TSTP Solution File: GRP129-1.003 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP129-1.003 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 16 22:26:11 EDT 2022
% Result : Unsatisfiable 0.20s 0.44s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP129-1.003 : TPTP v8.1.0. Released v1.2.0.
% 0.10/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n016.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Aug 31 15:25:47 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.20/0.44 % SZS status Unsatisfiable
% 0.20/0.44 % SZS output start Proof
% 0.20/0.44 tff(product_type, type, (
% 0.20/0.44 product: ( $i * $i * $i ) > $o)).
% 0.20/0.44 tff(e_1_type, type, (
% 0.20/0.44 e_1: $i)).
% 0.20/0.44 tff(e_2_type, type, (
% 0.20/0.44 e_2: $i)).
% 0.20/0.44 tff(e_3_type, type, (
% 0.20/0.44 e_3: $i)).
% 0.20/0.44 tff(equalish_type, type, (
% 0.20/0.44 equalish: ( $i * $i ) > $o)).
% 0.20/0.44 tff(group_element_type, type, (
% 0.20/0.44 group_element: $i > $o)).
% 0.20/0.44 tff(1,assumption,(product(e_3, e_2, e_1)), introduced(assumption)).
% 0.20/0.44 tff(2,assumption,(product(e_3, e_1, e_1)), introduced(assumption)).
% 0.20/0.44 tff(3,plain,
% 0.20/0.44 (^[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))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(4,plain,
% 0.20/0.44 (![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)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.44 tff(5,plain,
% 0.20/0.44 (![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)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(6,plain,
% 0.20/0.44 (^[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)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(7,plain,
% 0.20/0.44 (![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)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[6])).
% 0.20/0.44 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')).
% 0.20/0.44 tff(9,plain,
% 0.20/0.44 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.20/0.44 tff(10,plain,
% 0.20/0.44 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.20/0.44 tff(11,plain,(
% 0.20/0.44 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.44 inference(skolemize,[status(sab)],[10])).
% 0.20/0.44 tff(12,plain,
% 0.20/0.44 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.20/0.44 tff(13,plain,
% 0.20/0.44 ((~equalish(e_1, e_2)) <=> (~equalish(e_1, e_2))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(14,axiom,(~equalish(e_1, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_1_is_not_e_2')).
% 0.20/0.44 tff(15,plain,
% 0.20/0.44 (~equalish(e_1, e_2)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.20/0.44 tff(16,plain,
% 0.20/0.44 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_3, e_2, e_1)) | (~product(e_3, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_2) | (~product(e_3, e_2, e_1)) | (~product(e_3, e_1, e_1)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(17,plain,
% 0.20/0.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_3, e_2, e_1)) | (~product(e_3, e_1, e_1)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(18,plain,
% 0.20/0.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_2) | (~product(e_3, e_2, e_1)) | (~product(e_3, e_1, e_1))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.20/0.44 tff(19,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[18, 15, 12, 2, 1])).
% 0.20/0.44 tff(20,plain,((~product(e_3, e_1, e_1)) | (~product(e_3, e_2, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(21,plain,
% 0.20/0.44 (~product(e_3, e_1, e_1)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[20, 1])).
% 0.20/0.44 tff(22,assumption,(product(e_1, e_2, e_2)), introduced(assumption)).
% 0.20/0.44 tff(23,assumption,(product(e_2, e_2, e_3)), introduced(assumption)).
% 0.20/0.44 tff(24,assumption,(product(e_2, e_1, e_3)), introduced(assumption)).
% 0.20/0.44 tff(25,plain,
% 0.20/0.44 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_3)) | (~product(e_2, 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_2) | (~product(e_2, e_2, e_3)) | (~product(e_2, e_1, e_3)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(26,plain,
% 0.20/0.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_3)) | (~product(e_2, e_1, e_3)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(27,plain,
% 0.20/0.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_2) | (~product(e_2, e_2, e_3)) | (~product(e_2, e_1, e_3))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.20/0.44 tff(28,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[27, 15, 12, 23, 24])).
% 0.20/0.44 tff(29,plain,((~product(e_2, e_1, e_3)) | (~product(e_2, e_2, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(30,plain,
% 0.20/0.44 (~product(e_2, e_1, e_3)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[29, 23])).
% 0.20/0.44 tff(31,plain,
% 0.20/0.44 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : refl((product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1))) <=> (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(32,plain,
% 0.20/0.44 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[31])).
% 0.20/0.44 tff(33,plain,
% 0.20/0.44 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(34,plain,
% 0.20/0.44 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : trans(monotonicity(rewrite(((~product(Y, X, Z1)) | (~product(X, Z1, Z2))) <=> ((~product(X, Z1, Z2)) | (~product(Y, X, Z1)))), ((((~product(Y, X, Z1)) | (~product(X, Z1, Z2))) | product(Z1, Y, Z2)) <=> (((~product(X, Z1, Z2)) | (~product(Y, X, Z1))) | product(Z1, Y, Z2)))), rewrite((((~product(X, Z1, Z2)) | (~product(Y, X, Z1))) | product(Z1, Y, Z2)) <=> (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))), ((((~product(Y, X, Z1)) | (~product(X, Z1, Z2))) | product(Z1, Y, Z2)) <=> (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(35,plain,
% 0.20/0.44 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(Y, X, Z1)) | (~product(X, Z1, Z2))) | product(Z1, Y, Z2)) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[34])).
% 0.20/0.44 tff(36,axiom,(![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(Y, X, Z1)) | (~product(X, Z1, Z2))) | product(Z1, Y, Z2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','qg3')).
% 0.20/0.44 tff(37,plain,
% 0.20/0.44 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.20/0.44 tff(38,plain,
% 0.20/0.44 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.20/0.44 tff(39,plain,(
% 0.20/0.44 ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))),
% 0.20/0.45 inference(skolemize,[status(sab)],[38])).
% 0.20/0.45 tff(40,plain,
% 0.20/0.45 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[39, 32])).
% 0.20/0.45 tff(41,plain,
% 0.20/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_2, e_2, e_3)) | (~product(e_1, e_2, e_2)) | product(e_2, e_1, e_3))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_2, e_2, e_3)) | (~product(e_1, e_2, e_2)) | product(e_2, e_1, e_3))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(42,plain,
% 0.20/0.45 ((product(e_2, e_1, e_3) | (~product(e_2, e_2, e_3)) | (~product(e_1, e_2, e_2))) <=> ((~product(e_2, e_2, e_3)) | (~product(e_1, e_2, e_2)) | product(e_2, e_1, e_3))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(43,plain,
% 0.20/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_3) | (~product(e_2, e_2, e_3)) | (~product(e_1, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_2, e_2, e_3)) | (~product(e_1, e_2, e_2)) | product(e_2, e_1, e_3)))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[42])).
% 0.20/0.45 tff(44,plain,
% 0.20/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_3) | (~product(e_2, e_2, e_3)) | (~product(e_1, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_2, e_2, e_3)) | (~product(e_1, e_2, e_2)) | product(e_2, e_1, e_3))),
% 0.20/0.45 inference(transitivity,[status(thm)],[43, 41])).
% 0.20/0.45 tff(45,plain,
% 0.20/0.45 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_3) | (~product(e_2, e_2, e_3)) | (~product(e_1, e_2, e_2)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(46,plain,
% 0.20/0.45 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_2, e_2, e_3)) | (~product(e_1, e_2, e_2)) | product(e_2, e_1, e_3)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.20/0.45 tff(47,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[46, 40, 23, 22, 30])).
% 0.20/0.45 tff(48,plain,((~product(e_2, e_2, e_3)) | (~product(e_1, e_2, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(49,plain,
% 0.20/0.45 (~product(e_2, e_2, e_3)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[48, 22])).
% 0.20/0.45 tff(50,assumption,(~product(e_3, e_2, e_1)), introduced(assumption)).
% 0.20/0.45 tff(51,assumption,(~product(e_2, e_2, e_3)), introduced(assumption)).
% 0.20/0.45 tff(52,assumption,(product(e_2, e_2, e_2)), introduced(assumption)).
% 0.20/0.45 tff(53,assumption,(product(e_3, e_2, e_2)), introduced(assumption)).
% 0.20/0.45 tff(54,plain,
% 0.20/0.45 (^[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))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(55,plain,
% 0.20/0.45 (![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)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[54])).
% 0.20/0.45 tff(56,plain,
% 0.20/0.45 (![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)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(57,plain,
% 0.20/0.45 (^[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)))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(58,plain,
% 0.20/0.45 (![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)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[57])).
% 0.20/0.45 tff(59,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')).
% 0.20/0.45 tff(60,plain,
% 0.20/0.45 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.20/0.45 tff(61,plain,
% 0.20/0.45 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.20/0.45 tff(62,plain,(
% 0.20/0.45 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.45 inference(skolemize,[status(sab)],[61])).
% 0.20/0.45 tff(63,plain,
% 0.20/0.45 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[62, 55])).
% 0.20/0.45 tff(64,plain,
% 0.20/0.45 ((~equalish(e_3, e_2)) <=> (~equalish(e_3, e_2))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(65,axiom,(~equalish(e_3, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_3_is_not_e_2')).
% 0.20/0.45 tff(66,plain,
% 0.20/0.45 (~equalish(e_3, e_2)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.20/0.45 tff(67,plain,
% 0.20/0.45 (((~![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_3, e_2, e_2)) | (~product(e_2, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(68,plain,
% 0.20/0.45 ((equalish(e_3, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_3, e_2, e_2))) <=> (equalish(e_3, e_2) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(69,plain,
% 0.20/0.45 (((~![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_3, e_2, e_2)) | (~product(e_2, e_2, e_2))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[68])).
