TSTP Solution File: GRP124-7.004 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP124-7.004 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n026.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 22:26:01 EDT 2022
% Result : Unsatisfiable 0.20s 0.46s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : GRP124-7.004 : TPTP v8.1.0. Released v1.2.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n026.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Aug 31 15:09:22 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.20/0.46 % SZS status Unsatisfiable
% 0.20/0.46 % SZS output start Proof
% 0.20/0.46 tff(product1_type, type, (
% 0.20/0.46 product1: ( $i * $i * $i ) > $o)).
% 0.20/0.46 tff(e_1_type, type, (
% 0.20/0.46 e_1: $i)).
% 0.20/0.46 tff(e_3_type, type, (
% 0.20/0.46 e_3: $i)).
% 0.20/0.46 tff(e_4_type, type, (
% 0.20/0.46 e_4: $i)).
% 0.20/0.46 tff(e_2_type, type, (
% 0.20/0.46 e_2: $i)).
% 0.20/0.46 tff(product2_type, type, (
% 0.20/0.46 product2: ( $i * $i * $i ) > $o)).
% 0.20/0.46 tff(equalish_type, type, (
% 0.20/0.46 equalish: ( $i * $i ) > $o)).
% 0.20/0.46 tff(group_element_type, type, (
% 0.20/0.46 group_element: $i > $o)).
% 0.20/0.46 tff(1,assumption,(product2(e_3, e_3, e_4)), introduced(assumption)).
% 0.20/0.46 tff(2,plain,
% 0.20/0.46 (^[X: $i] : refl(product2(X, X, X) <=> product2(X, X, X))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(3,plain,
% 0.20/0.46 (![X: $i] : product2(X, X, X) <=> ![X: $i] : product2(X, X, X)),
% 0.20/0.46 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.46 tff(4,plain,
% 0.20/0.46 (![X: $i] : product2(X, X, X) <=> ![X: $i] : product2(X, X, X)),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(5,axiom,(![X: $i] : product2(X, X, X)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product2_idempotence')).
% 0.20/0.46 tff(6,plain,
% 0.20/0.46 (![X: $i] : product2(X, X, X)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.46 tff(7,plain,(
% 0.20/0.46 ![X: $i] : product2(X, X, X)),
% 0.20/0.46 inference(skolemize,[status(sab)],[6])).
% 0.20/0.46 tff(8,plain,
% 0.20/0.46 (![X: $i] : product2(X, X, X)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.46 tff(9,plain,
% 0.20/0.46 ((~![X: $i] : product2(X, X, X)) | product2(e_3, e_3, e_3)),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(10,plain,
% 0.20/0.46 (product2(e_3, e_3, e_3)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[9, 8])).
% 0.20/0.46 tff(11,plain,
% 0.20/0.46 (^[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))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(12,plain,
% 0.20/0.46 (![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)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[11])).
% 0.20/0.46 tff(13,plain,
% 0.20/0.46 (![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)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(14,plain,
% 0.20/0.46 (^[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)))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(15,plain,
% 0.20/0.46 (![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)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[14])).
% 0.20/0.46 tff(16,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')).
% 0.20/0.46 tff(17,plain,
% 0.20/0.46 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.20/0.46 tff(18,plain,
% 0.20/0.46 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.20/0.46 tff(19,plain,(
% 0.20/0.46 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))),
% 0.20/0.46 inference(skolemize,[status(sab)],[18])).
% 0.20/0.46 tff(20,plain,
% 0.20/0.46 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.20/0.46 tff(21,plain,
% 0.20/0.46 ((~equalish(e_4, e_3)) <=> (~equalish(e_4, e_3))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(22,axiom,(~equalish(e_4, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_3')).
% 0.20/0.46 tff(23,plain,
% 0.20/0.46 (~equalish(e_4, e_3)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.20/0.46 tff(24,plain,
% 0.20/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))) | (equalish(e_4, e_3) | (~product2(e_3, e_3, e_3)) | (~product2(e_3, e_3, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))) | equalish(e_4, e_3) | (~product2(e_3, e_3, e_3)) | (~product2(e_3, e_3, e_4)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(25,plain,
% 0.20/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))) | (equalish(e_4, e_3) | (~product2(e_3, e_3, e_3)) | (~product2(e_3, e_3, e_4)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(26,plain,
% 0.20/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))) | equalish(e_4, e_3) | (~product2(e_3, e_3, e_3)) | (~product2(e_3, e_3, e_4))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.20/0.46 tff(27,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[26, 23, 20, 10, 1])).
% 0.20/0.46 tff(28,plain,(~product2(e_3, e_3, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(29,assumption,(product1(e_2, e_3, e_1)), introduced(assumption)).
% 0.20/0.46 tff(30,assumption,(product1(e_4, e_3, e_1)), introduced(assumption)).
% 0.20/0.46 tff(31,plain,
% 0.20/0.46 (^[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))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(32,plain,
% 0.20/0.46 (![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)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[31])).
% 0.20/0.46 tff(33,plain,
% 0.20/0.46 (![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)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(34,plain,
% 0.20/0.46 (^[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)))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(35,plain,
% 0.20/0.46 (![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)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[34])).
% 0.20/0.46 tff(36,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')).
% 0.20/0.46 tff(37,plain,
% 0.20/0.46 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.20/0.46 tff(38,plain,
% 0.20/0.46 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.20/0.46 tff(39,plain,(
% 0.20/0.46 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))),
% 0.20/0.46 inference(skolemize,[status(sab)],[38])).
% 0.20/0.46 tff(40,plain,
% 0.20/0.46 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[39, 32])).
% 0.20/0.46 tff(41,plain,
% 0.20/0.46 ((~equalish(e_2, e_4)) <=> (~equalish(e_2, e_4))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(42,axiom,(~equalish(e_2, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_4')).
