4, e_3)), introduced(assumption)).
% 0.20/0.50 tff(358,assumption,(product(e_1, e_4, e_3)), introduced(assumption)).
% 0.20/0.50 tff(359,plain,
% 0.20/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_4, e_3)) | product(e_4, e_4, e_3) | (~product(e_4, e_1, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_4, e_3)) | product(e_4, e_4, e_3) | (~product(e_4, e_1, e_4)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(360,plain,
% 0.20/0.50 ((product(e_4, e_4, e_3) | (~product(e_1, e_4, e_3)) | (~product(e_4, e_1, e_4))) <=> ((~product(e_1, e_4, e_3)) | product(e_4, e_4, e_3) | (~product(e_4, e_1, e_4)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(361,plain,
% 0.20/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_4, e_3) | (~product(e_1, e_4, e_3)) | (~product(e_4, e_1, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_4, e_3)) | product(e_4, e_4, e_3) | (~product(e_4, e_1, e_4))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[360])).
% 0.20/0.50 tff(362,plain,
% 0.20/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_4, e_3) | (~product(e_1, e_4, e_3)) | (~product(e_4, e_1, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_4, e_3)) | product(e_4, e_4, e_3) | (~product(e_4, e_1, e_4)))),
% 0.20/0.50 inference(transitivity,[status(thm)],[361, 359])).
% 0.20/0.50 tff(363,plain,
% 0.20/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_4, e_3) | (~product(e_1, e_4, e_3)) | (~product(e_4, e_1, e_4)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(364,plain,
% 0.20/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_4, e_3)) | product(e_4, e_4, e_3) | (~product(e_4, e_1, e_4))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[363, 362])).
% 0.20/0.50 tff(365,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[364, 12, 326, 358, 357])).
% 0.20/0.50 tff(366,plain,(product(e_4, e_4, e_3) | (~product(e_4, e_1, e_4)) | (~product(e_1, e_4, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(367,plain,
% 0.20/0.50 (product(e_4, e_4, e_3)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[366, 311, 356])).
% 0.20/0.50 tff(368,plain,
% 0.20/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_1) | (~product(e_1, e_4, e_3)) | (~product(e_4, e_4, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_1) | (~product(e_1, e_4, e_3)) | (~product(e_4, e_4, e_3)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(369,plain,
% 0.20/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_1) | (~product(e_1, e_4, e_3)) | (~product(e_4, e_4, e_3)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(370,plain,
% 0.20/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_1) | (~product(e_1, e_4, e_3)) | (~product(e_4, e_4, e_3))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[369, 368])).
% 0.20/0.50 tff(371,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[370, 97, 94, 356, 367])).
% 0.20/0.50 tff(372,plain,(~product(e_1, e_2, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(373,assumption,(product(e_3, e_2, e_2)), introduced(assumption)).
% 0.20/0.50 tff(374,assumption,(product(e_2, e_3, e_1)), introduced(assumption)).
% 0.20/0.50 tff(375,plain,
% 0.20/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_3) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_3) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_2, e_1)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(376,plain,
% 0.20/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_3) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_2, e_1)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(377,plain,
% 0.20/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_3) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_2, e_1))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[376, 375])).
% 0.20/0.50 tff(378,plain,
% 0.20/0.50 (~product(e_1, e_2, e_1)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[377, 12, 61, 279])).
% 0.20/0.50 tff(379,plain,
% 0.20/0.50 (product(e_1, e_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[198, 74, 153, 71, 378])).
% 0.20/0.50 tff(380,plain,
% 0.20/0.50 (product(e_1, e_2, e_2)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[379, 106, 372])).
% 0.20/0.50 tff(381,plain,
% 0.20/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_2, e_1, e_3)) | product(e_1, e_2, e_3) | (~product(e_2, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_2, e_1, e_3)) | product(e_1, e_2, e_3) | (~product(e_2, e_2, e_1)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(382,plain,
% 0.20/0.50 ((product(e_1, e_2, e_3) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_2, e_1))) <=> ((~product(e_2, e_1, e_3)) | product(e_1, e_2, e_3) | (~product(e_2, e_2, e_1)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(383,plain,
% 0.20/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_3) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_2, e_1, e_3)) | product(e_1, e_2, e_3) | (~product(e_2, e_2, e_1))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[382])).
% 0.20/0.50 tff(384,plain,
% 0.20/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_3) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_2, e_1, e_3)) | product(e_1, e_2, e_3) | (~product(e_2, e_2, e_1)))),
% 0.20/0.50 inference(transitivity,[status(thm)],[383, 381])).
% 0.20/0.50 tff(385,plain,
% 0.20/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_3) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_2, e_1)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(386,plain,
% 0.20/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_2, e_1, e_3)) | product(e_1, e_2, e_3) | (~product(e_2, e_2, e_1))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[385, 384])).
% 0.20/0.50 tff(387,plain,
% 0.20/0.50 ((~product(e_2, e_1, e_3)) | product(e_1, e_2, e_3) | (~product(e_2, e_2, e_1))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[386, 12])).
% 0.20/0.50 tff(388,plain,
% 0.20/0.50 (product(e_1, e_2, e_3) | (~product(e_2, e_2, e_1))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[387, 279])).
% 0.20/0.50 tff(389,plain,
% 0.20/0.50 (~product(e_2, e_2, e_1)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[388, 106])).
% 0.20/0.50 tff(390,plain,
% 0.20/0.50 ((~product(e_2, e_2, e_4)) | product(e_1, e_2, e_3)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[208, 378])).
