TSTP Solution File: GRP124-9.004 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP124-9.004 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n011.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 22:26:02 EDT 2022
% Result : Unsatisfiable 0.20s 0.53s
% Output : Proof 0.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP124-9.004 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.13/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n011.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 31 14:53:56 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.36 Usage: tptp [options] [-file:]file
% 0.13/0.36 -h, -? prints this message.
% 0.13/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.36 -m, -model generate model.
% 0.13/0.36 -p, -proof generate proof.
% 0.13/0.36 -c, -core generate unsat core of named formulas.
% 0.13/0.36 -st, -statistics display statistics.
% 0.13/0.36 -t:timeout set timeout (in second).
% 0.13/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.36 -<param>:<value> configuration parameter and value.
% 0.13/0.36 -o:<output-file> file to place output in.
% 0.20/0.53 % SZS status Unsatisfiable
% 0.20/0.53 % SZS output start Proof
% 0.20/0.53 tff(product1_type, type, (
% 0.20/0.53 product1: ( $i * $i * $i ) > $o)).
% 0.20/0.53 tff(e_4_type, type, (
% 0.20/0.53 e_4: $i)).
% 0.20/0.53 tff(e_1_type, type, (
% 0.20/0.53 e_1: $i)).
% 0.20/0.53 tff(e_2_type, type, (
% 0.20/0.53 e_2: $i)).
% 0.20/0.53 tff(product2_type, type, (
% 0.20/0.53 product2: ( $i * $i * $i ) > $o)).
% 0.20/0.53 tff(equalish_type, type, (
% 0.20/0.53 equalish: ( $i * $i ) > $o)).
% 0.20/0.53 tff(e_3_type, type, (
% 0.20/0.53 e_3: $i)).
% 0.20/0.53 tff(group_element_type, type, (
% 0.20/0.53 group_element: $i > $o)).
% 0.20/0.53 tff(1,assumption,(product1(e_2, e_1, e_1)), introduced(assumption)).
% 0.20/0.53 tff(2,assumption,(product2(e_1, e_4, e_1)), introduced(assumption)).
% 0.20/0.53 tff(3,plain,
% 0.20/0.53 (^[X: $i] : refl(product2(X, X, X) <=> product2(X, X, X))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(4,plain,
% 0.20/0.53 (![X: $i] : product2(X, X, X) <=> ![X: $i] : product2(X, X, X)),
% 0.20/0.53 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.53 tff(5,plain,
% 0.20/0.53 (![X: $i] : product2(X, X, X) <=> ![X: $i] : product2(X, X, X)),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(6,axiom,(![X: $i] : product2(X, X, X)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product2_idempotence')).
% 0.20/0.53 tff(7,plain,
% 0.20/0.53 (![X: $i] : product2(X, X, X)),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.20/0.53 tff(8,plain,(
% 0.20/0.53 ![X: $i] : product2(X, X, X)),
% 0.20/0.53 inference(skolemize,[status(sab)],[7])).
% 0.20/0.53 tff(9,plain,
% 0.20/0.53 (![X: $i] : product2(X, X, X)),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.20/0.53 tff(10,plain,
% 0.20/0.53 ((~![X: $i] : product2(X, X, X)) | product2(e_1, e_1, e_1)),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(11,plain,
% 0.20/0.53 (product2(e_1, e_1, e_1)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[10, 9])).
% 0.20/0.53 tff(12,plain,
% 0.20/0.53 (^[W: $i, Z: $i, Y: $i, X: $i] : refl((equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y))) <=> (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(13,plain,
% 0.20/0.53 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[12])).
% 0.20/0.53 tff(14,plain,
% 0.20/0.53 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(15,plain,
% 0.20/0.53 (^[W: $i, Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite(((~product2(X, W, Y)) | (~product2(X, Z, Y))) <=> ((~product2(X, Z, Y)) | (~product2(X, W, Y)))), ((((~product2(X, W, Y)) | (~product2(X, Z, Y))) | equalish(W, Z)) <=> (((~product2(X, Z, Y)) | (~product2(X, W, Y))) | equalish(W, Z)))), rewrite((((~product2(X, Z, Y)) | (~product2(X, W, Y))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))), ((((~product2(X, W, Y)) | (~product2(X, Z, Y))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(16,plain,
% 0.20/0.53 (![W: $i, Z: $i, Y: $i, X: $i] : (((~product2(X, W, Y)) | (~product2(X, Z, Y))) | equalish(W, Z)) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[15])).
% 0.20/0.53 tff(17,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product2(X, W, Y)) | (~product2(X, Z, Y))) | equalish(W, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product2_right_cancellation')).
% 0.20/0.53 tff(18,plain,
% 0.20/0.53 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.20/0.53 tff(19,plain,
% 0.20/0.53 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.20/0.53 tff(20,plain,(
% 0.20/0.53 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))),
% 0.20/0.53 inference(skolemize,[status(sab)],[19])).
% 0.20/0.53 tff(21,plain,
% 0.20/0.53 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.20/0.53 tff(22,plain,
% 0.20/0.53 ((~equalish(e_4, e_1)) <=> (~equalish(e_4, e_1))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(23,axiom,(~equalish(e_4, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_1')).
% 0.20/0.53 tff(24,plain,
% 0.20/0.53 (~equalish(e_4, e_1)),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.20/0.53 tff(25,plain,
% 0.20/0.53 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | (equalish(e_4, e_1) | (~product2(e_1, e_1, e_1)) | (~product2(e_1, e_4, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | equalish(e_4, e_1) | (~product2(e_1, e_1, e_1)) | (~product2(e_1, e_4, e_1)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(26,plain,
% 0.20/0.53 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | (equalish(e_4, e_1) | (~product2(e_1, e_1, e_1)) | (~product2(e_1, e_4, e_1)))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(27,plain,
% 0.20/0.53 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | equalish(e_4, e_1) | (~product2(e_1, e_1, e_1)) | (~product2(e_1, e_4, e_1))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.20/0.53 tff(28,plain,
% 0.20/0.53 ($false),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[27, 24, 21, 11, 2])).
% 0.20/0.53 tff(29,plain,(~product2(e_1, e_4, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.53 tff(30,assumption,(product1(e_4, e_3, e_1)), introduced(assumption)).
% 0.20/0.53 tff(31,assumption,(product1(e_4, e_2, e_1)), introduced(assumption)).
% 0.20/0.53 tff(32,plain,
% 0.20/0.53 (^[W: $i, Z: $i, Y: $i, X: $i] : refl((equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y))) <=> (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(33,plain,
% 0.20/0.53 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[32])).
% 0.20/0.53 tff(34,plain,
% 0.20/0.53 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(35,plain,
% 0.20/0.53 (^[W: $i, Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite(((~product1(X, W, Y)) | (~product1(X, Z, Y))) <=> ((~product1(X, Z, Y)) | (~product1(X, W, Y)))), ((((~product1(X, W, Y)) | (~product1(X, Z, Y))) | equalish(W, Z)) <=> (((~product1(X, Z, Y)) | (~product1(X, W, Y))) | equalish(W, Z)))), rewrite((((~product1(X, Z, Y)) | (~product1(X, W, Y))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))), ((((~product1(X, W, Y)) | (~product1(X, Z, Y))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(36,plain,
% 0.20/0.53 (![W: $i, Z: $i, Y: $i, X: $i] : (((~product1(X, W, Y)) | (~product1(X, Z, Y))) | equalish(W, Z)) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[35])).
% 0.20/0.53 tff(37,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product1(X, W, Y)) | (~product1(X, Z, Y))) | equalish(W, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product1_right_cancellation')).
% 0.20/0.53 tff(38,plain,
% 0.20/0.53 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.20/0.53 tff(39,plain,
% 0.20/0.53 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.20/0.53 tff(40,plain,(
% 0.20/0.53 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))),
% 0.20/0.53 inference(skolemize,[status(sab)],[39])).
% 0.20/0.53 tff(41,plain,
% 0.20/0.53 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[40, 33])).
% 0.20/0.53 tff(42,plain,
% 0.20/0.54 ((~equalish(e_3, e_2)) <=> (~equalish(e_3, e_2))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(43,axiom,(~equalish(e_3, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_2')).
% 0.20/0.54 tff(44,plain,
% 0.20/0.54 (~equalish(e_3, e_2)),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.20/0.54 tff(45,plain,
% 0.20/0.54 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_3, e_2) | (~product1(e_4, e_2, e_1)) | (~product1(e_4, e_3, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_3, e_2) | (~product1(e_4, e_2, e_1)) | (~product1(e_4, e_3, e_1)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(46,plain,
% 0.20/0.54 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_3, e_2) | (~product1(e_4, e_2, e_1)) | (~product1(e_4, e_3, e_1)))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(47,plain,
% 0.20/0.54 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_3, e_2) | (~product1(e_4, e_2, e_1)) | (~product1(e_4, e_3, e_1))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.20/0.54 tff(48,plain,
% 0.20/0.54 ($false),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[47, 44, 41, 31, 30])).
% 0.20/0.54 tff(49,plain,((~product1(e_4, e_3, e_1)) | (~product1(e_4, e_2, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.54 tff(50,plain,
% 0.20/0.54 (~product1(e_4, e_2, e_1)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[49, 30])).
% 0.20/0.54 tff(51,assumption,(~product1(e_2, e_2, e_2)), introduced(assumption)).
% 0.20/0.54 tff(52,plain,
% 0.20/0.54 (^[X: $i] : refl(product1(X, X, X) <=> product1(X, X, X))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(53,plain,
% 0.20/0.54 (![X: $i] : product1(X, X, X) <=> ![X: $i] : product1(X, X, X)),
% 0.20/0.54 inference(quant_intro,[status(thm)],[52])).
% 0.20/0.54 tff(54,plain,
% 0.20/0.54 (![X: $i] : product1(X, X, X) <=> ![X: $i] : product1(X, X, X)),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(55,axiom,(![X: $i] : product1(X, X, X)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product1_idempotence')).
% 0.20/0.54 tff(56,plain,
% 0.20/0.54 (![X: $i] : product1(X, X, X)),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.20/0.54 tff(57,plain,(
% 0.20/0.54 ![X: $i] : product1(X, X, X)),
% 0.20/0.54 inference(skolemize,[status(sab)],[56])).
% 0.20/0.54 tff(58,plain,
% 0.20/0.54 (![X: $i] : product1(X, X, X)),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.20/0.54 tff(59,plain,
% 0.20/0.54 ((~![X: $i] : product1(X, X, X)) | product1(e_2, e_2, e_2)),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(60,plain,
% 0.20/0.54 ($false),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[59, 58, 51])).
% 0.20/0.54 tff(61,plain,(product1(e_2, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.54 tff(62,assumption,(product1(e_2, e_2, e_2)), introduced(assumption)).
% 0.20/0.54 tff(63,assumption,(product1(e_4, e_2, e_2)), introduced(assumption)).
% 0.20/0.54 tff(64,plain,
% 0.20/0.54 (^[W: $i, Z: $i, Y: $i, X: $i] : refl((equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X))) <=> (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X))))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(65,plain,
% 0.20/0.54 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[64])).
% 0.20/0.54 tff(66,plain,
% 0.20/0.54 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(67,plain,
% 0.20/0.54 (^[W: $i, Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite(((~product1(W, Y, X)) | (~product1(Z, Y, X))) <=> ((~product1(Z, Y, X)) | (~product1(W, Y, X)))), ((((~product1(W, Y, X)) | (~product1(Z, Y, X))) | equalish(W, Z)) <=> (((~product1(Z, Y, X)) | (~product1(W, Y, X))) | equalish(W, Z)))), rewrite((((~product1(Z, Y, X)) | (~product1(W, Y, X))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))), ((((~product1(W, Y, X)) | (~product1(Z, Y, X))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(68,plain,
% 0.20/0.54 (![W: $i, Z: $i, Y: $i, X: $i] : (((~product1(W, Y, X)) | (~product1(Z, Y, X))) | equalish(W, Z)) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[67])).
% 0.20/0.54 tff(69,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product1(W, Y, X)) | (~product1(Z, Y, X))) | equalish(W, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product1_left_cancellation')).
% 0.20/0.54 tff(70,plain,
% 0.20/0.54 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.20/0.54 tff(71,plain,
% 0.20/0.54 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.20/0.54 tff(72,plain,(
% 0.20/0.54 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))),
% 0.20/0.54 inference(skolemize,[status(sab)],[71])).
% 0.20/0.54 tff(73,plain,
% 0.20/0.54 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[72, 65])).
% 0.20/0.54 tff(74,plain,
% 0.20/0.54 ((~equalish(e_2, e_4)) <=> (~equalish(e_2, e_4))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(75,axiom,(~equalish(e_2, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_4')).
% 0.20/0.54 tff(76,plain,
% 0.20/0.54 (~equalish(e_2, e_4)),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.20/0.54 tff(77,plain,
% 0.20/0.54 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_2, e_4) | (~product1(e_4, e_2, e_2)) | (~product1(e_2, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_2, e_4) | (~product1(e_4, e_2, e_2)) | (~product1(e_2, e_2, e_2)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(78,plain,
% 0.20/0.54 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_2, e_4) | (~product1(e_4, e_2, e_2)) | (~product1(e_2, e_2, e_2)))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(79,plain,
% 0.20/0.54 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_2, e_4) | (~product1(e_4, e_2, e_2)) | (~product1(e_2, e_2, e_2))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.20/0.54 tff(80,plain,
% 0.20/0.54 ($false),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[79, 76, 73, 63, 62])).
% 0.20/0.54 tff(81,plain,((~product1(e_2, e_2, e_2)) | (~product1(e_4, e_2, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.54 tff(82,plain,
% 0.20/0.54 (~product1(e_4, e_2, e_2)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[81, 61])).
% 0.20/0.54 tff(83,plain,
% 0.20/0.54 ((~![X: $i] : product1(X, X, X)) | product1(e_4, e_4, e_4)),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(84,plain,
% 0.20/0.54 (product1(e_4, e_4, e_4)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[83, 58])).
% 0.20/0.54 tff(85,assumption,(product1(e_4, e_2, e_4)), introduced(assumption)).
% 0.20/0.54 tff(86,plain,
% 0.20/0.54 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_2, e_4) | (~product1(e_4, e_2, e_4)) | (~product1(e_4, e_4, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_2, e_4) | (~product1(e_4, e_2, e_4)) | (~product1(e_4, e_4, e_4)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(87,plain,
% 0.20/0.54 ((equalish(e_2, e_4) | (~product1(e_4, e_4, e_4)) | (~product1(e_4, e_2, e_4))) <=> (equalish(e_2, e_4) | (~product1(e_4, e_2, e_4)) | (~product1(e_4, e_4, e_4)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(88,plain,
% 0.20/0.54 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_2, e_4) | (~product1(e_4, e_4, e_4)) | (~product1(e_4, e_2, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_2, e_4) | (~product1(e_4, e_2, e_4)) | (~product1(e_4, e_4, e_4))))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[87])).
% 0.20/0.54 tff(89,plain,
% 0.20/0.54 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_2, e_4) | (~product1(e_4, e_4, e_4)) | (~product1(e_4, e_2, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_2, e_4) | (~product1(e_4, e_2, e_4)) | (~product1(e_4, e_4, e_4)))),
% 0.20/0.54 inference(transitivity,[status(thm)],[88, 86])).
% 0.20/0.54 tff(90,plain,
% 0.20/0.54 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_2, e_4) | (~product1(e_4, e_4, e_4)) | (~product1(e_4, e_2, e_4)))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(91,plain,
% 0.20/0.54 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_2, e_4) | (~product1(e_4, e_2, e_4)) | (~product1(e_4, e_4, e_4))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.20/0.54 tff(92,plain,
% 0.20/0.54 ($false),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[91, 76, 41, 85, 84])).
% 0.20/0.54 tff(93,plain,(~product1(e_4, e_2, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.54 tff(94,plain,
% 0.20/0.54 (^[Y: $i, X: $i] : refl(((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1)) <=> ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1)))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(95,plain,
% 0.20/0.54 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1)) <=> ![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[94])).
% 0.20/0.54 tff(96,plain,
% 0.20/0.54 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1)) <=> ![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(97,plain,
% 0.20/0.54 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~group_element(X)) | (~group_element(Y))) | product1(X, Y, e_1)) <=> ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_1))), (((((~group_element(X)) | (~group_element(Y))) | product1(X, Y, e_1)) | product1(X, Y, e_2)) <=> (((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_1)) | product1(X, Y, e_2)))), rewrite((((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_1)) | product1(X, Y, e_2)) <=> ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_2) | product1(X, Y, e_1))), (((((~group_element(X)) | (~group_element(Y))) | product1(X, Y, e_1)) | product1(X, Y, e_2)) <=> ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_2) | product1(X, Y, e_1)))), ((((((~group_element(X)) | (~group_element(Y))) | product1(X, Y, e_1)) | product1(X, Y, e_2)) | product1(X, Y, e_3)) <=> (((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_2) | product1(X, Y, e_1)) | product1(X, Y, e_3)))), rewrite((((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_2) | product1(X, Y, e_1)) | product1(X, Y, e_3)) <=> ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))), ((((((~group_element(X)) | (~group_element(Y))) | product1(X, Y, e_1)) | product1(X, Y, e_2)) | product1(X, Y, e_3)) <=> ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1)))), (((((((~group_element(X)) | (~group_element(Y))) | product1(X, Y, e_1)) | product1(X, Y, e_2)) | product1(X, Y, e_3)) | product1(X, Y, e_4)) <=> (((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1)) | product1(X, Y, e_4)))), rewrite((((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1)) | product1(X, Y, e_4)) <=> ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))), (((((((~group_element(X)) | (~group_element(Y))) | product1(X, Y, e_1)) | product1(X, Y, e_2)) | product1(X, Y, e_3)) | product1(X, Y, e_4)) <=> ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(98,plain,
% 0.20/0.54 (![Y: $i, X: $i] : ((((((~group_element(X)) | (~group_element(Y))) | product1(X, Y, e_1)) | product1(X, Y, e_2)) | product1(X, Y, e_3)) | product1(X, Y, e_4)) <=> ![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[97])).