% 0.20/0.46 tff(43,plain,
% 0.20/0.46 (~equalish(e_2, e_4)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.20/0.46 tff(44,plain,
% 0.20/0.46 (((~![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)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(45,plain,
% 0.20/0.46 ((~![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)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(46,plain,
% 0.20/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_2, e_4) | (~product1(e_4, e_3, e_1)) | (~product1(e_2, e_3, e_1))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.20/0.46 tff(47,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[46, 43, 40, 29, 30])).
% 0.20/0.46 tff(48,plain,((~product1(e_2, e_3, e_1)) | (~product1(e_4, e_3, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(49,plain,
% 0.20/0.46 (~product1(e_4, e_3, e_1)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[48, 29])).
% 0.20/0.46 tff(50,assumption,(product1(e_4, e_3, e_3)), introduced(assumption)).
% 0.20/0.46 tff(51,plain,
% 0.20/0.46 (^[X: $i] : refl(product1(X, X, X) <=> product1(X, X, X))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(52,plain,
% 0.20/0.46 (![X: $i] : product1(X, X, X) <=> ![X: $i] : product1(X, X, X)),
% 0.20/0.46 inference(quant_intro,[status(thm)],[51])).
% 0.20/0.46 tff(53,plain,
% 0.20/0.46 (![X: $i] : product1(X, X, X) <=> ![X: $i] : product1(X, X, X)),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(54,axiom,(![X: $i] : product1(X, X, X)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product1_idempotence')).
% 0.20/0.46 tff(55,plain,
% 0.20/0.46 (![X: $i] : product1(X, X, X)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.20/0.46 tff(56,plain,(
% 0.20/0.46 ![X: $i] : product1(X, X, X)),
% 0.20/0.46 inference(skolemize,[status(sab)],[55])).
% 0.20/0.46 tff(57,plain,
% 0.20/0.46 (![X: $i] : product1(X, X, X)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.20/0.46 tff(58,plain,
% 0.20/0.46 ((~![X: $i] : product1(X, X, X)) | product1(e_3, e_3, e_3)),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(59,plain,
% 0.20/0.46 (product1(e_3, e_3, e_3)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.20/0.46 tff(60,plain,
% 0.20/0.46 (((~![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)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(61,plain,
% 0.20/0.46 ((~![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)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(62,plain,
% 0.20/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_4, e_3) | (~product1(e_3, e_3, e_3)) | (~product1(e_4, e_3, e_3))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.20/0.46 tff(63,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[62, 23, 40, 59, 50])).
% 0.20/0.46 tff(64,plain,(~product1(e_4, e_3, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(65,plain,
% 0.20/0.46 ((~![X: $i] : product1(X, X, X)) | product1(e_4, e_4, e_4)),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(66,plain,
% 0.20/0.46 (product1(e_4, e_4, e_4)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[65, 57])).
% 0.20/0.46 tff(67,assumption,(product1(e_4, e_3, e_4)), introduced(assumption)).
% 0.20/0.46 tff(68,plain,
% 0.20/0.46 (^[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))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(69,plain,
% 0.20/0.46 (![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)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[68])).
% 0.20/0.46 tff(70,plain,
% 0.20/0.46 (![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)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(71,plain,
% 0.20/0.46 (^[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)))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(72,plain,
% 0.20/0.46 (![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)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[71])).
% 0.20/0.46 tff(73,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')).
% 0.20/0.46 tff(74,plain,
% 0.20/0.46 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.20/0.46 tff(75,plain,
% 0.20/0.46 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[74, 70])).
% 0.20/0.46 tff(76,plain,(
% 0.20/0.46 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))),
% 0.20/0.46 inference(skolemize,[status(sab)],[75])).
% 0.20/0.46 tff(77,plain,
% 0.20/0.46 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[76, 69])).
% 0.20/0.46 tff(78,plain,
% 0.20/0.46 ((~equalish(e_3, e_4)) <=> (~equalish(e_3, e_4))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(79,axiom,(~equalish(e_3, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_4')).
% 0.20/0.46 tff(80,plain,
% 0.20/0.46 (~equalish(e_3, e_4)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.20/0.46 tff(81,plain,
% 0.20/0.46 (((~![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)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(82,plain,
% 0.20/0.46 ((~![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)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(83,plain,
% 0.20/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_3, e_4) | (~product1(e_4, e_4, e_4)) | (~product1(e_4, e_3, e_4))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.20/0.46 tff(84,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[83, 80, 77, 67, 66])).
% 0.20/0.46 tff(85,plain,(~product1(e_4, e_3, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(86,plain,
% 0.20/0.46 (^[Y: $i, X: $i] : refl((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) | (~group_element(Y)) | (~group_element(X))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(87,plain,
% 0.20/0.46 (![Y: $i, X: $i] : (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))) <=> ![Y: $i, X: $i] : (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)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[86])).
% 0.20/0.46 tff(88,plain,
% 0.20/0.46 (![Y: $i, X: $i] : (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))) <=> ![Y: $i, X: $i] : (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)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(89,plain,
% 0.20/0.46 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~group_element(X)) | (~group_element(Y))) | product1(X, Y, e_1)) <=> (product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))), (((((~group_element(X)) | (~group_element(Y))) | product1(X, Y, e_1)) | product1(X, Y, e_2)) <=> ((product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product1(X, Y, e_2)))), rewrite(((product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product1(X, Y, e_2)) <=> (product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))), (((((~group_element(X)) | (~group_element(Y))) | product1(X, Y, e_1)) | product1(X, Y, e_2)) <=> (product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))))), ((((((~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_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product1(X, Y, e_3)))), rewrite(((product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product1(X, Y, e_3)) <=> (product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))), ((((((~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_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))))), (((((((~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)) <=> ((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)))), rewrite(((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_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))), (((((((~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)) <=> (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)))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(90,plain,
% 0.20/0.46 (![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] : (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)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[89])).
% 0.20/0.46 tff(91,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')).
