TSTP Solution File: GRP127-2.006 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP127-2.006 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n028.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 22:26:07 EDT 2022
% Result : Unsatisfiable 0.19s 0.54s
% Output : Proof 0.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP127-2.006 : TPTP v8.1.0. Released v1.2.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n028.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Aug 31 15:09:20 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.19/0.54 % SZS status Unsatisfiable
% 0.19/0.54 % SZS output start Proof
% 0.19/0.54 tff(product_type, type, (
% 0.19/0.54 product: ( $i * $i * $i ) > $o)).
% 0.19/0.54 tff(e_3_type, type, (
% 0.19/0.54 e_3: $i)).
% 0.19/0.54 tff(e_2_type, type, (
% 0.19/0.54 e_2: $i)).
% 0.19/0.54 tff(e_6_type, type, (
% 0.19/0.54 e_6: $i)).
% 0.19/0.54 tff(e_4_type, type, (
% 0.19/0.54 e_4: $i)).
% 0.19/0.54 tff(e_5_type, type, (
% 0.19/0.54 e_5: $i)).
% 0.19/0.54 tff(e_1_type, type, (
% 0.19/0.54 e_1: $i)).
% 0.19/0.54 tff(equalish_type, type, (
% 0.19/0.54 equalish: ( $i * $i ) > $o)).
% 0.19/0.54 tff(next_type, type, (
% 0.19/0.54 next: ( $i * $i ) > $o)).
% 0.19/0.54 tff(greater_type, type, (
% 0.19/0.54 greater: ( $i * $i ) > $o)).
% 0.19/0.54 tff(group_element_type, type, (
% 0.19/0.54 group_element: $i > $o)).
% 0.19/0.54 tff(1,assumption,(~product(e_5, e_6, e_4)), introduced(assumption)).
% 0.19/0.54 tff(2,assumption,(product(e_3, e_4, e_1)), introduced(assumption)).
% 0.19/0.54 tff(3,assumption,(~product(e_4, e_1, e_5)), introduced(assumption)).
% 0.19/0.54 tff(4,assumption,(~product(e_1, e_4, e_2)), introduced(assumption)).
% 0.19/0.54 tff(5,assumption,(~product(e_1, e_3, e_6)), introduced(assumption)).
% 0.19/0.54 tff(6,assumption,(product(e_1, e_6, e_4)), introduced(assumption)).
% 0.19/0.54 tff(7,assumption,(product(e_1, e_5, e_4)), introduced(assumption)).
% 0.19/0.54 tff(8,plain,
% 0.19/0.54 (^[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))))),
% 0.19/0.54 inference(bind,[status(th)],[])).
% 0.19/0.54 tff(9,plain,
% 0.19/0.54 (![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)))),
% 0.19/0.54 inference(quant_intro,[status(thm)],[8])).
% 0.19/0.54 tff(10,plain,
% 0.19/0.54 (![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)))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(11,plain,
% 0.19/0.54 (^[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)))))),
% 0.19/0.54 inference(bind,[status(th)],[])).
% 0.19/0.54 tff(12,plain,
% 0.19/0.54 (![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)))),
% 0.19/0.54 inference(quant_intro,[status(thm)],[11])).
% 0.19/0.54 tff(13,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')).
% 0.19/0.54 tff(14,plain,
% 0.19/0.54 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.19/0.54 tff(15,plain,
% 0.19/0.54 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.19/0.54 tff(16,plain,(
% 0.19/0.54 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.19/0.54 inference(skolemize,[status(sab)],[15])).
% 0.19/0.54 tff(17,plain,
% 0.19/0.54 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[16, 9])).
% 0.19/0.54 tff(18,plain,
% 0.19/0.54 ((~equalish(e_5, e_6)) <=> (~equalish(e_5, e_6))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(19,axiom,(~equalish(e_5, e_6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_5_is_not_e_6')).
% 0.19/0.54 tff(20,plain,
% 0.19/0.54 (~equalish(e_5, e_6)),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.19/0.54 tff(21,plain,
% 0.19/0.54 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_6) | (~product(e_1, e_6, e_4)) | (~product(e_1, e_5, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_6) | (~product(e_1, e_6, e_4)) | (~product(e_1, e_5, e_4)))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(22,plain,
% 0.19/0.55 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_6) | (~product(e_1, e_6, e_4)) | (~product(e_1, e_5, e_4)))),
% 0.19/0.55 inference(quant_inst,[status(thm)],[])).
% 0.19/0.55 tff(23,plain,
% 0.19/0.55 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_6) | (~product(e_1, e_6, e_4)) | (~product(e_1, e_5, e_4))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.19/0.55 tff(24,plain,
% 0.19/0.55 ($false),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[23, 20, 17, 7, 6])).
% 0.19/0.55 tff(25,plain,((~product(e_1, e_5, e_4)) | (~product(e_1, e_6, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.55 tff(26,plain,
% 0.19/0.55 (~product(e_1, e_5, e_4)),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[25, 6])).
% 0.19/0.55 tff(27,assumption,(product(e_1, e_5, e_2)), introduced(assumption)).
% 0.19/0.55 tff(28,assumption,(product(e_2, e_1, e_3)), introduced(assumption)).
% 0.19/0.55 tff(29,plain,
% 0.19/0.55 (^[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))))),
% 0.19/0.55 inference(bind,[status(th)],[])).
% 0.19/0.55 tff(30,plain,
% 0.19/0.55 (![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)))),
% 0.19/0.55 inference(quant_intro,[status(thm)],[29])).
% 0.19/0.55 tff(31,plain,
% 0.19/0.55 (![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)))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(32,plain,
% 0.19/0.55 (^[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)))))),
% 0.19/0.55 inference(bind,[status(th)],[])).
% 0.19/0.55 tff(33,plain,
% 0.19/0.55 (![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)))),
% 0.19/0.55 inference(quant_intro,[status(thm)],[32])).
% 0.19/0.55 tff(34,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')).
% 0.19/0.55 tff(35,plain,
% 0.19/0.55 (![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.19/0.55 tff(36,plain,
% 0.19/0.55 (![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.19/0.55 tff(37,plain,(
% 0.19/0.55 ![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))),
% 0.19/0.55 inference(skolemize,[status(sab)],[36])).
% 0.19/0.55 tff(38,plain,
% 0.19/0.55 (![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[37, 30])).
% 0.19/0.55 tff(39,plain,
% 0.19/0.55 (greater(e_5, e_4) <=> greater(e_5, e_4)),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(40,axiom,(greater(e_5, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_5_greater_e_4')).
% 0.19/0.55 tff(41,plain,
% 0.19/0.55 (greater(e_5, e_4)),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.19/0.55 tff(42,plain,
% 0.19/0.55 (next(e_3, e_4) <=> next(e_3, e_4)),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(43,axiom,(next(e_3, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_then_e_4')).
% 0.19/0.55 tff(44,plain,
% 0.19/0.55 (next(e_3, e_4)),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.19/0.55 tff(45,plain,
% 0.19/0.55 (((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_5, e_4)) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_5)))) <=> ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_5, e_4)) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_5)))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(46,plain,
% 0.19/0.55 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_5, e_4)) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_5)))),
% 0.19/0.55 inference(quant_inst,[status(thm)],[])).
% 0.19/0.55 tff(47,plain,
% 0.19/0.55 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_5, e_4)) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_5))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.19/0.55 tff(48,plain,
% 0.19/0.55 (~product(e_3, e_1, e_5)),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[47, 44, 41, 38])).
% 0.19/0.55 tff(49,plain,
% 0.19/0.55 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : refl((product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1))) <=> (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1))))),
% 0.19/0.55 inference(bind,[status(th)],[])).
% 0.19/0.55 tff(50,plain,
% 0.19/0.55 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))),
% 0.19/0.55 inference(quant_intro,[status(thm)],[49])).
% 0.19/0.55 tff(51,plain,
% 0.19/0.55 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(52,plain,
% 0.19/0.55 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : trans(monotonicity(rewrite(((~product(Y, X, Z1)) | (~product(Z1, Y, Z2))) <=> ((~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))), ((((~product(Y, X, Z1)) | (~product(Z1, Y, Z2))) | product(Z2, Y, X)) <=> (((~product(Z1, Y, Z2)) | (~product(Y, X, Z1))) | product(Z2, Y, X)))), rewrite((((~product(Z1, Y, Z2)) | (~product(Y, X, Z1))) | product(Z2, Y, X)) <=> (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))), ((((~product(Y, X, Z1)) | (~product(Z1, Y, Z2))) | product(Z2, Y, X)) <=> (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))))),
% 0.19/0.55 inference(bind,[status(th)],[])).
% 0.19/0.55 tff(53,plain,
% 0.19/0.55 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(Y, X, Z1)) | (~product(Z1, Y, Z2))) | product(Z2, Y, X)) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))),
% 0.19/0.55 inference(quant_intro,[status(thm)],[52])).
% 0.19/0.55 tff(54,axiom,(![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(Y, X, Z1)) | (~product(Z1, Y, Z2))) | product(Z2, Y, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qg3')).
% 0.19/0.55 tff(55,plain,
% 0.19/0.55 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.19/0.55 tff(56,plain,
% 0.19/0.55 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.19/0.55 tff(57,plain,(
% 0.19/0.55 ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))),
% 0.19/0.55 inference(skolemize,[status(sab)],[56])).
% 0.19/0.55 tff(58,plain,
% 0.19/0.55 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[57, 50])).
% 0.19/0.55 tff(59,plain,
% 0.19/0.55 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_5) | (~product(e_1, e_5, e_2)) | (~product(e_2, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_5) | (~product(e_1, e_5, e_2)) | (~product(e_2, e_1, e_3)))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(60,plain,
% 0.19/0.55 ((product(e_3, e_1, e_5) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_5, e_2))) <=> (product(e_3, e_1, e_5) | (~product(e_1, e_5, e_2)) | (~product(e_2, e_1, e_3)))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(61,plain,
% 0.19/0.55 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_5) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_5, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_5) | (~product(e_1, e_5, e_2)) | (~product(e_2, e_1, e_3))))),
% 0.19/0.55 inference(monotonicity,[status(thm)],[60])).
% 0.19/0.55 tff(62,plain,
% 0.19/0.55 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_5) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_5, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_5) | (~product(e_1, e_5, e_2)) | (~product(e_2, e_1, e_3)))),
% 0.19/0.55 inference(transitivity,[status(thm)],[61, 59])).
% 0.19/0.55 tff(63,plain,
% 0.19/0.55 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_5) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_5, e_2)))),
% 0.19/0.55 inference(quant_inst,[status(thm)],[])).
% 0.19/0.55 tff(64,plain,
% 0.19/0.55 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_5) | (~product(e_1, e_5, e_2)) | (~product(e_2, e_1, e_3))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.19/0.55 tff(65,plain,
% 0.19/0.55 ($false),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[64, 58, 48, 28, 27])).
% 0.19/0.55 tff(66,plain,((~product(e_2, e_1, e_3)) | (~product(e_1, e_5, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.55 tff(67,plain,
% 0.19/0.55 (~product(e_2, e_1, e_3)),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[66, 27])).
% 0.19/0.55 tff(68,assumption,(product(e_2, e_1, e_1)), introduced(assumption)).
% 0.19/0.55 tff(69,plain,
% 0.19/0.55 (^[X: $i] : refl(product(X, X, X) <=> product(X, X, X))),
% 0.19/0.55 inference(bind,[status(th)],[])).
% 0.19/0.55 tff(70,plain,
% 0.19/0.55 (![X: $i] : product(X, X, X) <=> ![X: $i] : product(X, X, X)),
% 0.19/0.55 inference(quant_intro,[status(thm)],[69])).
% 0.19/0.55 tff(71,plain,
% 0.19/0.55 (![X: $i] : product(X, X, X) <=> ![X: $i] : product(X, X, X)),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(72,axiom,(![X: $i] : product(X, X, X)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product_idempotence')).
% 0.19/0.55 tff(73,plain,
% 0.19/0.55 (![X: $i] : product(X, X, X)),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.19/0.55 tff(74,plain,(
% 0.19/0.55 ![X: $i] : product(X, X, X)),
% 0.19/0.55 inference(skolemize,[status(sab)],[73])).
% 0.19/0.55 tff(75,plain,
% 0.19/0.55 (![X: $i] : product(X, X, X)),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[74, 70])).
% 0.19/0.55 tff(76,plain,
% 0.19/0.55 ((~![X: $i] : product(X, X, X)) | product(e_1, e_1, e_1)),
% 0.19/0.55 inference(quant_inst,[status(thm)],[])).
% 0.19/0.55 tff(77,plain,
% 0.19/0.55 (product(e_1, e_1, e_1)),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[76, 75])).
% 0.19/0.55 tff(78,plain,
% 0.19/0.55 (^[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))))),
% 0.19/0.55 inference(bind,[status(th)],[])).
% 0.19/0.55 tff(79,plain,
% 0.19/0.55 (![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)))),
% 0.19/0.55 inference(quant_intro,[status(thm)],[78])).
% 0.19/0.55 tff(80,plain,
% 0.19/0.55 (![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)))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(81,plain,
% 0.19/0.55 (^[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)))))),
% 0.19/0.55 inference(bind,[status(th)],[])).
% 0.19/0.55 tff(82,plain,
% 0.19/0.55 (![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)))),
% 0.19/0.55 inference(quant_intro,[status(thm)],[81])).
% 0.19/0.55 tff(83,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')).
% 0.19/0.55 tff(84,plain,
% 0.19/0.55 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.19/0.55 tff(85,plain,
% 0.19/0.55 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[84, 80])).
% 0.19/0.55 tff(86,plain,(
% 0.19/0.55 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.19/0.55 inference(skolemize,[status(sab)],[85])).
% 0.19/0.55 tff(87,plain,
% 0.19/0.55 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[86, 79])).
% 0.19/0.55 tff(88,plain,
% 0.19/0.55 ((~equalish(e_2, e_1)) <=> (~equalish(e_2, e_1))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(89,axiom,(~equalish(e_2, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_1')).
% 0.19/0.55 tff(90,plain,
% 0.19/0.55 (~equalish(e_2, e_1)),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.19/0.55 tff(91,plain,
% 0.19/0.55 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_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)))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(92,plain,
% 0.19/0.55 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1)))),
% 0.19/0.55 inference(quant_inst,[status(thm)],[])).
% 0.19/0.55 tff(93,plain,
% 0.19/0.55 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.19/0.55 tff(94,plain,
% 0.19/0.55 ($false),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[93, 90, 87, 77, 68])).
% 0.19/0.55 tff(95,plain,(~product(e_2, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.55 tff(96,plain,
% 0.19/0.55 (greater(e_6, e_3) <=> greater(e_6, e_3)),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(97,axiom,(greater(e_6, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_6_greater_e_3')).
% 0.19/0.55 tff(98,plain,
% 0.19/0.55 (greater(e_6, e_3)),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.19/0.55 tff(99,plain,
% 0.19/0.55 (next(e_2, e_3) <=> next(e_2, e_3)),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(100,axiom,(next(e_2, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_then_e_3')).
% 0.19/0.55 tff(101,plain,
% 0.19/0.55 (next(e_2, e_3)),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.19/0.55 tff(102,plain,
% 0.19/0.55 (((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_6, e_3)) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_6)))) <=> ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_6, e_3)) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_6)))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(103,plain,
% 0.19/0.55 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_6, e_3)) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_6)))),
% 0.19/0.55 inference(quant_inst,[status(thm)],[])).
% 0.19/0.55 tff(104,plain,
% 0.19/0.55 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_6, e_3)) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_6))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.19/0.55 tff(105,plain,
% 0.19/0.55 (~product(e_2, e_1, e_6)),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[104, 101, 98, 38])).
% 0.19/0.55 tff(106,plain,
% 0.19/0.55 (greater(e_5, e_3) <=> greater(e_5, e_3)),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(107,axiom,(greater(e_5, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_5_greater_e_3')).
% 0.19/0.55 tff(108,plain,
% 0.19/0.55 (greater(e_5, e_3)),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.19/0.55 tff(109,plain,
% 0.19/0.55 (((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_5, e_3)) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_5)))) <=> ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_5, e_3)) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_5)))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(110,plain,
% 0.19/0.55 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_5, e_3)) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_5)))),
% 0.19/0.55 inference(quant_inst,[status(thm)],[])).
% 0.19/0.55 tff(111,plain,
% 0.19/0.55 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_5, e_3)) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_5))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.19/0.55 tff(112,plain,
% 0.19/0.55 (~product(e_2, e_1, e_5)),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[111, 101, 108, 38])).
% 0.19/0.55 tff(113,plain,
% 0.19/0.55 (greater(e_4, e_3) <=> greater(e_4, e_3)),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(114,axiom,(greater(e_4, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_greater_e_3')).
% 0.19/0.55 tff(115,plain,
% 0.19/0.55 (greater(e_4, e_3)),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.19/0.55 tff(116,plain,
% 0.19/0.55 (((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_4, e_3)) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4)))) <=> ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_4, e_3)) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4)))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(117,plain,
% 0.19/0.55 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_4, e_3)) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4)))),
% 0.19/0.55 inference(quant_inst,[status(thm)],[])).
% 0.19/0.55 tff(118,plain,
% 0.19/0.55 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_4, e_3)) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.19/0.55 tff(119,plain,
% 0.19/0.55 (~product(e_2, e_1, e_4)),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[118, 101, 115, 38])).
% 0.19/0.55 tff(120,plain,
% 0.19/0.55 (^[Y: $i, X: $i] : refl((product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) <=> (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))))),
% 0.19/0.55 inference(bind,[status(th)],[])).
% 0.19/0.55 tff(121,plain,
% 0.19/0.55 (![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) <=> ![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.19/0.55 inference(quant_intro,[status(thm)],[120])).
% 0.19/0.55 tff(122,plain,
% 0.19/0.55 (![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) <=> ![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(123,plain,
% 0.19/0.55 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) <=> (product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))), (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) <=> ((product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_2)))), rewrite(((product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_2)) <=> (product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))), (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) <=> (product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))))), ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) <=> ((product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_3)))), rewrite(((product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_3)) <=> (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))), ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) <=> (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))))), (((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) | product(X, Y, e_4)) <=> ((product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_4)))), rewrite(((product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_4)) <=> (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))), (((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) | product(X, Y, e_4)) <=> (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))))), ((((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) | product(X, Y, e_4)) | product(X, Y, e_5)) <=> ((product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_5)))), rewrite(((product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_5)) <=> (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))), ((((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) | product(X, Y, e_4)) | product(X, Y, e_5)) <=> (product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))))), (((((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) | product(X, Y, e_4)) | product(X, Y, e_5)) | product(X, Y, e_6)) <=> ((product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_6)))), rewrite(((product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_6)) <=> (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))), (((((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) | product(X, Y, e_4)) | product(X, Y, e_5)) | product(X, Y, e_6)) <=> (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))))),
% 0.19/0.56 inference(bind,[status(th)],[])).