% 0.20/0.50 tff(391,plain,
% 0.20/0.50 (~product(e_2, e_2, e_4)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[390, 106])).
% 0.20/0.50 tff(392,plain,
% 0.20/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_2, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_2, e_3)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(393,plain,
% 0.20/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_2, e_3)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(394,plain,
% 0.20/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_2, e_3))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[393, 392])).
% 0.20/0.50 tff(395,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[394, 120, 117, 281, 237])).
% 0.20/0.50 tff(396,plain,((~product(e_2, e_2, e_3)) | (~product(e_2, e_1, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(397,plain,
% 0.20/0.50 (~product(e_2, e_2, e_3)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[396, 279])).
% 0.20/0.50 tff(398,plain,
% 0.20/0.50 (product(e_2, e_2, e_2) | product(e_2, e_2, e_4) | product(e_2, e_2, e_1)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[216, 397])).
% 0.20/0.50 tff(399,plain,
% 0.20/0.50 (product(e_2, e_2, e_2)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[398, 391, 389])).
% 0.20/0.50 tff(400,assumption,(product(e_1, e_2, e_2)), introduced(assumption)).
% 0.20/0.50 tff(401,plain,
% 0.20/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(402,plain,
% 0.20/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(403,plain,
% 0.20/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_2))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[402, 401])).
% 0.20/0.50 tff(404,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[403, 120, 94, 107, 400])).
% 0.20/0.50 tff(405,plain,((~product(e_2, e_2, e_2)) | (~product(e_1, e_2, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(406,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[405, 399, 380])).
% 0.20/0.50 tff(407,plain,(product(e_1, e_2, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(408,assumption,(~product(e_3, e_1, e_1)), introduced(assumption)).
% 0.20/0.50 tff(409,plain,
% 0.20/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_2, e_3)) | product(e_3, e_1, e_1) | (~product(e_2, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_2, e_3)) | product(e_3, e_1, e_1) | (~product(e_2, e_3, e_1)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(410,plain,
% 0.20/0.50 ((product(e_3, e_1, e_1) | (~product(e_2, e_3, e_1)) | (~product(e_1, e_2, e_3))) <=> ((~product(e_1, e_2, e_3)) | product(e_3, e_1, e_1) | (~product(e_2, e_3, e_1)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(411,plain,
% 0.20/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_1) | (~product(e_2, e_3, e_1)) | (~product(e_1, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_2, e_3)) | product(e_3, e_1, e_1) | (~product(e_2, e_3, e_1))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[410])).
% 0.20/0.51 tff(412,plain,
% 0.20/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_1) | (~product(e_2, e_3, e_1)) | (~product(e_1, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_2, e_3)) | product(e_3, e_1, e_1) | (~product(e_2, e_3, e_1)))),
% 0.20/0.51 inference(transitivity,[status(thm)],[411, 409])).
% 0.20/0.51 tff(413,plain,
% 0.20/0.51 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_1) | (~product(e_2, e_3, e_1)) | (~product(e_1, e_2, e_3)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(414,plain,
% 0.20/0.51 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_2, e_3)) | product(e_3, e_1, e_1) | (~product(e_2, e_3, e_1))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[413, 412])).
% 0.20/0.51 tff(415,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[414, 12, 236, 374, 408])).
% 0.20/0.51 tff(416,plain,((~product(e_2, e_3, e_1)) | (~product(e_1, e_2, e_3)) | product(e_3, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(417,plain,
% 0.20/0.51 ((~product(e_2, e_3, e_1)) | product(e_3, e_1, e_1)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[416, 407])).
% 0.20/0.51 tff(418,plain,
% 0.20/0.51 (product(e_3, e_1, e_1)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[417, 374])).
% 0.20/0.51 tff(419,plain,
% 0.20/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_1) | (~product(e_3, e_1, e_1)) | (~product(e_2, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_2, e_1) | (~product(e_3, e_1, e_1)) | (~product(e_2, e_3, e_1)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(420,plain,
% 0.20/0.51 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_1) | (~product(e_3, e_1, e_1)) | (~product(e_2, e_3, e_1)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(421,plain,
% 0.20/0.51 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_2, e_1) | (~product(e_3, e_1, e_1)) | (~product(e_2, e_3, e_1))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[420, 419])).
% 0.20/0.51 tff(422,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[421, 12, 374, 378, 418])).
% 0.20/0.51 tff(423,plain,(~product(e_2, e_3, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(424,assumption,(product(e_2, e_3, e_3)), introduced(assumption)).
% 0.20/0.51 tff(425,plain,
% 0.20/0.51 ((~equalish(e_3, e_1)) <=> (~equalish(e_3, e_1))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(426,axiom,(~equalish(e_3, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_1')).
% 0.20/0.51 tff(427,plain,
% 0.20/0.51 (~equalish(e_3, e_1)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[426, 425])).
% 0.20/0.51 tff(428,plain,
% 0.20/0.51 (((~![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_2, e_1, e_3)) | (~product(e_2, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_3, e_3)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(429,plain,
% 0.20/0.51 ((~![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_2, e_1, e_3)) | (~product(e_2, e_3, e_3)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(430,plain,
% 0.20/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_3, e_3))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[429, 428])).
% 0.20/0.51 tff(431,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[430, 427, 117, 279, 424])).