% 0.20/0.45 tff(70,plain,
% 0.20/0.45 (((~![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_3, e_2, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.20/0.45 inference(transitivity,[status(thm)],[69, 67])).
% 0.20/0.45 tff(71,plain,
% 0.20/0.45 ((~![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)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(72,plain,
% 0.20/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_2, e_2))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.20/0.45 tff(73,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[72, 66, 63, 53, 52])).
% 0.20/0.45 tff(74,plain,((~product(e_3, e_2, e_2)) | (~product(e_2, e_2, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(75,plain,
% 0.20/0.45 (~product(e_3, e_2, e_2)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[74, 52])).
% 0.20/0.45 tff(76,plain,
% 0.20/0.45 (^[Y: $i, X: $i] : refl((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) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(77,plain,
% 0.20/0.45 (![Y: $i, X: $i] : (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_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[76])).
% 0.20/0.45 tff(78,plain,
% 0.20/0.45 (![Y: $i, X: $i] : (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_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(79,plain,
% 0.20/0.45 (^[Y: $i, X: $i] : 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)))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(80,plain,
% 0.20/0.45 (![Y: $i, X: $i] : (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) <=> ![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[79])).
% 0.20/0.45 tff(81,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))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','product_total_function1')).
% 0.20/0.45 tff(82,plain,
% 0.20/0.45 (![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.20/0.45 tff(83,plain,
% 0.20/0.45 (![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[82, 78])).
% 0.20/0.45 tff(84,plain,(
% 0.20/0.45 ![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.20/0.45 inference(skolemize,[status(sab)],[83])).
% 0.20/0.45 tff(85,plain,
% 0.20/0.45 (![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[84, 77])).
% 0.20/0.45 tff(86,plain,
% 0.20/0.45 (group_element(e_3) <=> group_element(e_3)),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(87,axiom,(group_element(e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_3')).
% 0.20/0.45 tff(88,plain,
% 0.20/0.45 (group_element(e_3)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.20/0.45 tff(89,plain,
% 0.20/0.45 (group_element(e_2) <=> group_element(e_2)),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(90,axiom,(group_element(e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_2')).
% 0.20/0.46 tff(91,plain,
% 0.20/0.46 (group_element(e_2)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.20/0.46 tff(92,plain,
% 0.20/0.46 (((~![Y: $i, X: $i] : (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_2)) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1))) <=> ((~![Y: $i, X: $i] : (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_2)) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(93,plain,
% 0.20/0.46 ((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))) <=> ((~group_element(e_3)) | (~group_element(e_2)) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(94,plain,
% 0.20/0.46 (((~![Y: $i, X: $i] : (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_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_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_3)) | (~group_element(e_2)) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1)))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[93])).
% 0.20/0.46 tff(95,plain,
% 0.20/0.46 (((~![Y: $i, X: $i] : (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_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_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_3)) | (~group_element(e_2)) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1))),
% 0.20/0.46 inference(transitivity,[status(thm)],[94, 92])).
% 0.20/0.46 tff(96,plain,
% 0.20/0.46 ((~![Y: $i, X: $i] : (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_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_3)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(97,plain,
% 0.20/0.46 ((~![Y: $i, X: $i] : (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_2)) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.20/0.46 tff(98,plain,
% 0.20/0.46 (product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[97, 91, 88, 85])).
% 0.20/0.46 tff(99,plain,
% 0.20/0.46 (product(e_3, e_2, e_3)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[98, 75, 50])).
% 0.20/0.46 tff(100,assumption,(product(e_3, e_2, e_3)), introduced(assumption)).
% 0.20/0.46 tff(101,assumption,(product(e_3, e_1, e_3)), introduced(assumption)).
% 0.20/0.46 tff(102,plain,
% 0.20/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_3, e_2, e_3)) | (~product(e_3, 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_2) | (~product(e_3, e_2, e_3)) | (~product(e_3, e_1, e_3)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(103,plain,
% 0.20/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_3, e_2, e_3)) | (~product(e_3, e_1, e_3)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(104,plain,
% 0.20/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_2) | (~product(e_3, e_2, e_3)) | (~product(e_3, e_1, e_3))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.20/0.46 tff(105,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[104, 15, 12, 101, 100])).
% 0.20/0.46 tff(106,plain,((~product(e_3, e_1, e_3)) | (~product(e_3, e_2, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(107,plain,
% 0.20/0.46 (~product(e_3, e_1, e_3)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[106, 99])).
% 0.20/0.46 tff(108,plain,
% 0.20/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_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)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(109,plain,
% 0.20/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_1, e_2, e_2)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(110,plain,
% 0.20/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_1, e_2, e_2))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.20/0.46 tff(111,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[110, 15, 63, 52, 22])).
% 0.20/0.46 tff(112,plain,((~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(113,plain,
% 0.20/0.46 (~product(e_1, e_2, e_2)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[112, 52])).
% 0.20/0.46 tff(114,assumption,(product(e_1, e_2, e_3)), introduced(assumption)).
% 0.20/0.46 tff(115,plain,
% 0.20/0.46 ((~equalish(e_1, e_3)) <=> (~equalish(e_1, e_3))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(116,axiom,(~equalish(e_1, e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_1_is_not_e_3')).
% 0.20/0.46 tff(117,plain,
% 0.20/0.46 (~equalish(e_1, e_3)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.20/0.46 tff(118,plain,
% 0.20/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_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)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(119,plain,
% 0.20/0.46 ((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)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(120,plain,
% 0.20/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_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))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[119])).
% 0.20/0.46 tff(121,plain,
% 0.20/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_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)))),
% 0.20/0.46 inference(transitivity,[status(thm)],[120, 118])).
% 0.20/0.46 tff(122,plain,
% 0.20/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_1, e_2, e_3)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(123,plain,
% 0.20/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_3, e_2, e_3))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.20/0.46 tff(124,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[123, 117, 63, 100, 114])).
% 0.20/0.46 tff(125,plain,((~product(e_1, e_2, e_3)) | (~product(e_3, e_2, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(126,plain,
% 0.20/0.46 (~product(e_1, e_2, e_3)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[125, 99])).
% 0.20/0.46 tff(127,plain,
% 0.20/0.46 (group_element(e_1) <=> group_element(e_1)),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(128,axiom,(group_element(e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_1')).
% 0.20/0.46 tff(129,plain,
% 0.20/0.46 (group_element(e_1)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.20/0.46 tff(130,plain,
% 0.20/0.46 (((~![Y: $i, X: $i] : (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_3) | product(e_1, e_2, e_2) | (~group_element(e_2)) | product(e_1, e_2, e_1) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (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_3) | product(e_1, e_2, e_2) | (~group_element(e_2)) | product(e_1, e_2, e_1) | (~group_element(e_1)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(131,plain,
% 0.20/0.46 ((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))) <=> (product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | (~group_element(e_2)) | product(e_1, e_2, e_1) | (~group_element(e_1)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(132,plain,
% 0.20/0.46 (((~![Y: $i, X: $i] : (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_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_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | (~group_element(e_2)) | product(e_1, e_2, e_1) | (~group_element(e_1))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[131])).
% 0.20/0.46 tff(133,plain,
% 0.20/0.46 (((~![Y: $i, X: $i] : (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_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_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | (~group_element(e_2)) | product(e_1, e_2, e_1) | (~group_element(e_1)))),
% 0.20/0.46 inference(transitivity,[status(thm)],[132, 130])).
% 0.20/0.46 tff(134,plain,
% 0.20/0.46 ((~![Y: $i, X: $i] : (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_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_1)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(135,plain,
% 0.20/0.46 ((~![Y: $i, X: $i] : (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_3) | product(e_1, e_2, e_2) | (~group_element(e_2)) | product(e_1, e_2, e_1) | (~group_element(e_1))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.20/0.46 tff(136,plain,
% 0.20/0.46 (product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[135, 129, 91, 85])).
% 0.20/0.46 tff(137,plain,
% 0.20/0.46 (product(e_1, e_2, e_1)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[136, 126, 113])).
% 0.20/0.46 tff(138,assumption,(product(e_1, e_2, e_1)), introduced(assumption)).
% 0.20/0.46 tff(139,assumption,(product(e_3, e_1, e_2)), introduced(assumption)).
% 0.20/0.46 tff(140,assumption,(~product(e_1, e_2, e_2)), introduced(assumption)).
% 0.20/0.46 tff(141,plain,
% 0.20/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_2) | (~product(e_3, e_1, e_2)) | (~product(e_2, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_2, e_2) | (~product(e_3, e_1, e_2)) | (~product(e_2, e_3, e_1)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(142,plain,
% 0.20/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_2) | (~product(e_3, e_1, e_2)) | (~product(e_2, e_3, e_1)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(143,plain,
% 0.20/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_2, e_2) | (~product(e_3, e_1, e_2)) | (~product(e_2, e_3, e_1))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.20/0.47 tff(144,plain,
% 0.20/0.47 (product(e_1, e_2, e_2) | (~product(e_3, e_1, e_2)) | (~product(e_2, e_3, e_1))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[143, 40])).
% 0.20/0.47 tff(145,plain,
% 0.20/0.47 (~product(e_2, e_3, e_1)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[144, 139, 140])).
% 0.20/0.47 tff(146,assumption,(~product(e_2, e_3, e_1)), introduced(assumption)).