% 0.19/0.56 tff(124,plain,
% 0.19/0.56 (![Y: $i, X: $i] : ((((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) | product(X, Y, e_4)) | product(X, Y, e_5)) | product(X, Y, e_6)) <=> ![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.19/0.56 inference(quant_intro,[status(thm)],[123])).
% 0.19/0.56 tff(125,axiom,(![Y: $i, X: $i] : ((((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) | product(X, Y, e_4)) | product(X, Y, e_5)) | product(X, Y, e_6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product_total_function1')).
% 0.19/0.56 tff(126,plain,
% 0.19/0.56 (![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.19/0.56 tff(127,plain,
% 0.19/0.56 (![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[126, 122])).
% 0.19/0.56 tff(128,plain,(
% 0.19/0.56 ![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.19/0.56 inference(skolemize,[status(sab)],[127])).
% 0.19/0.56 tff(129,plain,
% 0.19/0.56 (![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[128, 121])).
% 0.19/0.56 tff(130,plain,
% 0.19/0.56 (group_element(e_2) <=> group_element(e_2)),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(131,axiom,(group_element(e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_2')).
% 0.19/0.56 tff(132,plain,
% 0.19/0.56 (group_element(e_2)),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.19/0.56 tff(133,plain,
% 0.19/0.56 (group_element(e_1) <=> group_element(e_1)),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(134,axiom,(group_element(e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_1')).
% 0.19/0.56 tff(135,plain,
% 0.19/0.56 (group_element(e_1)),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.19/0.56 tff(136,plain,
% 0.19/0.56 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_1, e_4) | product(e_2, e_1, e_5) | product(e_2, e_1, e_6) | (~group_element(e_1)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_2, e_1, e_4) | product(e_2, e_1, e_5) | product(e_2, e_1, e_6) | (~group_element(e_1)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_2)))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(137,plain,
% 0.19/0.56 ((product(e_2, e_1, e_6) | product(e_2, e_1, e_5) | product(e_2, e_1, e_4) | 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))) <=> (product(e_2, e_1, e_4) | product(e_2, e_1, e_5) | product(e_2, e_1, e_6) | (~group_element(e_1)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_2)))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(138,plain,
% 0.19/0.56 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_1, e_6) | product(e_2, e_1, e_5) | product(e_2, e_1, e_4) | 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_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_1, e_4) | product(e_2, e_1, e_5) | product(e_2, e_1, e_6) | (~group_element(e_1)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_2))))),
% 0.19/0.56 inference(monotonicity,[status(thm)],[137])).
% 0.19/0.56 tff(139,plain,
% 0.19/0.56 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_1, e_6) | product(e_2, e_1, e_5) | product(e_2, e_1, e_4) | 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_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_2, e_1, e_4) | product(e_2, e_1, e_5) | product(e_2, e_1, e_6) | (~group_element(e_1)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_2)))),
% 0.19/0.56 inference(transitivity,[status(thm)],[138, 136])).
% 0.19/0.56 tff(140,plain,
% 0.19/0.56 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_1, e_6) | product(e_2, e_1, e_5) | product(e_2, e_1, e_4) | 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)))),
% 0.19/0.56 inference(quant_inst,[status(thm)],[])).
% 0.19/0.56 tff(141,plain,
% 0.19/0.56 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_2, e_1, e_4) | product(e_2, e_1, e_5) | product(e_2, e_1, e_6) | (~group_element(e_1)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_2))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.19/0.56 tff(142,plain,
% 0.19/0.56 (product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1)),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[141, 135, 132, 129, 119, 112, 105])).
% 0.19/0.56 tff(143,plain,
% 0.19/0.56 (product(e_2, e_1, e_3) | product(e_2, e_1, e_2)),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[142, 95])).
% 0.19/0.56 tff(144,plain,
% 0.19/0.56 (product(e_2, e_1, e_2)),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[143, 67])).
% 0.19/0.56 tff(145,plain,
% 0.19/0.56 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_5) | (~product(e_1, e_5, e_2)) | (~product(e_2, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_5) | (~product(e_1, e_5, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(146,plain,
% 0.19/0.56 ((product(e_2, e_1, e_5) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_5, e_2))) <=> (product(e_2, e_1, e_5) | (~product(e_1, e_5, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(147,plain,
% 0.19/0.56 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_5) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_5, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_5) | (~product(e_1, e_5, e_2)) | (~product(e_2, e_1, e_2))))),
% 0.19/0.56 inference(monotonicity,[status(thm)],[146])).
% 0.19/0.56 tff(148,plain,
% 0.19/0.56 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_5) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_5, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_5) | (~product(e_1, e_5, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.19/0.56 inference(transitivity,[status(thm)],[147, 145])).
% 0.19/0.56 tff(149,plain,
% 0.19/0.56 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_5) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_5, e_2)))),
% 0.19/0.56 inference(quant_inst,[status(thm)],[])).
% 0.19/0.56 tff(150,plain,
% 0.19/0.56 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_5) | (~product(e_1, e_5, e_2)) | (~product(e_2, e_1, e_2))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.19/0.56 tff(151,plain,
% 0.19/0.56 ($false),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[150, 58, 112, 144, 27])).
% 0.19/0.56 tff(152,plain,(~product(e_1, e_5, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.56 tff(153,assumption,(~product(e_1, e_5, e_4)), introduced(assumption)).
% 0.19/0.56 tff(154,assumption,(~product(e_1, e_5, e_2)), introduced(assumption)).
% 0.19/0.56 tff(155,assumption,(~product(e_1, e_5, e_3)), introduced(assumption)).
% 0.19/0.56 tff(156,assumption,(product(e_1, e_5, e_6)), introduced(assumption)).
% 0.19/0.56 tff(157,assumption,(product(e_1, e_6, e_6)), introduced(assumption)).
% 0.19/0.56 tff(158,plain,
% 0.19/0.56 ((~equalish(e_6, e_5)) <=> (~equalish(e_6, e_5))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(159,axiom,(~equalish(e_6, e_5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_6_is_not_e_5')).
% 0.19/0.56 tff(160,plain,
% 0.19/0.56 (~equalish(e_6, e_5)),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[159, 158])).
% 0.19/0.56 tff(161,plain,
% 0.19/0.56 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_6, e_5) | (~product(e_1, e_6, e_6)) | (~product(e_1, e_5, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_6, e_5) | (~product(e_1, e_6, e_6)) | (~product(e_1, e_5, e_6)))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(162,plain,
% 0.19/0.56 ((equalish(e_6, e_5) | (~product(e_1, e_5, e_6)) | (~product(e_1, e_6, e_6))) <=> (equalish(e_6, e_5) | (~product(e_1, e_6, e_6)) | (~product(e_1, e_5, e_6)))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(163,plain,
% 0.19/0.56 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_6, e_5) | (~product(e_1, e_5, e_6)) | (~product(e_1, e_6, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_6, e_5) | (~product(e_1, e_6, e_6)) | (~product(e_1, e_5, e_6))))),
% 0.19/0.56 inference(monotonicity,[status(thm)],[162])).
% 0.19/0.56 tff(164,plain,
% 0.19/0.56 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_6, e_5) | (~product(e_1, e_5, e_6)) | (~product(e_1, e_6, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_6, e_5) | (~product(e_1, e_6, e_6)) | (~product(e_1, e_5, e_6)))),
% 0.19/0.56 inference(transitivity,[status(thm)],[163, 161])).
% 0.19/0.56 tff(165,plain,
% 0.19/0.56 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_6, e_5) | (~product(e_1, e_5, e_6)) | (~product(e_1, e_6, e_6)))),
% 0.19/0.56 inference(quant_inst,[status(thm)],[])).
% 0.19/0.56 tff(166,plain,
% 0.19/0.56 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_6, e_5) | (~product(e_1, e_6, e_6)) | (~product(e_1, e_5, e_6))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[165, 164])).
% 0.19/0.56 tff(167,plain,
% 0.19/0.56 ($false),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[166, 160, 17, 156, 157])).
% 0.19/0.56 tff(168,plain,((~product(e_1, e_6, e_6)) | (~product(e_1, e_5, e_6))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.56 tff(169,plain,
% 0.19/0.56 (~product(e_1, e_6, e_6)),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[168, 156])).
% 0.19/0.56 tff(170,assumption,(product(e_1, e_4, e_6)), introduced(assumption)).
% 0.19/0.56 tff(171,plain,
% 0.19/0.56 ((~equalish(e_5, e_4)) <=> (~equalish(e_5, e_4))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(172,axiom,(~equalish(e_5, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_5_is_not_e_4')).
% 0.19/0.56 tff(173,plain,
% 0.19/0.56 (~equalish(e_5, e_4)),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[172, 171])).
% 0.19/0.56 tff(174,plain,
% 0.19/0.56 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_4) | (~product(e_1, e_5, e_6)) | (~product(e_1, e_4, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_4) | (~product(e_1, e_5, e_6)) | (~product(e_1, e_4, e_6)))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(175,plain,
% 0.19/0.56 ((equalish(e_5, e_4) | (~product(e_1, e_4, e_6)) | (~product(e_1, e_5, e_6))) <=> (equalish(e_5, e_4) | (~product(e_1, e_5, e_6)) | (~product(e_1, e_4, e_6)))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(176,plain,
% 0.19/0.56 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_4) | (~product(e_1, e_4, e_6)) | (~product(e_1, e_5, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_4) | (~product(e_1, e_5, e_6)) | (~product(e_1, e_4, e_6))))),
% 0.19/0.56 inference(monotonicity,[status(thm)],[175])).
% 0.19/0.56 tff(177,plain,
% 0.19/0.56 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_4) | (~product(e_1, e_4, e_6)) | (~product(e_1, e_5, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_4) | (~product(e_1, e_5, e_6)) | (~product(e_1, e_4, e_6)))),
% 0.19/0.56 inference(transitivity,[status(thm)],[176, 174])).
% 0.19/0.56 tff(178,plain,
% 0.19/0.56 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_4) | (~product(e_1, e_4, e_6)) | (~product(e_1, e_5, e_6)))),
% 0.19/0.56 inference(quant_inst,[status(thm)],[])).
% 0.19/0.56 tff(179,plain,
% 0.19/0.56 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_4) | (~product(e_1, e_5, e_6)) | (~product(e_1, e_4, e_6))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.19/0.56 tff(180,plain,
% 0.19/0.56 ($false),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[179, 173, 17, 156, 170])).
% 0.19/0.56 tff(181,plain,((~product(e_1, e_5, e_6)) | (~product(e_1, e_4, e_6))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.56 tff(182,plain,
% 0.19/0.56 (~product(e_1, e_4, e_6)),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[181, 156])).
% 0.19/0.56 tff(183,plain,
% 0.19/0.56 ((~![X: $i] : product(X, X, X)) | product(e_4, e_4, e_4)),
% 0.19/0.56 inference(quant_inst,[status(thm)],[])).
% 0.19/0.56 tff(184,plain,
% 0.19/0.56 (product(e_4, e_4, e_4)),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[183, 75])).
% 0.19/0.56 tff(185,assumption,(product(e_1, e_4, e_4)), introduced(assumption)).
% 0.19/0.56 tff(186,plain,
% 0.19/0.56 ((~equalish(e_1, e_4)) <=> (~equalish(e_1, e_4))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(187,axiom,(~equalish(e_1, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_4')).
% 0.19/0.56 tff(188,plain,
% 0.19/0.56 (~equalish(e_1, e_4)),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[187, 186])).
% 0.19/0.56 tff(189,plain,
% 0.19/0.56 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_4) | (~product(e_1, e_4, e_4)) | (~product(e_4, e_4, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_4) | (~product(e_1, e_4, e_4)) | (~product(e_4, e_4, e_4)))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(190,plain,
% 0.19/0.56 ((equalish(e_1, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_1, e_4, e_4))) <=> (equalish(e_1, e_4) | (~product(e_1, e_4, e_4)) | (~product(e_4, e_4, e_4)))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(191,plain,
% 0.19/0.56 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_1, e_4, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_4) | (~product(e_1, e_4, e_4)) | (~product(e_4, e_4, e_4))))),
% 0.19/0.57 inference(monotonicity,[status(thm)],[190])).
% 0.19/0.57 tff(192,plain,
% 0.19/0.57 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_1, e_4, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_4) | (~product(e_1, e_4, e_4)) | (~product(e_4, e_4, e_4)))),
% 0.19/0.57 inference(transitivity,[status(thm)],[191, 189])).
% 0.19/0.57 tff(193,plain,
% 0.19/0.57 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_1, e_4, e_4)))),
% 0.19/0.57 inference(quant_inst,[status(thm)],[])).
% 0.19/0.57 tff(194,plain,
% 0.19/0.57 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_4) | (~product(e_1, e_4, e_4)) | (~product(e_4, e_4, e_4))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[193, 192])).
% 0.19/0.57 tff(195,plain,
% 0.19/0.57 ($false),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[194, 188, 87, 185, 184])).
% 0.19/0.57 tff(196,plain,(~product(e_1, e_4, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.57 tff(197,assumption,(product(e_1, e_4, e_3)), introduced(assumption)).
% 0.19/0.57 tff(198,assumption,(product(e_3, e_1, e_1)), introduced(assumption)).
% 0.19/0.57 tff(199,plain,
% 0.19/0.57 (greater(e_4, e_2) <=> greater(e_4, e_2)),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(200,axiom,(greater(e_4, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_greater_e_2')).
% 0.19/0.57 tff(201,plain,
% 0.19/0.57 (greater(e_4, e_2)),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[200, 199])).
% 0.19/0.57 tff(202,plain,
% 0.19/0.57 (next(e_1, e_2) <=> next(e_1, e_2)),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(203,axiom,(next(e_1, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_then_e_2')).
% 0.19/0.57 tff(204,plain,
% 0.19/0.57 (next(e_1, e_2)),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[203, 202])).
% 0.19/0.57 tff(205,plain,
% 0.19/0.57 (((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_4, e_2)) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_4)))) <=> ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_4, e_2)) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_4)))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(206,plain,
% 0.19/0.57 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_4, e_2)) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_4)))),
% 0.19/0.57 inference(quant_inst,[status(thm)],[])).
% 0.19/0.57 tff(207,plain,
% 0.19/0.57 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_4, e_2)) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_4))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[206, 205])).
% 0.19/0.57 tff(208,plain,
% 0.19/0.57 (~product(e_1, e_1, e_4)),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[207, 204, 201, 38])).
% 0.19/0.57 tff(209,plain,
% 0.19/0.57 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_4) | (~product(e_3, e_1, e_1)) | (~product(e_1, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_4) | (~product(e_3, e_1, e_1)) | (~product(e_1, e_4, e_3)))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(210,plain,
% 0.19/0.57 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_4) | (~product(e_3, e_1, e_1)) | (~product(e_1, e_4, e_3)))),
% 0.19/0.57 inference(quant_inst,[status(thm)],[])).
% 0.19/0.57 tff(211,plain,
% 0.19/0.57 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_4) | (~product(e_3, e_1, e_1)) | (~product(e_1, e_4, e_3))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[210, 209])).
% 0.19/0.57 tff(212,plain,
% 0.19/0.57 ($false),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[211, 58, 208, 198, 197])).
% 0.19/0.57 tff(213,plain,((~product(e_3, e_1, e_1)) | (~product(e_1, e_4, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.57 tff(214,plain,
% 0.19/0.57 (~product(e_3, e_1, e_1)),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[213, 197])).
% 0.19/0.57 tff(215,assumption,(product(e_3, e_1, e_2)), introduced(assumption)).
% 0.19/0.57 tff(216,plain,
% 0.19/0.57 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_1, e_4, e_3)) | (~product(e_3, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_4) | (~product(e_1, e_4, e_3)) | (~product(e_3, e_1, e_2)))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(217,plain,
% 0.19/0.57 ((product(e_2, e_1, e_4) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_4, e_3))) <=> (product(e_2, e_1, e_4) | (~product(e_1, e_4, e_3)) | (~product(e_3, e_1, e_2)))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(218,plain,
% 0.19/0.57 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_1, e_4, e_3)) | (~product(e_3, e_1, e_2))))),
% 0.19/0.57 inference(monotonicity,[status(thm)],[217])).
% 0.19/0.57 tff(219,plain,
% 0.19/0.57 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_4) | (~product(e_1, e_4, e_3)) | (~product(e_3, e_1, e_2)))),
% 0.19/0.57 inference(transitivity,[status(thm)],[218, 216])).
% 0.19/0.57 tff(220,plain,
% 0.19/0.57 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_4, e_3)))),
% 0.19/0.57 inference(quant_inst,[status(thm)],[])).
% 0.19/0.57 tff(221,plain,
% 0.19/0.57 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_4) | (~product(e_1, e_4, e_3)) | (~product(e_3, e_1, e_2))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[220, 219])).
% 0.19/0.57 tff(222,plain,
% 0.19/0.57 ($false),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[221, 58, 119, 215, 197])).
% 0.19/0.57 tff(223,plain,((~product(e_3, e_1, e_2)) | (~product(e_1, e_4, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.57 tff(224,plain,
% 0.19/0.57 (~product(e_3, e_1, e_2)),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[223, 197])).
% 0.19/0.57 tff(225,assumption,(product(e_4, e_1, e_4)), introduced(assumption)).
% 0.19/0.57 tff(226,plain,
% 0.19/0.57 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_4) | (~product(e_4, e_1, e_4)) | (~product(e_4, e_4, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_4) | (~product(e_4, e_1, e_4)) | (~product(e_4, e_4, e_4)))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(227,plain,
% 0.19/0.57 ((equalish(e_1, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_1, e_4))) <=> (equalish(e_1, e_4) | (~product(e_4, e_1, e_4)) | (~product(e_4, e_4, e_4)))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(228,plain,
% 0.19/0.57 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_1, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_4) | (~product(e_4, e_1, e_4)) | (~product(e_4, e_4, e_4))))),
% 0.19/0.57 inference(monotonicity,[status(thm)],[227])).
% 0.19/0.57 tff(229,plain,
% 0.19/0.57 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_1, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_4) | (~product(e_4, e_1, e_4)) | (~product(e_4, e_4, e_4)))),
% 0.19/0.57 inference(transitivity,[status(thm)],[228, 226])).
% 0.19/0.57 tff(230,plain,
% 0.19/0.57 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_1, e_4)))),
% 0.19/0.57 inference(quant_inst,[status(thm)],[])).
% 0.19/0.57 tff(231,plain,
% 0.19/0.57 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_4) | (~product(e_4, e_1, e_4)) | (~product(e_4, e_4, e_4))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[230, 229])).
% 0.19/0.57 tff(232,plain,
% 0.19/0.57 ($false),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[231, 188, 17, 225, 184])).