% 0.20/0.54 tff(99,axiom,(![Y: $i, X: $i] : ((((((~group_element(X)) | (~group_element(Y))) | product1(X, Y, e_1)) | product1(X, Y, e_2)) | product1(X, Y, e_3)) | product1(X, Y, e_4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product1_total_function1')).
% 0.20/0.54 tff(100,plain,
% 0.20/0.54 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.20/0.54 tff(101,plain,
% 0.20/0.54 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[100, 96])).
% 0.20/0.54 tff(102,plain,(
% 0.20/0.54 ![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))),
% 0.20/0.54 inference(skolemize,[status(sab)],[101])).
% 0.20/0.54 tff(103,plain,
% 0.20/0.54 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[102, 95])).
% 0.20/0.54 tff(104,plain,
% 0.20/0.54 (group_element(e_4) <=> group_element(e_4)),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(105,axiom,(group_element(e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_4')).
% 0.20/0.54 tff(106,plain,
% 0.20/0.54 (group_element(e_4)),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.20/0.54 tff(107,plain,
% 0.20/0.54 (group_element(e_2) <=> group_element(e_2)),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(108,axiom,(group_element(e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_2')).
% 0.20/0.54 tff(109,plain,
% 0.20/0.54 (group_element(e_2)),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.20/0.54 tff(110,plain,
% 0.20/0.54 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_4)) | (~group_element(e_2)) | product1(e_4, e_2, e_4) | product1(e_4, e_2, e_3) | product1(e_4, e_2, e_1) | product1(e_4, e_2, e_2))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | (~group_element(e_4)) | (~group_element(e_2)) | product1(e_4, e_2, e_4) | product1(e_4, e_2, e_3) | product1(e_4, e_2, e_1) | product1(e_4, e_2, e_2))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(111,plain,
% 0.20/0.54 (((~group_element(e_2)) | (~group_element(e_4)) | product1(e_4, e_2, e_4) | product1(e_4, e_2, e_3) | product1(e_4, e_2, e_2) | product1(e_4, e_2, e_1)) <=> ((~group_element(e_4)) | (~group_element(e_2)) | product1(e_4, e_2, e_4) | product1(e_4, e_2, e_3) | product1(e_4, e_2, e_1) | product1(e_4, e_2, e_2))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(112,plain,
% 0.20/0.54 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_2)) | (~group_element(e_4)) | product1(e_4, e_2, e_4) | product1(e_4, e_2, e_3) | product1(e_4, e_2, e_2) | product1(e_4, e_2, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_4)) | (~group_element(e_2)) | product1(e_4, e_2, e_4) | product1(e_4, e_2, e_3) | product1(e_4, e_2, e_1) | product1(e_4, e_2, e_2)))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[111])).
% 0.20/0.54 tff(113,plain,
% 0.20/0.54 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_2)) | (~group_element(e_4)) | product1(e_4, e_2, e_4) | product1(e_4, e_2, e_3) | product1(e_4, e_2, e_2) | product1(e_4, e_2, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | (~group_element(e_4)) | (~group_element(e_2)) | product1(e_4, e_2, e_4) | product1(e_4, e_2, e_3) | product1(e_4, e_2, e_1) | product1(e_4, e_2, e_2))),
% 0.20/0.54 inference(transitivity,[status(thm)],[112, 110])).
% 0.20/0.54 tff(114,plain,
% 0.20/0.54 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_2)) | (~group_element(e_4)) | product1(e_4, e_2, e_4) | product1(e_4, e_2, e_3) | product1(e_4, e_2, e_2) | product1(e_4, e_2, e_1))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(115,plain,
% 0.20/0.54 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | (~group_element(e_4)) | (~group_element(e_2)) | product1(e_4, e_2, e_4) | product1(e_4, e_2, e_3) | product1(e_4, e_2, e_1) | product1(e_4, e_2, e_2)),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.20/0.54 tff(116,plain,
% 0.20/0.54 (product1(e_4, e_2, e_4) | product1(e_4, e_2, e_3) | product1(e_4, e_2, e_1) | product1(e_4, e_2, e_2)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[115, 109, 106, 103])).
% 0.20/0.54 tff(117,plain,
% 0.20/0.54 (product1(e_4, e_2, e_3) | product1(e_4, e_2, e_1)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[116, 93, 82])).
% 0.20/0.54 tff(118,plain,
% 0.20/0.54 (product1(e_4, e_2, e_3)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[117, 50])).
% 0.20/0.54 tff(119,assumption,(product1(e_2, e_3, e_1)), introduced(assumption)).
% 0.20/0.54 tff(120,plain,
% 0.20/0.54 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_2, e_4) | (~product1(e_4, e_3, e_1)) | (~product1(e_2, e_3, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_2, e_4) | (~product1(e_4, e_3, e_1)) | (~product1(e_2, e_3, e_1)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(121,plain,
% 0.20/0.54 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_2, e_4) | (~product1(e_4, e_3, e_1)) | (~product1(e_2, e_3, e_1)))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(122,plain,
% 0.20/0.54 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_2, e_4) | (~product1(e_4, e_3, e_1)) | (~product1(e_2, e_3, e_1))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.20/0.54 tff(123,plain,
% 0.20/0.54 ($false),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[122, 76, 73, 30, 119])).
% 0.20/0.54 tff(124,plain,((~product1(e_2, e_3, e_1)) | (~product1(e_4, e_3, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.54 tff(125,plain,
% 0.20/0.54 (~product1(e_2, e_3, e_1)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[124, 30])).
% 0.20/0.54 tff(126,assumption,(product1(e_2, e_3, e_2)), introduced(assumption)).
% 0.20/0.54 tff(127,plain,
% 0.20/0.54 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_3, e_2) | (~product1(e_2, e_2, e_2)) | (~product1(e_2, e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_3, e_2) | (~product1(e_2, e_2, e_2)) | (~product1(e_2, e_3, e_2)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(128,plain,
% 0.20/0.55 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_3, e_2) | (~product1(e_2, e_2, e_2)) | (~product1(e_2, e_3, e_2)))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(129,plain,
% 0.20/0.55 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_3, e_2) | (~product1(e_2, e_2, e_2)) | (~product1(e_2, e_3, e_2))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.20/0.55 tff(130,plain,
% 0.20/0.55 ($false),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[129, 44, 41, 61, 126])).
% 0.20/0.55 tff(131,plain,(~product1(e_2, e_3, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.55 tff(132,assumption,(product1(e_2, e_3, e_3)), introduced(assumption)).
% 0.20/0.55 tff(133,plain,
% 0.20/0.55 ((~![X: $i] : product1(X, X, X)) | product1(e_3, e_3, e_3)),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(134,plain,
% 0.20/0.55 (product1(e_3, e_3, e_3)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[133, 58])).
% 0.20/0.55 tff(135,plain,
% 0.20/0.55 ((~equalish(e_2, e_3)) <=> (~equalish(e_2, e_3))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(136,axiom,(~equalish(e_2, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_3')).
% 0.20/0.55 tff(137,plain,
% 0.20/0.55 (~equalish(e_2, e_3)),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.20/0.55 tff(138,plain,
% 0.20/0.55 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_2, e_3) | (~product1(e_3, e_3, e_3)) | (~product1(e_2, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_2, e_3) | (~product1(e_3, e_3, e_3)) | (~product1(e_2, e_3, e_3)))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(139,plain,
% 0.20/0.55 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_2, e_3) | (~product1(e_3, e_3, e_3)) | (~product1(e_2, e_3, e_3)))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(140,plain,
% 0.20/0.55 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_2, e_3) | (~product1(e_3, e_3, e_3)) | (~product1(e_2, e_3, e_3))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.20/0.55 tff(141,plain,
% 0.20/0.55 ($false),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[140, 137, 73, 134, 132])).
% 0.20/0.55 tff(142,plain,(~product1(e_2, e_3, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.55 tff(143,plain,
% 0.20/0.55 (group_element(e_3) <=> group_element(e_3)),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(144,axiom,(group_element(e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_3')).
% 0.20/0.55 tff(145,plain,
% 0.20/0.55 (group_element(e_3)),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.20/0.55 tff(146,plain,
% 0.20/0.55 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_3)) | (~group_element(e_2)) | product1(e_2, e_3, e_3) | product1(e_2, e_3, e_2) | product1(e_2, e_3, e_4) | product1(e_2, e_3, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | (~group_element(e_3)) | (~group_element(e_2)) | product1(e_2, e_3, e_3) | product1(e_2, e_3, e_2) | product1(e_2, e_3, e_4) | product1(e_2, e_3, e_1))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(147,plain,
% 0.20/0.55 (((~group_element(e_3)) | (~group_element(e_2)) | product1(e_2, e_3, e_4) | product1(e_2, e_3, e_3) | product1(e_2, e_3, e_2) | product1(e_2, e_3, e_1)) <=> ((~group_element(e_3)) | (~group_element(e_2)) | product1(e_2, e_3, e_3) | product1(e_2, e_3, e_2) | product1(e_2, e_3, e_4) | product1(e_2, e_3, e_1))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(148,plain,
% 0.20/0.55 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_3)) | (~group_element(e_2)) | product1(e_2, e_3, e_4) | product1(e_2, e_3, e_3) | product1(e_2, e_3, e_2) | product1(e_2, e_3, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_3)) | (~group_element(e_2)) | product1(e_2, e_3, e_3) | product1(e_2, e_3, e_2) | product1(e_2, e_3, e_4) | product1(e_2, e_3, e_1)))),
% 0.20/0.55 inference(monotonicity,[status(thm)],[147])).
% 0.20/0.55 tff(149,plain,
% 0.20/0.55 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_3)) | (~group_element(e_2)) | product1(e_2, e_3, e_4) | product1(e_2, e_3, e_3) | product1(e_2, e_3, e_2) | product1(e_2, e_3, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | (~group_element(e_3)) | (~group_element(e_2)) | product1(e_2, e_3, e_3) | product1(e_2, e_3, e_2) | product1(e_2, e_3, e_4) | product1(e_2, e_3, e_1))),
% 0.20/0.55 inference(transitivity,[status(thm)],[148, 146])).
% 0.20/0.55 tff(150,plain,
% 0.20/0.55 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_3)) | (~group_element(e_2)) | product1(e_2, e_3, e_4) | product1(e_2, e_3, e_3) | product1(e_2, e_3, e_2) | product1(e_2, e_3, e_1))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(151,plain,
% 0.20/0.55 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | (~group_element(e_3)) | (~group_element(e_2)) | product1(e_2, e_3, e_3) | product1(e_2, e_3, e_2) | product1(e_2, e_3, e_4) | product1(e_2, e_3, e_1)),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.20/0.55 tff(152,plain,
% 0.20/0.55 (product1(e_2, e_3, e_3) | product1(e_2, e_3, e_2) | product1(e_2, e_3, e_4) | product1(e_2, e_3, e_1)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[151, 109, 145, 103])).
% 0.20/0.55 tff(153,plain,
% 0.20/0.55 (product1(e_2, e_3, e_2) | product1(e_2, e_3, e_4) | product1(e_2, e_3, e_1)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[152, 142])).
% 0.20/0.55 tff(154,plain,
% 0.20/0.55 (product1(e_2, e_3, e_4) | product1(e_2, e_3, e_1)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[153, 131])).
% 0.20/0.55 tff(155,plain,
% 0.20/0.55 (product1(e_2, e_3, e_4)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[154, 125])).
% 0.20/0.55 tff(156,assumption,(product2(e_3, e_3, e_2)), introduced(assumption)).
% 0.20/0.55 tff(157,plain,
% 0.20/0.55 ((~![X: $i] : product2(X, X, X)) | product2(e_3, e_3, e_3)),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(158,plain,
% 0.20/0.55 (product2(e_3, e_3, e_3)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[157, 9])).
% 0.20/0.55 tff(159,plain,
% 0.20/0.55 (^[W: $i, Z: $i, Y: $i, X: $i] : refl((equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W))) <=> (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W))))),
% 0.20/0.55 inference(bind,[status(th)],[])).
% 0.20/0.55 tff(160,plain,
% 0.20/0.55 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))),
% 0.20/0.55 inference(quant_intro,[status(thm)],[159])).
% 0.20/0.55 tff(161,plain,
% 0.20/0.55 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(162,plain,
% 0.20/0.55 (^[W: $i, Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite(((~product2(X, Y, W)) | (~product2(X, Y, Z))) <=> ((~product2(X, Y, Z)) | (~product2(X, Y, W)))), ((((~product2(X, Y, W)) | (~product2(X, Y, Z))) | equalish(W, Z)) <=> (((~product2(X, Y, Z)) | (~product2(X, Y, W))) | equalish(W, Z)))), rewrite((((~product2(X, Y, Z)) | (~product2(X, Y, W))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))), ((((~product2(X, Y, W)) | (~product2(X, Y, Z))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))))),
% 0.20/0.55 inference(bind,[status(th)],[])).
% 0.20/0.55 tff(163,plain,
% 0.20/0.55 (![W: $i, Z: $i, Y: $i, X: $i] : (((~product2(X, Y, W)) | (~product2(X, Y, Z))) | equalish(W, Z)) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))),
% 0.20/0.55 inference(quant_intro,[status(thm)],[162])).
% 0.20/0.55 tff(164,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product2(X, Y, W)) | (~product2(X, Y, Z))) | equalish(W, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product2_total_function2')).
% 0.20/0.55 tff(165,plain,
% 0.20/0.55 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[164, 163])).
% 0.20/0.55 tff(166,plain,
% 0.20/0.55 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[165, 161])).
% 0.20/0.55 tff(167,plain,(
% 0.20/0.55 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))),
% 0.20/0.55 inference(skolemize,[status(sab)],[166])).
% 0.20/0.55 tff(168,plain,
% 0.20/0.55 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[167, 160])).
% 0.20/0.55 tff(169,plain,
% 0.20/0.55 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))) | (equalish(e_2, e_3) | (~product2(e_3, e_3, e_3)) | (~product2(e_3, e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))) | equalish(e_2, e_3) | (~product2(e_3, e_3, e_3)) | (~product2(e_3, e_3, e_2)))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(170,plain,
% 0.20/0.55 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))) | (equalish(e_2, e_3) | (~product2(e_3, e_3, e_3)) | (~product2(e_3, e_3, e_2)))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(171,plain,
% 0.20/0.55 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))) | equalish(e_2, e_3) | (~product2(e_3, e_3, e_3)) | (~product2(e_3, e_3, e_2))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[170, 169])).
% 0.20/0.55 tff(172,plain,
% 0.20/0.55 ($false),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[171, 137, 168, 158, 156])).
% 0.20/0.55 tff(173,plain,(~product2(e_3, e_3, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.55 tff(174,plain,
% 0.20/0.55 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : refl(((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1))) <=> ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1))))),
% 0.20/0.55 inference(bind,[status(th)],[])).
% 0.20/0.55 tff(175,plain,
% 0.20/0.55 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))),
% 0.20/0.55 inference(quant_intro,[status(thm)],[174])).
% 0.20/0.55 tff(176,plain,
% 0.20/0.55 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(177,plain,
% 0.20/0.55 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : rewrite((((~product1(X, Y, Z1)) | (~product1(Z1, X, Z2))) | product2(Z2, Y, X)) <=> ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1))))),
% 0.20/0.55 inference(bind,[status(th)],[])).
% 0.20/0.55 tff(178,plain,
% 0.20/0.55 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product1(X, Y, Z1)) | (~product1(Z1, X, Z2))) | product2(Z2, Y, X)) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))),
% 0.20/0.55 inference(quant_intro,[status(thm)],[177])).
% 0.20/0.55 tff(179,axiom,(![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product1(X, Y, Z1)) | (~product1(Z1, X, Z2))) | product2(Z2, Y, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qg2a')).
% 0.20/0.55 tff(180,plain,
% 0.20/0.55 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[179, 178])).
% 0.20/0.55 tff(181,plain,
% 0.20/0.55 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[180, 176])).
% 0.20/0.55 tff(182,plain,(
% 0.20/0.55 ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))),
% 0.20/0.55 inference(skolemize,[status(sab)],[181])).
% 0.20/0.55 tff(183,plain,
% 0.20/0.55 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[182, 175])).
% 0.20/0.55 tff(184,plain,
% 0.20/0.55 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_4, e_2, e_3)) | product2(e_3, e_3, e_2) | (~product1(e_2, e_3, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | (~product1(e_4, e_2, e_3)) | product2(e_3, e_3, e_2) | (~product1(e_2, e_3, e_4)))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(185,plain,
% 0.20/0.55 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_4, e_2, e_3)) | product2(e_3, e_3, e_2) | (~product1(e_2, e_3, e_4)))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(186,plain,
% 0.20/0.55 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | (~product1(e_4, e_2, e_3)) | product2(e_3, e_3, e_2) | (~product1(e_2, e_3, e_4))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[185, 184])).
% 0.20/0.55 tff(187,plain,
% 0.20/0.55 ((~product1(e_4, e_2, e_3)) | product2(e_3, e_3, e_2) | (~product1(e_2, e_3, e_4))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[186, 183])).
% 0.20/0.55 tff(188,plain,
% 0.20/0.55 ((~product1(e_4, e_2, e_3)) | (~product1(e_2, e_3, e_4))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[187, 173])).
% 0.20/0.55 tff(189,plain,
% 0.20/0.55 ($false),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[188, 155, 118])).
% 0.20/0.55 tff(190,plain,(~product1(e_4, e_3, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.55 tff(191,assumption,(product1(e_4, e_3, e_4)), introduced(assumption)).
% 0.20/0.55 tff(192,plain,
% 0.20/0.55 ((~equalish(e_3, e_4)) <=> (~equalish(e_3, e_4))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(193,axiom,(~equalish(e_3, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_4')).
% 0.20/0.55 tff(194,plain,
% 0.20/0.55 (~equalish(e_3, e_4)),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[193, 192])).