% 0.20/0.47 tff(147,plain,
% 0.20/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_3, e_1, e_2)) | product(e_2, e_3, e_1) | (~product(e_1, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_3, e_1, e_2)) | product(e_2, e_3, e_1) | (~product(e_1, e_2, e_1)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(148,plain,
% 0.20/0.47 ((product(e_2, e_3, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_3, e_1, e_2))) <=> ((~product(e_3, e_1, e_2)) | product(e_2, e_3, e_1) | (~product(e_1, e_2, e_1)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(149,plain,
% 0.20/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_3, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_3, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_3, e_1, e_2)) | product(e_2, e_3, e_1) | (~product(e_1, e_2, e_1))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[148])).
% 0.20/0.47 tff(150,plain,
% 0.20/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_3, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_3, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_3, e_1, e_2)) | product(e_2, e_3, e_1) | (~product(e_1, e_2, e_1)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[149, 147])).
% 0.20/0.47 tff(151,plain,
% 0.20/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_3, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_3, e_1, e_2)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(152,plain,
% 0.20/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_3, e_1, e_2)) | product(e_2, e_3, e_1) | (~product(e_1, e_2, e_1))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.20/0.47 tff(153,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[152, 40, 139, 138, 146])).
% 0.20/0.47 tff(154,plain,((~product(e_1, e_2, e_1)) | (~product(e_3, e_1, e_2)) | product(e_2, e_3, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(155,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[154, 145, 139, 138])).
% 0.20/0.47 tff(156,plain,((~product(e_3, e_1, e_2)) | (~product(e_1, e_2, e_1)) | product(e_1, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(157,plain,
% 0.20/0.47 (~product(e_3, e_1, e_2)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[156, 137, 113])).
% 0.20/0.47 tff(158,plain,
% 0.20/0.47 (((~![Y: $i, X: $i] : (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_1, e_3) | (~group_element(e_3)) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (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_1, e_3) | (~group_element(e_3)) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(159,plain,
% 0.20/0.47 ((product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_3))) <=> (product(e_3, e_1, e_3) | (~group_element(e_3)) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(160,plain,
% 0.20/0.47 (((~![Y: $i, X: $i] : (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_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (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_1, e_3) | (~group_element(e_3)) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[159])).
% 0.20/0.47 tff(161,plain,
% 0.20/0.47 (((~![Y: $i, X: $i] : (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_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (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_1, e_3) | (~group_element(e_3)) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[160, 158])).
% 0.20/0.47 tff(162,plain,
% 0.20/0.47 ((~![Y: $i, X: $i] : (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_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_3)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(163,plain,
% 0.20/0.47 ((~![Y: $i, X: $i] : (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_1, e_3) | (~group_element(e_3)) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.20/0.47 tff(164,plain,
% 0.20/0.47 (product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[163, 129, 88, 85])).
% 0.20/0.47 tff(165,plain,
% 0.20/0.47 (product(e_3, e_1, e_1)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[164, 157, 107])).
% 0.20/0.47 tff(166,assumption,(~product(e_1, e_1, e_2)), introduced(assumption)).
% 0.20/0.47 tff(167,assumption,(~product(e_1, e_3, e_2)), introduced(assumption)).
% 0.20/0.47 tff(168,assumption,(product(e_1, e_1, e_1)), introduced(assumption)).
% 0.20/0.47 tff(169,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_3) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_1, e_1)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(170,plain,
% 0.20/0.47 ((equalish(e_1, e_3) | (~product(e_3, e_1, e_1)) | (~product(e_1, e_1, e_1))) <=> (equalish(e_1, e_3) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_1, e_1)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(171,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_3) | (~product(e_3, e_1, e_1)) | (~product(e_1, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_1, e_1))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[170])).
% 0.20/0.47 tff(172,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_3) | (~product(e_3, e_1, e_1)) | (~product(e_1, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_1, e_1)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[171, 169])).
% 0.20/0.47 tff(173,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_3) | (~product(e_3, e_1, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(174,plain,
% 0.20/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_1, e_1))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.20/0.47 tff(175,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[174, 117, 63, 2, 168])).
% 0.20/0.47 tff(176,plain,((~product(e_1, e_1, e_1)) | (~product(e_3, e_1, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(177,plain,
% 0.20/0.47 (~product(e_1, e_1, e_1)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[176, 2])).
% 0.20/0.47 tff(178,plain,
% 0.20/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_3, e_1)) | product(e_1, e_1, e_1) | (~product(e_3, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_3, e_1)) | product(e_1, e_1, e_1) | (~product(e_3, e_1, e_1)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(179,plain,
% 0.20/0.47 ((product(e_1, e_1, e_1) | (~product(e_3, e_1, e_1)) | (~product(e_1, e_3, e_1))) <=> ((~product(e_1, e_3, e_1)) | product(e_1, e_1, e_1) | (~product(e_3, e_1, e_1)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(180,plain,
% 0.20/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_1) | (~product(e_3, e_1, e_1)) | (~product(e_1, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_3, e_1)) | product(e_1, e_1, e_1) | (~product(e_3, e_1, e_1))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[179])).
% 0.20/0.47 tff(181,plain,
% 0.20/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_1) | (~product(e_3, e_1, e_1)) | (~product(e_1, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_3, e_1)) | product(e_1, e_1, e_1) | (~product(e_3, e_1, e_1)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[180, 178])).
% 0.20/0.47 tff(182,plain,
% 0.20/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_1) | (~product(e_3, e_1, e_1)) | (~product(e_1, e_3, e_1)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(183,plain,
% 0.20/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_3, e_1)) | product(e_1, e_1, e_1) | (~product(e_3, e_1, e_1))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[182, 181])).
% 0.20/0.47 tff(184,plain,
% 0.20/0.47 (~product(e_1, e_3, e_1)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[183, 40, 2, 177])).
% 0.20/0.47 tff(185,plain,
% 0.20/0.47 (((~![Y: $i, X: $i] : (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_1)) | product(e_1, e_3, e_1) | product(e_1, e_3, e_2) | product(e_1, e_3, e_3))) <=> ((~![Y: $i, X: $i] : (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_1)) | product(e_1, e_3, e_1) | product(e_1, e_3, e_2) | product(e_1, e_3, e_3))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(186,plain,
% 0.20/0.47 ((product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_1))) <=> ((~group_element(e_3)) | (~group_element(e_1)) | product(e_1, e_3, e_1) | product(e_1, e_3, e_2) | product(e_1, e_3, e_3))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(187,plain,
% 0.20/0.47 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_3)) | (~group_element(e_1)) | product(e_1, e_3, e_1) | product(e_1, e_3, e_2) | product(e_1, e_3, e_3)))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[186])).
% 0.20/0.48 tff(188,plain,
% 0.20/0.48 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_3)) | (~group_element(e_1)) | product(e_1, e_3, e_1) | product(e_1, e_3, e_2) | product(e_1, e_3, e_3))),
% 0.20/0.48 inference(transitivity,[status(thm)],[187, 185])).
% 0.20/0.48 tff(189,plain,
% 0.20/0.48 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_1)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(190,plain,
% 0.20/0.48 ((~![Y: $i, X: $i] : (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_1)) | product(e_1, e_3, e_1) | product(e_1, e_3, e_2) | product(e_1, e_3, e_3)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[189, 188])).
% 0.20/0.48 tff(191,plain,
% 0.20/0.48 (product(e_1, e_3, e_1) | product(e_1, e_3, e_2) | product(e_1, e_3, e_3)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[190, 129, 88, 85])).
% 0.20/0.48 tff(192,plain,
% 0.20/0.48 (product(e_1, e_3, e_3)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[191, 184, 167])).
% 0.20/0.48 tff(193,plain,
% 0.20/0.48 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_1)) | product(e_1, e_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | product(e_1, e_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(194,plain,
% 0.20/0.48 ((product(e_1, e_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_1))) <=> ((~group_element(e_1)) | product(e_1, e_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(195,plain,
% 0.20/0.48 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_1)) | product(e_1, e_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1)))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[194])).
% 0.20/0.48 tff(196,plain,
% 0.20/0.48 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | product(e_1, e_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1))),
% 0.20/0.48 inference(transitivity,[status(thm)],[195, 193])).
% 0.20/0.48 tff(197,plain,
% 0.20/0.48 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_1)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(198,plain,
% 0.20/0.48 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | product(e_1, e_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[197, 196])).
% 0.20/0.48 tff(199,plain,
% 0.20/0.48 (product(e_1, e_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[198, 129, 85])).
% 0.20/0.48 tff(200,plain,
% 0.20/0.48 (product(e_1, e_1, e_3)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[199, 177, 166])).
% 0.20/0.48 tff(201,plain,
% 0.20/0.48 ((~equalish(e_3, e_1)) <=> (~equalish(e_3, e_1))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(202,axiom,(~equalish(e_3, e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_3_is_not_e_1')).
% 0.20/0.48 tff(203,plain,
% 0.20/0.48 (~equalish(e_3, e_1)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[202, 201])).
% 0.20/0.48 tff(204,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_3, e_1) | (~product(e_1, e_1, e_3)) | (~product(e_1, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_1) | (~product(e_1, e_1, e_3)) | (~product(e_1, e_3, e_3)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(205,plain,
% 0.20/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_1) | (~product(e_1, e_1, e_3)) | (~product(e_1, e_3, e_3)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(206,plain,
% 0.20/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_1) | (~product(e_1, e_1, e_3)) | (~product(e_1, e_3, e_3))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[205, 204])).
% 0.20/0.48 tff(207,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[206, 203, 12, 200, 192])).