% 0.19/0.57 tff(233,plain,(~product(e_4, e_1, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.57 tff(234,assumption,(product(e_3, e_1, e_4)), introduced(assumption)).
% 0.19/0.57 tff(235,plain,
% 0.19/0.57 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_1, e_4) | (~product(e_1, e_4, e_3)) | (~product(e_3, e_1, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_4, e_1, e_4) | (~product(e_1, e_4, e_3)) | (~product(e_3, e_1, e_4)))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(236,plain,
% 0.19/0.57 ((product(e_4, e_1, e_4) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_4, e_3))) <=> (product(e_4, e_1, e_4) | (~product(e_1, e_4, e_3)) | (~product(e_3, e_1, e_4)))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(237,plain,
% 0.19/0.57 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_1, e_4) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_1, e_4) | (~product(e_1, e_4, e_3)) | (~product(e_3, e_1, e_4))))),
% 0.19/0.57 inference(monotonicity,[status(thm)],[236])).
% 0.19/0.57 tff(238,plain,
% 0.19/0.57 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_1, e_4) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_4, e_1, e_4) | (~product(e_1, e_4, e_3)) | (~product(e_3, e_1, e_4)))),
% 0.19/0.57 inference(transitivity,[status(thm)],[237, 235])).
% 0.19/0.57 tff(239,plain,
% 0.19/0.57 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_1, e_4) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_4, e_3)))),
% 0.19/0.57 inference(quant_inst,[status(thm)],[])).
% 0.19/0.57 tff(240,plain,
% 0.19/0.57 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_4, e_1, e_4) | (~product(e_1, e_4, e_3)) | (~product(e_3, e_1, e_4))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[239, 238])).
% 0.19/0.57 tff(241,plain,
% 0.19/0.57 ($false),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[240, 58, 234, 233, 197])).
% 0.19/0.57 tff(242,plain,((~product(e_3, e_1, e_4)) | (~product(e_1, e_4, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.57 tff(243,plain,
% 0.19/0.57 (~product(e_3, e_1, e_4)),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[242, 197])).
% 0.19/0.57 tff(244,plain,
% 0.19/0.57 (greater(e_6, e_4) <=> greater(e_6, e_4)),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(245,axiom,(greater(e_6, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_6_greater_e_4')).
% 0.19/0.57 tff(246,plain,
% 0.19/0.57 (greater(e_6, e_4)),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[245, 244])).
% 0.19/0.57 tff(247,plain,
% 0.19/0.57 (((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_6, e_4)) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_6)))) <=> ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_6, e_4)) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_6)))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(248,plain,
% 0.19/0.57 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_6, e_4)) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_6)))),
% 0.19/0.57 inference(quant_inst,[status(thm)],[])).
% 0.19/0.57 tff(249,plain,
% 0.19/0.57 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_6, e_4)) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_6))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[248, 247])).
% 0.19/0.57 tff(250,plain,
% 0.19/0.57 (~product(e_3, e_1, e_6)),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[249, 44, 246, 38])).
% 0.19/0.57 tff(251,plain,
% 0.19/0.57 (group_element(e_3) <=> group_element(e_3)),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(252,axiom,(group_element(e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_3')).
% 0.19/0.57 tff(253,plain,
% 0.19/0.57 (group_element(e_3)),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[252, 251])).
% 0.19/0.57 tff(254,plain,
% 0.19/0.57 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_1, e_5) | product(e_3, e_1, e_6) | (~group_element(e_1)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_3, e_1, e_5) | product(e_3, e_1, e_6) | (~group_element(e_1)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_3)))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(255,plain,
% 0.19/0.57 ((product(e_3, e_1, e_6) | product(e_3, e_1, e_5) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_3))) <=> (product(e_3, e_1, e_5) | product(e_3, e_1, e_6) | (~group_element(e_1)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_3)))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(256,plain,
% 0.19/0.57 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_1, e_6) | product(e_3, e_1, e_5) | product(e_3, e_1, e_4) | 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_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_1, e_5) | product(e_3, e_1, e_6) | (~group_element(e_1)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_3))))),
% 0.19/0.57 inference(monotonicity,[status(thm)],[255])).
% 0.19/0.57 tff(257,plain,
% 0.19/0.57 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_1, e_6) | product(e_3, e_1, e_5) | product(e_3, e_1, e_4) | 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_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_3, e_1, e_5) | product(e_3, e_1, e_6) | (~group_element(e_1)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_3)))),
% 0.19/0.57 inference(transitivity,[status(thm)],[256, 254])).
% 0.19/0.57 tff(258,plain,
% 0.19/0.57 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_1, e_6) | product(e_3, e_1, e_5) | product(e_3, e_1, e_4) | 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)))),
% 0.19/0.58 inference(quant_inst,[status(thm)],[])).
% 0.19/0.58 tff(259,plain,
% 0.19/0.58 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_3, e_1, e_5) | product(e_3, e_1, e_6) | (~group_element(e_1)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_3))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[258, 257])).
% 0.19/0.58 tff(260,plain,
% 0.19/0.58 (product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1)),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[259, 135, 253, 129, 48, 250])).
% 0.19/0.58 tff(261,plain,
% 0.19/0.58 (product(e_3, e_1, e_3)),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[260, 243, 224, 214])).
% 0.19/0.58 tff(262,plain,
% 0.19/0.58 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_4) | (~product(e_1, e_4, e_3)) | (~product(e_3, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_4) | (~product(e_1, e_4, e_3)) | (~product(e_3, e_1, e_3)))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(263,plain,
% 0.19/0.58 ((product(e_3, e_1, e_4) | (~product(e_3, e_1, e_3)) | (~product(e_1, e_4, e_3))) <=> (product(e_3, e_1, e_4) | (~product(e_1, e_4, e_3)) | (~product(e_3, e_1, e_3)))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(264,plain,
% 0.19/0.58 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_4) | (~product(e_3, e_1, e_3)) | (~product(e_1, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_4) | (~product(e_1, e_4, e_3)) | (~product(e_3, e_1, e_3))))),
% 0.19/0.58 inference(monotonicity,[status(thm)],[263])).
% 0.19/0.58 tff(265,plain,
% 0.19/0.58 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_4) | (~product(e_3, e_1, e_3)) | (~product(e_1, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_4) | (~product(e_1, e_4, e_3)) | (~product(e_3, e_1, e_3)))),
% 0.19/0.58 inference(transitivity,[status(thm)],[264, 262])).
% 0.19/0.58 tff(266,plain,
% 0.19/0.58 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_4) | (~product(e_3, e_1, e_3)) | (~product(e_1, e_4, e_3)))),
% 0.19/0.58 inference(quant_inst,[status(thm)],[])).
% 0.19/0.58 tff(267,plain,
% 0.19/0.58 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_4) | (~product(e_1, e_4, e_3)) | (~product(e_3, e_1, e_3))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[266, 265])).
% 0.19/0.58 tff(268,plain,
% 0.19/0.58 ($false),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[267, 58, 243, 261, 197])).
% 0.19/0.58 tff(269,plain,(~product(e_1, e_4, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.58 tff(270,plain,
% 0.19/0.58 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_4) | (~product(e_1, e_4, e_1)) | (~product(e_1, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_4) | (~product(e_1, e_4, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(271,plain,
% 0.19/0.58 ((product(e_1, e_1, e_4) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_4, e_1))) <=> (product(e_1, e_1, e_4) | (~product(e_1, e_4, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(272,plain,
% 0.19/0.58 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_4) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_4) | (~product(e_1, e_4, e_1)) | (~product(e_1, e_1, e_1))))),
% 0.19/0.58 inference(monotonicity,[status(thm)],[271])).
% 0.19/0.58 tff(273,plain,
% 0.19/0.58 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_4) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_4) | (~product(e_1, e_4, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.19/0.58 inference(transitivity,[status(thm)],[272, 270])).
% 0.19/0.58 tff(274,plain,
% 0.19/0.58 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_4) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_4, e_1)))),
% 0.19/0.58 inference(quant_inst,[status(thm)],[])).
% 0.19/0.58 tff(275,plain,
% 0.19/0.58 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_4) | (~product(e_1, e_4, e_1)) | (~product(e_1, e_1, e_1))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[274, 273])).
% 0.19/0.58 tff(276,plain,
% 0.19/0.58 (~product(e_1, e_4, e_1)),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[275, 58, 208, 77])).
% 0.19/0.58 tff(277,plain,
% 0.19/0.58 (group_element(e_4) <=> group_element(e_4)),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(278,axiom,(group_element(e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_4')).
% 0.19/0.58 tff(279,plain,
% 0.19/0.58 (group_element(e_4)),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[278, 277])).
% 0.19/0.58 tff(280,plain,
% 0.19/0.58 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_1)) | (~group_element(e_4)) | product(e_1, e_4, e_1) | product(e_1, e_4, e_6) | product(e_1, e_4, e_5) | product(e_1, e_4, e_4) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | (~group_element(e_4)) | product(e_1, e_4, e_1) | product(e_1, e_4, e_6) | product(e_1, e_4, e_5) | product(e_1, e_4, e_4) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(281,plain,
% 0.19/0.58 ((product(e_1, e_4, e_6) | product(e_1, e_4, e_5) | product(e_1, e_4, e_4) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_1))) <=> ((~group_element(e_1)) | (~group_element(e_4)) | product(e_1, e_4, e_1) | product(e_1, e_4, e_6) | product(e_1, e_4, e_5) | product(e_1, e_4, e_4) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(282,plain,
% 0.19/0.58 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_4, e_6) | product(e_1, e_4, e_5) | product(e_1, e_4, e_4) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_1)) | (~group_element(e_4)) | product(e_1, e_4, e_1) | product(e_1, e_4, e_6) | product(e_1, e_4, e_5) | product(e_1, e_4, e_4) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2)))),
% 0.19/0.58 inference(monotonicity,[status(thm)],[281])).
% 0.19/0.58 tff(283,plain,
% 0.19/0.58 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_4, e_6) | product(e_1, e_4, e_5) | product(e_1, e_4, e_4) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | (~group_element(e_4)) | product(e_1, e_4, e_1) | product(e_1, e_4, e_6) | product(e_1, e_4, e_5) | product(e_1, e_4, e_4) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2))),
% 0.19/0.58 inference(transitivity,[status(thm)],[282, 280])).
% 0.19/0.58 tff(284,plain,
% 0.19/0.58 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_4, e_6) | product(e_1, e_4, e_5) | product(e_1, e_4, e_4) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_1)))),
% 0.19/0.58 inference(quant_inst,[status(thm)],[])).
% 0.19/0.58 tff(285,plain,
% 0.19/0.58 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | (~group_element(e_4)) | product(e_1, e_4, e_1) | product(e_1, e_4, e_6) | product(e_1, e_4, e_5) | product(e_1, e_4, e_4) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2)),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[284, 283])).
% 0.19/0.58 tff(286,plain,
% 0.19/0.58 (product(e_1, e_4, e_6) | product(e_1, e_4, e_5) | product(e_1, e_4, e_4) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2)),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[285, 135, 279, 129, 276])).
% 0.19/0.58 tff(287,plain,
% 0.19/0.58 (product(e_1, e_4, e_6) | product(e_1, e_4, e_5) | product(e_1, e_4, e_2)),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[286, 269, 196])).
% 0.19/0.58 tff(288,plain,
% 0.19/0.58 (product(e_1, e_4, e_5)),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[287, 182, 4])).
% 0.19/0.58 tff(289,assumption,(product(e_1, e_6, e_5)), introduced(assumption)).
% 0.19/0.58 tff(290,assumption,(product(e_1, e_4, e_5)), introduced(assumption)).
% 0.19/0.58 tff(291,plain,
% 0.19/0.58 ((~equalish(e_4, e_6)) <=> (~equalish(e_4, e_6))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(292,axiom,(~equalish(e_4, e_6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_6')).
% 0.19/0.58 tff(293,plain,
% 0.19/0.58 (~equalish(e_4, e_6)),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[292, 291])).
% 0.19/0.58 tff(294,plain,
% 0.19/0.58 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_6) | (~product(e_1, e_6, e_5)) | (~product(e_1, e_4, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_6) | (~product(e_1, e_6, e_5)) | (~product(e_1, e_4, e_5)))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(295,plain,
% 0.19/0.58 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_6) | (~product(e_1, e_6, e_5)) | (~product(e_1, e_4, e_5)))),
% 0.19/0.58 inference(quant_inst,[status(thm)],[])).
% 0.19/0.58 tff(296,plain,
% 0.19/0.58 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_6) | (~product(e_1, e_6, e_5)) | (~product(e_1, e_4, e_5))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[295, 294])).
% 0.19/0.58 tff(297,plain,
% 0.19/0.58 ($false),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[296, 293, 17, 290, 289])).
% 0.19/0.58 tff(298,plain,((~product(e_1, e_4, e_5)) | (~product(e_1, e_6, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.58 tff(299,plain,
% 0.19/0.58 (~product(e_1, e_6, e_5)),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[298, 288])).
% 0.19/0.58 tff(300,assumption,(product(e_1, e_6, e_3)), introduced(assumption)).
% 0.19/0.58 tff(301,assumption,(product(e_3, e_1, e_3)), introduced(assumption)).
% 0.19/0.58 tff(302,plain,
% 0.19/0.58 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_6) | (~product(e_3, e_1, e_3)) | (~product(e_1, e_6, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_6) | (~product(e_3, e_1, e_3)) | (~product(e_1, e_6, e_3)))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(303,plain,
% 0.19/0.58 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_6) | (~product(e_3, e_1, e_3)) | (~product(e_1, e_6, e_3)))),
% 0.19/0.58 inference(quant_inst,[status(thm)],[])).
% 0.19/0.58 tff(304,plain,
% 0.19/0.58 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_6) | (~product(e_3, e_1, e_3)) | (~product(e_1, e_6, e_3))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[303, 302])).
% 0.19/0.58 tff(305,plain,
% 0.19/0.58 ($false),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[304, 58, 250, 301, 300])).
% 0.19/0.58 tff(306,plain,((~product(e_3, e_1, e_3)) | (~product(e_1, e_6, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.58 tff(307,plain,
% 0.19/0.58 (~product(e_3, e_1, e_3)),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[306, 300])).
% 0.19/0.58 tff(308,plain,
% 0.19/0.58 (greater(e_6, e_2) <=> greater(e_6, e_2)),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(309,axiom,(greater(e_6, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_6_greater_e_2')).
% 0.19/0.58 tff(310,plain,
% 0.19/0.58 (greater(e_6, e_2)),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[309, 308])).
% 0.19/0.58 tff(311,plain,
% 0.19/0.58 (((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_6, e_2)) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_6)))) <=> ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_6, e_2)) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_6)))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(312,plain,
% 0.19/0.58 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_6, e_2)) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_6)))),
% 0.19/0.58 inference(quant_inst,[status(thm)],[])).
% 0.19/0.58 tff(313,plain,
% 0.19/0.58 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_6, e_2)) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_6))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[312, 311])).
% 0.19/0.58 tff(314,plain,
% 0.19/0.58 (~product(e_1, e_1, e_6)),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[313, 204, 310, 38])).
% 0.19/0.58 tff(315,plain,
% 0.19/0.58 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_6) | (~product(e_3, e_1, e_1)) | (~product(e_1, e_6, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_6) | (~product(e_3, e_1, e_1)) | (~product(e_1, e_6, e_3)))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(316,plain,
% 0.19/0.58 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_6) | (~product(e_3, e_1, e_1)) | (~product(e_1, e_6, e_3)))),
% 0.19/0.58 inference(quant_inst,[status(thm)],[])).
% 0.19/0.58 tff(317,plain,
% 0.19/0.58 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_6) | (~product(e_3, e_1, e_1)) | (~product(e_1, e_6, e_3))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[316, 315])).
% 0.19/0.58 tff(318,plain,
% 0.19/0.58 ($false),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[317, 58, 314, 198, 300])).
% 0.19/0.58 tff(319,plain,((~product(e_3, e_1, e_1)) | (~product(e_1, e_6, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.58 tff(320,plain,
% 0.19/0.58 (~product(e_3, e_1, e_1)),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[319, 300])).
% 0.19/0.58 tff(321,plain,
% 0.19/0.58 (greater(e_6, e_5) <=> greater(e_6, e_5)),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(322,axiom,(greater(e_6, e_5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_6_greater_e_5')).
% 0.19/0.58 tff(323,plain,
% 0.19/0.58 (greater(e_6, e_5)),
% 0.19/0.59 inference(modus_ponens,[status(thm)],[322, 321])).
% 0.19/0.59 tff(324,plain,
% 0.19/0.59 (next(e_4, e_5) <=> next(e_4, e_5)),
% 0.19/0.59 inference(rewrite,[status(thm)],[])).
% 0.19/0.59 tff(325,axiom,(next(e_4, e_5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_then_e_5')).
% 0.19/0.59 tff(326,plain,
% 0.19/0.59 (next(e_4, e_5)),
% 0.19/0.59 inference(modus_ponens,[status(thm)],[325, 324])).
% 0.19/0.59 tff(327,plain,
% 0.19/0.59 (((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_6, e_5)) | (~next(e_4, e_5)) | (~product(e_4, e_1, e_6)))) <=> ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_6, e_5)) | (~next(e_4, e_5)) | (~product(e_4, e_1, e_6)))),
% 0.19/0.59 inference(rewrite,[status(thm)],[])).
% 0.19/0.59 tff(328,plain,
% 0.19/0.59 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_6, e_5)) | (~next(e_4, e_5)) | (~product(e_4, e_1, e_6)))),
% 0.19/0.59 inference(quant_inst,[status(thm)],[])).
% 0.19/0.59 tff(329,plain,
% 0.19/0.59 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_6, e_5)) | (~next(e_4, e_5)) | (~product(e_4, e_1, e_6))),
% 0.19/0.59 inference(modus_ponens,[status(thm)],[328, 327])).
% 0.19/0.59 tff(330,plain,
% 0.19/0.59 (~product(e_4, e_1, e_6)),
% 0.19/0.59 inference(unit_resolution,[status(thm)],[329, 326, 323, 38])).
% 0.19/0.59 tff(331,plain,
% 0.19/0.59 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_1, e_6) | (~product(e_1, e_6, e_3)) | (~product(e_3, e_1, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_4, e_1, e_6) | (~product(e_1, e_6, e_3)) | (~product(e_3, e_1, e_4)))),
% 0.19/0.59 inference(rewrite,[status(thm)],[])).
% 0.19/0.59 tff(332,plain,
% 0.19/0.59 ((product(e_4, e_1, e_6) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_6, e_3))) <=> (product(e_4, e_1, e_6) | (~product(e_1, e_6, e_3)) | (~product(e_3, e_1, e_4)))),
% 0.19/0.59 inference(rewrite,[status(thm)],[])).