% 0.20/0.46 tff(92,plain,
% 0.20/0.46 (![Y: $i, X: $i] : (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)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.20/0.46 tff(93,plain,
% 0.20/0.46 (![Y: $i, X: $i] : (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)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[92, 88])).
% 0.20/0.47 tff(94,plain,(
% 0.20/0.47 ![Y: $i, X: $i] : (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)))),
% 0.20/0.47 inference(skolemize,[status(sab)],[93])).
% 0.20/0.47 tff(95,plain,
% 0.20/0.47 (![Y: $i, X: $i] : (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)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[94, 87])).
% 0.20/0.47 tff(96,plain,
% 0.20/0.47 (group_element(e_4) <=> group_element(e_4)),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(97,axiom,(group_element(e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_4')).
% 0.20/0.47 tff(98,plain,
% 0.20/0.47 (group_element(e_4)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.20/0.47 tff(99,plain,
% 0.20/0.47 (group_element(e_3) <=> group_element(e_3)),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(100,axiom,(group_element(e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_3')).
% 0.20/0.47 tff(101,plain,
% 0.20/0.47 (group_element(e_3)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.20/0.47 tff(102,plain,
% 0.20/0.47 (((~![Y: $i, X: $i] : (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(e_4, e_3, e_1) | (~group_element(e_4)) | (~group_element(e_3)) | product1(e_4, e_3, e_2) | product1(e_4, e_3, e_3) | product1(e_4, e_3, e_4))) <=> ((~![Y: $i, X: $i] : (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(e_4, e_3, e_1) | (~group_element(e_4)) | (~group_element(e_3)) | product1(e_4, e_3, e_2) | product1(e_4, e_3, e_3) | product1(e_4, e_3, e_4))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(103,plain,
% 0.20/0.47 ((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_1) | (~group_element(e_4)) | (~group_element(e_3)) | product1(e_4, e_3, e_2) | product1(e_4, e_3, e_3) | product1(e_4, e_3, e_4))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(104,plain,
% 0.20/0.47 (((~![Y: $i, X: $i] : (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(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)))) <=> ((~![Y: $i, X: $i] : (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(e_4, e_3, e_1) | (~group_element(e_4)) | (~group_element(e_3)) | product1(e_4, e_3, e_2) | product1(e_4, e_3, e_3) | product1(e_4, e_3, e_4)))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[103])).
% 0.20/0.47 tff(105,plain,
% 0.20/0.47 (((~![Y: $i, X: $i] : (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(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)))) <=> ((~![Y: $i, X: $i] : (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(e_4, e_3, e_1) | (~group_element(e_4)) | (~group_element(e_3)) | product1(e_4, e_3, e_2) | product1(e_4, e_3, e_3) | product1(e_4, e_3, e_4))),
% 0.20/0.47 inference(transitivity,[status(thm)],[104, 102])).
% 0.20/0.47 tff(106,plain,
% 0.20/0.47 ((~![Y: $i, X: $i] : (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(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)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(107,plain,
% 0.20/0.47 ((~![Y: $i, X: $i] : (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(e_4, e_3, e_1) | (~group_element(e_4)) | (~group_element(e_3)) | product1(e_4, e_3, e_2) | product1(e_4, e_3, e_3) | product1(e_4, e_3, e_4)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.20/0.47 tff(108,plain,
% 0.20/0.47 (product1(e_4, e_3, e_1) | product1(e_4, e_3, e_2) | product1(e_4, e_3, e_3) | product1(e_4, e_3, e_4)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[107, 101, 98, 95])).
% 0.20/0.47 tff(109,plain,
% 0.20/0.47 (product1(e_4, e_3, e_1) | product1(e_4, e_3, e_2) | product1(e_4, e_3, e_3)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[108, 85])).
% 0.20/0.47 tff(110,plain,
% 0.20/0.47 (product1(e_4, e_3, e_1) | product1(e_4, e_3, e_2)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[109, 64])).
% 0.20/0.47 tff(111,plain,
% 0.20/0.47 (product1(e_4, e_3, e_2)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[110, 49])).
% 0.20/0.47 tff(112,plain,
% 0.20/0.47 ((~![X: $i] : product1(X, X, X)) | product1(e_2, e_2, e_2)),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(113,plain,
% 0.20/0.47 (product1(e_2, e_2, e_2)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[112, 57])).
% 0.20/0.47 tff(114,assumption,(product1(e_2, e_4, e_2)), introduced(assumption)).
% 0.20/0.47 tff(115,assumption,(product1(e_2, e_2, e_2)), introduced(assumption)).
% 0.20/0.47 tff(116,plain,
% 0.20/0.47 ((~equalish(e_4, e_2)) <=> (~equalish(e_4, e_2))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(117,axiom,(~equalish(e_4, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_2')).
% 0.20/0.47 tff(118,plain,
% 0.20/0.47 (~equalish(e_4, e_2)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.20/0.47 tff(119,plain,
% 0.20/0.47 (((~![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)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(120,plain,
% 0.20/0.47 ((~![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)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(121,plain,
% 0.20/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_4, e_2) | (~product1(e_2, e_2, e_2)) | (~product1(e_2, e_4, e_2))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.20/0.47 tff(122,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[121, 118, 77, 115, 114])).
% 0.20/0.47 tff(123,plain,((~product1(e_2, e_4, e_2)) | (~product1(e_2, e_2, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(124,plain,
% 0.20/0.47 (~product1(e_2, e_4, e_2)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[123, 113])).
% 0.20/0.47 tff(125,assumption,(product1(e_2, e_4, e_1)), introduced(assumption)).
% 0.20/0.47 tff(126,plain,
% 0.20/0.47 (((~![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_2, e_3, e_1)) | (~product1(e_2, 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_3) | (~product1(e_2, e_3, e_1)) | (~product1(e_2, e_4, e_1)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(127,plain,
% 0.20/0.47 ((~![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_2, e_3, e_1)) | (~product1(e_2, e_4, e_1)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(128,plain,
% 0.20/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_4, e_3) | (~product1(e_2, e_3, e_1)) | (~product1(e_2, e_4, e_1))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.20/0.47 tff(129,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[128, 23, 77, 29, 125])).