% 0.20/0.48 tff(208,plain,((~product(e_3, e_1, e_1)) | product(e_1, e_3, e_2) | product(e_1, e_1, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(209,plain,
% 0.20/0.48 (product(e_1, e_3, e_2)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[208, 166, 2])).
% 0.20/0.48 tff(210,plain,
% 0.20/0.48 (product(e_1, e_1, e_3)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[199, 166, 177])).
% 0.20/0.48 tff(211,assumption,(~product(e_3, e_1, e_2)), introduced(assumption)).
% 0.20/0.48 tff(212,plain,
% 0.20/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_2) | (~product(e_1, e_1, e_3)) | (~product(e_1, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_2) | (~product(e_1, e_1, e_3)) | (~product(e_1, e_3, e_2)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(213,plain,
% 0.20/0.48 ((product(e_3, e_1, e_2) | (~product(e_1, e_3, e_2)) | (~product(e_1, e_1, e_3))) <=> (product(e_3, e_1, e_2) | (~product(e_1, e_1, e_3)) | (~product(e_1, e_3, e_2)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(214,plain,
% 0.20/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_2) | (~product(e_1, e_3, e_2)) | (~product(e_1, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_2) | (~product(e_1, e_1, e_3)) | (~product(e_1, e_3, e_2))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[213])).
% 0.20/0.48 tff(215,plain,
% 0.20/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_2) | (~product(e_1, e_3, e_2)) | (~product(e_1, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_2) | (~product(e_1, e_1, e_3)) | (~product(e_1, e_3, e_2)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[214, 212])).
% 0.20/0.49 tff(216,plain,
% 0.20/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_2) | (~product(e_1, e_3, e_2)) | (~product(e_1, e_1, e_3)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(217,plain,
% 0.20/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_2) | (~product(e_1, e_1, e_3)) | (~product(e_1, e_3, e_2))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[216, 215])).
% 0.20/0.49 tff(218,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[217, 40, 211, 210, 209])).
% 0.20/0.49 tff(219,plain,(product(e_1, e_1, e_2) | product(e_3, e_1, e_2) | (~product(e_3, e_1, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(220,plain,
% 0.20/0.49 (product(e_1, e_1, e_2)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[219, 157, 165])).
% 0.20/0.49 tff(221,plain,
% 0.20/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_2) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_2, e_2) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_2)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(222,plain,
% 0.20/0.49 ((product(e_1, e_2, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_2, e_1, e_1))) <=> (product(e_1, e_2, e_2) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_2)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(223,plain,
% 0.20/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_2, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_2) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_2))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[222])).
% 0.20/0.49 tff(224,plain,
% 0.20/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_2, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_2, e_2) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_2)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[223, 221])).
% 0.20/0.49 tff(225,plain,
% 0.20/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_2, e_1, e_1)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(226,plain,
% 0.20/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_2, e_2) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_2))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[225, 224])).
% 0.20/0.49 tff(227,plain,
% 0.20/0.49 (~product(e_2, e_1, e_1)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[226, 40, 113, 220])).
% 0.20/0.49 tff(228,plain,
% 0.20/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_1, e_2)) | product(e_2, e_1, e_1) | (~product(e_1, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_1, e_2)) | product(e_2, e_1, e_1) | (~product(e_1, e_2, e_1)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(229,plain,
% 0.20/0.49 ((product(e_2, e_1, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_1, e_2))) <=> ((~product(e_1, e_1, e_2)) | product(e_2, e_1, e_1) | (~product(e_1, e_2, e_1)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(230,plain,
% 0.20/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_1, e_2)) | product(e_2, e_1, e_1) | (~product(e_1, e_2, e_1))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[229])).
% 0.20/0.49 tff(231,plain,
% 0.20/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_1, e_2)) | product(e_2, e_1, e_1) | (~product(e_1, e_2, e_1)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[230, 228])).
% 0.20/0.49 tff(232,plain,
% 0.20/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_1, e_2)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(233,plain,
% 0.20/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_1, e_2)) | product(e_2, e_1, e_1) | (~product(e_1, e_2, e_1))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[232, 231])).
% 0.20/0.49 tff(234,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[233, 40, 137, 220, 227])).
% 0.20/0.49 tff(235,plain,((~product(e_2, e_2, e_2)) | product(e_3, e_2, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(236,plain,
% 0.20/0.49 (~product(e_2, e_2, e_2)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[235, 50])).
% 0.20/0.49 tff(237,plain,
% 0.20/0.49 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_2)) | product(e_2, e_2, e_3) | product(e_2, e_2, e_2) | product(e_2, e_2, e_1))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_2)) | product(e_2, e_2, e_3) | product(e_2, e_2, e_2) | product(e_2, e_2, e_1))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(238,plain,
% 0.20/0.49 ((product(e_2, e_2, e_3) | product(e_2, e_2, e_2) | product(e_2, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_2))) <=> ((~group_element(e_2)) | product(e_2, e_2, e_3) | product(e_2, e_2, e_2) | product(e_2, e_2, e_1))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(239,plain,
% 0.20/0.49 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_2, e_3) | product(e_2, e_2, e_2) | product(e_2, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_2)) | product(e_2, e_2, e_3) | product(e_2, e_2, e_2) | product(e_2, e_2, e_1)))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[238])).
% 0.20/0.49 tff(240,plain,
% 0.20/0.49 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_2, e_3) | product(e_2, e_2, e_2) | product(e_2, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_2)) | product(e_2, e_2, e_3) | product(e_2, e_2, e_2) | product(e_2, e_2, e_1))),
% 0.20/0.49 inference(transitivity,[status(thm)],[239, 237])).
% 0.20/0.49 tff(241,plain,
% 0.20/0.49 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_2, e_3) | product(e_2, e_2, e_2) | product(e_2, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_2)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(242,plain,
% 0.20/0.49 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_2)) | product(e_2, e_2, e_3) | product(e_2, e_2, e_2) | product(e_2, e_2, e_1)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[241, 240])).
% 0.20/0.49 tff(243,plain,
% 0.20/0.49 (product(e_2, e_2, e_3) | product(e_2, e_2, e_2) | product(e_2, e_2, e_1)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[242, 91, 85])).
% 0.20/0.49 tff(244,plain,
% 0.20/0.49 (product(e_2, e_2, e_1)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[243, 236, 51])).
% 0.20/0.49 tff(245,assumption,(product(e_2, e_2, e_1)), introduced(assumption)).
% 0.20/0.49 tff(246,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_1, e_2) | (~product(e_2, e_2, e_1)) | (~product(e_1, e_2, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_2) | (~product(e_2, e_2, e_1)) | (~product(e_1, e_2, e_1)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(247,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_1, e_2) | (~product(e_2, e_2, e_1)) | (~product(e_1, e_2, e_1)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(248,plain,
% 0.20/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_2) | (~product(e_2, e_2, e_1)) | (~product(e_1, e_2, e_1))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[247, 246])).
% 0.20/0.49 tff(249,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[248, 15, 63, 245, 138])).
% 0.20/0.49 tff(250,plain,((~product(e_1, e_2, e_1)) | (~product(e_2, e_2, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(251,plain,
% 0.20/0.49 (~product(e_1, e_2, e_1)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[250, 244])).
% 0.20/0.49 tff(252,assumption,(product(e_2, e_1, e_1)), introduced(assumption)).
% 0.20/0.49 tff(253,plain,
% 0.20/0.49 (~product(e_1, e_2, e_1)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[250, 245])).
% 0.20/0.49 tff(254,plain,
% 0.20/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_1) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_2, e_1) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_1, e_1)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(255,plain,
% 0.20/0.49 ((product(e_1, e_2, e_1) | (~product(e_2, e_1, e_1)) | (~product(e_2, e_2, e_1))) <=> (product(e_1, e_2, e_1) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_1, e_1)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(256,plain,
% 0.20/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_1) | (~product(e_2, e_1, e_1)) | (~product(e_2, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_1) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_1, e_1))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[255])).
% 0.20/0.49 tff(257,plain,
% 0.20/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_1) | (~product(e_2, e_1, e_1)) | (~product(e_2, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_2, e_1) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_1, e_1)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[256, 254])).
% 0.20/0.49 tff(258,plain,
% 0.20/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_1) | (~product(e_2, e_1, e_1)) | (~product(e_2, e_2, e_1)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(259,plain,
% 0.20/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_2, e_1) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_1, e_1))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[258, 257])).
% 0.20/0.49 tff(260,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[259, 40, 245, 253, 252])).
% 0.20/0.49 tff(261,plain,((~product(e_2, e_1, e_1)) | (~product(e_2, e_2, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(262,plain,
% 0.20/0.49 (~product(e_2, e_1, e_1)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[261, 244])).
% 0.20/0.49 tff(263,assumption,(~product(e_2, e_1, e_1)), introduced(assumption)).
% 0.20/0.50 tff(264,plain,
% 0.20/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_2, e_2, e_1)) | product(e_2, e_1, e_1) | (~product(e_1, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_2, e_2, e_1)) | product(e_2, e_1, e_1) | (~product(e_1, e_2, e_2)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(265,plain,
% 0.20/0.50 ((product(e_2, e_1, e_1) | (~product(e_2, e_2, e_1)) | (~product(e_1, e_2, e_2))) <=> ((~product(e_2, e_2, e_1)) | product(e_2, e_1, e_1) | (~product(e_1, e_2, e_2)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(266,plain,
% 0.20/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_1) | (~product(e_2, e_2, e_1)) | (~product(e_1, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_2, e_2, e_1)) | product(e_2, e_1, e_1) | (~product(e_1, e_2, e_2))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[265])).