% 0.19/0.59 tff(333,plain,
% 0.19/0.59 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_1, e_6) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_6, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_1, e_6) | (~product(e_1, e_6, e_3)) | (~product(e_3, e_1, e_4))))),
% 0.19/0.59 inference(monotonicity,[status(thm)],[332])).
% 0.19/0.59 tff(334,plain,
% 0.19/0.59 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_1, e_6) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_6, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_4, e_1, e_6) | (~product(e_1, e_6, e_3)) | (~product(e_3, e_1, e_4)))),
% 0.19/0.59 inference(transitivity,[status(thm)],[333, 331])).
% 0.19/0.59 tff(335,plain,
% 0.19/0.59 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_1, e_6) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_6, e_3)))),
% 0.19/0.59 inference(quant_inst,[status(thm)],[])).
% 0.19/0.59 tff(336,plain,
% 0.19/0.59 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_4, e_1, e_6) | (~product(e_1, e_6, e_3)) | (~product(e_3, e_1, e_4))),
% 0.19/0.59 inference(modus_ponens,[status(thm)],[335, 334])).
% 0.19/0.59 tff(337,plain,
% 0.19/0.59 ($false),
% 0.19/0.59 inference(unit_resolution,[status(thm)],[336, 58, 330, 234, 300])).
% 0.19/0.59 tff(338,plain,((~product(e_3, e_1, e_4)) | (~product(e_1, e_6, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.59 tff(339,plain,
% 0.19/0.59 (~product(e_3, e_1, e_4)),
% 0.19/0.59 inference(unit_resolution,[status(thm)],[338, 300])).
% 0.19/0.59 tff(340,plain,
% 0.19/0.59 (product(e_3, e_1, e_2)),
% 0.19/0.59 inference(unit_resolution,[status(thm)],[260, 339, 320, 307])).
% 0.19/0.59 tff(341,plain,
% 0.19/0.59 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_6) | (~product(e_1, e_6, e_3)) | (~product(e_3, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_6) | (~product(e_1, e_6, e_3)) | (~product(e_3, e_1, e_2)))),
% 0.19/0.59 inference(rewrite,[status(thm)],[])).
% 0.19/0.59 tff(342,plain,
% 0.19/0.59 ((product(e_2, e_1, e_6) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_6, e_3))) <=> (product(e_2, e_1, e_6) | (~product(e_1, e_6, e_3)) | (~product(e_3, e_1, e_2)))),
% 0.19/0.59 inference(rewrite,[status(thm)],[])).
% 0.19/0.59 tff(343,plain,
% 0.19/0.59 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_6) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_6, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_6) | (~product(e_1, e_6, e_3)) | (~product(e_3, e_1, e_2))))),
% 0.19/0.59 inference(monotonicity,[status(thm)],[342])).
% 0.19/0.59 tff(344,plain,
% 0.19/0.59 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_6) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_6, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_6) | (~product(e_1, e_6, e_3)) | (~product(e_3, e_1, e_2)))),
% 0.19/0.59 inference(transitivity,[status(thm)],[343, 341])).
% 0.19/0.59 tff(345,plain,
% 0.19/0.59 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_6) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_6, e_3)))),
% 0.19/0.59 inference(quant_inst,[status(thm)],[])).
% 0.19/0.59 tff(346,plain,
% 0.19/0.59 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_6) | (~product(e_1, e_6, e_3)) | (~product(e_3, e_1, e_2))),
% 0.19/0.59 inference(modus_ponens,[status(thm)],[345, 344])).
% 0.19/0.59 tff(347,plain,
% 0.19/0.59 ($false),
% 0.19/0.59 inference(unit_resolution,[status(thm)],[346, 58, 105, 340, 300])).
% 0.19/0.59 tff(348,plain,(~product(e_1, e_6, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.59 tff(349,assumption,(product(e_1, e_6, e_2)), introduced(assumption)).
% 0.19/0.59 tff(350,assumption,(product(e_2, e_1, e_2)), introduced(assumption)).
% 0.19/0.59 tff(351,plain,
% 0.19/0.59 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_6) | (~product(e_1, e_6, e_2)) | (~product(e_2, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_6) | (~product(e_1, e_6, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.19/0.59 inference(rewrite,[status(thm)],[])).
% 0.19/0.59 tff(352,plain,
% 0.19/0.59 ((product(e_2, e_1, e_6) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_6, e_2))) <=> (product(e_2, e_1, e_6) | (~product(e_1, e_6, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.19/0.59 inference(rewrite,[status(thm)],[])).
% 0.19/0.59 tff(353,plain,
% 0.19/0.59 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_6) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_6, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_6) | (~product(e_1, e_6, e_2)) | (~product(e_2, e_1, e_2))))),
% 0.19/0.59 inference(monotonicity,[status(thm)],[352])).
% 0.19/0.59 tff(354,plain,
% 0.19/0.59 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_6) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_6, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_6) | (~product(e_1, e_6, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.19/0.59 inference(transitivity,[status(thm)],[353, 351])).
% 0.19/0.59 tff(355,plain,
% 0.19/0.59 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_6) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_6, e_2)))),
% 0.19/0.59 inference(quant_inst,[status(thm)],[])).
% 0.19/0.59 tff(356,plain,
% 0.19/0.59 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_6) | (~product(e_1, e_6, e_2)) | (~product(e_2, e_1, e_2))),
% 0.54/0.59 inference(modus_ponens,[status(thm)],[355, 354])).
% 0.54/0.59 tff(357,plain,
% 0.54/0.59 ($false),
% 0.54/0.59 inference(unit_resolution,[status(thm)],[356, 58, 105, 350, 349])).
% 0.54/0.59 tff(358,plain,((~product(e_2, e_1, e_2)) | (~product(e_1, e_6, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.59 tff(359,plain,
% 0.54/0.59 (~product(e_2, e_1, e_2)),
% 0.54/0.59 inference(unit_resolution,[status(thm)],[358, 349])).
% 0.54/0.59 tff(360,plain,
% 0.54/0.59 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_6) | (~product(e_1, e_6, e_2)) | (~product(e_2, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_6) | (~product(e_1, e_6, e_2)) | (~product(e_2, e_1, e_3)))),
% 0.54/0.59 inference(rewrite,[status(thm)],[])).
% 0.54/0.59 tff(361,plain,
% 0.54/0.59 ((product(e_3, e_1, e_6) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_6, e_2))) <=> (product(e_3, e_1, e_6) | (~product(e_1, e_6, e_2)) | (~product(e_2, e_1, e_3)))),
% 0.54/0.59 inference(rewrite,[status(thm)],[])).
% 0.54/0.59 tff(362,plain,
% 0.54/0.59 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_6) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_6, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_6) | (~product(e_1, e_6, e_2)) | (~product(e_2, e_1, e_3))))),
% 0.54/0.59 inference(monotonicity,[status(thm)],[361])).
% 0.54/0.59 tff(363,plain,
% 0.54/0.59 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_6) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_6, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_6) | (~product(e_1, e_6, e_2)) | (~product(e_2, e_1, e_3)))),
% 0.54/0.59 inference(transitivity,[status(thm)],[362, 360])).
% 0.54/0.59 tff(364,plain,
% 0.54/0.59 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_6) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_6, e_2)))),
% 0.54/0.59 inference(quant_inst,[status(thm)],[])).
% 0.54/0.59 tff(365,plain,
% 0.54/0.59 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_6) | (~product(e_1, e_6, e_2)) | (~product(e_2, e_1, e_3))),
% 0.54/0.59 inference(modus_ponens,[status(thm)],[364, 363])).
% 0.54/0.59 tff(366,plain,
% 0.54/0.59 ($false),
% 0.54/0.59 inference(unit_resolution,[status(thm)],[365, 58, 250, 28, 349])).
% 0.54/0.59 tff(367,plain,((~product(e_2, e_1, e_3)) | (~product(e_1, e_6, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.59 tff(368,plain,
% 0.54/0.59 (~product(e_2, e_1, e_3)),
% 0.54/0.59 inference(unit_resolution,[status(thm)],[367, 349])).
% 0.54/0.59 tff(369,plain,
% 0.54/0.59 (product(e_2, e_1, e_1)),
% 0.54/0.59 inference(unit_resolution,[status(thm)],[142, 368, 359])).
% 0.54/0.59 tff(370,plain,
% 0.54/0.59 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_6) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_6, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_6) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_6, e_2)))),
% 0.54/0.59 inference(rewrite,[status(thm)],[])).
% 0.54/0.59 tff(371,plain,
% 0.54/0.59 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_6) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_6, e_2)))),
% 0.54/0.59 inference(quant_inst,[status(thm)],[])).
% 0.54/0.59 tff(372,plain,
% 0.54/0.59 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_6) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_6, e_2))),
% 0.54/0.59 inference(modus_ponens,[status(thm)],[371, 370])).
% 0.54/0.59 tff(373,plain,
% 0.54/0.59 ($false),
% 0.54/0.59 inference(unit_resolution,[status(thm)],[372, 58, 314, 369, 349])).
% 0.54/0.59 tff(374,plain,(~product(e_1, e_6, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.54/0.59 tff(375,plain,
% 0.54/0.59 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_6) | (~product(e_1, e_6, e_1)) | (~product(e_1, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_6) | (~product(e_1, e_6, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.54/0.59 inference(rewrite,[status(thm)],[])).
% 0.54/0.59 tff(376,plain,
% 0.54/0.59 ((product(e_1, e_1, e_6) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_6, e_1))) <=> (product(e_1, e_1, e_6) | (~product(e_1, e_6, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.54/0.59 inference(rewrite,[status(thm)],[])).
% 0.54/0.59 tff(377,plain,
% 0.54/0.59 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_6) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_6, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_6) | (~product(e_1, e_6, e_1)) | (~product(e_1, e_1, e_1))))),
% 0.54/0.59 inference(monotonicity,[status(thm)],[376])).
% 0.54/0.59 tff(378,plain,
% 0.54/0.59 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_6) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_6, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_6) | (~product(e_1, e_6, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.54/0.59 inference(transitivity,[status(thm)],[377, 375])).
% 0.54/0.59 tff(379,plain,
% 0.54/0.59 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_6) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_6, e_1)))),
% 0.54/0.59 inference(quant_inst,[status(thm)],[])).
% 0.54/0.59 tff(380,plain,
% 0.54/0.59 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_6) | (~product(e_1, e_6, e_1)) | (~product(e_1, e_1, e_1))),
% 0.54/0.59 inference(modus_ponens,[status(thm)],[379, 378])).
% 0.54/0.59 tff(381,plain,
% 0.54/0.59 (~product(e_1, e_6, e_1)),
% 0.54/0.59 inference(unit_resolution,[status(thm)],[380, 58, 314, 77])).
% 0.54/0.59 tff(382,plain,
% 0.54/0.59 (group_element(e_6) <=> group_element(e_6)),
% 0.54/0.59 inference(rewrite,[status(thm)],[])).
% 0.54/0.59 tff(383,axiom,(group_element(e_6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_6')).
% 0.54/0.59 tff(384,plain,
% 0.54/0.59 (group_element(e_6)),
% 0.54/0.59 inference(modus_ponens,[status(thm)],[383, 382])).
% 0.54/0.59 tff(385,plain,
% 0.54/0.59 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_1)) | product(e_1, e_6, e_1) | product(e_1, e_6, e_6) | product(e_1, e_6, e_5) | product(e_1, e_6, e_4) | product(e_1, e_6, e_3) | product(e_1, e_6, e_2) | (~group_element(e_6)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | product(e_1, e_6, e_1) | product(e_1, e_6, e_6) | product(e_1, e_6, e_5) | product(e_1, e_6, e_4) | product(e_1, e_6, e_3) | product(e_1, e_6, e_2) | (~group_element(e_6)))),
% 0.54/0.59 inference(rewrite,[status(thm)],[])).
% 0.54/0.59 tff(386,plain,
% 0.54/0.59 ((product(e_1, e_6, e_6) | product(e_1, e_6, e_5) | product(e_1, e_6, e_4) | product(e_1, e_6, e_3) | product(e_1, e_6, e_2) | product(e_1, e_6, e_1) | (~group_element(e_6)) | (~group_element(e_1))) <=> ((~group_element(e_1)) | product(e_1, e_6, e_1) | product(e_1, e_6, e_6) | product(e_1, e_6, e_5) | product(e_1, e_6, e_4) | product(e_1, e_6, e_3) | product(e_1, e_6, e_2) | (~group_element(e_6)))),
% 0.54/0.59 inference(rewrite,[status(thm)],[])).
% 0.54/0.59 tff(387,plain,
% 0.54/0.59 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_6, e_6) | product(e_1, e_6, e_5) | product(e_1, e_6, e_4) | product(e_1, e_6, e_3) | product(e_1, e_6, e_2) | product(e_1, e_6, e_1) | (~group_element(e_6)) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_1)) | product(e_1, e_6, e_1) | product(e_1, e_6, e_6) | product(e_1, e_6, e_5) | product(e_1, e_6, e_4) | product(e_1, e_6, e_3) | product(e_1, e_6, e_2) | (~group_element(e_6))))),
% 0.54/0.60 inference(monotonicity,[status(thm)],[386])).
% 0.54/0.60 tff(388,plain,
% 0.54/0.60 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_6, e_6) | product(e_1, e_6, e_5) | product(e_1, e_6, e_4) | product(e_1, e_6, e_3) | product(e_1, e_6, e_2) | product(e_1, e_6, e_1) | (~group_element(e_6)) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | product(e_1, e_6, e_1) | product(e_1, e_6, e_6) | product(e_1, e_6, e_5) | product(e_1, e_6, e_4) | product(e_1, e_6, e_3) | product(e_1, e_6, e_2) | (~group_element(e_6)))),
% 0.54/0.60 inference(transitivity,[status(thm)],[387, 385])).
% 0.54/0.60 tff(389,plain,
% 0.54/0.60 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_6, e_6) | product(e_1, e_6, e_5) | product(e_1, e_6, e_4) | product(e_1, e_6, e_3) | product(e_1, e_6, e_2) | product(e_1, e_6, e_1) | (~group_element(e_6)) | (~group_element(e_1)))),
% 0.54/0.60 inference(quant_inst,[status(thm)],[])).
% 0.54/0.60 tff(390,plain,
% 0.54/0.60 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | product(e_1, e_6, e_1) | product(e_1, e_6, e_6) | product(e_1, e_6, e_5) | product(e_1, e_6, e_4) | product(e_1, e_6, e_3) | product(e_1, e_6, e_2) | (~group_element(e_6))),
% 0.54/0.60 inference(modus_ponens,[status(thm)],[389, 388])).
% 0.54/0.60 tff(391,plain,
% 0.54/0.60 (product(e_1, e_6, e_6) | product(e_1, e_6, e_5) | product(e_1, e_6, e_4) | product(e_1, e_6, e_3) | product(e_1, e_6, e_2)),
% 0.54/0.60 inference(unit_resolution,[status(thm)],[390, 135, 384, 129, 381])).
% 0.54/0.60 tff(392,plain,
% 0.54/0.60 (product(e_1, e_6, e_6) | product(e_1, e_6, e_5) | product(e_1, e_6, e_4) | product(e_1, e_6, e_3)),
% 0.54/0.60 inference(unit_resolution,[status(thm)],[391, 374])).
% 0.54/0.60 tff(393,plain,
% 0.54/0.60 (product(e_1, e_6, e_6) | product(e_1, e_6, e_5) | product(e_1, e_6, e_4)),
% 0.54/0.60 inference(unit_resolution,[status(thm)],[392, 348])).
% 0.54/0.60 tff(394,plain,
% 0.54/0.60 (product(e_1, e_6, e_4)),
% 0.54/0.60 inference(unit_resolution,[status(thm)],[393, 299, 169])).
% 0.54/0.60 tff(395,assumption,(product(e_1, e_3, e_4)), introduced(assumption)).
% 0.54/0.60 tff(396,plain,
% 0.54/0.60 ((~equalish(e_3, e_6)) <=> (~equalish(e_3, e_6))),
% 0.54/0.60 inference(rewrite,[status(thm)],[])).
% 0.54/0.60 tff(397,axiom,(~equalish(e_3, e_6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_6')).
% 0.54/0.60 tff(398,plain,
% 0.54/0.60 (~equalish(e_3, e_6)),
% 0.54/0.60 inference(modus_ponens,[status(thm)],[397, 396])).
% 0.54/0.60 tff(399,plain,
% 0.54/0.60 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_6) | (~product(e_1, e_6, e_4)) | (~product(e_1, e_3, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_6) | (~product(e_1, e_6, e_4)) | (~product(e_1, e_3, e_4)))),
% 0.54/0.60 inference(rewrite,[status(thm)],[])).
% 0.54/0.60 tff(400,plain,
% 0.54/0.60 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_6) | (~product(e_1, e_6, e_4)) | (~product(e_1, e_3, e_4)))),
% 0.54/0.60 inference(quant_inst,[status(thm)],[])).
% 0.54/0.60 tff(401,plain,
% 0.54/0.60 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_6) | (~product(e_1, e_6, e_4)) | (~product(e_1, e_3, e_4))),
% 0.54/0.60 inference(modus_ponens,[status(thm)],[400, 399])).
% 0.54/0.60 tff(402,plain,
% 0.54/0.60 ($false),
% 0.54/0.60 inference(unit_resolution,[status(thm)],[401, 398, 17, 395, 6])).
% 0.54/0.60 tff(403,plain,((~product(e_1, e_3, e_4)) | (~product(e_1, e_6, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.60 tff(404,plain,
% 0.54/0.60 (~product(e_1, e_3, e_4)),
% 0.54/0.60 inference(unit_resolution,[status(thm)],[403, 394])).
% 0.54/0.60 tff(405,assumption,(~product(e_1, e_3, e_4)), introduced(assumption)).
% 0.54/0.60 tff(406,assumption,(~product(e_1, e_3, e_2)), introduced(assumption)).
% 0.54/0.60 tff(407,assumption,(product(e_1, e_3, e_6)), introduced(assumption)).
% 0.54/0.60 tff(408,plain,
% 0.54/0.60 ((~equalish(e_3, e_4)) <=> (~equalish(e_3, e_4))),
% 0.54/0.60 inference(rewrite,[status(thm)],[])).
% 0.54/0.60 tff(409,axiom,(~equalish(e_3, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_4')).
% 0.54/0.60 tff(410,plain,
% 0.54/0.60 (~equalish(e_3, e_4)),
% 0.54/0.60 inference(modus_ponens,[status(thm)],[409, 408])).
% 0.54/0.60 tff(411,plain,
% 0.54/0.60 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_4) | (~product(e_1, e_4, e_6)) | (~product(e_1, e_3, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_4) | (~product(e_1, e_4, e_6)) | (~product(e_1, e_3, e_6)))),
% 0.54/0.60 inference(rewrite,[status(thm)],[])).
