TSTP Solution File: GRP134-2.003 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP134-2.003 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n022.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 22:26:18 EDT 2022
% Result : Unsatisfiable 0.19s 0.42s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP134-2.003 : TPTP v8.1.0. Released v1.2.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 31 15:10:40 EDT 2022
% 0.13/0.34 % 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.
% 0.19/0.42 % SZS status Unsatisfiable
% 0.19/0.42 % SZS output start Proof
% 0.19/0.42 tff(product_type, type, (
% 0.19/0.42 product: ( $i * $i * $i ) > $o)).
% 0.19/0.42 tff(e_2_type, type, (
% 0.19/0.42 e_2: $i)).
% 0.19/0.42 tff(e_3_type, type, (
% 0.19/0.42 e_3: $i)).
% 0.19/0.42 tff(e_1_type, type, (
% 0.19/0.42 e_1: $i)).
% 0.19/0.42 tff(equalish_type, type, (
% 0.19/0.42 equalish: ( $i * $i ) > $o)).
% 0.19/0.42 tff(next_type, type, (
% 0.19/0.42 next: ( $i * $i ) > $o)).
% 0.19/0.42 tff(greater_type, type, (
% 0.19/0.42 greater: ( $i * $i ) > $o)).
% 0.19/0.42 tff(group_element_type, type, (
% 0.19/0.42 group_element: $i > $o)).
% 0.19/0.42 tff(1,assumption,(product(e_3, e_1, e_2)), introduced(assumption)).
% 0.19/0.42 tff(2,assumption,(product(e_3, e_2, e_2)), introduced(assumption)).
% 0.19/0.42 tff(3,plain,
% 0.19/0.42 (^[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))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(4,plain,
% 0.19/0.42 (![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)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[3])).
% 0.19/0.42 tff(5,plain,
% 0.19/0.42 (![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)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(6,plain,
% 0.19/0.42 (^[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)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(7,plain,
% 0.19/0.42 (![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)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[6])).
% 0.19/0.42 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/sandbox2/benchmark/theBenchmark.p','product_right_cancellation')).
% 0.19/0.42 tff(9,plain,
% 0.19/0.42 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.19/0.42 tff(10,plain,
% 0.19/0.42 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.19/0.42 tff(11,plain,(
% 0.19/0.42 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.19/0.42 inference(skolemize,[status(sab)],[10])).
% 0.19/0.42 tff(12,plain,
% 0.19/0.42 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.19/0.42 tff(13,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(14,axiom,(~equalish(e_2, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_1')).
% 0.19/0.42 tff(15,plain,
% 0.19/0.42 (~equalish(e_2, e_1)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.19/0.42 tff(16,plain,
% 0.19/0.42 (((~![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_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_2, e_1) | (~product(e_3, e_1, e_2)) | (~product(e_3, e_2, e_2)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(17,plain,
% 0.19/0.42 ((~![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_3, e_1, e_2)) | (~product(e_3, e_2, e_2)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(18,plain,
% 0.19/0.42 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_3, e_1, e_2)) | (~product(e_3, e_2, e_2))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.19/0.43 tff(19,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[18, 15, 12, 1, 2])).
% 0.19/0.43 tff(20,plain,((~product(e_3, e_2, e_2)) | (~product(e_3, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(21,plain,
% 0.19/0.43 (~product(e_3, e_2, e_2)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[20, 1])).
% 0.19/0.43 tff(22,assumption,(product(e_1, e_1, e_2)), introduced(assumption)).
% 0.19/0.43 tff(23,plain,
% 0.19/0.43 (^[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))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(24,plain,
% 0.19/0.43 (![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)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[23])).
% 0.19/0.43 tff(25,plain,
% 0.19/0.43 (![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)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(26,plain,
% 0.19/0.43 (^[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)))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(27,plain,
% 0.19/0.43 (![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)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[26])).
% 0.19/0.43 tff(28,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')).
% 0.19/0.43 tff(29,plain,
% 0.19/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.19/0.43 tff(30,plain,
% 0.19/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.19/0.43 tff(31,plain,(
% 0.19/0.43 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.19/0.43 inference(skolemize,[status(sab)],[30])).
% 0.19/0.43 tff(32,plain,
% 0.19/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.19/0.43 tff(33,plain,
% 0.19/0.43 ((~equalish(e_3, e_1)) <=> (~equalish(e_3, e_1))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(34,axiom,(~equalish(e_3, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_1')).
% 0.19/0.43 tff(35,plain,
% 0.19/0.43 (~equalish(e_3, e_1)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.19/0.43 tff(36,plain,
% 0.19/0.43 (((~![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_1, e_2)) | (~product(e_3, 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_3, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_3, e_1, e_2)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(37,plain,
% 0.19/0.43 ((~![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_1, e_2)) | (~product(e_3, e_1, e_2)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(38,plain,
% 0.19/0.43 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_3, e_1, e_2))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.19/0.43 tff(39,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[38, 35, 32, 22, 1])).
% 0.19/0.43 tff(40,plain,((~product(e_3, e_1, e_2)) | (~product(e_1, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(41,plain,
% 0.19/0.43 (~product(e_1, e_1, e_2)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[40, 1])).
% 0.19/0.43 tff(42,assumption,(~product(e_3, e_2, e_2)), introduced(assumption)).
% 0.19/0.43 tff(43,assumption,(~product(e_1, e_3, e_3)), introduced(assumption)).
% 0.19/0.43 tff(44,assumption,(~product(e_1, e_1, e_2)), introduced(assumption)).
% 0.19/0.43 tff(45,plain,
% 0.19/0.43 (^[Y: $i, X: $i, X1: $i] : refl(((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y))) <=> ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(46,plain,
% 0.19/0.43 (![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y))) <=> ![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[45])).
% 0.19/0.43 tff(47,plain,
% 0.19/0.43 (![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y))) <=> ![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(48,plain,
% 0.19/0.43 (^[Y: $i, X: $i, X1: $i] : trans(monotonicity(rewrite(((~product(X, e_1, Y)) | (~next(X, X1))) <=> ((~next(X, X1)) | (~product(X, e_1, Y)))), ((((~product(X, e_1, Y)) | (~next(X, X1))) | (~greater(Y, X1))) <=> (((~next(X, X1)) | (~product(X, e_1, Y))) | (~greater(Y, X1))))), rewrite((((~next(X, X1)) | (~product(X, e_1, Y))) | (~greater(Y, X1))) <=> ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))), ((((~product(X, e_1, Y)) | (~next(X, X1))) | (~greater(Y, X1))) <=> ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(49,plain,
% 0.19/0.43 (![Y: $i, X: $i, X1: $i] : (((~product(X, e_1, Y)) | (~next(X, X1))) | (~greater(Y, X1))) <=> ![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[48])).