% 0.20/0.55 tff(195,plain,
% 0.20/0.55 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_3, e_4) | (~product1(e_4, e_4, e_4)) | (~product1(e_4, e_3, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_3, e_4) | (~product1(e_4, e_4, e_4)) | (~product1(e_4, e_3, e_4)))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(196,plain,
% 0.20/0.55 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_3, e_4) | (~product1(e_4, e_4, e_4)) | (~product1(e_4, e_3, e_4)))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(197,plain,
% 0.20/0.55 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_3, e_4) | (~product1(e_4, e_4, e_4)) | (~product1(e_4, e_3, e_4))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[196, 195])).
% 0.20/0.55 tff(198,plain,
% 0.20/0.55 ($false),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[197, 194, 41, 84, 191])).
% 0.20/0.55 tff(199,plain,(~product1(e_4, e_3, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.55 tff(200,assumption,(product1(e_4, e_3, e_3)), introduced(assumption)).
% 0.20/0.55 tff(201,plain,
% 0.20/0.55 ((~equalish(e_4, e_3)) <=> (~equalish(e_4, e_3))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(202,axiom,(~equalish(e_4, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_3')).
% 0.20/0.55 tff(203,plain,
% 0.20/0.55 (~equalish(e_4, e_3)),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[202, 201])).
% 0.20/0.55 tff(204,plain,
% 0.20/0.55 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_4, e_3) | (~product1(e_3, e_3, e_3)) | (~product1(e_4, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_4, e_3) | (~product1(e_3, e_3, e_3)) | (~product1(e_4, e_3, e_3)))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(205,plain,
% 0.20/0.55 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_4, e_3) | (~product1(e_3, e_3, e_3)) | (~product1(e_4, e_3, e_3)))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(206,plain,
% 0.20/0.55 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_4, e_3) | (~product1(e_3, e_3, e_3)) | (~product1(e_4, e_3, e_3))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[205, 204])).
% 0.20/0.55 tff(207,plain,
% 0.20/0.55 ($false),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[206, 203, 73, 134, 200])).
% 0.20/0.55 tff(208,plain,(~product1(e_4, e_3, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.55 tff(209,plain,
% 0.20/0.55 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_3)) | (~group_element(e_4)) | product1(e_4, e_3, e_2) | product1(e_4, e_3, e_1) | product1(e_4, e_3, e_4) | product1(e_4, e_3, e_3))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | (~group_element(e_3)) | (~group_element(e_4)) | product1(e_4, e_3, e_2) | product1(e_4, e_3, e_1) | product1(e_4, e_3, e_4) | product1(e_4, e_3, e_3))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(210,plain,
% 0.20/0.55 (((~group_element(e_3)) | (~group_element(e_4)) | product1(e_4, e_3, e_4) | product1(e_4, e_3, e_3) | product1(e_4, e_3, e_2) | product1(e_4, e_3, e_1)) <=> ((~group_element(e_3)) | (~group_element(e_4)) | product1(e_4, e_3, e_2) | product1(e_4, e_3, e_1) | product1(e_4, e_3, e_4) | product1(e_4, e_3, e_3))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(211,plain,
% 0.20/0.55 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_3)) | (~group_element(e_4)) | product1(e_4, e_3, e_4) | product1(e_4, e_3, e_3) | product1(e_4, e_3, e_2) | product1(e_4, e_3, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_3)) | (~group_element(e_4)) | product1(e_4, e_3, e_2) | product1(e_4, e_3, e_1) | product1(e_4, e_3, e_4) | product1(e_4, e_3, e_3)))),
% 0.20/0.55 inference(monotonicity,[status(thm)],[210])).
% 0.20/0.55 tff(212,plain,
% 0.20/0.55 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_3)) | (~group_element(e_4)) | product1(e_4, e_3, e_4) | product1(e_4, e_3, e_3) | product1(e_4, e_3, e_2) | product1(e_4, e_3, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | (~group_element(e_3)) | (~group_element(e_4)) | product1(e_4, e_3, e_2) | product1(e_4, e_3, e_1) | product1(e_4, e_3, e_4) | product1(e_4, e_3, e_3))),
% 0.20/0.55 inference(transitivity,[status(thm)],[211, 209])).
% 0.20/0.55 tff(213,plain,
% 0.20/0.55 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_3)) | (~group_element(e_4)) | product1(e_4, e_3, e_4) | product1(e_4, e_3, e_3) | product1(e_4, e_3, e_2) | product1(e_4, e_3, e_1))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(214,plain,
% 0.20/0.55 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | (~group_element(e_3)) | (~group_element(e_4)) | product1(e_4, e_3, e_2) | product1(e_4, e_3, e_1) | product1(e_4, e_3, e_4) | product1(e_4, e_3, e_3)),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[213, 212])).
% 0.20/0.55 tff(215,plain,
% 0.20/0.55 (product1(e_4, e_3, e_2) | product1(e_4, e_3, e_1) | product1(e_4, e_3, e_4) | product1(e_4, e_3, e_3)),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[214, 145, 106, 103])).
% 0.20/0.56 tff(216,plain,
% 0.20/0.56 (product1(e_4, e_3, e_2) | product1(e_4, e_3, e_1) | product1(e_4, e_3, e_4)),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[215, 208])).
% 0.20/0.56 tff(217,plain,
% 0.20/0.56 (product1(e_4, e_3, e_2) | product1(e_4, e_3, e_1)),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[216, 199])).
% 0.20/0.56 tff(218,plain,
% 0.20/0.56 (product1(e_4, e_3, e_2)),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[217, 190])).
% 0.20/0.56 tff(219,assumption,(product1(e_4, e_3, e_2)), introduced(assumption)).
% 0.20/0.56 tff(220,assumption,(product1(e_4, e_1, e_2)), introduced(assumption)).
% 0.20/0.56 tff(221,plain,
% 0.20/0.56 ((~equalish(e_1, e_3)) <=> (~equalish(e_1, e_3))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(222,axiom,(~equalish(e_1, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_3')).
% 0.20/0.56 tff(223,plain,
% 0.20/0.56 (~equalish(e_1, e_3)),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[222, 221])).
% 0.20/0.56 tff(224,plain,
% 0.20/0.56 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_1, e_3) | (~product1(e_4, e_3, e_2)) | (~product1(e_4, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_1, e_3) | (~product1(e_4, e_3, e_2)) | (~product1(e_4, e_1, e_2)))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(225,plain,
% 0.20/0.56 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_1, e_3) | (~product1(e_4, e_3, e_2)) | (~product1(e_4, e_1, e_2)))),
% 0.20/0.56 inference(quant_inst,[status(thm)],[])).
% 0.20/0.56 tff(226,plain,
% 0.20/0.56 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_1, e_3) | (~product1(e_4, e_3, e_2)) | (~product1(e_4, e_1, e_2))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[225, 224])).
% 0.20/0.56 tff(227,plain,
% 0.20/0.56 ($false),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[226, 223, 41, 220, 219])).
% 0.20/0.56 tff(228,plain,((~product1(e_4, e_1, e_2)) | (~product1(e_4, e_3, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.56 tff(229,plain,
% 0.20/0.56 (~product1(e_4, e_1, e_2)),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[228, 218])).
% 0.20/0.56 tff(230,assumption,(product1(e_4, e_1, e_1)), introduced(assumption)).
% 0.20/0.56 tff(231,plain,
% 0.20/0.56 ((~![X: $i] : product1(X, X, X)) | product1(e_1, e_1, e_1)),
% 0.20/0.56 inference(quant_inst,[status(thm)],[])).
% 0.20/0.56 tff(232,plain,
% 0.20/0.56 (product1(e_1, e_1, e_1)),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[231, 58])).
% 0.20/0.56 tff(233,plain,
% 0.20/0.56 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_4, e_1) | (~product1(e_1, e_1, e_1)) | (~product1(e_4, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_4, e_1) | (~product1(e_1, e_1, e_1)) | (~product1(e_4, e_1, e_1)))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(234,plain,
% 0.20/0.56 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_4, e_1) | (~product1(e_1, e_1, e_1)) | (~product1(e_4, e_1, e_1)))),
% 0.20/0.56 inference(quant_inst,[status(thm)],[])).
% 0.20/0.56 tff(235,plain,
% 0.20/0.56 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_4, e_1) | (~product1(e_1, e_1, e_1)) | (~product1(e_4, e_1, e_1))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[234, 233])).
% 0.20/0.56 tff(236,plain,
% 0.20/0.56 ($false),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[235, 24, 73, 232, 230])).
% 0.20/0.56 tff(237,plain,(~product1(e_4, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.56 tff(238,plain,
% 0.20/0.56 ((~![X: $i] : product2(X, X, X)) | product2(e_4, e_4, e_4)),
% 0.20/0.56 inference(quant_inst,[status(thm)],[])).
% 0.20/0.56 tff(239,plain,
% 0.20/0.56 (product2(e_4, e_4, e_4)),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[238, 9])).
% 0.20/0.56 tff(240,assumption,(product2(e_4, e_1, e_4)), introduced(assumption)).
% 0.20/0.56 tff(241,plain,
% 0.20/0.56 ((~equalish(e_1, e_4)) <=> (~equalish(e_1, e_4))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(242,axiom,(~equalish(e_1, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_4')).
% 0.20/0.56 tff(243,plain,
% 0.20/0.56 (~equalish(e_1, e_4)),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[242, 241])).
% 0.20/0.56 tff(244,plain,
% 0.20/0.56 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | (equalish(e_1, e_4) | (~product2(e_4, e_4, e_4)) | (~product2(e_4, e_1, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | equalish(e_1, e_4) | (~product2(e_4, e_4, e_4)) | (~product2(e_4, e_1, e_4)))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(245,plain,
% 0.20/0.56 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | (equalish(e_1, e_4) | (~product2(e_4, e_4, e_4)) | (~product2(e_4, e_1, e_4)))),
% 0.20/0.56 inference(quant_inst,[status(thm)],[])).
% 0.20/0.56 tff(246,plain,
% 0.20/0.56 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | equalish(e_1, e_4) | (~product2(e_4, e_4, e_4)) | (~product2(e_4, e_1, e_4))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[245, 244])).
% 0.20/0.56 tff(247,plain,
% 0.20/0.56 ($false),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[246, 243, 21, 240, 239])).
% 0.20/0.56 tff(248,plain,(~product2(e_4, e_1, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.56 tff(249,plain,
% 0.20/0.56 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_4, e_4, e_4)) | product2(e_4, e_1, e_4) | (~product1(e_4, e_1, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | (~product1(e_4, e_4, e_4)) | product2(e_4, e_1, e_4) | (~product1(e_4, e_1, e_4)))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(250,plain,
% 0.20/0.56 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_4, e_4, e_4)) | product2(e_4, e_1, e_4) | (~product1(e_4, e_1, e_4)))),
% 0.20/0.56 inference(quant_inst,[status(thm)],[])).
% 0.20/0.56 tff(251,plain,
% 0.20/0.56 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | (~product1(e_4, e_4, e_4)) | product2(e_4, e_1, e_4) | (~product1(e_4, e_1, e_4))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[250, 249])).
% 0.20/0.56 tff(252,plain,
% 0.20/0.56 (~product1(e_4, e_1, e_4)),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[251, 183, 84, 248])).
% 0.20/0.56 tff(253,plain,
% 0.20/0.56 (group_element(e_1) <=> group_element(e_1)),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(254,axiom,(group_element(e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_1')).
% 0.20/0.56 tff(255,plain,
% 0.20/0.56 (group_element(e_1)),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[254, 253])).
% 0.20/0.56 tff(256,plain,
% 0.20/0.56 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_4)) | (~group_element(e_1)) | product1(e_4, e_1, e_3) | product1(e_4, e_1, e_1) | product1(e_4, e_1, e_2) | product1(e_4, e_1, e_4))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | (~group_element(e_4)) | (~group_element(e_1)) | product1(e_4, e_1, e_3) | product1(e_4, e_1, e_1) | product1(e_4, e_1, e_2) | product1(e_4, e_1, e_4))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(257,plain,
% 0.20/0.56 (((~group_element(e_1)) | (~group_element(e_4)) | product1(e_4, e_1, e_4) | product1(e_4, e_1, e_3) | product1(e_4, e_1, e_2) | product1(e_4, e_1, e_1)) <=> ((~group_element(e_4)) | (~group_element(e_1)) | product1(e_4, e_1, e_3) | product1(e_4, e_1, e_1) | product1(e_4, e_1, e_2) | product1(e_4, e_1, e_4))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(258,plain,
% 0.20/0.56 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_1)) | (~group_element(e_4)) | product1(e_4, e_1, e_4) | product1(e_4, e_1, e_3) | product1(e_4, e_1, e_2) | product1(e_4, e_1, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_4)) | (~group_element(e_1)) | product1(e_4, e_1, e_3) | product1(e_4, e_1, e_1) | product1(e_4, e_1, e_2) | product1(e_4, e_1, e_4)))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[257])).
% 0.20/0.56 tff(259,plain,
% 0.20/0.56 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_1)) | (~group_element(e_4)) | product1(e_4, e_1, e_4) | product1(e_4, e_1, e_3) | product1(e_4, e_1, e_2) | product1(e_4, e_1, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | (~group_element(e_4)) | (~group_element(e_1)) | product1(e_4, e_1, e_3) | product1(e_4, e_1, e_1) | product1(e_4, e_1, e_2) | product1(e_4, e_1, e_4))),
% 0.20/0.56 inference(transitivity,[status(thm)],[258, 256])).
% 0.20/0.56 tff(260,plain,
% 0.20/0.56 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_1)) | (~group_element(e_4)) | product1(e_4, e_1, e_4) | product1(e_4, e_1, e_3) | product1(e_4, e_1, e_2) | product1(e_4, e_1, e_1))),
% 0.20/0.56 inference(quant_inst,[status(thm)],[])).
% 0.20/0.56 tff(261,plain,
% 0.20/0.56 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | (~group_element(e_4)) | (~group_element(e_1)) | product1(e_4, e_1, e_3) | product1(e_4, e_1, e_1) | product1(e_4, e_1, e_2) | product1(e_4, e_1, e_4)),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[260, 259])).
% 0.20/0.56 tff(262,plain,
% 0.20/0.56 (product1(e_4, e_1, e_3) | product1(e_4, e_1, e_1) | product1(e_4, e_1, e_2) | product1(e_4, e_1, e_4)),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[261, 255, 106, 103])).
% 0.20/0.56 tff(263,plain,
% 0.20/0.56 (product1(e_4, e_1, e_3) | product1(e_4, e_1, e_1) | product1(e_4, e_1, e_2)),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[262, 252])).
% 0.20/0.56 tff(264,plain,
% 0.20/0.56 (product1(e_4, e_1, e_3) | product1(e_4, e_1, e_2)),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[263, 237])).
% 0.20/0.56 tff(265,plain,
% 0.20/0.56 (product1(e_4, e_1, e_3)),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[264, 229])).
% 0.20/0.56 tff(266,assumption,(product1(e_4, e_1, e_3)), introduced(assumption)).
% 0.20/0.56 tff(267,assumption,(product1(e_4, e_2, e_3)), introduced(assumption)).
% 0.20/0.56 tff(268,plain,
% 0.20/0.56 ((~equalish(e_1, e_2)) <=> (~equalish(e_1, e_2))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(269,axiom,(~equalish(e_1, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_2')).
% 0.20/0.56 tff(270,plain,
% 0.20/0.56 (~equalish(e_1, e_2)),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[269, 268])).
% 0.20/0.56 tff(271,plain,
% 0.20/0.56 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_1, e_2) | (~product1(e_4, e_2, e_3)) | (~product1(e_4, e_1, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_1, e_2) | (~product1(e_4, e_2, e_3)) | (~product1(e_4, e_1, e_3)))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(272,plain,
% 0.20/0.56 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_1, e_2) | (~product1(e_4, e_2, e_3)) | (~product1(e_4, e_1, e_3)))),
% 0.20/0.56 inference(quant_inst,[status(thm)],[])).
% 0.20/0.56 tff(273,plain,
% 0.20/0.56 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_1, e_2) | (~product1(e_4, e_2, e_3)) | (~product1(e_4, e_1, e_3))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[272, 271])).
% 0.20/0.56 tff(274,plain,
% 0.20/0.56 ($false),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[273, 270, 41, 267, 266])).
% 0.20/0.56 tff(275,plain,((~product1(e_4, e_1, e_3)) | (~product1(e_4, e_2, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.56 tff(276,plain,
% 0.20/0.56 (~product1(e_4, e_2, e_3)),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[275, 265])).
% 0.20/0.56 tff(277,plain,
% 0.20/0.56 (product1(e_4, e_2, e_1)),
% 0.49/0.56 inference(unit_resolution,[status(thm)],[117, 276])).
% 0.49/0.56 tff(278,assumption,(product1(e_1, e_4, e_3)), introduced(assumption)).
% 0.49/0.56 tff(279,plain,
% 0.49/0.56 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_4, e_2, e_1)) | (~product1(e_1, e_4, e_3)) | product2(e_3, e_2, e_4))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | (~product1(e_4, e_2, e_1)) | (~product1(e_1, e_4, e_3)) | product2(e_3, e_2, e_4))),
% 0.49/0.56 inference(rewrite,[status(thm)],[])).
% 0.49/0.56 tff(280,plain,
% 0.49/0.56 (((~product1(e_1, e_4, e_3)) | product2(e_3, e_2, e_4) | (~product1(e_4, e_2, e_1))) <=> ((~product1(e_4, e_2, e_1)) | (~product1(e_1, e_4, e_3)) | product2(e_3, e_2, e_4))),
% 0.49/0.56 inference(rewrite,[status(thm)],[])).
% 0.49/0.56 tff(281,plain,
% 0.49/0.56 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_1, e_4, e_3)) | product2(e_3, e_2, e_4) | (~product1(e_4, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_4, e_2, e_1)) | (~product1(e_1, e_4, e_3)) | product2(e_3, e_2, e_4)))),
% 0.49/0.56 inference(monotonicity,[status(thm)],[280])).