% 0.20/0.51 tff(432,plain,(~product(e_2, e_3, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(433,plain,
% 0.20/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_3, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_3, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_3, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_3, e_1, e_2)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(434,plain,
% 0.20/0.51 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_3, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_3, e_1, e_2)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(435,plain,
% 0.20/0.51 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_3, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_3, e_1, e_2))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[434, 433])).
% 0.20/0.51 tff(436,plain,
% 0.20/0.51 (~product(e_3, e_1, e_2)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[435, 12, 407, 432])).
% 0.20/0.51 tff(437,assumption,(product(e_2, e_3, e_2)), introduced(assumption)).
% 0.20/0.51 tff(438,plain,
% 0.20/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_2, e_3)) | product(e_3, e_1, e_2) | (~product(e_2, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_2, e_3)) | product(e_3, e_1, e_2) | (~product(e_2, e_3, e_2)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(439,plain,
% 0.20/0.51 ((product(e_3, e_1, e_2) | (~product(e_2, e_3, e_2)) | (~product(e_1, e_2, e_3))) <=> ((~product(e_1, e_2, e_3)) | product(e_3, e_1, e_2) | (~product(e_2, e_3, e_2)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(440,plain,
% 0.20/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_2) | (~product(e_2, e_3, e_2)) | (~product(e_1, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_2, e_3)) | product(e_3, e_1, e_2) | (~product(e_2, e_3, e_2))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[439])).
% 0.20/0.51 tff(441,plain,
% 0.20/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_2) | (~product(e_2, e_3, e_2)) | (~product(e_1, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_2, e_3)) | product(e_3, e_1, e_2) | (~product(e_2, e_3, e_2)))),
% 0.20/0.51 inference(transitivity,[status(thm)],[440, 438])).
% 0.20/0.51 tff(442,plain,
% 0.20/0.51 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_2) | (~product(e_2, e_3, e_2)) | (~product(e_1, e_2, e_3)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(443,plain,
% 0.20/0.51 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_2, e_3)) | product(e_3, e_1, e_2) | (~product(e_2, e_3, e_2))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[442, 441])).
% 0.20/0.51 tff(444,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[443, 12, 407, 437, 436])).
% 0.20/0.51 tff(445,plain,(~product(e_2, e_3, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(446,plain,
% 0.20/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_2, e_2, e_2)) | product(e_2, e_3, e_2) | (~product(e_3, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_2, e_2, e_2)) | product(e_2, e_3, e_2) | (~product(e_3, e_2, e_2)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(447,plain,
% 0.20/0.51 ((product(e_2, e_3, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_3, e_2, e_2))) <=> ((~product(e_2, e_2, e_2)) | product(e_2, e_3, e_2) | (~product(e_3, e_2, e_2)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(448,plain,
% 0.20/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_3, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_3, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_2, e_2, e_2)) | product(e_2, e_3, e_2) | (~product(e_3, e_2, e_2))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[447])).
% 0.20/0.51 tff(449,plain,
% 0.20/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_3, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_3, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_2, e_2, e_2)) | product(e_2, e_3, e_2) | (~product(e_3, e_2, e_2)))),
% 0.20/0.51 inference(transitivity,[status(thm)],[448, 446])).
% 0.20/0.51 tff(450,plain,
% 0.20/0.51 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_3, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_3, e_2, e_2)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(451,plain,
% 0.20/0.51 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_2, e_2, e_2)) | product(e_2, e_3, e_2) | (~product(e_3, e_2, e_2))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[450, 449])).
% 0.20/0.51 tff(452,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[451, 12, 107, 445, 373])).
% 0.20/0.51 tff(453,plain,((~product(e_2, e_2, e_2)) | (~product(e_3, e_2, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(454,plain,
% 0.20/0.51 (~product(e_2, e_2, e_2)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[453, 373])).
% 0.20/0.51 tff(455,plain,
% 0.20/0.51 (group_element(e_3) <=> group_element(e_3)),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(456,axiom,(group_element(e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_3')).
% 0.20/0.51 tff(457,plain,
% 0.20/0.51 (group_element(e_3)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[456, 455])).
% 0.20/0.51 tff(458,plain,
% 0.20/0.51 (((~![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)) | product(e_2, e_3, e_3) | (~group_element(e_3)) | product(e_2, e_3, e_2) | product(e_2, e_3, e_4) | product(e_2, 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_2)) | product(e_2, e_3, e_3) | (~group_element(e_3)) | product(e_2, e_3, e_2) | product(e_2, e_3, e_4) | product(e_2, e_3, e_1))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(459,plain,
% 0.20/0.51 ((product(e_2, e_3, e_4) | product(e_2, e_3, e_3) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_2))) <=> ((~group_element(e_2)) | product(e_2, e_3, e_3) | (~group_element(e_3)) | product(e_2, e_3, e_2) | product(e_2, e_3, e_4) | product(e_2, e_3, e_1))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(460,plain,
% 0.20/0.51 (((~![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_3, e_4) | product(e_2, e_3, e_3) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1) | (~group_element(e_3)) | (~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)) | product(e_2, e_3, e_3) | (~group_element(e_3)) | product(e_2, e_3, e_2) | product(e_2, e_3, e_4) | product(e_2, e_3, e_1)))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[459])).
% 0.20/0.51 tff(461,plain,
% 0.20/0.51 (((~![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_3, e_4) | product(e_2, e_3, e_3) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1) | (~group_element(e_3)) | (~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)) | product(e_2, e_3, e_3) | (~group_element(e_3)) | product(e_2, e_3, e_2) | product(e_2, e_3, e_4) | product(e_2, e_3, e_1))),
% 0.20/0.51 inference(transitivity,[status(thm)],[460, 458])).