% 0.19/0.43 tff(50,axiom,(![Y: $i, X: $i, X1: $i] : (((~product(X, e_1, Y)) | (~next(X, X1))) | (~greater(Y, X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','no_redundancy')).
% 0.19/0.43 tff(51,plain,
% 0.19/0.43 (![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.19/0.43 tff(52,plain,
% 0.19/0.43 (![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.19/0.43 tff(53,plain,(
% 0.19/0.43 ![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))),
% 0.19/0.43 inference(skolemize,[status(sab)],[52])).
% 0.19/0.43 tff(54,plain,
% 0.19/0.43 (![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[53, 46])).
% 0.19/0.43 tff(55,plain,
% 0.19/0.43 (greater(e_3, e_2) <=> greater(e_3, e_2)),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(56,axiom,(greater(e_3, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_greater_e_2')).
% 0.19/0.43 tff(57,plain,
% 0.19/0.43 (greater(e_3, e_2)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.19/0.43 tff(58,plain,
% 0.19/0.43 (next(e_1, e_2) <=> next(e_1, e_2)),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(59,axiom,(next(e_1, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_then_e_2')).
% 0.19/0.43 tff(60,plain,
% 0.19/0.43 (next(e_1, e_2)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.19/0.43 tff(61,plain,
% 0.19/0.43 (((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_3, e_2)) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_3)))) <=> ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_3, e_2)) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_3)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(62,plain,
% 0.19/0.43 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_3, e_2)) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_3)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(63,plain,
% 0.19/0.43 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_3, e_2)) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_3))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.19/0.43 tff(64,plain,
% 0.19/0.43 (~product(e_1, e_1, e_3)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[63, 60, 57, 54])).
% 0.19/0.43 tff(65,plain,
% 0.19/0.43 (^[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))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(66,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))) <=> ![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)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[65])).
% 0.19/0.43 tff(67,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))) <=> ![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)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(68,plain,
% 0.19/0.43 (^[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)))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(69,plain,
% 0.19/0.43 (![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)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[68])).
% 0.19/0.43 tff(70,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')).
% 0.19/0.43 tff(71,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)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.19/0.43 tff(72,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)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.19/0.43 tff(73,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)))),
% 0.19/0.43 inference(skolemize,[status(sab)],[72])).
% 0.19/0.44 tff(74,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)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[73, 66])).
% 0.19/0.44 tff(75,plain,
% 0.19/0.44 (group_element(e_1) <=> group_element(e_1)),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(76,axiom,(group_element(e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_1')).
% 0.19/0.44 tff(77,plain,
% 0.19/0.44 (group_element(e_1)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.19/0.44 tff(78,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(79,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(80,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)],[79])).
% 0.19/0.44 tff(81,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)],[80, 78])).
% 0.19/0.44 tff(82,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(83,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)],[82, 81])).
% 0.19/0.44 tff(84,plain,
% 0.19/0.44 (product(e_1, e_1, e_2) | product(e_1, e_1, e_1)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[83, 77, 74, 64])).
% 0.19/0.44 tff(85,plain,
% 0.19/0.44 (product(e_1, e_1, e_1)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[84, 44])).
% 0.19/0.44 tff(86,assumption,(~product(e_2, e_1, e_3)), introduced(assumption)).
% 0.19/0.44 tff(87,assumption,(product(e_1, e_1, e_1)), introduced(assumption)).
% 0.19/0.44 tff(88,assumption,(product(e_3, e_1, e_1)), introduced(assumption)).
% 0.19/0.44 tff(89,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_3, e_1) | (~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_3, e_1) | (~product(e_3, e_1, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(90,plain,
% 0.19/0.44 ((equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_1, e_1))) <=> (equalish(e_3, e_1) | (~product(e_3, e_1, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(91,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_3, e_1) | (~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_3, e_1) | (~product(e_3, e_1, e_1)) | (~product(e_1, e_1, e_1))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[90])).
% 0.19/0.44 tff(92,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_3, e_1) | (~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_3, e_1) | (~product(e_3, e_1, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.19/0.44 inference(transitivity,[status(thm)],[91, 89])).
% 0.19/0.44 tff(93,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_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_1, e_1)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(94,plain,
% 0.19/0.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_3, e_1, e_1)) | (~product(e_1, e_1, e_1))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.19/0.44 tff(95,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[94, 35, 32, 87, 88])).
% 0.19/0.44 tff(96,plain,((~product(e_3, e_1, e_1)) | (~product(e_1, e_1, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44 tff(97,plain,
% 0.19/0.44 (~product(e_3, e_1, e_1)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[96, 87])).
% 0.19/0.44 tff(98,assumption,(product(e_3, e_1, e_3)), introduced(assumption)).
% 0.19/0.44 tff(99,assumption,(product(e_2, e_1, e_3)), introduced(assumption)).
% 0.19/0.44 tff(100,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(101,axiom,(~equalish(e_2, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_3')).
% 0.19/0.44 tff(102,plain,
% 0.19/0.44 (~equalish(e_2, e_3)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.19/0.44 tff(103,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_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)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(104,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_1, e_3)) | (~product(e_2, e_1, e_3)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(105,plain,
% 0.19/0.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_3) | (~product(e_3, e_1, e_3)) | (~product(e_2, e_1, e_3))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.19/0.44 tff(106,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[105, 102, 32, 98, 99])).
% 0.19/0.44 tff(107,plain,((~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44 tff(108,plain,
% 0.19/0.44 (~product(e_2, e_1, e_3)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[107, 98])).
% 0.19/0.44 tff(109,plain,
% 0.19/0.44 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : refl(((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1))) <=> ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(110,plain,
% 0.19/0.44 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[109])).
% 0.19/0.44 tff(111,plain,
% 0.19/0.44 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(112,plain,
% 0.19/0.44 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : rewrite((((~product(X, Y, Z1)) | (~product(Y, X, Z2))) | product(Z1, Z2, Y)) <=> ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(113,plain,
% 0.19/0.44 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(X, Y, Z1)) | (~product(Y, X, Z2))) | product(Z1, Z2, Y)) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[112])).
% 0.19/0.44 tff(114,axiom,(![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(X, Y, Z1)) | (~product(Y, X, Z2))) | product(Z1, Z2, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qg4')).
% 0.19/0.44 tff(115,plain,
% 0.19/0.44 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.19/0.44 tff(116,plain,
% 0.19/0.44 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[115, 111])).
% 0.19/0.44 tff(117,plain,(
% 0.19/0.44 ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))),
% 0.19/0.44 inference(skolemize,[status(sab)],[116])).
% 0.19/0.44 tff(118,plain,
% 0.19/0.44 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[117, 110])).
