TSTP Solution File: GRP124-1.004 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP124-1.004 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n023.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 22:25:58 EDT 2022
% Result : Unsatisfiable 0.20s 0.45s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GRP124-1.004 : TPTP v8.1.0. Released v1.2.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 31 15:14:34 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.20/0.45 % SZS status Unsatisfiable
% 0.20/0.45 % SZS output start Proof
% 0.20/0.45 tff(product_type, type, (
% 0.20/0.45 product: ( $i * $i * $i ) > $o)).
% 0.20/0.45 tff(e_4_type, type, (
% 0.20/0.45 e_4: $i)).
% 0.20/0.45 tff(e_2_type, type, (
% 0.20/0.45 e_2: $i)).
% 0.20/0.45 tff(e_1_type, type, (
% 0.20/0.45 e_1: $i)).
% 0.20/0.45 tff(e_3_type, type, (
% 0.20/0.45 e_3: $i)).
% 0.20/0.45 tff(equalish_type, type, (
% 0.20/0.45 equalish: ( $i * $i ) > $o)).
% 0.20/0.45 tff(group_element_type, type, (
% 0.20/0.45 group_element: $i > $o)).
% 0.20/0.45 tff(1,assumption,(product(e_4, e_3, e_3)), introduced(assumption)).
% 0.20/0.45 tff(2,assumption,(product(e_4, e_1, e_3)), introduced(assumption)).
% 0.20/0.45 tff(3,plain,
% 0.20/0.45 (^[W: $i, Z: $i, Y: $i, X: $i] : refl((equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y))) <=> (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(4,plain,
% 0.20/0.45 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.45 tff(5,plain,
% 0.20/0.45 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(6,plain,
% 0.20/0.45 (^[W: $i, Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite(((~product(X, W, Y)) | (~product(X, Z, Y))) <=> ((~product(X, Z, Y)) | (~product(X, W, Y)))), ((((~product(X, W, Y)) | (~product(X, Z, Y))) | equalish(W, Z)) <=> (((~product(X, Z, Y)) | (~product(X, W, Y))) | equalish(W, Z)))), rewrite((((~product(X, Z, Y)) | (~product(X, W, Y))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))), ((((~product(X, W, Y)) | (~product(X, Z, Y))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(7,plain,
% 0.20/0.45 (![W: $i, Z: $i, Y: $i, X: $i] : (((~product(X, W, Y)) | (~product(X, Z, Y))) | equalish(W, Z)) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[6])).
% 0.20/0.45 tff(8,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product(X, W, Y)) | (~product(X, Z, Y))) | equalish(W, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','product_right_cancellation')).
% 0.20/0.45 tff(9,plain,
% 0.20/0.45 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.20/0.45 tff(10,plain,
% 0.20/0.45 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.20/0.45 tff(11,plain,(
% 0.20/0.45 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.45 inference(skolemize,[status(sab)],[10])).
% 0.20/0.45 tff(12,plain,
% 0.20/0.45 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.20/0.45 tff(13,plain,
% 0.20/0.45 ((~equalish(e_1, e_3)) <=> (~equalish(e_1, e_3))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(14,axiom,(~equalish(e_1, e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_1_is_not_e_3')).
% 0.20/0.45 tff(15,plain,
% 0.20/0.45 (~equalish(e_1, e_3)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.20/0.45 tff(16,plain,
% 0.20/0.45 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_3) | (~product(e_4, e_1, e_3)) | (~product(e_4, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_3) | (~product(e_4, e_1, e_3)) | (~product(e_4, e_3, e_3)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(17,plain,
% 0.20/0.45 ((equalish(e_1, e_3) | (~product(e_4, e_3, e_3)) | (~product(e_4, e_1, e_3))) <=> (equalish(e_1, e_3) | (~product(e_4, e_1, e_3)) | (~product(e_4, e_3, e_3)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(18,plain,
% 0.20/0.45 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_3) | (~product(e_4, e_3, e_3)) | (~product(e_4, e_1, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_3) | (~product(e_4, e_1, e_3)) | (~product(e_4, e_3, e_3))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[17])).
% 0.20/0.46 tff(19,plain,
% 0.20/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_3) | (~product(e_4, e_3, e_3)) | (~product(e_4, e_1, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_3) | (~product(e_4, e_1, e_3)) | (~product(e_4, e_3, e_3)))),
% 0.20/0.46 inference(transitivity,[status(thm)],[18, 16])).
% 0.20/0.46 tff(20,plain,
% 0.20/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_3) | (~product(e_4, e_3, e_3)) | (~product(e_4, e_1, e_3)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(21,plain,
% 0.20/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_3) | (~product(e_4, e_1, e_3)) | (~product(e_4, e_3, e_3))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.20/0.46 tff(22,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[21, 15, 12, 1, 2])).
% 0.20/0.46 tff(23,plain,((~product(e_4, e_1, e_3)) | (~product(e_4, e_3, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(24,plain,
% 0.20/0.46 (~product(e_4, e_1, e_3)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[23, 1])).
% 0.20/0.46 tff(25,assumption,(~product(e_3, e_3, e_3)), introduced(assumption)).
% 0.20/0.46 tff(26,plain,
% 0.20/0.46 (^[X: $i] : refl(product(X, X, X) <=> product(X, X, X))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(27,plain,
% 0.20/0.46 (![X: $i] : product(X, X, X) <=> ![X: $i] : product(X, X, X)),
% 0.20/0.46 inference(quant_intro,[status(thm)],[26])).
% 0.20/0.46 tff(28,plain,
% 0.20/0.46 (![X: $i] : product(X, X, X) <=> ![X: $i] : product(X, X, X)),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(29,axiom,(![X: $i] : product(X, X, X)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','product_idempotence')).
% 0.20/0.46 tff(30,plain,
% 0.20/0.46 (![X: $i] : product(X, X, X)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.20/0.46 tff(31,plain,(
% 0.20/0.46 ![X: $i] : product(X, X, X)),
% 0.20/0.46 inference(skolemize,[status(sab)],[30])).
% 0.20/0.46 tff(32,plain,
% 0.20/0.46 (![X: $i] : product(X, X, X)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.20/0.46 tff(33,plain,
% 0.20/0.46 ((~![X: $i] : product(X, X, X)) | product(e_3, e_3, e_3)),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(34,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[33, 32, 25])).
% 0.20/0.46 tff(35,plain,(product(e_3, e_3, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(36,assumption,(product(e_4, e_1, e_2)), introduced(assumption)).
% 0.20/0.46 tff(37,plain,
% 0.20/0.46 ((~![X: $i] : product(X, X, X)) | product(e_4, e_4, e_4)),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(38,plain,
% 0.20/0.46 (product(e_4, e_4, e_4)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[37, 32])).
% 0.20/0.46 tff(39,plain,
% 0.20/0.46 (^[Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : refl(((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2)) <=> ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2)))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(40,plain,
% 0.20/0.46 (![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2)) <=> ![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[39])).
% 0.20/0.46 tff(41,plain,
% 0.20/0.46 (![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2)) <=> ![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(42,plain,
% 0.20/0.46 (^[Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~product(X1, Y1, Z1)) | (~product(X2, Y2, Z1))) | (~product(Z2, X1, Y1))) <=> ((~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)))), (((((~product(X1, Y1, Z1)) | (~product(X2, Y2, Z1))) | (~product(Z2, X1, Y1))) | (~product(Z2, X2, Y2))) <=> (((~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1))) | (~product(Z2, X2, Y2))))), rewrite((((~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1))) | (~product(Z2, X2, Y2))) <=> ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)))), (((((~product(X1, Y1, Z1)) | (~product(X2, Y2, Z1))) | (~product(Z2, X1, Y1))) | (~product(Z2, X2, Y2))) <=> ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1))))), ((((((~product(X1, Y1, Z1)) | (~product(X2, Y2, Z1))) | (~product(Z2, X1, Y1))) | (~product(Z2, X2, Y2))) | equalish(Y1, Y2)) <=> (((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1))) | equalish(Y1, Y2)))), rewrite((((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1))) | equalish(Y1, Y2)) <=> ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))), ((((((~product(X1, Y1, Z1)) | (~product(X2, Y2, Z1))) | (~product(Z2, X1, Y1))) | (~product(Z2, X2, Y2))) | equalish(Y1, Y2)) <=> ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(43,plain,
% 0.20/0.46 (![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : (((((~product(X1, Y1, Z1)) | (~product(X2, Y2, Z1))) | (~product(Z2, X1, Y1))) | (~product(Z2, X2, Y2))) | equalish(Y1, Y2)) <=> ![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[42])).