% 0.20/0.51 tff(462,plain,
% 0.20/0.51 ((~![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_3, e_4) | product(e_2, e_3, e_3) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_2)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(463,plain,
% 0.20/0.51 ((~![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)) | product(e_2, e_3, e_3) | (~group_element(e_3)) | product(e_2, e_3, e_2) | product(e_2, e_3, e_4) | product(e_2, e_3, e_1)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[462, 461])).
% 0.20/0.51 tff(464,plain,
% 0.20/0.51 (product(e_2, e_3, e_3) | product(e_2, e_3, e_2) | product(e_2, e_3, e_4) | product(e_2, e_3, e_1)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[463, 153, 457, 71])).
% 0.20/0.51 tff(465,plain,
% 0.20/0.51 (product(e_2, e_3, e_2) | product(e_2, e_3, e_4) | product(e_2, e_3, e_1)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[464, 432])).
% 0.20/0.51 tff(466,plain,
% 0.20/0.51 (product(e_2, e_3, e_4) | product(e_2, e_3, e_1)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[465, 445])).
% 0.20/0.51 tff(467,plain,
% 0.20/0.51 (product(e_2, e_3, e_4)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[466, 423])).
% 0.20/0.51 tff(468,assumption,(product(e_2, e_3, e_4)), introduced(assumption)).
% 0.20/0.51 tff(469,plain,
% 0.20/0.51 ((~equalish(e_3, e_2)) <=> (~equalish(e_3, e_2))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(470,axiom,(~equalish(e_3, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_2')).
% 0.20/0.51 tff(471,plain,
% 0.20/0.51 (~equalish(e_3, e_2)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[470, 469])).
% 0.20/0.51 tff(472,plain,
% 0.20/0.51 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_2, e_2, e_4)) | (~product(e_2, e_3, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_2, e_2, e_4)) | (~product(e_2, e_3, e_4)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(473,plain,
% 0.20/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_2, e_2, e_4)) | (~product(e_2, e_3, e_4)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(474,plain,
% 0.20/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_2, e_2, e_4)) | (~product(e_2, e_3, e_4))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[473, 472])).
% 0.20/0.51 tff(475,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[474, 471, 117, 182, 468])).
% 0.20/0.51 tff(476,plain,((~product(e_2, e_3, e_4)) | (~product(e_2, e_2, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(477,plain,
% 0.20/0.51 (~product(e_2, e_2, e_4)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[476, 467])).
% 0.20/0.51 tff(478,plain,
% 0.20/0.51 (product(e_2, e_2, e_2) | product(e_2, e_2, e_1)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[398, 477])).
% 0.20/0.51 tff(479,plain,
% 0.20/0.51 (product(e_2, e_2, e_1)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[478, 454])).
% 0.20/0.51 tff(480,plain,
% 0.20/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_2, e_2, e_1)) | product(e_2, e_3, e_1) | (~product(e_3, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_2, e_2, e_1)) | product(e_2, e_3, e_1) | (~product(e_3, e_2, e_2)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(481,plain,
% 0.20/0.52 ((product(e_2, e_3, e_1) | (~product(e_2, e_2, e_1)) | (~product(e_3, e_2, e_2))) <=> ((~product(e_2, e_2, e_1)) | product(e_2, e_3, e_1) | (~product(e_3, e_2, e_2)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(482,plain,
% 0.20/0.52 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_3, e_1) | (~product(e_2, e_2, e_1)) | (~product(e_3, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_2, e_2, e_1)) | product(e_2, e_3, e_1) | (~product(e_3, e_2, e_2))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[481])).
% 0.20/0.52 tff(483,plain,
% 0.20/0.52 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_3, e_1) | (~product(e_2, e_2, e_1)) | (~product(e_3, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_2, e_2, e_1)) | product(e_2, e_3, e_1) | (~product(e_3, e_2, e_2)))),
% 0.20/0.52 inference(transitivity,[status(thm)],[482, 480])).
% 0.20/0.52 tff(484,plain,
% 0.20/0.52 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_3, e_1) | (~product(e_2, e_2, e_1)) | (~product(e_3, e_2, e_2)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(485,plain,
% 0.20/0.52 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_2, e_2, e_1)) | product(e_2, e_3, e_1) | (~product(e_3, e_2, e_2))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[484, 483])).
% 0.20/0.52 tff(486,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[485, 12, 479, 423, 373])).
% 0.20/0.52 tff(487,plain,(~product(e_3, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(488,assumption,(~product(e_3, e_2, e_2)), introduced(assumption)).
% 0.20/0.52 tff(489,assumption,(product(e_1, e_3, e_2)), introduced(assumption)).
% 0.20/0.52 tff(490,plain,
% 0.20/0.52 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_2, e_1, e_3)) | product(e_3, e_2, e_2) | (~product(e_1, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_2, e_1, e_3)) | product(e_3, e_2, e_2) | (~product(e_1, e_3, e_2)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(491,plain,
% 0.20/0.52 ((product(e_3, e_2, e_2) | (~product(e_1, e_3, e_2)) | (~product(e_2, e_1, e_3))) <=> ((~product(e_2, e_1, e_3)) | product(e_3, e_2, e_2) | (~product(e_1, e_3, e_2)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(492,plain,
% 0.20/0.52 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_2, e_2) | (~product(e_1, e_3, e_2)) | (~product(e_2, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_2, e_1, e_3)) | product(e_3, e_2, e_2) | (~product(e_1, e_3, e_2))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[491])).