% 0.20/0.47 tff(130,plain,((~product1(e_2, e_4, e_1)) | (~product1(e_2, e_3, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(131,plain,
% 0.20/0.47 (~product1(e_2, e_4, e_1)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[130, 29])).
% 0.20/0.47 tff(132,assumption,(product1(e_2, e_4, e_4)), introduced(assumption)).
% 0.20/0.47 tff(133,plain,
% 0.20/0.47 (((~![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)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(134,plain,
% 0.20/0.47 ((~![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)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(135,plain,
% 0.20/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_2, e_4) | (~product1(e_4, e_4, e_4)) | (~product1(e_2, e_4, e_4))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.20/0.47 tff(136,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[135, 43, 40, 66, 132])).
% 0.20/0.47 tff(137,plain,(~product1(e_2, e_4, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(138,plain,
% 0.20/0.47 (group_element(e_2) <=> group_element(e_2)),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(139,axiom,(group_element(e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_2')).
% 0.20/0.47 tff(140,plain,
% 0.20/0.47 (group_element(e_2)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.20/0.47 tff(141,plain,
% 0.20/0.47 (((~![Y: $i, X: $i] : (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)))) | ((~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] : (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)))) | (~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))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(142,plain,
% 0.20/0.47 ((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))) <=> ((~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))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(143,plain,
% 0.20/0.47 (((~![Y: $i, X: $i] : (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(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)))) <=> ((~![Y: $i, X: $i] : (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)))) | ((~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)))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[142])).
% 0.20/0.47 tff(144,plain,
% 0.20/0.47 (((~![Y: $i, X: $i] : (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(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)))) <=> ((~![Y: $i, X: $i] : (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)))) | (~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))),
% 0.20/0.47 inference(transitivity,[status(thm)],[143, 141])).
% 0.20/0.47 tff(145,plain,
% 0.20/0.47 ((~![Y: $i, X: $i] : (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(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)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(146,plain,
% 0.20/0.47 ((~![Y: $i, X: $i] : (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)))) | (~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)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.20/0.47 tff(147,plain,
% 0.20/0.47 (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)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[146, 140, 98, 95])).
% 0.20/0.47 tff(148,plain,
% 0.20/0.47 (product1(e_2, e_4, e_1) | product1(e_2, e_4, e_2) | product1(e_2, e_4, e_3)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[147, 137])).
% 0.20/0.47 tff(149,plain,
% 0.20/0.47 (product1(e_2, e_4, e_3)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[148, 131, 124])).
% 0.20/0.47 tff(150,plain,
% 0.20/0.47 (^[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))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(151,plain,
% 0.20/0.47 (![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)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[150])).
% 0.20/0.47 tff(152,plain,
% 0.20/0.47 (![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)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(153,plain,
% 0.20/0.47 (^[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))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(154,plain,
% 0.20/0.47 (![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)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[153])).
% 0.20/0.47 tff(155,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')).
% 0.20/0.47 tff(156,plain,
% 0.20/0.47 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.20/0.47 tff(157,plain,
% 0.20/0.47 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[156, 152])).
% 0.20/0.47 tff(158,plain,(
% 0.20/0.47 ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))),
% 0.20/0.47 inference(skolemize,[status(sab)],[157])).
% 0.20/0.47 tff(159,plain,
% 0.20/0.47 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[158, 151])).
% 0.20/0.47 tff(160,plain,
% 0.20/0.47 (((~![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_2)) | (~product1(e_2, 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_2)) | (~product1(e_2, e_4, e_3)) | product2(e_3, e_3, e_4))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(161,plain,
% 0.20/0.47 (((~product1(e_2, e_4, e_3)) | product2(e_3, e_3, e_4) | (~product1(e_4, e_3, e_2))) <=> ((~product1(e_4, e_3, e_2)) | (~product1(e_2, e_4, e_3)) | product2(e_3, e_3, e_4))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(162,plain,
% 0.20/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_2, e_4, e_3)) | product2(e_3, e_3, e_4) | (~product1(e_4, e_3, e_2)))) <=> ((~![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_2)) | (~product1(e_2, e_4, e_3)) | product2(e_3, e_3, e_4)))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[161])).
% 0.20/0.47 tff(163,plain,
% 0.20/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_2, e_4, e_3)) | product2(e_3, e_3, e_4) | (~product1(e_4, e_3, e_2)))) <=> ((~![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_2)) | (~product1(e_2, e_4, e_3)) | product2(e_3, e_3, e_4))),
% 0.20/0.47 inference(transitivity,[status(thm)],[162, 160])).
% 0.20/0.47 tff(164,plain,
% 0.20/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_2, e_4, e_3)) | product2(e_3, e_3, e_4) | (~product1(e_4, e_3, e_2)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(165,plain,
% 0.20/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | (~product1(e_4, e_3, e_2)) | (~product1(e_2, e_4, e_3)) | product2(e_3, e_3, e_4)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[164, 163])).
% 0.20/0.47 tff(166,plain,
% 0.20/0.47 ((~product1(e_4, e_3, e_2)) | (~product1(e_2, e_4, e_3)) | product2(e_3, e_3, e_4)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[165, 159])).
% 0.20/0.47 tff(167,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[166, 149, 111, 28])).
% 0.20/0.47 tff(168,plain,(~product1(e_2, e_3, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(169,assumption,(product1(e_2, e_3, e_2)), introduced(assumption)).
% 0.20/0.47 tff(170,plain,
% 0.20/0.47 ((~equalish(e_3, e_2)) <=> (~equalish(e_3, e_2))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(171,axiom,(~equalish(e_3, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_2')).