% 0.20/0.46 tff(44,axiom,(![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : (((((~product(X1, Y1, Z1)) | (~product(X2, Y2, Z1))) | (~product(Z2, X1, Y1))) | (~product(Z2, X2, Y2))) | equalish(Y1, Y2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','qg2_2')).
% 0.20/0.46 tff(45,plain,
% 0.20/0.46 (![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.20/0.46 tff(46,plain,
% 0.20/0.46 (![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.20/0.46 tff(47,plain,(
% 0.20/0.46 ![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))),
% 0.20/0.46 inference(skolemize,[status(sab)],[46])).
% 0.20/0.46 tff(48,plain,
% 0.20/0.46 (![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[47, 40])).
% 0.20/0.46 tff(49,plain,
% 0.20/0.46 ((~equalish(e_2, e_4)) <=> (~equalish(e_2, e_4))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(50,axiom,(~equalish(e_2, e_4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_is_not_e_4')).
% 0.20/0.46 tff(51,plain,
% 0.20/0.46 (~equalish(e_2, e_4)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.20/0.46 tff(52,plain,
% 0.20/0.46 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_2, e_4) | (~product(e_1, e_2, e_4)) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_1, e_2)))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_2, e_4) | (~product(e_1, e_2, e_4)) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_1, e_2)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(53,plain,
% 0.20/0.46 (((~product(e_4, e_4, e_4)) | (~product(e_4, e_1, e_2)) | (~product(e_4, e_4, e_4)) | (~product(e_1, e_2, e_4)) | equalish(e_2, e_4)) <=> (equalish(e_2, e_4) | (~product(e_1, e_2, e_4)) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_1, e_2)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(54,plain,
% 0.20/0.46 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_4, e_4, e_4)) | (~product(e_4, e_1, e_2)) | (~product(e_4, e_4, e_4)) | (~product(e_1, e_2, e_4)) | equalish(e_2, e_4))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_2, e_4) | (~product(e_1, e_2, e_4)) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_1, e_2))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[53])).
% 0.20/0.46 tff(55,plain,
% 0.20/0.46 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_4, e_4, e_4)) | (~product(e_4, e_1, e_2)) | (~product(e_4, e_4, e_4)) | (~product(e_1, e_2, e_4)) | equalish(e_2, e_4))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_2, e_4) | (~product(e_1, e_2, e_4)) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_1, e_2)))),
% 0.20/0.46 inference(transitivity,[status(thm)],[54, 52])).
% 0.20/0.46 tff(56,plain,
% 0.20/0.46 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_4, e_4, e_4)) | (~product(e_4, e_1, e_2)) | (~product(e_4, e_4, e_4)) | (~product(e_1, e_2, e_4)) | equalish(e_2, e_4))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(57,plain,
% 0.20/0.46 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_2, e_4) | (~product(e_1, e_2, e_4)) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_1, e_2))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.20/0.46 tff(58,plain,
% 0.20/0.46 (~product(e_1, e_2, e_4)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[57, 51, 48, 38, 36])).
% 0.20/0.46 tff(59,assumption,(product(e_1, e_2, e_2)), introduced(assumption)).
% 0.20/0.46 tff(60,plain,
% 0.20/0.46 ((~![X: $i] : product(X, X, X)) | product(e_2, e_2, e_2)),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(61,plain,
% 0.20/0.46 (product(e_2, e_2, e_2)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[60, 32])).
% 0.20/0.46 tff(62,plain,
% 0.20/0.46 (^[W: $i, Z: $i, Y: $i, X: $i] : refl((equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X))) <=> (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(63,plain,
% 0.20/0.46 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[62])).
% 0.20/0.46 tff(64,plain,
% 0.20/0.46 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(65,plain,
% 0.20/0.46 (^[W: $i, Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite(((~product(W, Y, X)) | (~product(Z, Y, X))) <=> ((~product(Z, Y, X)) | (~product(W, Y, X)))), ((((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z)) <=> (((~product(Z, Y, X)) | (~product(W, Y, X))) | equalish(W, Z)))), rewrite((((~product(Z, Y, X)) | (~product(W, Y, X))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))), ((((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(66,plain,
% 0.20/0.47 (![W: $i, Z: $i, Y: $i, X: $i] : (((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z)) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[65])).
% 0.20/0.47 tff(67,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','product_left_cancellation')).
% 0.20/0.47 tff(68,plain,
% 0.20/0.47 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.20/0.47 tff(69,plain,
% 0.20/0.47 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.20/0.47 tff(70,plain,(
% 0.20/0.47 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.47 inference(skolemize,[status(sab)],[69])).
% 0.20/0.47 tff(71,plain,
% 0.20/0.47 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[70, 63])).
% 0.20/0.47 tff(72,plain,
% 0.20/0.47 ((~equalish(e_1, e_2)) <=> (~equalish(e_1, e_2))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(73,axiom,(~equalish(e_1, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_1_is_not_e_2')).
% 0.20/0.47 tff(74,plain,
% 0.20/0.47 (~equalish(e_1, e_2)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.20/0.47 tff(75,plain,
% 0.20/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_1, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_1, e_2, e_2)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(76,plain,
% 0.20/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_1, e_2, e_2)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(77,plain,
% 0.20/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_1, e_2, e_2))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.20/0.47 tff(78,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[77, 74, 71, 61, 59])).
% 0.20/0.47 tff(79,plain,(~product(e_1, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(80,assumption,(product(e_1, e_2, e_1)), introduced(assumption)).
% 0.20/0.47 tff(81,plain,
% 0.20/0.47 ((~![X: $i] : product(X, X, X)) | product(e_1, e_1, e_1)),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(82,plain,
% 0.20/0.47 (product(e_1, e_1, e_1)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[81, 32])).
% 0.20/0.47 tff(83,plain,
% 0.20/0.47 ((~equalish(e_2, e_1)) <=> (~equalish(e_2, e_1))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(84,axiom,(~equalish(e_2, e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_is_not_e_1')).
% 0.20/0.47 tff(85,plain,
% 0.20/0.47 (~equalish(e_2, e_1)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.20/0.47 tff(86,plain,
% 0.20/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_2, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_2, e_1)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(87,plain,
% 0.20/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_2, e_1)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(88,plain,
% 0.20/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_2, e_1))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.20/0.47 tff(89,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[88, 85, 12, 82, 80])).
% 0.20/0.47 tff(90,plain,(~product(e_1, e_2, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(91,plain,
% 0.20/0.47 (^[Y: $i, X: $i] : refl((product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) <=> (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(92,plain,
% 0.20/0.47 (![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) <=> ![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[91])).
% 0.20/0.47 tff(93,plain,
% 0.20/0.47 (![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) <=> ![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(94,plain,
% 0.20/0.47 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) <=> (product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))), (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) <=> ((product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_2)))), rewrite(((product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_2)) <=> (product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))), (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) <=> (product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))))), ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) <=> ((product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_3)))), rewrite(((product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_3)) <=> (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))), ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) <=> (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))))), (((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) | product(X, Y, e_4)) <=> ((product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_4)))), rewrite(((product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_4)) <=> (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))), (((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) | product(X, Y, e_4)) <=> (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(95,plain,
% 0.20/0.47 (![Y: $i, X: $i] : ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) | product(X, Y, e_4)) <=> ![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[94])).
% 0.20/0.47 tff(96,axiom,(![Y: $i, X: $i] : ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) | product(X, Y, e_4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','product_total_function1')).
% 0.20/0.47 tff(97,plain,
% 0.20/0.47 (![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.20/0.47 tff(98,plain,
% 0.20/0.47 (![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[97, 93])).
% 0.20/0.47 tff(99,plain,(
% 0.20/0.47 ![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.20/0.47 inference(skolemize,[status(sab)],[98])).
% 0.20/0.47 tff(100,plain,
% 0.20/0.47 (![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[99, 92])).
% 0.20/0.47 tff(101,plain,
% 0.20/0.47 (group_element(e_2) <=> group_element(e_2)),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(102,axiom,(group_element(e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_2')).
% 0.20/0.47 tff(103,plain,
% 0.20/0.47 (group_element(e_2)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.20/0.47 tff(104,plain,
% 0.20/0.47 (group_element(e_1) <=> group_element(e_1)),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(105,axiom,(group_element(e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_1')).
% 0.20/0.47 tff(106,plain,
% 0.20/0.47 (group_element(e_1)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.20/0.47 tff(107,plain,
% 0.20/0.47 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_2)) | product(e_1, e_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_1) | product(e_1, e_2, e_2) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_2)) | product(e_1, e_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_1) | product(e_1, e_2, e_2) | (~group_element(e_1)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(108,plain,
% 0.20/0.47 ((product(e_1, e_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_1))) <=> ((~group_element(e_2)) | product(e_1, e_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_1) | product(e_1, e_2, e_2) | (~group_element(e_1)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(109,plain,
% 0.20/0.47 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_2)) | product(e_1, e_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_1) | product(e_1, e_2, e_2) | (~group_element(e_1))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[108])).
