TSTP Solution File: GRP124-6.004 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP124-6.004 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 16 22:26:00 EDT 2022
% Result : Unsatisfiable 0.14s 0.43s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : GRP124-6.004 : TPTP v8.1.0. Released v1.2.0.
% 0.09/0.10 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.09/0.29 % Computer : n006.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Wed Aug 31 14:53:39 EDT 2022
% 0.09/0.30 % CPUTime :
% 0.09/0.30 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.09/0.30 Usage: tptp [options] [-file:]file
% 0.09/0.30 -h, -? prints this message.
% 0.09/0.30 -smt2 print SMT-LIB2 benchmark.
% 0.09/0.30 -m, -model generate model.
% 0.09/0.30 -p, -proof generate proof.
% 0.09/0.30 -c, -core generate unsat core of named formulas.
% 0.09/0.30 -st, -statistics display statistics.
% 0.09/0.30 -t:timeout set timeout (in second).
% 0.09/0.30 -smt2status display status in smt2 format instead of SZS.
% 0.09/0.30 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.09/0.30 -<param>:<value> configuration parameter and value.
% 0.09/0.30 -o:<output-file> file to place output in.
% 0.14/0.43 % SZS status Unsatisfiable
% 0.14/0.43 % SZS output start Proof
% 0.14/0.43 tff(product1_type, type, (
% 0.14/0.43 product1: ( $i * $i * $i ) > $o)).
% 0.14/0.43 tff(e_2_type, type, (
% 0.14/0.43 e_2: $i)).
% 0.14/0.43 tff(e_3_type, type, (
% 0.14/0.43 e_3: $i)).
% 0.14/0.43 tff(e_4_type, type, (
% 0.14/0.43 e_4: $i)).
% 0.14/0.43 tff(e_1_type, type, (
% 0.14/0.43 e_1: $i)).
% 0.14/0.43 tff(product2_type, type, (
% 0.14/0.43 product2: ( $i * $i * $i ) > $o)).
% 0.14/0.43 tff(equalish_type, type, (
% 0.14/0.43 equalish: ( $i * $i ) > $o)).
% 0.14/0.43 tff(group_element_type, type, (
% 0.14/0.43 group_element: $i > $o)).
% 0.14/0.43 tff(1,assumption,(product2(e_2, e_2, e_4)), introduced(assumption)).
% 0.14/0.43 tff(2,plain,
% 0.14/0.43 (^[X: $i] : refl(product2(X, X, X) <=> product2(X, X, X))),
% 0.14/0.43 inference(bind,[status(th)],[])).
% 0.14/0.43 tff(3,plain,
% 0.14/0.43 (![X: $i] : product2(X, X, X) <=> ![X: $i] : product2(X, X, X)),
% 0.14/0.43 inference(quant_intro,[status(thm)],[2])).
% 0.14/0.43 tff(4,plain,
% 0.14/0.43 (![X: $i] : product2(X, X, X) <=> ![X: $i] : product2(X, X, X)),
% 0.14/0.43 inference(rewrite,[status(thm)],[])).
% 0.14/0.43 tff(5,axiom,(![X: $i] : product2(X, X, X)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product2_idempotence')).
% 0.14/0.43 tff(6,plain,
% 0.14/0.43 (![X: $i] : product2(X, X, X)),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.14/0.43 tff(7,plain,(
% 0.14/0.43 ![X: $i] : product2(X, X, X)),
% 0.14/0.43 inference(skolemize,[status(sab)],[6])).
% 0.14/0.43 tff(8,plain,
% 0.14/0.43 (![X: $i] : product2(X, X, X)),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.14/0.43 tff(9,plain,
% 0.14/0.43 ((~![X: $i] : product2(X, X, X)) | product2(e_2, e_2, e_2)),
% 0.14/0.43 inference(quant_inst,[status(thm)],[])).
% 0.14/0.43 tff(10,plain,
% 0.14/0.43 (product2(e_2, e_2, e_2)),
% 0.14/0.43 inference(unit_resolution,[status(thm)],[9, 8])).
% 0.14/0.43 tff(11,plain,
% 0.14/0.43 (^[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))))),
% 0.14/0.43 inference(bind,[status(th)],[])).
% 0.14/0.43 tff(12,plain,
% 0.14/0.43 (![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)))),
% 0.14/0.43 inference(quant_intro,[status(thm)],[11])).
% 0.14/0.43 tff(13,plain,
% 0.14/0.43 (![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)))),
% 0.14/0.43 inference(rewrite,[status(thm)],[])).
% 0.14/0.43 tff(14,plain,
% 0.14/0.43 (^[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)))))),
% 0.14/0.43 inference(bind,[status(th)],[])).
% 0.14/0.43 tff(15,plain,
% 0.14/0.43 (![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)))),
% 0.14/0.43 inference(quant_intro,[status(thm)],[14])).
% 0.14/0.43 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')).
% 0.14/0.43 tff(17,plain,
% 0.14/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.14/0.43 tff(18,plain,
% 0.14/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.14/0.43 tff(19,plain,(
% 0.14/0.43 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))),
% 0.14/0.43 inference(skolemize,[status(sab)],[18])).
% 0.14/0.43 tff(20,plain,
% 0.14/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.14/0.43 tff(21,plain,
% 0.14/0.43 ((~equalish(e_4, e_2)) <=> (~equalish(e_4, e_2))),
% 0.14/0.43 inference(rewrite,[status(thm)],[])).
% 0.14/0.43 tff(22,axiom,(~equalish(e_4, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_2')).
% 0.14/0.43 tff(23,plain,
% 0.14/0.43 (~equalish(e_4, e_2)),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.14/0.43 tff(24,plain,
% 0.14/0.43 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))) | (equalish(e_4, e_2) | (~product2(e_2, e_2, e_2)) | (~product2(e_2, e_2, 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_2) | (~product2(e_2, e_2, e_2)) | (~product2(e_2, e_2, e_4)))),
% 0.14/0.43 inference(rewrite,[status(thm)],[])).
% 0.14/0.43 tff(25,plain,
% 0.14/0.43 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))) | (equalish(e_4, e_2) | (~product2(e_2, e_2, e_2)) | (~product2(e_2, e_2, e_4)))),
% 0.14/0.43 inference(quant_inst,[status(thm)],[])).
% 0.14/0.43 tff(26,plain,
% 0.14/0.43 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))) | equalish(e_4, e_2) | (~product2(e_2, e_2, e_2)) | (~product2(e_2, e_2, e_4))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.14/0.43 tff(27,plain,
% 0.14/0.43 ($false),
% 0.14/0.43 inference(unit_resolution,[status(thm)],[26, 23, 20, 10, 1])).
% 0.14/0.43 tff(28,plain,(~product2(e_2, e_2, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.14/0.43 tff(29,assumption,(product1(e_1, e_2, e_2)), introduced(assumption)).
% 0.14/0.43 tff(30,plain,
% 0.14/0.43 (^[X: $i] : refl(product1(X, X, X) <=> product1(X, X, X))),
% 0.14/0.43 inference(bind,[status(th)],[])).
% 0.14/0.43 tff(31,plain,
% 0.14/0.43 (![X: $i] : product1(X, X, X) <=> ![X: $i] : product1(X, X, X)),
% 0.14/0.43 inference(quant_intro,[status(thm)],[30])).
% 0.14/0.43 tff(32,plain,
% 0.14/0.43 (![X: $i] : product1(X, X, X) <=> ![X: $i] : product1(X, X, X)),
% 0.14/0.43 inference(rewrite,[status(thm)],[])).
% 0.14/0.43 tff(33,axiom,(![X: $i] : product1(X, X, X)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product1_idempotence')).
% 0.14/0.43 tff(34,plain,
% 0.14/0.43 (![X: $i] : product1(X, X, X)),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.14/0.43 tff(35,plain,(
% 0.14/0.43 ![X: $i] : product1(X, X, X)),
% 0.14/0.43 inference(skolemize,[status(sab)],[34])).
% 0.14/0.43 tff(36,plain,
% 0.14/0.43 (![X: $i] : product1(X, X, X)),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.14/0.43 tff(37,plain,
% 0.14/0.43 ((~![X: $i] : product1(X, X, X)) | product1(e_2, e_2, e_2)),
% 0.14/0.43 inference(quant_inst,[status(thm)],[])).
% 0.14/0.43 tff(38,plain,
% 0.14/0.43 (product1(e_2, e_2, e_2)),
% 0.14/0.43 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.14/0.43 tff(39,plain,
% 0.14/0.43 (^[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))))),
% 0.14/0.43 inference(bind,[status(th)],[])).
% 0.14/0.43 tff(40,plain,
% 0.14/0.43 (![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)))),
% 0.14/0.43 inference(quant_intro,[status(thm)],[39])).
% 0.14/0.43 tff(41,plain,
% 0.14/0.43 (![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)))),
% 0.14/0.43 inference(rewrite,[status(thm)],[])).
% 0.14/0.43 tff(42,plain,
% 0.14/0.43 (^[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)))))),
% 0.14/0.43 inference(bind,[status(th)],[])).
% 0.14/0.43 tff(43,plain,
% 0.14/0.43 (![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)))),
% 0.14/0.43 inference(quant_intro,[status(thm)],[42])).
% 0.14/0.43 tff(44,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')).
% 0.14/0.43 tff(45,plain,
% 0.14/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.14/0.43 tff(46,plain,
% 0.14/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.14/0.43 tff(47,plain,(
% 0.14/0.43 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))),
% 0.14/0.43 inference(skolemize,[status(sab)],[46])).
% 0.14/0.43 tff(48,plain,
% 0.14/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[47, 40])).
% 0.14/0.43 tff(49,plain,
% 0.14/0.43 ((~equalish(e_1, e_2)) <=> (~equalish(e_1, e_2))),
% 0.14/0.43 inference(rewrite,[status(thm)],[])).
% 0.14/0.43 tff(50,axiom,(~equalish(e_1, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_2')).
% 0.14/0.43 tff(51,plain,
% 0.14/0.43 (~equalish(e_1, e_2)),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.14/0.43 tff(52,plain,
% 0.14/0.43 (((~![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)))),
% 0.14/0.43 inference(rewrite,[status(thm)],[])).
% 0.14/0.43 tff(53,plain,
% 0.14/0.43 ((~![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)))),
% 0.14/0.43 inference(quant_inst,[status(thm)],[])).
% 0.14/0.43 tff(54,plain,
% 0.14/0.43 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_1, e_2) | (~product1(e_2, e_2, e_2)) | (~product1(e_1, e_2, e_2))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.14/0.43 tff(55,plain,
% 0.14/0.43 ($false),
% 0.14/0.43 inference(unit_resolution,[status(thm)],[54, 51, 48, 38, 29])).
% 0.14/0.43 tff(56,plain,(~product1(e_1, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.14/0.43 tff(57,assumption,(product1(e_4, e_2, e_1)), introduced(assumption)).