% 0.20/0.52 tff(493,plain,
% 0.20/0.52 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_2, e_2) | (~product(e_1, e_3, e_2)) | (~product(e_2, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_2, e_1, e_3)) | product(e_3, e_2, e_2) | (~product(e_1, e_3, e_2)))),
% 0.20/0.52 inference(transitivity,[status(thm)],[492, 490])).
% 0.20/0.52 tff(494,plain,
% 0.20/0.52 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_2, e_2) | (~product(e_1, e_3, e_2)) | (~product(e_2, e_1, e_3)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(495,plain,
% 0.20/0.52 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_2, e_1, e_3)) | product(e_3, e_2, e_2) | (~product(e_1, e_3, e_2))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[494, 493])).
% 0.20/0.52 tff(496,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[495, 12, 279, 489, 488])).
% 0.20/0.52 tff(497,plain,((~product(e_1, e_3, e_2)) | product(e_3, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(498,plain,
% 0.20/0.52 (~product(e_1, e_3, e_2)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[497, 487])).
% 0.20/0.52 tff(499,assumption,(product(e_1, e_3, e_4)), introduced(assumption)).
% 0.20/0.52 tff(500,plain,
% 0.20/0.52 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_2, e_3, e_4)) | (~product(e_1, e_3, 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_1) | (~product(e_2, e_3, e_4)) | (~product(e_1, e_3, e_4)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(501,plain,
% 0.20/0.52 ((equalish(e_2, e_1) | (~product(e_1, e_3, e_4)) | (~product(e_2, e_3, e_4))) <=> (equalish(e_2, e_1) | (~product(e_2, e_3, e_4)) | (~product(e_1, e_3, e_4)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(502,plain,
% 0.20/0.52 (((~![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_3, e_4)) | (~product(e_2, e_3, 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_1) | (~product(e_2, e_3, e_4)) | (~product(e_1, e_3, e_4))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[501])).
% 0.20/0.52 tff(503,plain,
% 0.20/0.52 (((~![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_3, e_4)) | (~product(e_2, e_3, 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_1) | (~product(e_2, e_3, e_4)) | (~product(e_1, e_3, e_4)))),
% 0.20/0.52 inference(transitivity,[status(thm)],[502, 500])).
% 0.20/0.52 tff(504,plain,
% 0.20/0.52 ((~![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_3, e_4)) | (~product(e_2, e_3, e_4)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(505,plain,
% 0.20/0.52 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_2, e_3, e_4)) | (~product(e_1, e_3, e_4))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[504, 503])).
% 0.20/0.52 tff(506,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[505, 120, 94, 499, 468])).
% 0.20/0.52 tff(507,plain,((~product(e_2, e_3, e_4)) | (~product(e_1, e_3, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(508,plain,
% 0.20/0.52 (~product(e_1, e_3, e_4)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[507, 467])).
% 0.20/0.52 tff(509,assumption,(product(e_1, e_3, e_3)), introduced(assumption)).
% 0.20/0.52 tff(510,plain,
% 0.20/0.52 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_3, e_3)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(511,plain,
% 0.20/0.52 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_3, e_3)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(512,plain,
% 0.20/0.52 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_3, e_3))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[511, 510])).
% 0.20/0.52 tff(513,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[512, 471, 117, 236, 509])).
% 0.20/0.52 tff(514,plain,((~product(e_1, e_3, e_3)) | (~product(e_1, e_2, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(515,plain,
% 0.20/0.52 (~product(e_1, e_3, e_3)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[514, 407])).
% 0.20/0.52 tff(516,plain,
% 0.20/0.52 (((~![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_1)) | product(e_1, e_3, e_2) | (~group_element(e_3)) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3) | 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_1)) | product(e_1, e_3, e_2) | (~group_element(e_3)) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3) | product(e_1, e_3, e_1))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(517,plain,
% 0.20/0.52 ((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_1)) | product(e_1, e_3, e_2) | (~group_element(e_3)) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3) | product(e_1, e_3, e_1))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(518,plain,
% 0.20/0.52 (((~![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_1)) | product(e_1, e_3, e_2) | (~group_element(e_3)) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3) | product(e_1, e_3, e_1)))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[517])).
% 0.20/0.52 tff(519,plain,
% 0.20/0.52 (((~![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_1)) | product(e_1, e_3, e_2) | (~group_element(e_3)) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3) | product(e_1, e_3, e_1))),
% 0.20/0.52 inference(transitivity,[status(thm)],[518, 516])).
% 0.20/0.52 tff(520,plain,
% 0.20/0.52 ((~![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)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(521,plain,
% 0.20/0.52 ((~![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_1)) | product(e_1, e_3, e_2) | (~group_element(e_3)) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3) | product(e_1, e_3, e_1)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[520, 519])).
% 0.20/0.52 tff(522,plain,
% 0.20/0.52 (product(e_1, e_3, e_2) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3) | product(e_1, e_3, e_1)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[521, 74, 457, 71])).
% 0.20/0.52 tff(523,plain,
% 0.20/0.52 (product(e_1, e_3, e_2) | product(e_1, e_3, e_4) | product(e_1, e_3, e_1)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[522, 515])).
% 0.20/0.52 tff(524,plain,
% 0.20/0.52 (product(e_1, e_3, e_2) | product(e_1, e_3, e_1)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[523, 508])).