% 0.20/0.47 tff(110,plain,
% 0.20/0.47 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_2)) | product(e_1, e_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_1) | product(e_1, e_2, e_2) | (~group_element(e_1)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[109, 107])).
% 0.20/0.48 tff(111,plain,
% 0.20/0.48 ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_1)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(112,plain,
% 0.20/0.48 ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_2)) | product(e_1, e_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_1) | product(e_1, e_2, e_2) | (~group_element(e_1))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.20/0.48 tff(113,plain,
% 0.20/0.48 (product(e_1, e_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[112, 106, 103, 100, 90])).
% 0.20/0.48 tff(114,plain,
% 0.20/0.48 (product(e_1, e_2, e_4) | product(e_1, e_2, e_3)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[113, 79])).
% 0.20/0.48 tff(115,plain,
% 0.20/0.48 (product(e_1, e_2, e_3)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[114, 58])).
% 0.20/0.48 tff(116,plain,
% 0.20/0.48 ((~equalish(e_3, e_2)) <=> (~equalish(e_3, e_2))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(117,axiom,(~equalish(e_3, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_3_is_not_e_2')).
% 0.20/0.48 tff(118,plain,
% 0.20/0.48 (~equalish(e_3, e_2)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.20/0.48 tff(119,plain,
% 0.20/0.48 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_3, e_2) | (~product(e_1, e_2, e_3)) | (~product(e_4, e_3, e_3)) | (~product(e_4, e_1, e_2)) | (~product(e_3, e_3, e_3)))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_3, e_2) | (~product(e_1, e_2, e_3)) | (~product(e_4, e_3, e_3)) | (~product(e_4, e_1, e_2)) | (~product(e_3, e_3, e_3)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(120,plain,
% 0.20/0.48 (((~product(e_4, e_1, e_2)) | (~product(e_4, e_3, e_3)) | (~product(e_1, e_2, e_3)) | (~product(e_3, e_3, e_3)) | equalish(e_3, e_2)) <=> (equalish(e_3, e_2) | (~product(e_1, e_2, e_3)) | (~product(e_4, e_3, e_3)) | (~product(e_4, e_1, e_2)) | (~product(e_3, e_3, e_3)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(121,plain,
% 0.20/0.48 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_4, e_1, e_2)) | (~product(e_4, e_3, e_3)) | (~product(e_1, e_2, e_3)) | (~product(e_3, e_3, e_3)) | equalish(e_3, e_2))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_3, e_2) | (~product(e_1, e_2, e_3)) | (~product(e_4, e_3, e_3)) | (~product(e_4, e_1, e_2)) | (~product(e_3, e_3, e_3))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[120])).
% 0.20/0.48 tff(122,plain,
% 0.20/0.48 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_4, e_1, e_2)) | (~product(e_4, e_3, e_3)) | (~product(e_1, e_2, e_3)) | (~product(e_3, e_3, e_3)) | equalish(e_3, e_2))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_3, e_2) | (~product(e_1, e_2, e_3)) | (~product(e_4, e_3, e_3)) | (~product(e_4, e_1, e_2)) | (~product(e_3, e_3, e_3)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[121, 119])).
% 0.20/0.48 tff(123,plain,
% 0.20/0.48 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_4, e_1, e_2)) | (~product(e_4, e_3, e_3)) | (~product(e_1, e_2, e_3)) | (~product(e_3, e_3, e_3)) | equalish(e_3, e_2))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(124,plain,
% 0.20/0.48 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_3, e_2) | (~product(e_1, e_2, e_3)) | (~product(e_4, e_3, e_3)) | (~product(e_4, e_1, e_2)) | (~product(e_3, e_3, e_3))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.20/0.48 tff(125,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[124, 118, 48, 1, 36, 115, 35])).
% 0.20/0.48 tff(126,plain,((~product(e_4, e_3, e_3)) | (~product(e_4, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(127,plain,
% 0.20/0.48 (~product(e_4, e_1, e_2)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[126, 1])).
% 0.20/0.48 tff(128,assumption,(product(e_4, e_1, e_4)), introduced(assumption)).
% 0.20/0.48 tff(129,plain,
% 0.20/0.48 ((~equalish(e_1, e_4)) <=> (~equalish(e_1, e_4))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(130,axiom,(~equalish(e_1, e_4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_1_is_not_e_4')).
% 0.20/0.48 tff(131,plain,
% 0.20/0.48 (~equalish(e_1, e_4)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.20/0.48 tff(132,plain,
% 0.20/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_4) | (~product(e_4, e_1, e_4)) | (~product(e_4, e_4, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_4) | (~product(e_4, e_1, e_4)) | (~product(e_4, e_4, e_4)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(133,plain,
% 0.20/0.48 ((equalish(e_1, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_1, e_4))) <=> (equalish(e_1, e_4) | (~product(e_4, e_1, e_4)) | (~product(e_4, e_4, e_4)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(134,plain,
% 0.20/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_1, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_4) | (~product(e_4, e_1, e_4)) | (~product(e_4, e_4, e_4))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[133])).
% 0.20/0.48 tff(135,plain,
% 0.20/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_1, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_4) | (~product(e_4, e_1, e_4)) | (~product(e_4, e_4, e_4)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[134, 132])).
% 0.20/0.48 tff(136,plain,
% 0.20/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_1, e_4)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(137,plain,
% 0.20/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_4) | (~product(e_4, e_1, e_4)) | (~product(e_4, e_4, e_4))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.20/0.48 tff(138,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[137, 131, 12, 38, 128])).
% 0.20/0.48 tff(139,plain,(~product(e_4, e_1, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(140,assumption,(product(e_4, e_1, e_1)), introduced(assumption)).
% 0.20/0.48 tff(141,plain,
% 0.20/0.48 ((~equalish(e_4, e_1)) <=> (~equalish(e_4, e_1))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(142,axiom,(~equalish(e_4, e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_4_is_not_e_1')).
% 0.20/0.48 tff(143,plain,
% 0.20/0.48 (~equalish(e_4, e_1)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.20/0.48 tff(144,plain,
% 0.20/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_1) | (~product(e_4, e_1, e_1)) | (~product(e_1, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_1) | (~product(e_4, e_1, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(145,plain,
% 0.20/0.48 ((equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_4, e_1, e_1))) <=> (equalish(e_4, e_1) | (~product(e_4, e_1, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(146,plain,
% 0.20/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_4, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_1) | (~product(e_4, e_1, e_1)) | (~product(e_1, e_1, e_1))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[145])).
% 0.20/0.48 tff(147,plain,
% 0.20/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_4, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_1) | (~product(e_4, e_1, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[146, 144])).
% 0.20/0.48 tff(148,plain,
% 0.20/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_4, e_1, e_1)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(149,plain,
% 0.20/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_1) | (~product(e_4, e_1, e_1)) | (~product(e_1, e_1, e_1))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.20/0.48 tff(150,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[149, 143, 71, 82, 140])).
% 0.20/0.48 tff(151,plain,(~product(e_4, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(152,plain,
% 0.20/0.48 (group_element(e_4) <=> group_element(e_4)),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(153,axiom,(group_element(e_4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_4')).
% 0.20/0.48 tff(154,plain,
% 0.20/0.48 (group_element(e_4)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.20/0.48 tff(155,plain,
% 0.20/0.48 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_4)) | product(e_4, e_1, e_2) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_1) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_4)) | product(e_4, e_1, e_2) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_1) | (~group_element(e_1)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(156,plain,
% 0.20/0.48 ((product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_4))) <=> ((~group_element(e_4)) | product(e_4, e_1, e_2) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_1) | (~group_element(e_1)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(157,plain,
% 0.20/0.48 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_4)) | product(e_4, e_1, e_2) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_1) | (~group_element(e_1))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[156])).
% 0.20/0.48 tff(158,plain,
% 0.20/0.48 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_4)) | product(e_4, e_1, e_2) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_1) | (~group_element(e_1)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[157, 155])).
% 0.20/0.49 tff(159,plain,
% 0.20/0.49 ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_4)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(160,plain,
% 0.20/0.49 ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_4)) | product(e_4, e_1, e_2) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_1) | (~group_element(e_1))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[159, 158])).
% 0.20/0.49 tff(161,plain,
% 0.20/0.49 (product(e_4, e_1, e_2) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[160, 106, 154, 100, 151])).
% 0.20/0.49 tff(162,plain,
% 0.20/0.49 (product(e_4, e_1, e_2) | product(e_4, e_1, e_3)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[161, 139])).