% 0.19/0.44 tff(119,plain,
% 0.19/0.44 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_1)) | product(e_1, e_3, e_3) | (~product(e_3, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_1, e_3, e_1)) | product(e_1, e_3, e_3) | (~product(e_3, e_1, e_3)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(120,plain,
% 0.19/0.44 (((~product(e_3, e_1, e_3)) | product(e_1, e_3, e_3) | (~product(e_1, e_3, e_1))) <=> ((~product(e_1, e_3, e_1)) | product(e_1, e_3, e_3) | (~product(e_3, e_1, e_3)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(121,plain,
% 0.19/0.44 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_3)) | product(e_1, e_3, e_3) | (~product(e_1, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_1)) | product(e_1, e_3, e_3) | (~product(e_3, e_1, e_3))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[120])).
% 0.19/0.44 tff(122,plain,
% 0.19/0.44 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_3)) | product(e_1, e_3, e_3) | (~product(e_1, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_1, e_3, e_1)) | product(e_1, e_3, e_3) | (~product(e_3, e_1, e_3)))),
% 0.19/0.44 inference(transitivity,[status(thm)],[121, 119])).
% 0.19/0.44 tff(123,plain,
% 0.19/0.44 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_3)) | product(e_1, e_3, e_3) | (~product(e_1, e_3, e_1)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(124,plain,
% 0.19/0.44 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_1, e_3, e_1)) | product(e_1, e_3, e_3) | (~product(e_3, e_1, e_3))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.19/0.44 tff(125,plain,
% 0.19/0.44 (~product(e_1, e_3, e_1)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[124, 118, 98, 43])).
% 0.19/0.44 tff(126,plain,
% 0.19/0.44 (group_element(e_3) <=> group_element(e_3)),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(127,axiom,(group_element(e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_3')).
% 0.19/0.44 tff(128,plain,
% 0.19/0.44 (group_element(e_3)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.19/0.44 tff(129,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_1)) | (~group_element(e_3)) | product(e_1, e_3, e_2) | product(e_1, e_3, e_3) | product(e_1, 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_1)) | (~group_element(e_3)) | product(e_1, e_3, e_2) | product(e_1, e_3, e_3) | product(e_1, e_3, e_1))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(130,plain,
% 0.19/0.45 ((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_1)) | (~group_element(e_3)) | product(e_1, e_3, e_2) | product(e_1, e_3, e_3) | product(e_1, e_3, e_1))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(131,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_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_1)) | (~group_element(e_3)) | product(e_1, e_3, e_2) | product(e_1, e_3, e_3) | product(e_1, e_3, e_1)))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[130])).
% 0.19/0.45 tff(132,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_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_1)) | (~group_element(e_3)) | product(e_1, e_3, e_2) | product(e_1, e_3, e_3) | product(e_1, e_3, e_1))),
% 0.19/0.45 inference(transitivity,[status(thm)],[131, 129])).
% 0.19/0.45 tff(133,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_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)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(134,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_1)) | (~group_element(e_3)) | product(e_1, e_3, e_2) | product(e_1, e_3, e_3) | product(e_1, e_3, e_1)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.19/0.45 tff(135,plain,
% 0.19/0.45 (product(e_1, e_3, e_2)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[134, 77, 128, 74, 43, 125])).
% 0.19/0.45 tff(136,assumption,(product(e_1, e_2, e_2)), introduced(assumption)).
% 0.19/0.45 tff(137,assumption,(product(e_1, e_3, e_2)), introduced(assumption)).
% 0.19/0.45 tff(138,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_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_3) | (~product(e_1, e_3, e_2)) | (~product(e_1, e_2, e_2)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(139,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_2)) | (~product(e_1, e_2, e_2)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(140,plain,
% 0.19/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_3) | (~product(e_1, e_3, e_2)) | (~product(e_1, e_2, e_2))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.19/0.45 tff(141,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[140, 102, 12, 137, 136])).
% 0.19/0.45 tff(142,plain,((~product(e_1, e_2, e_2)) | (~product(e_1, e_3, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(143,plain,
% 0.19/0.45 (~product(e_1, e_2, e_2)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[142, 135])).
% 0.19/0.45 tff(144,assumption,(~product(e_3, e_2, e_1)), introduced(assumption)).
% 0.19/0.45 tff(145,plain,
% 0.19/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_3)) | (~product(e_1, e_3, e_2)) | product(e_3, e_2, e_1))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_3)) | (~product(e_1, e_3, e_2)) | product(e_3, e_2, e_1))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(146,plain,
% 0.19/0.45 (((~product(e_1, e_3, e_2)) | product(e_3, e_2, e_1) | (~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_2, e_1))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(147,plain,
% 0.19/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_2)) | product(e_3, e_2, e_1) | (~product(e_3, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_3)) | (~product(e_1, e_3, e_2)) | product(e_3, e_2, e_1)))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[146])).
% 0.19/0.45 tff(148,plain,
% 0.19/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_2)) | product(e_3, e_2, e_1) | (~product(e_3, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_3)) | (~product(e_1, e_3, e_2)) | product(e_3, e_2, e_1))),
% 0.19/0.45 inference(transitivity,[status(thm)],[147, 145])).
% 0.19/0.45 tff(149,plain,
% 0.19/0.45 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_2)) | product(e_3, e_2, e_1) | (~product(e_3, e_1, e_3)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(150,plain,
% 0.19/0.45 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_3)) | (~product(e_1, e_3, e_2)) | product(e_3, e_2, e_1)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.19/0.45 tff(151,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[150, 118, 98, 137, 144])).
% 0.19/0.45 tff(152,plain,(product(e_3, e_2, e_1) | (~product(e_3, e_1, e_3)) | (~product(e_1, e_3, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(153,plain,
% 0.19/0.45 (product(e_3, e_2, e_1)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[152, 135, 98])).
% 0.19/0.45 tff(154,assumption,(product(e_1, e_2, e_1)), introduced(assumption)).
% 0.19/0.45 tff(155,assumption,(product(e_3, e_2, e_1)), introduced(assumption)).
% 0.19/0.45 tff(156,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(157,axiom,(~equalish(e_1, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_3')).
% 0.19/0.45 tff(158,plain,
% 0.19/0.45 (~equalish(e_1, e_3)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.19/0.45 tff(159,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(160,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(161,plain,
% 0.19/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_1, e_2, e_1))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.19/0.45 tff(162,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[161, 158, 32, 155, 154])).
% 0.19/0.45 tff(163,plain,((~product(e_1, e_2, e_1)) | (~product(e_3, e_2, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(164,plain,
% 0.19/0.45 (~product(e_1, e_2, e_1)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[163, 153])).
% 0.19/0.45 tff(165,plain,
% 0.19/0.45 (group_element(e_2) <=> group_element(e_2)),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(166,axiom,(group_element(e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_2')).
% 0.19/0.45 tff(167,plain,
% 0.19/0.45 (group_element(e_2)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.19/0.45 tff(168,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_1)) | (~group_element(e_2)) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | 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_1)) | (~group_element(e_2)) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(169,plain,
% 0.19/0.45 ((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_1)) | (~group_element(e_2)) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(170,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_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_1)) | (~group_element(e_2)) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1)))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[169])).