% 0.20/0.47 tff(172,plain,
% 0.20/0.47 (~equalish(e_3, e_2)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.20/0.47 tff(173,plain,
% 0.20/0.47 (((~![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_3, e_2)) | (~product1(e_2, e_2, 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_3, e_2)) | (~product1(e_2, e_2, e_2)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(174,plain,
% 0.20/0.47 ((equalish(e_3, e_2) | (~product1(e_2, e_2, e_2)) | (~product1(e_2, e_3, e_2))) <=> (equalish(e_3, e_2) | (~product1(e_2, e_3, e_2)) | (~product1(e_2, e_2, e_2)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(175,plain,
% 0.20/0.47 (((~![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_3, e_2)) | (~product1(e_2, e_2, e_2))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[174])).
% 0.20/0.47 tff(176,plain,
% 0.20/0.47 (((~![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_3, e_2)) | (~product1(e_2, e_2, e_2)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[175, 173])).
% 0.20/0.47 tff(177,plain,
% 0.20/0.47 ((~![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)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(178,plain,
% 0.20/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_3, e_2) | (~product1(e_2, e_3, e_2)) | (~product1(e_2, e_2, e_2))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[177, 176])).
% 0.20/0.47 tff(179,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[178, 172, 77, 169, 113])).
% 0.20/0.47 tff(180,plain,(~product1(e_2, e_3, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(181,assumption,(product1(e_2, e_3, e_3)), introduced(assumption)).
% 0.20/0.47 tff(182,plain,
% 0.20/0.47 ((~equalish(e_2, e_3)) <=> (~equalish(e_2, e_3))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(183,axiom,(~equalish(e_2, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_3')).
% 0.20/0.47 tff(184,plain,
% 0.20/0.47 (~equalish(e_2, e_3)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[183, 182])).
% 0.20/0.47 tff(185,plain,
% 0.20/0.47 (((~![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)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(186,plain,
% 0.20/0.47 ((~![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)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(187,plain,
% 0.20/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_2, e_3) | (~product1(e_3, e_3, e_3)) | (~product1(e_2, e_3, e_3))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.20/0.47 tff(188,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[187, 184, 40, 181, 59])).
% 0.20/0.47 tff(189,plain,(~product1(e_2, e_3, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(190,plain,
% 0.20/0.47 (((~![Y: $i, X: $i] : (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(e_2, e_3, e_4) | (~group_element(e_2)) | 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)))) <=> ((~![Y: $i, X: $i] : (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(e_2, e_3, e_4) | (~group_element(e_2)) | 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)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(191,plain,
% 0.20/0.47 ((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_4) | (~group_element(e_2)) | 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)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(192,plain,
% 0.20/0.47 (((~![Y: $i, X: $i] : (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(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)))) <=> ((~![Y: $i, X: $i] : (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(e_2, e_3, e_4) | (~group_element(e_2)) | 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))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[191])).
% 0.20/0.47 tff(193,plain,
% 0.20/0.47 (((~![Y: $i, X: $i] : (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(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)))) <=> ((~![Y: $i, X: $i] : (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(e_2, e_3, e_4) | (~group_element(e_2)) | 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)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[192, 190])).
% 0.20/0.47 tff(194,plain,
% 0.20/0.47 ((~![Y: $i, X: $i] : (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(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)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(195,plain,
% 0.20/0.47 ((~![Y: $i, X: $i] : (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(e_2, e_3, e_4) | (~group_element(e_2)) | 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))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[194, 193])).
% 0.20/0.47 tff(196,plain,
% 0.20/0.47 (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)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[195, 140, 101, 95])).
% 0.20/0.47 tff(197,plain,
% 0.20/0.47 (product1(e_2, e_3, e_4) | product1(e_2, e_3, e_2) | product1(e_2, e_3, e_1)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[196, 189])).
% 0.20/0.47 tff(198,plain,
% 0.20/0.47 (product1(e_2, e_3, e_4)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[197, 180, 168])).
% 0.20/0.47 tff(199,assumption,(product1(e_1, e_3, e_4)), introduced(assumption)).
% 0.20/0.47 tff(200,assumption,(product1(e_2, e_3, e_4)), introduced(assumption)).
% 0.20/0.47 tff(201,plain,
% 0.20/0.47 ((~equalish(e_2, e_1)) <=> (~equalish(e_2, e_1))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(202,axiom,(~equalish(e_2, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_1')).
% 0.20/0.47 tff(203,plain,
% 0.20/0.47 (~equalish(e_2, e_1)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[202, 201])).
% 0.20/0.47 tff(204,plain,
% 0.20/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_2, e_1) | (~product1(e_1, e_3, e_4)) | (~product1(e_2, e_3, 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_1) | (~product1(e_1, e_3, e_4)) | (~product1(e_2, e_3, e_4)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(205,plain,
% 0.20/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_2, e_1) | (~product1(e_1, e_3, e_4)) | (~product1(e_2, e_3, e_4)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(206,plain,
% 0.20/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_2, e_1) | (~product1(e_1, e_3, e_4)) | (~product1(e_2, e_3, e_4))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[205, 204])).
% 0.20/0.48 tff(207,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[206, 203, 40, 200, 199])).
% 0.20/0.48 tff(208,plain,((~product1(e_2, e_3, e_4)) | (~product1(e_1, e_3, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(209,plain,
% 0.20/0.48 (~product1(e_1, e_3, e_4)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[208, 198])).
% 0.20/0.48 tff(210,assumption,(product1(e_1, e_3, e_3)), introduced(assumption)).
% 0.20/0.48 tff(211,plain,
% 0.20/0.48 ((~equalish(e_1, e_3)) <=> (~equalish(e_1, e_3))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(212,axiom,(~equalish(e_1, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_3')).
% 0.20/0.48 tff(213,plain,
% 0.20/0.48 (~equalish(e_1, e_3)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[212, 211])).
