TSTP Solution File: GRP130-1.003 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP130-1.003 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n027.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 22:26:13 EDT 2022
% Result : Unsatisfiable 0.19s 0.41s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP130-1.003 : TPTP v8.1.0. Released v1.2.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n027.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Aug 31 15:21:02 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.19/0.41 % SZS status Unsatisfiable
% 0.19/0.41 % SZS output start Proof
% 0.19/0.41 tff(product_type, type, (
% 0.19/0.41 product: ( $i * $i * $i ) > $o)).
% 0.19/0.41 tff(e_1_type, type, (
% 0.19/0.41 e_1: $i)).
% 0.19/0.41 tff(e_2_type, type, (
% 0.19/0.41 e_2: $i)).
% 0.19/0.41 tff(e_3_type, type, (
% 0.19/0.41 e_3: $i)).
% 0.19/0.41 tff(equalish_type, type, (
% 0.19/0.41 equalish: ( $i * $i ) > $o)).
% 0.19/0.41 tff(group_element_type, type, (
% 0.19/0.41 group_element: $i > $o)).
% 0.19/0.41 tff(1,assumption,(product(e_1, e_2, e_1)), introduced(assumption)).
% 0.19/0.41 tff(2,assumption,(product(e_2, e_2, e_1)), introduced(assumption)).
% 0.19/0.41 tff(3,assumption,(product(e_2, e_3, e_1)), introduced(assumption)).
% 0.19/0.41 tff(4,plain,
% 0.19/0.41 (^[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))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(5,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[4])).
% 0.19/0.41 tff(6,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(7,plain,
% 0.19/0.41 (^[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)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(8,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[7])).
% 0.19/0.41 tff(9,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product(X, W, Y)) | (~product(X, Z, Y))) | equalish(W, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product_right_cancellation')).
% 0.19/0.41 tff(10,plain,
% 0.19/0.41 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.19/0.41 tff(11,plain,
% 0.19/0.41 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.19/0.41 tff(12,plain,(
% 0.19/0.41 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[11])).
% 0.19/0.41 tff(13,plain,
% 0.19/0.41 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.19/0.41 tff(14,plain,
% 0.19/0.41 ((~equalish(e_3, e_2)) <=> (~equalish(e_3, e_2))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(15,axiom,(~equalish(e_3, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_2')).
% 0.19/0.41 tff(16,plain,
% 0.19/0.41 (~equalish(e_3, e_2)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.19/0.41 tff(17,plain,
% 0.19/0.41 (((~![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_2, e_2, e_1)) | (~product(e_2, e_3, e_1)))) <=> ((~![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_2, e_2, e_1)) | (~product(e_2, e_3, e_1)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(18,plain,
% 0.19/0.41 ((~![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_2, e_2, e_1)) | (~product(e_2, e_3, e_1)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(19,plain,
% 0.19/0.41 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_3, e_1))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.19/0.41 tff(20,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[19, 16, 13, 2, 3])).
% 0.19/0.41 tff(21,plain,((~product(e_2, e_3, e_1)) | (~product(e_2, e_2, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(22,plain,
% 0.19/0.41 (~product(e_2, e_3, e_1)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[21, 2])).
% 0.19/0.41 tff(23,assumption,(product(e_1, e_1, e_2)), introduced(assumption)).
% 0.19/0.41 tff(24,plain,
% 0.19/0.41 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : refl((product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1))) <=> (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(25,plain,
% 0.19/0.41 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[24])).
% 0.19/0.41 tff(26,plain,
% 0.19/0.41 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(27,plain,
% 0.19/0.41 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : trans(monotonicity(rewrite(((~product(X, Y, Z1)) | (~product(X, Z1, Z2))) <=> ((~product(X, Z1, Z2)) | (~product(X, Y, Z1)))), ((((~product(X, Y, Z1)) | (~product(X, Z1, Z2))) | product(Z2, Y, X)) <=> (((~product(X, Z1, Z2)) | (~product(X, Y, Z1))) | product(Z2, Y, X)))), rewrite((((~product(X, Z1, Z2)) | (~product(X, Y, Z1))) | product(Z2, Y, X)) <=> (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))), ((((~product(X, Y, Z1)) | (~product(X, Z1, Z2))) | product(Z2, Y, X)) <=> (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(28,plain,
% 0.19/0.41 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(X, Y, Z1)) | (~product(X, Z1, Z2))) | product(Z2, Y, X)) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[27])).
% 0.19/0.41 tff(29,axiom,(![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(X, Y, Z1)) | (~product(X, Z1, Z2))) | product(Z2, Y, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qg3')).
% 0.19/0.41 tff(30,plain,
% 0.19/0.41 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.19/0.41 tff(31,plain,
% 0.19/0.41 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.19/0.41 tff(32,plain,(
% 0.19/0.41 ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[31])).
% 0.19/0.41 tff(33,plain,
% 0.19/0.41 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[32, 25])).
% 0.19/0.41 tff(34,plain,
% 0.19/0.41 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_1, e_1, e_2)) | (~product(e_1, e_3, e_1)) | product(e_2, e_3, e_1))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_3, e_1)) | product(e_2, e_3, e_1))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(35,plain,
% 0.19/0.41 ((product(e_2, e_3, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_3, e_1))) <=> ((~product(e_1, e_1, e_2)) | (~product(e_1, e_3, e_1)) | product(e_2, e_3, e_1))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(36,plain,
% 0.19/0.41 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_3, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_1, e_1, e_2)) | (~product(e_1, e_3, e_1)) | product(e_2, e_3, e_1)))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[35])).