% 0.19/0.45 tff(171,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_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_1)) | (~group_element(e_2)) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1))),
% 0.19/0.45 inference(transitivity,[status(thm)],[170, 168])).
% 0.19/0.45 tff(172,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_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)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(173,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_1)) | (~group_element(e_2)) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[172, 171])).
% 0.19/0.45 tff(174,plain,
% 0.19/0.45 (product(e_1, e_2, e_3) | product(e_1, e_2, e_2)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[173, 77, 167, 74, 164])).
% 0.19/0.45 tff(175,plain,
% 0.19/0.45 (product(e_1, e_2, e_3)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[174, 143])).
% 0.19/0.45 tff(176,plain,
% 0.19/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_3, e_1)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(177,plain,
% 0.19/0.45 (((~product(e_3, e_2, e_1)) | product(e_1, e_1, e_3) | (~product(e_2, e_3, e_1))) <=> (product(e_1, e_1, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_3, e_1)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(178,plain,
% 0.19/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_2, e_1)) | product(e_1, e_1, e_3) | (~product(e_2, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_3, e_1))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[177])).
% 0.19/0.46 tff(179,plain,
% 0.19/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_2, e_1)) | product(e_1, e_1, e_3) | (~product(e_2, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_3, e_1)))),
% 0.19/0.46 inference(transitivity,[status(thm)],[178, 176])).
% 0.19/0.46 tff(180,plain,
% 0.19/0.46 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_2, e_1)) | product(e_1, e_1, e_3) | (~product(e_2, e_3, e_1)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(181,plain,
% 0.19/0.46 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_3, e_1))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[180, 179])).
% 0.19/0.46 tff(182,plain,
% 0.19/0.46 (~product(e_2, e_3, e_1)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[181, 118, 64, 153])).
% 0.19/0.46 tff(183,plain,
% 0.19/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_2, e_3, e_1) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_2, e_3, e_1) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_2, e_3)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(184,plain,
% 0.19/0.46 (((~product(e_1, e_2, e_3)) | product(e_2, e_3, e_1) | (~product(e_2, e_1, e_2))) <=> (product(e_2, e_3, e_1) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_2, e_3)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(185,plain,
% 0.19/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_2, e_3)) | product(e_2, e_3, e_1) | (~product(e_2, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_2, e_3, e_1) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_2, e_3))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[184])).
% 0.19/0.46 tff(186,plain,
% 0.19/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_2, e_3)) | product(e_2, e_3, e_1) | (~product(e_2, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_2, e_3, e_1) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_2, e_3)))),
% 0.19/0.46 inference(transitivity,[status(thm)],[185, 183])).
% 0.19/0.46 tff(187,plain,
% 0.19/0.46 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_2, e_3)) | product(e_2, e_3, e_1) | (~product(e_2, e_1, e_2)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(188,plain,
% 0.19/0.46 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_2, e_3, e_1) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_2, e_3))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[187, 186])).
% 0.19/0.46 tff(189,plain,
% 0.19/0.46 (~product(e_2, e_1, e_2)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[188, 118, 182, 175])).
% 0.19/0.46 tff(190,plain,
% 0.19/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_1, e_3, e_1) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_3, e_1) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_1, e_1)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(191,plain,
% 0.19/0.46 (((~product(e_1, e_2, e_3)) | product(e_1, e_3, e_1) | (~product(e_2, e_1, e_1))) <=> (product(e_1, e_3, e_1) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_1, e_1)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(192,plain,
% 0.19/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_2, e_3)) | product(e_1, e_3, e_1) | (~product(e_2, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_1, e_3, e_1) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_1, e_1))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[191])).
% 0.19/0.46 tff(193,plain,
% 0.19/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_2, e_3)) | product(e_1, e_3, e_1) | (~product(e_2, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_3, e_1) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_1, e_1)))),
% 0.19/0.46 inference(transitivity,[status(thm)],[192, 190])).
% 0.19/0.46 tff(194,plain,
% 0.19/0.46 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_2, e_3)) | product(e_1, e_3, e_1) | (~product(e_2, e_1, e_1)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(195,plain,
% 0.19/0.46 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_3, e_1) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_1, e_1))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[194, 193])).
% 0.19/0.46 tff(196,plain,
% 0.19/0.46 (~product(e_2, e_1, e_1)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[195, 118, 125, 175])).
% 0.19/0.46 tff(197,plain,
% 0.19/0.46 (((~![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_1)) | (~group_element(e_2)) | product(e_2, e_1, e_2) | product(e_2, e_1, e_3) | product(e_2, 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)) | (~group_element(e_2)) | product(e_2, e_1, e_2) | product(e_2, e_1, e_3) | product(e_2, e_1, e_1))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(198,plain,
% 0.19/0.46 ((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_1)) | (~group_element(e_2)) | product(e_2, e_1, e_2) | product(e_2, e_1, e_3) | product(e_2, e_1, e_1))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(199,plain,
% 0.19/0.46 (((~![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_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_1)) | (~group_element(e_2)) | product(e_2, e_1, e_2) | product(e_2, e_1, e_3) | product(e_2, e_1, e_1)))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[198])).
% 0.19/0.46 tff(200,plain,
% 0.19/0.46 (((~![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_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_1)) | (~group_element(e_2)) | product(e_2, e_1, e_2) | product(e_2, e_1, e_3) | product(e_2, e_1, e_1))),
% 0.19/0.46 inference(transitivity,[status(thm)],[199, 197])).
% 0.19/0.46 tff(201,plain,
% 0.19/0.46 ((~![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_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)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(202,plain,
% 0.19/0.46 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | (~group_element(e_2)) | product(e_2, e_1, e_2) | product(e_2, e_1, e_3) | product(e_2, e_1, e_1)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[201, 200])).
% 0.19/0.46 tff(203,plain,
% 0.19/0.46 (product(e_2, e_1, e_2) | product(e_2, e_1, e_3) | product(e_2, e_1, e_1)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[202, 77, 167, 74])).
% 0.19/0.46 tff(204,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[203, 196, 189, 108])).
% 0.19/0.46 tff(205,plain,(product(e_1, e_3, e_3) | (~product(e_3, e_1, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(206,plain,
% 0.19/0.46 (product(e_1, e_3, e_3)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[205, 98])).
% 0.19/0.46 tff(207,plain,
% 0.19/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_3)) | product(e_3, e_3, e_3) | (~product(e_3, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_1, e_3, e_3)) | product(e_3, e_3, e_3) | (~product(e_3, e_1, e_3)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(208,plain,
% 0.19/0.46 (((~product(e_3, e_1, e_3)) | product(e_3, e_3, e_3) | (~product(e_1, e_3, e_3))) <=> ((~product(e_1, e_3, e_3)) | product(e_3, e_3, e_3) | (~product(e_3, e_1, e_3)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(209,plain,
% 0.19/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_3)) | product(e_3, e_3, e_3) | (~product(e_1, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_3)) | product(e_3, e_3, e_3) | (~product(e_3, e_1, e_3))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[208])).