% 0.20/0.48 tff(214,plain,
% 0.20/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_1, e_3) | (~product1(e_3, e_3, e_3)) | (~product1(e_1, 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_1, e_3) | (~product1(e_3, e_3, e_3)) | (~product1(e_1, e_3, e_3)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(215,plain,
% 0.20/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_1, e_3) | (~product1(e_3, e_3, e_3)) | (~product1(e_1, e_3, e_3)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(216,plain,
% 0.20/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_1, e_3) | (~product1(e_3, e_3, e_3)) | (~product1(e_1, e_3, e_3))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[215, 214])).
% 0.20/0.48 tff(217,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[216, 213, 40, 59, 210])).
% 0.20/0.48 tff(218,plain,(~product1(e_1, e_3, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(219,plain,
% 0.20/0.48 ((~![X: $i] : product1(X, X, X)) | product1(e_1, e_1, e_1)),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(220,plain,
% 0.20/0.48 (product1(e_1, e_1, e_1)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[219, 57])).
% 0.20/0.48 tff(221,plain,
% 0.20/0.48 ((~![X: $i] : product2(X, X, X)) | product2(e_1, e_1, e_1)),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(222,plain,
% 0.20/0.48 (product2(e_1, e_1, e_1)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[221, 8])).
% 0.20/0.48 tff(223,assumption,(product2(e_1, e_3, e_1)), introduced(assumption)).
% 0.20/0.48 tff(224,plain,
% 0.20/0.48 (^[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))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(225,plain,
% 0.20/0.48 (![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)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[224])).
% 0.20/0.48 tff(226,plain,
% 0.20/0.48 (![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)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(227,plain,
% 0.20/0.48 (^[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)))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(228,plain,
% 0.20/0.48 (![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)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[227])).
% 0.20/0.48 tff(229,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')).
% 0.20/0.48 tff(230,plain,
% 0.20/0.48 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[229, 228])).
% 0.20/0.48 tff(231,plain,
% 0.20/0.48 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[230, 226])).
% 0.20/0.48 tff(232,plain,(
% 0.20/0.48 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))),
% 0.20/0.48 inference(skolemize,[status(sab)],[231])).
% 0.20/0.48 tff(233,plain,
% 0.20/0.48 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[232, 225])).
% 0.20/0.48 tff(234,plain,
% 0.20/0.48 ((~equalish(e_3, e_1)) <=> (~equalish(e_3, e_1))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(235,axiom,(~equalish(e_3, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_1')).
% 0.20/0.48 tff(236,plain,
% 0.20/0.48 (~equalish(e_3, e_1)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[235, 234])).
% 0.20/0.48 tff(237,plain,
% 0.20/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | (equalish(e_3, e_1) | (~product2(e_1, e_1, e_1)) | (~product2(e_1, e_3, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | equalish(e_3, e_1) | (~product2(e_1, e_1, e_1)) | (~product2(e_1, e_3, e_1)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(238,plain,
% 0.20/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | (equalish(e_3, e_1) | (~product2(e_1, e_1, e_1)) | (~product2(e_1, e_3, e_1)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(239,plain,
% 0.20/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | equalish(e_3, e_1) | (~product2(e_1, e_1, e_1)) | (~product2(e_1, e_3, e_1))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[238, 237])).
% 0.20/0.48 tff(240,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[239, 236, 233, 223, 222])).
% 0.20/0.48 tff(241,plain,(~product2(e_1, e_3, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(242,plain,
% 0.20/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | (product2(e_1, e_3, e_1) | (~product1(e_1, e_1, e_1)) | (~product1(e_1, e_3, 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_3, e_1) | (~product1(e_1, e_1, e_1)) | (~product1(e_1, e_3, e_1)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(243,plain,
% 0.20/0.48 (((~product1(e_1, e_1, e_1)) | product2(e_1, e_3, e_1) | (~product1(e_1, e_3, e_1))) <=> (product2(e_1, e_3, e_1) | (~product1(e_1, e_1, e_1)) | (~product1(e_1, e_3, e_1)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(244,plain,
% 0.20/0.48 (((~![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_3, e_1) | (~product1(e_1, e_3, 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_3, e_1) | (~product1(e_1, e_1, e_1)) | (~product1(e_1, e_3, e_1))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[243])).
% 0.20/0.48 tff(245,plain,
% 0.20/0.48 (((~![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_3, e_1) | (~product1(e_1, e_3, 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_3, e_1) | (~product1(e_1, e_1, e_1)) | (~product1(e_1, e_3, e_1)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[244, 242])).
% 0.20/0.48 tff(246,plain,
% 0.20/0.48 ((~![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_3, e_1) | (~product1(e_1, e_3, e_1)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(247,plain,
% 0.20/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | product2(e_1, e_3, e_1) | (~product1(e_1, e_1, e_1)) | (~product1(e_1, e_3, e_1))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[246, 245])).
% 0.20/0.48 tff(248,plain,
% 0.20/0.48 (~product1(e_1, e_3, e_1)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[247, 159, 241, 220])).
% 0.20/0.48 tff(249,plain,
% 0.20/0.48 (group_element(e_1) <=> group_element(e_1)),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(250,axiom,(group_element(e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_1')).
% 0.20/0.48 tff(251,plain,
% 0.20/0.48 (group_element(e_1)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[250, 249])).