% 0.19/0.41 tff(37,plain,
% 0.19/0.41 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_3, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_3, e_1)) | product(e_2, e_3, e_1))),
% 0.19/0.41 inference(transitivity,[status(thm)],[36, 34])).
% 0.19/0.41 tff(38,plain,
% 0.19/0.41 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_3, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_3, e_1)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(39,plain,
% 0.19/0.41 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_3, e_1)) | product(e_2, e_3, e_1)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.19/0.41 tff(40,plain,
% 0.19/0.41 (~product(e_1, e_3, e_1)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[39, 33, 23, 22])).
% 0.19/0.41 tff(41,assumption,(product(e_1, e_3, e_2)), introduced(assumption)).
% 0.19/0.41 tff(42,plain,
% 0.19/0.41 ((~equalish(e_3, e_1)) <=> (~equalish(e_3, e_1))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(43,axiom,(~equalish(e_3, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_1')).
% 0.19/0.41 tff(44,plain,
% 0.19/0.41 (~equalish(e_3, e_1)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.19/0.41 tff(45,plain,
% 0.19/0.41 (((~![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_2)) | (~product(e_1, e_3, e_2)))) <=> ((~![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_2)) | (~product(e_1, e_3, e_2)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(46,plain,
% 0.19/0.41 ((~![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_2)) | (~product(e_1, e_3, e_2)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(47,plain,
% 0.19/0.41 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_3, e_2))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.19/0.41 tff(48,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[47, 44, 13, 23, 41])).
% 0.19/0.41 tff(49,plain,((~product(e_1, e_3, e_2)) | (~product(e_1, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(50,plain,
% 0.19/0.41 (~product(e_1, e_3, e_2)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[49, 23])).
% 0.19/0.41 tff(51,plain,
% 0.19/0.41 (^[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))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(52,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[51])).
% 0.19/0.41 tff(53,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(54,plain,
% 0.19/0.41 (^[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)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(55,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[54])).
% 0.19/0.41 tff(56,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/sandbox2/benchmark/theBenchmark.p','product_total_function1')).
% 0.19/0.41 tff(57,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.19/0.41 tff(58,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.19/0.41 tff(59,plain,(
% 0.19/0.41 ![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)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[58])).
% 0.19/0.41 tff(60,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[59, 52])).
% 0.19/0.41 tff(61,plain,
% 0.19/0.41 (group_element(e_3) <=> group_element(e_3)),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(62,axiom,(group_element(e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_3')).
% 0.19/0.41 tff(63,plain,
% 0.19/0.41 (group_element(e_3)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.19/0.41 tff(64,plain,
% 0.19/0.41 (group_element(e_1) <=> group_element(e_1)),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(65,axiom,(group_element(e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_1')).
% 0.19/0.41 tff(66,plain,
% 0.19/0.41 (group_element(e_1)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.19/0.41 tff(67,plain,
% 0.19/0.41 (((~![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_3) | product(e_1, e_3, 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_1)) | product(e_1, e_3, e_1) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(68,plain,
% 0.19/0.41 ((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_3) | product(e_1, e_3, e_2))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(69,plain,
% 0.19/0.41 (((~![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_3) | product(e_1, e_3, e_2)))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[68])).
% 0.19/0.42 tff(70,plain,
% 0.19/0.42 (((~![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_3) | product(e_1, e_3, e_2))),
% 0.19/0.42 inference(transitivity,[status(thm)],[69, 67])).
% 0.19/0.42 tff(71,plain,
% 0.19/0.42 ((~![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)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(72,plain,
% 0.19/0.42 ((~![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_3) | product(e_1, e_3, e_2)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.19/0.42 tff(73,plain,
% 0.19/0.42 (product(e_1, e_3, e_1) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[72, 66, 63, 60])).
% 0.19/0.42 tff(74,plain,
% 0.19/0.42 (product(e_1, e_3, e_3)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[73, 50, 40])).
% 0.19/0.42 tff(75,assumption,(product(e_2, e_3, e_3)), introduced(assumption)).
% 0.19/0.42 tff(76,assumption,(product(e_1, e_3, e_3)), introduced(assumption)).
% 0.19/0.42 tff(77,plain,
% 0.19/0.42 (^[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))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(78,plain,
% 0.19/0.42 (![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)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[77])).
% 0.19/0.42 tff(79,plain,
% 0.19/0.42 (![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)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(80,plain,
% 0.19/0.42 (^[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)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(81,plain,
% 0.19/0.42 (![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)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[80])).
% 0.19/0.42 tff(82,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product_left_cancellation')).
% 0.19/0.42 tff(83,plain,
% 0.19/0.42 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.19/0.42 tff(84,plain,
% 0.19/0.42 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[83, 79])).
% 0.19/0.42 tff(85,plain,(
% 0.19/0.42 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.19/0.42 inference(skolemize,[status(sab)],[84])).
% 0.19/0.42 tff(86,plain,
% 0.19/0.42 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[85, 78])).
% 0.19/0.42 tff(87,plain,
% 0.19/0.42 ((~equalish(e_2, e_1)) <=> (~equalish(e_2, e_1))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(88,axiom,(~equalish(e_2, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_1')).