% 0.20/0.52 tff(525,plain,
% 0.20/0.52 (product(e_1, e_3, e_1)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[524, 498])).
% 0.20/0.52 tff(526,assumption,(product(e_1, e_3, e_1)), introduced(assumption)).
% 0.20/0.52 tff(527,plain,
% 0.20/0.52 (((~![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)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(528,plain,
% 0.20/0.52 ((~![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)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(529,plain,
% 0.20/0.52 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_1))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[528, 527])).
% 0.20/0.52 tff(530,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[529, 427, 117, 84, 526])).
% 0.20/0.52 tff(531,plain,((~product(e_1, e_3, e_1)) | (~product(e_1, e_1, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(532,plain,
% 0.20/0.52 (~product(e_1, e_1, e_1)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[531, 525])).
% 0.20/0.52 tff(533,plain,
% 0.20/0.52 (product(e_1, e_1, e_2)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[81, 532])).
% 0.20/0.52 tff(534,assumption,(product(e_4, e_1, e_2)), introduced(assumption)).
% 0.20/0.52 tff(535,plain,
% 0.20/0.52 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_4, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_4, e_1, e_2)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(536,plain,
% 0.20/0.52 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_4, e_1, e_2)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(537,plain,
% 0.20/0.52 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_4, e_1, e_2))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[536, 535])).
% 0.20/0.52 tff(538,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[537, 97, 94, 265, 534])).
% 0.20/0.52 tff(539,plain,((~product(e_4, e_1, e_2)) | (~product(e_1, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(540,plain,
% 0.20/0.52 (~product(e_4, e_1, e_2)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[539, 265])).
% 0.20/0.52 tff(541,plain,
% 0.20/0.52 (product(e_4, e_1, e_1)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[301, 540, 2])).
% 0.20/0.52 tff(542,plain,
% 0.20/0.52 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_4, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_4, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_4, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_4, e_1, e_1)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(543,plain,
% 0.20/0.52 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_4, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_4, e_1, e_1)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(544,plain,
% 0.20/0.52 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_4, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_4, e_1, e_1))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[543, 542])).
% 0.20/0.52 tff(545,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[544, 12, 265, 83, 345])).
% 0.20/0.52 tff(546,plain,(product(e_1, e_4, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_4, e_1, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(547,plain,
% 0.20/0.52 (product(e_1, e_4, e_2)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[546, 265, 541])).
% 0.20/0.52 tff(548,plain,
% 0.20/0.52 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_1) | (~product(e_1, e_4, e_2)) | (~product(e_1, 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_1, e_4, e_2)) | (~product(e_1, e_1, e_2)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(549,plain,
% 0.20/0.53 ((equalish(e_4, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_4, e_2))) <=> (equalish(e_4, e_1) | (~product(e_1, e_4, e_2)) | (~product(e_1, e_1, e_2)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(550,plain,
% 0.20/0.53 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_1, 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_1, e_4, e_2)) | (~product(e_1, e_1, e_2))))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[549])).
% 0.20/0.53 tff(551,plain,
% 0.20/0.53 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_1, 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_1, e_4, e_2)) | (~product(e_1, e_1, e_2)))),
% 0.20/0.53 inference(transitivity,[status(thm)],[550, 548])).
% 0.20/0.53 tff(552,plain,
% 0.20/0.53 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_4, e_2)))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(553,plain,
% 0.20/0.53 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_1) | (~product(e_1, e_4, e_2)) | (~product(e_1, e_1, e_2))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[552, 551])).
% 0.20/0.53 tff(554,plain,
% 0.20/0.53 ($false),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[553, 97, 117, 265, 547])).
% 0.20/0.53 tff(555,plain,((~product(e_1, e_1, e_2)) | product(e_4, e_1, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.53 tff(556,plain,
% 0.20/0.53 (product(e_4, e_1, e_4)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[555, 533])).
% 0.20/0.53 tff(557,plain,
% 0.20/0.53 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_4) | (~product(e_2, e_4, e_1)) | (~product(e_4, e_1, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_2, e_4) | (~product(e_2, e_4, e_1)) | (~product(e_4, e_1, e_4)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(558,plain,
% 0.20/0.53 ((product(e_1, e_2, e_4) | (~product(e_4, e_1, e_4)) | (~product(e_2, e_4, e_1))) <=> (product(e_1, e_2, e_4) | (~product(e_2, e_4, e_1)) | (~product(e_4, e_1, e_4)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(559,plain,
% 0.20/0.53 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_4) | (~product(e_4, e_1, e_4)) | (~product(e_2, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_4) | (~product(e_2, e_4, e_1)) | (~product(e_4, e_1, e_4))))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[558])).
% 0.20/0.53 tff(560,plain,
% 0.20/0.53 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_4) | (~product(e_4, e_1, e_4)) | (~product(e_2, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_2, e_4) | (~product(e_2, e_4, e_1)) | (~product(e_4, e_1, e_4)))),
% 0.20/0.53 inference(transitivity,[status(thm)],[559, 557])).
% 0.20/0.53 tff(561,plain,
% 0.20/0.53 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_4) | (~product(e_4, e_1, e_4)) | (~product(e_2, e_4, e_1)))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(562,plain,
% 0.20/0.53 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_2, e_4) | (~product(e_2, e_4, e_1)) | (~product(e_4, e_1, e_4))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[561, 560])).
% 0.20/0.53 tff(563,plain,
% 0.20/0.53 (~product(e_2, e_4, e_1)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[562, 12, 556, 372])).