% 0.14/0.43 tff(58,assumption,(product1(e_3, e_2, e_1)), introduced(assumption)).
% 0.14/0.43 tff(59,plain,
% 0.14/0.43 ((~equalish(e_4, e_3)) <=> (~equalish(e_4, e_3))),
% 0.14/0.43 inference(rewrite,[status(thm)],[])).
% 0.14/0.43 tff(60,axiom,(~equalish(e_4, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_3')).
% 0.14/0.43 tff(61,plain,
% 0.14/0.43 (~equalish(e_4, e_3)),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.14/0.43 tff(62,plain,
% 0.14/0.43 (((~![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_2, e_1)) | (~product1(e_4, 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_4, e_3) | (~product1(e_3, e_2, e_1)) | (~product1(e_4, e_2, e_1)))),
% 0.14/0.43 inference(rewrite,[status(thm)],[])).
% 0.14/0.43 tff(63,plain,
% 0.14/0.43 ((~![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_2, e_1)) | (~product1(e_4, e_2, e_1)))),
% 0.14/0.43 inference(quant_inst,[status(thm)],[])).
% 0.14/0.43 tff(64,plain,
% 0.14/0.43 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_4, e_3) | (~product1(e_3, e_2, e_1)) | (~product1(e_4, e_2, e_1))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.14/0.43 tff(65,plain,
% 0.14/0.43 ($false),
% 0.14/0.43 inference(unit_resolution,[status(thm)],[64, 61, 48, 58, 57])).
% 0.14/0.43 tff(66,plain,((~product1(e_4, e_2, e_1)) | (~product1(e_3, e_2, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.14/0.43 tff(67,plain,
% 0.14/0.43 (~product1(e_3, e_2, e_1)),
% 0.14/0.43 inference(unit_resolution,[status(thm)],[66, 57])).
% 0.14/0.43 tff(68,plain,
% 0.14/0.43 ((~![X: $i] : product1(X, X, X)) | product1(e_3, e_3, e_3)),
% 0.14/0.43 inference(quant_inst,[status(thm)],[])).
% 0.14/0.44 tff(69,plain,
% 0.14/0.44 (product1(e_3, e_3, e_3)),
% 0.14/0.44 inference(unit_resolution,[status(thm)],[68, 36])).
% 0.14/0.44 tff(70,assumption,(product1(e_3, e_2, e_3)), introduced(assumption)).
% 0.14/0.44 tff(71,plain,
% 0.14/0.44 (^[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))))),
% 0.14/0.44 inference(bind,[status(th)],[])).
% 0.14/0.44 tff(72,plain,
% 0.14/0.44 (![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)))),
% 0.14/0.44 inference(quant_intro,[status(thm)],[71])).
% 0.14/0.44 tff(73,plain,
% 0.14/0.44 (![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)))),
% 0.14/0.44 inference(rewrite,[status(thm)],[])).
% 0.14/0.44 tff(74,plain,
% 0.14/0.44 (^[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)))))),
% 0.14/0.44 inference(bind,[status(th)],[])).
% 0.14/0.44 tff(75,plain,
% 0.14/0.44 (![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)))),
% 0.14/0.44 inference(quant_intro,[status(thm)],[74])).
% 0.14/0.44 tff(76,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')).
% 0.14/0.44 tff(77,plain,
% 0.14/0.44 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))),
% 0.14/0.44 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.14/0.44 tff(78,plain,
% 0.14/0.44 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))),
% 0.14/0.44 inference(modus_ponens,[status(thm)],[77, 73])).
% 0.14/0.44 tff(79,plain,(
% 0.14/0.44 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))),
% 0.14/0.44 inference(skolemize,[status(sab)],[78])).
% 0.14/0.44 tff(80,plain,
% 0.14/0.44 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))),
% 0.14/0.44 inference(modus_ponens,[status(thm)],[79, 72])).
% 0.14/0.44 tff(81,plain,
% 0.14/0.44 ((~equalish(e_2, e_3)) <=> (~equalish(e_2, e_3))),
% 0.14/0.44 inference(rewrite,[status(thm)],[])).
% 0.14/0.44 tff(82,axiom,(~equalish(e_2, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_3')).
% 0.14/0.44 tff(83,plain,
% 0.14/0.44 (~equalish(e_2, e_3)),
% 0.14/0.44 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.14/0.44 tff(84,plain,
% 0.14/0.44 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_2, e_3) | (~product1(e_3, e_3, e_3)) | (~product1(e_3, e_2, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_2, e_3) | (~product1(e_3, e_3, e_3)) | (~product1(e_3, e_2, e_3)))),
% 0.14/0.44 inference(rewrite,[status(thm)],[])).
% 0.14/0.44 tff(85,plain,
% 0.14/0.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_2, e_3) | (~product1(e_3, e_3, e_3)) | (~product1(e_3, e_2, e_3)))),
% 0.14/0.44 inference(quant_inst,[status(thm)],[])).
% 0.14/0.44 tff(86,plain,
% 0.14/0.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_2, e_3) | (~product1(e_3, e_3, e_3)) | (~product1(e_3, e_2, e_3))),
% 0.14/0.44 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.14/0.44 tff(87,plain,
% 0.14/0.44 ($false),
% 0.14/0.44 inference(unit_resolution,[status(thm)],[86, 83, 80, 70, 69])).
% 0.14/0.44 tff(88,plain,(~product1(e_3, e_2, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.14/0.44 tff(89,assumption,(product1(e_3, e_2, e_2)), introduced(assumption)).
% 0.14/0.44 tff(90,plain,
% 0.14/0.44 ((~equalish(e_3, e_2)) <=> (~equalish(e_3, e_2))),
% 0.14/0.44 inference(rewrite,[status(thm)],[])).
% 0.14/0.44 tff(91,axiom,(~equalish(e_3, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_2')).
% 0.14/0.44 tff(92,plain,
% 0.14/0.44 (~equalish(e_3, e_2)),
% 0.14/0.44 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.14/0.44 tff(93,plain,
% 0.14/0.44 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_3, e_2) | (~product1(e_2, e_2, e_2)) | (~product1(e_3, 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_3, e_2) | (~product1(e_2, e_2, e_2)) | (~product1(e_3, e_2, e_2)))),
% 0.14/0.44 inference(rewrite,[status(thm)],[])).
% 0.14/0.44 tff(94,plain,
% 0.14/0.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_3, e_2) | (~product1(e_2, e_2, e_2)) | (~product1(e_3, e_2, e_2)))),
% 0.14/0.44 inference(quant_inst,[status(thm)],[])).
% 0.14/0.44 tff(95,plain,
% 0.14/0.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_3, e_2) | (~product1(e_2, e_2, e_2)) | (~product1(e_3, e_2, e_2))),
% 0.14/0.44 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.14/0.44 tff(96,plain,
% 0.14/0.44 ($false),
% 0.14/0.44 inference(unit_resolution,[status(thm)],[95, 92, 48, 38, 89])).
% 0.14/0.44 tff(97,plain,(~product1(e_3, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.14/0.44 tff(98,plain,
% 0.14/0.44 (^[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))))),
% 0.14/0.44 inference(bind,[status(th)],[])).
% 0.14/0.44 tff(99,plain,
% 0.14/0.44 (![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)))),
% 0.14/0.44 inference(quant_intro,[status(thm)],[98])).
% 0.14/0.44 tff(100,plain,
% 0.14/0.44 (![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)))),
% 0.14/0.44 inference(rewrite,[status(thm)],[])).
% 0.14/0.44 tff(101,plain,
% 0.14/0.44 (^[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)))))),
% 0.14/0.44 inference(bind,[status(th)],[])).
% 0.14/0.44 tff(102,plain,
% 0.14/0.44 (![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)))),
% 0.14/0.44 inference(quant_intro,[status(thm)],[101])).
% 0.14/0.44 tff(103,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')).
% 0.14/0.44 tff(104,plain,
% 0.14/0.44 (![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)))),
% 0.14/0.44 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.14/0.44 tff(105,plain,
% 0.14/0.44 (![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)))),
% 0.14/0.44 inference(modus_ponens,[status(thm)],[104, 100])).
% 0.14/0.44 tff(106,plain,(
% 0.14/0.44 ![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)))),
% 0.14/0.44 inference(skolemize,[status(sab)],[105])).
% 0.14/0.44 tff(107,plain,
% 0.14/0.44 (![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)))),
% 0.14/0.44 inference(modus_ponens,[status(thm)],[106, 99])).
% 0.14/0.44 tff(108,plain,
% 0.14/0.44 (group_element(e_3) <=> group_element(e_3)),
% 0.14/0.44 inference(rewrite,[status(thm)],[])).
% 0.14/0.44 tff(109,axiom,(group_element(e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_3')).
% 0.14/0.44 tff(110,plain,
% 0.14/0.44 (group_element(e_3)),
% 0.14/0.44 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.14/0.44 tff(111,plain,
% 0.14/0.44 (group_element(e_2) <=> group_element(e_2)),
% 0.14/0.44 inference(rewrite,[status(thm)],[])).
% 0.14/0.44 tff(112,axiom,(group_element(e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_2')).
% 0.14/0.44 tff(113,plain,
% 0.14/0.44 (group_element(e_2)),
% 0.14/0.44 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.14/0.44 tff(114,plain,
% 0.14/0.44 (((~![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)) | product1(e_3, e_2, e_1) | product1(e_3, e_2, e_2) | (~group_element(e_2)) | product1(e_3, e_2, e_4) | product1(e_3, e_2, 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_3)) | product1(e_3, e_2, e_1) | product1(e_3, e_2, e_2) | (~group_element(e_2)) | product1(e_3, e_2, e_4) | product1(e_3, e_2, e_3))),
% 0.14/0.44 inference(rewrite,[status(thm)],[])).
% 0.14/0.44 tff(115,plain,
% 0.14/0.44 ((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_2)) | (~group_element(e_3))) <=> ((~group_element(e_3)) | product1(e_3, e_2, e_1) | product1(e_3, e_2, e_2) | (~group_element(e_2)) | product1(e_3, e_2, e_4) | product1(e_3, e_2, e_3))),
% 0.14/0.44 inference(rewrite,[status(thm)],[])).
% 0.14/0.45 tff(116,plain,
% 0.14/0.45 (((~![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_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_2)) | (~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)))) | ((~group_element(e_3)) | product1(e_3, e_2, e_1) | product1(e_3, e_2, e_2) | (~group_element(e_2)) | product1(e_3, e_2, e_4) | product1(e_3, e_2, e_3)))),
% 0.14/0.45 inference(monotonicity,[status(thm)],[115])).
% 0.14/0.45 tff(117,plain,
% 0.14/0.45 (((~![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_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_2)) | (~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)))) | (~group_element(e_3)) | product1(e_3, e_2, e_1) | product1(e_3, e_2, e_2) | (~group_element(e_2)) | product1(e_3, e_2, e_4) | product1(e_3, e_2, e_3))),
% 0.14/0.45 inference(transitivity,[status(thm)],[116, 114])).