% 0.20/0.49 tff(163,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[162, 127, 24])).
% 0.20/0.49 tff(164,plain,(~product(e_4, e_3, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(165,assumption,(product(e_2, e_4, e_1)), introduced(assumption)).
% 0.20/0.49 tff(166,plain,
% 0.20/0.49 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_4, e_1)) | (~product(e_4, e_1, e_2)))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_4, e_1)) | (~product(e_4, e_1, e_2)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(167,plain,
% 0.20/0.49 (((~product(e_2, e_2, e_2)) | (~product(e_2, e_4, e_1)) | (~product(e_2, e_2, e_2)) | (~product(e_4, e_1, e_2)) | equalish(e_1, e_2)) <=> (equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_4, e_1)) | (~product(e_4, e_1, e_2)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(168,plain,
% 0.20/0.49 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_2, e_2, e_2)) | (~product(e_2, e_4, e_1)) | (~product(e_2, e_2, e_2)) | (~product(e_4, e_1, e_2)) | equalish(e_1, e_2))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_4, e_1)) | (~product(e_4, e_1, e_2))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[167])).
% 0.20/0.49 tff(169,plain,
% 0.20/0.49 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_2, e_2, e_2)) | (~product(e_2, e_4, e_1)) | (~product(e_2, e_2, e_2)) | (~product(e_4, e_1, e_2)) | equalish(e_1, e_2))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_4, e_1)) | (~product(e_4, e_1, e_2)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[168, 166])).
% 0.20/0.49 tff(170,plain,
% 0.20/0.49 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_2, e_2, e_2)) | (~product(e_2, e_4, e_1)) | (~product(e_2, e_2, e_2)) | (~product(e_4, e_1, e_2)) | equalish(e_1, e_2))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(171,plain,
% 0.20/0.49 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_4, e_1)) | (~product(e_4, e_1, e_2))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[170, 169])).
% 0.20/0.49 tff(172,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[171, 74, 48, 61, 165, 36])).
% 0.20/0.49 tff(173,plain,((~product(e_2, e_4, e_1)) | (~product(e_4, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(174,plain,
% 0.20/0.49 (~product(e_2, e_4, e_1)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[173, 36])).
% 0.20/0.49 tff(175,assumption,(product(e_2, e_4, e_2)), introduced(assumption)).
% 0.20/0.49 tff(176,plain,
% 0.20/0.49 ((~equalish(e_4, e_2)) <=> (~equalish(e_4, e_2))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(177,axiom,(~equalish(e_4, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_4_is_not_e_2')).
% 0.20/0.49 tff(178,plain,
% 0.20/0.49 (~equalish(e_4, e_2)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[177, 176])).
% 0.20/0.49 tff(179,plain,
% 0.20/0.49 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_4, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_4, e_2)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(180,plain,
% 0.20/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_4, e_2)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(181,plain,
% 0.20/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_4, e_2))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[180, 179])).
% 0.20/0.49 tff(182,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[181, 178, 12, 61, 175])).
% 0.20/0.49 tff(183,plain,(~product(e_2, e_4, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(184,assumption,(product(e_2, e_4, e_4)), introduced(assumption)).
% 0.20/0.49 tff(185,plain,
% 0.20/0.49 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_4) | (~product(e_2, e_4, e_4)) | (~product(e_4, e_4, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_4) | (~product(e_2, e_4, e_4)) | (~product(e_4, e_4, e_4)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(186,plain,
% 0.20/0.49 ((equalish(e_2, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_2, e_4, e_4))) <=> (equalish(e_2, e_4) | (~product(e_2, e_4, e_4)) | (~product(e_4, e_4, e_4)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(187,plain,
% 0.20/0.49 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_2, e_4, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_4) | (~product(e_2, e_4, e_4)) | (~product(e_4, e_4, e_4))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[186])).
% 0.20/0.49 tff(188,plain,
% 0.20/0.49 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_2, e_4, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_4) | (~product(e_2, e_4, e_4)) | (~product(e_4, e_4, e_4)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[187, 185])).
% 0.20/0.49 tff(189,plain,
% 0.20/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_2, e_4, e_4)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(190,plain,
% 0.20/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_4) | (~product(e_2, e_4, e_4)) | (~product(e_4, e_4, e_4))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[189, 188])).
% 0.20/0.49 tff(191,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[190, 51, 71, 184, 38])).
% 0.20/0.49 tff(192,plain,(~product(e_2, e_4, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(193,plain,
% 0.20/0.49 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_4, e_4) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | (~group_element(e_2)) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_2, e_4, e_4) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | (~group_element(e_2)) | (~group_element(e_4)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(194,plain,
% 0.20/0.49 ((product(e_2, e_4, e_4) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_2))) <=> (product(e_2, e_4, e_4) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | (~group_element(e_2)) | (~group_element(e_4)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(195,plain,
% 0.20/0.49 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_4, e_4) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_4, e_4) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | (~group_element(e_2)) | (~group_element(e_4))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[194])).
% 0.20/0.49 tff(196,plain,
% 0.20/0.49 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_4, e_4) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_2, e_4, e_4) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | (~group_element(e_2)) | (~group_element(e_4)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[195, 193])).
% 0.20/0.49 tff(197,plain,
% 0.20/0.49 ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_4, e_4) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_2)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(198,plain,
% 0.20/0.49 ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_2, e_4, e_4) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | (~group_element(e_2)) | (~group_element(e_4))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[197, 196])).
% 0.20/0.49 tff(199,plain,
% 0.20/0.49 (product(e_2, e_4, e_4) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[198, 103, 154, 100])).
% 0.20/0.49 tff(200,plain,
% 0.20/0.50 (product(e_2, e_4, e_3) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[199, 192])).
% 0.20/0.50 tff(201,plain,
% 0.20/0.50 (product(e_2, e_4, e_3) | product(e_2, e_4, e_1)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[200, 183])).
% 0.20/0.50 tff(202,plain,
% 0.20/0.50 (product(e_2, e_4, e_3)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[201, 174])).
% 0.20/0.50 tff(203,assumption,(~product(e_4, e_3, e_3)), introduced(assumption)).
% 0.20/0.50 tff(204,assumption,(product(e_1, e_4, e_1)), introduced(assumption)).
% 0.20/0.50 tff(205,plain,
% 0.20/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_1) | (~product(e_1, e_4, e_1)) | (~product(e_1, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_1) | (~product(e_1, e_4, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(206,plain,
% 0.20/0.50 ((equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_4, e_1))) <=> (equalish(e_4, e_1) | (~product(e_1, e_4, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(207,plain,
% 0.20/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_4, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_1) | (~product(e_1, e_4, e_1)) | (~product(e_1, e_1, e_1))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[206])).
% 0.20/0.50 tff(208,plain,
% 0.20/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_4, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_1) | (~product(e_1, e_4, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.20/0.50 inference(transitivity,[status(thm)],[207, 205])).
% 0.20/0.50 tff(209,plain,
% 0.20/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_4, e_1)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(210,plain,
% 0.20/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_1) | (~product(e_1, e_4, e_1)) | (~product(e_1, e_1, e_1))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[209, 208])).
% 0.20/0.50 tff(211,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[210, 143, 12, 82, 204])).
% 0.20/0.50 tff(212,plain,(~product(e_1, e_4, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(213,assumption,(~product(e_3, e_4, e_1)), introduced(assumption)).
% 0.20/0.50 tff(214,assumption,(product(e_2, e_4, e_3)), introduced(assumption)).
% 0.20/0.50 tff(215,assumption,(product(e_3, e_4, e_3)), introduced(assumption)).
% 0.20/0.50 tff(216,plain,
% 0.20/0.50 ((~equalish(e_2, e_3)) <=> (~equalish(e_2, e_3))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(217,axiom,(~equalish(e_2, e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_is_not_e_3')).
% 0.20/0.50 tff(218,plain,
% 0.20/0.50 (~equalish(e_2, e_3)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[217, 216])).
% 0.20/0.50 tff(219,plain,
% 0.20/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_3) | (~product(e_3, e_4, e_3)) | (~product(e_2, e_4, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_3) | (~product(e_3, e_4, e_3)) | (~product(e_2, e_4, e_3)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(220,plain,
% 0.20/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_3) | (~product(e_3, e_4, e_3)) | (~product(e_2, e_4, e_3)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(221,plain,
% 0.20/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_3) | (~product(e_3, e_4, e_3)) | (~product(e_2, e_4, e_3))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[220, 219])).
% 0.20/0.50 tff(222,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[221, 218, 71, 215, 214])).