% 0.54/0.60 tff(412,plain,
% 0.54/0.60 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_4) | (~product(e_1, e_4, e_6)) | (~product(e_1, e_3, e_6)))),
% 0.54/0.60 inference(quant_inst,[status(thm)],[])).
% 0.54/0.60 tff(413,plain,
% 0.54/0.60 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_4) | (~product(e_1, e_4, e_6)) | (~product(e_1, e_3, e_6))),
% 0.54/0.60 inference(modus_ponens,[status(thm)],[412, 411])).
% 0.54/0.60 tff(414,plain,
% 0.54/0.60 ($false),
% 0.54/0.60 inference(unit_resolution,[status(thm)],[413, 410, 17, 170, 407])).
% 0.54/0.60 tff(415,plain,((~product(e_1, e_3, e_6)) | (~product(e_1, e_4, e_6))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.60 tff(416,plain,
% 0.54/0.60 (~product(e_1, e_4, e_6)),
% 0.54/0.60 inference(unit_resolution,[status(thm)],[415, 407])).
% 0.54/0.60 tff(417,plain,
% 0.54/0.60 (product(e_1, e_4, e_5)),
% 0.54/0.60 inference(unit_resolution,[status(thm)],[287, 416, 4])).
% 0.54/0.60 tff(418,plain,
% 0.54/0.60 ((~equalish(e_3, e_5)) <=> (~equalish(e_3, e_5))),
% 0.54/0.60 inference(rewrite,[status(thm)],[])).
% 0.54/0.60 tff(419,axiom,(~equalish(e_3, e_5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_5')).
% 0.54/0.60 tff(420,plain,
% 0.54/0.60 (~equalish(e_3, e_5)),
% 0.54/0.60 inference(modus_ponens,[status(thm)],[419, 418])).
% 0.54/0.60 tff(421,plain,
% 0.54/0.60 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_5) | (~product(e_1, e_5, e_6)) | (~product(e_1, e_3, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_5) | (~product(e_1, e_5, e_6)) | (~product(e_1, e_3, e_6)))),
% 0.54/0.60 inference(rewrite,[status(thm)],[])).
% 0.54/0.60 tff(422,plain,
% 0.54/0.60 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_5) | (~product(e_1, e_5, e_6)) | (~product(e_1, e_3, e_6)))),
% 0.54/0.60 inference(quant_inst,[status(thm)],[])).
% 0.54/0.60 tff(423,plain,
% 0.54/0.60 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_5) | (~product(e_1, e_5, e_6)) | (~product(e_1, e_3, e_6))),
% 0.54/0.60 inference(modus_ponens,[status(thm)],[422, 421])).
% 0.54/0.60 tff(424,plain,
% 0.54/0.60 ($false),
% 0.54/0.60 inference(unit_resolution,[status(thm)],[423, 420, 17, 156, 407])).
% 0.54/0.60 tff(425,plain,((~product(e_1, e_3, e_6)) | (~product(e_1, e_5, e_6))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.60 tff(426,plain,
% 0.54/0.60 (~product(e_1, e_5, e_6)),
% 0.54/0.60 inference(unit_resolution,[status(thm)],[425, 407])).
% 0.54/0.60 tff(427,plain,
% 0.54/0.60 (greater(e_5, e_2) <=> greater(e_5, e_2)),
% 0.54/0.60 inference(rewrite,[status(thm)],[])).
% 0.54/0.60 tff(428,axiom,(greater(e_5, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_5_greater_e_2')).
% 0.54/0.60 tff(429,plain,
% 0.54/0.60 (greater(e_5, e_2)),
% 0.54/0.60 inference(modus_ponens,[status(thm)],[428, 427])).
% 0.54/0.60 tff(430,plain,
% 0.54/0.60 (((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_5, e_2)) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_5)))) <=> ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_5, e_2)) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_5)))),
% 0.54/0.60 inference(rewrite,[status(thm)],[])).
% 0.54/0.60 tff(431,plain,
% 0.54/0.60 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_5, e_2)) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_5)))),
% 0.54/0.60 inference(quant_inst,[status(thm)],[])).
% 0.54/0.60 tff(432,plain,
% 0.54/0.60 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_5, e_2)) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_5))),
% 0.54/0.60 inference(modus_ponens,[status(thm)],[431, 430])).
% 0.54/0.60 tff(433,plain,
% 0.54/0.60 (~product(e_1, e_1, e_5)),
% 0.54/0.60 inference(unit_resolution,[status(thm)],[432, 204, 429, 38])).
% 0.54/0.60 tff(434,plain,
% 0.54/0.60 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_5) | (~product(e_1, e_5, e_1)) | (~product(e_1, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_5) | (~product(e_1, e_5, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.54/0.60 inference(rewrite,[status(thm)],[])).
% 0.54/0.60 tff(435,plain,
% 0.54/0.60 ((product(e_1, e_1, e_5) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_5, e_1))) <=> (product(e_1, e_1, e_5) | (~product(e_1, e_5, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.54/0.60 inference(rewrite,[status(thm)],[])).
% 0.54/0.60 tff(436,plain,
% 0.54/0.60 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_5) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_5, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_5) | (~product(e_1, e_5, e_1)) | (~product(e_1, e_1, e_1))))),
% 0.54/0.60 inference(monotonicity,[status(thm)],[435])).
% 0.54/0.60 tff(437,plain,
% 0.54/0.60 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_5) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_5, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_5) | (~product(e_1, e_5, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.54/0.60 inference(transitivity,[status(thm)],[436, 434])).
% 0.54/0.60 tff(438,plain,
% 0.54/0.60 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_5) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_5, e_1)))),
% 0.54/0.60 inference(quant_inst,[status(thm)],[])).
% 0.54/0.60 tff(439,plain,
% 0.54/0.60 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_5) | (~product(e_1, e_5, e_1)) | (~product(e_1, e_1, e_1))),
% 0.54/0.60 inference(modus_ponens,[status(thm)],[438, 437])).
% 0.54/0.60 tff(440,plain,
% 0.54/0.60 (~product(e_1, e_5, e_1)),
% 0.54/0.60 inference(unit_resolution,[status(thm)],[439, 58, 433, 77])).
% 0.54/0.60 tff(441,plain,
% 0.54/0.60 (group_element(e_5) <=> group_element(e_5)),
% 0.54/0.60 inference(rewrite,[status(thm)],[])).
% 0.54/0.60 tff(442,axiom,(group_element(e_5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_5')).
% 0.54/0.60 tff(443,plain,
% 0.54/0.60 (group_element(e_5)),
% 0.54/0.60 inference(modus_ponens,[status(thm)],[442, 441])).
% 0.54/0.60 tff(444,plain,
% 0.54/0.60 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_1)) | product(e_1, e_5, e_1) | product(e_1, e_5, e_6) | product(e_1, e_5, e_5) | product(e_1, e_5, e_4) | product(e_1, e_5, e_3) | product(e_1, e_5, e_2) | (~group_element(e_5)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | product(e_1, e_5, e_1) | product(e_1, e_5, e_6) | product(e_1, e_5, e_5) | product(e_1, e_5, e_4) | product(e_1, e_5, e_3) | product(e_1, e_5, e_2) | (~group_element(e_5)))),
% 0.54/0.60 inference(rewrite,[status(thm)],[])).
% 0.54/0.60 tff(445,plain,
% 0.54/0.60 ((product(e_1, e_5, e_6) | product(e_1, e_5, e_5) | product(e_1, e_5, e_4) | product(e_1, e_5, e_3) | product(e_1, e_5, e_2) | product(e_1, e_5, e_1) | (~group_element(e_5)) | (~group_element(e_1))) <=> ((~group_element(e_1)) | product(e_1, e_5, e_1) | product(e_1, e_5, e_6) | product(e_1, e_5, e_5) | product(e_1, e_5, e_4) | product(e_1, e_5, e_3) | product(e_1, e_5, e_2) | (~group_element(e_5)))),
% 0.54/0.60 inference(rewrite,[status(thm)],[])).
% 0.54/0.60 tff(446,plain,
% 0.54/0.60 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_5, e_6) | product(e_1, e_5, e_5) | product(e_1, e_5, e_4) | product(e_1, e_5, e_3) | product(e_1, e_5, e_2) | product(e_1, e_5, e_1) | (~group_element(e_5)) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_1)) | product(e_1, e_5, e_1) | product(e_1, e_5, e_6) | product(e_1, e_5, e_5) | product(e_1, e_5, e_4) | product(e_1, e_5, e_3) | product(e_1, e_5, e_2) | (~group_element(e_5))))),
% 0.54/0.60 inference(monotonicity,[status(thm)],[445])).
% 0.54/0.60 tff(447,plain,
% 0.54/0.60 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_5, e_6) | product(e_1, e_5, e_5) | product(e_1, e_5, e_4) | product(e_1, e_5, e_3) | product(e_1, e_5, e_2) | product(e_1, e_5, e_1) | (~group_element(e_5)) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | product(e_1, e_5, e_1) | product(e_1, e_5, e_6) | product(e_1, e_5, e_5) | product(e_1, e_5, e_4) | product(e_1, e_5, e_3) | product(e_1, e_5, e_2) | (~group_element(e_5)))),
% 0.54/0.60 inference(transitivity,[status(thm)],[446, 444])).
% 0.54/0.60 tff(448,plain,
% 0.54/0.60 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_5, e_6) | product(e_1, e_5, e_5) | product(e_1, e_5, e_4) | product(e_1, e_5, e_3) | product(e_1, e_5, e_2) | product(e_1, e_5, e_1) | (~group_element(e_5)) | (~group_element(e_1)))),
% 0.54/0.60 inference(quant_inst,[status(thm)],[])).
% 0.54/0.60 tff(449,plain,
% 0.54/0.60 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | product(e_1, e_5, e_1) | product(e_1, e_5, e_6) | product(e_1, e_5, e_5) | product(e_1, e_5, e_4) | product(e_1, e_5, e_3) | product(e_1, e_5, e_2) | (~group_element(e_5))),
% 0.54/0.60 inference(modus_ponens,[status(thm)],[448, 447])).
% 0.54/0.60 tff(450,plain,
% 0.54/0.60 (product(e_1, e_5, e_6) | product(e_1, e_5, e_5) | product(e_1, e_5, e_4) | product(e_1, e_5, e_3) | product(e_1, e_5, e_2)),
% 0.54/0.60 inference(unit_resolution,[status(thm)],[449, 135, 443, 129, 440])).
% 0.54/0.60 tff(451,plain,
% 0.54/0.60 (product(e_1, e_5, e_5)),
% 0.54/0.60 inference(unit_resolution,[status(thm)],[450, 426, 153, 155, 154])).
% 0.54/0.60 tff(452,assumption,(product(e_1, e_5, e_5)), introduced(assumption)).
% 0.54/0.60 tff(453,plain,
% 0.54/0.60 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_4) | (~product(e_1, e_4, e_5)) | (~product(e_1, e_5, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_4) | (~product(e_1, e_4, e_5)) | (~product(e_1, e_5, e_5)))),
% 0.54/0.61 inference(rewrite,[status(thm)],[])).
% 0.54/0.61 tff(454,plain,
% 0.54/0.61 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_4) | (~product(e_1, e_4, e_5)) | (~product(e_1, e_5, e_5)))),
% 0.54/0.61 inference(quant_inst,[status(thm)],[])).
% 0.54/0.61 tff(455,plain,
% 0.54/0.61 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_4) | (~product(e_1, e_4, e_5)) | (~product(e_1, e_5, e_5))),
% 0.54/0.61 inference(modus_ponens,[status(thm)],[454, 453])).
% 0.54/0.61 tff(456,plain,
% 0.54/0.61 ($false),
% 0.54/0.61 inference(unit_resolution,[status(thm)],[455, 173, 17, 290, 452])).
% 0.54/0.61 tff(457,plain,((~product(e_1, e_5, e_5)) | (~product(e_1, e_4, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.61 tff(458,plain,
% 0.54/0.61 ($false),
% 0.54/0.61 inference(unit_resolution,[status(thm)],[457, 451, 417])).
% 0.54/0.61 tff(459,plain,((~product(e_1, e_3, e_6)) | product(e_1, e_5, e_4) | product(e_1, e_5, e_3) | product(e_1, e_5, e_2) | product(e_1, e_4, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.54/0.61 tff(460,plain,
% 0.54/0.61 (~product(e_1, e_3, e_6)),
% 0.54/0.61 inference(unit_resolution,[status(thm)],[459, 4, 155, 154, 153])).
% 0.54/0.61 tff(461,plain,
% 0.54/0.61 ((~![X: $i] : product(X, X, X)) | product(e_3, e_3, e_3)),
% 0.54/0.61 inference(quant_inst,[status(thm)],[])).
% 0.54/0.61 tff(462,plain,
% 0.54/0.61 (product(e_3, e_3, e_3)),
% 0.54/0.61 inference(unit_resolution,[status(thm)],[461, 75])).
% 0.54/0.61 tff(463,assumption,(product(e_1, e_3, e_3)), introduced(assumption)).
% 0.54/0.61 tff(464,plain,
% 0.54/0.61 ((~equalish(e_1, e_3)) <=> (~equalish(e_1, e_3))),
% 0.54/0.61 inference(rewrite,[status(thm)],[])).
% 0.54/0.61 tff(465,axiom,(~equalish(e_1, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_3')).
% 0.54/0.61 tff(466,plain,
% 0.54/0.61 (~equalish(e_1, e_3)),
% 0.54/0.61 inference(modus_ponens,[status(thm)],[465, 464])).
% 0.54/0.61 tff(467,plain,
% 0.54/0.61 (((~![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)))),
% 0.54/0.61 inference(rewrite,[status(thm)],[])).
% 0.54/0.61 tff(468,plain,
% 0.54/0.61 ((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)))),
% 0.54/0.61 inference(rewrite,[status(thm)],[])).
% 0.54/0.61 tff(469,plain,
% 0.54/0.61 (((~![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))))),
% 0.54/0.61 inference(monotonicity,[status(thm)],[468])).
% 0.54/0.61 tff(470,plain,
% 0.54/0.61 (((~![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)))),
% 0.54/0.61 inference(transitivity,[status(thm)],[469, 467])).
% 0.54/0.61 tff(471,plain,
% 0.54/0.61 ((~![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)))),
% 0.54/0.61 inference(quant_inst,[status(thm)],[])).
% 0.54/0.61 tff(472,plain,
% 0.54/0.61 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_3))),
% 0.54/0.61 inference(modus_ponens,[status(thm)],[471, 470])).
% 0.56/0.61 tff(473,plain,
% 0.56/0.61 ($false),
% 0.56/0.61 inference(unit_resolution,[status(thm)],[472, 466, 87, 463, 462])).
% 0.56/0.61 tff(474,plain,(~product(e_1, e_3, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.56/0.61 tff(475,plain,
% 0.56/0.61 (greater(e_3, e_2) <=> greater(e_3, e_2)),
% 0.56/0.61 inference(rewrite,[status(thm)],[])).
% 0.56/0.61 tff(476,axiom,(greater(e_3, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_greater_e_2')).
% 0.56/0.61 tff(477,plain,
% 0.56/0.61 (greater(e_3, e_2)),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[476, 475])).
% 0.56/0.61 tff(478,plain,
% 0.56/0.61 (((~![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)))),
% 0.56/0.61 inference(rewrite,[status(thm)],[])).
% 0.56/0.61 tff(479,plain,
% 0.56/0.61 ((~![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)))),
% 0.56/0.61 inference(quant_inst,[status(thm)],[])).
% 0.56/0.61 tff(480,plain,
% 0.56/0.61 ((~![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))),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[479, 478])).
% 0.56/0.61 tff(481,plain,
% 0.56/0.61 (~product(e_1, e_1, e_3)),
% 0.56/0.61 inference(unit_resolution,[status(thm)],[480, 204, 477, 38])).
% 0.56/0.61 tff(482,plain,
% 0.56/0.61 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_3) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_3) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_1)))),
% 0.56/0.61 inference(rewrite,[status(thm)],[])).
% 0.56/0.61 tff(483,plain,
% 0.56/0.61 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_3) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_1)))),
% 0.56/0.61 inference(quant_inst,[status(thm)],[])).
% 0.56/0.61 tff(484,plain,
% 0.56/0.61 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_3) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_1))),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[483, 482])).
% 0.56/0.61 tff(485,plain,
% 0.56/0.61 (~product(e_1, e_3, e_1)),
% 0.56/0.61 inference(unit_resolution,[status(thm)],[484, 58, 481, 77])).
% 0.56/0.61 tff(486,plain,
% 0.56/0.61 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_1)) | (~group_element(e_3)) | product(e_1, e_3, e_2) | product(e_1, e_3, e_6) | product(e_1, e_3, e_5) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3) | product(e_1, e_3, e_1))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_1, e_3, e_2) | product(e_1, e_3, e_6) | product(e_1, e_3, e_5) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3) | product(e_1, e_3, e_1))),
% 0.56/0.61 inference(rewrite,[status(thm)],[])).
% 0.56/0.61 tff(487,plain,
% 0.56/0.61 ((product(e_1, e_3, e_6) | product(e_1, e_3, e_5) | product(e_1, e_3, e_4) | 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_6) | product(e_1, e_3, e_5) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3) | product(e_1, e_3, e_1))),
% 0.56/0.61 inference(rewrite,[status(thm)],[])).
% 0.56/0.61 tff(488,plain,
% 0.56/0.61 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_3, e_6) | product(e_1, e_3, e_5) | product(e_1, e_3, e_4) | 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_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_1)) | (~group_element(e_3)) | product(e_1, e_3, e_2) | product(e_1, e_3, e_6) | product(e_1, e_3, e_5) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3) | product(e_1, e_3, e_1)))),
% 0.56/0.61 inference(monotonicity,[status(thm)],[487])).
% 0.56/0.61 tff(489,plain,
% 0.56/0.61 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_3, e_6) | product(e_1, e_3, e_5) | product(e_1, e_3, e_4) | 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_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_1, e_3, e_2) | product(e_1, e_3, e_6) | product(e_1, e_3, e_5) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3) | product(e_1, e_3, e_1))),
% 0.56/0.61 inference(transitivity,[status(thm)],[488, 486])).
% 0.56/0.61 tff(490,plain,
% 0.56/0.61 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_3, e_6) | product(e_1, e_3, e_5) | product(e_1, e_3, e_4) | 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)))),
% 0.56/0.61 inference(quant_inst,[status(thm)],[])).
% 0.56/0.61 tff(491,plain,
% 0.56/0.61 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_1, e_3, e_2) | product(e_1, e_3, e_6) | product(e_1, e_3, e_5) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3) | product(e_1, e_3, e_1)),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[490, 489])).