% 0.49/0.56 tff(282,plain,
% 0.49/0.56 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_1, e_4, e_3)) | product2(e_3, e_2, e_4) | (~product1(e_4, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | (~product1(e_4, e_2, e_1)) | (~product1(e_1, e_4, e_3)) | product2(e_3, e_2, e_4))),
% 0.49/0.56 inference(transitivity,[status(thm)],[281, 279])).
% 0.49/0.56 tff(283,plain,
% 0.49/0.56 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_1, e_4, e_3)) | product2(e_3, e_2, e_4) | (~product1(e_4, e_2, e_1)))),
% 0.49/0.56 inference(quant_inst,[status(thm)],[])).
% 0.49/0.56 tff(284,plain,
% 0.49/0.56 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | (~product1(e_4, e_2, e_1)) | (~product1(e_1, e_4, e_3)) | product2(e_3, e_2, e_4)),
% 0.49/0.56 inference(modus_ponens,[status(thm)],[283, 282])).
% 0.49/0.56 tff(285,plain,
% 0.49/0.56 ((~product1(e_4, e_2, e_1)) | (~product1(e_1, e_4, e_3)) | product2(e_3, e_2, e_4)),
% 0.49/0.56 inference(unit_resolution,[status(thm)],[284, 183])).
% 0.49/0.56 tff(286,plain,
% 0.49/0.56 (product2(e_3, e_2, e_4)),
% 0.49/0.56 inference(unit_resolution,[status(thm)],[285, 278, 277])).
% 0.49/0.56 tff(287,assumption,(~product2(e_3, e_2, e_1)), introduced(assumption)).
% 0.49/0.56 tff(288,assumption,(product2(e_3, e_2, e_3)), introduced(assumption)).
% 0.49/0.56 tff(289,plain,
% 0.49/0.56 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | (equalish(e_2, e_3) | (~product2(e_3, e_3, e_3)) | (~product2(e_3, e_2, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | equalish(e_2, e_3) | (~product2(e_3, e_3, e_3)) | (~product2(e_3, e_2, e_3)))),
% 0.49/0.56 inference(rewrite,[status(thm)],[])).
% 0.49/0.56 tff(290,plain,
% 0.49/0.56 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | (equalish(e_2, e_3) | (~product2(e_3, e_3, e_3)) | (~product2(e_3, e_2, e_3)))),
% 0.49/0.56 inference(quant_inst,[status(thm)],[])).
% 0.49/0.56 tff(291,plain,
% 0.49/0.56 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | equalish(e_2, e_3) | (~product2(e_3, e_3, e_3)) | (~product2(e_3, e_2, e_3))),
% 0.49/0.56 inference(modus_ponens,[status(thm)],[290, 289])).
% 0.49/0.56 tff(292,plain,
% 0.49/0.56 ($false),
% 0.49/0.56 inference(unit_resolution,[status(thm)],[291, 137, 21, 158, 288])).
% 0.49/0.56 tff(293,plain,(~product2(e_3, e_2, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.49/0.56 tff(294,assumption,(product2(e_3, e_2, e_2)), introduced(assumption)).
% 0.49/0.56 tff(295,plain,
% 0.49/0.56 ((~![X: $i] : product2(X, X, X)) | product2(e_2, e_2, e_2)),
% 0.49/0.56 inference(quant_inst,[status(thm)],[])).
% 0.49/0.56 tff(296,plain,
% 0.49/0.56 (product2(e_2, e_2, e_2)),
% 0.49/0.56 inference(unit_resolution,[status(thm)],[295, 9])).
% 0.49/0.56 tff(297,plain,
% 0.49/0.56 (^[W: $i, Z: $i, Y: $i, X: $i] : refl((equalish(W, Z) | (~product2(Z, Y, X)) | (~product2(W, Y, X))) <=> (equalish(W, Z) | (~product2(Z, Y, X)) | (~product2(W, Y, X))))),
% 0.49/0.56 inference(bind,[status(th)],[])).
% 0.49/0.56 tff(298,plain,
% 0.49/0.56 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(Z, Y, X)) | (~product2(W, Y, X))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(Z, Y, X)) | (~product2(W, Y, X)))),
% 0.49/0.56 inference(quant_intro,[status(thm)],[297])).
% 0.49/0.56 tff(299,plain,
% 0.49/0.56 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(Z, Y, X)) | (~product2(W, Y, X))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(Z, Y, X)) | (~product2(W, Y, X)))),
% 0.49/0.56 inference(rewrite,[status(thm)],[])).
% 0.49/0.56 tff(300,plain,
% 0.49/0.56 (^[W: $i, Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite(((~product2(W, Y, X)) | (~product2(Z, Y, X))) <=> ((~product2(Z, Y, X)) | (~product2(W, Y, X)))), ((((~product2(W, Y, X)) | (~product2(Z, Y, X))) | equalish(W, Z)) <=> (((~product2(Z, Y, X)) | (~product2(W, Y, X))) | equalish(W, Z)))), rewrite((((~product2(Z, Y, X)) | (~product2(W, Y, X))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product2(Z, Y, X)) | (~product2(W, Y, X)))), ((((~product2(W, Y, X)) | (~product2(Z, Y, X))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product2(Z, Y, X)) | (~product2(W, Y, X)))))),
% 0.49/0.57 inference(bind,[status(th)],[])).
% 0.49/0.57 tff(301,plain,
% 0.49/0.57 (![W: $i, Z: $i, Y: $i, X: $i] : (((~product2(W, Y, X)) | (~product2(Z, Y, X))) | equalish(W, Z)) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(Z, Y, X)) | (~product2(W, Y, X)))),
% 0.49/0.57 inference(quant_intro,[status(thm)],[300])).
% 0.49/0.57 tff(302,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product2(W, Y, X)) | (~product2(Z, Y, X))) | equalish(W, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product2_left_cancellation')).
% 0.49/0.57 tff(303,plain,
% 0.49/0.57 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(Z, Y, X)) | (~product2(W, Y, X)))),
% 0.49/0.57 inference(modus_ponens,[status(thm)],[302, 301])).
% 0.49/0.57 tff(304,plain,
% 0.49/0.57 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(Z, Y, X)) | (~product2(W, Y, X)))),
% 0.49/0.57 inference(modus_ponens,[status(thm)],[303, 299])).
% 0.49/0.57 tff(305,plain,(
% 0.49/0.57 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(Z, Y, X)) | (~product2(W, Y, X)))),
% 0.49/0.57 inference(skolemize,[status(sab)],[304])).
% 0.49/0.57 tff(306,plain,
% 0.49/0.57 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(Z, Y, X)) | (~product2(W, Y, X)))),
% 0.49/0.57 inference(modus_ponens,[status(thm)],[305, 298])).
% 0.49/0.57 tff(307,plain,
% 0.49/0.57 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(Z, Y, X)) | (~product2(W, Y, X)))) | (equalish(e_3, e_2) | (~product2(e_2, e_2, e_2)) | (~product2(e_3, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(Z, Y, X)) | (~product2(W, Y, X)))) | equalish(e_3, e_2) | (~product2(e_2, e_2, e_2)) | (~product2(e_3, e_2, e_2)))),
% 0.49/0.57 inference(rewrite,[status(thm)],[])).
% 0.49/0.57 tff(308,plain,
% 0.49/0.57 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(Z, Y, X)) | (~product2(W, Y, X)))) | (equalish(e_3, e_2) | (~product2(e_2, e_2, e_2)) | (~product2(e_3, e_2, e_2)))),
% 0.49/0.57 inference(quant_inst,[status(thm)],[])).
% 0.49/0.57 tff(309,plain,
% 0.49/0.57 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(Z, Y, X)) | (~product2(W, Y, X)))) | equalish(e_3, e_2) | (~product2(e_2, e_2, e_2)) | (~product2(e_3, e_2, e_2))),
% 0.49/0.57 inference(modus_ponens,[status(thm)],[308, 307])).
% 0.49/0.57 tff(310,plain,
% 0.49/0.57 ($false),
% 0.49/0.57 inference(unit_resolution,[status(thm)],[309, 44, 306, 296, 294])).
% 0.49/0.57 tff(311,plain,(~product2(e_3, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.49/0.57 tff(312,plain,
% 0.49/0.57 (^[Y: $i, X: $i] : refl(((~group_element(Y)) | (~group_element(X)) | product2(X, Y, e_4) | product2(X, Y, e_3) | product2(X, Y, e_2) | product2(X, Y, e_1)) <=> ((~group_element(Y)) | (~group_element(X)) | product2(X, Y, e_4) | product2(X, Y, e_3) | product2(X, Y, e_2) | product2(X, Y, e_1)))),
% 0.49/0.57 inference(bind,[status(th)],[])).
% 0.49/0.57 tff(313,plain,
% 0.49/0.57 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product2(X, Y, e_4) | product2(X, Y, e_3) | product2(X, Y, e_2) | product2(X, Y, e_1)) <=> ![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product2(X, Y, e_4) | product2(X, Y, e_3) | product2(X, Y, e_2) | product2(X, Y, e_1))),
% 0.49/0.57 inference(quant_intro,[status(thm)],[312])).
% 0.49/0.57 tff(314,plain,
% 0.49/0.57 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product2(X, Y, e_4) | product2(X, Y, e_3) | product2(X, Y, e_2) | product2(X, Y, e_1)) <=> ![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product2(X, Y, e_4) | product2(X, Y, e_3) | product2(X, Y, e_2) | product2(X, Y, e_1))),
% 0.49/0.57 inference(rewrite,[status(thm)],[])).
% 0.49/0.57 tff(315,plain,
% 0.49/0.57 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~group_element(X)) | (~group_element(Y))) | product2(X, Y, e_1)) <=> ((~group_element(Y)) | (~group_element(X)) | product2(X, Y, e_1))), (((((~group_element(X)) | (~group_element(Y))) | product2(X, Y, e_1)) | product2(X, Y, e_2)) <=> (((~group_element(Y)) | (~group_element(X)) | product2(X, Y, e_1)) | product2(X, Y, e_2)))), rewrite((((~group_element(Y)) | (~group_element(X)) | product2(X, Y, e_1)) | product2(X, Y, e_2)) <=> ((~group_element(Y)) | (~group_element(X)) | product2(X, Y, e_2) | product2(X, Y, e_1))), (((((~group_element(X)) | (~group_element(Y))) | product2(X, Y, e_1)) | product2(X, Y, e_2)) <=> ((~group_element(Y)) | (~group_element(X)) | product2(X, Y, e_2) | product2(X, Y, e_1)))), ((((((~group_element(X)) | (~group_element(Y))) | product2(X, Y, e_1)) | product2(X, Y, e_2)) | product2(X, Y, e_3)) <=> (((~group_element(Y)) | (~group_element(X)) | product2(X, Y, e_2) | product2(X, Y, e_1)) | product2(X, Y, e_3)))), rewrite((((~group_element(Y)) | (~group_element(X)) | product2(X, Y, e_2) | product2(X, Y, e_1)) | product2(X, Y, e_3)) <=> ((~group_element(Y)) | (~group_element(X)) | product2(X, Y, e_3) | product2(X, Y, e_2) | product2(X, Y, e_1))), ((((((~group_element(X)) | (~group_element(Y))) | product2(X, Y, e_1)) | product2(X, Y, e_2)) | product2(X, Y, e_3)) <=> ((~group_element(Y)) | (~group_element(X)) | product2(X, Y, e_3) | product2(X, Y, e_2) | product2(X, Y, e_1)))), (((((((~group_element(X)) | (~group_element(Y))) | product2(X, Y, e_1)) | product2(X, Y, e_2)) | product2(X, Y, e_3)) | product2(X, Y, e_4)) <=> (((~group_element(Y)) | (~group_element(X)) | product2(X, Y, e_3) | product2(X, Y, e_2) | product2(X, Y, e_1)) | product2(X, Y, e_4)))), rewrite((((~group_element(Y)) | (~group_element(X)) | product2(X, Y, e_3) | product2(X, Y, e_2) | product2(X, Y, e_1)) | product2(X, Y, e_4)) <=> ((~group_element(Y)) | (~group_element(X)) | product2(X, Y, e_4) | product2(X, Y, e_3) | product2(X, Y, e_2) | product2(X, Y, e_1))), (((((((~group_element(X)) | (~group_element(Y))) | product2(X, Y, e_1)) | product2(X, Y, e_2)) | product2(X, Y, e_3)) | product2(X, Y, e_4)) <=> ((~group_element(Y)) | (~group_element(X)) | product2(X, Y, e_4) | product2(X, Y, e_3) | product2(X, Y, e_2) | product2(X, Y, e_1))))),
% 0.49/0.57 inference(bind,[status(th)],[])).
% 0.49/0.57 tff(316,plain,
% 0.49/0.57 (![Y: $i, X: $i] : ((((((~group_element(X)) | (~group_element(Y))) | product2(X, Y, e_1)) | product2(X, Y, e_2)) | product2(X, Y, e_3)) | product2(X, Y, e_4)) <=> ![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product2(X, Y, e_4) | product2(X, Y, e_3) | product2(X, Y, e_2) | product2(X, Y, e_1))),
% 0.49/0.57 inference(quant_intro,[status(thm)],[315])).
% 0.49/0.57 tff(317,axiom,(![Y: $i, X: $i] : ((((((~group_element(X)) | (~group_element(Y))) | product2(X, Y, e_1)) | product2(X, Y, e_2)) | product2(X, Y, e_3)) | product2(X, Y, e_4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product2_total_function1')).
% 0.49/0.57 tff(318,plain,
% 0.49/0.57 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product2(X, Y, e_4) | product2(X, Y, e_3) | product2(X, Y, e_2) | product2(X, Y, e_1))),
% 0.49/0.57 inference(modus_ponens,[status(thm)],[317, 316])).
% 0.49/0.57 tff(319,plain,
% 0.49/0.57 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product2(X, Y, e_4) | product2(X, Y, e_3) | product2(X, Y, e_2) | product2(X, Y, e_1))),
% 0.49/0.57 inference(modus_ponens,[status(thm)],[318, 314])).
% 0.49/0.57 tff(320,plain,(
% 0.49/0.57 ![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product2(X, Y, e_4) | product2(X, Y, e_3) | product2(X, Y, e_2) | product2(X, Y, e_1))),
% 0.49/0.57 inference(skolemize,[status(sab)],[319])).
% 0.49/0.57 tff(321,plain,
% 0.49/0.57 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product2(X, Y, e_4) | product2(X, Y, e_3) | product2(X, Y, e_2) | product2(X, Y, e_1))),
% 0.49/0.57 inference(modus_ponens,[status(thm)],[320, 313])).
% 0.49/0.57 tff(322,plain,
% 0.49/0.57 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product2(X, Y, e_4) | product2(X, Y, e_3) | product2(X, Y, e_2) | product2(X, Y, e_1))) | ((~group_element(e_3)) | (~group_element(e_2)) | product2(e_3, e_2, e_4) | product2(e_3, e_2, e_3) | product2(e_3, e_2, e_2) | product2(e_3, e_2, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product2(X, Y, e_4) | product2(X, Y, e_3) | product2(X, Y, e_2) | product2(X, Y, e_1))) | (~group_element(e_3)) | (~group_element(e_2)) | product2(e_3, e_2, e_4) | product2(e_3, e_2, e_3) | product2(e_3, e_2, e_2) | product2(e_3, e_2, e_1))),
% 0.49/0.57 inference(rewrite,[status(thm)],[])).
% 0.49/0.57 tff(323,plain,
% 0.49/0.57 (((~group_element(e_2)) | (~group_element(e_3)) | product2(e_3, e_2, e_4) | product2(e_3, e_2, e_3) | product2(e_3, e_2, e_2) | product2(e_3, e_2, e_1)) <=> ((~group_element(e_3)) | (~group_element(e_2)) | product2(e_3, e_2, e_4) | product2(e_3, e_2, e_3) | product2(e_3, e_2, e_2) | product2(e_3, e_2, e_1))),
% 0.49/0.57 inference(rewrite,[status(thm)],[])).
% 0.49/0.57 tff(324,plain,
% 0.49/0.57 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product2(X, Y, e_4) | product2(X, Y, e_3) | product2(X, Y, e_2) | product2(X, Y, e_1))) | ((~group_element(e_2)) | (~group_element(e_3)) | product2(e_3, e_2, e_4) | product2(e_3, e_2, e_3) | product2(e_3, e_2, e_2) | product2(e_3, e_2, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product2(X, Y, e_4) | product2(X, Y, e_3) | product2(X, Y, e_2) | product2(X, Y, e_1))) | ((~group_element(e_3)) | (~group_element(e_2)) | product2(e_3, e_2, e_4) | product2(e_3, e_2, e_3) | product2(e_3, e_2, e_2) | product2(e_3, e_2, e_1)))),
% 0.49/0.57 inference(monotonicity,[status(thm)],[323])).
% 0.49/0.57 tff(325,plain,
% 0.49/0.57 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product2(X, Y, e_4) | product2(X, Y, e_3) | product2(X, Y, e_2) | product2(X, Y, e_1))) | ((~group_element(e_2)) | (~group_element(e_3)) | product2(e_3, e_2, e_4) | product2(e_3, e_2, e_3) | product2(e_3, e_2, e_2) | product2(e_3, e_2, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product2(X, Y, e_4) | product2(X, Y, e_3) | product2(X, Y, e_2) | product2(X, Y, e_1))) | (~group_element(e_3)) | (~group_element(e_2)) | product2(e_3, e_2, e_4) | product2(e_3, e_2, e_3) | product2(e_3, e_2, e_2) | product2(e_3, e_2, e_1))),
% 0.49/0.57 inference(transitivity,[status(thm)],[324, 322])).
% 0.49/0.57 tff(326,plain,
% 0.49/0.57 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product2(X, Y, e_4) | product2(X, Y, e_3) | product2(X, Y, e_2) | product2(X, Y, e_1))) | ((~group_element(e_2)) | (~group_element(e_3)) | product2(e_3, e_2, e_4) | product2(e_3, e_2, e_3) | product2(e_3, e_2, e_2) | product2(e_3, e_2, e_1))),
% 0.49/0.57 inference(quant_inst,[status(thm)],[])).