% 0.20/0.48 tff(252,plain,
% 0.20/0.48 (((~![Y: $i, X: $i] : (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)))) | ((~group_element(e_3)) | (~group_element(e_1)) | product1(e_1, e_3, e_1) | product1(e_1, e_3, e_4) | product1(e_1, e_3, e_3) | product1(e_1, e_3, e_2))) <=> ((~![Y: $i, X: $i] : (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)))) | (~group_element(e_3)) | (~group_element(e_1)) | product1(e_1, e_3, e_1) | product1(e_1, e_3, e_4) | product1(e_1, e_3, e_3) | product1(e_1, e_3, e_2))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(253,plain,
% 0.20/0.48 ((product1(e_1, e_3, e_4) | product1(e_1, e_3, e_3) | product1(e_1, e_3, e_2) | product1(e_1, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_1))) <=> ((~group_element(e_3)) | (~group_element(e_1)) | product1(e_1, e_3, e_1) | product1(e_1, e_3, e_4) | product1(e_1, e_3, e_3) | product1(e_1, e_3, e_2))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(254,plain,
% 0.20/0.48 (((~![Y: $i, X: $i] : (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(e_1, e_3, e_4) | product1(e_1, e_3, e_3) | product1(e_1, e_3, e_2) | product1(e_1, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (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)))) | ((~group_element(e_3)) | (~group_element(e_1)) | product1(e_1, e_3, e_1) | product1(e_1, e_3, e_4) | product1(e_1, e_3, e_3) | product1(e_1, e_3, e_2)))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[253])).
% 0.20/0.48 tff(255,plain,
% 0.20/0.48 (((~![Y: $i, X: $i] : (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(e_1, e_3, e_4) | product1(e_1, e_3, e_3) | product1(e_1, e_3, e_2) | product1(e_1, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (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)))) | (~group_element(e_3)) | (~group_element(e_1)) | product1(e_1, e_3, e_1) | product1(e_1, e_3, e_4) | product1(e_1, e_3, e_3) | product1(e_1, e_3, e_2))),
% 0.20/0.48 inference(transitivity,[status(thm)],[254, 252])).
% 0.20/0.48 tff(256,plain,
% 0.20/0.48 ((~![Y: $i, X: $i] : (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(e_1, e_3, e_4) | product1(e_1, e_3, e_3) | product1(e_1, e_3, e_2) | product1(e_1, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_1)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(257,plain,
% 0.20/0.48 ((~![Y: $i, X: $i] : (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)))) | (~group_element(e_3)) | (~group_element(e_1)) | product1(e_1, e_3, e_1) | product1(e_1, e_3, e_4) | product1(e_1, e_3, e_3) | product1(e_1, e_3, e_2)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[256, 255])).
% 0.20/0.48 tff(258,plain,
% 0.20/0.48 (product1(e_1, e_3, e_4) | product1(e_1, e_3, e_3) | product1(e_1, e_3, e_2)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[257, 251, 101, 95, 248])).
% 0.20/0.48 tff(259,plain,
% 0.20/0.48 (product1(e_1, e_3, e_4) | product1(e_1, e_3, e_2)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[258, 218])).
% 0.20/0.48 tff(260,plain,
% 0.20/0.48 (product1(e_1, e_3, e_2)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[259, 209])).
% 0.20/0.48 tff(261,assumption,(product1(e_1, e_3, e_2)), introduced(assumption)).
% 0.20/0.48 tff(262,assumption,(product1(e_4, e_3, e_2)), introduced(assumption)).
% 0.20/0.48 tff(263,plain,
% 0.20/0.48 ((~equalish(e_4, e_1)) <=> (~equalish(e_4, e_1))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(264,axiom,(~equalish(e_4, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_1')).
% 0.20/0.48 tff(265,plain,
% 0.20/0.48 (~equalish(e_4, e_1)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[264, 263])).
% 0.20/0.48 tff(266,plain,
% 0.20/0.48 (((~![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_4, e_3, e_2)) | (~product1(e_1, e_3, e_2)))) <=> ((~![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_4, e_3, e_2)) | (~product1(e_1, e_3, e_2)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(267,plain,
% 0.20/0.48 ((equalish(e_4, e_1) | (~product1(e_1, e_3, e_2)) | (~product1(e_4, e_3, e_2))) <=> (equalish(e_4, e_1) | (~product1(e_4, e_3, e_2)) | (~product1(e_1, e_3, e_2)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(268,plain,
% 0.20/0.48 (((~![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_3, e_2)) | (~product1(e_4, e_3, e_2)))) <=> ((~![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_4, e_3, e_2)) | (~product1(e_1, e_3, e_2))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[267])).
% 0.20/0.48 tff(269,plain,
% 0.20/0.48 (((~![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_3, e_2)) | (~product1(e_4, e_3, e_2)))) <=> ((~![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_4, e_3, e_2)) | (~product1(e_1, e_3, e_2)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[268, 266])).
% 0.20/0.48 tff(270,plain,
% 0.20/0.48 ((~![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_3, e_2)) | (~product1(e_4, e_3, e_2)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(271,plain,
% 0.20/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_4, e_1) | (~product1(e_4, e_3, e_2)) | (~product1(e_1, e_3, e_2))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[270, 269])).
% 0.20/0.48 tff(272,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[271, 265, 40, 262, 261])).
% 0.20/0.48 tff(273,plain,((~product1(e_4, e_3, e_2)) | (~product1(e_1, e_3, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(274,plain,
% 0.20/0.48 (~product1(e_4, e_3, e_2)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[273, 260])).
% 0.20/0.48 tff(275,plain,
% 0.20/0.48 (product1(e_4, e_3, e_1)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[110, 274])).
% 0.20/0.48 tff(276,assumption,(product1(e_1, e_4, e_2)), introduced(assumption)).
% 0.20/0.48 tff(277,plain,
% 0.20/0.48 (((~![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_1, e_3, e_2)) | (~product1(e_1, 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_3) | (~product1(e_1, e_3, e_2)) | (~product1(e_1, e_4, e_2)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(278,plain,
% 0.20/0.48 ((~![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_1, e_3, e_2)) | (~product1(e_1, e_4, e_2)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(279,plain,
% 0.20/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_4, e_3) | (~product1(e_1, e_3, e_2)) | (~product1(e_1, e_4, e_2))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[278, 277])).
% 0.20/0.48 tff(280,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[279, 23, 77, 261, 276])).
% 0.20/0.48 tff(281,plain,((~product1(e_1, e_4, e_2)) | (~product1(e_1, e_3, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(282,plain,
% 0.20/0.48 (~product1(e_1, e_4, e_2)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[281, 260])).