% 0.20/0.50 tff(267,plain,
% 0.20/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_1) | (~product(e_2, e_2, e_1)) | (~product(e_1, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_2, e_2, e_1)) | product(e_2, e_1, e_1) | (~product(e_1, e_2, e_2)))),
% 0.20/0.50 inference(transitivity,[status(thm)],[266, 264])).
% 0.20/0.50 tff(268,plain,
% 0.20/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_1) | (~product(e_2, e_2, e_1)) | (~product(e_1, e_2, e_2)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(269,plain,
% 0.20/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_2, e_2, e_1)) | product(e_2, e_1, e_1) | (~product(e_1, e_2, e_2))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[268, 267])).
% 0.20/0.50 tff(270,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[269, 40, 245, 22, 263])).
% 0.20/0.50 tff(271,plain,(product(e_2, e_1, e_1) | (~product(e_2, e_2, e_1)) | (~product(e_1, e_2, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(272,plain,
% 0.20/0.50 (~product(e_1, e_2, e_2)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[271, 262, 244])).
% 0.20/0.50 tff(273,plain,
% 0.20/0.50 (product(e_1, e_2, e_3)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[136, 272, 251])).
% 0.20/0.50 tff(274,plain,
% 0.20/0.50 (~product(e_3, e_2, e_3)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[125, 273])).
% 0.20/0.50 tff(275,plain,
% 0.20/0.50 (product(e_3, e_2, e_2)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[98, 274, 50])).
% 0.20/0.50 tff(276,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_1, e_2) | (~product(e_3, e_1, e_2)) | (~product(e_3, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_2) | (~product(e_3, e_1, e_2)) | (~product(e_3, e_2, e_2)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(277,plain,
% 0.20/0.50 ((equalish(e_1, e_2) | (~product(e_3, e_2, e_2)) | (~product(e_3, e_1, e_2))) <=> (equalish(e_1, e_2) | (~product(e_3, e_1, e_2)) | (~product(e_3, e_2, e_2)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(278,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_1, e_2) | (~product(e_3, e_2, e_2)) | (~product(e_3, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_3, e_1, e_2)) | (~product(e_3, e_2, e_2))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[277])).
% 0.20/0.50 tff(279,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_1, e_2) | (~product(e_3, e_2, e_2)) | (~product(e_3, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_2) | (~product(e_3, e_1, e_2)) | (~product(e_3, e_2, e_2)))),
% 0.20/0.51 inference(transitivity,[status(thm)],[278, 276])).
% 0.20/0.51 tff(280,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_1, e_2) | (~product(e_3, e_2, e_2)) | (~product(e_3, e_1, e_2)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(281,plain,
% 0.20/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_2) | (~product(e_3, e_1, e_2)) | (~product(e_3, e_2, e_2))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[280, 279])).
% 0.20/0.51 tff(282,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[281, 15, 12, 139, 53])).
% 0.20/0.51 tff(283,plain,((~product(e_3, e_1, e_2)) | (~product(e_3, e_2, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(284,plain,
% 0.20/0.51 (~product(e_3, e_1, e_2)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[283, 275])).
% 0.20/0.51 tff(285,assumption,(~product(e_3, e_1, e_3)), introduced(assumption)).
% 0.20/0.51 tff(286,plain,
% 0.20/0.51 (product(e_3, e_1, e_1)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[164, 211, 285])).
% 0.20/0.51 tff(287,plain,
% 0.20/0.51 (product(e_1, e_1, e_2)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[219, 286, 211])).
% 0.20/0.51 tff(288,plain,
% 0.20/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_1) | (~product(e_2, e_3, e_1)) | (~product(e_3, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_2, e_1) | (~product(e_2, e_3, e_1)) | (~product(e_3, e_1, e_1)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(289,plain,
% 0.20/0.51 ((product(e_1, e_2, e_1) | (~product(e_3, e_1, e_1)) | (~product(e_2, e_3, e_1))) <=> (product(e_1, e_2, e_1) | (~product(e_2, e_3, e_1)) | (~product(e_3, e_1, e_1)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(290,plain,
% 0.20/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_1) | (~product(e_3, e_1, e_1)) | (~product(e_2, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_1) | (~product(e_2, e_3, e_1)) | (~product(e_3, e_1, e_1))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[289])).
% 0.20/0.51 tff(291,plain,
% 0.20/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_1) | (~product(e_3, e_1, e_1)) | (~product(e_2, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_2, e_1) | (~product(e_2, e_3, e_1)) | (~product(e_3, e_1, e_1)))),
% 0.20/0.51 inference(transitivity,[status(thm)],[290, 288])).
% 0.20/0.51 tff(292,plain,
% 0.20/0.51 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_1) | (~product(e_3, e_1, e_1)) | (~product(e_2, e_3, e_1)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(293,plain,
% 0.20/0.51 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_2, e_1) | (~product(e_2, e_3, e_1)) | (~product(e_3, e_1, e_1))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[292, 291])).
% 0.20/0.51 tff(294,plain,
% 0.20/0.51 (~product(e_2, e_3, e_1)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[293, 40, 286, 253])).
% 0.20/0.51 tff(295,plain,
% 0.20/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_3, e_2, e_2)) | product(e_2, e_3, e_1) | (~product(e_2, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_3, e_2, e_2)) | product(e_2, e_3, e_1) | (~product(e_2, e_2, e_1)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(296,plain,
% 0.20/0.51 ((product(e_2, e_3, e_1) | (~product(e_2, e_2, e_1)) | (~product(e_3, e_2, e_2))) <=> ((~product(e_3, e_2, e_2)) | product(e_2, e_3, e_1) | (~product(e_2, e_2, e_1)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(297,plain,
% 0.20/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_3, e_1) | (~product(e_2, e_2, e_1)) | (~product(e_3, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_3, e_2, e_2)) | product(e_2, e_3, e_1) | (~product(e_2, e_2, e_1))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[296])).
% 0.20/0.51 tff(298,plain,
% 0.20/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_3, e_1) | (~product(e_2, e_2, e_1)) | (~product(e_3, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_3, e_2, e_2)) | product(e_2, e_3, e_1) | (~product(e_2, e_2, e_1)))),
% 0.20/0.51 inference(transitivity,[status(thm)],[297, 295])).
% 0.20/0.51 tff(299,plain,
% 0.20/0.51 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_3, e_1) | (~product(e_2, e_2, e_1)) | (~product(e_3, e_2, e_2)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(300,plain,
% 0.20/0.51 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_3, e_2, e_2)) | product(e_2, e_3, e_1) | (~product(e_2, e_2, e_1))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[299, 298])).
% 0.20/0.51 tff(301,plain,
% 0.20/0.51 (~product(e_3, e_2, e_2)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[300, 40, 245, 294])).
% 0.20/0.51 tff(302,plain,
% 0.20/0.51 (product(e_3, e_2, e_3)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[98, 301, 50])).
% 0.20/0.51 tff(303,plain,
% 0.20/0.51 (~product(e_1, e_2, e_3)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[125, 302])).
% 0.20/0.51 tff(304,plain,
% 0.20/0.51 (product(e_1, e_2, e_2)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[136, 303, 253])).
% 0.20/0.51 tff(305,plain,
% 0.20/0.51 ((~equalish(e_2, e_1)) <=> (~equalish(e_2, e_1))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(306,axiom,(~equalish(e_2, e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_is_not_e_1')).
% 0.20/0.51 tff(307,plain,
% 0.20/0.51 (~equalish(e_2, e_1)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[306, 305])).
% 0.20/0.51 tff(308,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_1) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_2, e_2)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(309,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_1) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_2, e_2)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(310,plain,
% 0.20/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_2, e_2))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[309, 308])).
% 0.20/0.51 tff(311,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[310, 307, 12, 304, 287])).
% 0.20/0.51 tff(312,plain,(product(e_3, e_1, e_2) | product(e_3, e_2, e_1) | (~product(e_2, e_2, e_1)) | product(e_3, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(313,plain,
% 0.20/0.51 (product(e_3, e_1, e_3)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[312, 284, 244, 50])).
% 0.20/0.51 tff(314,plain,
% 0.20/0.51 ((~equalish(e_2, e_3)) <=> (~equalish(e_2, e_3))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(315,axiom,(~equalish(e_2, e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_is_not_e_3')).
% 0.20/0.51 tff(316,plain,
% 0.20/0.51 (~equalish(e_2, e_3)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[315, 314])).
% 0.20/0.51 tff(317,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_2, e_3) | (~product(e_3, e_1, e_3)) | (~product(e_2, e_1, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_3) | (~product(e_3, e_1, e_3)) | (~product(e_2, e_1, e_3)))),
% 0.20/0.51 inference(rewrite,[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(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_3) | (~product(e_3, e_1, e_3)) | (~product(e_2, e_1, e_3)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(319,plain,
% 0.20/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_3) | (~product(e_3, e_1, e_3)) | (~product(e_2, e_1, e_3))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[318, 317])).
% 0.20/0.51 tff(320,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[319, 316, 63, 101, 24])).
% 0.20/0.51 tff(321,plain,((~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(322,plain,
% 0.20/0.51 (~product(e_2, e_1, e_3)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[321, 313])).