% 0.14/0.45 tff(118,plain,
% 0.14/0.45 ((~![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_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_2)) | (~group_element(e_3)))),
% 0.14/0.45 inference(quant_inst,[status(thm)],[])).
% 0.14/0.45 tff(119,plain,
% 0.14/0.45 ((~![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)) | product1(e_3, e_2, e_1) | product1(e_3, e_2, e_2) | (~group_element(e_2)) | product1(e_3, e_2, e_4) | product1(e_3, e_2, e_3)),
% 0.14/0.45 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.14/0.45 tff(120,plain,
% 0.14/0.45 (product1(e_3, e_2, e_1) | product1(e_3, e_2, e_2) | product1(e_3, e_2, e_4) | product1(e_3, e_2, e_3)),
% 0.14/0.45 inference(unit_resolution,[status(thm)],[119, 113, 110, 107])).
% 0.14/0.45 tff(121,plain,
% 0.14/0.45 (product1(e_3, e_2, e_1) | product1(e_3, e_2, e_4) | product1(e_3, e_2, e_3)),
% 0.14/0.45 inference(unit_resolution,[status(thm)],[120, 97])).
% 0.14/0.45 tff(122,plain,
% 0.14/0.45 (product1(e_3, e_2, e_1) | product1(e_3, e_2, e_4)),
% 0.14/0.45 inference(unit_resolution,[status(thm)],[121, 88])).
% 0.14/0.45 tff(123,plain,
% 0.14/0.45 (product1(e_3, e_2, e_4)),
% 0.14/0.45 inference(unit_resolution,[status(thm)],[122, 67])).
% 0.14/0.45 tff(124,assumption,(product1(e_1, e_2, e_4)), introduced(assumption)).
% 0.14/0.45 tff(125,assumption,(product1(e_3, e_2, e_4)), introduced(assumption)).
% 0.14/0.45 tff(126,plain,
% 0.14/0.45 ((~equalish(e_1, e_3)) <=> (~equalish(e_1, e_3))),
% 0.14/0.45 inference(rewrite,[status(thm)],[])).
% 0.14/0.45 tff(127,axiom,(~equalish(e_1, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_3')).
% 0.14/0.45 tff(128,plain,
% 0.14/0.45 (~equalish(e_1, e_3)),
% 0.14/0.45 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.14/0.45 tff(129,plain,
% 0.14/0.45 (((~![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_2, e_4)) | (~product1(e_1, 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_1, e_3) | (~product1(e_3, e_2, e_4)) | (~product1(e_1, e_2, e_4)))),
% 0.14/0.45 inference(rewrite,[status(thm)],[])).
% 0.14/0.45 tff(130,plain,
% 0.14/0.45 ((~![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_2, e_4)) | (~product1(e_1, e_2, e_4)))),
% 0.14/0.45 inference(quant_inst,[status(thm)],[])).
% 0.14/0.45 tff(131,plain,
% 0.14/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_1, e_3) | (~product1(e_3, e_2, e_4)) | (~product1(e_1, e_2, e_4))),
% 0.14/0.45 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.14/0.45 tff(132,plain,
% 0.14/0.45 ($false),
% 0.14/0.45 inference(unit_resolution,[status(thm)],[131, 128, 48, 125, 124])).
% 0.14/0.45 tff(133,plain,((~product1(e_1, e_2, e_4)) | (~product1(e_3, e_2, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.14/0.45 tff(134,plain,
% 0.14/0.45 (~product1(e_1, e_2, e_4)),
% 0.14/0.45 inference(unit_resolution,[status(thm)],[133, 123])).
% 0.14/0.45 tff(135,assumption,(product2(e_1, e_2, e_1)), introduced(assumption)).
% 0.14/0.45 tff(136,plain,
% 0.14/0.45 ((~![X: $i] : product2(X, X, X)) | product2(e_1, e_1, e_1)),
% 0.14/0.45 inference(quant_inst,[status(thm)],[])).
% 0.14/0.45 tff(137,plain,
% 0.14/0.45 (product2(e_1, e_1, e_1)),
% 0.14/0.45 inference(unit_resolution,[status(thm)],[136, 8])).
% 0.14/0.45 tff(138,plain,
% 0.14/0.45 (^[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))))),
% 0.14/0.45 inference(bind,[status(th)],[])).
% 0.14/0.45 tff(139,plain,
% 0.14/0.45 (![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)))),
% 0.14/0.45 inference(quant_intro,[status(thm)],[138])).
% 0.14/0.45 tff(140,plain,
% 0.14/0.45 (![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)))),
% 0.14/0.45 inference(rewrite,[status(thm)],[])).
% 0.14/0.45 tff(141,plain,
% 0.14/0.45 (^[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)))))),
% 0.14/0.45 inference(bind,[status(th)],[])).
% 0.14/0.45 tff(142,plain,
% 0.14/0.45 (![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)))),
% 0.14/0.45 inference(quant_intro,[status(thm)],[141])).
% 0.14/0.45 tff(143,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')).
% 0.14/0.45 tff(144,plain,
% 0.14/0.45 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))),
% 0.14/0.45 inference(modus_ponens,[status(thm)],[143, 142])).
% 0.14/0.45 tff(145,plain,
% 0.14/0.45 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))),
% 0.14/0.45 inference(modus_ponens,[status(thm)],[144, 140])).
% 0.14/0.45 tff(146,plain,(
% 0.14/0.45 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))),
% 0.14/0.45 inference(skolemize,[status(sab)],[145])).
% 0.14/0.45 tff(147,plain,
% 0.14/0.45 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))),
% 0.14/0.45 inference(modus_ponens,[status(thm)],[146, 139])).
% 0.14/0.45 tff(148,plain,
% 0.14/0.45 ((~equalish(e_2, e_1)) <=> (~equalish(e_2, e_1))),
% 0.14/0.45 inference(rewrite,[status(thm)],[])).
% 0.14/0.45 tff(149,axiom,(~equalish(e_2, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_1')).
% 0.14/0.45 tff(150,plain,
% 0.14/0.45 (~equalish(e_2, e_1)),
% 0.14/0.45 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.14/0.45 tff(151,plain,
% 0.14/0.45 (((~![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)))),
% 0.14/0.45 inference(rewrite,[status(thm)],[])).
% 0.14/0.45 tff(152,plain,
% 0.14/0.45 ((~![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)))),
% 0.14/0.45 inference(quant_inst,[status(thm)],[])).
% 0.14/0.45 tff(153,plain,
% 0.14/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | equalish(e_2, e_1) | (~product2(e_1, e_1, e_1)) | (~product2(e_1, e_2, e_1))),
% 0.14/0.45 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.14/0.45 tff(154,plain,
% 0.14/0.45 ($false),
% 0.14/0.45 inference(unit_resolution,[status(thm)],[153, 150, 147, 137, 135])).
% 0.14/0.45 tff(155,plain,(~product2(e_1, e_2, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.14/0.45 tff(156,plain,
% 0.14/0.45 ((~![X: $i] : product1(X, X, X)) | product1(e_1, e_1, e_1)),
% 0.14/0.45 inference(quant_inst,[status(thm)],[])).
% 0.14/0.45 tff(157,plain,
% 0.14/0.45 (product1(e_1, e_1, e_1)),
% 0.14/0.45 inference(unit_resolution,[status(thm)],[156, 36])).
% 0.14/0.45 tff(158,plain,
% 0.14/0.45 (^[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))))),
% 0.14/0.45 inference(bind,[status(th)],[])).
% 0.14/0.45 tff(159,plain,
% 0.14/0.45 (![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)))),
% 0.14/0.45 inference(quant_intro,[status(thm)],[158])).
% 0.14/0.45 tff(160,plain,
% 0.14/0.45 (![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)))),
% 0.14/0.45 inference(rewrite,[status(thm)],[])).
% 0.14/0.45 tff(161,plain,
% 0.14/0.45 (^[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))))),
% 0.14/0.45 inference(bind,[status(th)],[])).
% 0.14/0.45 tff(162,plain,
% 0.14/0.45 (![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)))),
% 0.14/0.45 inference(quant_intro,[status(thm)],[161])).
% 0.14/0.45 tff(163,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')).
% 0.14/0.45 tff(164,plain,
% 0.14/0.45 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))),
% 0.14/0.45 inference(modus_ponens,[status(thm)],[163, 162])).
% 0.14/0.45 tff(165,plain,
% 0.14/0.45 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))),
% 0.14/0.45 inference(modus_ponens,[status(thm)],[164, 160])).
% 0.14/0.45 tff(166,plain,(
% 0.14/0.45 ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))),
% 0.14/0.45 inference(skolemize,[status(sab)],[165])).
% 0.14/0.45 tff(167,plain,
% 0.14/0.45 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))),
% 0.14/0.45 inference(modus_ponens,[status(thm)],[166, 159])).
% 0.14/0.45 tff(168,plain,
% 0.14/0.45 (((~![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)))),
% 0.14/0.45 inference(rewrite,[status(thm)],[])).
% 0.14/0.45 tff(169,plain,
% 0.14/0.45 ((~![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)))),
% 0.14/0.45 inference(quant_inst,[status(thm)],[])).
% 0.14/0.45 tff(170,plain,
% 0.14/0.45 ((~![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))),
% 0.14/0.45 inference(modus_ponens,[status(thm)],[169, 168])).
% 0.14/0.45 tff(171,plain,
% 0.14/0.45 (~product1(e_1, e_2, e_1)),
% 0.14/0.45 inference(unit_resolution,[status(thm)],[170, 167, 157, 155])).
% 0.14/0.46 tff(172,plain,
% 0.14/0.46 (group_element(e_1) <=> group_element(e_1)),
% 0.14/0.46 inference(rewrite,[status(thm)],[])).
% 0.14/0.46 tff(173,axiom,(group_element(e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_1')).
% 0.14/0.46 tff(174,plain,
% 0.14/0.46 (group_element(e_1)),
% 0.14/0.46 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.14/0.46 tff(175,plain,
% 0.14/0.46 (((~![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)))) | ((~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_1) | product1(e_1, e_2, 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_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_1) | product1(e_1, e_2, e_2))),
% 0.14/0.46 inference(rewrite,[status(thm)],[])).
% 0.14/0.46 tff(176,plain,
% 0.14/0.46 ((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_2)) | (~group_element(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_1) | product1(e_1, e_2, e_2))),
% 0.14/0.46 inference(rewrite,[status(thm)],[])).
% 0.14/0.46 tff(177,plain,
% 0.14/0.46 (((~![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)))) | (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_2)) | (~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_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_1) | product1(e_1, e_2, e_2)))),
% 0.14/0.46 inference(monotonicity,[status(thm)],[176])).