% 0.20/0.53 tff(564,assumption,(product(e_4, e_2, e_4)), introduced(assumption)).
% 0.20/0.53 tff(565,plain,
% 0.20/0.53 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_1) | (~product(e_4, e_2, e_4)) | (~product(e_4, e_1, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_4, e_2, e_4)) | (~product(e_4, e_1, e_4)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(566,plain,
% 0.20/0.53 ((equalish(e_2, e_1) | (~product(e_4, e_1, e_4)) | (~product(e_4, e_2, e_4))) <=> (equalish(e_2, e_1) | (~product(e_4, e_2, e_4)) | (~product(e_4, e_1, e_4)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(567,plain,
% 0.20/0.53 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_1) | (~product(e_4, e_1, e_4)) | (~product(e_4, e_2, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_1) | (~product(e_4, e_2, e_4)) | (~product(e_4, e_1, e_4))))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[566])).
% 0.20/0.53 tff(568,plain,
% 0.20/0.53 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_1) | (~product(e_4, e_1, e_4)) | (~product(e_4, e_2, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_4, e_2, e_4)) | (~product(e_4, e_1, e_4)))),
% 0.20/0.53 inference(transitivity,[status(thm)],[567, 565])).
% 0.20/0.53 tff(569,plain,
% 0.20/0.53 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_1) | (~product(e_4, e_1, e_4)) | (~product(e_4, e_2, e_4)))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(570,plain,
% 0.20/0.53 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_4, e_2, e_4)) | (~product(e_4, e_1, e_4))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[569, 568])).
% 0.20/0.53 tff(571,plain,
% 0.20/0.53 ($false),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[570, 120, 117, 564, 556])).
% 0.20/0.53 tff(572,plain,(~product(e_4, e_2, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.53 tff(573,assumption,(product(e_4, e_2, e_3)), introduced(assumption)).
% 0.20/0.53 tff(574,plain,
% 0.20/0.53 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_1) | (~product(e_1, e_2, e_3)) | (~product(e_4, e_2, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_1) | (~product(e_1, e_2, e_3)) | (~product(e_4, e_2, e_3)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(575,plain,
% 0.20/0.53 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_1) | (~product(e_1, e_2, e_3)) | (~product(e_4, e_2, e_3)))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(576,plain,
% 0.20/0.53 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_1) | (~product(e_1, e_2, e_3)) | (~product(e_4, e_2, e_3))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[575, 574])).
% 0.20/0.53 tff(577,plain,
% 0.20/0.53 ($false),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[576, 97, 94, 573, 407])).
% 0.20/0.53 tff(578,plain,(~product(e_4, e_2, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.53 tff(579,plain,
% 0.20/0.53 ((~equalish(e_2, e_4)) <=> (~equalish(e_2, e_4))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(580,axiom,(~equalish(e_2, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_4')).
% 0.20/0.53 tff(581,plain,
% 0.20/0.53 (~equalish(e_2, e_4)),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[580, 579])).
% 0.20/0.53 tff(582,plain,
% 0.20/0.53 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_4) | (~product(e_1, e_4, e_3)) | (~product(e_1, e_2, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_4) | (~product(e_1, e_4, e_3)) | (~product(e_1, e_2, e_3)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(583,plain,
% 0.20/0.53 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_4) | (~product(e_1, e_4, e_3)) | (~product(e_1, e_2, e_3)))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(584,plain,
% 0.20/0.53 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_4) | (~product(e_1, e_4, e_3)) | (~product(e_1, e_2, e_3))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[583, 582])).
% 0.20/0.53 tff(585,plain,
% 0.20/0.53 ($false),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[584, 581, 117, 358, 236])).
% 0.20/0.53 tff(586,plain,((~product(e_1, e_2, e_3)) | (~product(e_1, e_4, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.53 tff(587,plain,
% 0.20/0.53 (~product(e_1, e_4, e_3)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[586, 407])).
% 0.20/0.53 tff(588,plain,
% 0.20/0.53 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_2, e_1, e_3)) | (~product(e_4, e_2, e_1)) | product(e_1, e_4, e_3))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_2, e_1, e_3)) | (~product(e_4, e_2, e_1)) | product(e_1, e_4, e_3))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(589,plain,
% 0.20/0.53 ((product(e_1, e_4, e_3) | (~product(e_2, e_1, e_3)) | (~product(e_4, e_2, e_1))) <=> ((~product(e_2, e_1, e_3)) | (~product(e_4, e_2, e_1)) | product(e_1, e_4, e_3))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(590,plain,
% 0.20/0.53 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_4, e_3) | (~product(e_2, e_1, e_3)) | (~product(e_4, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_2, e_1, e_3)) | (~product(e_4, e_2, e_1)) | product(e_1, e_4, e_3)))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[589])).
% 0.20/0.53 tff(591,plain,
% 0.20/0.53 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_4, e_3) | (~product(e_2, e_1, e_3)) | (~product(e_4, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_2, e_1, e_3)) | (~product(e_4, e_2, e_1)) | product(e_1, e_4, e_3))),
% 0.20/0.53 inference(transitivity,[status(thm)],[590, 588])).
% 0.20/0.53 tff(592,plain,
% 0.20/0.53 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_4, e_3) | (~product(e_2, e_1, e_3)) | (~product(e_4, e_2, e_1)))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(593,plain,
% 0.20/0.53 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_2, e_1, e_3)) | (~product(e_4, e_2, e_1)) | product(e_1, e_4, e_3)),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[592, 591])).