% 0.56/0.61 tff(492,plain,
% 0.56/0.61 (product(e_1, e_3, e_2) | product(e_1, e_3, e_6) | product(e_1, e_3, e_5) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3)),
% 0.56/0.61 inference(unit_resolution,[status(thm)],[491, 135, 253, 129, 485])).
% 0.56/0.61 tff(493,plain,
% 0.56/0.61 (product(e_1, e_3, e_2) | product(e_1, e_3, e_6) | product(e_1, e_3, e_5) | product(e_1, e_3, e_4)),
% 0.56/0.61 inference(unit_resolution,[status(thm)],[492, 474])).
% 0.56/0.61 tff(494,plain,
% 0.56/0.61 (product(e_1, e_3, e_5)),
% 0.56/0.61 inference(unit_resolution,[status(thm)],[493, 460, 406, 405])).
% 0.56/0.61 tff(495,assumption,(product(e_1, e_3, e_5)), introduced(assumption)).
% 0.56/0.61 tff(496,plain,
% 0.56/0.61 ((~equalish(e_4, e_3)) <=> (~equalish(e_4, e_3))),
% 0.56/0.61 inference(rewrite,[status(thm)],[])).
% 0.56/0.61 tff(497,axiom,(~equalish(e_4, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_3')).
% 0.56/0.61 tff(498,plain,
% 0.56/0.61 (~equalish(e_4, e_3)),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[497, 496])).
% 0.56/0.61 tff(499,plain,
% 0.56/0.61 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_3) | (~product(e_1, e_4, e_5)) | (~product(e_1, e_3, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_3) | (~product(e_1, e_4, e_5)) | (~product(e_1, e_3, e_5)))),
% 0.56/0.61 inference(rewrite,[status(thm)],[])).
% 0.56/0.61 tff(500,plain,
% 0.56/0.61 ((equalish(e_4, e_3) | (~product(e_1, e_3, e_5)) | (~product(e_1, e_4, e_5))) <=> (equalish(e_4, e_3) | (~product(e_1, e_4, e_5)) | (~product(e_1, e_3, e_5)))),
% 0.56/0.61 inference(rewrite,[status(thm)],[])).
% 0.56/0.61 tff(501,plain,
% 0.56/0.61 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_3) | (~product(e_1, e_3, e_5)) | (~product(e_1, e_4, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_3) | (~product(e_1, e_4, e_5)) | (~product(e_1, e_3, e_5))))),
% 0.56/0.61 inference(monotonicity,[status(thm)],[500])).
% 0.56/0.61 tff(502,plain,
% 0.56/0.61 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_3) | (~product(e_1, e_3, e_5)) | (~product(e_1, e_4, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_3) | (~product(e_1, e_4, e_5)) | (~product(e_1, e_3, e_5)))),
% 0.56/0.61 inference(transitivity,[status(thm)],[501, 499])).
% 0.56/0.61 tff(503,plain,
% 0.56/0.61 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_3) | (~product(e_1, e_3, e_5)) | (~product(e_1, e_4, e_5)))),
% 0.56/0.61 inference(quant_inst,[status(thm)],[])).
% 0.56/0.61 tff(504,plain,
% 0.56/0.61 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_3) | (~product(e_1, e_4, e_5)) | (~product(e_1, e_3, e_5))),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[503, 502])).
% 0.56/0.61 tff(505,plain,
% 0.56/0.61 ($false),
% 0.56/0.61 inference(unit_resolution,[status(thm)],[504, 498, 17, 290, 495])).
% 0.56/0.61 tff(506,plain,((~product(e_1, e_4, e_5)) | (~product(e_1, e_3, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.56/0.61 tff(507,plain,
% 0.56/0.61 (~product(e_1, e_4, e_5)),
% 0.56/0.61 inference(unit_resolution,[status(thm)],[506, 494])).
% 0.56/0.61 tff(508,plain,
% 0.56/0.61 (product(e_1, e_4, e_6)),
% 0.56/0.61 inference(unit_resolution,[status(thm)],[287, 507, 4])).
% 0.56/0.61 tff(509,plain,
% 0.56/0.61 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_5) | (~product(e_1, e_5, e_5)) | (~product(e_1, e_3, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_5) | (~product(e_1, e_5, e_5)) | (~product(e_1, e_3, e_5)))),
% 0.56/0.61 inference(rewrite,[status(thm)],[])).
% 0.56/0.61 tff(510,plain,
% 0.56/0.61 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_5) | (~product(e_1, e_5, e_5)) | (~product(e_1, e_3, e_5)))),
% 0.56/0.61 inference(quant_inst,[status(thm)],[])).
% 0.56/0.61 tff(511,plain,
% 0.56/0.61 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_5) | (~product(e_1, e_5, e_5)) | (~product(e_1, e_3, e_5))),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[510, 509])).
% 0.56/0.61 tff(512,plain,
% 0.56/0.61 ($false),
% 0.56/0.61 inference(unit_resolution,[status(thm)],[511, 420, 17, 452, 495])).
% 0.56/0.61 tff(513,plain,((~product(e_1, e_3, e_5)) | (~product(e_1, e_5, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.56/0.61 tff(514,plain,
% 0.56/0.61 (~product(e_1, e_5, e_5)),
% 0.56/0.61 inference(unit_resolution,[status(thm)],[513, 494])).
% 0.56/0.61 tff(515,plain,
% 0.56/0.61 (product(e_1, e_5, e_6)),
% 0.56/0.61 inference(unit_resolution,[status(thm)],[450, 514, 153, 155, 154])).
% 0.56/0.61 tff(516,plain,
% 0.56/0.61 ($false),
% 0.56/0.61 inference(unit_resolution,[status(thm)],[181, 515, 508])).
% 0.56/0.61 tff(517,plain,(product(e_1, e_4, e_2) | product(e_1, e_5, e_4) | product(e_1, e_5, e_3) | product(e_1, e_5, e_2) | product(e_1, e_3, e_2) | product(e_1, e_3, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.56/0.61 tff(518,plain,
% 0.56/0.61 (product(e_1, e_3, e_2)),
% 0.56/0.61 inference(unit_resolution,[status(thm)],[517, 404, 155, 4, 154, 153])).
% 0.56/0.61 tff(519,assumption,(product(e_1, e_2, e_5)), introduced(assumption)).
% 0.56/0.61 tff(520,plain,
% 0.56/0.61 ((~equalish(e_2, e_4)) <=> (~equalish(e_2, e_4))),
% 0.56/0.61 inference(rewrite,[status(thm)],[])).
% 0.56/0.61 tff(521,axiom,(~equalish(e_2, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_4')).
% 0.56/0.61 tff(522,plain,
% 0.56/0.61 (~equalish(e_2, e_4)),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[521, 520])).
% 0.56/0.61 tff(523,plain,
% 0.56/0.61 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_4) | (~product(e_1, e_4, e_5)) | (~product(e_1, e_2, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_4) | (~product(e_1, e_4, e_5)) | (~product(e_1, e_2, e_5)))),
% 0.56/0.61 inference(rewrite,[status(thm)],[])).
% 0.56/0.61 tff(524,plain,
% 0.56/0.61 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_4) | (~product(e_1, e_4, e_5)) | (~product(e_1, e_2, e_5)))),
% 0.56/0.61 inference(quant_inst,[status(thm)],[])).
% 0.56/0.61 tff(525,plain,
% 0.56/0.61 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_4) | (~product(e_1, e_4, e_5)) | (~product(e_1, e_2, e_5))),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[524, 523])).
% 0.56/0.61 tff(526,plain,
% 0.56/0.61 ($false),
% 0.56/0.61 inference(unit_resolution,[status(thm)],[525, 522, 17, 290, 519])).
% 0.56/0.61 tff(527,plain,((~product(e_1, e_2, e_5)) | (~product(e_1, e_4, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.56/0.61 tff(528,plain,
% 0.56/0.61 (~product(e_1, e_2, e_5)),
% 0.56/0.61 inference(unit_resolution,[status(thm)],[527, 288])).
% 0.56/0.61 tff(529,assumption,(product(e_1, e_2, e_6)), introduced(assumption)).
% 0.56/0.61 tff(530,plain,
% 0.56/0.61 ((~equalish(e_5, e_2)) <=> (~equalish(e_5, e_2))),
% 0.56/0.61 inference(rewrite,[status(thm)],[])).
% 0.56/0.61 tff(531,axiom,(~equalish(e_5, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_5_is_not_e_2')).
% 0.56/0.61 tff(532,plain,
% 0.56/0.61 (~equalish(e_5, e_2)),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[531, 530])).
% 0.56/0.61 tff(533,plain,
% 0.56/0.61 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_2) | (~product(e_1, e_5, e_6)) | (~product(e_1, e_2, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_2) | (~product(e_1, e_5, e_6)) | (~product(e_1, e_2, e_6)))),
% 0.56/0.61 inference(rewrite,[status(thm)],[])).
% 0.56/0.61 tff(534,plain,
% 0.56/0.61 ((equalish(e_5, e_2) | (~product(e_1, e_2, e_6)) | (~product(e_1, e_5, e_6))) <=> (equalish(e_5, e_2) | (~product(e_1, e_5, e_6)) | (~product(e_1, e_2, e_6)))),
% 0.56/0.61 inference(rewrite,[status(thm)],[])).
% 0.56/0.61 tff(535,plain,
% 0.56/0.61 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_2) | (~product(e_1, e_2, e_6)) | (~product(e_1, e_5, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_2) | (~product(e_1, e_5, e_6)) | (~product(e_1, e_2, e_6))))),
% 0.56/0.61 inference(monotonicity,[status(thm)],[534])).
% 0.56/0.61 tff(536,plain,
% 0.56/0.61 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_2) | (~product(e_1, e_2, e_6)) | (~product(e_1, e_5, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_2) | (~product(e_1, e_5, e_6)) | (~product(e_1, e_2, e_6)))),
% 0.56/0.61 inference(transitivity,[status(thm)],[535, 533])).
% 0.56/0.61 tff(537,plain,
% 0.56/0.61 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_2) | (~product(e_1, e_2, e_6)) | (~product(e_1, e_5, e_6)))),
% 0.56/0.61 inference(quant_inst,[status(thm)],[])).
% 0.56/0.61 tff(538,plain,
% 0.56/0.61 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_2) | (~product(e_1, e_5, e_6)) | (~product(e_1, e_2, e_6))),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[537, 536])).
% 0.56/0.61 tff(539,plain,
% 0.56/0.61 ($false),
% 0.56/0.61 inference(unit_resolution,[status(thm)],[538, 532, 17, 156, 529])).
% 0.56/0.61 tff(540,plain,((~product(e_1, e_5, e_6)) | (~product(e_1, e_2, e_6))), inference(lemma,lemma(discharge,[]))).
% 0.56/0.61 tff(541,plain,
% 0.56/0.61 (~product(e_1, e_2, e_6)),
% 0.56/0.61 inference(unit_resolution,[status(thm)],[540, 156])).
% 0.56/0.61 tff(542,assumption,(product(e_1, e_2, e_4)), introduced(assumption)).
% 0.56/0.61 tff(543,plain,
% 0.56/0.61 ((~equalish(e_2, e_6)) <=> (~equalish(e_2, e_6))),
% 0.56/0.61 inference(rewrite,[status(thm)],[])).
% 0.56/0.61 tff(544,axiom,(~equalish(e_2, e_6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_6')).
% 0.56/0.61 tff(545,plain,
% 0.56/0.61 (~equalish(e_2, e_6)),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[544, 543])).
% 0.56/0.61 tff(546,plain,
% 0.56/0.61 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_6) | (~product(e_1, e_6, e_4)) | (~product(e_1, e_2, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_6) | (~product(e_1, e_6, e_4)) | (~product(e_1, e_2, e_4)))),
% 0.56/0.62 inference(rewrite,[status(thm)],[])).
% 0.56/0.62 tff(547,plain,
% 0.56/0.62 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_6) | (~product(e_1, e_6, e_4)) | (~product(e_1, e_2, e_4)))),
% 0.56/0.62 inference(quant_inst,[status(thm)],[])).
% 0.56/0.62 tff(548,plain,
% 0.56/0.62 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_6) | (~product(e_1, e_6, e_4)) | (~product(e_1, e_2, e_4))),
% 0.56/0.62 inference(modus_ponens,[status(thm)],[547, 546])).
% 0.56/0.62 tff(549,plain,
% 0.56/0.62 ($false),
% 0.56/0.62 inference(unit_resolution,[status(thm)],[548, 545, 17, 6, 542])).
% 0.56/0.62 tff(550,plain,((~product(e_1, e_2, e_4)) | (~product(e_1, e_6, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.56/0.62 tff(551,plain,
% 0.56/0.62 (~product(e_1, e_2, e_4)),
% 0.56/0.62 inference(unit_resolution,[status(thm)],[550, 394])).
% 0.56/0.62 tff(552,assumption,(product(e_1, e_2, e_2)), introduced(assumption)).
% 0.56/0.62 tff(553,assumption,(product(e_1, e_3, e_2)), introduced(assumption)).
% 0.56/0.62 tff(554,plain,
% 0.56/0.62 ((~equalish(e_2, e_3)) <=> (~equalish(e_2, e_3))),
% 0.56/0.62 inference(rewrite,[status(thm)],[])).
% 0.56/0.62 tff(555,axiom,(~equalish(e_2, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_3')).
% 0.56/0.62 tff(556,plain,
% 0.56/0.62 (~equalish(e_2, e_3)),
% 0.56/0.62 inference(modus_ponens,[status(thm)],[555, 554])).
% 0.56/0.62 tff(557,plain,
% 0.56/0.62 (((~![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)))),
% 0.56/0.62 inference(rewrite,[status(thm)],[])).
% 0.56/0.62 tff(558,plain,
% 0.56/0.62 ((~![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)))),
% 0.56/0.62 inference(quant_inst,[status(thm)],[])).
% 0.56/0.62 tff(559,plain,
% 0.56/0.62 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_3) | (~product(e_1, e_3, e_2)) | (~product(e_1, e_2, e_2))),
% 0.56/0.62 inference(modus_ponens,[status(thm)],[558, 557])).
% 0.56/0.62 tff(560,plain,
% 0.56/0.62 ($false),
% 0.56/0.62 inference(unit_resolution,[status(thm)],[559, 556, 17, 553, 552])).
% 0.56/0.62 tff(561,plain,((~product(e_1, e_2, e_2)) | (~product(e_1, e_3, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.56/0.62 tff(562,plain,
% 0.56/0.62 (~product(e_1, e_2, e_2)),
% 0.56/0.62 inference(unit_resolution,[status(thm)],[561, 518])).
% 0.56/0.62 tff(563,assumption,(product(e_1, e_2, e_1)), introduced(assumption)).
% 0.56/0.62 tff(564,plain,
% 0.56/0.62 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_2, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_2, e_1)))),
% 0.56/0.62 inference(rewrite,[status(thm)],[])).
% 0.56/0.62 tff(565,plain,
% 0.56/0.62 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_2, e_1)))),
% 0.56/0.62 inference(quant_inst,[status(thm)],[])).
% 0.56/0.62 tff(566,plain,
% 0.56/0.62 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_2, e_1))),
% 0.56/0.62 inference(modus_ponens,[status(thm)],[565, 564])).
% 0.56/0.62 tff(567,plain,
% 0.56/0.62 ($false),
% 0.56/0.62 inference(unit_resolution,[status(thm)],[566, 90, 17, 77, 563])).
% 0.56/0.62 tff(568,plain,(~product(e_1, e_2, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.56/0.62 tff(569,plain,
% 0.56/0.62 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_1)) | (~group_element(e_2)) | product(e_1, e_2, e_6) | product(e_1, e_2, e_3) | product(e_1, e_2, e_5) | product(e_1, e_2, e_4) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | (~group_element(e_2)) | product(e_1, e_2, e_6) | product(e_1, e_2, e_3) | product(e_1, e_2, e_5) | product(e_1, e_2, e_4) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1))),
% 0.56/0.62 inference(rewrite,[status(thm)],[])).
% 0.56/0.62 tff(570,plain,
% 0.56/0.62 ((product(e_1, e_2, e_6) | product(e_1, e_2, e_5) | product(e_1, e_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_1))) <=> ((~group_element(e_1)) | (~group_element(e_2)) | product(e_1, e_2, e_6) | product(e_1, e_2, e_3) | product(e_1, e_2, e_5) | product(e_1, e_2, e_4) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1))),
% 0.56/0.62 inference(rewrite,[status(thm)],[])).
% 0.56/0.62 tff(571,plain,
% 0.56/0.62 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_2, e_6) | product(e_1, e_2, e_5) | product(e_1, e_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_1)) | (~group_element(e_2)) | product(e_1, e_2, e_6) | product(e_1, e_2, e_3) | product(e_1, e_2, e_5) | product(e_1, e_2, e_4) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1)))),
% 0.56/0.62 inference(monotonicity,[status(thm)],[570])).
% 0.56/0.62 tff(572,plain,
% 0.56/0.62 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_2, e_6) | product(e_1, e_2, e_5) | product(e_1, e_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | (~group_element(e_2)) | product(e_1, e_2, e_6) | product(e_1, e_2, e_3) | product(e_1, e_2, e_5) | product(e_1, e_2, e_4) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1))),
% 0.56/0.62 inference(transitivity,[status(thm)],[571, 569])).
% 0.56/0.62 tff(573,plain,
% 0.56/0.62 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_2, e_6) | product(e_1, e_2, e_5) | product(e_1, e_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_1)))),
% 0.56/0.62 inference(quant_inst,[status(thm)],[])).
% 0.56/0.62 tff(574,plain,
% 0.56/0.62 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | (~group_element(e_2)) | product(e_1, e_2, e_6) | product(e_1, e_2, e_3) | product(e_1, e_2, e_5) | product(e_1, e_2, e_4) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1)),
% 0.56/0.62 inference(modus_ponens,[status(thm)],[573, 572])).
% 0.56/0.62 tff(575,plain,
% 0.56/0.62 (product(e_1, e_2, e_6) | product(e_1, e_2, e_3) | product(e_1, e_2, e_5) | product(e_1, e_2, e_4) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1)),
% 0.56/0.62 inference(unit_resolution,[status(thm)],[574, 135, 132, 129])).
% 0.56/0.62 tff(576,plain,
% 0.56/0.62 (product(e_1, e_2, e_6) | product(e_1, e_2, e_3) | product(e_1, e_2, e_5) | product(e_1, e_2, e_4) | product(e_1, e_2, e_2)),
% 0.56/0.62 inference(unit_resolution,[status(thm)],[575, 568])).
% 0.56/0.62 tff(577,plain,
% 0.56/0.62 (product(e_1, e_2, e_3)),
% 0.56/0.62 inference(unit_resolution,[status(thm)],[576, 562, 551, 541, 528])).