% 0.14/0.46 tff(178,plain,
% 0.14/0.46 (((~![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)))) | (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_2)) | (~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_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_1) | product1(e_1, e_2, e_2))),
% 0.14/0.46 inference(transitivity,[status(thm)],[177, 175])).
% 0.14/0.46 tff(179,plain,
% 0.14/0.46 ((~![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)))) | (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_2)) | (~group_element(e_1)))),
% 0.14/0.46 inference(quant_inst,[status(thm)],[])).
% 0.14/0.46 tff(180,plain,
% 0.14/0.46 ((~![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)))) | (~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_1) | product1(e_1, e_2, e_2)),
% 0.14/0.46 inference(modus_ponens,[status(thm)],[179, 178])).
% 0.14/0.46 tff(181,plain,
% 0.14/0.46 (product1(e_1, e_2, e_4) | product1(e_1, e_2, e_3) | product1(e_1, e_2, e_2)),
% 0.14/0.46 inference(unit_resolution,[status(thm)],[180, 174, 113, 107, 171])).
% 0.14/0.46 tff(182,plain,
% 0.14/0.46 (product1(e_1, e_2, e_3)),
% 0.14/0.46 inference(unit_resolution,[status(thm)],[181, 134, 56])).
% 0.14/0.46 tff(183,assumption,(product1(e_1, e_2, e_3)), introduced(assumption)).
% 0.14/0.46 tff(184,assumption,(product1(e_1, e_4, e_3)), introduced(assumption)).
% 0.14/0.46 tff(185,plain,
% 0.14/0.46 (((~![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_4, e_3)) | (~product1(e_1, e_2, 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_4, e_3)) | (~product1(e_1, e_2, e_3)))),
% 0.14/0.46 inference(rewrite,[status(thm)],[])).
% 0.14/0.46 tff(186,plain,
% 0.14/0.46 ((equalish(e_4, e_2) | (~product1(e_1, e_2, e_3)) | (~product1(e_1, e_4, e_3))) <=> (equalish(e_4, e_2) | (~product1(e_1, e_4, e_3)) | (~product1(e_1, e_2, e_3)))),
% 0.14/0.46 inference(rewrite,[status(thm)],[])).
% 0.14/0.46 tff(187,plain,
% 0.14/0.46 (((~![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_4, e_3)) | (~product1(e_1, e_2, e_3))))),
% 0.14/0.46 inference(monotonicity,[status(thm)],[186])).
% 0.14/0.46 tff(188,plain,
% 0.14/0.46 (((~![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_4, e_3)) | (~product1(e_1, e_2, e_3)))),
% 0.14/0.46 inference(transitivity,[status(thm)],[187, 185])).
% 0.14/0.46 tff(189,plain,
% 0.14/0.46 ((~![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)))),
% 0.14/0.46 inference(quant_inst,[status(thm)],[])).
% 0.14/0.46 tff(190,plain,
% 0.14/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_4, e_2) | (~product1(e_1, e_4, e_3)) | (~product1(e_1, e_2, e_3))),
% 0.14/0.46 inference(modus_ponens,[status(thm)],[189, 188])).
% 0.14/0.46 tff(191,plain,
% 0.14/0.46 ($false),
% 0.14/0.46 inference(unit_resolution,[status(thm)],[190, 23, 80, 184, 183])).
% 0.14/0.46 tff(192,plain,((~product1(e_1, e_4, e_3)) | (~product1(e_1, e_2, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.14/0.46 tff(193,plain,
% 0.14/0.46 (~product1(e_1, e_4, e_3)),
% 0.14/0.46 inference(unit_resolution,[status(thm)],[192, 182])).
% 0.14/0.46 tff(194,plain,
% 0.14/0.46 ((~![X: $i] : product1(X, X, X)) | product1(e_4, e_4, e_4)),
% 0.14/0.46 inference(quant_inst,[status(thm)],[])).
% 0.14/0.46 tff(195,plain,
% 0.14/0.46 (product1(e_4, e_4, e_4)),
% 0.14/0.46 inference(unit_resolution,[status(thm)],[194, 36])).
% 0.14/0.46 tff(196,assumption,(product1(e_1, e_4, e_4)), introduced(assumption)).
% 0.14/0.46 tff(197,plain,
% 0.14/0.46 ((~equalish(e_1, e_4)) <=> (~equalish(e_1, e_4))),
% 0.14/0.46 inference(rewrite,[status(thm)],[])).
% 0.14/0.46 tff(198,axiom,(~equalish(e_1, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_4')).
% 0.14/0.46 tff(199,plain,
% 0.14/0.46 (~equalish(e_1, e_4)),
% 0.14/0.46 inference(modus_ponens,[status(thm)],[198, 197])).
% 0.14/0.46 tff(200,plain,
% 0.14/0.46 (((~![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_1, e_4, e_4)) | (~product1(e_4, 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_1, e_4, e_4)) | (~product1(e_4, e_4, e_4)))),
% 0.14/0.46 inference(rewrite,[status(thm)],[])).
% 0.14/0.46 tff(201,plain,
% 0.14/0.46 ((equalish(e_1, e_4) | (~product1(e_4, e_4, e_4)) | (~product1(e_1, e_4, e_4))) <=> (equalish(e_1, e_4) | (~product1(e_1, e_4, e_4)) | (~product1(e_4, e_4, e_4)))),
% 0.14/0.46 inference(rewrite,[status(thm)],[])).
% 0.14/0.46 tff(202,plain,
% 0.14/0.46 (((~![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_1, e_4, e_4)) | (~product1(e_4, e_4, e_4))))),
% 0.14/0.46 inference(monotonicity,[status(thm)],[201])).
% 0.14/0.46 tff(203,plain,
% 0.14/0.46 (((~![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_1, e_4, e_4)) | (~product1(e_4, e_4, e_4)))),
% 0.14/0.46 inference(transitivity,[status(thm)],[202, 200])).
% 0.14/0.46 tff(204,plain,
% 0.14/0.46 ((~![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)))),
% 0.14/0.46 inference(quant_inst,[status(thm)],[])).
% 0.14/0.46 tff(205,plain,
% 0.14/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_1, e_4) | (~product1(e_1, e_4, e_4)) | (~product1(e_4, e_4, e_4))),
% 0.14/0.46 inference(modus_ponens,[status(thm)],[204, 203])).
% 0.14/0.46 tff(206,plain,
% 0.14/0.46 ($false),
% 0.14/0.46 inference(unit_resolution,[status(thm)],[205, 199, 48, 196, 195])).
% 0.14/0.46 tff(207,plain,(~product1(e_1, e_4, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.14/0.46 tff(208,assumption,(product2(e_1, e_4, e_1)), introduced(assumption)).
% 0.14/0.46 tff(209,plain,
% 0.14/0.46 ((~equalish(e_4, e_1)) <=> (~equalish(e_4, e_1))),
% 0.14/0.46 inference(rewrite,[status(thm)],[])).
% 0.14/0.46 tff(210,axiom,(~equalish(e_4, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_1')).
% 0.14/0.46 tff(211,plain,
% 0.14/0.46 (~equalish(e_4, e_1)),
% 0.14/0.46 inference(modus_ponens,[status(thm)],[210, 209])).
% 0.14/0.46 tff(212,plain,
% 0.14/0.46 (((~![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)))),
% 0.14/0.46 inference(rewrite,[status(thm)],[])).
% 0.14/0.46 tff(213,plain,
% 0.14/0.46 ((~![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)))),
% 0.14/0.46 inference(quant_inst,[status(thm)],[])).
% 0.14/0.46 tff(214,plain,
% 0.14/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | equalish(e_4, e_1) | (~product2(e_1, e_1, e_1)) | (~product2(e_1, e_4, e_1))),
% 0.14/0.46 inference(modus_ponens,[status(thm)],[213, 212])).
% 0.14/0.46 tff(215,plain,
% 0.14/0.46 ($false),
% 0.14/0.46 inference(unit_resolution,[status(thm)],[214, 211, 147, 137, 208])).
% 0.14/0.46 tff(216,plain,(~product2(e_1, e_4, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.14/0.46 tff(217,plain,
% 0.14/0.46 (((~![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_1)) | (~product1(e_1, e_1, 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_4, e_1)) | (~product1(e_1, e_1, e_1)) | product2(e_1, e_4, e_1))),
% 0.14/0.46 inference(rewrite,[status(thm)],[])).
% 0.14/0.46 tff(218,plain,
% 0.14/0.46 (((~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_4, e_1)) | (~product1(e_1, e_1, e_1)) | product2(e_1, e_4, e_1))),
% 0.14/0.46 inference(rewrite,[status(thm)],[])).
% 0.14/0.46 tff(219,plain,
% 0.14/0.46 (((~![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_4, e_1)) | (~product1(e_1, e_1, e_1)) | product2(e_1, e_4, e_1)))),
% 0.14/0.46 inference(monotonicity,[status(thm)],[218])).
% 0.14/0.46 tff(220,plain,
% 0.14/0.46 (((~![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_4, e_1)) | (~product1(e_1, e_1, e_1)) | product2(e_1, e_4, e_1))),
% 0.14/0.46 inference(transitivity,[status(thm)],[219, 217])).
% 0.14/0.46 tff(221,plain,
% 0.14/0.47 ((~![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)))),
% 0.14/0.47 inference(quant_inst,[status(thm)],[])).
% 0.14/0.47 tff(222,plain,
% 0.14/0.47 ((~![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_1)) | (~product1(e_1, e_1, e_1)) | product2(e_1, e_4, e_1)),
% 0.14/0.47 inference(modus_ponens,[status(thm)],[221, 220])).
% 0.14/0.47 tff(223,plain,
% 0.14/0.47 (~product1(e_1, e_4, e_1)),
% 0.14/0.47 inference(unit_resolution,[status(thm)],[222, 167, 157, 216])).
% 0.14/0.47 tff(224,plain,
% 0.14/0.47 (group_element(e_4) <=> group_element(e_4)),
% 0.14/0.47 inference(rewrite,[status(thm)],[])).
% 0.14/0.47 tff(225,axiom,(group_element(e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_4')).
% 0.14/0.47 tff(226,plain,
% 0.14/0.47 (group_element(e_4)),
% 0.14/0.47 inference(modus_ponens,[status(thm)],[225, 224])).
% 0.14/0.47 tff(227,plain,
% 0.14/0.47 (((~![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)) | product1(e_1, e_4, e_2) | product1(e_1, e_4, e_4) | product1(e_1, e_4, e_1) | product1(e_1, e_4, 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_4)) | product1(e_1, e_4, e_2) | product1(e_1, e_4, e_4) | product1(e_1, e_4, e_1) | product1(e_1, e_4, e_3) | (~group_element(e_1)))),
% 0.14/0.47 inference(rewrite,[status(thm)],[])).