% 0.49/0.57 tff(327,plain,
% 0.49/0.57 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product2(X, Y, e_4) | product2(X, Y, e_3) | product2(X, Y, e_2) | product2(X, Y, e_1))) | (~group_element(e_3)) | (~group_element(e_2)) | product2(e_3, e_2, e_4) | product2(e_3, e_2, e_3) | product2(e_3, e_2, e_2) | product2(e_3, e_2, e_1)),
% 0.49/0.57 inference(modus_ponens,[status(thm)],[326, 325])).
% 0.49/0.57 tff(328,plain,
% 0.49/0.57 (product2(e_3, e_2, e_4) | product2(e_3, e_2, e_3) | product2(e_3, e_2, e_2) | product2(e_3, e_2, e_1)),
% 0.49/0.57 inference(unit_resolution,[status(thm)],[327, 109, 145, 321])).
% 0.49/0.57 tff(329,plain,
% 0.49/0.57 (product2(e_3, e_2, e_4) | product2(e_3, e_2, e_1)),
% 0.49/0.57 inference(unit_resolution,[status(thm)],[328, 311, 293])).
% 0.49/0.57 tff(330,plain,
% 0.49/0.57 (product2(e_3, e_2, e_4)),
% 0.49/0.57 inference(unit_resolution,[status(thm)],[329, 287])).
% 0.49/0.57 tff(331,assumption,(product2(e_3, e_3, e_4)), introduced(assumption)).
% 0.49/0.57 tff(332,assumption,(product2(e_3, e_2, e_4)), introduced(assumption)).
% 0.49/0.57 tff(333,plain,
% 0.49/0.57 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | (equalish(e_3, e_2) | (~product2(e_3, e_3, e_4)) | (~product2(e_3, e_2, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | equalish(e_3, e_2) | (~product2(e_3, e_3, e_4)) | (~product2(e_3, e_2, e_4)))),
% 0.49/0.57 inference(rewrite,[status(thm)],[])).
% 0.49/0.57 tff(334,plain,
% 0.49/0.57 ((equalish(e_3, e_2) | (~product2(e_3, e_2, e_4)) | (~product2(e_3, e_3, e_4))) <=> (equalish(e_3, e_2) | (~product2(e_3, e_3, e_4)) | (~product2(e_3, e_2, e_4)))),
% 0.49/0.57 inference(rewrite,[status(thm)],[])).
% 0.49/0.57 tff(335,plain,
% 0.49/0.57 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | (equalish(e_3, e_2) | (~product2(e_3, e_2, e_4)) | (~product2(e_3, e_3, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | (equalish(e_3, e_2) | (~product2(e_3, e_3, e_4)) | (~product2(e_3, e_2, e_4))))),
% 0.49/0.57 inference(monotonicity,[status(thm)],[334])).
% 0.49/0.57 tff(336,plain,
% 0.49/0.57 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | (equalish(e_3, e_2) | (~product2(e_3, e_2, e_4)) | (~product2(e_3, e_3, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | equalish(e_3, e_2) | (~product2(e_3, e_3, e_4)) | (~product2(e_3, e_2, e_4)))),
% 0.49/0.57 inference(transitivity,[status(thm)],[335, 333])).
% 0.49/0.57 tff(337,plain,
% 0.49/0.57 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | (equalish(e_3, e_2) | (~product2(e_3, e_2, e_4)) | (~product2(e_3, e_3, e_4)))),
% 0.49/0.57 inference(quant_inst,[status(thm)],[])).
% 0.49/0.57 tff(338,plain,
% 0.49/0.57 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | equalish(e_3, e_2) | (~product2(e_3, e_3, e_4)) | (~product2(e_3, e_2, e_4))),
% 0.49/0.57 inference(modus_ponens,[status(thm)],[337, 336])).
% 0.49/0.57 tff(339,plain,
% 0.49/0.57 ($false),
% 0.49/0.57 inference(unit_resolution,[status(thm)],[338, 44, 21, 332, 331])).
% 0.49/0.57 tff(340,plain,((~product2(e_3, e_3, e_4)) | (~product2(e_3, e_2, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.49/0.57 tff(341,plain,
% 0.49/0.57 (~product2(e_3, e_3, e_4)),
% 0.49/0.57 inference(unit_resolution,[status(thm)],[340, 330])).
% 0.49/0.57 tff(342,plain,
% 0.49/0.57 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_4, e_3, e_1)) | (~product1(e_1, e_4, e_3)) | product2(e_3, e_3, e_4))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | (~product1(e_4, e_3, e_1)) | (~product1(e_1, e_4, e_3)) | product2(e_3, e_3, e_4))),
% 0.49/0.57 inference(rewrite,[status(thm)],[])).
% 0.49/0.57 tff(343,plain,
% 0.49/0.57 (((~product1(e_1, e_4, e_3)) | product2(e_3, e_3, e_4) | (~product1(e_4, e_3, e_1))) <=> ((~product1(e_4, e_3, e_1)) | (~product1(e_1, e_4, e_3)) | product2(e_3, e_3, e_4))),
% 0.49/0.57 inference(rewrite,[status(thm)],[])).
% 0.49/0.57 tff(344,plain,
% 0.49/0.57 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_1, e_4, e_3)) | product2(e_3, e_3, e_4) | (~product1(e_4, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_4, e_3, e_1)) | (~product1(e_1, e_4, e_3)) | product2(e_3, e_3, e_4)))),
% 0.49/0.57 inference(monotonicity,[status(thm)],[343])).
% 0.49/0.57 tff(345,plain,
% 0.49/0.57 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_1, e_4, e_3)) | product2(e_3, e_3, e_4) | (~product1(e_4, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | (~product1(e_4, e_3, e_1)) | (~product1(e_1, e_4, e_3)) | product2(e_3, e_3, e_4))),
% 0.49/0.57 inference(transitivity,[status(thm)],[344, 342])).
% 0.49/0.57 tff(346,plain,
% 0.49/0.57 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_1, e_4, e_3)) | product2(e_3, e_3, e_4) | (~product1(e_4, e_3, e_1)))),
% 0.49/0.57 inference(quant_inst,[status(thm)],[])).
% 0.49/0.57 tff(347,plain,
% 0.49/0.57 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | (~product1(e_4, e_3, e_1)) | (~product1(e_1, e_4, e_3)) | product2(e_3, e_3, e_4)),
% 0.49/0.57 inference(modus_ponens,[status(thm)],[346, 345])).
% 0.49/0.57 tff(348,plain,
% 0.49/0.57 ((~product1(e_4, e_3, e_1)) | (~product1(e_1, e_4, e_3)) | product2(e_3, e_3, e_4)),
% 0.49/0.57 inference(unit_resolution,[status(thm)],[347, 183])).
% 0.49/0.57 tff(349,plain,
% 0.49/0.57 (~product1(e_4, e_3, e_1)),
% 0.49/0.57 inference(unit_resolution,[status(thm)],[348, 278, 341])).
% 0.49/0.57 tff(350,plain,
% 0.49/0.57 (product1(e_4, e_3, e_2)),
% 0.49/0.57 inference(unit_resolution,[status(thm)],[217, 349])).
% 0.49/0.57 tff(351,assumption,(product1(e_1, e_2, e_3)), introduced(assumption)).
% 0.49/0.57 tff(352,plain,
% 0.49/0.57 ((~equalish(e_4, e_2)) <=> (~equalish(e_4, e_2))),
% 0.49/0.57 inference(rewrite,[status(thm)],[])).
% 0.49/0.57 tff(353,axiom,(~equalish(e_4, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_2')).
% 0.49/0.57 tff(354,plain,
% 0.49/0.57 (~equalish(e_4, e_2)),
% 0.49/0.57 inference(modus_ponens,[status(thm)],[353, 352])).
% 0.49/0.57 tff(355,plain,
% 0.49/0.57 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_4, e_2) | (~product1(e_1, e_2, e_3)) | (~product1(e_1, e_4, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_4, e_2) | (~product1(e_1, e_2, e_3)) | (~product1(e_1, e_4, e_3)))),
% 0.49/0.57 inference(rewrite,[status(thm)],[])).
% 0.49/0.57 tff(356,plain,
% 0.49/0.57 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_4, e_2) | (~product1(e_1, e_2, e_3)) | (~product1(e_1, e_4, e_3)))),
% 0.49/0.57 inference(quant_inst,[status(thm)],[])).
% 0.49/0.57 tff(357,plain,
% 0.49/0.57 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_4, e_2) | (~product1(e_1, e_2, e_3)) | (~product1(e_1, e_4, e_3))),
% 0.49/0.57 inference(modus_ponens,[status(thm)],[356, 355])).
% 0.49/0.57 tff(358,plain,
% 0.49/0.57 ($false),
% 0.49/0.57 inference(unit_resolution,[status(thm)],[357, 354, 41, 351, 278])).
% 0.49/0.57 tff(359,plain,((~product1(e_1, e_4, e_3)) | (~product1(e_1, e_2, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.49/0.57 tff(360,plain,
% 0.49/0.57 (~product1(e_1, e_2, e_3)),
% 0.49/0.57 inference(unit_resolution,[status(thm)],[359, 278])).
% 0.49/0.57 tff(361,plain,
% 0.49/0.57 (~product1(e_4, e_2, e_3)),
% 0.49/0.57 inference(unit_resolution,[status(thm)],[275, 266])).
% 0.49/0.57 tff(362,plain,
% 0.49/0.57 (product1(e_4, e_2, e_1)),
% 0.49/0.57 inference(unit_resolution,[status(thm)],[117, 361])).
% 0.49/0.57 tff(363,assumption,(~product1(e_1, e_2, e_3)), introduced(assumption)).
% 0.49/0.57 tff(364,plain,
% 0.49/0.57 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_4, e_1, e_3)) | product2(e_3, e_2, e_1) | (~product1(e_1, e_2, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | (~product1(e_4, e_1, e_3)) | product2(e_3, e_2, e_1) | (~product1(e_1, e_2, e_4)))),
% 0.49/0.57 inference(rewrite,[status(thm)],[])).
% 0.49/0.57 tff(365,plain,
% 0.49/0.57 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_4, e_1, e_3)) | product2(e_3, e_2, e_1) | (~product1(e_1, e_2, e_4)))),
% 0.49/0.57 inference(quant_inst,[status(thm)],[])).
% 0.49/0.57 tff(366,plain,
% 0.49/0.57 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | (~product1(e_4, e_1, e_3)) | product2(e_3, e_2, e_1) | (~product1(e_1, e_2, e_4))),
% 0.49/0.57 inference(modus_ponens,[status(thm)],[365, 364])).
% 0.49/0.57 tff(367,plain,
% 0.49/0.57 ((~product1(e_4, e_1, e_3)) | product2(e_3, e_2, e_1) | (~product1(e_1, e_2, e_4))),
% 0.49/0.57 inference(unit_resolution,[status(thm)],[366, 183])).
% 0.49/0.57 tff(368,plain,
% 0.49/0.57 (~product1(e_1, e_2, e_4)),
% 0.49/0.57 inference(unit_resolution,[status(thm)],[367, 266, 287])).
% 0.49/0.58 tff(369,assumption,(product1(e_1, e_2, e_2)), introduced(assumption)).
% 0.49/0.58 tff(370,plain,
% 0.49/0.58 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_1, e_2) | (~product1(e_2, e_2, e_2)) | (~product1(e_1, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_1, e_2) | (~product1(e_2, e_2, e_2)) | (~product1(e_1, e_2, e_2)))),
% 0.49/0.58 inference(rewrite,[status(thm)],[])).
% 0.49/0.58 tff(371,plain,
% 0.49/0.58 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_1, e_2) | (~product1(e_2, e_2, e_2)) | (~product1(e_1, e_2, e_2)))),
% 0.49/0.58 inference(quant_inst,[status(thm)],[])).
% 0.49/0.58 tff(372,plain,
% 0.49/0.58 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_1, e_2) | (~product1(e_2, e_2, e_2)) | (~product1(e_1, e_2, e_2))),
% 0.49/0.58 inference(modus_ponens,[status(thm)],[371, 370])).
% 0.49/0.58 tff(373,plain,
% 0.49/0.58 ($false),
% 0.49/0.58 inference(unit_resolution,[status(thm)],[372, 270, 73, 61, 369])).
% 0.49/0.58 tff(374,plain,(~product1(e_1, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.49/0.58 tff(375,plain,
% 0.49/0.58 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_1)) | (~group_element(e_2)) | product1(e_1, e_2, e_2) | product1(e_1, e_2, e_4) | product1(e_1, e_2, e_1) | product1(e_1, e_2, e_3))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | (~group_element(e_1)) | (~group_element(e_2)) | product1(e_1, e_2, e_2) | product1(e_1, e_2, e_4) | product1(e_1, e_2, e_1) | product1(e_1, e_2, e_3))),
% 0.49/0.58 inference(rewrite,[status(thm)],[])).
% 0.49/0.58 tff(376,plain,
% 0.49/0.58 (((~group_element(e_2)) | (~group_element(e_1)) | product1(e_1, e_2, e_4) | product1(e_1, e_2, e_3) | product1(e_1, e_2, e_2) | product1(e_1, e_2, e_1)) <=> ((~group_element(e_1)) | (~group_element(e_2)) | product1(e_1, e_2, e_2) | product1(e_1, e_2, e_4) | product1(e_1, e_2, e_1) | product1(e_1, e_2, e_3))),
% 0.49/0.58 inference(rewrite,[status(thm)],[])).
% 0.49/0.58 tff(377,plain,
% 0.49/0.58 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_2)) | (~group_element(e_1)) | product1(e_1, e_2, e_4) | product1(e_1, e_2, e_3) | product1(e_1, e_2, e_2) | product1(e_1, e_2, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_1)) | (~group_element(e_2)) | product1(e_1, e_2, e_2) | product1(e_1, e_2, e_4) | product1(e_1, e_2, e_1) | product1(e_1, e_2, e_3)))),
% 0.49/0.58 inference(monotonicity,[status(thm)],[376])).
% 0.49/0.58 tff(378,plain,
% 0.49/0.58 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_2)) | (~group_element(e_1)) | product1(e_1, e_2, e_4) | product1(e_1, e_2, e_3) | product1(e_1, e_2, e_2) | product1(e_1, e_2, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | (~group_element(e_1)) | (~group_element(e_2)) | product1(e_1, e_2, e_2) | product1(e_1, e_2, e_4) | product1(e_1, e_2, e_1) | product1(e_1, e_2, e_3))),
% 0.49/0.58 inference(transitivity,[status(thm)],[377, 375])).
% 0.49/0.58 tff(379,plain,
% 0.49/0.58 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_2)) | (~group_element(e_1)) | product1(e_1, e_2, e_4) | product1(e_1, e_2, e_3) | product1(e_1, e_2, e_2) | product1(e_1, e_2, e_1))),
% 0.49/0.58 inference(quant_inst,[status(thm)],[])).
% 0.49/0.58 tff(380,plain,
% 0.49/0.58 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | (~group_element(e_1)) | (~group_element(e_2)) | product1(e_1, e_2, e_2) | product1(e_1, e_2, e_4) | product1(e_1, e_2, e_1) | product1(e_1, e_2, e_3)),
% 0.49/0.58 inference(modus_ponens,[status(thm)],[379, 378])).
% 0.49/0.58 tff(381,plain,
% 0.49/0.58 (product1(e_1, e_2, e_2) | product1(e_1, e_2, e_4) | product1(e_1, e_2, e_1) | product1(e_1, e_2, e_3)),
% 0.49/0.58 inference(unit_resolution,[status(thm)],[380, 255, 109, 103])).
% 0.49/0.58 tff(382,plain,
% 0.49/0.58 (product1(e_1, e_2, e_4) | product1(e_1, e_2, e_1) | product1(e_1, e_2, e_3)),
% 0.49/0.58 inference(unit_resolution,[status(thm)],[381, 374])).
% 0.49/0.58 tff(383,plain,
% 0.49/0.58 (product1(e_1, e_2, e_1)),
% 0.49/0.58 inference(unit_resolution,[status(thm)],[382, 368, 363])).
% 0.49/0.58 tff(384,assumption,(product1(e_1, e_2, e_1)), introduced(assumption)).
% 0.49/0.58 tff(385,plain,
% 0.49/0.58 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_1, e_4) | (~product1(e_4, e_2, e_1)) | (~product1(e_1, e_2, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_1, e_4) | (~product1(e_4, e_2, e_1)) | (~product1(e_1, e_2, e_1)))),
% 0.49/0.58 inference(rewrite,[status(thm)],[])).
% 0.49/0.58 tff(386,plain,
% 0.49/0.58 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_1, e_4) | (~product1(e_4, e_2, e_1)) | (~product1(e_1, e_2, e_1)))),
% 0.49/0.58 inference(quant_inst,[status(thm)],[])).
% 0.49/0.58 tff(387,plain,
% 0.49/0.58 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_1, e_4) | (~product1(e_4, e_2, e_1)) | (~product1(e_1, e_2, e_1))),
% 0.49/0.58 inference(modus_ponens,[status(thm)],[386, 385])).
% 0.49/0.58 tff(388,plain,
% 0.49/0.58 ($false),
% 0.49/0.58 inference(unit_resolution,[status(thm)],[387, 243, 73, 31, 384])).
% 0.49/0.58 tff(389,plain,((~product1(e_1, e_2, e_1)) | (~product1(e_4, e_2, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.49/0.58 tff(390,plain,
% 0.49/0.58 ($false),
% 0.49/0.58 inference(unit_resolution,[status(thm)],[389, 383, 362])).
% 0.49/0.58 tff(391,plain,((~product1(e_4, e_1, e_3)) | product1(e_1, e_2, e_3) | product2(e_3, e_2, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.49/0.58 tff(392,plain,
% 0.49/0.58 (~product1(e_4, e_1, e_3)),
% 0.49/0.58 inference(unit_resolution,[status(thm)],[391, 360, 287])).