% 0.19/0.46 tff(210,plain,
% 0.19/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_3)) | product(e_3, e_3, e_3) | (~product(e_1, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_1, e_3, e_3)) | product(e_3, e_3, e_3) | (~product(e_3, e_1, e_3)))),
% 0.19/0.46 inference(transitivity,[status(thm)],[209, 207])).
% 0.19/0.46 tff(211,plain,
% 0.19/0.46 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_3)) | product(e_3, e_3, e_3) | (~product(e_1, e_3, e_3)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(212,plain,
% 0.19/0.46 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_1, e_3, e_3)) | product(e_3, e_3, e_3) | (~product(e_3, e_1, e_3))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[211, 210])).
% 0.19/0.46 tff(213,plain,
% 0.19/0.46 ((~product(e_1, e_3, e_3)) | product(e_3, e_3, e_3) | (~product(e_3, e_1, e_3))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[212, 118])).
% 0.19/0.46 tff(214,plain,
% 0.19/0.46 (product(e_3, e_3, e_3)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[213, 206, 98])).
% 0.19/0.46 tff(215,plain,
% 0.19/0.46 (((~![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_3, e_3)) | (~product(e_3, 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_1, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(216,plain,
% 0.19/0.46 ((equalish(e_1, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_1, e_3, e_3))) <=> (equalish(e_1, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(217,plain,
% 0.19/0.46 (((~![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_3, e_3)) | (~product(e_1, 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_1, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_3))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[216])).
% 0.19/0.46 tff(218,plain,
% 0.19/0.46 (((~![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_3, e_3)) | (~product(e_1, 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_1, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.19/0.46 inference(transitivity,[status(thm)],[217, 215])).
% 0.19/0.46 tff(219,plain,
% 0.19/0.46 ((~![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_3, e_3)) | (~product(e_1, e_3, e_3)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(220,plain,
% 0.19/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_3))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[219, 218])).
% 0.19/0.46 tff(221,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[220, 158, 32, 206, 214])).
% 0.19/0.46 tff(222,plain,(~product(e_3, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(223,plain,
% 0.19/0.46 (((~![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_1)) | (~group_element(e_3)) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, 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)) | (~group_element(e_3)) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(224,plain,
% 0.19/0.46 ((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))) <=> ((~group_element(e_1)) | (~group_element(e_3)) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(225,plain,
% 0.19/0.46 (((~![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_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)))) | ((~group_element(e_1)) | (~group_element(e_3)) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1)))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[224])).
% 0.19/0.46 tff(226,plain,
% 0.19/0.46 (((~![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_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)))) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1))),
% 0.19/0.46 inference(transitivity,[status(thm)],[225, 223])).
% 0.19/0.46 tff(227,plain,
% 0.19/0.46 ((~![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_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)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(228,plain,
% 0.19/0.46 ((~![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_1)) | (~group_element(e_3)) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[227, 226])).
% 0.19/0.47 tff(229,plain,
% 0.19/0.47 (product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[228, 77, 128, 74])).
% 0.19/0.47 tff(230,plain,
% 0.19/0.47 (product(e_3, e_1, e_2) | product(e_3, e_1, e_1)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[229, 222])).
% 0.19/0.47 tff(231,plain,
% 0.19/0.47 (product(e_3, e_1, e_2)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[230, 97])).
% 0.19/0.47 tff(232,assumption,(product(e_2, e_1, e_2)), introduced(assumption)).
% 0.19/0.47 tff(233,plain,
% 0.19/0.47 (((~![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_2)) | (~product(e_2, 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_2, e_3) | (~product(e_3, e_1, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(234,plain,
% 0.19/0.47 ((~![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_2)) | (~product(e_2, e_1, e_2)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(235,plain,
% 0.19/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_3) | (~product(e_3, e_1, e_2)) | (~product(e_2, e_1, e_2))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[234, 233])).
% 0.19/0.47 tff(236,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[235, 102, 32, 1, 232])).
% 0.19/0.47 tff(237,plain,((~product(e_2, e_1, e_2)) | (~product(e_3, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(238,plain,
% 0.19/0.47 (~product(e_2, e_1, e_2)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[237, 231])).
% 0.19/0.47 tff(239,plain,
% 0.19/0.47 (product(e_2, e_1, e_1)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[203, 238, 86])).
% 0.19/0.47 tff(240,plain,
% 0.19/0.47 (((~![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_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_1) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(241,plain,
% 0.19/0.47 ((~![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_1, e_1)) | (~product(e_2, e_1, e_1)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(242,plain,
% 0.19/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[241, 240])).
% 0.19/0.47 tff(243,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[242, 15, 32, 87, 239])).
% 0.19/0.47 tff(244,plain,((~product(e_1, e_1, e_1)) | product(e_2, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(245,plain,
% 0.19/0.47 (product(e_2, e_1, e_3)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[244, 85])).
% 0.19/0.47 tff(246,assumption,(product(e_2, e_3, e_3)), introduced(assumption)).
% 0.19/0.47 tff(247,plain,
% 0.19/0.47 (((~![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)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(248,plain,
% 0.19/0.47 ((~![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)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(249,plain,
% 0.19/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_3, e_3))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[248, 247])).
% 0.19/0.47 tff(250,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[249, 35, 12, 99, 246])).
% 0.19/0.47 tff(251,plain,((~product(e_2, e_3, e_3)) | (~product(e_2, e_1, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(252,plain,
% 0.19/0.47 (~product(e_2, e_3, e_3)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[251, 245])).
% 0.19/0.47 tff(253,assumption,(product(e_1, e_3, e_1)), introduced(assumption)).
% 0.19/0.47 tff(254,plain,
% 0.19/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_3) | (~product(e_1, e_3, e_1)) | (~product(e_3, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_3) | (~product(e_1, e_3, e_1)) | (~product(e_3, e_1, e_1)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(255,plain,
% 0.19/0.47 (((~product(e_3, e_1, e_1)) | product(e_1, 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_1)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(256,plain,
% 0.19/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_1)) | product(e_1, e_1, e_3) | (~product(e_1, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_3) | (~product(e_1, e_3, e_1)) | (~product(e_3, e_1, e_1))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[255])).
% 0.19/0.47 tff(257,plain,
% 0.19/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_1)) | product(e_1, e_1, e_3) | (~product(e_1, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_3) | (~product(e_1, e_3, e_1)) | (~product(e_3, e_1, e_1)))),
% 0.19/0.47 inference(transitivity,[status(thm)],[256, 254])).
% 0.19/0.47 tff(258,plain,
% 0.19/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_1)) | product(e_1, e_1, e_3) | (~product(e_1, e_3, e_1)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(259,plain,
% 0.19/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_3) | (~product(e_1, e_3, e_1)) | (~product(e_3, e_1, e_1))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[258, 257])).