% 0.14/0.47 tff(228,plain,
% 0.14/0.47 ((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)) | product1(e_1, e_4, e_2) | product1(e_1, e_4, e_4) | product1(e_1, e_4, e_1) | product1(e_1, e_4, e_3) | (~group_element(e_1)))),
% 0.14/0.47 inference(rewrite,[status(thm)],[])).
% 0.14/0.47 tff(229,plain,
% 0.14/0.47 (((~![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_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)) | product1(e_1, e_4, e_2) | product1(e_1, e_4, e_4) | product1(e_1, e_4, e_1) | product1(e_1, e_4, e_3) | (~group_element(e_1))))),
% 0.14/0.47 inference(monotonicity,[status(thm)],[228])).
% 0.14/0.47 tff(230,plain,
% 0.14/0.47 (((~![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_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)) | product1(e_1, e_4, e_2) | product1(e_1, e_4, e_4) | product1(e_1, e_4, e_1) | product1(e_1, e_4, e_3) | (~group_element(e_1)))),
% 0.14/0.47 inference(transitivity,[status(thm)],[229, 227])).
% 0.14/0.47 tff(231,plain,
% 0.14/0.47 ((~![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_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)))),
% 0.14/0.47 inference(quant_inst,[status(thm)],[])).
% 0.14/0.47 tff(232,plain,
% 0.14/0.47 ((~![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)) | product1(e_1, e_4, e_2) | product1(e_1, e_4, e_4) | product1(e_1, e_4, e_1) | product1(e_1, e_4, e_3) | (~group_element(e_1))),
% 0.14/0.47 inference(modus_ponens,[status(thm)],[231, 230])).
% 0.14/0.47 tff(233,plain,
% 0.14/0.47 (product1(e_1, e_4, e_2) | product1(e_1, e_4, e_4) | product1(e_1, e_4, e_3)),
% 0.14/0.47 inference(unit_resolution,[status(thm)],[232, 174, 226, 107, 223])).
% 0.14/0.47 tff(234,plain,
% 0.14/0.47 (product1(e_1, e_4, e_2) | product1(e_1, e_4, e_3)),
% 0.14/0.47 inference(unit_resolution,[status(thm)],[233, 207])).
% 0.14/0.47 tff(235,plain,
% 0.14/0.47 (product1(e_1, e_4, e_2)),
% 0.14/0.47 inference(unit_resolution,[status(thm)],[234, 193])).
% 0.14/0.47 tff(236,plain,
% 0.14/0.47 (((~![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_2)) | product2(e_2, 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_1, e_4, e_2)) | product2(e_2, e_2, e_4) | (~product1(e_4, e_2, e_1)))),
% 0.14/0.47 inference(rewrite,[status(thm)],[])).
% 0.14/0.47 tff(237,plain,
% 0.14/0.47 ((~![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_2)) | product2(e_2, e_2, e_4) | (~product1(e_4, e_2, e_1)))),
% 0.14/0.47 inference(quant_inst,[status(thm)],[])).
% 0.14/0.47 tff(238,plain,
% 0.14/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | (~product1(e_1, e_4, e_2)) | product2(e_2, e_2, e_4) | (~product1(e_4, e_2, e_1))),
% 0.14/0.47 inference(modus_ponens,[status(thm)],[237, 236])).
% 0.14/0.47 tff(239,plain,
% 0.14/0.47 ($false),
% 0.14/0.47 inference(unit_resolution,[status(thm)],[238, 167, 57, 235, 28])).
% 0.14/0.47 tff(240,plain,(~product1(e_4, e_2, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.14/0.47 tff(241,assumption,(product1(e_4, e_2, e_2)), introduced(assumption)).
% 0.14/0.47 tff(242,plain,
% 0.14/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_4, e_2) | (~product1(e_2, e_2, e_2)) | (~product1(e_4, 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_4, e_2) | (~product1(e_2, e_2, e_2)) | (~product1(e_4, e_2, e_2)))),
% 0.14/0.47 inference(rewrite,[status(thm)],[])).
% 0.14/0.47 tff(243,plain,
% 0.14/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_4, e_2) | (~product1(e_2, e_2, e_2)) | (~product1(e_4, e_2, e_2)))),
% 0.14/0.47 inference(quant_inst,[status(thm)],[])).
% 0.14/0.47 tff(244,plain,
% 0.14/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_4, e_2) | (~product1(e_2, e_2, e_2)) | (~product1(e_4, e_2, e_2))),
% 0.14/0.47 inference(modus_ponens,[status(thm)],[243, 242])).
% 0.14/0.47 tff(245,plain,
% 0.14/0.47 ($false),
% 0.14/0.47 inference(unit_resolution,[status(thm)],[244, 23, 48, 38, 241])).
% 0.14/0.47 tff(246,plain,(~product1(e_4, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.14/0.47 tff(247,assumption,(product1(e_4, e_2, e_4)), introduced(assumption)).
% 0.14/0.47 tff(248,plain,
% 0.14/0.47 ((~equalish(e_2, e_4)) <=> (~equalish(e_2, e_4))),
% 0.14/0.47 inference(rewrite,[status(thm)],[])).
% 0.14/0.47 tff(249,axiom,(~equalish(e_2, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_4')).
% 0.14/0.47 tff(250,plain,
% 0.14/0.47 (~equalish(e_2, e_4)),
% 0.14/0.47 inference(modus_ponens,[status(thm)],[249, 248])).
% 0.14/0.47 tff(251,plain,
% 0.14/0.47 (((~![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_4, e_4)) | (~product1(e_4, e_2, e_4)))),
% 0.14/0.47 inference(rewrite,[status(thm)],[])).
% 0.14/0.47 tff(252,plain,
% 0.14/0.47 ((~![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)))),
% 0.14/0.47 inference(quant_inst,[status(thm)],[])).
% 0.14/0.47 tff(253,plain,
% 0.14/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_2, e_4) | (~product1(e_4, e_4, e_4)) | (~product1(e_4, e_2, e_4))),
% 0.14/0.47 inference(modus_ponens,[status(thm)],[252, 251])).
% 0.14/0.48 tff(254,plain,
% 0.14/0.48 ($false),
% 0.14/0.48 inference(unit_resolution,[status(thm)],[253, 250, 80, 247, 195])).
% 0.14/0.48 tff(255,plain,(~product1(e_4, e_2, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.14/0.48 tff(256,plain,
% 0.14/0.48 (((~![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_2)) | (~group_element(e_4)) | product1(e_4, e_2, e_2) | product1(e_4, e_2, e_1) | product1(e_4, e_2, e_4) | product1(e_4, e_2, 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_2)) | (~group_element(e_4)) | product1(e_4, e_2, e_2) | product1(e_4, e_2, e_1) | product1(e_4, e_2, e_4) | product1(e_4, e_2, e_3))),
% 0.14/0.48 inference(rewrite,[status(thm)],[])).
% 0.14/0.48 tff(257,plain,
% 0.14/0.48 ((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_2)) | (~group_element(e_4))) <=> ((~group_element(e_2)) | (~group_element(e_4)) | product1(e_4, e_2, e_2) | product1(e_4, e_2, e_1) | product1(e_4, e_2, e_4) | product1(e_4, e_2, e_3))),
% 0.14/0.48 inference(rewrite,[status(thm)],[])).
% 0.14/0.48 tff(258,plain,
% 0.14/0.48 (((~![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_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_2)) | (~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)))) | ((~group_element(e_2)) | (~group_element(e_4)) | product1(e_4, e_2, e_2) | product1(e_4, e_2, e_1) | product1(e_4, e_2, e_4) | product1(e_4, e_2, e_3)))),
% 0.14/0.48 inference(monotonicity,[status(thm)],[257])).
% 0.14/0.48 tff(259,plain,
% 0.14/0.48 (((~![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_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_2)) | (~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)))) | (~group_element(e_2)) | (~group_element(e_4)) | product1(e_4, e_2, e_2) | product1(e_4, e_2, e_1) | product1(e_4, e_2, e_4) | product1(e_4, e_2, e_3))),
% 0.14/0.48 inference(transitivity,[status(thm)],[258, 256])).
% 0.14/0.48 tff(260,plain,
% 0.14/0.48 ((~![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_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_2)) | (~group_element(e_4)))),
% 0.14/0.48 inference(quant_inst,[status(thm)],[])).
% 0.14/0.48 tff(261,plain,
% 0.14/0.48 ((~![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_2)) | (~group_element(e_4)) | product1(e_4, e_2, e_2) | product1(e_4, e_2, e_1) | product1(e_4, e_2, e_4) | product1(e_4, e_2, e_3)),
% 0.14/0.48 inference(modus_ponens,[status(thm)],[260, 259])).
% 0.14/0.48 tff(262,plain,
% 0.14/0.48 (product1(e_4, e_2, e_2) | product1(e_4, e_2, e_1) | product1(e_4, e_2, e_4) | product1(e_4, e_2, e_3)),
% 0.14/0.48 inference(unit_resolution,[status(thm)],[261, 113, 226, 107])).
% 0.14/0.48 tff(263,plain,
% 0.14/0.48 (product1(e_4, e_2, e_1) | product1(e_4, e_2, e_3)),
% 0.14/0.48 inference(unit_resolution,[status(thm)],[262, 255, 246])).
% 0.14/0.48 tff(264,plain,
% 0.14/0.48 (product1(e_4, e_2, e_3)),
% 0.14/0.48 inference(unit_resolution,[status(thm)],[263, 240])).
% 0.14/0.48 tff(265,assumption,(product1(e_4, e_1, e_3)), introduced(assumption)).
% 0.14/0.48 tff(266,assumption,(product1(e_4, e_2, e_3)), introduced(assumption)).
% 0.14/0.48 tff(267,plain,
% 0.14/0.48 (((~![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)))),
% 0.14/0.48 inference(rewrite,[status(thm)],[])).
% 0.14/0.48 tff(268,plain,
% 0.14/0.48 ((~![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)))),
% 0.14/0.48 inference(quant_inst,[status(thm)],[])).
% 0.14/0.48 tff(269,plain,
% 0.14/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_1, e_2) | (~product1(e_4, e_2, e_3)) | (~product1(e_4, e_1, e_3))),
% 0.14/0.48 inference(modus_ponens,[status(thm)],[268, 267])).
% 0.14/0.48 tff(270,plain,
% 0.14/0.48 ($false),
% 0.14/0.48 inference(unit_resolution,[status(thm)],[269, 51, 80, 266, 265])).
% 0.14/0.48 tff(271,plain,((~product1(e_4, e_1, e_3)) | (~product1(e_4, e_2, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.14/0.48 tff(272,plain,
% 0.14/0.48 (~product1(e_4, e_1, e_3)),
% 0.14/0.48 inference(unit_resolution,[status(thm)],[271, 264])).
% 0.14/0.48 tff(273,assumption,(product1(e_4, e_1, e_4)), introduced(assumption)).