% 0.20/0.50 tff(223,plain,((~product(e_2, e_4, e_3)) | (~product(e_3, e_4, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(224,plain,
% 0.20/0.50 (~product(e_3, e_4, e_3)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[223, 214])).
% 0.20/0.50 tff(225,assumption,(product(e_3, e_4, e_4)), introduced(assumption)).
% 0.20/0.50 tff(226,plain,
% 0.20/0.50 ((~equalish(e_3, e_4)) <=> (~equalish(e_3, e_4))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(227,axiom,(~equalish(e_3, e_4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_3_is_not_e_4')).
% 0.20/0.50 tff(228,plain,
% 0.20/0.50 (~equalish(e_3, e_4)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[227, 226])).
% 0.20/0.50 tff(229,plain,
% 0.20/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_4) | (~product(e_3, e_4, e_4)) | (~product(e_4, e_4, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_4) | (~product(e_3, e_4, e_4)) | (~product(e_4, e_4, e_4)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(230,plain,
% 0.20/0.50 ((equalish(e_3, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_3, e_4, e_4))) <=> (equalish(e_3, e_4) | (~product(e_3, e_4, e_4)) | (~product(e_4, e_4, e_4)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(231,plain,
% 0.20/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_3, e_4, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_4) | (~product(e_3, e_4, e_4)) | (~product(e_4, e_4, e_4))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[230])).
% 0.20/0.50 tff(232,plain,
% 0.20/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_3, e_4, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_4) | (~product(e_3, e_4, e_4)) | (~product(e_4, e_4, e_4)))),
% 0.20/0.50 inference(transitivity,[status(thm)],[231, 229])).
% 0.20/0.50 tff(233,plain,
% 0.20/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_3, e_4, e_4)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(234,plain,
% 0.20/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_4) | (~product(e_3, e_4, e_4)) | (~product(e_4, e_4, e_4))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[233, 232])).
% 0.20/0.50 tff(235,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[234, 228, 71, 225, 38])).
% 0.20/0.50 tff(236,plain,(~product(e_3, e_4, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(237,plain,
% 0.20/0.50 (group_element(e_3) <=> group_element(e_3)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(238,axiom,(group_element(e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_3')).
% 0.20/0.50 tff(239,plain,
% 0.20/0.50 (group_element(e_3)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[238, 237])).
% 0.20/0.50 tff(240,plain,
% 0.20/0.50 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_4, e_1) | (~group_element(e_3)) | (~group_element(e_4)) | product(e_3, e_4, e_4) | product(e_3, e_4, e_3) | product(e_3, e_4, e_2))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_3, e_4, e_1) | (~group_element(e_3)) | (~group_element(e_4)) | product(e_3, e_4, e_4) | product(e_3, e_4, e_3) | product(e_3, e_4, e_2))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(241,plain,
% 0.20/0.50 ((product(e_3, e_4, e_4) | product(e_3, e_4, e_3) | product(e_3, e_4, e_2) | product(e_3, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_3))) <=> (product(e_3, e_4, e_1) | (~group_element(e_3)) | (~group_element(e_4)) | product(e_3, e_4, e_4) | product(e_3, e_4, e_3) | product(e_3, e_4, e_2))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(242,plain,
% 0.20/0.50 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_4, e_4) | product(e_3, e_4, e_3) | product(e_3, e_4, e_2) | product(e_3, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_4, e_1) | (~group_element(e_3)) | (~group_element(e_4)) | product(e_3, e_4, e_4) | product(e_3, e_4, e_3) | product(e_3, e_4, e_2)))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[241])).
% 0.20/0.50 tff(243,plain,
% 0.20/0.50 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_4, e_4) | product(e_3, e_4, e_3) | product(e_3, e_4, e_2) | product(e_3, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_3, e_4, e_1) | (~group_element(e_3)) | (~group_element(e_4)) | product(e_3, e_4, e_4) | product(e_3, e_4, e_3) | product(e_3, e_4, e_2))),
% 0.20/0.50 inference(transitivity,[status(thm)],[242, 240])).
% 0.20/0.50 tff(244,plain,
% 0.20/0.50 ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_4, e_4) | product(e_3, e_4, e_3) | product(e_3, e_4, e_2) | product(e_3, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_3)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(245,plain,
% 0.20/0.50 ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_3, e_4, e_1) | (~group_element(e_3)) | (~group_element(e_4)) | product(e_3, e_4, e_4) | product(e_3, e_4, e_3) | product(e_3, e_4, e_2)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[244, 243])).
% 0.20/0.50 tff(246,plain,
% 0.20/0.50 (product(e_3, e_4, e_1) | product(e_3, e_4, e_4) | product(e_3, e_4, e_3) | product(e_3, e_4, e_2)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[245, 239, 154, 100])).
% 0.20/0.50 tff(247,plain,
% 0.20/0.50 (product(e_3, e_4, e_1) | product(e_3, e_4, e_3) | product(e_3, e_4, e_2)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[246, 236])).
% 0.20/0.50 tff(248,plain,
% 0.20/0.50 (product(e_3, e_4, e_2)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[247, 224, 213])).
% 0.20/0.50 tff(249,assumption,(product(e_1, e_4, e_2)), introduced(assumption)).
% 0.20/0.50 tff(250,assumption,(product(e_3, e_4, e_2)), introduced(assumption)).
% 0.20/0.50 tff(251,plain,
% 0.20/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_3, e_4, e_2)) | (~product(e_1, e_4, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_3, e_4, e_2)) | (~product(e_1, e_4, e_2)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(252,plain,
% 0.20/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_3, e_4, e_2)) | (~product(e_1, e_4, e_2)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(253,plain,
% 0.20/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_3, e_4, e_2)) | (~product(e_1, e_4, e_2))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[252, 251])).
% 0.20/0.50 tff(254,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[253, 15, 71, 250, 249])).
% 0.20/0.50 tff(255,plain,((~product(e_1, e_4, e_2)) | (~product(e_3, e_4, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(256,plain,
% 0.20/0.50 (~product(e_1, e_4, e_2)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[255, 248])).
% 0.20/0.50 tff(257,assumption,(product(e_1, e_4, e_4)), introduced(assumption)).
% 0.20/0.50 tff(258,plain,
% 0.20/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_4) | (~product(e_1, e_4, e_4)) | (~product(e_4, e_4, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_4) | (~product(e_1, e_4, e_4)) | (~product(e_4, e_4, e_4)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(259,plain,
% 0.20/0.50 ((equalish(e_1, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_1, e_4, e_4))) <=> (equalish(e_1, e_4) | (~product(e_1, e_4, e_4)) | (~product(e_4, e_4, e_4)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(260,plain,
% 0.20/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_1, e_4, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_4) | (~product(e_1, e_4, e_4)) | (~product(e_4, e_4, e_4))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[259])).
% 0.20/0.50 tff(261,plain,
% 0.20/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_1, e_4, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_4) | (~product(e_1, e_4, e_4)) | (~product(e_4, e_4, e_4)))),
% 0.20/0.50 inference(transitivity,[status(thm)],[260, 258])).
% 0.20/0.50 tff(262,plain,
% 0.20/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_1, e_4, e_4)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(263,plain,
% 0.20/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_4) | (~product(e_1, e_4, e_4)) | (~product(e_4, e_4, e_4))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[262, 261])).
% 0.20/0.50 tff(264,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[263, 131, 71, 38, 257])).
% 0.20/0.50 tff(265,plain,(~product(e_1, e_4, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(266,plain,
% 0.20/0.50 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_4)) | product(e_1, e_4, e_4) | product(e_1, e_4, e_1) | (~group_element(e_1)) | product(e_1, e_4, e_2) | product(e_1, e_4, e_3))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_4)) | product(e_1, e_4, e_4) | product(e_1, e_4, e_1) | (~group_element(e_1)) | product(e_1, e_4, e_2) | product(e_1, e_4, e_3))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(267,plain,
% 0.20/0.50 ((product(e_1, e_4, e_4) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_1))) <=> ((~group_element(e_4)) | product(e_1, e_4, e_4) | product(e_1, e_4, e_1) | (~group_element(e_1)) | product(e_1, e_4, e_2) | product(e_1, e_4, e_3))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(268,plain,
% 0.20/0.50 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_4, e_4) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_4)) | product(e_1, e_4, e_4) | product(e_1, e_4, e_1) | (~group_element(e_1)) | product(e_1, e_4, e_2) | product(e_1, e_4, e_3)))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[267])).
% 0.20/0.50 tff(269,plain,
% 0.20/0.50 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_4, e_4) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_4)) | product(e_1, e_4, e_4) | product(e_1, e_4, e_1) | (~group_element(e_1)) | product(e_1, e_4, e_2) | product(e_1, e_4, e_3))),
% 0.20/0.50 inference(transitivity,[status(thm)],[268, 266])).