% 0.19/0.42 tff(89,plain,
% 0.19/0.42 (~equalish(e_2, e_1)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.19/0.42 tff(90,plain,
% 0.19/0.42 (((~![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_3)) | (~product(e_2, e_3, 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_1) | (~product(e_1, e_3, e_3)) | (~product(e_2, e_3, e_3)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(91,plain,
% 0.19/0.42 ((~![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_3)) | (~product(e_2, e_3, e_3)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(92,plain,
% 0.19/0.42 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_1, e_3, e_3)) | (~product(e_2, e_3, e_3))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.19/0.42 tff(93,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[92, 89, 86, 76, 75])).
% 0.19/0.42 tff(94,plain,((~product(e_2, e_3, e_3)) | (~product(e_1, e_3, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(95,plain,
% 0.19/0.42 (~product(e_2, e_3, e_3)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[94, 74])).
% 0.19/0.42 tff(96,plain,
% 0.19/0.42 (group_element(e_2) <=> group_element(e_2)),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(97,axiom,(group_element(e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_2')).
% 0.19/0.42 tff(98,plain,
% 0.19/0.42 (group_element(e_2)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.19/0.42 tff(99,plain,
% 0.19/0.42 (((~![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_3) | product(e_2, e_3, 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_2, e_3, e_2) | product(e_2, e_3, e_3) | product(e_2, e_3, e_1))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(100,plain,
% 0.19/0.42 ((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_3) | product(e_2, e_3, e_1))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(101,plain,
% 0.19/0.42 (((~![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_3) | product(e_2, e_3, e_1)))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[100])).
% 0.19/0.42 tff(102,plain,
% 0.19/0.42 (((~![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_3) | product(e_2, e_3, e_1))),
% 0.19/0.43 inference(transitivity,[status(thm)],[101, 99])).
% 0.19/0.43 tff(103,plain,
% 0.19/0.43 ((~![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)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(104,plain,
% 0.19/0.43 ((~![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_3) | product(e_2, e_3, e_1)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.19/0.43 tff(105,plain,
% 0.19/0.43 (product(e_2, e_3, e_2) | product(e_2, e_3, e_3)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[104, 98, 63, 60, 22])).
% 0.19/0.43 tff(106,plain,
% 0.19/0.43 (product(e_2, e_3, e_2)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[105, 95])).
% 0.19/0.43 tff(107,plain,
% 0.19/0.43 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_2, e_2, e_1)) | product(e_1, e_3, e_2) | (~product(e_2, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (~product(e_2, e_2, e_1)) | product(e_1, e_3, e_2) | (~product(e_2, e_3, e_2)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(108,plain,
% 0.19/0.43 ((product(e_1, e_3, e_2) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_3, e_2))) <=> ((~product(e_2, e_2, e_1)) | product(e_1, e_3, e_2) | (~product(e_2, e_3, e_2)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(109,plain,
% 0.19/0.43 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_3, e_2) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_2, e_2, e_1)) | product(e_1, e_3, e_2) | (~product(e_2, e_3, e_2))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[108])).
% 0.19/0.43 tff(110,plain,
% 0.19/0.43 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_3, e_2) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (~product(e_2, e_2, e_1)) | product(e_1, e_3, e_2) | (~product(e_2, e_3, e_2)))),
% 0.19/0.43 inference(transitivity,[status(thm)],[109, 107])).
% 0.19/0.43 tff(111,plain,
% 0.19/0.43 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_3, e_2) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_3, e_2)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(112,plain,
% 0.19/0.43 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (~product(e_2, e_2, e_1)) | product(e_1, e_3, e_2) | (~product(e_2, e_3, e_2))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.19/0.43 tff(113,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[112, 33, 2, 50, 106])).
% 0.19/0.43 tff(114,plain,((~product(e_1, e_1, e_2)) | (~product(e_2, e_2, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(115,plain,
% 0.19/0.43 (~product(e_1, e_1, e_2)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[114, 2])).
% 0.19/0.43 tff(116,plain,
% 0.19/0.43 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_2) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_2) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_1, e_2)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(117,plain,
% 0.19/0.43 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_2) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_1, e_2)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(118,plain,
% 0.19/0.43 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_2) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_1, e_2))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.19/0.43 tff(119,plain,
% 0.19/0.43 (~product(e_2, e_1, e_2)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[118, 33, 2, 115])).
% 0.19/0.43 tff(120,assumption,(product(e_2, e_1, e_1)), introduced(assumption)).
% 0.19/0.43 tff(121,assumption,(~product(e_1, e_1, e_2)), introduced(assumption)).
% 0.19/0.43 tff(122,plain,
% 0.19/0.43 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_2) | (~product(e_2, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_2) | (~product(e_2, e_1, e_1)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(123,plain,
% 0.19/0.43 ((product(e_1, e_1, e_2) | (~product(e_2, e_1, e_1)) | (~product(e_2, e_1, e_1))) <=> (product(e_1, e_1, e_2) | (~product(e_2, e_1, e_1)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(124,plain,
% 0.19/0.43 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_2) | (~product(e_2, e_1, e_1)) | (~product(e_2, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_2) | (~product(e_2, e_1, e_1))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[123])).