% 0.14/0.48 tff(274,plain,
% 0.14/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_1, e_4) | (~product1(e_4, e_4, e_4)) | (~product1(e_4, 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_4) | (~product1(e_4, e_4, e_4)) | (~product1(e_4, e_1, e_4)))),
% 0.14/0.48 inference(rewrite,[status(thm)],[])).
% 0.14/0.48 tff(275,plain,
% 0.14/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_1, e_4) | (~product1(e_4, e_4, e_4)) | (~product1(e_4, e_1, e_4)))),
% 0.14/0.48 inference(quant_inst,[status(thm)],[])).
% 0.14/0.48 tff(276,plain,
% 0.14/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_1, e_4) | (~product1(e_4, e_4, e_4)) | (~product1(e_4, e_1, e_4))),
% 0.14/0.48 inference(modus_ponens,[status(thm)],[275, 274])).
% 0.14/0.48 tff(277,plain,
% 0.14/0.48 ($false),
% 0.14/0.48 inference(unit_resolution,[status(thm)],[276, 199, 80, 273, 195])).
% 0.14/0.48 tff(278,plain,(~product1(e_4, e_1, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.14/0.48 tff(279,assumption,(product1(e_4, e_1, e_1)), introduced(assumption)).
% 0.14/0.48 tff(280,plain,
% 0.14/0.48 (((~![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_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)))),
% 0.14/0.48 inference(rewrite,[status(thm)],[])).
% 0.14/0.48 tff(281,plain,
% 0.14/0.48 ((~![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_1, e_1)) | (~product1(e_4, e_1, e_1)))),
% 0.14/0.48 inference(quant_inst,[status(thm)],[])).
% 0.14/0.48 tff(282,plain,
% 0.14/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_4, e_1) | (~product1(e_1, e_1, e_1)) | (~product1(e_4, e_1, e_1))),
% 0.14/0.48 inference(modus_ponens,[status(thm)],[281, 280])).
% 0.14/0.48 tff(283,plain,
% 0.14/0.48 ($false),
% 0.14/0.48 inference(unit_resolution,[status(thm)],[282, 211, 48, 157, 279])).
% 0.14/0.48 tff(284,plain,(~product1(e_4, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.14/0.48 tff(285,plain,
% 0.14/0.48 (((~![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_4, e_1, e_2) | product1(e_4, e_1, e_1) | product1(e_4, e_1, e_4) | product1(e_4, e_1, 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_1)) | product1(e_4, e_1, e_2) | product1(e_4, e_1, e_1) | product1(e_4, e_1, e_4) | product1(e_4, e_1, e_3))),
% 0.14/0.48 inference(rewrite,[status(thm)],[])).
% 0.14/0.48 tff(286,plain,
% 0.14/0.48 ((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_1)) | (~group_element(e_4))) <=> ((~group_element(e_4)) | (~group_element(e_1)) | product1(e_4, e_1, e_2) | product1(e_4, e_1, e_1) | product1(e_4, e_1, e_4) | product1(e_4, e_1, e_3))),
% 0.14/0.48 inference(rewrite,[status(thm)],[])).
% 0.14/0.48 tff(287,plain,
% 0.14/0.48 (((~![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_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_1)) | (~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)))) | ((~group_element(e_4)) | (~group_element(e_1)) | product1(e_4, e_1, e_2) | product1(e_4, e_1, e_1) | product1(e_4, e_1, e_4) | product1(e_4, e_1, e_3)))),
% 0.14/0.48 inference(monotonicity,[status(thm)],[286])).
% 0.14/0.48 tff(288,plain,
% 0.14/0.48 (((~![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_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_1)) | (~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)))) | (~group_element(e_4)) | (~group_element(e_1)) | product1(e_4, e_1, e_2) | product1(e_4, e_1, e_1) | product1(e_4, e_1, e_4) | product1(e_4, e_1, e_3))),
% 0.14/0.48 inference(transitivity,[status(thm)],[287, 285])).
% 0.14/0.48 tff(289,plain,
% 0.14/0.48 ((~![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_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_1)) | (~group_element(e_4)))),
% 0.14/0.48 inference(quant_inst,[status(thm)],[])).
% 0.14/0.48 tff(290,plain,
% 0.14/0.48 ((~![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_4, e_1, e_2) | product1(e_4, e_1, e_1) | product1(e_4, e_1, e_4) | product1(e_4, e_1, e_3)),
% 0.14/0.48 inference(modus_ponens,[status(thm)],[289, 288])).
% 0.14/0.48 tff(291,plain,
% 0.14/0.48 (product1(e_4, e_1, e_2) | product1(e_4, e_1, e_1) | product1(e_4, e_1, e_4) | product1(e_4, e_1, e_3)),
% 0.14/0.48 inference(unit_resolution,[status(thm)],[290, 174, 226, 107])).
% 0.14/0.48 tff(292,plain,
% 0.14/0.48 (product1(e_4, e_1, e_2) | product1(e_4, e_1, e_4) | product1(e_4, e_1, e_3)),
% 0.14/0.48 inference(unit_resolution,[status(thm)],[291, 284])).
% 0.14/0.48 tff(293,plain,
% 0.14/0.48 (product1(e_4, e_1, e_2) | product1(e_4, e_1, e_3)),
% 0.14/0.48 inference(unit_resolution,[status(thm)],[292, 278])).
% 0.14/0.48 tff(294,plain,
% 0.14/0.48 (product1(e_4, e_1, e_2)),
% 0.14/0.48 inference(unit_resolution,[status(thm)],[293, 272])).
% 0.14/0.48 tff(295,assumption,(product1(e_4, e_3, e_2)), introduced(assumption)).
% 0.14/0.48 tff(296,assumption,(product1(e_4, e_1, e_2)), introduced(assumption)).
% 0.14/0.48 tff(297,plain,
% 0.14/0.48 (((~![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)))),
% 0.14/0.48 inference(rewrite,[status(thm)],[])).
% 0.14/0.48 tff(298,plain,
% 0.14/0.48 ((~![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)))),
% 0.14/0.48 inference(quant_inst,[status(thm)],[])).
% 0.14/0.48 tff(299,plain,
% 0.14/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_1, e_3) | (~product1(e_4, e_3, e_2)) | (~product1(e_4, e_1, e_2))),
% 0.14/0.49 inference(modus_ponens,[status(thm)],[298, 297])).
% 0.14/0.49 tff(300,plain,
% 0.14/0.49 ($false),
% 0.14/0.49 inference(unit_resolution,[status(thm)],[299, 128, 80, 296, 295])).
% 0.14/0.49 tff(301,plain,((~product1(e_4, e_1, e_2)) | (~product1(e_4, e_3, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.14/0.49 tff(302,plain,
% 0.14/0.49 (~product1(e_4, e_3, e_2)),
% 0.14/0.49 inference(unit_resolution,[status(thm)],[301, 294])).
% 0.14/0.49 tff(303,assumption,(~product2(e_1, e_2, e_4)), introduced(assumption)).
% 0.14/0.49 tff(304,plain,
% 0.14/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_4, e_2, e_3)) | (~product1(e_3, e_4, e_2)) | product2(e_2, 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_3)) | (~product1(e_3, e_4, e_2)) | product2(e_2, e_2, e_4))),
% 0.14/0.49 inference(rewrite,[status(thm)],[])).
% 0.14/0.49 tff(305,plain,
% 0.14/0.49 (((~product1(e_3, e_4, e_2)) | product2(e_2, e_2, e_4) | (~product1(e_4, e_2, e_3))) <=> ((~product1(e_4, e_2, e_3)) | (~product1(e_3, e_4, e_2)) | product2(e_2, e_2, e_4))),
% 0.14/0.49 inference(rewrite,[status(thm)],[])).
% 0.14/0.49 tff(306,plain,
% 0.14/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_3, e_4, e_2)) | product2(e_2, e_2, e_4) | (~product1(e_4, 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_4, e_2, e_3)) | (~product1(e_3, e_4, e_2)) | product2(e_2, e_2, e_4)))),
% 0.14/0.49 inference(monotonicity,[status(thm)],[305])).
% 0.14/0.49 tff(307,plain,
% 0.14/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_3, e_4, e_2)) | product2(e_2, e_2, e_4) | (~product1(e_4, 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_4, e_2, e_3)) | (~product1(e_3, e_4, e_2)) | product2(e_2, e_2, e_4))),
% 0.14/0.49 inference(transitivity,[status(thm)],[306, 304])).
% 0.14/0.49 tff(308,plain,
% 0.14/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_3, e_4, e_2)) | product2(e_2, e_2, e_4) | (~product1(e_4, e_2, e_3)))),
% 0.14/0.49 inference(quant_inst,[status(thm)],[])).
% 0.14/0.49 tff(309,plain,
% 0.14/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | (~product1(e_4, e_2, e_3)) | (~product1(e_3, e_4, e_2)) | product2(e_2, e_2, e_4)),
% 0.14/0.49 inference(modus_ponens,[status(thm)],[308, 307])).
% 0.14/0.49 tff(310,plain,
% 0.14/0.49 ((~product1(e_4, e_2, e_3)) | (~product1(e_3, e_4, e_2)) | product2(e_2, e_2, e_4)),
% 0.14/0.49 inference(unit_resolution,[status(thm)],[309, 167])).
% 0.14/0.49 tff(311,plain,
% 0.14/0.49 ((~product1(e_4, e_2, e_3)) | (~product1(e_3, e_4, e_2))),
% 0.14/0.49 inference(unit_resolution,[status(thm)],[310, 28])).
% 0.14/0.49 tff(312,plain,
% 0.14/0.49 (~product1(e_3, e_4, e_2)),
% 0.14/0.49 inference(unit_resolution,[status(thm)],[311, 266])).
% 0.14/0.49 tff(313,assumption,(product1(e_3, e_4, e_4)), introduced(assumption)).
% 0.14/0.49 tff(314,plain,
% 0.14/0.49 ((~equalish(e_3, e_4)) <=> (~equalish(e_3, e_4))),
% 0.14/0.49 inference(rewrite,[status(thm)],[])).
% 0.14/0.49 tff(315,axiom,(~equalish(e_3, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_4')).
% 0.14/0.49 tff(316,plain,
% 0.14/0.49 (~equalish(e_3, e_4)),
% 0.14/0.49 inference(modus_ponens,[status(thm)],[315, 314])).
% 0.14/0.49 tff(317,plain,
% 0.14/0.49 (((~![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_3, e_4, e_4)) | (~product1(e_4, 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_3, e_4, e_4)) | (~product1(e_4, e_4, e_4)))),
% 0.14/0.49 inference(rewrite,[status(thm)],[])).
% 0.14/0.49 tff(318,plain,
% 0.14/0.49 ((equalish(e_3, e_4) | (~product1(e_4, e_4, e_4)) | (~product1(e_3, e_4, e_4))) <=> (equalish(e_3, e_4) | (~product1(e_3, e_4, e_4)) | (~product1(e_4, e_4, e_4)))),
% 0.14/0.49 inference(rewrite,[status(thm)],[])).