% 0.20/0.50 tff(270,plain,
% 0.20/0.50 ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_4, e_4) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_1)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(271,plain,
% 0.20/0.50 ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_4)) | product(e_1, e_4, e_4) | product(e_1, e_4, e_1) | (~group_element(e_1)) | product(e_1, e_4, e_2) | product(e_1, e_4, e_3)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[270, 269])).
% 0.20/0.50 tff(272,plain,
% 0.20/0.50 (product(e_1, e_4, e_1) | product(e_1, e_4, e_2) | product(e_1, e_4, e_3)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[271, 106, 154, 100, 265])).
% 0.20/0.50 tff(273,plain,
% 0.20/0.50 (product(e_1, e_4, e_3)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[272, 256, 212])).
% 0.20/0.50 tff(274,assumption,(product(e_1, e_4, e_3)), introduced(assumption)).
% 0.20/0.50 tff(275,assumption,(product(e_4, e_3, e_1)), introduced(assumption)).
% 0.20/0.50 tff(276,plain,
% 0.20/0.50 ((~equalish(e_3, e_1)) <=> (~equalish(e_3, e_1))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(277,axiom,(~equalish(e_3, e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_3_is_not_e_1')).
% 0.20/0.50 tff(278,plain,
% 0.20/0.50 (~equalish(e_3, e_1)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[277, 276])).
% 0.20/0.50 tff(279,plain,
% 0.20/0.50 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_3, e_1) | (~product(e_4, e_3, e_1)) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_4, e_3)))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_3, e_1) | (~product(e_4, e_3, e_1)) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_4, e_3)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(280,plain,
% 0.20/0.50 (((~product(e_1, e_1, e_1)) | (~product(e_1, e_4, e_3)) | (~product(e_1, e_1, e_1)) | (~product(e_4, e_3, e_1)) | equalish(e_3, e_1)) <=> (equalish(e_3, e_1) | (~product(e_4, e_3, e_1)) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_4, e_3)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(281,plain,
% 0.20/0.50 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_1, e_1, e_1)) | (~product(e_1, e_4, e_3)) | (~product(e_1, e_1, e_1)) | (~product(e_4, e_3, e_1)) | equalish(e_3, e_1))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_3, e_1) | (~product(e_4, e_3, e_1)) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_4, e_3))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[280])).
% 0.20/0.50 tff(282,plain,
% 0.20/0.50 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_1, e_1, e_1)) | (~product(e_1, e_4, e_3)) | (~product(e_1, e_1, e_1)) | (~product(e_4, e_3, e_1)) | equalish(e_3, e_1))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_3, e_1) | (~product(e_4, e_3, e_1)) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_4, e_3)))),
% 0.20/0.51 inference(transitivity,[status(thm)],[281, 279])).
% 0.20/0.51 tff(283,plain,
% 0.20/0.51 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_1, e_1, e_1)) | (~product(e_1, e_4, e_3)) | (~product(e_1, e_1, e_1)) | (~product(e_4, e_3, e_1)) | equalish(e_3, e_1))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(284,plain,
% 0.20/0.51 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_3, e_1) | (~product(e_4, e_3, e_1)) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_4, e_3))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[283, 282])).
% 0.20/0.51 tff(285,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[284, 278, 48, 82, 275, 274])).
% 0.20/0.51 tff(286,plain,((~product(e_1, e_4, e_3)) | (~product(e_4, e_3, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(287,plain,
% 0.20/0.51 (~product(e_4, e_3, e_1)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[286, 273])).
% 0.20/0.51 tff(288,assumption,(product(e_4, e_3, e_4)), introduced(assumption)).
% 0.20/0.51 tff(289,plain,
% 0.20/0.51 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_4) | (~product(e_4, e_3, e_4)) | (~product(e_4, e_4, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_4) | (~product(e_4, e_3, e_4)) | (~product(e_4, e_4, e_4)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(290,plain,
% 0.20/0.51 ((equalish(e_3, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_3, e_4))) <=> (equalish(e_3, e_4) | (~product(e_4, e_3, e_4)) | (~product(e_4, e_4, e_4)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(291,plain,
% 0.20/0.51 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_3, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_4) | (~product(e_4, e_3, e_4)) | (~product(e_4, e_4, e_4))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[290])).
% 0.20/0.51 tff(292,plain,
% 0.20/0.51 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_3, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_4) | (~product(e_4, e_3, e_4)) | (~product(e_4, e_4, e_4)))),
% 0.20/0.51 inference(transitivity,[status(thm)],[291, 289])).
% 0.20/0.51 tff(293,plain,
% 0.20/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_3, e_4)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(294,plain,
% 0.20/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_4) | (~product(e_4, e_3, e_4)) | (~product(e_4, e_4, e_4))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[293, 292])).
% 0.20/0.51 tff(295,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[294, 228, 12, 38, 288])).
% 0.20/0.51 tff(296,plain,(~product(e_4, e_3, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(297,plain,
% 0.20/0.51 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_3)) | (~group_element(e_4)) | product(e_4, e_3, e_1) | product(e_4, e_3, e_4) | product(e_4, e_3, e_3) | product(e_4, e_3, e_2))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_3)) | (~group_element(e_4)) | product(e_4, e_3, e_1) | product(e_4, e_3, e_4) | product(e_4, e_3, e_3) | product(e_4, e_3, e_2))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(298,plain,
% 0.20/0.51 ((product(e_4, e_3, e_4) | product(e_4, e_3, e_3) | product(e_4, e_3, e_2) | product(e_4, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_4))) <=> ((~group_element(e_3)) | (~group_element(e_4)) | product(e_4, e_3, e_1) | product(e_4, e_3, e_4) | product(e_4, e_3, e_3) | product(e_4, e_3, e_2))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(299,plain,
% 0.20/0.51 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_3, e_4) | product(e_4, e_3, e_3) | product(e_4, e_3, e_2) | product(e_4, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_3)) | (~group_element(e_4)) | product(e_4, e_3, e_1) | product(e_4, e_3, e_4) | product(e_4, e_3, e_3) | product(e_4, e_3, e_2)))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[298])).
% 0.20/0.51 tff(300,plain,
% 0.20/0.51 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_3, e_4) | product(e_4, e_3, e_3) | product(e_4, e_3, e_2) | product(e_4, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_3)) | (~group_element(e_4)) | product(e_4, e_3, e_1) | product(e_4, e_3, e_4) | product(e_4, e_3, e_3) | product(e_4, e_3, e_2))),
% 0.20/0.51 inference(transitivity,[status(thm)],[299, 297])).
% 0.20/0.51 tff(301,plain,
% 0.20/0.51 ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_3, e_4) | product(e_4, e_3, e_3) | product(e_4, e_3, e_2) | product(e_4, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_4)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(302,plain,
% 0.20/0.51 ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_3)) | (~group_element(e_4)) | product(e_4, e_3, e_1) | product(e_4, e_3, e_4) | product(e_4, e_3, e_3) | product(e_4, e_3, e_2)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[301, 300])).
% 0.20/0.51 tff(303,plain,
% 0.20/0.51 (product(e_4, e_3, e_1) | product(e_4, e_3, e_3) | product(e_4, e_3, e_2)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[302, 239, 154, 100, 296])).
% 0.20/0.51 tff(304,plain,
% 0.20/0.51 (product(e_4, e_3, e_2)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[303, 287, 203])).
% 0.20/0.51 tff(305,plain,
% 0.20/0.51 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_3, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_4, e_3, e_2)) | (~product(e_2, e_4, e_3)))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_3, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_4, e_3, e_2)) | (~product(e_2, e_4, e_3)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(306,plain,
% 0.20/0.51 (((~product(e_2, e_2, e_2)) | (~product(e_2, e_4, e_3)) | (~product(e_2, e_2, e_2)) | (~product(e_4, e_3, e_2)) | equalish(e_3, e_2)) <=> (equalish(e_3, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_4, e_3, e_2)) | (~product(e_2, e_4, e_3)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(307,plain,
% 0.20/0.51 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_2, e_2, e_2)) | (~product(e_2, e_4, e_3)) | (~product(e_2, e_2, e_2)) | (~product(e_4, e_3, e_2)) | equalish(e_3, e_2))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_3, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_4, e_3, e_2)) | (~product(e_2, e_4, e_3))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[306])).
% 0.20/0.51 tff(308,plain,
% 0.20/0.51 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_2, e_2, e_2)) | (~product(e_2, e_4, e_3)) | (~product(e_2, e_2, e_2)) | (~product(e_4, e_3, e_2)) | equalish(e_3, e_2))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_3, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_4, e_3, e_2)) | (~product(e_2, e_4, e_3)))),
% 0.20/0.51 inference(transitivity,[status(thm)],[307, 305])).