% 0.19/0.43 tff(125,plain,
% 0.19/0.43 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_2) | (~product(e_2, e_1, e_1)) | (~product(e_2, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_2) | (~product(e_2, e_1, e_1)))),
% 0.19/0.43 inference(transitivity,[status(thm)],[124, 122])).
% 0.19/0.43 tff(126,plain,
% 0.19/0.43 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_2) | (~product(e_2, e_1, e_1)) | (~product(e_2, e_1, e_1)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(127,plain,
% 0.19/0.43 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_2) | (~product(e_2, e_1, e_1))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.19/0.43 tff(128,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[127, 33, 121, 120])).
% 0.19/0.43 tff(129,plain,((~product(e_2, e_1, e_1)) | product(e_1, e_1, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(130,plain,
% 0.19/0.43 (~product(e_2, e_1, e_1)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[129, 115])).
% 0.19/0.43 tff(131,plain,
% 0.19/0.43 (((~![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)) | (~group_element(e_1)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_1) | product(e_2, e_1, 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)) | (~group_element(e_1)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_1) | product(e_2, e_1, e_2))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(132,plain,
% 0.19/0.43 ((product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_2))) <=> ((~group_element(e_2)) | (~group_element(e_1)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_1) | product(e_2, e_1, e_2))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(133,plain,
% 0.19/0.43 (((~![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_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_1)) | (~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)) | (~group_element(e_1)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_1) | product(e_2, e_1, e_2)))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[132])).
% 0.19/0.43 tff(134,plain,
% 0.19/0.43 (((~![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_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_1)) | (~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)) | (~group_element(e_1)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_1) | product(e_2, e_1, e_2))),
% 0.19/0.43 inference(transitivity,[status(thm)],[133, 131])).
% 0.19/0.43 tff(135,plain,
% 0.19/0.43 ((~![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_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_2)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(136,plain,
% 0.19/0.43 ((~![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)) | (~group_element(e_1)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_1) | product(e_2, e_1, e_2)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.19/0.43 tff(137,plain,
% 0.19/0.43 (product(e_2, e_1, e_3) | product(e_2, e_1, e_1)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[136, 66, 98, 60, 119])).
% 0.19/0.43 tff(138,plain,
% 0.19/0.43 (product(e_2, e_1, e_3)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[137, 130])).
% 0.19/0.43 tff(139,assumption,(~product(e_2, e_1, e_2)), introduced(assumption)).
% 0.19/0.43 tff(140,assumption,(product(e_2, e_3, e_2)), introduced(assumption)).
% 0.19/0.43 tff(141,assumption,(product(e_2, e_1, e_3)), introduced(assumption)).
% 0.19/0.43 tff(142,plain,
% 0.19/0.43 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_1, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_3, e_2)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(143,plain,
% 0.19/0.43 ((product(e_2, e_1, e_2) | (~product(e_2, e_3, e_2)) | (~product(e_2, e_1, e_3))) <=> (product(e_2, e_1, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_3, e_2)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(144,plain,
% 0.19/0.43 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_2) | (~product(e_2, e_3, e_2)) | (~product(e_2, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_3, e_2))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[143])).
% 0.19/0.43 tff(145,plain,
% 0.19/0.43 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_2) | (~product(e_2, e_3, e_2)) | (~product(e_2, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_1, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_3, e_2)))),
% 0.19/0.43 inference(transitivity,[status(thm)],[144, 142])).
% 0.19/0.43 tff(146,plain,
% 0.19/0.43 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_2) | (~product(e_2, e_3, e_2)) | (~product(e_2, e_1, e_3)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(147,plain,
% 0.19/0.43 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_1, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_3, e_2))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.19/0.43 tff(148,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[147, 33, 141, 140, 139])).
% 0.19/0.43 tff(149,plain,((~product(e_2, e_3, e_2)) | (~product(e_2, e_1, e_3)) | product(e_2, e_1, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(150,plain,
% 0.19/0.43 (~product(e_2, e_3, e_2)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[149, 138, 119])).
% 0.19/0.43 tff(151,plain,
% 0.19/0.43 (product(e_2, e_3, e_3)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[105, 150])).
% 0.19/0.43 tff(152,plain,
% 0.19/0.43 (((~![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_2, e_1, e_3)) | (~product(e_2, 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_2, e_1, e_3)) | (~product(e_2, e_3, e_3)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(153,plain,
% 0.19/0.43 ((~![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_2, e_1, e_3)) | (~product(e_2, e_3, e_3)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(154,plain,
% 0.19/0.43 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_3, e_3))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.19/0.43 tff(155,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[154, 44, 13, 138, 151])).
% 0.19/0.43 tff(156,plain,(~product(e_2, e_2, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(157,assumption,(~product(e_3, e_2, e_1)), introduced(assumption)).
% 0.19/0.43 tff(158,assumption,(~product(e_2, e_2, e_1)), introduced(assumption)).
% 0.19/0.43 tff(159,assumption,(product(e_1, e_1, e_3)), introduced(assumption)).
% 0.19/0.43 tff(160,plain,
% 0.19/0.43 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_2, e_1) | (~product(e_1, e_1, e_3)) | (~product(e_1, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_3, e_2, e_1) | (~product(e_1, e_1, e_3)) | (~product(e_1, e_2, e_1)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(161,plain,
% 0.19/0.43 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_2, e_1) | (~product(e_1, e_1, e_3)) | (~product(e_1, e_2, e_1)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(162,plain,
% 0.19/0.43 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_3, e_2, e_1) | (~product(e_1, e_1, e_3)) | (~product(e_1, e_2, e_1))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.19/0.43 tff(163,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[162, 33, 157, 159, 1])).