% 0.20/0.53 tff(594,plain,
% 0.20/0.53 ((~product(e_2, e_1, e_3)) | (~product(e_4, e_2, e_1)) | product(e_1, e_4, e_3)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[593, 12])).
% 0.20/0.53 tff(595,plain,
% 0.20/0.53 ((~product(e_4, e_2, e_1)) | product(e_1, e_4, e_3)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[594, 279])).
% 0.20/0.53 tff(596,plain,
% 0.20/0.53 (~product(e_4, e_2, e_1)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[595, 587])).
% 0.20/0.53 tff(597,plain,
% 0.20/0.53 (((~![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)) | product(e_4, e_2, e_4) | product(e_4, e_2, e_1) | product(e_4, e_2, e_3) | product(e_4, e_2, 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_2)) | product(e_4, e_2, e_4) | product(e_4, e_2, e_1) | product(e_4, e_2, e_3) | product(e_4, e_2, e_2) | (~group_element(e_4)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(598,plain,
% 0.20/0.53 ((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_2)) | product(e_4, e_2, e_4) | product(e_4, e_2, e_1) | product(e_4, e_2, e_3) | product(e_4, e_2, e_2) | (~group_element(e_4)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(599,plain,
% 0.20/0.53 (((~![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_2)) | product(e_4, e_2, e_4) | product(e_4, e_2, e_1) | product(e_4, e_2, e_3) | product(e_4, e_2, e_2) | (~group_element(e_4))))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[598])).
% 0.20/0.53 tff(600,plain,
% 0.20/0.53 (((~![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_2)) | product(e_4, e_2, e_4) | product(e_4, e_2, e_1) | product(e_4, e_2, e_3) | product(e_4, e_2, e_2) | (~group_element(e_4)))),
% 0.20/0.53 inference(transitivity,[status(thm)],[599, 597])).
% 0.20/0.53 tff(601,plain,
% 0.20/0.53 ((~![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)))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(602,plain,
% 0.20/0.53 ((~![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)) | product(e_4, e_2, e_4) | product(e_4, e_2, e_1) | product(e_4, e_2, e_3) | product(e_4, e_2, e_2) | (~group_element(e_4))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[601, 600])).
% 0.20/0.53 tff(603,plain,
% 0.20/0.53 (product(e_4, e_2, e_4) | product(e_4, e_2, e_1) | product(e_4, e_2, e_3) | product(e_4, e_2, e_2)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[602, 153, 293, 71])).
% 0.20/0.53 tff(604,plain,
% 0.20/0.53 (product(e_4, e_2, e_4) | product(e_4, e_2, e_3) | product(e_4, e_2, e_2)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[603, 596])).
% 0.20/0.53 tff(605,plain,
% 0.20/0.53 (product(e_4, e_2, e_2)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[604, 578, 572])).
% 0.20/0.53 tff(606,assumption,(product(e_4, e_2, e_2)), introduced(assumption)).
% 0.20/0.53 tff(607,plain,
% 0.20/0.53 (((~![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)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(608,plain,
% 0.20/0.53 ((~![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)))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(609,plain,
% 0.20/0.53 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_4, e_2, e_2))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[608, 607])).
% 0.20/0.54 tff(610,plain,
% 0.20/0.54 ($false),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[609, 284, 94, 606, 107])).
% 0.20/0.54 tff(611,plain,((~product(e_4, e_2, e_2)) | (~product(e_2, e_2, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.54 tff(612,plain,
% 0.20/0.54 (~product(e_2, e_2, e_2)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[611, 605])).
% 0.20/0.54 tff(613,plain,
% 0.20/0.54 (product(e_2, e_2, e_1)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[478, 612])).
% 0.20/0.54 tff(614,plain,
% 0.20/0.54 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_2, e_2, e_1)) | product(e_2, e_4, e_1) | (~product(e_4, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_2, e_2, e_1)) | product(e_2, e_4, e_1) | (~product(e_4, e_2, e_2)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(615,plain,
% 0.20/0.54 ((product(e_2, e_4, e_1) | (~product(e_2, e_2, e_1)) | (~product(e_4, e_2, e_2))) <=> ((~product(e_2, e_2, e_1)) | product(e_2, e_4, e_1) | (~product(e_4, e_2, e_2)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(616,plain,
% 0.20/0.54 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_4, e_1) | (~product(e_2, e_2, e_1)) | (~product(e_4, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_2, e_2, e_1)) | product(e_2, e_4, e_1) | (~product(e_4, e_2, e_2))))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[615])).
% 0.20/0.54 tff(617,plain,
% 0.20/0.54 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_4, e_1) | (~product(e_2, e_2, e_1)) | (~product(e_4, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_2, e_2, e_1)) | product(e_2, e_4, e_1) | (~product(e_4, e_2, e_2)))),
% 0.20/0.54 inference(transitivity,[status(thm)],[616, 614])).
% 0.20/0.54 tff(618,plain,
% 0.20/0.54 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_4, e_1) | (~product(e_2, e_2, e_1)) | (~product(e_4, e_2, e_2)))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(619,plain,
% 0.20/0.54 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_2, e_2, e_1)) | product(e_2, e_4, e_1) | (~product(e_4, e_2, e_2))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[618, 617])).
% 0.20/0.54 tff(620,plain,
% 0.20/0.54 ($false),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[619, 12, 605, 613, 563])).
% 0.20/0.54 % SZS output end Proof
%------------------------------------------------------------------------------