% 0.20/0.51 tff(309,plain,
% 0.20/0.51 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_2, e_2, e_2)) | (~product(e_2, e_4, e_3)) | (~product(e_2, e_2, e_2)) | (~product(e_4, e_3, e_2)) | equalish(e_3, e_2))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(310,plain,
% 0.20/0.51 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_3, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_4, e_3, e_2)) | (~product(e_2, e_4, e_3))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[309, 308])).
% 0.20/0.51 tff(311,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[310, 118, 48, 61, 214, 304])).
% 0.20/0.51 tff(312,plain,((~product(e_2, e_4, e_3)) | product(e_4, e_3, e_3) | product(e_3, e_4, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(313,plain,
% 0.20/0.51 (product(e_3, e_4, e_1)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[312, 202, 164])).
% 0.20/0.51 tff(314,assumption,(product(e_3, e_2, e_1)), introduced(assumption)).
% 0.20/0.51 tff(315,assumption,(product(e_3, e_4, e_1)), introduced(assumption)).
% 0.20/0.51 tff(316,plain,
% 0.20/0.51 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_4) | (~product(e_3, e_4, e_1)) | (~product(e_3, e_2, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_4) | (~product(e_3, e_4, e_1)) | (~product(e_3, e_2, e_1)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(317,plain,
% 0.20/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_4) | (~product(e_3, e_4, e_1)) | (~product(e_3, e_2, e_1)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(318,plain,
% 0.20/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_4) | (~product(e_3, e_4, e_1)) | (~product(e_3, e_2, e_1))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[317, 316])).
% 0.20/0.51 tff(319,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[318, 51, 12, 315, 314])).
% 0.20/0.51 tff(320,plain,((~product(e_3, e_2, e_1)) | (~product(e_3, e_4, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(321,plain,
% 0.20/0.51 (~product(e_3, e_2, e_1)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[320, 313])).
% 0.20/0.51 tff(322,assumption,(product(e_1, e_2, e_3)), introduced(assumption)).
% 0.20/0.51 tff(323,assumption,(product(e_3, e_2, e_3)), introduced(assumption)).
% 0.20/0.51 tff(324,plain,
% 0.20/0.51 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_3, e_2, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_3, e_2, e_3)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(325,plain,
% 0.20/0.51 ((equalish(e_1, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_1, e_2, e_3))) <=> (equalish(e_1, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_3, e_2, e_3)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(326,plain,
% 0.20/0.51 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_1, e_2, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_3, e_2, e_3))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[325])).
% 0.20/0.51 tff(327,plain,
% 0.20/0.51 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_1, e_2, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_3, e_2, e_3)))),
% 0.20/0.51 inference(transitivity,[status(thm)],[326, 324])).
% 0.20/0.51 tff(328,plain,
% 0.20/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_1, e_2, e_3)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(329,plain,
% 0.20/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_3, e_2, e_3))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[328, 327])).
% 0.20/0.51 tff(330,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[329, 15, 71, 323, 322])).
% 0.20/0.51 tff(331,plain,((~product(e_1, e_2, e_3)) | (~product(e_3, e_2, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(332,plain,
% 0.20/0.51 (~product(e_3, e_2, e_3)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[331, 115])).
% 0.20/0.51 tff(333,assumption,(product(e_3, e_2, e_2)), introduced(assumption)).
% 0.20/0.51 tff(334,plain,
% 0.20/0.51 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_3, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_3, e_2, e_2)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(335,plain,
% 0.20/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_3, e_2, e_2)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(336,plain,
% 0.20/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_3, e_2, e_2))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[335, 334])).
% 0.20/0.51 tff(337,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[336, 118, 71, 61, 333])).
% 0.20/0.51 tff(338,plain,(~product(e_3, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(339,plain,
% 0.20/0.51 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_2, e_1) | product(e_3, e_2, e_2) | (~group_element(e_3)) | (~group_element(e_2)) | product(e_3, e_2, e_4) | product(e_3, e_2, e_3))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_3, e_2, e_1) | product(e_3, e_2, e_2) | (~group_element(e_3)) | (~group_element(e_2)) | product(e_3, e_2, e_4) | product(e_3, e_2, e_3))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(340,plain,
% 0.20/0.51 ((product(e_3, e_2, e_4) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_3))) <=> (product(e_3, e_2, e_1) | product(e_3, e_2, e_2) | (~group_element(e_3)) | (~group_element(e_2)) | product(e_3, e_2, e_4) | product(e_3, e_2, e_3))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(341,plain,
% 0.20/0.51 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_2, e_4) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_2, e_1) | product(e_3, e_2, e_2) | (~group_element(e_3)) | (~group_element(e_2)) | product(e_3, e_2, e_4) | product(e_3, e_2, e_3)))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[340])).
% 0.20/0.52 tff(342,plain,
% 0.20/0.52 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_2, e_4) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_3, e_2, e_1) | product(e_3, e_2, e_2) | (~group_element(e_3)) | (~group_element(e_2)) | product(e_3, e_2, e_4) | product(e_3, e_2, e_3))),
% 0.20/0.52 inference(transitivity,[status(thm)],[341, 339])).
% 0.20/0.52 tff(343,plain,
% 0.20/0.52 ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_2, e_4) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_3)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(344,plain,
% 0.20/0.52 ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_3, e_2, e_1) | product(e_3, e_2, e_2) | (~group_element(e_3)) | (~group_element(e_2)) | product(e_3, e_2, e_4) | product(e_3, e_2, e_3)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[343, 342])).
% 0.20/0.52 tff(345,plain,
% 0.20/0.52 (product(e_3, e_2, e_1) | product(e_3, e_2, e_2) | product(e_3, e_2, e_4) | product(e_3, e_2, e_3)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[344, 103, 239, 100])).
% 0.20/0.52 tff(346,plain,
% 0.20/0.52 (product(e_3, e_2, e_1) | product(e_3, e_2, e_4) | product(e_3, e_2, e_3)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[345, 338])).
% 0.20/0.52 tff(347,plain,
% 0.20/0.52 (product(e_3, e_2, e_4)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[346, 332, 321])).
% 0.20/0.52 tff(348,plain,
% 0.20/0.52 ((~equalish(e_4, e_3)) <=> (~equalish(e_4, e_3))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(349,axiom,(~equalish(e_4, e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_4_is_not_e_3')).
% 0.20/0.52 tff(350,plain,
% 0.20/0.52 (~equalish(e_4, e_3)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[349, 348])).
% 0.20/0.52 tff(351,plain,
% 0.20/0.52 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_4, e_3) | (~product(e_3, e_2, e_4)) | (~product(e_2, e_4, e_3)) | (~product(e_3, e_3, e_3)))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_4, e_3) | (~product(e_3, e_2, e_4)) | (~product(e_2, e_4, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(352,plain,
% 0.20/0.52 (((~product(e_3, e_3, e_3)) | (~product(e_3, e_2, e_4)) | (~product(e_3, e_3, e_3)) | (~product(e_2, e_4, e_3)) | equalish(e_4, e_3)) <=> (equalish(e_4, e_3) | (~product(e_3, e_2, e_4)) | (~product(e_2, e_4, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(353,plain,
% 0.20/0.52 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_3, e_3, e_3)) | (~product(e_3, e_2, e_4)) | (~product(e_3, e_3, e_3)) | (~product(e_2, e_4, e_3)) | equalish(e_4, e_3))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_4, e_3) | (~product(e_3, e_2, e_4)) | (~product(e_2, e_4, e_3)) | (~product(e_3, e_3, e_3))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[352])).
% 0.20/0.52 tff(354,plain,
% 0.20/0.52 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_3, e_3, e_3)) | (~product(e_3, e_2, e_4)) | (~product(e_3, e_3, e_3)) | (~product(e_2, e_4, e_3)) | equalish(e_4, e_3))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_4, e_3) | (~product(e_3, e_2, e_4)) | (~product(e_2, e_4, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.20/0.52 inference(transitivity,[status(thm)],[353, 351])).
% 0.20/0.52 tff(355,plain,
% 0.20/0.52 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_3, e_3, e_3)) | (~product(e_3, e_2, e_4)) | (~product(e_3, e_3, e_3)) | (~product(e_2, e_4, e_3)) | equalish(e_4, e_3))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(356,plain,
% 0.20/0.52 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_4, e_3) | (~product(e_3, e_2, e_4)) | (~product(e_2, e_4, e_3)) | (~product(e_3, e_3, e_3))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[355, 354])).
% 0.20/0.52 tff(357,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[356, 350, 48, 347, 202, 35])).