% 0.19/0.43 tff(164,plain,((~product(e_1, e_1, e_3)) | product(e_3, e_2, e_1) | (~product(e_1, e_2, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(165,plain,
% 0.19/0.43 (~product(e_1, e_1, e_3)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[164, 1, 157])).
% 0.19/0.43 tff(166,plain,
% 0.19/0.43 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_2, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_2, e_1)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(167,plain,
% 0.19/0.43 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_2, e_1)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(168,plain,
% 0.19/0.43 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_2, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_2, e_1))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[167, 166])).
% 0.19/0.43 tff(169,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[168, 33, 158, 23, 1])).
% 0.19/0.44 tff(170,plain,((~product(e_1, e_1, e_2)) | product(e_2, e_2, e_1) | (~product(e_1, e_2, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44 tff(171,plain,
% 0.19/0.44 (~product(e_1, e_1, e_2)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[170, 1, 158])).
% 0.19/0.44 tff(172,plain,
% 0.19/0.44 (((~![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)))) <=> ((~![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)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(173,plain,
% 0.19/0.44 ((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))) <=> (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)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(174,plain,
% 0.19/0.44 (((~![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)))) | (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))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[173])).
% 0.19/0.44 tff(175,plain,
% 0.19/0.44 (((~![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)))) | 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)))),
% 0.19/0.44 inference(transitivity,[status(thm)],[174, 172])).
% 0.19/0.44 tff(176,plain,
% 0.19/0.44 ((~![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)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(177,plain,
% 0.19/0.44 ((~![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))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.19/0.44 tff(178,plain,
% 0.19/0.44 (product(e_1, e_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[177, 66, 60])).
% 0.19/0.44 tff(179,plain,
% 0.19/0.44 (product(e_1, e_1, e_1)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[178, 171, 165])).
% 0.19/0.44 tff(180,plain,
% 0.19/0.44 ((~equalish(e_1, e_2)) <=> (~equalish(e_1, e_2))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(181,axiom,(~equalish(e_1, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_2')).
% 0.19/0.44 tff(182,plain,
% 0.19/0.44 (~equalish(e_1, e_2)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[181, 180])).
% 0.19/0.44 tff(183,plain,
% 0.19/0.44 (((~![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_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)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(184,plain,
% 0.19/0.44 ((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)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(185,plain,
% 0.19/0.44 (((~![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_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))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[184])).
% 0.19/0.44 tff(186,plain,
% 0.19/0.44 (((~![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_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)))),
% 0.19/0.44 inference(transitivity,[status(thm)],[185, 183])).
% 0.19/0.44 tff(187,plain,
% 0.19/0.44 ((~![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_1, e_2, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(188,plain,
% 0.19/0.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_2) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_2, e_1))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[187, 186])).
% 0.19/0.44 tff(189,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[188, 182, 13, 179, 1])).
% 0.19/0.44 tff(190,plain,((~product(e_1, e_2, e_1)) | product(e_2, e_2, e_1) | product(e_3, e_2, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44 tff(191,plain,
% 0.19/0.44 (~product(e_1, e_2, e_1)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[190, 158, 157])).
% 0.19/0.44 tff(192,assumption,(product(e_1, e_2, e_2)), introduced(assumption)).
% 0.19/0.44 tff(193,plain,
% 0.19/0.44 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_1) | (~product(e_1, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_2, e_1) | (~product(e_1, e_2, e_2)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(194,plain,
% 0.19/0.44 ((product(e_2, e_2, e_1) | (~product(e_1, e_2, e_2)) | (~product(e_1, e_2, e_2))) <=> (product(e_2, e_2, e_1) | (~product(e_1, e_2, e_2)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(195,plain,
% 0.19/0.44 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_1) | (~product(e_1, e_2, e_2)) | (~product(e_1, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_1) | (~product(e_1, e_2, e_2))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[194])).
% 0.19/0.44 tff(196,plain,
% 0.19/0.44 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_1) | (~product(e_1, e_2, e_2)) | (~product(e_1, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_2, e_1) | (~product(e_1, e_2, e_2)))),
% 0.19/0.44 inference(transitivity,[status(thm)],[195, 193])).
% 0.19/0.44 tff(197,plain,
% 0.19/0.44 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_1) | (~product(e_1, e_2, e_2)) | (~product(e_1, e_2, e_2)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(198,plain,
% 0.19/0.44 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_2, e_1) | (~product(e_1, e_2, e_2))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[197, 196])).
% 0.19/0.44 tff(199,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[198, 33, 158, 192])).
% 0.19/0.44 tff(200,plain,((~product(e_1, e_2, e_2)) | product(e_2, e_2, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44 tff(201,plain,
% 0.19/0.44 (~product(e_1, e_2, e_2)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[200, 158])).