% 0.14/0.49 tff(319,plain,
% 0.14/0.49 (((~![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_3, e_4, e_4)) | (~product1(e_4, e_4, e_4))))),
% 0.14/0.49 inference(monotonicity,[status(thm)],[318])).
% 0.14/0.49 tff(320,plain,
% 0.14/0.49 (((~![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_3, e_4, e_4)) | (~product1(e_4, e_4, e_4)))),
% 0.14/0.49 inference(transitivity,[status(thm)],[319, 317])).
% 0.14/0.49 tff(321,plain,
% 0.14/0.49 ((~![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)))),
% 0.14/0.49 inference(quant_inst,[status(thm)],[])).
% 0.14/0.49 tff(322,plain,
% 0.14/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_3, e_4) | (~product1(e_3, e_4, e_4)) | (~product1(e_4, e_4, e_4))),
% 0.14/0.49 inference(modus_ponens,[status(thm)],[321, 320])).
% 0.14/0.49 tff(323,plain,
% 0.14/0.49 ($false),
% 0.14/0.49 inference(unit_resolution,[status(thm)],[322, 316, 48, 313, 195])).
% 0.14/0.49 tff(324,plain,(~product1(e_3, e_4, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.14/0.49 tff(325,assumption,(product1(e_3, e_4, e_3)), introduced(assumption)).
% 0.14/0.49 tff(326,plain,
% 0.14/0.49 (((~![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)))),
% 0.14/0.49 inference(rewrite,[status(thm)],[])).
% 0.14/0.49 tff(327,plain,
% 0.14/0.49 ((~![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)))),
% 0.14/0.49 inference(quant_inst,[status(thm)],[])).
% 0.14/0.49 tff(328,plain,
% 0.14/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_4, e_3) | (~product1(e_3, e_3, e_3)) | (~product1(e_3, e_4, e_3))),
% 0.14/0.49 inference(modus_ponens,[status(thm)],[327, 326])).
% 0.14/0.49 tff(329,plain,
% 0.14/0.49 ($false),
% 0.14/0.49 inference(unit_resolution,[status(thm)],[328, 61, 80, 325, 69])).
% 0.14/0.49 tff(330,plain,(~product1(e_3, e_4, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.14/0.49 tff(331,plain,
% 0.14/0.49 (((~![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)) | product1(e_3, e_4, e_4) | product1(e_3, e_4, e_1) | product1(e_3, e_4, e_3) | product1(e_3, e_4, e_2) | (~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)))) | (~group_element(e_3)) | product1(e_3, e_4, e_4) | product1(e_3, e_4, e_1) | product1(e_3, e_4, e_3) | product1(e_3, e_4, e_2) | (~group_element(e_4)))),
% 0.14/0.49 inference(rewrite,[status(thm)],[])).
% 0.14/0.49 tff(332,plain,
% 0.14/0.49 ((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_4)) | (~group_element(e_3))) <=> ((~group_element(e_3)) | product1(e_3, e_4, e_4) | product1(e_3, e_4, e_1) | product1(e_3, e_4, e_3) | product1(e_3, e_4, e_2) | (~group_element(e_4)))),
% 0.14/0.49 inference(rewrite,[status(thm)],[])).
% 0.14/0.49 tff(333,plain,
% 0.14/0.49 (((~![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_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_4)) | (~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)))) | ((~group_element(e_3)) | product1(e_3, e_4, e_4) | product1(e_3, e_4, e_1) | product1(e_3, e_4, e_3) | product1(e_3, e_4, e_2) | (~group_element(e_4))))),
% 0.14/0.50 inference(monotonicity,[status(thm)],[332])).
% 0.14/0.50 tff(334,plain,
% 0.14/0.50 (((~![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_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_4)) | (~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)))) | (~group_element(e_3)) | product1(e_3, e_4, e_4) | product1(e_3, e_4, e_1) | product1(e_3, e_4, e_3) | product1(e_3, e_4, e_2) | (~group_element(e_4)))),
% 0.14/0.50 inference(transitivity,[status(thm)],[333, 331])).
% 0.14/0.50 tff(335,plain,
% 0.14/0.50 ((~![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_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_4)) | (~group_element(e_3)))),
% 0.14/0.50 inference(quant_inst,[status(thm)],[])).
% 0.14/0.50 tff(336,plain,
% 0.14/0.50 ((~![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)) | product1(e_3, e_4, e_4) | product1(e_3, e_4, e_1) | product1(e_3, e_4, e_3) | product1(e_3, e_4, e_2) | (~group_element(e_4))),
% 0.14/0.50 inference(modus_ponens,[status(thm)],[335, 334])).
% 0.14/0.50 tff(337,plain,
% 0.14/0.50 (product1(e_3, e_4, e_4) | product1(e_3, e_4, e_1) | product1(e_3, e_4, e_3) | product1(e_3, e_4, e_2)),
% 0.14/0.50 inference(unit_resolution,[status(thm)],[336, 110, 226, 107])).
% 0.14/0.50 tff(338,plain,
% 0.14/0.50 (product1(e_3, e_4, e_4) | product1(e_3, e_4, e_1) | product1(e_3, e_4, e_2)),
% 0.14/0.50 inference(unit_resolution,[status(thm)],[337, 330])).
% 0.14/0.50 tff(339,plain,
% 0.14/0.50 (product1(e_3, e_4, e_1) | product1(e_3, e_4, e_2)),
% 0.14/0.50 inference(unit_resolution,[status(thm)],[338, 324])).
% 0.14/0.50 tff(340,plain,
% 0.14/0.50 (product1(e_3, e_4, e_1)),
% 0.14/0.50 inference(unit_resolution,[status(thm)],[339, 312])).
% 0.14/0.50 tff(341,plain,
% 0.14/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | (product2(e_1, e_2, e_4) | (~product1(e_4, e_2, e_3)) | (~product1(e_3, e_4, 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_2, e_4) | (~product1(e_4, e_2, e_3)) | (~product1(e_3, e_4, e_1)))),
% 0.14/0.50 inference(rewrite,[status(thm)],[])).
% 0.14/0.50 tff(342,plain,
% 0.14/0.50 (((~product1(e_3, e_4, e_1)) | product2(e_1, e_2, e_4) | (~product1(e_4, e_2, e_3))) <=> (product2(e_1, e_2, e_4) | (~product1(e_4, e_2, e_3)) | (~product1(e_3, e_4, e_1)))),
% 0.14/0.50 inference(rewrite,[status(thm)],[])).
% 0.14/0.50 tff(343,plain,
% 0.14/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_3, e_4, e_1)) | product2(e_1, e_2, e_4) | (~product1(e_4, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | (product2(e_1, e_2, e_4) | (~product1(e_4, e_2, e_3)) | (~product1(e_3, e_4, e_1))))),
% 0.14/0.50 inference(monotonicity,[status(thm)],[342])).
% 0.14/0.50 tff(344,plain,
% 0.14/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_3, e_4, e_1)) | product2(e_1, e_2, e_4) | (~product1(e_4, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | product2(e_1, e_2, e_4) | (~product1(e_4, e_2, e_3)) | (~product1(e_3, e_4, e_1)))),
% 0.14/0.50 inference(transitivity,[status(thm)],[343, 341])).
% 0.14/0.50 tff(345,plain,
% 0.14/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_3, e_4, e_1)) | product2(e_1, e_2, e_4) | (~product1(e_4, e_2, e_3)))),
% 0.14/0.50 inference(quant_inst,[status(thm)],[])).
% 0.14/0.50 tff(346,plain,
% 0.14/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | product2(e_1, e_2, e_4) | (~product1(e_4, e_2, e_3)) | (~product1(e_3, e_4, e_1))),
% 0.14/0.50 inference(modus_ponens,[status(thm)],[345, 344])).
% 0.14/0.50 tff(347,plain,
% 0.14/0.50 ($false),
% 0.14/0.50 inference(unit_resolution,[status(thm)],[346, 167, 340, 266, 303])).
% 0.14/0.50 tff(348,plain,(product2(e_1, e_2, e_4) | (~product1(e_4, e_2, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.14/0.50 tff(349,plain,
% 0.14/0.50 (product2(e_1, e_2, e_4)),
% 0.14/0.50 inference(unit_resolution,[status(thm)],[348, 264])).
% 0.14/0.50 tff(350,assumption,(product2(e_1, e_2, e_4)), introduced(assumption)).
% 0.14/0.50 tff(351,assumption,(product2(e_1, e_2, e_3)), introduced(assumption)).
% 0.14/0.50 tff(352,plain,
% 0.14/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))) | (equalish(e_3, e_4) | (~product2(e_1, e_2, e_4)) | (~product2(e_1, e_2, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))) | equalish(e_3, e_4) | (~product2(e_1, e_2, e_4)) | (~product2(e_1, e_2, e_3)))),
% 0.14/0.50 inference(rewrite,[status(thm)],[])).
% 0.14/0.50 tff(353,plain,
% 0.14/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))) | (equalish(e_3, e_4) | (~product2(e_1, e_2, e_4)) | (~product2(e_1, e_2, e_3)))),
% 0.14/0.50 inference(quant_inst,[status(thm)],[])).
% 0.14/0.50 tff(354,plain,
% 0.14/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))) | equalish(e_3, e_4) | (~product2(e_1, e_2, e_4)) | (~product2(e_1, e_2, e_3))),
% 0.14/0.50 inference(modus_ponens,[status(thm)],[353, 352])).
% 0.14/0.50 tff(355,plain,
% 0.14/0.50 ($false),
% 0.14/0.50 inference(unit_resolution,[status(thm)],[354, 316, 20, 351, 350])).
% 0.14/0.50 tff(356,plain,((~product2(e_1, e_2, e_3)) | (~product2(e_1, e_2, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.14/0.50 tff(357,plain,
% 0.14/0.50 (~product2(e_1, e_2, e_3)),
% 0.14/0.50 inference(unit_resolution,[status(thm)],[356, 349])).
% 0.14/0.50 tff(358,assumption,(~product2(e_1, e_2, e_3)), introduced(assumption)).
% 0.14/0.50 tff(359,assumption,(product1(e_4, e_3, e_1)), introduced(assumption)).
% 0.14/0.50 tff(360,plain,
% 0.14/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | (product2(e_1, e_2, e_3) | (~product1(e_3, e_2, 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)))) | product2(e_1, e_2, e_3) | (~product1(e_3, e_2, e_4)) | (~product1(e_4, e_3, e_1)))),
% 0.14/0.50 inference(rewrite,[status(thm)],[])).