% 0.49/0.58 tff(393,plain,
% 0.49/0.58 (product1(e_4, e_1, e_2)),
% 0.49/0.58 inference(unit_resolution,[status(thm)],[264, 392])).
% 0.49/0.58 tff(394,plain,
% 0.49/0.58 ($false),
% 0.49/0.58 inference(unit_resolution,[status(thm)],[228, 393, 350])).
% 0.49/0.58 tff(395,plain,((~product1(e_1, e_4, e_3)) | product2(e_3, e_2, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.49/0.58 tff(396,plain,
% 0.49/0.58 (product2(e_3, e_2, e_1)),
% 0.49/0.58 inference(unit_resolution,[status(thm)],[395, 278])).
% 0.49/0.58 tff(397,assumption,(product2(e_3, e_2, e_1)), introduced(assumption)).
% 0.49/0.58 tff(398,plain,
% 0.49/0.58 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))) | (equalish(e_1, e_4) | (~product2(e_3, e_2, e_4)) | (~product2(e_3, e_2, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))) | equalish(e_1, e_4) | (~product2(e_3, e_2, e_4)) | (~product2(e_3, e_2, e_1)))),
% 0.49/0.58 inference(rewrite,[status(thm)],[])).
% 0.49/0.58 tff(399,plain,
% 0.49/0.58 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))) | (equalish(e_1, e_4) | (~product2(e_3, e_2, e_4)) | (~product2(e_3, e_2, e_1)))),
% 0.49/0.58 inference(quant_inst,[status(thm)],[])).
% 0.49/0.58 tff(400,plain,
% 0.49/0.58 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))) | equalish(e_1, e_4) | (~product2(e_3, e_2, e_4)) | (~product2(e_3, e_2, e_1))),
% 0.49/0.58 inference(modus_ponens,[status(thm)],[399, 398])).
% 0.49/0.58 tff(401,plain,
% 0.49/0.58 ($false),
% 0.49/0.58 inference(unit_resolution,[status(thm)],[400, 243, 168, 332, 397])).
% 0.49/0.58 tff(402,plain,((~product2(e_3, e_2, e_1)) | (~product2(e_3, e_2, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.49/0.58 tff(403,plain,
% 0.49/0.58 ($false),
% 0.49/0.58 inference(unit_resolution,[status(thm)],[402, 396, 286])).
% 0.49/0.58 tff(404,plain,(~product1(e_1, e_4, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.49/0.58 tff(405,assumption,(product1(e_1, e_4, e_4)), introduced(assumption)).
% 0.49/0.58 tff(406,plain,
% 0.49/0.58 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_1, e_4) | (~product1(e_4, e_4, e_4)) | (~product1(e_1, e_4, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_1, e_4) | (~product1(e_4, e_4, e_4)) | (~product1(e_1, e_4, e_4)))),
% 0.49/0.58 inference(rewrite,[status(thm)],[])).
% 0.49/0.58 tff(407,plain,
% 0.49/0.58 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_1, e_4) | (~product1(e_4, e_4, e_4)) | (~product1(e_1, e_4, e_4)))),
% 0.49/0.58 inference(quant_inst,[status(thm)],[])).
% 0.49/0.58 tff(408,plain,
% 0.49/0.58 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_1, e_4) | (~product1(e_4, e_4, e_4)) | (~product1(e_1, e_4, e_4))),
% 0.49/0.58 inference(modus_ponens,[status(thm)],[407, 406])).
% 0.49/0.58 tff(409,plain,
% 0.49/0.58 ($false),
% 0.49/0.58 inference(unit_resolution,[status(thm)],[408, 243, 73, 84, 405])).
% 0.49/0.58 tff(410,plain,(~product1(e_1, e_4, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.49/0.58 tff(411,assumption,(product1(e_1, e_4, e_1)), introduced(assumption)).
% 0.49/0.58 tff(412,plain,
% 0.49/0.58 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_4, e_1) | (~product1(e_1, e_1, e_1)) | (~product1(e_1, e_4, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_4, e_1) | (~product1(e_1, e_1, e_1)) | (~product1(e_1, e_4, e_1)))),
% 0.49/0.58 inference(rewrite,[status(thm)],[])).
% 0.49/0.58 tff(413,plain,
% 0.49/0.58 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_4, e_1) | (~product1(e_1, e_1, e_1)) | (~product1(e_1, e_4, e_1)))),
% 0.49/0.58 inference(quant_inst,[status(thm)],[])).
% 0.49/0.58 tff(414,plain,
% 0.49/0.58 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_4, e_1) | (~product1(e_1, e_1, e_1)) | (~product1(e_1, e_4, e_1))),
% 0.49/0.58 inference(modus_ponens,[status(thm)],[413, 412])).
% 0.49/0.58 tff(415,plain,
% 0.49/0.58 ($false),
% 0.49/0.58 inference(unit_resolution,[status(thm)],[414, 24, 41, 232, 411])).
% 0.49/0.58 tff(416,plain,(~product1(e_1, e_4, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.49/0.58 tff(417,plain,
% 0.49/0.58 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_4)) | (~group_element(e_1)) | product1(e_1, e_4, e_4) | product1(e_1, e_4, e_2) | product1(e_1, e_4, e_3) | product1(e_1, e_4, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | (~group_element(e_4)) | (~group_element(e_1)) | product1(e_1, e_4, e_4) | product1(e_1, e_4, e_2) | product1(e_1, e_4, e_3) | product1(e_1, e_4, e_1))),
% 0.49/0.58 inference(rewrite,[status(thm)],[])).
% 0.49/0.58 tff(418,plain,
% 0.49/0.58 (((~group_element(e_4)) | (~group_element(e_1)) | product1(e_1, e_4, e_4) | product1(e_1, e_4, e_3) | product1(e_1, e_4, e_2) | product1(e_1, e_4, e_1)) <=> ((~group_element(e_4)) | (~group_element(e_1)) | product1(e_1, e_4, e_4) | product1(e_1, e_4, e_2) | product1(e_1, e_4, e_3) | product1(e_1, e_4, e_1))),
% 0.49/0.58 inference(rewrite,[status(thm)],[])).
% 0.49/0.58 tff(419,plain,
% 0.49/0.58 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_4)) | (~group_element(e_1)) | product1(e_1, e_4, e_4) | product1(e_1, e_4, e_3) | product1(e_1, e_4, e_2) | product1(e_1, e_4, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_4)) | (~group_element(e_1)) | product1(e_1, e_4, e_4) | product1(e_1, e_4, e_2) | product1(e_1, e_4, e_3) | product1(e_1, e_4, e_1)))),
% 0.51/0.58 inference(monotonicity,[status(thm)],[418])).
% 0.51/0.58 tff(420,plain,
% 0.51/0.58 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_4)) | (~group_element(e_1)) | product1(e_1, e_4, e_4) | product1(e_1, e_4, e_3) | product1(e_1, e_4, e_2) | product1(e_1, e_4, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | (~group_element(e_4)) | (~group_element(e_1)) | product1(e_1, e_4, e_4) | product1(e_1, e_4, e_2) | product1(e_1, e_4, e_3) | product1(e_1, e_4, e_1))),
% 0.51/0.58 inference(transitivity,[status(thm)],[419, 417])).
% 0.51/0.58 tff(421,plain,
% 0.51/0.58 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_4)) | (~group_element(e_1)) | product1(e_1, e_4, e_4) | product1(e_1, e_4, e_3) | product1(e_1, e_4, e_2) | product1(e_1, e_4, e_1))),
% 0.51/0.58 inference(quant_inst,[status(thm)],[])).
% 0.51/0.58 tff(422,plain,
% 0.51/0.58 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | (~group_element(e_4)) | (~group_element(e_1)) | product1(e_1, e_4, e_4) | product1(e_1, e_4, e_2) | product1(e_1, e_4, e_3) | product1(e_1, e_4, e_1)),
% 0.51/0.58 inference(modus_ponens,[status(thm)],[421, 420])).
% 0.51/0.58 tff(423,plain,
% 0.51/0.58 (product1(e_1, e_4, e_4) | product1(e_1, e_4, e_2) | product1(e_1, e_4, e_3) | product1(e_1, e_4, e_1)),
% 0.51/0.58 inference(unit_resolution,[status(thm)],[422, 255, 106, 103])).
% 0.51/0.58 tff(424,plain,
% 0.51/0.58 (product1(e_1, e_4, e_4) | product1(e_1, e_4, e_2) | product1(e_1, e_4, e_3)),
% 0.51/0.58 inference(unit_resolution,[status(thm)],[423, 416])).
% 0.51/0.58 tff(425,plain,
% 0.51/0.58 (product1(e_1, e_4, e_2) | product1(e_1, e_4, e_3)),
% 0.51/0.58 inference(unit_resolution,[status(thm)],[424, 410])).
% 0.51/0.58 tff(426,plain,
% 0.51/0.58 (product1(e_1, e_4, e_2)),
% 0.51/0.58 inference(unit_resolution,[status(thm)],[425, 404])).
% 0.51/0.58 tff(427,plain,
% 0.51/0.58 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | (product2(e_1, e_4, e_1) | (~product1(e_1, e_4, e_2)) | (~product1(e_2, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | product2(e_1, e_4, e_1) | (~product1(e_1, e_4, e_2)) | (~product1(e_2, e_1, e_1)))),
% 0.51/0.58 inference(rewrite,[status(thm)],[])).
% 0.51/0.58 tff(428,plain,
% 0.51/0.58 (((~product1(e_2, e_1, e_1)) | product2(e_1, e_4, e_1) | (~product1(e_1, e_4, e_2))) <=> (product2(e_1, e_4, e_1) | (~product1(e_1, e_4, e_2)) | (~product1(e_2, e_1, e_1)))),
% 0.51/0.58 inference(rewrite,[status(thm)],[])).
% 0.51/0.58 tff(429,plain,
% 0.51/0.58 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_2, e_1, e_1)) | product2(e_1, e_4, e_1) | (~product1(e_1, e_4, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | (product2(e_1, e_4, e_1) | (~product1(e_1, e_4, e_2)) | (~product1(e_2, e_1, e_1))))),
% 0.51/0.58 inference(monotonicity,[status(thm)],[428])).
% 0.51/0.58 tff(430,plain,
% 0.51/0.58 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_2, e_1, e_1)) | product2(e_1, e_4, e_1) | (~product1(e_1, e_4, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | product2(e_1, e_4, e_1) | (~product1(e_1, e_4, e_2)) | (~product1(e_2, e_1, e_1)))),
% 0.51/0.58 inference(transitivity,[status(thm)],[429, 427])).
% 0.51/0.58 tff(431,plain,
% 0.51/0.58 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_2, e_1, e_1)) | product2(e_1, e_4, e_1) | (~product1(e_1, e_4, e_2)))),
% 0.51/0.58 inference(quant_inst,[status(thm)],[])).
% 0.51/0.58 tff(432,plain,
% 0.51/0.58 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | product2(e_1, e_4, e_1) | (~product1(e_1, e_4, e_2)) | (~product1(e_2, e_1, e_1))),
% 0.51/0.59 inference(modus_ponens,[status(thm)],[431, 430])).
% 0.51/0.59 tff(433,plain,
% 0.51/0.59 ($false),
% 0.51/0.59 inference(unit_resolution,[status(thm)],[432, 183, 426, 29, 1])).
% 0.51/0.59 tff(434,plain,(~product1(e_2, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.51/0.59 tff(435,assumption,(product1(e_2, e_1, e_3)), introduced(assumption)).
% 0.51/0.59 tff(436,plain,
% 0.51/0.59 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_2, e_4) | (~product1(e_2, e_1, e_3)) | (~product1(e_4, e_1, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_2, e_4) | (~product1(e_2, e_1, e_3)) | (~product1(e_4, e_1, e_3)))),
% 0.51/0.59 inference(rewrite,[status(thm)],[])).
% 0.51/0.59 tff(437,plain,
% 0.51/0.59 ((equalish(e_2, e_4) | (~product1(e_4, e_1, e_3)) | (~product1(e_2, e_1, e_3))) <=> (equalish(e_2, e_4) | (~product1(e_2, e_1, e_3)) | (~product1(e_4, e_1, e_3)))),
% 0.51/0.59 inference(rewrite,[status(thm)],[])).
% 0.51/0.59 tff(438,plain,
% 0.51/0.59 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_2, e_4) | (~product1(e_4, e_1, e_3)) | (~product1(e_2, e_1, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_2, e_4) | (~product1(e_2, e_1, e_3)) | (~product1(e_4, e_1, e_3))))),
% 0.51/0.59 inference(monotonicity,[status(thm)],[437])).
% 0.51/0.59 tff(439,plain,
% 0.51/0.59 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_2, e_4) | (~product1(e_4, e_1, e_3)) | (~product1(e_2, e_1, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_2, e_4) | (~product1(e_2, e_1, e_3)) | (~product1(e_4, e_1, e_3)))),
% 0.51/0.59 inference(transitivity,[status(thm)],[438, 436])).
% 0.51/0.59 tff(440,plain,
% 0.51/0.59 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_2, e_4) | (~product1(e_4, e_1, e_3)) | (~product1(e_2, e_1, e_3)))),
% 0.51/0.59 inference(quant_inst,[status(thm)],[])).
% 0.51/0.59 tff(441,plain,
% 0.51/0.59 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_2, e_4) | (~product1(e_2, e_1, e_3)) | (~product1(e_4, e_1, e_3))),
% 0.51/0.59 inference(modus_ponens,[status(thm)],[440, 439])).
% 0.51/0.59 tff(442,plain,
% 0.51/0.59 ($false),
% 0.51/0.59 inference(unit_resolution,[status(thm)],[441, 76, 73, 265, 435])).
% 0.51/0.59 tff(443,plain,(~product1(e_2, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.51/0.59 tff(444,assumption,(product2(e_2, e_1, e_2)), introduced(assumption)).
% 0.51/0.59 tff(445,plain,
% 0.51/0.59 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | (equalish(e_1, e_2) | (~product2(e_2, e_2, e_2)) | (~product2(e_2, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | equalish(e_1, e_2) | (~product2(e_2, e_2, e_2)) | (~product2(e_2, e_1, e_2)))),
% 0.51/0.59 inference(rewrite,[status(thm)],[])).
% 0.51/0.59 tff(446,plain,
% 0.51/0.59 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | (equalish(e_1, e_2) | (~product2(e_2, e_2, e_2)) | (~product2(e_2, e_1, e_2)))),
% 0.51/0.59 inference(quant_inst,[status(thm)],[])).
% 0.51/0.59 tff(447,plain,
% 0.51/0.59 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | equalish(e_1, e_2) | (~product2(e_2, e_2, e_2)) | (~product2(e_2, e_1, e_2))),
% 0.51/0.59 inference(modus_ponens,[status(thm)],[446, 445])).
% 0.51/0.59 tff(448,plain,
% 0.51/0.59 ($false),
% 0.51/0.59 inference(unit_resolution,[status(thm)],[447, 270, 21, 296, 444])).
% 0.51/0.59 tff(449,plain,(~product2(e_2, e_1, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.51/0.59 tff(450,plain,
% 0.51/0.59 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_2, e_2, e_2)) | product2(e_2, e_1, e_2) | (~product1(e_2, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | (~product1(e_2, e_2, e_2)) | product2(e_2, e_1, e_2) | (~product1(e_2, e_1, e_2)))),
% 0.51/0.59 inference(rewrite,[status(thm)],[])).
% 0.51/0.59 tff(451,plain,
% 0.51/0.59 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_2, e_2, e_2)) | product2(e_2, e_1, e_2) | (~product1(e_2, e_1, e_2)))),
% 0.51/0.59 inference(quant_inst,[status(thm)],[])).
% 0.51/0.59 tff(452,plain,
% 0.51/0.59 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | (~product1(e_2, e_2, e_2)) | product2(e_2, e_1, e_2) | (~product1(e_2, e_1, e_2))),
% 0.51/0.59 inference(modus_ponens,[status(thm)],[451, 450])).
% 0.51/0.59 tff(453,plain,
% 0.51/0.59 (~product1(e_2, e_1, e_2)),
% 0.51/0.59 inference(unit_resolution,[status(thm)],[452, 183, 61, 449])).
% 0.51/0.59 tff(454,plain,
% 0.51/0.59 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_1)) | (~group_element(e_2)) | product1(e_2, e_1, e_4) | product1(e_2, e_1, e_3) | product1(e_2, e_1, e_2) | product1(e_2, e_1, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | (~group_element(e_1)) | (~group_element(e_2)) | product1(e_2, e_1, e_4) | product1(e_2, e_1, e_3) | product1(e_2, e_1, e_2) | product1(e_2, e_1, e_1))),
% 0.51/0.59 inference(rewrite,[status(thm)],[])).
% 0.51/0.59 tff(455,plain,
% 0.51/0.59 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_1)) | (~group_element(e_2)) | product1(e_2, e_1, e_4) | product1(e_2, e_1, e_3) | product1(e_2, e_1, e_2) | product1(e_2, e_1, e_1))),
% 0.51/0.59 inference(quant_inst,[status(thm)],[])).
% 0.51/0.59 tff(456,plain,
% 0.51/0.59 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | (~group_element(e_1)) | (~group_element(e_2)) | product1(e_2, e_1, e_4) | product1(e_2, e_1, e_3) | product1(e_2, e_1, e_2) | product1(e_2, e_1, e_1)),
% 0.51/0.59 inference(modus_ponens,[status(thm)],[455, 454])).
% 0.51/0.59 tff(457,plain,
% 0.51/0.59 (product1(e_2, e_1, e_4) | product1(e_2, e_1, e_3) | product1(e_2, e_1, e_2) | product1(e_2, e_1, e_1)),
% 0.51/0.59 inference(unit_resolution,[status(thm)],[456, 255, 109, 103])).
% 0.51/0.59 tff(458,plain,
% 0.51/0.59 (product1(e_2, e_1, e_4) | product1(e_2, e_1, e_3) | product1(e_2, e_1, e_1)),
% 0.51/0.59 inference(unit_resolution,[status(thm)],[457, 453])).