% 0.20/0.51 tff(323,assumption,(product(e_1, e_1, 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_1, e_3)) | (~product(e_3, e_1, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_1, e_1, e_3)) | (~product(e_3, e_1, 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_1, e_3)) | (~product(e_1, e_1, e_3))) <=> (equalish(e_1, e_3) | (~product(e_1, e_1, e_3)) | (~product(e_3, e_1, 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_1, e_3)) | (~product(e_1, e_1, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_1, e_1, e_3)) | (~product(e_3, e_1, 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_1, e_3)) | (~product(e_1, e_1, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_1, e_1, e_3)) | (~product(e_3, e_1, 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_1, e_3)) | (~product(e_1, e_1, 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: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_1, e_1, e_3)) | (~product(e_3, e_1, e_3))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[328, 327])).
% 0.20/0.51 tff(330,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[329, 117, 63, 101, 323])).
% 0.20/0.51 tff(331,plain,((~product(e_1, e_1, e_3)) | (~product(e_3, e_1, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(332,plain,
% 0.20/0.51 (~product(e_1, e_1, e_3)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[331, 313])).
% 0.20/0.51 tff(333,assumption,(product(e_1, e_3, e_3)), 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(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_3, e_3)))),
% 0.20/0.51 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(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_3, e_3)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(336,plain,
% 0.20/0.52 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_3, e_3))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[335, 334])).
% 0.20/0.52 tff(337,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[336, 66, 12, 114, 333])).
% 0.20/0.52 tff(338,plain,((~product(e_1, e_3, e_3)) | (~product(e_1, e_2, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(339,plain,
% 0.20/0.52 (~product(e_1, e_3, e_3)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[338, 273])).
% 0.20/0.52 tff(340,plain,
% 0.20/0.52 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_2, e_2) | (~product(e_2, e_3, e_2)) | (~product(e_3, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_2, e_2) | (~product(e_2, e_3, e_2)) | (~product(e_3, e_2, e_2)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(341,plain,
% 0.20/0.52 ((product(e_2, e_2, e_2) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_3, e_2))) <=> (product(e_2, e_2, e_2) | (~product(e_2, e_3, e_2)) | (~product(e_3, e_2, e_2)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(342,plain,
% 0.20/0.52 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_2, e_2) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_2, e_2) | (~product(e_2, e_3, e_2)) | (~product(e_3, e_2, e_2))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[341])).
% 0.20/0.52 tff(343,plain,
% 0.20/0.52 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_2, e_2) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_2, e_2) | (~product(e_2, e_3, e_2)) | (~product(e_3, e_2, e_2)))),
% 0.20/0.52 inference(transitivity,[status(thm)],[342, 340])).
% 0.20/0.52 tff(344,plain,
% 0.20/0.52 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_2, e_2) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_3, e_2)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(345,plain,
% 0.20/0.52 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_2, e_2) | (~product(e_2, e_3, e_2)) | (~product(e_3, e_2, e_2))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[344, 343])).
% 0.20/0.52 tff(346,plain,
% 0.20/0.52 (~product(e_2, e_3, e_2)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[345, 40, 275, 236])).
% 0.20/0.52 tff(347,plain,
% 0.20/0.52 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_3, e_2) | (~product(e_3, e_2, e_2)) | (~product(e_3, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_3, e_2) | (~product(e_3, e_2, e_2)) | (~product(e_3, e_3, e_2)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(348,plain,
% 0.20/0.52 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_3, e_2) | (~product(e_3, e_2, e_2)) | (~product(e_3, e_3, e_2)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(349,plain,
% 0.20/0.52 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_3, e_2) | (~product(e_3, e_2, e_2)) | (~product(e_3, e_3, e_2))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[348, 347])).
% 0.20/0.52 tff(350,plain,
% 0.20/0.52 (~product(e_3, e_3, e_2)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[349, 40, 275, 346])).
% 0.20/0.52 tff(351,assumption,(~product(e_3, e_3, e_2)), introduced(assumption)).
% 0.20/0.52 tff(352,assumption,(product(e_1, e_3, e_2)), introduced(assumption)).
% 0.20/0.52 tff(353,plain,
% 0.20/0.52 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_3, e_1, e_3)) | (~product(e_1, e_3, e_2)) | product(e_3, e_3, e_2))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_3, e_1, e_3)) | (~product(e_1, e_3, e_2)) | product(e_3, e_3, e_2))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(354,plain,
% 0.20/0.52 ((product(e_3, e_3, e_2) | (~product(e_1, e_3, e_2)) | (~product(e_3, e_1, e_3))) <=> ((~product(e_3, e_1, e_3)) | (~product(e_1, e_3, e_2)) | product(e_3, e_3, e_2))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(355,plain,
% 0.20/0.52 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_3, e_2) | (~product(e_1, e_3, e_2)) | (~product(e_3, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_3, e_1, e_3)) | (~product(e_1, e_3, e_2)) | product(e_3, e_3, e_2)))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[354])).
% 0.20/0.52 tff(356,plain,
% 0.20/0.52 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_3, e_2) | (~product(e_1, e_3, e_2)) | (~product(e_3, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_3, e_1, e_3)) | (~product(e_1, e_3, e_2)) | product(e_3, e_3, e_2))),
% 0.20/0.52 inference(transitivity,[status(thm)],[355, 353])).
% 0.20/0.52 tff(357,plain,
% 0.20/0.52 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_3, e_2) | (~product(e_1, e_3, e_2)) | (~product(e_3, e_1, e_3)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(358,plain,
% 0.20/0.52 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_3, e_1, e_3)) | (~product(e_1, e_3, e_2)) | product(e_3, e_3, e_2)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[357, 356])).
% 0.20/0.52 tff(359,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[358, 40, 101, 352, 351])).
% 0.20/0.52 tff(360,plain,((~product(e_1, e_3, e_2)) | (~product(e_3, e_1, e_3)) | product(e_3, e_3, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(361,plain,
% 0.20/0.52 (~product(e_1, e_3, e_2)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[360, 313, 350])).
% 0.20/0.52 tff(362,plain,
% 0.20/0.52 (product(e_1, e_3, e_1)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[191, 361, 339])).
% 0.20/0.52 tff(363,assumption,(product(e_1, e_3, e_1)), introduced(assumption)).
% 0.20/0.52 tff(364,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_1, e_3) | (~product(e_1, e_3, 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_1, e_3) | (~product(e_1, e_3, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(365,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_1, e_3) | (~product(e_1, e_3, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(366,plain,
% 0.20/0.52 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_3) | (~product(e_1, e_3, e_1)) | (~product(e_1, e_1, e_1))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[365, 364])).
% 0.20/0.52 tff(367,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[366, 117, 12, 168, 363])).
% 0.20/0.52 tff(368,plain,((~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(369,plain,
% 0.20/0.52 (~product(e_1, e_1, e_1)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[368, 362])).
% 0.20/0.52 tff(370,plain,
% 0.20/0.52 (product(e_1, e_1, e_2)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[199, 369, 332])).
% 0.20/0.52 tff(371,plain,
% 0.20/0.52 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_2, e_3)) | (~product(e_1, e_1, e_2)) | product(e_2, e_1, e_3))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_1, e_2)) | product(e_2, e_1, e_3))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(372,plain,
% 0.20/0.53 ((product(e_2, e_1, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_1, e_2))) <=> ((~product(e_1, e_2, e_3)) | (~product(e_1, e_1, e_2)) | product(e_2, e_1, e_3))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(373,plain,
% 0.20/0.53 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_2, e_3)) | (~product(e_1, e_1, e_2)) | product(e_2, e_1, e_3)))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[372])).
% 0.20/0.53 tff(374,plain,
% 0.20/0.53 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_1, e_2)) | product(e_2, e_1, e_3))),
% 0.20/0.53 inference(transitivity,[status(thm)],[373, 371])).
% 0.20/0.53 tff(375,plain,
% 0.20/0.53 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_1, e_2)))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(376,plain,
% 0.20/0.53 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_1, e_2)) | product(e_2, e_1, e_3)),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[375, 374])).
% 0.20/0.53 tff(377,plain,
% 0.20/0.53 ($false),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[376, 40, 273, 370, 322])).
% 0.20/0.53 tff(378,plain,(product(e_3, e_2, e_1) | product(e_2, e_2, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.53 tff(379,plain,
% 0.20/0.53 (product(e_3, e_2, e_1)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[378, 49])).
% 0.20/0.53 tff(380,plain,
% 0.20/0.53 (~product(e_2, e_2, e_2)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[112, 22])).
% 0.20/0.53 tff(381,plain,
% 0.20/0.53 (product(e_2, e_2, e_1)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[243, 49, 380])).
% 0.20/0.53 tff(382,plain,
% 0.20/0.53 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_2, e_1)))) <=> ((~![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_2, e_1)) | (~product(e_2, e_2, e_1)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(383,plain,
% 0.20/0.53 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_2, e_1)))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(384,plain,
% 0.20/0.53 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_2, e_1))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[383, 382])).
% 0.20/0.53 tff(385,plain,
% 0.20/0.53 ($false),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[384, 316, 63, 1, 245])).
% 0.20/0.53 tff(386,plain,((~product(e_2, e_2, e_1)) | (~product(e_3, e_2, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.53 tff(387,plain,
% 0.20/0.53 ($false),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[386, 381, 379])).
% 0.20/0.53 tff(388,plain,(~product(e_1, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.53 tff(389,assumption,(~product(e_3, e_1, e_1)), introduced(assumption)).
% 0.20/0.53 tff(390,plain,
% 0.20/0.53 (product(e_3, e_1, e_2)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[164, 285, 389])).
% 0.20/0.53 tff(391,plain,
% 0.20/0.53 (~product(e_1, e_2, e_1)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[156, 390, 140])).
% 0.20/0.53 tff(392,plain,
% 0.20/0.53 (product(e_1, e_2, e_3)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[136, 391, 140])).