% 0.19/0.44 tff(202,plain,
% 0.19/0.44 (((~![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)) | (~group_element(e_1)) | product(e_1, e_2, e_2) | product(e_1, e_2, e_3) | product(e_1, 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)) | (~group_element(e_1)) | product(e_1, e_2, e_2) | product(e_1, e_2, e_3) | product(e_1, e_2, e_1))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(203,plain,
% 0.19/0.44 ((product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_1))) <=> ((~group_element(e_2)) | (~group_element(e_1)) | product(e_1, e_2, e_2) | product(e_1, e_2, e_3) | product(e_1, e_2, e_1))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(204,plain,
% 0.19/0.44 (((~![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)))) | ((~group_element(e_2)) | (~group_element(e_1)) | product(e_1, e_2, e_2) | product(e_1, e_2, e_3) | product(e_1, e_2, e_1)))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[203])).
% 0.19/0.44 tff(205,plain,
% 0.19/0.44 (((~![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)))) | (~group_element(e_2)) | (~group_element(e_1)) | product(e_1, e_2, e_2) | product(e_1, e_2, e_3) | product(e_1, e_2, e_1))),
% 0.19/0.44 inference(transitivity,[status(thm)],[204, 202])).
% 0.19/0.44 tff(206,plain,
% 0.19/0.44 ((~![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)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(207,plain,
% 0.19/0.44 ((~![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)) | (~group_element(e_1)) | product(e_1, e_2, e_2) | product(e_1, e_2, e_3) | product(e_1, e_2, e_1)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[206, 205])).
% 0.19/0.44 tff(208,plain,
% 0.19/0.44 (product(e_1, e_2, e_2) | product(e_1, e_2, e_3) | product(e_1, e_2, e_1)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[207, 66, 98, 60])).
% 0.19/0.44 tff(209,plain,
% 0.19/0.44 (product(e_1, e_2, e_3)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[208, 201, 191])).
% 0.19/0.44 tff(210,assumption,(product(e_3, e_2, e_2)), introduced(assumption)).
% 0.19/0.44 tff(211,assumption,(product(e_2, e_2, e_2)), introduced(assumption)).
% 0.19/0.44 tff(212,plain,
% 0.19/0.44 ((~equalish(e_2, e_3)) <=> (~equalish(e_2, e_3))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(213,axiom,(~equalish(e_2, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_3')).
% 0.19/0.44 tff(214,plain,
% 0.19/0.44 (~equalish(e_2, e_3)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[213, 212])).
% 0.19/0.44 tff(215,plain,
% 0.19/0.44 (((~![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_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_2, e_3) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(216,plain,
% 0.19/0.44 ((~![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_2)) | (~product(e_2, e_2, e_2)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(217,plain,
% 0.19/0.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_3) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_2, e_2))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[216, 215])).
% 0.19/0.44 tff(218,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[217, 214, 86, 210, 211])).
% 0.19/0.44 tff(219,plain,((~product(e_2, e_2, e_2)) | (~product(e_3, e_2, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44 tff(220,plain,
% 0.19/0.44 (~product(e_2, e_2, e_2)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[219, 210])).
% 0.19/0.44 tff(221,plain,
% 0.19/0.44 (((~![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))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(222,plain,
% 0.19/0.44 ((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))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(223,plain,
% 0.19/0.44 (((~![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)))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[222])).
% 0.19/0.44 tff(224,plain,
% 0.19/0.44 (((~![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))),
% 0.19/0.44 inference(transitivity,[status(thm)],[223, 221])).
% 0.19/0.44 tff(225,plain,
% 0.19/0.44 ((~![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)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(226,plain,
% 0.19/0.44 ((~![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)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[225, 224])).
% 0.19/0.44 tff(227,plain,
% 0.19/0.44 (product(e_2, e_2, e_3) | product(e_2, e_2, e_2) | product(e_2, e_2, e_1)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[226, 98, 60])).
% 0.19/0.44 tff(228,plain,
% 0.19/0.44 (product(e_2, e_2, e_3)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[227, 220, 158])).
% 0.19/0.44 tff(229,assumption,(product(e_3, e_1, e_2)), introduced(assumption)).
% 0.19/0.44 tff(230,plain,
% 0.19/0.44 (((~![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_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)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(231,plain,
% 0.19/0.44 ((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)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(232,plain,
% 0.19/0.44 (((~![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_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))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[231])).
% 0.19/0.45 tff(233,plain,
% 0.19/0.45 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_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)))),
% 0.19/0.45 inference(transitivity,[status(thm)],[232, 230])).
% 0.19/0.45 tff(234,plain,
% 0.19/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_3, e_2, e_2)) | (~product(e_3, e_1, e_2)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(235,plain,
% 0.19/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_2) | (~product(e_3, e_1, e_2)) | (~product(e_3, e_2, e_2))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[234, 233])).
% 0.19/0.45 tff(236,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[235, 182, 13, 229, 210])).
% 0.19/0.45 tff(237,plain,((~product(e_3, e_1, e_2)) | (~product(e_3, e_2, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(238,plain,
% 0.19/0.45 (~product(e_3, e_1, e_2)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[237, 210])).
% 0.19/0.45 tff(239,plain,
% 0.19/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_3)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(240,plain,
% 0.19/0.45 ((product(e_3, e_1, e_2) | (~product(e_2, e_2, e_3)) | (~product(e_2, e_1, e_2))) <=> (product(e_3, e_1, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_3)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(241,plain,
% 0.19/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_2) | (~product(e_2, e_2, e_3)) | (~product(e_2, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_3))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[240])).