% 0.56/0.62 tff(578,assumption,(product(e_1, e_2, e_3)), introduced(assumption)).
% 0.56/0.62 tff(579,plain,
% 0.56/0.62 (((~![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_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_2, e_3) | (~product(e_2, e_1, e_2)) | (~product(e_3, e_1, e_2)))),
% 0.56/0.62 inference(rewrite,[status(thm)],[])).
% 0.56/0.62 tff(580,plain,
% 0.56/0.62 ((equalish(e_2, e_3) | (~product(e_3, e_1, e_2)) | (~product(e_2, e_1, e_2))) <=> (equalish(e_2, e_3) | (~product(e_2, e_1, e_2)) | (~product(e_3, e_1, e_2)))),
% 0.56/0.62 inference(rewrite,[status(thm)],[])).
% 0.56/0.62 tff(581,plain,
% 0.56/0.62 (((~![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_2, e_1, e_2)) | (~product(e_3, e_1, e_2))))),
% 0.56/0.62 inference(monotonicity,[status(thm)],[580])).
% 0.56/0.62 tff(582,plain,
% 0.56/0.62 (((~![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_2, e_1, e_2)) | (~product(e_3, e_1, e_2)))),
% 0.56/0.62 inference(transitivity,[status(thm)],[581, 579])).
% 0.56/0.62 tff(583,plain,
% 0.56/0.62 ((~![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)))),
% 0.56/0.62 inference(quant_inst,[status(thm)],[])).
% 0.56/0.62 tff(584,plain,
% 0.56/0.62 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_3) | (~product(e_2, e_1, e_2)) | (~product(e_3, e_1, e_2))),
% 0.56/0.62 inference(modus_ponens,[status(thm)],[583, 582])).
% 0.56/0.62 tff(585,plain,
% 0.56/0.62 ($false),
% 0.56/0.62 inference(unit_resolution,[status(thm)],[584, 556, 87, 350, 215])).
% 0.56/0.62 tff(586,plain,((~product(e_2, e_1, e_2)) | (~product(e_3, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.56/0.62 tff(587,plain,
% 0.56/0.62 (~product(e_2, e_1, e_2)),
% 0.56/0.62 inference(unit_resolution,[status(thm)],[586, 215])).
% 0.56/0.62 tff(588,plain,
% 0.56/0.62 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_2) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_2) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_2, e_3)))),
% 0.56/0.62 inference(rewrite,[status(thm)],[])).
% 0.56/0.62 tff(589,plain,
% 0.56/0.62 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_2) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_2, e_3)))),
% 0.56/0.62 inference(quant_inst,[status(thm)],[])).
% 0.56/0.62 tff(590,plain,
% 0.56/0.62 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_2) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_2, e_3))),
% 0.56/0.62 inference(modus_ponens,[status(thm)],[589, 588])).
% 0.56/0.62 tff(591,plain,
% 0.56/0.62 (product(e_2, e_1, e_2) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_2, e_3))),
% 0.56/0.62 inference(unit_resolution,[status(thm)],[590, 58])).
% 0.56/0.62 tff(592,plain,
% 0.56/0.62 ($false),
% 0.56/0.62 inference(unit_resolution,[status(thm)],[591, 587, 215, 578])).
% 0.56/0.62 tff(593,plain,((~product(e_3, e_1, e_2)) | (~product(e_1, e_2, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.56/0.62 tff(594,plain,
% 0.56/0.62 (~product(e_3, e_1, e_2)),
% 0.56/0.62 inference(unit_resolution,[status(thm)],[593, 577])).
% 0.56/0.62 tff(595,plain,
% 0.56/0.62 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_2) | (~product(e_3, e_1, e_3)) | (~product(e_1, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_2) | (~product(e_3, e_1, e_3)) | (~product(e_1, e_2, e_3)))),
% 0.56/0.62 inference(rewrite,[status(thm)],[])).
% 0.56/0.62 tff(596,plain,
% 0.56/0.62 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_2) | (~product(e_3, e_1, e_3)) | (~product(e_1, e_2, e_3)))),
% 0.56/0.62 inference(quant_inst,[status(thm)],[])).
% 0.56/0.62 tff(597,plain,
% 0.56/0.62 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_2) | (~product(e_3, e_1, e_3)) | (~product(e_1, e_2, e_3))),
% 0.56/0.62 inference(modus_ponens,[status(thm)],[596, 595])).
% 0.56/0.62 tff(598,plain,
% 0.56/0.62 (product(e_3, e_1, e_2) | (~product(e_3, e_1, e_3)) | (~product(e_1, e_2, e_3))),
% 0.56/0.62 inference(unit_resolution,[status(thm)],[597, 58])).
% 0.56/0.62 tff(599,plain,
% 0.56/0.62 (~product(e_3, e_1, e_3)),
% 0.56/0.62 inference(unit_resolution,[status(thm)],[598, 594, 577])).
% 0.56/0.62 tff(600,assumption,(~product(e_3, e_1, e_3)), introduced(assumption)).
% 0.56/0.62 tff(601,plain,
% 0.56/0.62 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_3) | (~product(e_1, e_3, e_2)) | (~product(e_2, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_3) | (~product(e_1, e_3, e_2)) | (~product(e_2, e_1, e_3)))),
% 0.56/0.62 inference(rewrite,[status(thm)],[])).
% 0.56/0.62 tff(602,plain,
% 0.56/0.62 ((product(e_3, e_1, e_3) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_3, e_2))) <=> (product(e_3, e_1, e_3) | (~product(e_1, e_3, e_2)) | (~product(e_2, e_1, e_3)))),
% 0.56/0.62 inference(rewrite,[status(thm)],[])).
% 0.56/0.62 tff(603,plain,
% 0.56/0.62 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_3) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_3) | (~product(e_1, e_3, e_2)) | (~product(e_2, e_1, e_3))))),
% 0.56/0.62 inference(monotonicity,[status(thm)],[602])).
% 0.56/0.62 tff(604,plain,
% 0.56/0.62 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_3) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_3) | (~product(e_1, e_3, e_2)) | (~product(e_2, e_1, e_3)))),
% 0.56/0.62 inference(transitivity,[status(thm)],[603, 601])).
% 0.56/0.62 tff(605,plain,
% 0.56/0.62 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_3) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_3, e_2)))),
% 0.56/0.62 inference(quant_inst,[status(thm)],[])).
% 0.56/0.62 tff(606,plain,
% 0.56/0.62 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_3) | (~product(e_1, e_3, e_2)) | (~product(e_2, e_1, e_3))),
% 0.56/0.62 inference(modus_ponens,[status(thm)],[605, 604])).
% 0.56/0.62 tff(607,plain,
% 0.56/0.62 ($false),
% 0.56/0.62 inference(unit_resolution,[status(thm)],[606, 58, 28, 600, 553])).
% 0.56/0.62 tff(608,plain,((~product(e_2, e_1, e_3)) | product(e_3, e_1, e_3) | (~product(e_1, e_3, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.56/0.62 tff(609,plain,
% 0.56/0.62 (~product(e_2, e_1, e_3)),
% 0.56/0.62 inference(unit_resolution,[status(thm)],[608, 599, 518])).
% 0.56/0.62 tff(610,plain,
% 0.56/0.62 (product(e_2, e_1, e_2)),
% 0.56/0.62 inference(unit_resolution,[status(thm)],[143, 609])).
% 0.56/0.62 tff(611,plain,
% 0.56/0.62 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_3) | (~product(e_1, e_3, e_2)) | (~product(e_2, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_3) | (~product(e_1, e_3, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.56/0.63 inference(rewrite,[status(thm)],[])).
% 0.56/0.63 tff(612,plain,
% 0.56/0.63 ((product(e_2, e_1, e_3) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_3, e_2))) <=> (product(e_2, e_1, e_3) | (~product(e_1, e_3, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.56/0.63 inference(rewrite,[status(thm)],[])).
% 0.56/0.63 tff(613,plain,
% 0.56/0.63 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_3) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_3) | (~product(e_1, e_3, e_2)) | (~product(e_2, e_1, e_2))))),
% 0.56/0.63 inference(monotonicity,[status(thm)],[612])).
% 0.56/0.63 tff(614,plain,
% 0.56/0.63 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_3) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_3) | (~product(e_1, e_3, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.56/0.63 inference(transitivity,[status(thm)],[613, 611])).
% 0.56/0.63 tff(615,plain,
% 0.56/0.63 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_3) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_3, e_2)))),
% 0.56/0.63 inference(quant_inst,[status(thm)],[])).
% 0.56/0.63 tff(616,plain,
% 0.56/0.63 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_3) | (~product(e_1, e_3, e_2)) | (~product(e_2, e_1, e_2))),
% 0.56/0.63 inference(modus_ponens,[status(thm)],[615, 614])).
% 0.56/0.63 tff(617,plain,
% 0.56/0.63 (product(e_2, e_1, e_3) | (~product(e_1, e_3, e_2)) | (~product(e_2, e_1, e_2))),
% 0.56/0.63 inference(unit_resolution,[status(thm)],[616, 58])).
% 0.56/0.63 tff(618,plain,
% 0.56/0.63 ($false),
% 0.56/0.63 inference(unit_resolution,[status(thm)],[617, 610, 609, 518])).
% 0.56/0.63 tff(619,plain,((~product(e_1, e_5, e_6)) | product(e_1, e_5, e_3) | product(e_1, e_4, e_2) | product(e_1, e_5, e_2) | product(e_1, e_5, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.56/0.63 tff(620,plain,
% 0.56/0.63 (~product(e_1, e_5, e_6)),
% 0.56/0.63 inference(unit_resolution,[status(thm)],[619, 154, 4, 155, 153])).
% 0.56/0.63 tff(621,plain,
% 0.56/0.63 (product(e_1, e_5, e_5)),
% 0.56/0.63 inference(unit_resolution,[status(thm)],[450, 620, 153, 155, 154])).
% 0.56/0.63 tff(622,plain,
% 0.56/0.63 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_6, e_5) | (~product(e_1, e_6, e_5)) | (~product(e_1, e_5, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_6, e_5) | (~product(e_1, e_6, e_5)) | (~product(e_1, e_5, e_5)))),
% 0.56/0.63 inference(rewrite,[status(thm)],[])).
% 0.56/0.63 tff(623,plain,
% 0.56/0.63 ((equalish(e_6, e_5) | (~product(e_1, e_5, e_5)) | (~product(e_1, e_6, e_5))) <=> (equalish(e_6, e_5) | (~product(e_1, e_6, e_5)) | (~product(e_1, e_5, e_5)))),
% 0.56/0.63 inference(rewrite,[status(thm)],[])).
% 0.56/0.63 tff(624,plain,
% 0.56/0.63 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_6, e_5) | (~product(e_1, e_5, e_5)) | (~product(e_1, e_6, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_6, e_5) | (~product(e_1, e_6, e_5)) | (~product(e_1, e_5, e_5))))),
% 0.56/0.63 inference(monotonicity,[status(thm)],[623])).
% 0.56/0.63 tff(625,plain,
% 0.56/0.63 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_6, e_5) | (~product(e_1, e_5, e_5)) | (~product(e_1, e_6, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_6, e_5) | (~product(e_1, e_6, e_5)) | (~product(e_1, e_5, e_5)))),
% 0.56/0.63 inference(transitivity,[status(thm)],[624, 622])).
% 0.56/0.63 tff(626,plain,
% 0.58/0.63 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_6, e_5) | (~product(e_1, e_5, e_5)) | (~product(e_1, e_6, e_5)))),
% 0.58/0.63 inference(quant_inst,[status(thm)],[])).
% 0.58/0.63 tff(627,plain,
% 0.58/0.63 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_6, e_5) | (~product(e_1, e_6, e_5)) | (~product(e_1, e_5, e_5))),
% 0.58/0.63 inference(modus_ponens,[status(thm)],[626, 625])).
% 0.58/0.63 tff(628,plain,
% 0.58/0.63 ($false),
% 0.58/0.63 inference(unit_resolution,[status(thm)],[627, 160, 17, 289, 452])).
% 0.58/0.63 tff(629,plain,((~product(e_1, e_6, e_5)) | (~product(e_1, e_5, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.58/0.63 tff(630,plain,
% 0.58/0.63 (~product(e_1, e_6, e_5)),
% 0.58/0.63 inference(unit_resolution,[status(thm)],[629, 621])).
% 0.58/0.63 tff(631,plain,
% 0.58/0.63 (~product(e_1, e_4, e_5)),
% 0.58/0.63 inference(unit_resolution,[status(thm)],[457, 621])).
% 0.58/0.63 tff(632,plain,
% 0.58/0.63 (product(e_1, e_4, e_6)),
% 0.58/0.63 inference(unit_resolution,[status(thm)],[287, 631, 4])).
% 0.58/0.63 tff(633,plain,
% 0.58/0.63 ((~equalish(e_6, e_4)) <=> (~equalish(e_6, e_4))),
% 0.58/0.63 inference(rewrite,[status(thm)],[])).
% 0.58/0.63 tff(634,axiom,(~equalish(e_6, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_6_is_not_e_4')).
% 0.58/0.63 tff(635,plain,
% 0.58/0.63 (~equalish(e_6, e_4)),
% 0.58/0.63 inference(modus_ponens,[status(thm)],[634, 633])).
% 0.58/0.63 tff(636,plain,
% 0.58/0.63 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_6, e_4) | (~product(e_1, e_6, e_6)) | (~product(e_1, e_4, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_6, e_4) | (~product(e_1, e_6, e_6)) | (~product(e_1, e_4, e_6)))),
% 0.58/0.63 inference(rewrite,[status(thm)],[])).
% 0.58/0.63 tff(637,plain,
% 0.58/0.63 ((equalish(e_6, e_4) | (~product(e_1, e_4, e_6)) | (~product(e_1, e_6, e_6))) <=> (equalish(e_6, e_4) | (~product(e_1, e_6, e_6)) | (~product(e_1, e_4, e_6)))),
% 0.58/0.63 inference(rewrite,[status(thm)],[])).
% 0.58/0.63 tff(638,plain,
% 0.58/0.63 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_6, e_4) | (~product(e_1, e_4, e_6)) | (~product(e_1, e_6, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_6, e_4) | (~product(e_1, e_6, e_6)) | (~product(e_1, e_4, e_6))))),
% 0.58/0.63 inference(monotonicity,[status(thm)],[637])).
% 0.58/0.63 tff(639,plain,
% 0.58/0.63 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_6, e_4) | (~product(e_1, e_4, e_6)) | (~product(e_1, e_6, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_6, e_4) | (~product(e_1, e_6, e_6)) | (~product(e_1, e_4, e_6)))),
% 0.58/0.63 inference(transitivity,[status(thm)],[638, 636])).
% 0.58/0.63 tff(640,plain,
% 0.58/0.63 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_6, e_4) | (~product(e_1, e_4, e_6)) | (~product(e_1, e_6, e_6)))),
% 0.58/0.63 inference(quant_inst,[status(thm)],[])).
% 0.58/0.63 tff(641,plain,
% 0.58/0.63 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_6, e_4) | (~product(e_1, e_6, e_6)) | (~product(e_1, e_4, e_6))),
% 0.58/0.63 inference(modus_ponens,[status(thm)],[640, 639])).
% 0.58/0.63 tff(642,plain,
% 0.58/0.63 ($false),
% 0.58/0.63 inference(unit_resolution,[status(thm)],[641, 635, 17, 170, 157])).
% 0.58/0.63 tff(643,plain,((~product(e_1, e_6, e_6)) | (~product(e_1, e_4, e_6))), inference(lemma,lemma(discharge,[]))).
% 0.58/0.63 tff(644,plain,
% 0.58/0.63 (~product(e_1, e_6, e_6)),
% 0.58/0.63 inference(unit_resolution,[status(thm)],[643, 632])).
% 0.58/0.63 tff(645,plain,
% 0.58/0.63 (product(e_1, e_6, e_4)),
% 0.58/0.63 inference(unit_resolution,[status(thm)],[393, 644, 630])).
% 0.58/0.63 tff(646,plain,
% 0.58/0.63 (~product(e_1, e_3, e_4)),
% 0.58/0.63 inference(unit_resolution,[status(thm)],[403, 645])).
% 0.58/0.63 tff(647,plain,
% 0.58/0.63 (product(e_1, e_3, e_2)),
% 0.58/0.63 inference(unit_resolution,[status(thm)],[517, 646, 155, 4, 154, 153])).
% 0.58/0.63 tff(648,plain,
% 0.58/0.63 ((~equalish(e_2, e_5)) <=> (~equalish(e_2, e_5))),
% 0.58/0.63 inference(rewrite,[status(thm)],[])).
% 0.58/0.63 tff(649,axiom,(~equalish(e_2, e_5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_5')).
% 0.58/0.63 tff(650,plain,
% 0.58/0.63 (~equalish(e_2, e_5)),
% 0.58/0.63 inference(modus_ponens,[status(thm)],[649, 648])).
% 0.58/0.63 tff(651,plain,
% 0.58/0.63 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_5) | (~product(e_1, e_5, e_5)) | (~product(e_1, e_2, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_5) | (~product(e_1, e_5, e_5)) | (~product(e_1, e_2, e_5)))),
% 0.58/0.63 inference(rewrite,[status(thm)],[])).
% 0.58/0.63 tff(652,plain,
% 0.58/0.63 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_5) | (~product(e_1, e_5, e_5)) | (~product(e_1, e_2, e_5)))),
% 0.58/0.63 inference(quant_inst,[status(thm)],[])).
% 0.58/0.63 tff(653,plain,
% 0.58/0.63 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_5) | (~product(e_1, e_5, e_5)) | (~product(e_1, e_2, e_5))),
% 0.58/0.63 inference(modus_ponens,[status(thm)],[652, 651])).
% 0.58/0.63 tff(654,plain,
% 0.58/0.63 ($false),
% 0.58/0.63 inference(unit_resolution,[status(thm)],[653, 650, 17, 452, 519])).
% 0.58/0.63 tff(655,plain,((~product(e_1, e_2, e_5)) | (~product(e_1, e_5, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.58/0.63 tff(656,plain,
% 0.58/0.63 (~product(e_1, e_2, e_5)),
% 0.58/0.63 inference(unit_resolution,[status(thm)],[655, 621])).
% 0.58/0.63 tff(657,plain,
% 0.58/0.63 ((~equalish(e_4, e_2)) <=> (~equalish(e_4, e_2))),
% 0.58/0.63 inference(rewrite,[status(thm)],[])).
% 0.58/0.63 tff(658,axiom,(~equalish(e_4, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_2')).
% 0.58/0.63 tff(659,plain,
% 0.58/0.63 (~equalish(e_4, e_2)),
% 0.58/0.63 inference(modus_ponens,[status(thm)],[658, 657])).