% 0.51/0.59 tff(459,plain,
% 0.51/0.59 (product1(e_2, e_1, e_4)),
% 0.51/0.59 inference(unit_resolution,[status(thm)],[458, 443, 434])).
% 0.51/0.59 tff(460,assumption,(product1(e_3, e_4, e_2)), introduced(assumption)).
% 0.51/0.59 tff(461,assumption,(product1(e_1, e_4, e_2)), introduced(assumption)).
% 0.51/0.59 tff(462,plain,
% 0.51/0.59 ((~equalish(e_3, e_1)) <=> (~equalish(e_3, e_1))),
% 0.51/0.59 inference(rewrite,[status(thm)],[])).
% 0.51/0.59 tff(463,axiom,(~equalish(e_3, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_1')).
% 0.51/0.59 tff(464,plain,
% 0.51/0.59 (~equalish(e_3, e_1)),
% 0.51/0.59 inference(modus_ponens,[status(thm)],[463, 462])).
% 0.51/0.59 tff(465,plain,
% 0.51/0.59 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_3, e_1) | (~product1(e_1, e_4, e_2)) | (~product1(e_3, e_4, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_3, e_1) | (~product1(e_1, e_4, e_2)) | (~product1(e_3, e_4, e_2)))),
% 0.51/0.59 inference(rewrite,[status(thm)],[])).
% 0.51/0.59 tff(466,plain,
% 0.51/0.59 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_3, e_1) | (~product1(e_1, e_4, e_2)) | (~product1(e_3, e_4, e_2)))),
% 0.51/0.59 inference(quant_inst,[status(thm)],[])).
% 0.51/0.59 tff(467,plain,
% 0.51/0.59 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_3, e_1) | (~product1(e_1, e_4, e_2)) | (~product1(e_3, e_4, e_2))),
% 0.51/0.59 inference(modus_ponens,[status(thm)],[466, 465])).
% 0.51/0.59 tff(468,plain,
% 0.51/0.59 ($false),
% 0.51/0.59 inference(unit_resolution,[status(thm)],[467, 464, 73, 461, 460])).
% 0.51/0.59 tff(469,plain,((~product1(e_3, e_4, e_2)) | (~product1(e_1, e_4, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.59 tff(470,plain,
% 0.51/0.59 (~product1(e_3, e_4, e_2)),
% 0.51/0.59 inference(unit_resolution,[status(thm)],[469, 426])).
% 0.51/0.59 tff(471,assumption,(product1(e_3, e_4, e_4)), introduced(assumption)).
% 0.51/0.59 tff(472,plain,
% 0.51/0.59 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_3, e_4) | (~product1(e_4, e_4, e_4)) | (~product1(e_3, e_4, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_3, e_4) | (~product1(e_4, e_4, e_4)) | (~product1(e_3, e_4, e_4)))),
% 0.51/0.59 inference(rewrite,[status(thm)],[])).
% 0.51/0.59 tff(473,plain,
% 0.51/0.59 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_3, e_4) | (~product1(e_4, e_4, e_4)) | (~product1(e_3, e_4, e_4)))),
% 0.51/0.59 inference(quant_inst,[status(thm)],[])).
% 0.51/0.59 tff(474,plain,
% 0.51/0.59 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_3, e_4) | (~product1(e_4, e_4, e_4)) | (~product1(e_3, e_4, e_4))),
% 0.51/0.59 inference(modus_ponens,[status(thm)],[473, 472])).
% 0.51/0.59 tff(475,plain,
% 0.51/0.59 ($false),
% 0.51/0.59 inference(unit_resolution,[status(thm)],[474, 194, 73, 84, 471])).
% 0.51/0.59 tff(476,plain,(~product1(e_3, e_4, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.51/0.59 tff(477,assumption,(product1(e_3, e_4, e_3)), introduced(assumption)).
% 0.51/0.59 tff(478,plain,
% 0.51/0.59 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_4, e_3) | (~product1(e_3, e_3, e_3)) | (~product1(e_3, e_4, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_4, e_3) | (~product1(e_3, e_3, e_3)) | (~product1(e_3, e_4, e_3)))),
% 0.51/0.59 inference(rewrite,[status(thm)],[])).
% 0.51/0.59 tff(479,plain,
% 0.51/0.59 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_4, e_3) | (~product1(e_3, e_3, e_3)) | (~product1(e_3, e_4, e_3)))),
% 0.51/0.59 inference(quant_inst,[status(thm)],[])).
% 0.51/0.59 tff(480,plain,
% 0.51/0.59 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_4, e_3) | (~product1(e_3, e_3, e_3)) | (~product1(e_3, e_4, e_3))),
% 0.51/0.59 inference(modus_ponens,[status(thm)],[479, 478])).
% 0.51/0.59 tff(481,plain,
% 0.51/0.59 ($false),
% 0.51/0.59 inference(unit_resolution,[status(thm)],[480, 203, 41, 134, 477])).
% 0.51/0.59 tff(482,plain,(~product1(e_3, e_4, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.51/0.59 tff(483,plain,
% 0.51/0.59 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_3)) | (~group_element(e_4)) | product1(e_3, e_4, e_1) | product1(e_3, e_4, e_4) | product1(e_3, e_4, e_3) | product1(e_3, e_4, e_2))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | (~group_element(e_3)) | (~group_element(e_4)) | product1(e_3, e_4, e_1) | product1(e_3, e_4, e_4) | product1(e_3, e_4, e_3) | product1(e_3, e_4, e_2))),
% 0.51/0.59 inference(rewrite,[status(thm)],[])).
% 0.51/0.59 tff(484,plain,
% 0.51/0.59 (((~group_element(e_4)) | (~group_element(e_3)) | product1(e_3, e_4, e_4) | product1(e_3, e_4, e_3) | product1(e_3, e_4, e_2) | product1(e_3, e_4, e_1)) <=> ((~group_element(e_3)) | (~group_element(e_4)) | product1(e_3, e_4, e_1) | product1(e_3, e_4, e_4) | product1(e_3, e_4, e_3) | product1(e_3, e_4, e_2))),
% 0.51/0.59 inference(rewrite,[status(thm)],[])).
% 0.51/0.59 tff(485,plain,
% 0.51/0.59 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_4)) | (~group_element(e_3)) | product1(e_3, e_4, e_4) | product1(e_3, e_4, e_3) | product1(e_3, e_4, e_2) | product1(e_3, e_4, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_3)) | (~group_element(e_4)) | product1(e_3, e_4, e_1) | product1(e_3, e_4, e_4) | product1(e_3, e_4, e_3) | product1(e_3, e_4, e_2)))),
% 0.51/0.59 inference(monotonicity,[status(thm)],[484])).
% 0.51/0.59 tff(486,plain,
% 0.51/0.59 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_4)) | (~group_element(e_3)) | product1(e_3, e_4, e_4) | product1(e_3, e_4, e_3) | product1(e_3, e_4, e_2) | product1(e_3, e_4, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | (~group_element(e_3)) | (~group_element(e_4)) | product1(e_3, e_4, e_1) | product1(e_3, e_4, e_4) | product1(e_3, e_4, e_3) | product1(e_3, e_4, e_2))),
% 0.51/0.59 inference(transitivity,[status(thm)],[485, 483])).
% 0.51/0.59 tff(487,plain,
% 0.51/0.59 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_4)) | (~group_element(e_3)) | product1(e_3, e_4, e_4) | product1(e_3, e_4, e_3) | product1(e_3, e_4, e_2) | product1(e_3, e_4, e_1))),
% 0.51/0.59 inference(quant_inst,[status(thm)],[])).
% 0.51/0.59 tff(488,plain,
% 0.51/0.59 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | (~group_element(e_3)) | (~group_element(e_4)) | product1(e_3, e_4, e_1) | product1(e_3, e_4, e_4) | product1(e_3, e_4, e_3) | product1(e_3, e_4, e_2)),
% 0.51/0.59 inference(modus_ponens,[status(thm)],[487, 486])).
% 0.51/0.59 tff(489,plain,
% 0.51/0.59 (product1(e_3, e_4, e_1) | product1(e_3, e_4, e_4) | product1(e_3, e_4, e_3) | product1(e_3, e_4, e_2)),
% 0.51/0.59 inference(unit_resolution,[status(thm)],[488, 145, 106, 103])).
% 0.51/0.59 tff(490,plain,
% 0.51/0.59 (product1(e_3, e_4, e_1) | product1(e_3, e_4, e_4) | product1(e_3, e_4, e_2)),
% 0.51/0.59 inference(unit_resolution,[status(thm)],[489, 482])).
% 0.51/0.59 tff(491,plain,
% 0.51/0.59 (product1(e_3, e_4, e_1) | product1(e_3, e_4, e_2)),
% 0.51/0.59 inference(unit_resolution,[status(thm)],[490, 476])).
% 0.51/0.59 tff(492,plain,
% 0.51/0.59 (product1(e_3, e_4, e_1)),
% 0.51/0.59 inference(unit_resolution,[status(thm)],[491, 470])).
% 0.51/0.59 tff(493,assumption,(~product1(e_3, e_2, e_4)), introduced(assumption)).
% 0.51/0.59 tff(494,assumption,(product1(e_2, e_4, e_4)), introduced(assumption)).
% 0.51/0.59 tff(495,plain,
% 0.51/0.59 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_2, e_4) | (~product1(e_4, e_4, e_4)) | (~product1(e_2, e_4, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_2, e_4) | (~product1(e_4, e_4, e_4)) | (~product1(e_2, e_4, e_4)))),
% 0.51/0.59 inference(rewrite,[status(thm)],[])).
% 0.51/0.59 tff(496,plain,
% 0.51/0.59 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_2, e_4) | (~product1(e_4, e_4, e_4)) | (~product1(e_2, e_4, e_4)))),
% 0.51/0.59 inference(quant_inst,[status(thm)],[])).
% 0.51/0.59 tff(497,plain,
% 0.51/0.59 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_2, e_4) | (~product1(e_4, e_4, e_4)) | (~product1(e_2, e_4, e_4))),
% 0.51/0.59 inference(modus_ponens,[status(thm)],[496, 495])).
% 0.51/0.59 tff(498,plain,
% 0.51/0.59 ($false),
% 0.51/0.59 inference(unit_resolution,[status(thm)],[497, 76, 73, 84, 494])).
% 0.51/0.59 tff(499,plain,(~product1(e_2, e_4, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.51/0.59 tff(500,assumption,(product1(e_3, e_4, e_1)), introduced(assumption)).
% 0.51/0.59 tff(501,assumption,(product1(e_2, e_4, e_1)), introduced(assumption)).
% 0.51/0.59 tff(502,plain,
% 0.51/0.59 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_2, e_3) | (~product1(e_3, e_4, e_1)) | (~product1(e_2, e_4, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_2, e_3) | (~product1(e_3, e_4, e_1)) | (~product1(e_2, e_4, e_1)))),
% 0.51/0.60 inference(rewrite,[status(thm)],[])).
% 0.51/0.60 tff(503,plain,
% 0.51/0.60 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_2, e_3) | (~product1(e_3, e_4, e_1)) | (~product1(e_2, e_4, e_1)))),
% 0.51/0.60 inference(quant_inst,[status(thm)],[])).
% 0.51/0.60 tff(504,plain,
% 0.51/0.60 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_2, e_3) | (~product1(e_3, e_4, e_1)) | (~product1(e_2, e_4, e_1))),
% 0.51/0.60 inference(modus_ponens,[status(thm)],[503, 502])).
% 0.51/0.60 tff(505,plain,
% 0.51/0.60 ($false),
% 0.51/0.60 inference(unit_resolution,[status(thm)],[504, 137, 73, 500, 501])).
% 0.51/0.60 tff(506,plain,((~product1(e_2, e_4, e_1)) | (~product1(e_3, e_4, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.60 tff(507,plain,
% 0.51/0.60 (~product1(e_2, e_4, e_1)),
% 0.51/0.60 inference(unit_resolution,[status(thm)],[506, 500])).
% 0.51/0.60 tff(508,assumption,(product1(e_2, e_4, e_2)), introduced(assumption)).
% 0.51/0.60 tff(509,plain,
% 0.51/0.60 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_4, e_2) | (~product1(e_2, e_2, e_2)) | (~product1(e_2, e_4, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_4, e_2) | (~product1(e_2, e_2, e_2)) | (~product1(e_2, e_4, e_2)))),
% 0.51/0.60 inference(rewrite,[status(thm)],[])).
% 0.51/0.60 tff(510,plain,
% 0.51/0.60 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_4, e_2) | (~product1(e_2, e_2, e_2)) | (~product1(e_2, e_4, e_2)))),
% 0.51/0.60 inference(quant_inst,[status(thm)],[])).
% 0.51/0.60 tff(511,plain,
% 0.51/0.60 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_4, e_2) | (~product1(e_2, e_2, e_2)) | (~product1(e_2, e_4, e_2))),
% 0.51/0.60 inference(modus_ponens,[status(thm)],[510, 509])).
% 0.51/0.60 tff(512,plain,
% 0.51/0.60 ($false),
% 0.51/0.60 inference(unit_resolution,[status(thm)],[511, 354, 41, 61, 508])).
% 0.51/0.60 tff(513,plain,(~product1(e_2, e_4, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.51/0.60 tff(514,plain,
% 0.51/0.60 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_4)) | (~group_element(e_2)) | product1(e_2, e_4, e_1) | product1(e_2, e_4, e_4) | product1(e_2, e_4, e_2) | product1(e_2, e_4, e_3))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | (~group_element(e_4)) | (~group_element(e_2)) | product1(e_2, e_4, e_1) | product1(e_2, e_4, e_4) | product1(e_2, e_4, e_2) | product1(e_2, e_4, e_3))),
% 0.51/0.60 inference(rewrite,[status(thm)],[])).
% 0.51/0.60 tff(515,plain,
% 0.51/0.60 (((~group_element(e_4)) | (~group_element(e_2)) | product1(e_2, e_4, e_4) | product1(e_2, e_4, e_3) | product1(e_2, e_4, e_2) | product1(e_2, e_4, e_1)) <=> ((~group_element(e_4)) | (~group_element(e_2)) | product1(e_2, e_4, e_1) | product1(e_2, e_4, e_4) | product1(e_2, e_4, e_2) | product1(e_2, e_4, e_3))),
% 0.51/0.60 inference(rewrite,[status(thm)],[])).
% 0.51/0.60 tff(516,plain,
% 0.51/0.60 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_4)) | (~group_element(e_2)) | product1(e_2, e_4, e_4) | product1(e_2, e_4, e_3) | product1(e_2, e_4, e_2) | product1(e_2, e_4, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_4)) | (~group_element(e_2)) | product1(e_2, e_4, e_1) | product1(e_2, e_4, e_4) | product1(e_2, e_4, e_2) | product1(e_2, e_4, e_3)))),
% 0.51/0.60 inference(monotonicity,[status(thm)],[515])).
% 0.51/0.60 tff(517,plain,
% 0.51/0.60 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_4)) | (~group_element(e_2)) | product1(e_2, e_4, e_4) | product1(e_2, e_4, e_3) | product1(e_2, e_4, e_2) | product1(e_2, e_4, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | (~group_element(e_4)) | (~group_element(e_2)) | product1(e_2, e_4, e_1) | product1(e_2, e_4, e_4) | product1(e_2, e_4, e_2) | product1(e_2, e_4, e_3))),
% 0.51/0.60 inference(transitivity,[status(thm)],[516, 514])).
% 0.51/0.60 tff(518,plain,
% 0.51/0.60 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_4)) | (~group_element(e_2)) | product1(e_2, e_4, e_4) | product1(e_2, e_4, e_3) | product1(e_2, e_4, e_2) | product1(e_2, e_4, e_1))),
% 0.51/0.60 inference(quant_inst,[status(thm)],[])).
% 0.51/0.60 tff(519,plain,
% 0.51/0.60 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | (~group_element(e_4)) | (~group_element(e_2)) | product1(e_2, e_4, e_1) | product1(e_2, e_4, e_4) | product1(e_2, e_4, e_2) | product1(e_2, e_4, e_3)),
% 0.51/0.60 inference(modus_ponens,[status(thm)],[518, 517])).
% 0.51/0.60 tff(520,plain,
% 0.51/0.60 (product1(e_2, e_4, e_1) | product1(e_2, e_4, e_4) | product1(e_2, e_4, e_2) | product1(e_2, e_4, e_3)),
% 0.51/0.60 inference(unit_resolution,[status(thm)],[519, 109, 106, 103])).
% 0.51/0.60 tff(521,plain,
% 0.51/0.60 (product1(e_2, e_4, e_1) | product1(e_2, e_4, e_4) | product1(e_2, e_4, e_3)),
% 0.51/0.60 inference(unit_resolution,[status(thm)],[520, 513])).
% 0.51/0.60 tff(522,plain,
% 0.51/0.60 (product1(e_2, e_4, e_3)),
% 0.51/0.60 inference(unit_resolution,[status(thm)],[521, 507, 499])).
% 0.51/0.60 tff(523,assumption,(product1(e_3, e_2, e_2)), introduced(assumption)).
% 0.51/0.60 tff(524,assumption,(product2(e_2, e_4, e_2)), introduced(assumption)).
% 0.51/0.60 tff(525,plain,
% 0.51/0.60 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | (equalish(e_4, e_2) | (~product2(e_2, e_2, e_2)) | (~product2(e_2, e_4, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | equalish(e_4, e_2) | (~product2(e_2, e_2, e_2)) | (~product2(e_2, e_4, e_2)))),
% 0.51/0.60 inference(rewrite,[status(thm)],[])).
% 0.51/0.60 tff(526,plain,
% 0.51/0.60 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | (equalish(e_4, e_2) | (~product2(e_2, e_2, e_2)) | (~product2(e_2, e_4, e_2)))),
% 0.51/0.60 inference(quant_inst,[status(thm)],[])).