% 0.19/0.45 tff(242,plain,
% 0.19/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_2) | (~product(e_2, e_2, e_3)) | (~product(e_2, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_3)))),
% 0.19/0.45 inference(transitivity,[status(thm)],[241, 239])).
% 0.19/0.45 tff(243,plain,
% 0.19/0.45 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_2) | (~product(e_2, e_2, e_3)) | (~product(e_2, e_1, e_2)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(244,plain,
% 0.19/0.45 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_3))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[243, 242])).
% 0.19/0.45 tff(245,plain,
% 0.19/0.45 (~product(e_2, e_1, e_2)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[244, 33, 238, 228])).
% 0.19/0.45 tff(246,assumption,(product(e_2, e_2, e_3)), introduced(assumption)).
% 0.19/0.45 tff(247,plain,
% 0.19/0.45 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_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)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(248,plain,
% 0.19/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_3)) | (~product(e_2, e_1, e_3)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(249,plain,
% 0.19/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_2) | (~product(e_2, e_2, e_3)) | (~product(e_2, e_1, e_3))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[248, 247])).
% 0.19/0.45 tff(250,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[249, 182, 13, 246, 141])).
% 0.19/0.45 tff(251,plain,((~product(e_2, e_1, e_3)) | (~product(e_2, e_2, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(252,plain,
% 0.19/0.45 (~product(e_2, e_1, e_3)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[251, 228])).
% 0.19/0.45 tff(253,plain,
% 0.19/0.45 (product(e_2, e_1, e_1)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[136, 66, 98, 60, 252, 245])).
% 0.19/0.45 tff(254,plain,
% 0.19/0.45 ((~equalish(e_1, e_3)) <=> (~equalish(e_1, e_3))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(255,axiom,(~equalish(e_1, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_3')).
% 0.19/0.45 tff(256,plain,
% 0.19/0.45 (~equalish(e_1, e_3)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[255, 254])).
% 0.19/0.45 tff(257,plain,
% 0.19/0.45 (((~![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_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_3) | (~product(e_3, e_2, e_2)) | (~product(e_1, e_2, e_2)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(258,plain,
% 0.19/0.45 ((~![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_2)) | (~product(e_1, e_2, e_2)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(259,plain,
% 0.19/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_3, e_2, e_2)) | (~product(e_1, e_2, e_2))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[258, 257])).
% 0.19/0.45 tff(260,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[259, 256, 86, 210, 192])).
% 0.19/0.45 tff(261,plain,((~product(e_1, e_2, e_2)) | (~product(e_3, e_2, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(262,plain,
% 0.19/0.45 (~product(e_1, e_2, e_2)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[261, 210])).
% 0.19/0.45 tff(263,assumption,(product(e_1, e_2, e_3)), introduced(assumption)).
% 0.19/0.45 tff(264,plain,
% 0.19/0.45 (((~![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)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(265,plain,
% 0.19/0.45 ((~![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)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(266,plain,
% 0.19/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_2) | (~product(e_2, e_2, e_3)) | (~product(e_1, e_2, e_3))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[265, 264])).
% 0.19/0.45 tff(267,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[266, 182, 86, 246, 263])).
% 0.19/0.45 tff(268,plain,((~product(e_1, e_2, e_3)) | (~product(e_2, e_2, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(269,plain,
% 0.19/0.45 (~product(e_1, e_2, e_3)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[268, 228])).
% 0.19/0.45 tff(270,plain,
% 0.19/0.45 (product(e_1, e_2, e_1)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[208, 269, 262])).
% 0.19/0.45 tff(271,assumption,(product(e_1, e_1, e_1)), introduced(assumption)).
% 0.19/0.45 tff(272,plain,
% 0.19/0.45 (((~![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_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_2) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(273,plain,
% 0.19/0.45 ((~![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_1, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(274,plain,
% 0.19/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_2) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_1))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[273, 272])).
% 0.19/0.45 tff(275,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[274, 182, 86, 271, 120])).
% 0.19/0.45 tff(276,plain,((~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(277,plain,
% 0.19/0.45 (~product(e_1, e_1, e_1)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[276, 253])).
% 0.19/0.45 tff(278,plain,
% 0.19/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_2, e_1)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(279,plain,
% 0.19/0.45 ((product(e_1, e_1, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_1, e_2))) <=> (product(e_1, e_1, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_2, e_1)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(280,plain,
% 0.19/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, 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(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_2, e_1))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[279])).
% 0.19/0.45 tff(281,plain,
% 0.19/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, 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(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_2, e_1)))),
% 0.19/0.45 inference(transitivity,[status(thm)],[280, 278])).
% 0.19/0.45 tff(282,plain,
% 0.19/0.45 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_1, e_2)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(283,plain,
% 0.19/0.45 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_2, e_1))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[282, 281])).
% 0.19/0.45 tff(284,plain,
% 0.19/0.45 (~product(e_1, e_1, e_2)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[283, 33, 277, 270])).
% 0.19/0.45 tff(285,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[127, 33, 284, 253])).
% 0.19/0.45 tff(286,plain,((~product(e_3, e_2, e_2)) | product(e_2, e_2, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(287,plain,
% 0.19/0.45 (~product(e_3, e_2, e_2)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[286, 158])).
% 0.19/0.45 tff(288,plain,
% 0.19/0.45 (((~![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)))) | ((~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))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(289,plain,
% 0.19/0.45 ((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))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(290,plain,
% 0.19/0.45 (((~![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)))) | (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)))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[289])).