% 0.14/0.50 tff(361,plain,
% 0.14/0.50 (((~product1(e_4, e_3, e_1)) | product2(e_1, e_2, e_3) | (~product1(e_3, e_2, e_4))) <=> (product2(e_1, e_2, e_3) | (~product1(e_3, e_2, e_4)) | (~product1(e_4, e_3, e_1)))),
% 0.14/0.50 inference(rewrite,[status(thm)],[])).
% 0.14/0.50 tff(362,plain,
% 0.14/0.50 (((~![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)) | product2(e_1, e_2, e_3) | (~product1(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)))) | (product2(e_1, e_2, e_3) | (~product1(e_3, e_2, e_4)) | (~product1(e_4, e_3, e_1))))),
% 0.14/0.50 inference(monotonicity,[status(thm)],[361])).
% 0.14/0.50 tff(363,plain,
% 0.14/0.50 (((~![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)) | product2(e_1, e_2, e_3) | (~product1(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)))) | product2(e_1, e_2, e_3) | (~product1(e_3, e_2, e_4)) | (~product1(e_4, e_3, e_1)))),
% 0.14/0.50 inference(transitivity,[status(thm)],[362, 360])).
% 0.14/0.50 tff(364,plain,
% 0.14/0.50 ((~![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)) | product2(e_1, e_2, e_3) | (~product1(e_3, e_2, e_4)))),
% 0.14/0.50 inference(quant_inst,[status(thm)],[])).
% 0.14/0.50 tff(365,plain,
% 0.14/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | product2(e_1, e_2, e_3) | (~product1(e_3, e_2, e_4)) | (~product1(e_4, e_3, e_1))),
% 0.14/0.50 inference(modus_ponens,[status(thm)],[364, 363])).
% 0.14/0.50 tff(366,plain,
% 0.14/0.50 (product2(e_1, e_2, e_3) | (~product1(e_3, e_2, e_4)) | (~product1(e_4, e_3, e_1))),
% 0.14/0.50 inference(unit_resolution,[status(thm)],[365, 167])).
% 0.14/0.50 tff(367,plain,
% 0.14/0.50 (~product1(e_3, e_2, e_4)),
% 0.14/0.50 inference(unit_resolution,[status(thm)],[366, 359, 358])).
% 0.14/0.50 tff(368,plain,
% 0.14/0.50 (product1(e_3, e_2, e_1)),
% 0.14/0.50 inference(unit_resolution,[status(thm)],[122, 367])).
% 0.14/0.50 tff(369,assumption,(product1(e_3, e_4, e_1)), introduced(assumption)).
% 0.14/0.50 tff(370,plain,
% 0.14/0.50 (((~![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_2, e_1)) | (~product1(e_3, e_4, e_1)))),
% 0.14/0.50 inference(rewrite,[status(thm)],[])).
% 0.14/0.50 tff(371,plain,
% 0.14/0.50 ((~![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)))),
% 0.14/0.50 inference(quant_inst,[status(thm)],[])).
% 0.14/0.50 tff(372,plain,
% 0.14/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_4, e_2) | (~product1(e_3, e_2, e_1)) | (~product1(e_3, e_4, e_1))),
% 0.14/0.50 inference(modus_ponens,[status(thm)],[371, 370])).
% 0.14/0.50 tff(373,plain,
% 0.14/0.50 ($false),
% 0.14/0.50 inference(unit_resolution,[status(thm)],[372, 23, 80, 369, 58])).
% 0.14/0.50 tff(374,plain,((~product1(e_3, e_4, e_1)) | (~product1(e_3, e_2, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.14/0.50 tff(375,plain,
% 0.14/0.50 (~product1(e_3, e_4, e_1)),
% 0.14/0.50 inference(unit_resolution,[status(thm)],[374, 368])).
% 0.14/0.50 tff(376,plain,
% 0.14/0.50 (((~![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)))),
% 0.14/0.50 inference(rewrite,[status(thm)],[])).
% 0.14/0.50 tff(377,plain,
% 0.14/0.50 ((~![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)))),
% 0.14/0.50 inference(quant_inst,[status(thm)],[])).
% 0.14/0.50 tff(378,plain,
% 0.14/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_3, e_2) | (~product1(e_4, e_2, e_1)) | (~product1(e_4, e_3, e_1))),
% 0.14/0.50 inference(modus_ponens,[status(thm)],[377, 376])).
% 0.14/0.50 tff(379,plain,
% 0.14/0.50 ($false),
% 0.14/0.50 inference(unit_resolution,[status(thm)],[378, 92, 80, 57, 359])).
% 0.14/0.50 tff(380,plain,((~product1(e_4, e_3, e_1)) | (~product1(e_4, e_2, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.14/0.50 tff(381,plain,
% 0.14/0.50 (~product1(e_4, e_2, e_1)),
% 0.14/0.50 inference(unit_resolution,[status(thm)],[380, 359])).
% 0.14/0.50 tff(382,plain,
% 0.14/0.50 (product1(e_4, e_2, e_3)),
% 0.14/0.50 inference(unit_resolution,[status(thm)],[263, 381])).
% 0.14/0.50 tff(383,plain,
% 0.14/0.50 (~product1(e_3, e_4, e_2)),
% 0.14/0.50 inference(unit_resolution,[status(thm)],[311, 382])).
% 0.14/0.50 tff(384,plain,
% 0.14/0.50 ($false),
% 0.14/0.50 inference(unit_resolution,[status(thm)],[339, 383, 375])).
% 0.14/0.50 tff(385,plain,((~product1(e_4, e_3, e_1)) | product2(e_1, e_2, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.14/0.50 tff(386,plain,
% 0.14/0.50 (~product1(e_4, e_3, e_1)),
% 0.14/0.50 inference(unit_resolution,[status(thm)],[385, 357])).
% 0.14/0.50 tff(387,assumption,(product1(e_4, e_3, e_4)), introduced(assumption)).
% 0.14/0.50 tff(388,plain,
% 0.14/0.50 (((~![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)))),
% 0.14/0.51 inference(rewrite,[status(thm)],[])).
% 0.14/0.51 tff(389,plain,
% 0.14/0.51 ((~![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)))),
% 0.14/0.51 inference(quant_inst,[status(thm)],[])).
% 0.14/0.51 tff(390,plain,
% 0.14/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_3, e_4) | (~product1(e_4, e_4, e_4)) | (~product1(e_4, e_3, e_4))),
% 0.14/0.51 inference(modus_ponens,[status(thm)],[389, 388])).
% 0.14/0.51 tff(391,plain,
% 0.14/0.51 ($false),
% 0.14/0.51 inference(unit_resolution,[status(thm)],[390, 316, 80, 387, 195])).
% 0.14/0.51 tff(392,plain,(~product1(e_4, e_3, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.14/0.51 tff(393,assumption,(product1(e_4, e_3, e_3)), introduced(assumption)).
% 0.14/0.51 tff(394,plain,
% 0.14/0.51 (((~![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)))),
% 0.14/0.51 inference(rewrite,[status(thm)],[])).
% 0.14/0.51 tff(395,plain,
% 0.14/0.51 ((~![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)))),
% 0.14/0.51 inference(quant_inst,[status(thm)],[])).
% 0.14/0.51 tff(396,plain,
% 0.14/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_4, e_3) | (~product1(e_3, e_3, e_3)) | (~product1(e_4, e_3, e_3))),
% 0.14/0.51 inference(modus_ponens,[status(thm)],[395, 394])).
% 0.14/0.51 tff(397,plain,
% 0.14/0.51 ($false),
% 0.14/0.51 inference(unit_resolution,[status(thm)],[396, 61, 48, 69, 393])).
% 0.14/0.51 tff(398,plain,(~product1(e_4, e_3, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.14/0.51 tff(399,plain,
% 0.14/0.51 (((~![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_4)) | product1(e_4, e_3, e_3) | product1(e_4, e_3, e_4) | product1(e_4, e_3, e_2) | product1(e_4, e_3, 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_4)) | product1(e_4, e_3, e_3) | product1(e_4, e_3, e_4) | product1(e_4, e_3, e_2) | product1(e_4, e_3, e_1))),
% 0.14/0.51 inference(rewrite,[status(thm)],[])).
% 0.14/0.51 tff(400,plain,
% 0.14/0.51 ((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))) <=> ((~group_element(e_3)) | (~group_element(e_4)) | product1(e_4, e_3, e_3) | product1(e_4, e_3, e_4) | product1(e_4, e_3, e_2) | product1(e_4, e_3, e_1))),
% 0.14/0.51 inference(rewrite,[status(thm)],[])).
% 0.14/0.51 tff(401,plain,
% 0.14/0.51 (((~![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)))) | ((~group_element(e_3)) | (~group_element(e_4)) | product1(e_4, e_3, e_3) | product1(e_4, e_3, e_4) | product1(e_4, e_3, e_2) | product1(e_4, e_3, e_1)))),
% 0.14/0.51 inference(monotonicity,[status(thm)],[400])).
% 0.14/0.51 tff(402,plain,
% 0.14/0.51 (((~![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)))) | (~group_element(e_3)) | (~group_element(e_4)) | product1(e_4, e_3, e_3) | product1(e_4, e_3, e_4) | product1(e_4, e_3, e_2) | product1(e_4, e_3, e_1))),
% 0.14/0.51 inference(transitivity,[status(thm)],[401, 399])).
% 0.14/0.51 tff(403,plain,
% 0.14/0.51 ((~![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)))),
% 0.14/0.51 inference(quant_inst,[status(thm)],[])).
% 0.14/0.51 tff(404,plain,
% 0.14/0.51 ((~![Y: $i, X: $i] : (product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_3)) | (~group_element(e_4)) | product1(e_4, e_3, e_3) | product1(e_4, e_3, e_4) | product1(e_4, e_3, e_2) | product1(e_4, e_3, e_1)),
% 0.14/0.51 inference(modus_ponens,[status(thm)],[403, 402])).
% 0.14/0.51 tff(405,plain,
% 0.14/0.51 (product1(e_4, e_3, e_3) | product1(e_4, e_3, e_4) | product1(e_4, e_3, e_2) | product1(e_4, e_3, e_1)),
% 0.14/0.51 inference(unit_resolution,[status(thm)],[404, 110, 226, 107])).
% 0.14/0.51 tff(406,plain,
% 0.14/0.51 (product1(e_4, e_3, e_4) | product1(e_4, e_3, e_2) | product1(e_4, e_3, e_1)),
% 0.14/0.51 inference(unit_resolution,[status(thm)],[405, 398])).
% 0.14/0.51 tff(407,plain,
% 0.14/0.51 (product1(e_4, e_3, e_2) | product1(e_4, e_3, e_1)),
% 0.14/0.51 inference(unit_resolution,[status(thm)],[406, 392])).
% 0.14/0.51 tff(408,plain,
% 0.14/0.51 ($false),
% 0.14/0.51 inference(unit_resolution,[status(thm)],[407, 386, 302])).
% 0.14/0.51 % SZS output end Proof
%------------------------------------------------------------------------------