% 0.20/0.53 tff(393,plain,
% 0.20/0.53 (~product(e_1, e_3, e_3)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[338, 392])).
% 0.20/0.53 tff(394,assumption,(product(e_1, e_1, e_2)), introduced(assumption)).
% 0.20/0.53 tff(395,plain,
% 0.20/0.53 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_1, e_2)))),
% 0.20/0.53 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(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_1, e_2)))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(397,plain,
% 0.20/0.53 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_1, e_2))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[396, 395])).
% 0.20/0.53 tff(398,plain,
% 0.20/0.53 ($false),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[397, 117, 63, 139, 394])).
% 0.20/0.53 tff(399,plain,((~product(e_1, e_1, e_2)) | (~product(e_3, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.53 tff(400,plain,
% 0.20/0.53 (~product(e_1, e_1, e_2)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[399, 390])).
% 0.20/0.53 tff(401,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_1, e_2) | (~product(e_1, e_2, e_3)) | (~product(e_1, 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_2) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_1, e_3)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(402,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_1, e_2) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_1, e_3)))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(403,plain,
% 0.20/0.53 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_2) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_1, e_3))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[402, 401])).
% 0.20/0.53 tff(404,plain,
% 0.20/0.53 ($false),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[403, 15, 12, 114, 323])).
% 0.20/0.53 tff(405,plain,((~product(e_1, e_1, e_3)) | (~product(e_1, e_2, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.53 tff(406,plain,
% 0.20/0.53 (~product(e_1, e_1, e_3)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[405, 392])).
% 0.20/0.53 tff(407,plain,
% 0.20/0.53 (product(e_1, e_1, e_1)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[199, 406, 400])).
% 0.20/0.53 tff(408,plain,
% 0.20/0.53 (~product(e_1, e_3, e_1)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[368, 407])).
% 0.20/0.53 tff(409,plain,
% 0.20/0.53 (product(e_1, e_3, e_2)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[191, 408, 393])).
% 0.20/0.53 tff(410,assumption,(product(e_2, e_3, e_2)), introduced(assumption)).
% 0.20/0.53 tff(411,plain,
% 0.20/0.53 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_2, e_3, e_2)) | (~product(e_1, e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_2, e_3, e_2)) | (~product(e_1, e_3, e_2)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(412,plain,
% 0.20/0.53 ((equalish(e_2, e_1) | (~product(e_1, e_3, e_2)) | (~product(e_2, e_3, e_2))) <=> (equalish(e_2, e_1) | (~product(e_2, e_3, e_2)) | (~product(e_1, e_3, e_2)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(413,plain,
% 0.20/0.53 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_1, e_3, e_2)) | (~product(e_2, e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_2, e_3, e_2)) | (~product(e_1, e_3, e_2))))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[412])).
% 0.20/0.53 tff(414,plain,
% 0.20/0.53 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_1, e_3, e_2)) | (~product(e_2, e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_2, e_3, e_2)) | (~product(e_1, e_3, e_2)))),
% 0.20/0.53 inference(transitivity,[status(thm)],[413, 411])).
% 0.20/0.53 tff(415,plain,
% 0.20/0.53 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_1, e_3, e_2)) | (~product(e_2, e_3, e_2)))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(416,plain,
% 0.20/0.53 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_2, e_3, e_2)) | (~product(e_1, e_3, e_2))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[415, 414])).
% 0.20/0.53 tff(417,plain,
% 0.20/0.53 ($false),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[416, 307, 63, 352, 410])).
% 0.20/0.53 tff(418,plain,((~product(e_2, e_3, e_2)) | (~product(e_1, e_3, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.53 tff(419,plain,
% 0.20/0.53 (~product(e_2, e_3, e_2)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[418, 409])).
% 0.20/0.53 tff(420,plain,
% 0.20/0.53 (~product(e_2, e_3, e_1)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[144, 390, 140])).
% 0.20/0.53 tff(421,plain,
% 0.20/0.53 (((~![Y: $i, X: $i] : (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_2)) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1) | product(e_2, e_3, e_3))) <=> ((~![Y: $i, X: $i] : (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_2)) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1) | product(e_2, e_3, e_3))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(422,plain,
% 0.20/0.53 ((product(e_2, e_3, e_3) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_2))) <=> ((~group_element(e_3)) | (~group_element(e_2)) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1) | product(e_2, e_3, e_3))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(423,plain,
% 0.20/0.53 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_3, e_3) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_3)) | (~group_element(e_2)) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1) | product(e_2, e_3, e_3)))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[422])).
% 0.20/0.53 tff(424,plain,
% 0.20/0.53 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_3, e_3) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_3)) | (~group_element(e_2)) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1) | product(e_2, e_3, e_3))),
% 0.20/0.53 inference(transitivity,[status(thm)],[423, 421])).
% 0.20/0.53 tff(425,plain,
% 0.20/0.53 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_3, e_3) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_2)))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(426,plain,
% 0.20/0.53 ((~![Y: $i, X: $i] : (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_2)) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1) | product(e_2, e_3, e_3)),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[425, 424])).
% 0.20/0.54 tff(427,plain,
% 0.20/0.54 (product(e_2, e_3, e_2) | product(e_2, e_3, e_3)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[426, 91, 88, 85, 420])).
% 0.20/0.54 tff(428,plain,
% 0.20/0.54 (product(e_2, e_3, e_3)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[427, 419])).
% 0.20/0.54 tff(429,plain,
% 0.20/0.54 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_3) | (~product(e_2, e_3, e_3)) | (~product(e_1, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_3) | (~product(e_2, e_3, e_3)) | (~product(e_1, e_2, e_3)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(430,plain,
% 0.20/0.54 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_3) | (~product(e_2, e_3, e_3)) | (~product(e_1, e_2, e_3)))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(431,plain,
% 0.20/0.54 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_3) | (~product(e_2, e_3, e_3)) | (~product(e_1, e_2, e_3))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[430, 429])).
% 0.20/0.54 tff(432,plain,
% 0.20/0.54 ($false),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[431, 40, 285, 428, 392])).
% 0.20/0.54 tff(433,plain,(product(e_3, e_1, e_3) | product(e_1, e_2, e_2) | product(e_3, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.54 tff(434,plain,
% 0.20/0.54 (product(e_3, e_1, e_3) | product(e_3, e_1, e_1)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[433, 388])).
% 0.20/0.54 tff(435,plain,
% 0.20/0.54 (product(e_3, e_1, e_3)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[434, 21])).
% 0.20/0.54 tff(436,plain,
% 0.20/0.54 (~product(e_1, e_1, e_3)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[331, 101])).
% 0.20/0.54 tff(437,plain,
% 0.20/0.54 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_3) | (~product(e_1, e_3, e_1)) | (~product(e_3, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_3) | (~product(e_1, e_3, e_1)) | (~product(e_3, e_1, e_3)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(438,plain,
% 0.20/0.54 ((product(e_1, e_1, e_3) | (~product(e_3, e_1, e_3)) | (~product(e_1, e_3, e_1))) <=> (product(e_1, e_1, e_3) | (~product(e_1, e_3, e_1)) | (~product(e_3, e_1, e_3)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(439,plain,
% 0.20/0.54 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_3) | (~product(e_3, e_1, e_3)) | (~product(e_1, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_3) | (~product(e_1, e_3, e_1)) | (~product(e_3, e_1, e_3))))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[438])).
% 0.20/0.54 tff(440,plain,
% 0.20/0.54 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_3) | (~product(e_3, e_1, e_3)) | (~product(e_1, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_3) | (~product(e_1, e_3, e_1)) | (~product(e_3, e_1, e_3)))),
% 0.20/0.54 inference(transitivity,[status(thm)],[439, 437])).
% 0.20/0.54 tff(441,plain,
% 0.20/0.54 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_3) | (~product(e_3, e_1, e_3)) | (~product(e_1, e_3, e_1)))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(442,plain,
% 0.20/0.54 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_3) | (~product(e_1, e_3, e_1)) | (~product(e_3, e_1, e_3))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[441, 440])).
% 0.20/0.54 tff(443,plain,
% 0.20/0.54 ($false),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[442, 40, 101, 436, 363])).
% 0.20/0.54 tff(444,plain,((~product(e_1, e_3, e_1)) | (~product(e_3, e_1, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.54 tff(445,plain,
% 0.20/0.54 (~product(e_1, e_3, e_1)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[444, 435])).
% 0.20/0.54 tff(446,plain,
% 0.20/0.54 (product(e_3, e_3, e_2)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[360, 352, 101])).
% 0.20/0.54 tff(447,plain,
% 0.20/0.54 (((~![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_3, e_2)) | (~product(e_3, e_3, 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_1, e_3, e_2)) | (~product(e_3, e_3, e_2)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(448,plain,
% 0.20/0.54 ((equalish(e_1, e_3) | (~product(e_3, e_3, e_2)) | (~product(e_1, e_3, e_2))) <=> (equalish(e_1, e_3) | (~product(e_1, e_3, e_2)) | (~product(e_3, e_3, e_2)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(449,plain,
% 0.20/0.54 (((~![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_3, e_2)) | (~product(e_1, e_3, 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_1, e_3, e_2)) | (~product(e_3, e_3, e_2))))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[448])).
% 0.20/0.54 tff(450,plain,
% 0.20/0.54 (((~![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_3, e_2)) | (~product(e_1, e_3, 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_1, e_3, e_2)) | (~product(e_3, e_3, e_2)))),
% 0.20/0.54 inference(transitivity,[status(thm)],[449, 447])).