% 0.19/0.45 tff(291,plain,
% 0.19/0.45 (((~![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)))) | (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))),
% 0.19/0.45 inference(transitivity,[status(thm)],[290, 288])).
% 0.19/0.45 tff(292,plain,
% 0.19/0.45 ((~![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)))) | (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)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(293,plain,
% 0.19/0.45 ((~![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)))) | (~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)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[292, 291])).
% 0.19/0.45 tff(294,plain,
% 0.19/0.45 (product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[293, 98, 63, 60])).
% 0.19/0.45 tff(295,plain,
% 0.19/0.45 (product(e_3, e_2, e_3)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[294, 287, 157])).
% 0.19/0.45 tff(296,plain,
% 0.19/0.45 (((~![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_3, e_2, e_3)) | (~product(e_1, e_2, e_3)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(297,plain,
% 0.19/0.45 ((~![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)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(298,plain,
% 0.19/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_1, e_2, e_3))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[297, 296])).
% 0.19/0.45 tff(299,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[298, 256, 86, 295, 209])).
% 0.19/0.45 tff(300,plain,(product(e_2, e_2, e_1) | product(e_3, e_2, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(301,plain,
% 0.19/0.45 (product(e_3, e_2, e_1)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[300, 156])).
% 0.19/0.45 tff(302,plain,
% 0.19/0.45 (((~![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)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(303,plain,
% 0.19/0.45 ((~![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)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(304,plain,
% 0.19/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_1, e_2, e_1))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[303, 302])).
% 0.19/0.45 tff(305,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[304, 256, 86, 301, 1])).
% 0.19/0.45 tff(306,plain,(~product(e_1, e_2, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(307,plain,
% 0.19/0.45 (~product(e_1, e_2, e_2)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[200, 156])).
% 0.19/0.45 tff(308,plain,
% 0.19/0.45 (product(e_1, e_2, e_3) | product(e_1, e_2, e_1)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[208, 307])).
% 0.19/0.45 tff(309,plain,
% 0.19/0.45 (product(e_1, e_2, e_3)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[308, 306])).
% 0.19/0.45 tff(310,plain,
% 0.19/0.45 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_1, e_2, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_1, e_2, e_3)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(311,plain,
% 0.19/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_1, e_2, e_3)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(312,plain,
% 0.19/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_1, e_2, e_3))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[311, 310])).
% 0.19/0.45 tff(313,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[312, 214, 13, 76, 263])).
% 0.19/0.45 tff(314,plain,((~product(e_1, e_2, e_3)) | (~product(e_1, e_3, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(315,plain,
% 0.19/0.45 (~product(e_1, e_3, e_3)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[314, 309])).
% 0.19/0.45 tff(316,plain,
% 0.19/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_1) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_2, e_1) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_3, e_2)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(317,plain,
% 0.19/0.45 ((product(e_2, e_2, e_1) | (~product(e_1, e_3, e_2)) | (~product(e_1, e_2, e_3))) <=> (product(e_2, e_2, e_1) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_3, e_2)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(318,plain,
% 0.19/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_1) | (~product(e_1, e_3, e_2)) | (~product(e_1, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_1) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_3, e_2))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[317])).
% 0.19/0.45 tff(319,plain,
% 0.19/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_1) | (~product(e_1, e_3, e_2)) | (~product(e_1, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_2, e_1) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_3, e_2)))),
% 0.19/0.45 inference(transitivity,[status(thm)],[318, 316])).
% 0.19/0.45 tff(320,plain,
% 0.19/0.45 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_1) | (~product(e_1, e_3, e_2)) | (~product(e_1, e_2, e_3)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(321,plain,
% 0.19/0.46 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_2, e_1) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_3, e_2))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[320, 319])).
% 0.19/0.46 tff(322,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[321, 33, 156, 41, 309])).
% 0.19/0.46 tff(323,plain,(~product(e_1, e_3, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(324,plain,
% 0.19/0.46 (product(e_1, e_3, e_1)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[73, 323, 315])).
% 0.19/0.46 tff(325,plain,
% 0.19/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_2, e_1) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_2, e_1) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_3, e_1)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(326,plain,
% 0.19/0.46 ((product(e_1, e_2, e_1) | (~product(e_1, e_3, e_1)) | (~product(e_1, e_2, e_3))) <=> (product(e_1, e_2, e_1) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_3, e_1)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(327,plain,
% 0.19/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_2, e_1) | (~product(e_1, e_3, e_1)) | (~product(e_1, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_2, e_1) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_3, e_1))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[326])).
% 0.19/0.46 tff(328,plain,
% 0.19/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_2, e_1) | (~product(e_1, e_3, e_1)) | (~product(e_1, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_2, e_1) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_3, e_1)))),
% 0.19/0.46 inference(transitivity,[status(thm)],[327, 325])).
% 0.19/0.46 tff(329,plain,
% 0.19/0.46 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_2, e_1) | (~product(e_1, e_3, e_1)) | (~product(e_1, e_2, e_3)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(330,plain,
% 0.19/0.46 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_2, e_1) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_3, e_1))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[329, 328])).
% 0.19/0.46 tff(331,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[330, 33, 324, 309, 306])).
% 0.19/0.46 % SZS output end Proof
%------------------------------------------------------------------------------