% 0.51/0.60 tff(527,plain,
% 0.51/0.60 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | equalish(e_4, e_2) | (~product2(e_2, e_2, e_2)) | (~product2(e_2, e_4, e_2))),
% 0.51/0.60 inference(modus_ponens,[status(thm)],[526, 525])).
% 0.51/0.60 tff(528,plain,
% 0.51/0.60 ($false),
% 0.51/0.60 inference(unit_resolution,[status(thm)],[527, 354, 21, 296, 524])).
% 0.51/0.60 tff(529,plain,(~product2(e_2, e_4, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.51/0.60 tff(530,assumption,(product1(e_2, e_4, e_3)), introduced(assumption)).
% 0.51/0.60 tff(531,plain,
% 0.51/0.60 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | (product2(e_2, e_4, e_2) | (~product1(e_3, e_2, e_2)) | (~product1(e_2, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | product2(e_2, e_4, e_2) | (~product1(e_3, e_2, e_2)) | (~product1(e_2, e_4, e_3)))),
% 0.51/0.60 inference(rewrite,[status(thm)],[])).
% 0.51/0.60 tff(532,plain,
% 0.51/0.60 (((~product1(e_3, e_2, e_2)) | product2(e_2, e_4, e_2) | (~product1(e_2, e_4, e_3))) <=> (product2(e_2, e_4, e_2) | (~product1(e_3, e_2, e_2)) | (~product1(e_2, e_4, e_3)))),
% 0.51/0.60 inference(rewrite,[status(thm)],[])).
% 0.51/0.60 tff(533,plain,
% 0.51/0.60 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_3, e_2, e_2)) | product2(e_2, e_4, e_2) | (~product1(e_2, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | (product2(e_2, e_4, e_2) | (~product1(e_3, e_2, e_2)) | (~product1(e_2, e_4, e_3))))),
% 0.51/0.60 inference(monotonicity,[status(thm)],[532])).
% 0.51/0.60 tff(534,plain,
% 0.51/0.60 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_3, e_2, e_2)) | product2(e_2, e_4, e_2) | (~product1(e_2, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | product2(e_2, e_4, e_2) | (~product1(e_3, e_2, e_2)) | (~product1(e_2, e_4, e_3)))),
% 0.51/0.60 inference(transitivity,[status(thm)],[533, 531])).
% 0.51/0.60 tff(535,plain,
% 0.51/0.60 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_3, e_2, e_2)) | product2(e_2, e_4, e_2) | (~product1(e_2, e_4, e_3)))),
% 0.51/0.60 inference(quant_inst,[status(thm)],[])).
% 0.51/0.60 tff(536,plain,
% 0.51/0.60 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | product2(e_2, e_4, e_2) | (~product1(e_3, e_2, e_2)) | (~product1(e_2, e_4, e_3))),
% 0.51/0.60 inference(modus_ponens,[status(thm)],[535, 534])).
% 0.51/0.60 tff(537,plain,
% 0.51/0.60 ($false),
% 0.51/0.60 inference(unit_resolution,[status(thm)],[536, 183, 530, 529, 523])).
% 0.51/0.60 tff(538,plain,((~product1(e_3, e_2, e_2)) | (~product1(e_2, e_4, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.60 tff(539,plain,
% 0.51/0.60 (~product1(e_3, e_2, e_2)),
% 0.51/0.60 inference(unit_resolution,[status(thm)],[538, 522])).
% 0.51/0.60 tff(540,plain,
% 0.51/0.60 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_3, e_3, e_3)) | product2(e_3, e_2, e_3) | (~product1(e_3, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | (~product1(e_3, e_3, e_3)) | product2(e_3, e_2, e_3) | (~product1(e_3, e_2, e_3)))),
% 0.51/0.60 inference(rewrite,[status(thm)],[])).
% 0.51/0.60 tff(541,plain,
% 0.51/0.60 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_3, e_3, e_3)) | product2(e_3, e_2, e_3) | (~product1(e_3, e_2, e_3)))),
% 0.51/0.60 inference(quant_inst,[status(thm)],[])).
% 0.51/0.60 tff(542,plain,
% 0.51/0.60 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | (~product1(e_3, e_3, e_3)) | product2(e_3, e_2, e_3) | (~product1(e_3, e_2, e_3))),
% 0.51/0.60 inference(modus_ponens,[status(thm)],[541, 540])).
% 0.51/0.60 tff(543,plain,
% 0.51/0.60 (~product1(e_3, e_2, e_3)),
% 0.51/0.60 inference(unit_resolution,[status(thm)],[542, 183, 134, 293])).
% 0.51/0.60 tff(544,plain,
% 0.51/0.60 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_3)) | (~group_element(e_2)) | product1(e_3, e_2, e_2) | product1(e_3, e_2, e_3) | product1(e_3, e_2, e_4) | product1(e_3, e_2, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | (~group_element(e_3)) | (~group_element(e_2)) | product1(e_3, e_2, e_2) | product1(e_3, e_2, e_3) | product1(e_3, e_2, e_4) | product1(e_3, e_2, e_1))),
% 0.51/0.60 inference(rewrite,[status(thm)],[])).
% 0.51/0.60 tff(545,plain,
% 0.51/0.60 (((~group_element(e_2)) | (~group_element(e_3)) | product1(e_3, e_2, e_4) | product1(e_3, e_2, e_3) | product1(e_3, e_2, e_2) | product1(e_3, e_2, e_1)) <=> ((~group_element(e_3)) | (~group_element(e_2)) | product1(e_3, e_2, e_2) | product1(e_3, e_2, e_3) | product1(e_3, e_2, e_4) | product1(e_3, e_2, e_1))),
% 0.51/0.60 inference(rewrite,[status(thm)],[])).
% 0.51/0.60 tff(546,plain,
% 0.51/0.60 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_2)) | (~group_element(e_3)) | product1(e_3, e_2, e_4) | product1(e_3, e_2, e_3) | product1(e_3, e_2, e_2) | product1(e_3, e_2, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_3)) | (~group_element(e_2)) | product1(e_3, e_2, e_2) | product1(e_3, e_2, e_3) | product1(e_3, e_2, e_4) | product1(e_3, e_2, e_1)))),
% 0.51/0.60 inference(monotonicity,[status(thm)],[545])).
% 0.51/0.60 tff(547,plain,
% 0.51/0.60 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_2)) | (~group_element(e_3)) | product1(e_3, e_2, e_4) | product1(e_3, e_2, e_3) | product1(e_3, e_2, e_2) | product1(e_3, e_2, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | (~group_element(e_3)) | (~group_element(e_2)) | product1(e_3, e_2, e_2) | product1(e_3, e_2, e_3) | product1(e_3, e_2, e_4) | product1(e_3, e_2, e_1))),
% 0.51/0.60 inference(transitivity,[status(thm)],[546, 544])).
% 0.51/0.60 tff(548,plain,
% 0.51/0.60 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_2)) | (~group_element(e_3)) | product1(e_3, e_2, e_4) | product1(e_3, e_2, e_3) | product1(e_3, e_2, e_2) | product1(e_3, e_2, e_1))),
% 0.51/0.60 inference(quant_inst,[status(thm)],[])).
% 0.51/0.60 tff(549,plain,
% 0.51/0.60 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | (~group_element(e_3)) | (~group_element(e_2)) | product1(e_3, e_2, e_2) | product1(e_3, e_2, e_3) | product1(e_3, e_2, e_4) | product1(e_3, e_2, e_1)),
% 0.51/0.60 inference(modus_ponens,[status(thm)],[548, 547])).
% 0.51/0.60 tff(550,plain,
% 0.51/0.60 (product1(e_3, e_2, e_2) | product1(e_3, e_2, e_4) | product1(e_3, e_2, e_1)),
% 0.51/0.60 inference(unit_resolution,[status(thm)],[549, 109, 145, 103, 543])).
% 0.51/0.60 tff(551,plain,
% 0.51/0.60 (product1(e_3, e_2, e_1)),
% 0.51/0.60 inference(unit_resolution,[status(thm)],[550, 539, 493])).
% 0.51/0.60 tff(552,plain,
% 0.51/0.60 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_4, e_2) | (~product1(e_3, e_4, e_1)) | (~product1(e_3, e_2, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_4, e_2) | (~product1(e_3, e_4, e_1)) | (~product1(e_3, e_2, e_1)))),
% 0.51/0.60 inference(rewrite,[status(thm)],[])).
% 0.51/0.60 tff(553,plain,
% 0.51/0.60 ((equalish(e_4, e_2) | (~product1(e_3, e_2, e_1)) | (~product1(e_3, e_4, e_1))) <=> (equalish(e_4, e_2) | (~product1(e_3, e_4, e_1)) | (~product1(e_3, e_2, e_1)))),
% 0.51/0.60 inference(rewrite,[status(thm)],[])).
% 0.51/0.60 tff(554,plain,
% 0.51/0.60 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_4, e_2) | (~product1(e_3, e_2, e_1)) | (~product1(e_3, e_4, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_4, e_2) | (~product1(e_3, e_4, e_1)) | (~product1(e_3, e_2, e_1))))),
% 0.51/0.60 inference(monotonicity,[status(thm)],[553])).
% 0.51/0.60 tff(555,plain,
% 0.51/0.60 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_4, e_2) | (~product1(e_3, e_2, e_1)) | (~product1(e_3, e_4, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_4, e_2) | (~product1(e_3, e_4, e_1)) | (~product1(e_3, e_2, e_1)))),
% 0.51/0.60 inference(transitivity,[status(thm)],[554, 552])).
% 0.51/0.60 tff(556,plain,
% 0.51/0.60 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_4, e_2) | (~product1(e_3, e_2, e_1)) | (~product1(e_3, e_4, e_1)))),
% 0.51/0.60 inference(quant_inst,[status(thm)],[])).
% 0.51/0.60 tff(557,plain,
% 0.51/0.60 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_4, e_2) | (~product1(e_3, e_4, e_1)) | (~product1(e_3, e_2, e_1))),
% 0.51/0.60 inference(modus_ponens,[status(thm)],[556, 555])).
% 0.51/0.60 tff(558,plain,
% 0.51/0.60 ($false),
% 0.51/0.60 inference(unit_resolution,[status(thm)],[557, 354, 41, 500, 551])).
% 0.51/0.60 tff(559,plain,((~product1(e_3, e_4, e_1)) | product1(e_3, e_2, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.51/0.60 tff(560,plain,
% 0.51/0.61 (product1(e_3, e_2, e_4)),
% 0.51/0.61 inference(unit_resolution,[status(thm)],[559, 492])).
% 0.51/0.61 tff(561,assumption,(product1(e_3, e_2, e_4)), introduced(assumption)).
% 0.51/0.61 tff(562,assumption,(product1(e_1, e_2, e_4)), introduced(assumption)).
% 0.51/0.61 tff(563,plain,
% 0.51/0.61 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_3, e_1) | (~product1(e_1, e_2, e_4)) | (~product1(e_3, e_2, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_3, e_1) | (~product1(e_1, e_2, e_4)) | (~product1(e_3, e_2, e_4)))),
% 0.51/0.61 inference(rewrite,[status(thm)],[])).
% 0.51/0.61 tff(564,plain,
% 0.51/0.61 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_3, e_1) | (~product1(e_1, e_2, e_4)) | (~product1(e_3, e_2, e_4)))),
% 0.51/0.61 inference(quant_inst,[status(thm)],[])).
% 0.51/0.61 tff(565,plain,
% 0.51/0.61 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_3, e_1) | (~product1(e_1, e_2, e_4)) | (~product1(e_3, e_2, e_4))),
% 0.51/0.61 inference(modus_ponens,[status(thm)],[564, 563])).
% 0.51/0.61 tff(566,plain,
% 0.51/0.61 ($false),
% 0.51/0.61 inference(unit_resolution,[status(thm)],[565, 464, 73, 562, 561])).
% 0.51/0.61 tff(567,plain,((~product1(e_3, e_2, e_4)) | (~product1(e_1, e_2, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.61 tff(568,plain,
% 0.51/0.61 (~product1(e_1, e_2, e_4)),
% 0.51/0.61 inference(unit_resolution,[status(thm)],[567, 560])).
% 0.51/0.61 tff(569,assumption,(product2(e_1, e_2, e_1)), introduced(assumption)).
% 0.51/0.61 tff(570,plain,
% 0.51/0.61 ((~equalish(e_2, e_1)) <=> (~equalish(e_2, e_1))),
% 0.51/0.61 inference(rewrite,[status(thm)],[])).
% 0.51/0.61 tff(571,axiom,(~equalish(e_2, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_1')).
% 0.51/0.61 tff(572,plain,
% 0.51/0.61 (~equalish(e_2, e_1)),
% 0.51/0.61 inference(modus_ponens,[status(thm)],[571, 570])).
% 0.51/0.61 tff(573,plain,
% 0.51/0.61 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | (equalish(e_2, e_1) | (~product2(e_1, e_1, e_1)) | (~product2(e_1, e_2, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | equalish(e_2, e_1) | (~product2(e_1, e_1, e_1)) | (~product2(e_1, e_2, e_1)))),
% 0.51/0.61 inference(rewrite,[status(thm)],[])).
% 0.51/0.61 tff(574,plain,
% 0.51/0.61 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | (equalish(e_2, e_1) | (~product2(e_1, e_1, e_1)) | (~product2(e_1, e_2, e_1)))),
% 0.51/0.61 inference(quant_inst,[status(thm)],[])).
% 0.51/0.61 tff(575,plain,
% 0.51/0.61 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | equalish(e_2, e_1) | (~product2(e_1, e_1, e_1)) | (~product2(e_1, e_2, e_1))),
% 0.51/0.61 inference(modus_ponens,[status(thm)],[574, 573])).
% 0.51/0.61 tff(576,plain,
% 0.51/0.61 ($false),
% 0.51/0.61 inference(unit_resolution,[status(thm)],[575, 572, 21, 11, 569])).
% 0.51/0.61 tff(577,plain,(~product2(e_1, e_2, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.51/0.61 tff(578,plain,
% 0.51/0.61 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_1, e_1, e_1)) | product2(e_1, e_2, e_1) | (~product1(e_1, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | (~product1(e_1, e_1, e_1)) | product2(e_1, e_2, e_1) | (~product1(e_1, e_2, e_1)))),
% 0.51/0.61 inference(rewrite,[status(thm)],[])).
% 0.51/0.61 tff(579,plain,
% 0.51/0.61 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_1, e_1, e_1)) | product2(e_1, e_2, e_1) | (~product1(e_1, e_2, e_1)))),
% 0.51/0.61 inference(quant_inst,[status(thm)],[])).
% 0.51/0.61 tff(580,plain,
% 0.51/0.61 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | (~product1(e_1, e_1, e_1)) | product2(e_1, e_2, e_1) | (~product1(e_1, e_2, e_1))),
% 0.51/0.61 inference(modus_ponens,[status(thm)],[579, 578])).
% 0.51/0.61 tff(581,plain,
% 0.51/0.61 (~product1(e_1, e_2, e_1)),
% 0.51/0.61 inference(unit_resolution,[status(thm)],[580, 183, 232, 577])).
% 0.51/0.61 tff(582,plain,
% 0.51/0.61 (product1(e_1, e_2, e_4) | product1(e_1, e_2, e_3)),
% 0.51/0.61 inference(unit_resolution,[status(thm)],[382, 581])).
% 0.51/0.61 tff(583,plain,
% 0.51/0.61 (product1(e_1, e_2, e_3)),
% 0.51/0.61 inference(unit_resolution,[status(thm)],[582, 568])).
% 0.51/0.61 tff(584,plain,
% 0.51/0.61 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_1, e_2, e_3)) | product2(e_3, e_3, e_2) | (~product1(e_2, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | (~product1(e_1, e_2, e_3)) | product2(e_3, e_3, e_2) | (~product1(e_2, e_3, e_1)))),
% 0.51/0.61 inference(rewrite,[status(thm)],[])).
% 0.51/0.61 tff(585,plain,
% 0.51/0.61 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_1, e_2, e_3)) | product2(e_3, e_3, e_2) | (~product1(e_2, e_3, e_1)))),
% 0.51/0.61 inference(quant_inst,[status(thm)],[])).
% 0.51/0.61 tff(586,plain,
% 0.51/0.61 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | (~product1(e_1, e_2, e_3)) | product2(e_3, e_3, e_2) | (~product1(e_2, e_3, e_1))),
% 0.51/0.61 inference(modus_ponens,[status(thm)],[585, 584])).
% 0.51/0.61 tff(587,plain,
% 0.51/0.61 (~product1(e_2, e_3, e_1)),
% 0.51/0.61 inference(unit_resolution,[status(thm)],[586, 183, 583, 173])).
% 0.51/0.61 tff(588,plain,
% 0.51/0.61 (product1(e_2, e_3, e_4)),
% 0.51/0.61 inference(unit_resolution,[status(thm)],[154, 587])).
% 0.51/0.61 tff(589,plain,
% 0.51/0.61 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_1, e_3) | (~product1(e_2, e_3, e_4)) | (~product1(e_2, e_1, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_1, e_3) | (~product1(e_2, e_3, e_4)) | (~product1(e_2, e_1, e_4)))),
% 0.51/0.61 inference(rewrite,[status(thm)],[])).
% 0.51/0.61 tff(590,plain,
% 0.51/0.61 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_1, e_3) | (~product1(e_2, e_3, e_4)) | (~product1(e_2, e_1, e_4)))),
% 0.51/0.61 inference(quant_inst,[status(thm)],[])).
% 0.51/0.61 tff(591,plain,
% 0.51/0.61 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_1, e_3) | (~product1(e_2, e_3, e_4)) | (~product1(e_2, e_1, e_4))),
% 0.51/0.61 inference(modus_ponens,[status(thm)],[590, 589])).
% 0.51/0.61 tff(592,plain,
% 0.51/0.61 ($false),
% 0.51/0.61 inference(unit_resolution,[status(thm)],[591, 223, 41, 588, 459])).
% 0.51/0.61 % SZS output end Proof
%------------------------------------------------------------------------------