% 0.20/0.54 tff(451,plain,
% 0.20/0.54 ((~![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_3, e_2)) | (~product(e_1, e_3, e_2)))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(452,plain,
% 0.20/0.54 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_1, e_3, e_2)) | (~product(e_3, e_3, e_2))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[451, 450])).
% 0.20/0.54 tff(453,plain,
% 0.20/0.54 ($false),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[452, 117, 63, 352, 446])).
% 0.20/0.54 tff(454,plain,((~product(e_1, e_3, e_2)) | (~product(e_3, e_1, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.54 tff(455,plain,
% 0.20/0.54 (~product(e_1, e_3, e_2)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[454, 435])).
% 0.20/0.54 tff(456,plain,
% 0.20/0.54 (product(e_1, e_3, e_3)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[191, 455, 445])).
% 0.20/0.54 tff(457,plain,
% 0.20/0.54 (~product(e_1, e_2, e_3)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[338, 456])).
% 0.20/0.54 tff(458,plain,
% 0.20/0.54 (product(e_1, e_2, e_3) | product(e_1, e_2, e_1)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[136, 388])).
% 0.20/0.54 tff(459,plain,
% 0.20/0.54 (product(e_1, e_2, e_1)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[458, 457])).
% 0.20/0.54 tff(460,plain,
% 0.20/0.54 (((~![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_1)) | (~product(e_1, e_2, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_1, e_2, e_1)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(461,plain,
% 0.20/0.54 ((~![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_1)) | (~product(e_1, e_2, e_1)))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(462,plain,
% 0.20/0.54 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_1, e_2, e_1))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[461, 460])).
% 0.20/0.54 tff(463,plain,
% 0.20/0.54 ($false),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[462, 117, 63, 1, 459])).
% 0.20/0.54 tff(464,plain,(~product(e_3, e_2, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.54 tff(465,plain,
% 0.20/0.55 (product(e_2, e_2, e_3)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[378, 464])).
% 0.20/0.55 tff(466,plain,
% 0.20/0.55 (((~![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_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_2) | (~product(e_2, e_2, e_3)) | (~product(e_1, e_2, e_3)))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(467,plain,
% 0.20/0.55 ((~![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_3)) | (~product(e_1, e_2, e_3)))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(468,plain,
% 0.20/0.55 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_2) | (~product(e_2, e_2, e_3)) | (~product(e_1, e_2, e_3))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[467, 466])).
% 0.20/0.55 tff(469,plain,
% 0.20/0.55 ($false),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[468, 15, 63, 23, 114])).
% 0.20/0.55 tff(470,plain,((~product(e_1, e_2, e_3)) | (~product(e_2, e_2, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.55 tff(471,plain,
% 0.20/0.55 (~product(e_1, e_2, e_3)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[470, 465])).
% 0.20/0.55 tff(472,plain,
% 0.20/0.55 (product(e_1, e_2, e_1)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[458, 471])).
% 0.20/0.55 tff(473,plain,
% 0.20/0.55 ((~product(e_3, e_1, e_2)) | (~product(e_1, e_2, e_1))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[156, 388])).
% 0.20/0.55 tff(474,plain,
% 0.20/0.55 (~product(e_3, e_1, e_2)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[473, 472])).
% 0.20/0.55 tff(475,plain,
% 0.20/0.55 (~product(e_3, e_2, e_1)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[20, 286])).
% 0.20/0.55 tff(476,plain,
% 0.20/0.55 (product(e_2, e_2, e_3)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[378, 475])).
% 0.20/0.55 tff(477,plain,
% 0.20/0.55 (~product(e_1, e_2, e_3)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[470, 476])).
% 0.20/0.55 tff(478,plain,
% 0.20/0.55 (((~![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_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_3, e_2) | (~product(e_2, e_2, e_3)) | (~product(e_3, e_2, e_3)))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(479,plain,
% 0.20/0.55 ((~![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_3)) | (~product(e_3, e_2, e_3)))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(480,plain,
% 0.20/0.55 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_2, e_2, e_3)) | (~product(e_3, e_2, e_3))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[479, 478])).
% 0.20/0.55 tff(481,plain,
% 0.20/0.55 ($false),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[480, 66, 63, 100, 23])).
% 0.20/0.55 tff(482,plain,((~product(e_3, e_2, e_3)) | (~product(e_2, e_2, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.55 tff(483,plain,
% 0.20/0.55 (~product(e_3, e_2, e_3)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[482, 476])).
% 0.20/0.55 tff(484,plain,
% 0.20/0.55 (product(e_3, e_2, e_2)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[98, 483, 475])).
% 0.20/0.55 tff(485,plain,
% 0.20/0.55 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_3, 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_3, e_1) | (~product(e_3, e_2, e_2)) | (~product(e_1, e_2, e_2)))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(486,plain,
% 0.20/0.55 ((equalish(e_3, e_1) | (~product(e_1, e_2, e_2)) | (~product(e_3, e_2, e_2))) <=> (equalish(e_3, e_1) | (~product(e_3, e_2, e_2)) | (~product(e_1, e_2, e_2)))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(487,plain,
% 0.20/0.55 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_1, 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_1) | (~product(e_3, e_2, e_2)) | (~product(e_1, e_2, e_2))))),
% 0.20/0.55 inference(monotonicity,[status(thm)],[486])).
% 0.20/0.55 tff(488,plain,
% 0.20/0.55 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_1, 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_1) | (~product(e_3, e_2, e_2)) | (~product(e_1, e_2, e_2)))),
% 0.20/0.55 inference(transitivity,[status(thm)],[487, 485])).
% 0.20/0.55 tff(489,plain,
% 0.20/0.55 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_1, e_2, e_2)) | (~product(e_3, e_2, e_2)))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(490,plain,
% 0.20/0.55 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_3, e_2, e_2)) | (~product(e_1, e_2, e_2))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[489, 488])).
% 0.20/0.55 tff(491,plain,
% 0.20/0.55 ($false),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[490, 203, 63, 53, 22])).
% 0.20/0.55 tff(492,plain,((~product(e_3, e_2, e_2)) | (~product(e_1, e_2, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.55 tff(493,plain,
% 0.20/0.55 (~product(e_1, e_2, e_2)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[492, 484])).
% 0.20/0.55 tff(494,plain,
% 0.20/0.55 (product(e_1, e_2, e_1)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[136, 493, 477])).
% 0.20/0.55 tff(495,plain,
% 0.20/0.55 ($false),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[233, 40, 138, 394, 263])).
% 0.20/0.55 tff(496,plain,(product(e_2, e_1, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.55 tff(497,plain,
% 0.20/0.55 (product(e_2, e_1, e_1)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[496, 494, 287])).
% 0.20/0.55 tff(498,plain,
% 0.20/0.55 (((~![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_1, e_1)) | (~product(e_2, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_3) | (~product(e_3, e_1, e_1)) | (~product(e_2, e_1, e_1)))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(499,plain,
% 0.20/0.55 ((~![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_1, e_1)) | (~product(e_2, e_1, e_1)))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(500,plain,
% 0.20/0.55 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_3) | (~product(e_3, e_1, e_1)) | (~product(e_2, e_1, e_1))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[499, 498])).
% 0.20/0.55 tff(501,plain,
% 0.20/0.55 ($false),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[500, 316, 63, 286, 497])).
% 0.20/0.55 tff(502,plain,(product(e_3, e_1, e_2) | product(e_3, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.55 tff(503,plain,
% 0.20/0.55 (product(e_3, e_1, e_3)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[502, 474])).
% 0.20/0.55 tff(504,plain,
% 0.20/0.55 (~product(e_1, e_1, e_3)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[331, 503])).
% 0.20/0.55 tff(505,plain,
% 0.20/0.55 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_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_1, e_2) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_2, e_1)))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(506,plain,
% 0.20/0.55 ((equalish(e_1, e_2) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_1, e_1))) <=> (equalish(e_1, e_2) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_2, e_1)))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(507,plain,
% 0.20/0.55 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_1, e_2, 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_1, e_2) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_2, e_1))))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[506])).
% 0.20/0.56 tff(508,plain,
% 0.20/0.56 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_1, e_2, 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_1, e_2) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_2, e_1)))),
% 0.20/0.56 inference(transitivity,[status(thm)],[507, 505])).
% 0.20/0.56 tff(509,plain,
% 0.20/0.56 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.20/0.56 inference(quant_inst,[status(thm)],[])).
% 0.20/0.56 tff(510,plain,
% 0.20/0.56 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_2) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_2, e_1))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[509, 508])).
% 0.20/0.56 tff(511,plain,
% 0.20/0.56 ($false),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[510, 15, 12, 472, 168])).
% 0.20/0.56 tff(512,plain,(~product(e_1, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.56 tff(513,plain,
% 0.20/0.56 (product(e_1, e_1, e_2)),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[199, 512, 504])).
% 0.20/0.56 tff(514,plain,
% 0.20/0.56 (product(e_2, e_1, e_1)),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[496, 513, 472])).
% 0.20/0.56 tff(515,plain,
% 0.20/0.56 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_1) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_1) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_2, e_1)))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(516,plain,
% 0.20/0.56 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_1) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_2, e_1)))),
% 0.20/0.56 inference(quant_inst,[status(thm)],[])).
% 0.20/0.56 tff(517,plain,
% 0.20/0.56 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_1) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_2, e_1))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[516, 515])).
% 0.20/0.56 tff(518,plain,
% 0.20/0.56 ($false),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[517, 40, 472, 512, 514])).
% 0.20/0.56 % SZS output end Proof
%------------------------------------------------------------------------------