% 0.20/0.52 tff(358,plain,(~product(e_4, e_1, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(359,plain,
% 0.20/0.52 (product(e_4, e_1, e_3)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[162, 358])).
% 0.20/0.52 tff(360,plain,
% 0.20/0.52 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_1, e_3) | (~product(e_4, e_1, e_3)) | (~product(e_3, e_4, e_1)) | (~product(e_3, e_3, e_3)))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_1, e_3) | (~product(e_4, e_1, e_3)) | (~product(e_3, e_4, e_1)) | (~product(e_3, e_3, e_3)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(361,plain,
% 0.20/0.52 (((~product(e_3, e_3, e_3)) | (~product(e_3, e_4, e_1)) | (~product(e_3, e_3, e_3)) | (~product(e_4, e_1, e_3)) | equalish(e_1, e_3)) <=> (equalish(e_1, e_3) | (~product(e_4, e_1, e_3)) | (~product(e_3, e_4, e_1)) | (~product(e_3, e_3, e_3)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(362,plain,
% 0.20/0.52 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_3, e_3, e_3)) | (~product(e_3, e_4, e_1)) | (~product(e_3, e_3, e_3)) | (~product(e_4, e_1, e_3)) | equalish(e_1, e_3))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_1, e_3) | (~product(e_4, e_1, e_3)) | (~product(e_3, e_4, e_1)) | (~product(e_3, e_3, e_3))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[361])).
% 0.20/0.52 tff(363,plain,
% 0.20/0.52 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_3, e_3, e_3)) | (~product(e_3, e_4, e_1)) | (~product(e_3, e_3, e_3)) | (~product(e_4, e_1, e_3)) | equalish(e_1, e_3))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_1, e_3) | (~product(e_4, e_1, e_3)) | (~product(e_3, e_4, e_1)) | (~product(e_3, e_3, e_3)))),
% 0.20/0.52 inference(transitivity,[status(thm)],[362, 360])).
% 0.20/0.52 tff(364,plain,
% 0.20/0.52 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_3, e_3, e_3)) | (~product(e_3, e_4, e_1)) | (~product(e_3, e_3, e_3)) | (~product(e_4, e_1, e_3)) | equalish(e_1, e_3))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(365,plain,
% 0.20/0.52 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_1, e_3) | (~product(e_4, e_1, e_3)) | (~product(e_3, e_4, e_1)) | (~product(e_3, e_3, e_3))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[364, 363])).
% 0.20/0.52 tff(366,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[365, 15, 48, 315, 2, 35])).
% 0.20/0.52 tff(367,plain,((~product(e_3, e_4, e_1)) | (~product(e_4, e_1, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(368,plain,
% 0.20/0.52 (~product(e_3, e_4, e_1)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[367, 359])).
% 0.20/0.52 tff(369,plain,
% 0.20/0.52 (~product(e_2, e_4, e_3)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[312, 368, 164])).
% 0.20/0.52 tff(370,plain,
% 0.20/0.52 (product(e_2, e_4, e_1)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[201, 369])).
% 0.20/0.52 tff(371,assumption,(product(e_1, e_2, e_4)), introduced(assumption)).
% 0.20/0.52 tff(372,plain,
% 0.20/0.52 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_4, e_1) | (~product(e_1, e_2, e_4)) | (~product(e_2, e_4, e_1)) | (~product(e_1, e_1, e_1)))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_4, e_1) | (~product(e_1, e_2, e_4)) | (~product(e_2, e_4, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(373,plain,
% 0.20/0.52 (((~product(e_1, e_1, e_1)) | (~product(e_1, e_2, e_4)) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_4, e_1)) | equalish(e_4, e_1)) <=> (equalish(e_4, e_1) | (~product(e_1, e_2, e_4)) | (~product(e_2, e_4, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(374,plain,
% 0.20/0.52 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_1, e_1, e_1)) | (~product(e_1, e_2, e_4)) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_4, e_1)) | equalish(e_4, e_1))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_4, e_1) | (~product(e_1, e_2, e_4)) | (~product(e_2, e_4, e_1)) | (~product(e_1, e_1, e_1))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[373])).
% 0.20/0.52 tff(375,plain,
% 0.20/0.52 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_1, e_1, e_1)) | (~product(e_1, e_2, e_4)) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_4, e_1)) | equalish(e_4, e_1))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_4, e_1) | (~product(e_1, e_2, e_4)) | (~product(e_2, e_4, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.20/0.52 inference(transitivity,[status(thm)],[374, 372])).
% 0.20/0.52 tff(376,plain,
% 0.20/0.52 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_1, e_1, e_1)) | (~product(e_1, e_2, e_4)) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_4, e_1)) | equalish(e_4, e_1))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(377,plain,
% 0.20/0.52 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_4, e_1) | (~product(e_1, e_2, e_4)) | (~product(e_2, e_4, e_1)) | (~product(e_1, e_1, e_1))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[376, 375])).
% 0.20/0.52 tff(378,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[377, 143, 48, 165, 82, 371])).
% 0.20/0.52 tff(379,plain,((~product(e_1, e_2, e_4)) | (~product(e_2, e_4, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(380,plain,
% 0.20/0.52 (~product(e_1, e_2, e_4)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[379, 370])).
% 0.20/0.52 tff(381,plain,
% 0.20/0.52 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_3) | (~product(e_3, e_4, e_3)) | (~product(e_3, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_3) | (~product(e_3, e_4, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(382,plain,
% 0.20/0.52 ((equalish(e_4, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_4, e_3))) <=> (equalish(e_4, e_3) | (~product(e_3, e_4, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(383,plain,
% 0.20/0.52 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_4, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_3) | (~product(e_3, e_4, e_3)) | (~product(e_3, e_3, e_3))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[382])).
% 0.20/0.52 tff(384,plain,
% 0.20/0.52 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_4, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_3) | (~product(e_3, e_4, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.20/0.52 inference(transitivity,[status(thm)],[383, 381])).
% 0.20/0.52 tff(385,plain,
% 0.20/0.52 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_4, e_3)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(386,plain,
% 0.20/0.52 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_3) | (~product(e_3, e_4, e_3)) | (~product(e_3, e_3, e_3))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[385, 384])).
% 0.20/0.52 tff(387,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[386, 350, 12, 215, 35])).
% 0.20/0.52 tff(388,plain,(~product(e_3, e_4, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(389,plain,
% 0.20/0.52 (product(e_3, e_4, e_1) | product(e_3, e_4, e_2)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[247, 388])).
% 0.20/0.52 tff(390,plain,
% 0.20/0.52 (product(e_3, e_4, e_2)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[389, 368])).
% 0.20/0.52 tff(391,plain,
% 0.20/0.52 (~product(e_1, e_4, e_2)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[255, 390])).
% 0.20/0.52 tff(392,plain,
% 0.20/0.52 (product(e_1, e_4, e_2) | product(e_1, e_4, e_3)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[272, 212])).
% 0.20/0.52 tff(393,plain,
% 0.20/0.52 (product(e_1, e_4, e_3)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[392, 391])).
% 0.20/0.52 tff(394,plain,
% 0.20/0.52 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_4) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_4, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_4) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_4, e_3)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(395,plain,
% 0.20/0.52 ((equalish(e_2, e_4) | (~product(e_1, e_4, e_3)) | (~product(e_1, e_2, e_3))) <=> (equalish(e_2, e_4) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_4, e_3)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(396,plain,
% 0.20/0.53 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_4) | (~product(e_1, e_4, e_3)) | (~product(e_1, e_2, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_4) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_4, e_3))))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[395])).
% 0.20/0.53 tff(397,plain,
% 0.20/0.53 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_4) | (~product(e_1, e_4, e_3)) | (~product(e_1, e_2, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_4) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_4, e_3)))),
% 0.20/0.53 inference(transitivity,[status(thm)],[396, 394])).
% 0.20/0.53 tff(398,plain,
% 0.20/0.53 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_4) | (~product(e_1, e_4, e_3)) | (~product(e_1, e_2, e_3)))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(399,plain,
% 0.20/0.53 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_4) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_4, e_3))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[398, 397])).
% 0.20/0.53 tff(400,plain,
% 0.20/0.53 ($false),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[399, 51, 12, 322, 274])).
% 0.20/0.53 tff(401,plain,((~product(e_1, e_2, e_3)) | (~product(e_1, e_4, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.53 tff(402,plain,
% 0.20/0.53 (~product(e_1, e_2, e_3)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[401, 393])).
% 0.20/0.53 tff(403,plain,
% 0.20/0.53 ($false),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[114, 402, 380])).
% 0.20/0.53 % SZS output end Proof
%------------------------------------------------------------------------------