% 0.19/0.47 tff(260,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[259, 118, 64, 88, 253])).
% 0.19/0.47 tff(261,plain,((~product(e_3, e_1, e_1)) | (~product(e_1, e_3, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(262,plain,
% 0.19/0.47 (~product(e_3, e_1, e_1)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[261, 253])).
% 0.19/0.47 tff(263,plain,
% 0.19/0.47 (product(e_3, e_1, e_2)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[230, 262])).
% 0.19/0.47 tff(264,plain,
% 0.19/0.47 (~product(e_1, e_1, e_2)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[40, 263])).
% 0.19/0.47 tff(265,plain,
% 0.19/0.47 (product(e_1, e_1, e_1)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[84, 264])).
% 0.19/0.47 tff(266,plain,
% 0.19/0.47 (((~![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)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(267,plain,
% 0.19/0.47 ((~![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)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(268,plain,
% 0.19/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_3) | (~product(e_1, e_3, e_1)) | (~product(e_1, e_1, e_1))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[267, 266])).
% 0.19/0.47 tff(269,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[268, 158, 12, 265, 253])).
% 0.19/0.47 tff(270,plain,(~product(e_1, e_3, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(271,assumption,(~product(e_1, e_3, e_1)), introduced(assumption)).
% 0.19/0.47 tff(272,assumption,(~product(e_1, e_3, e_2)), introduced(assumption)).
% 0.19/0.47 tff(273,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[134, 77, 128, 74, 43, 272, 271])).
% 0.19/0.47 tff(274,plain,(product(e_1, e_3, e_1) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(275,plain,
% 0.19/0.47 (product(e_1, e_3, e_3) | product(e_1, e_3, e_2)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[274, 270])).
% 0.19/0.47 tff(276,plain,
% 0.19/0.47 (product(e_1, e_3, e_2)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[275, 43])).
% 0.19/0.47 tff(277,assumption,(product(e_2, e_3, e_2)), introduced(assumption)).
% 0.19/0.47 tff(278,plain,
% 0.19/0.47 (((~![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_1, e_3, e_2)) | (~product(e_2, e_3, e_2)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(279,plain,
% 0.19/0.47 ((~![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)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(280,plain,
% 0.19/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_1, e_3, e_2)) | (~product(e_2, e_3, e_2))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[279, 278])).
% 0.19/0.47 tff(281,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[280, 15, 32, 137, 277])).
% 0.19/0.47 tff(282,plain,((~product(e_2, e_3, e_2)) | (~product(e_1, e_3, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(283,plain,
% 0.19/0.47 (~product(e_2, e_3, e_2)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[282, 276])).
% 0.19/0.47 tff(284,plain,
% 0.19/0.47 (((~![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_2)) | product(e_2, e_3, e_3) | product(e_2, e_3, e_2) | 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_3) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(285,plain,
% 0.19/0.47 ((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_3) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(286,plain,
% 0.19/0.47 (((~![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_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_3) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1)))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[285])).
% 0.19/0.47 tff(287,plain,
% 0.19/0.47 (((~![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_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_3) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1))),
% 0.19/0.47 inference(transitivity,[status(thm)],[286, 284])).
% 0.19/0.47 tff(288,plain,
% 0.19/0.47 ((~![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_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)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(289,plain,
% 0.19/0.47 ((~![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_2)) | product(e_2, e_3, e_3) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1)),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[288, 287])).
% 0.19/0.47 tff(290,plain,
% 0.19/0.47 (product(e_2, e_3, e_3) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[289, 167, 128, 74])).
% 0.19/0.47 tff(291,plain,
% 0.19/0.47 (product(e_2, e_3, e_1)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[290, 283, 252])).
% 0.19/0.47 tff(292,assumption,(product(e_3, e_2, e_3)), introduced(assumption)).
% 0.19/0.47 tff(293,assumption,(product(e_2, e_3, e_1)), introduced(assumption)).
% 0.19/0.47 tff(294,plain,
% 0.19/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_1, e_3, e_3) | (~product(e_2, e_3, e_1)) | (~product(e_3, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_3, e_3) | (~product(e_2, e_3, e_1)) | (~product(e_3, e_2, e_3)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(295,plain,
% 0.19/0.47 (((~product(e_3, e_2, e_3)) | product(e_1, e_3, e_3) | (~product(e_2, e_3, e_1))) <=> (product(e_1, e_3, e_3) | (~product(e_2, e_3, e_1)) | (~product(e_3, e_2, e_3)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(296,plain,
% 0.19/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_2, e_3)) | product(e_1, e_3, e_3) | (~product(e_2, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_1, e_3, e_3) | (~product(e_2, e_3, e_1)) | (~product(e_3, e_2, e_3))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[295])).
% 0.19/0.47 tff(297,plain,
% 0.19/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_2, e_3)) | product(e_1, e_3, e_3) | (~product(e_2, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_3, e_3) | (~product(e_2, e_3, e_1)) | (~product(e_3, e_2, e_3)))),
% 0.19/0.47 inference(transitivity,[status(thm)],[296, 294])).
% 0.19/0.47 tff(298,plain,
% 0.19/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_2, e_3)) | product(e_1, e_3, e_3) | (~product(e_2, e_3, e_1)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(299,plain,
% 0.19/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_3, e_3) | (~product(e_2, e_3, e_1)) | (~product(e_3, e_2, e_3))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[298, 297])).
% 0.19/0.47 tff(300,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[299, 118, 43, 293, 292])).
% 0.19/0.47 tff(301,plain,((~product(e_3, e_2, e_3)) | product(e_1, e_3, e_3) | (~product(e_2, e_3, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(302,plain,
% 0.19/0.47 (~product(e_3, e_2, e_3)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[301, 291, 43])).
% 0.19/0.47 tff(303,plain,
% 0.19/0.47 (((~![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_2)) | product(e_3, e_2, e_1) | product(e_3, e_2, e_3) | product(e_3, e_2, 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_3, e_2, e_1) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(304,plain,
% 0.19/0.47 ((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_1) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(305,plain,
% 0.19/0.48 (((~![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_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_1) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2)))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[304])).
% 0.19/0.48 tff(306,plain,
% 0.19/0.48 (((~![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_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_1) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2))),
% 0.19/0.48 inference(transitivity,[status(thm)],[305, 303])).
% 0.19/0.48 tff(307,plain,
% 0.19/0.48 ((~![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_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)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(308,plain,
% 0.19/0.48 ((~![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_2)) | product(e_3, e_2, e_1) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2)),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[307, 306])).
% 0.19/0.48 tff(309,plain,
% 0.19/0.48 (product(e_3, e_2, e_1) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[308, 167, 128, 74])).
% 0.19/0.48 tff(310,plain,
% 0.19/0.48 (product(e_3, e_2, e_1)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[309, 302, 42])).