% 0.20/0.48 tff(283,assumption,(product1(e_1, e_4, e_4)), introduced(assumption)).
% 0.20/0.48 tff(284,plain,
% 0.20/0.48 ((~equalish(e_1, e_4)) <=> (~equalish(e_1, e_4))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(285,axiom,(~equalish(e_1, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_4')).
% 0.20/0.48 tff(286,plain,
% 0.20/0.48 (~equalish(e_1, e_4)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[285, 284])).
% 0.20/0.48 tff(287,plain,
% 0.20/0.48 (((~![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)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(288,plain,
% 0.20/0.48 ((~![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)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(289,plain,
% 0.20/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_1, e_4) | (~product1(e_4, e_4, e_4)) | (~product1(e_1, e_4, e_4))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[288, 287])).
% 0.20/0.48 tff(290,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[289, 286, 40, 66, 283])).
% 0.20/0.48 tff(291,plain,(~product1(e_1, e_4, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(292,assumption,(product2(e_1, e_4, e_1)), introduced(assumption)).
% 0.20/0.48 tff(293,plain,
% 0.20/0.48 (((~![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)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(294,plain,
% 0.20/0.48 ((~![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)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(295,plain,
% 0.20/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | equalish(e_4, e_1) | (~product2(e_1, e_1, e_1)) | (~product2(e_1, e_4, e_1))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[294, 293])).
% 0.20/0.48 tff(296,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[295, 265, 233, 222, 292])).
% 0.20/0.48 tff(297,plain,(~product2(e_1, e_4, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(298,plain,
% 0.20/0.48 (((~![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)) | (~product1(e_1, e_4, e_1)) | product2(e_1, e_4, 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)) | (~product1(e_1, e_4, e_1)) | product2(e_1, e_4, e_1))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(299,plain,
% 0.20/0.48 (((~product1(e_1, e_1, e_1)) | product2(e_1, e_4, e_1) | (~product1(e_1, e_4, e_1))) <=> ((~product1(e_1, e_1, e_1)) | (~product1(e_1, e_4, e_1)) | product2(e_1, e_4, e_1))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(300,plain,
% 0.20/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_1, e_1, e_1)) | product2(e_1, e_4, e_1) | (~product1(e_1, e_4, 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)) | (~product1(e_1, e_4, e_1)) | product2(e_1, e_4, e_1)))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[299])).
% 0.20/0.48 tff(301,plain,
% 0.20/0.48 (((~![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_4, e_1) | (~product1(e_1, e_4, 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)) | (~product1(e_1, e_4, e_1)) | product2(e_1, e_4, e_1))),
% 0.20/0.48 inference(transitivity,[status(thm)],[300, 298])).
% 0.20/0.48 tff(302,plain,
% 0.20/0.48 ((~![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_4, e_1) | (~product1(e_1, e_4, e_1)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(303,plain,
% 0.20/0.48 ((~![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)) | (~product1(e_1, e_4, e_1)) | product2(e_1, e_4, e_1)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[302, 301])).
% 0.20/0.48 tff(304,plain,
% 0.20/0.48 (~product1(e_1, e_4, e_1)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[303, 159, 220, 297])).
% 0.20/0.48 tff(305,plain,
% 0.20/0.48 (((~![Y: $i, X: $i] : (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)))) | ((~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] : (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)))) | (~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))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(306,plain,
% 0.20/0.48 ((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))) <=> ((~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))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(307,plain,
% 0.20/0.48 (((~![Y: $i, X: $i] : (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(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)))) <=> ((~![Y: $i, X: $i] : (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)))) | ((~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)))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[306])).
% 0.20/0.48 tff(308,plain,
% 0.20/0.48 (((~![Y: $i, X: $i] : (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(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)))) <=> ((~![Y: $i, X: $i] : (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)))) | (~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))),
% 0.20/0.48 inference(transitivity,[status(thm)],[307, 305])).
% 0.20/0.48 tff(309,plain,
% 0.20/0.48 ((~![Y: $i, X: $i] : (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(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)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(310,plain,
% 0.20/0.48 ((~![Y: $i, X: $i] : (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)))) | (~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)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[309, 308])).
% 0.20/0.48 tff(311,plain,
% 0.20/0.48 (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)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[310, 251, 98, 95])).
% 0.20/0.48 tff(312,plain,
% 0.20/0.48 (product1(e_1, e_4, e_4) | product1(e_1, e_4, e_3) | product1(e_1, e_4, e_2)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[311, 304])).
% 0.20/0.48 tff(313,plain,
% 0.20/0.48 (product1(e_1, e_4, e_3) | product1(e_1, e_4, e_2)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[312, 291])).
% 0.20/0.48 tff(314,plain,
% 0.20/0.48 (product1(e_1, e_4, e_3)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[313, 282])).
% 0.20/0.48 tff(315,assumption,(product1(e_1, e_4, e_3)), introduced(assumption)).
% 0.20/0.48 tff(316,plain,
% 0.20/0.48 (((~![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))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(317,plain,
% 0.20/0.49 (((~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))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(318,plain,
% 0.20/0.49 (((~![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)))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[317])).
% 0.20/0.49 tff(319,plain,
% 0.20/0.49 (((~![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))),
% 0.20/0.49 inference(transitivity,[status(thm)],[318, 316])).
% 0.20/0.49 tff(320,plain,
% 0.20/0.49 ((~![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)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(321,plain,
% 0.20/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | (~product1(e_4, e_3, e_1)) | (~product1(e_1, e_4, e_3)) | product2(e_3, e_3, e_4)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[320, 319])).
% 0.20/0.49 tff(322,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[321, 159, 30, 315, 28])).
% 0.20/0.49 tff(323,plain,((~product1(e_1, e_4, e_3)) | (~product1(e_4, e_3, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(324,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[323, 314, 275])).
% 0.20/0.49 % SZS output end Proof
%------------------------------------------------------------------------------