% 0.19/0.48 tff(311,plain,
% 0.19/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_2) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_2) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_3, e_1)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(312,plain,
% 0.19/0.48 (((~product(e_2, e_3, e_1)) | product(e_1, e_1, e_2) | (~product(e_3, e_2, e_1))) <=> (product(e_1, e_1, e_2) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_3, e_1)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(313,plain,
% 0.19/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_3, e_1)) | product(e_1, e_1, e_2) | (~product(e_3, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_2) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_3, e_1))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[312])).
% 0.19/0.48 tff(314,plain,
% 0.19/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_3, e_1)) | product(e_1, e_1, e_2) | (~product(e_3, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_2) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_3, e_1)))),
% 0.19/0.48 inference(transitivity,[status(thm)],[313, 311])).
% 0.19/0.48 tff(315,plain,
% 0.19/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_3, e_1)) | product(e_1, e_1, e_2) | (~product(e_3, e_2, e_1)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(316,plain,
% 0.19/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_2) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_3, e_1))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[315, 314])).
% 0.19/0.48 tff(317,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[316, 118, 44, 291, 310])).
% 0.19/0.48 tff(318,plain,(product(e_1, e_3, e_3) | product(e_1, e_1, e_2) | product(e_3, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(319,plain,
% 0.19/0.48 (product(e_1, e_3, e_3)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[318, 41, 21])).
% 0.19/0.48 tff(320,plain,
% 0.19/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_3)) | (~product(e_3, e_1, e_2)) | product(e_3, e_2, e_3))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_1, e_2)) | product(e_3, e_2, e_3))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(321,plain,
% 0.19/0.48 (((~product(e_3, e_1, e_2)) | product(e_3, e_2, e_3) | (~product(e_1, e_3, e_3))) <=> ((~product(e_1, e_3, e_3)) | (~product(e_3, e_1, e_2)) | product(e_3, e_2, e_3))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(322,plain,
% 0.19/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_2)) | product(e_3, e_2, e_3) | (~product(e_1, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_3)) | (~product(e_3, e_1, e_2)) | product(e_3, e_2, e_3)))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[321])).
% 0.19/0.48 tff(323,plain,
% 0.19/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_2)) | product(e_3, e_2, e_3) | (~product(e_1, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_1, e_2)) | product(e_3, e_2, e_3))),
% 0.19/0.48 inference(transitivity,[status(thm)],[322, 320])).
% 0.19/0.48 tff(324,plain,
% 0.19/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_2)) | product(e_3, e_2, e_3) | (~product(e_1, e_3, e_3)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(325,plain,
% 0.19/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_1, e_2)) | product(e_3, e_2, e_3)),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[324, 323])).
% 0.19/0.48 tff(326,plain,
% 0.19/0.48 ((~product(e_1, e_3, e_3)) | (~product(e_3, e_1, e_2)) | product(e_3, e_2, e_3)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[325, 118])).
% 0.19/0.48 tff(327,plain,
% 0.19/0.48 (product(e_3, e_2, e_3)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[326, 319, 1])).
% 0.19/0.48 tff(328,plain,
% 0.19/0.48 (product(e_1, e_1, e_1)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[84, 41])).
% 0.19/0.48 tff(329,plain,
% 0.19/0.48 (product(e_2, e_1, e_3)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[244, 328])).
% 0.19/0.48 tff(330,plain,
% 0.19/0.48 (~product(e_2, e_3, e_3)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[251, 329])).
% 0.19/0.48 tff(331,plain,
% 0.19/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_2, e_3, e_3) | (~product(e_2, e_3, e_2)) | (~product(e_3, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_2, e_3, e_3) | (~product(e_2, e_3, e_2)) | (~product(e_3, e_2, e_3)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(332,plain,
% 0.19/0.48 (((~product(e_3, e_2, e_3)) | product(e_2, e_3, e_3) | (~product(e_2, e_3, e_2))) <=> (product(e_2, e_3, e_3) | (~product(e_2, e_3, e_2)) | (~product(e_3, e_2, e_3)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(333,plain,
% 0.19/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_2, e_3)) | product(e_2, e_3, e_3) | (~product(e_2, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_2, e_3, e_3) | (~product(e_2, e_3, e_2)) | (~product(e_3, e_2, e_3))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[332])).
% 0.19/0.48 tff(334,plain,
% 0.19/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_2, e_3)) | product(e_2, e_3, e_3) | (~product(e_2, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_2, e_3, e_3) | (~product(e_2, e_3, e_2)) | (~product(e_3, e_2, e_3)))),
% 0.19/0.48 inference(transitivity,[status(thm)],[333, 331])).
% 0.19/0.48 tff(335,plain,
% 0.19/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_2, e_3)) | product(e_2, e_3, e_3) | (~product(e_2, e_3, e_2)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(336,plain,
% 0.19/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_2, e_3, e_3) | (~product(e_2, e_3, e_2)) | (~product(e_3, e_2, e_3))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[335, 334])).
% 0.19/0.48 tff(337,plain,
% 0.19/0.48 (~product(e_2, e_3, e_2)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[336, 118, 330, 327])).
% 0.19/0.48 tff(338,plain,
% 0.19/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_2, e_3, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_2, e_3, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_2, e_2)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(339,plain,
% 0.19/0.48 (((~product(e_2, e_1, e_3)) | product(e_2, e_3, e_2) | (~product(e_1, e_2, e_2))) <=> (product(e_2, e_3, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_2, e_2)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(340,plain,
% 0.19/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_1, e_3)) | product(e_2, e_3, e_2) | (~product(e_1, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_2, e_3, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_2, e_2))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[339])).
% 0.19/0.48 tff(341,plain,
% 0.19/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_1, e_3)) | product(e_2, e_3, e_2) | (~product(e_1, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_2, e_3, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_2, e_2)))),
% 0.19/0.48 inference(transitivity,[status(thm)],[340, 338])).
% 0.19/0.48 tff(342,plain,
% 0.19/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_1, e_3)) | product(e_2, e_3, e_2) | (~product(e_1, e_2, e_2)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(343,plain,
% 0.19/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_2, e_3, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_2, e_2))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[342, 341])).
% 0.19/0.48 tff(344,plain,
% 0.19/0.48 (~product(e_1, e_2, e_2)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[343, 118, 329, 337])).
% 0.19/0.48 tff(345,assumption,(product(e_2, e_2, e_3)), introduced(assumption)).
% 0.19/0.48 tff(346,plain,
% 0.19/0.48 (((~![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_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_2, e_3) | (~product(e_2, e_2, e_3)) | (~product(e_3, e_2, e_3)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(347,plain,
% 0.19/0.48 ((equalish(e_2, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_2, e_2, e_3))) <=> (equalish(e_2, e_3) | (~product(e_2, e_2, e_3)) | (~product(e_3, e_2, e_3)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(348,plain,
% 0.19/0.48 (((~![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_3)) | (~product(e_2, 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_2, e_3) | (~product(e_2, e_2, e_3)) | (~product(e_3, e_2, e_3))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[347])).
% 0.19/0.48 tff(349,plain,
% 0.19/0.48 (((~![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_3)) | (~product(e_2, 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_2, e_3) | (~product(e_2, e_2, e_3)) | (~product(e_3, e_2, e_3)))),
% 0.19/0.48 inference(transitivity,[status(thm)],[348, 346])).
% 0.19/0.48 tff(350,plain,
% 0.19/0.48 ((~![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_3)) | (~product(e_2, e_2, e_3)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(351,plain,
% 0.19/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_3) | (~product(e_2, e_2, e_3)) | (~product(e_3, e_2, e_3))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[350, 349])).
% 0.19/0.48 tff(352,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[351, 102, 32, 292, 345])).
% 0.19/0.48 tff(353,plain,((~product(e_2, e_2, e_3)) | (~product(e_3, e_2, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(354,plain,
% 0.19/0.48 (~product(e_2, e_2, e_3)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[353, 327])).
% 0.19/0.48 tff(355,plain,
% 0.19/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_2)) | product(e_2, e_2, e_3) | (~product(e_1, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_2)) | product(e_2, e_2, e_3) | (~product(e_1, e_3, e_2)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(356,plain,
% 0.19/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_2)) | product(e_2, e_2, e_3) | (~product(e_1, e_3, e_2)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(357,plain,
% 0.19/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_2)) | product(e_2, e_2, e_3) | (~product(e_1, e_3, e_2))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[356, 355])).
% 0.19/0.48 tff(358,plain,
% 0.19/0.48 (~product(e_1, e_3, e_2)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[357, 118, 1, 354])).
% 0.19/0.48 tff(359,plain,
% 0.19/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_1, e_3, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_3, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_2, e_1)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(360,plain,
% 0.19/0.48 (((~product(e_2, e_1, e_3)) | product(e_1, e_3, e_2) | (~product(e_1, e_2, e_1))) <=> (product(e_1, e_3, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_2, e_1)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(361,plain,
% 0.19/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_1, e_3)) | product(e_1, e_3, e_2) | (~product(e_1, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_1, e_3, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_2, e_1))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[360])).
% 0.19/0.49 tff(362,plain,
% 0.19/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_1, e_3)) | product(e_1, e_3, e_2) | (~product(e_1, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_3, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_2, e_1)))),
% 0.19/0.49 inference(transitivity,[status(thm)],[361, 359])).
% 0.19/0.49 tff(363,plain,
% 0.19/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_1, e_3)) | product(e_1, e_3, e_2) | (~product(e_1, e_2, e_1)))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(364,plain,
% 0.19/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_3, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_2, e_1))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[363, 362])).
% 0.19/0.49 tff(365,plain,
% 0.19/0.49 (~product(e_1, e_2, e_1)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[364, 118, 358, 329])).
% 0.19/0.49 tff(366,plain,
% 0.19/0.49 (product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[173, 77, 167, 74])).
% 0.19/0.49 tff(367,plain,
% 0.19/0.49 (product(e_1, e_2, e_3)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[366, 365, 344])).
% 0.19/0.49 tff(368,plain,
% 0.19/0.49 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_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)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(369,plain,
% 0.19/0.49 ((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)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(370,plain,
% 0.19/0.49 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_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))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[369])).
% 0.19/0.49 tff(371,plain,
% 0.19/0.49 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_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)))),
% 0.19/0.49 inference(transitivity,[status(thm)],[370, 368])).
% 0.19/0.49 tff(372,plain,
% 0.19/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_1, e_2, e_3)))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(373,plain,
% 0.19/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_3, e_2, e_3))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[372, 371])).
% 0.19/0.49 tff(374,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[373, 158, 32, 367, 327])).
% 0.19/0.49 tff(375,plain,(~product(e_3, e_1, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.49 tff(376,plain,
% 0.19/0.49 (product(e_3, e_1, e_1)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[230, 375])).
% 0.19/0.49 tff(377,assumption,(product(e_1, e_3, e_3)), introduced(assumption)).
% 0.19/0.49 tff(378,plain,
% 0.19/0.49 (~product(e_1, e_3, e_1)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[259, 118, 64, 88])).
% 0.19/0.49 tff(379,plain,
% 0.19/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_3)) | (~product(e_3, e_1, e_1)) | product(e_1, e_3, e_1))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_1, e_1)) | product(e_1, e_3, e_1))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(380,plain,
% 0.19/0.49 (((~product(e_1, e_3, e_3)) | product(e_1, e_3, e_1) | (~product(e_3, e_1, e_1))) <=> ((~product(e_1, e_3, e_3)) | (~product(e_3, e_1, e_1)) | product(e_1, e_3, e_1))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(381,plain,
% 0.19/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_3)) | product(e_1, e_3, e_1) | (~product(e_3, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_3)) | (~product(e_3, e_1, e_1)) | product(e_1, e_3, e_1)))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[380])).
% 0.19/0.49 tff(382,plain,
% 0.19/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_3)) | product(e_1, e_3, e_1) | (~product(e_3, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_1, e_1)) | product(e_1, e_3, e_1))),
% 0.19/0.49 inference(transitivity,[status(thm)],[381, 379])).
% 0.19/0.49 tff(383,plain,
% 0.19/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_3)) | product(e_1, e_3, e_1) | (~product(e_3, e_1, e_1)))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(384,plain,
% 0.19/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_1, e_1)) | product(e_1, e_3, e_1)),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[383, 382])).
% 0.19/0.49 tff(385,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[384, 118, 88, 378, 377])).
% 0.19/0.49 tff(386,plain,((~product(e_1, e_3, e_3)) | (~product(e_3, e_1, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.49 tff(387,plain,
% 0.19/0.49 (~product(e_1, e_3, e_3)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[386, 376])).
% 0.19/0.49 tff(388,plain,
% 0.19/0.49 (product(e_1, e_3, e_2)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[275, 387])).
% 0.19/0.49 tff(389,plain,
% 0.19/0.49 (~product(e_1, e_1, e_1)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[96, 376])).
% 0.19/0.49 tff(390,plain,
% 0.19/0.49 (product(e_1, e_1, e_2)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[84, 389])).
% 0.19/0.49 tff(391,plain,
% 0.19/0.49 (((~![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)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(392,plain,
% 0.19/0.49 ((~![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)))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(393,plain,
% 0.19/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_3, e_2))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[392, 391])).
% 0.19/0.49 tff(394,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[393, 35, 12, 22, 137])).
% 0.19/0.49 tff(395,plain,((~product(e_1, e_3, e_2)) | (~product(e_1, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.49 tff(396,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[395, 390, 388])).
% 0.19/0.49 % SZS output end Proof
%------------------------------------------------------------------------------