% 0.58/0.63 tff(660,plain,
% 0.58/0.63 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_2) | (~product(e_1, e_4, e_6)) | (~product(e_1, e_2, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_2) | (~product(e_1, e_4, e_6)) | (~product(e_1, e_2, e_6)))),
% 0.58/0.63 inference(rewrite,[status(thm)],[])).
% 0.58/0.63 tff(661,plain,
% 0.58/0.63 ((equalish(e_4, e_2) | (~product(e_1, e_2, e_6)) | (~product(e_1, e_4, e_6))) <=> (equalish(e_4, e_2) | (~product(e_1, e_4, e_6)) | (~product(e_1, e_2, e_6)))),
% 0.58/0.63 inference(rewrite,[status(thm)],[])).
% 0.58/0.63 tff(662,plain,
% 0.58/0.63 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_2) | (~product(e_1, e_2, e_6)) | (~product(e_1, e_4, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_2) | (~product(e_1, e_4, e_6)) | (~product(e_1, e_2, e_6))))),
% 0.58/0.63 inference(monotonicity,[status(thm)],[661])).
% 0.58/0.63 tff(663,plain,
% 0.58/0.63 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_2) | (~product(e_1, e_2, e_6)) | (~product(e_1, e_4, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_2) | (~product(e_1, e_4, e_6)) | (~product(e_1, e_2, e_6)))),
% 0.58/0.63 inference(transitivity,[status(thm)],[662, 660])).
% 0.58/0.63 tff(664,plain,
% 0.58/0.63 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_2) | (~product(e_1, e_2, e_6)) | (~product(e_1, e_4, e_6)))),
% 0.58/0.63 inference(quant_inst,[status(thm)],[])).
% 0.58/0.63 tff(665,plain,
% 0.58/0.63 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_2) | (~product(e_1, e_4, e_6)) | (~product(e_1, e_2, e_6))),
% 0.58/0.63 inference(modus_ponens,[status(thm)],[664, 663])).
% 0.58/0.63 tff(666,plain,
% 0.58/0.63 ($false),
% 0.58/0.63 inference(unit_resolution,[status(thm)],[665, 659, 17, 170, 529])).
% 0.58/0.63 tff(667,plain,((~product(e_1, e_4, e_6)) | (~product(e_1, e_2, e_6))), inference(lemma,lemma(discharge,[]))).
% 0.58/0.63 tff(668,plain,
% 0.58/0.63 (~product(e_1, e_2, e_6)),
% 0.58/0.63 inference(unit_resolution,[status(thm)],[667, 632])).
% 0.58/0.63 tff(669,plain,
% 0.58/0.63 (~product(e_1, e_2, e_4)),
% 0.58/0.63 inference(unit_resolution,[status(thm)],[550, 645])).
% 0.58/0.63 tff(670,plain,
% 0.58/0.63 (~product(e_1, e_2, e_2)),
% 0.58/0.63 inference(unit_resolution,[status(thm)],[561, 647])).
% 0.58/0.63 tff(671,plain,
% 0.58/0.63 (product(e_1, e_2, e_3)),
% 0.58/0.63 inference(unit_resolution,[status(thm)],[576, 670, 669, 668, 656])).
% 0.58/0.63 tff(672,plain,
% 0.58/0.63 (~product(e_3, e_1, e_2)),
% 0.58/0.63 inference(unit_resolution,[status(thm)],[593, 671])).
% 0.58/0.63 tff(673,plain,
% 0.58/0.63 (~product(e_3, e_1, e_3)),
% 0.58/0.63 inference(unit_resolution,[status(thm)],[598, 672, 671])).
% 0.58/0.63 tff(674,plain,
% 0.58/0.63 (~product(e_2, e_1, e_3)),
% 0.58/0.63 inference(unit_resolution,[status(thm)],[608, 673, 647])).
% 0.58/0.63 tff(675,plain,
% 0.58/0.63 (product(e_2, e_1, e_2)),
% 0.58/0.63 inference(unit_resolution,[status(thm)],[143, 674])).
% 0.58/0.63 tff(676,plain,
% 0.58/0.63 ($false),
% 0.58/0.63 inference(unit_resolution,[status(thm)],[617, 675, 674, 647])).
% 0.58/0.63 tff(677,plain,(product(e_1, e_5, e_2) | product(e_1, e_5, e_3) | product(e_1, e_4, e_2) | product(e_1, e_5, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.58/0.63 tff(678,plain,
% 0.58/0.63 (product(e_1, e_5, e_3) | product(e_1, e_4, e_2) | product(e_1, e_5, e_4)),
% 0.58/0.63 inference(unit_resolution,[status(thm)],[677, 152])).
% 0.58/0.63 tff(679,plain,
% 0.58/0.63 (product(e_1, e_5, e_3)),
% 0.58/0.63 inference(unit_resolution,[status(thm)],[678, 26, 4])).
% 0.58/0.63 tff(680,assumption,(product(e_1, e_5, e_3)), introduced(assumption)).
% 0.58/0.63 tff(681,plain,
% 0.58/0.63 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_2) | (~product(e_1, e_5, e_3)) | (~product(e_1, e_2, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_2) | (~product(e_1, e_5, e_3)) | (~product(e_1, e_2, e_3)))),
% 0.58/0.63 inference(rewrite,[status(thm)],[])).
% 0.58/0.63 tff(682,plain,
% 0.58/0.63 ((equalish(e_5, e_2) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_5, e_3))) <=> (equalish(e_5, e_2) | (~product(e_1, e_5, e_3)) | (~product(e_1, e_2, e_3)))),
% 0.58/0.63 inference(rewrite,[status(thm)],[])).
% 0.58/0.63 tff(683,plain,
% 0.58/0.63 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_2) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_5, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_2) | (~product(e_1, e_5, e_3)) | (~product(e_1, e_2, e_3))))),
% 0.58/0.63 inference(monotonicity,[status(thm)],[682])).
% 0.58/0.63 tff(684,plain,
% 0.58/0.63 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_2) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_5, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_2) | (~product(e_1, e_5, e_3)) | (~product(e_1, e_2, e_3)))),
% 0.58/0.63 inference(transitivity,[status(thm)],[683, 681])).
% 0.58/0.63 tff(685,plain,
% 0.58/0.63 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_2) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_5, e_3)))),
% 0.58/0.63 inference(quant_inst,[status(thm)],[])).
% 0.58/0.63 tff(686,plain,
% 0.58/0.63 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_2) | (~product(e_1, e_5, e_3)) | (~product(e_1, e_2, e_3))),
% 0.58/0.63 inference(modus_ponens,[status(thm)],[685, 684])).
% 0.58/0.63 tff(687,plain,
% 0.58/0.63 ($false),
% 0.58/0.63 inference(unit_resolution,[status(thm)],[686, 532, 17, 680, 578])).
% 0.58/0.63 tff(688,plain,((~product(e_1, e_5, e_3)) | (~product(e_1, e_2, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.58/0.63 tff(689,plain,
% 0.58/0.63 (~product(e_1, e_2, e_3)),
% 0.58/0.63 inference(unit_resolution,[status(thm)],[688, 679])).
% 0.58/0.63 tff(690,plain,
% 0.58/0.63 (~product(e_1, e_2, e_4)),
% 0.58/0.63 inference(unit_resolution,[status(thm)],[550, 6])).
% 0.58/0.63 tff(691,plain,
% 0.58/0.63 ((~![X: $i] : product(X, X, X)) | product(e_2, e_2, e_2)),
% 0.58/0.63 inference(quant_inst,[status(thm)],[])).
% 0.58/0.63 tff(692,plain,
% 0.58/0.63 (product(e_2, e_2, e_2)),
% 0.58/0.63 inference(unit_resolution,[status(thm)],[691, 75])).
% 0.58/0.63 tff(693,plain,
% 0.58/0.63 ((~equalish(e_1, e_2)) <=> (~equalish(e_1, e_2))),
% 0.58/0.63 inference(rewrite,[status(thm)],[])).
% 0.58/0.63 tff(694,axiom,(~equalish(e_1, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_2')).
% 0.58/0.64 tff(695,plain,
% 0.58/0.64 (~equalish(e_1, e_2)),
% 0.58/0.64 inference(modus_ponens,[status(thm)],[694, 693])).
% 0.58/0.64 tff(696,plain,
% 0.58/0.64 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_2) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_2) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.58/0.64 inference(rewrite,[status(thm)],[])).
% 0.58/0.64 tff(697,plain,
% 0.58/0.64 ((equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_1, e_2, e_2))) <=> (equalish(e_1, e_2) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.58/0.64 inference(rewrite,[status(thm)],[])).
% 0.58/0.64 tff(698,plain,
% 0.58/0.64 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_1, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_2) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_2))))),
% 0.58/0.64 inference(monotonicity,[status(thm)],[697])).
% 0.58/0.64 tff(699,plain,
% 0.58/0.64 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_1, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_2) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.58/0.64 inference(transitivity,[status(thm)],[698, 696])).
% 0.58/0.64 tff(700,plain,
% 0.58/0.64 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_1, e_2, e_2)))),
% 0.58/0.64 inference(quant_inst,[status(thm)],[])).
% 0.58/0.64 tff(701,plain,
% 0.58/0.64 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_2) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_2))),
% 0.58/0.64 inference(modus_ponens,[status(thm)],[700, 699])).
% 0.58/0.64 tff(702,plain,
% 0.58/0.64 ($false),
% 0.58/0.64 inference(unit_resolution,[status(thm)],[701, 695, 87, 552, 692])).
% 0.58/0.64 tff(703,plain,(~product(e_1, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.58/0.64 tff(704,plain,
% 0.58/0.64 (~product(e_1, e_3, e_4)),
% 0.58/0.64 inference(unit_resolution,[status(thm)],[403, 6])).
% 0.58/0.64 tff(705,plain,
% 0.58/0.64 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_5) | (~product(e_3, e_1, e_3)) | (~product(e_1, e_5, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_5) | (~product(e_3, e_1, e_3)) | (~product(e_1, e_5, e_3)))),
% 0.58/0.64 inference(rewrite,[status(thm)],[])).
% 0.58/0.64 tff(706,plain,
% 0.58/0.64 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_5) | (~product(e_3, e_1, e_3)) | (~product(e_1, e_5, e_3)))),
% 0.58/0.64 inference(quant_inst,[status(thm)],[])).
% 0.58/0.64 tff(707,plain,
% 0.58/0.64 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_5) | (~product(e_3, e_1, e_3)) | (~product(e_1, e_5, e_3))),
% 0.58/0.64 inference(modus_ponens,[status(thm)],[706, 705])).
% 0.58/0.64 tff(708,plain,
% 0.58/0.64 ($false),
% 0.58/0.64 inference(unit_resolution,[status(thm)],[707, 58, 48, 301, 680])).
% 0.58/0.64 tff(709,plain,((~product(e_3, e_1, e_3)) | (~product(e_1, e_5, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.58/0.64 tff(710,plain,
% 0.58/0.64 (~product(e_3, e_1, e_3)),
% 0.58/0.64 inference(unit_resolution,[status(thm)],[709, 679])).
% 0.58/0.64 tff(711,plain,
% 0.58/0.64 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.58/0.64 inference(rewrite,[status(thm)],[])).
% 0.58/0.64 tff(712,plain,
% 0.58/0.64 ((equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2))) <=> (equalish(e_1, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.58/0.64 inference(rewrite,[status(thm)],[])).
% 0.58/0.64 tff(713,plain,
% 0.58/0.64 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_2))))),
% 0.58/0.64 inference(monotonicity,[status(thm)],[712])).
% 0.58/0.64 tff(714,plain,
% 0.58/0.64 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.58/0.64 inference(transitivity,[status(thm)],[713, 711])).
% 0.58/0.64 tff(715,plain,
% 0.58/0.64 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.58/0.64 inference(quant_inst,[status(thm)],[])).
% 0.58/0.64 tff(716,plain,
% 0.58/0.64 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_2))),
% 0.58/0.64 inference(modus_ponens,[status(thm)],[715, 714])).
% 0.58/0.64 tff(717,plain,
% 0.58/0.64 ($false),
% 0.58/0.64 inference(unit_resolution,[status(thm)],[716, 695, 17, 350, 692])).
% 0.58/0.64 tff(718,plain,(~product(e_2, e_1, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.58/0.64 tff(719,plain,
% 0.58/0.64 (product(e_2, e_1, e_3)),
% 0.58/0.64 inference(unit_resolution,[status(thm)],[143, 718])).
% 0.58/0.64 tff(720,plain,
% 0.58/0.64 (product(e_3, e_1, e_3) | (~product(e_1, e_3, e_2))),
% 0.58/0.64 inference(unit_resolution,[status(thm)],[608, 719])).
% 0.58/0.64 tff(721,plain,
% 0.58/0.64 (~product(e_1, e_3, e_2)),
% 0.58/0.64 inference(unit_resolution,[status(thm)],[720, 710])).
% 0.58/0.64 tff(722,plain,
% 0.58/0.64 (product(e_1, e_3, e_5)),
% 0.58/0.64 inference(unit_resolution,[status(thm)],[493, 721, 704, 5])).
% 0.58/0.64 tff(723,plain,
% 0.58/0.64 (((~![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_5)) | (~product(e_1, e_2, e_5)))) <=> ((~![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_5)) | (~product(e_1, e_2, e_5)))),
% 0.58/0.64 inference(rewrite,[status(thm)],[])).
% 0.58/0.64 tff(724,plain,
% 0.58/0.64 ((~![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_5)) | (~product(e_1, e_2, e_5)))),
% 0.58/0.64 inference(quant_inst,[status(thm)],[])).
% 0.58/0.64 tff(725,plain,
% 0.58/0.64 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_3) | (~product(e_1, e_3, e_5)) | (~product(e_1, e_2, e_5))),
% 0.58/0.64 inference(modus_ponens,[status(thm)],[724, 723])).
% 0.58/0.64 tff(726,plain,
% 0.58/0.64 ($false),
% 0.58/0.64 inference(unit_resolution,[status(thm)],[725, 556, 17, 495, 519])).
% 0.58/0.64 tff(727,plain,((~product(e_1, e_2, e_5)) | (~product(e_1, e_3, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.58/0.64 tff(728,plain,
% 0.58/0.64 (~product(e_1, e_2, e_5)),
% 0.58/0.64 inference(unit_resolution,[status(thm)],[727, 722])).
% 0.58/0.64 tff(729,plain,
% 0.58/0.64 ((~![X: $i] : product(X, X, X)) | product(e_5, e_5, e_5)),
% 0.58/0.64 inference(quant_inst,[status(thm)],[])).
% 0.58/0.64 tff(730,plain,
% 0.58/0.64 (product(e_5, e_5, e_5)),
% 0.58/0.64 inference(unit_resolution,[status(thm)],[729, 75])).
% 0.58/0.64 tff(731,plain,
% 0.58/0.64 ((~equalish(e_1, e_5)) <=> (~equalish(e_1, e_5))),
% 0.58/0.64 inference(rewrite,[status(thm)],[])).
% 0.58/0.64 tff(732,axiom,(~equalish(e_1, e_5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_5')).
% 0.58/0.64 tff(733,plain,
% 0.58/0.64 (~equalish(e_1, e_5)),
% 0.58/0.64 inference(modus_ponens,[status(thm)],[732, 731])).
% 0.58/0.64 tff(734,plain,
% 0.58/0.64 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_5) | (~product(e_1, e_5, e_5)) | (~product(e_5, e_5, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_5) | (~product(e_1, e_5, e_5)) | (~product(e_5, e_5, e_5)))),
% 0.58/0.64 inference(rewrite,[status(thm)],[])).
% 0.58/0.64 tff(735,plain,
% 0.58/0.64 ((equalish(e_1, e_5) | (~product(e_5, e_5, e_5)) | (~product(e_1, e_5, e_5))) <=> (equalish(e_1, e_5) | (~product(e_1, e_5, e_5)) | (~product(e_5, e_5, e_5)))),
% 0.58/0.64 inference(rewrite,[status(thm)],[])).
% 0.58/0.64 tff(736,plain,
% 0.58/0.64 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_5) | (~product(e_5, e_5, e_5)) | (~product(e_1, e_5, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_5) | (~product(e_1, e_5, e_5)) | (~product(e_5, e_5, e_5))))),
% 0.58/0.64 inference(monotonicity,[status(thm)],[735])).
% 0.58/0.64 tff(737,plain,
% 0.58/0.64 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_5) | (~product(e_5, e_5, e_5)) | (~product(e_1, e_5, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_5) | (~product(e_1, e_5, e_5)) | (~product(e_5, e_5, e_5)))),
% 0.58/0.64 inference(transitivity,[status(thm)],[736, 734])).
% 0.58/0.64 tff(738,plain,
% 0.58/0.64 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_5) | (~product(e_5, e_5, e_5)) | (~product(e_1, e_5, e_5)))),
% 0.58/0.64 inference(quant_inst,[status(thm)],[])).
% 0.58/0.64 tff(739,plain,
% 0.58/0.64 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_5) | (~product(e_1, e_5, e_5)) | (~product(e_5, e_5, e_5))),
% 0.58/0.64 inference(modus_ponens,[status(thm)],[738, 737])).
% 0.58/0.64 tff(740,plain,
% 0.58/0.64 ($false),
% 0.58/0.64 inference(unit_resolution,[status(thm)],[739, 733, 87, 452, 730])).
% 0.58/0.64 tff(741,plain,(~product(e_1, e_5, e_5)), inference(lemma,lemma(discharge,[]))).
% 0.58/0.64 tff(742,assumption,(~product(e_1, e_5, e_5)), introduced(assumption)).
% 0.58/0.64 tff(743,assumption,(~product(e_1, e_4, e_6)), introduced(assumption)).
% 0.58/0.64 tff(744,assumption,(~product(e_1, e_4, e_4)), introduced(assumption)).
% 0.58/0.64 tff(745,assumption,(~product(e_1, e_6, e_2)), introduced(assumption)).
% 0.58/0.64 tff(746,assumption,(~product(e_1, e_2, e_1)), introduced(assumption)).
% 0.58/0.64 tff(747,assumption,(~product(e_1, e_2, e_2)), introduced(assumption)).
% 0.58/0.64 tff(748,assumption,(~product(e_1, e_2, e_3)), introduced(assumption)).
% 0.58/0.64 tff(749,assumption,(~product(e_1, e_3, e_3)), introduced(assumption)).
% 0.58/0.64 tff(750,assumption,(~product(e_1, e_6, e_4)), introduced(assumption)).
% 0.58/0.64 tff(751,plain,
% 0.58/0.64 ((~equalish(e_3, e_2)) <=> (~equalish(e_3, e_2))),
% 0.58/0.64 inference(rewrite,[status(thm)],[])).
% 0.58/0.64 tff(752,axiom,(~equalish(e_3, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_2')).
% 0.58/0.64 tff(753,plain,
% 0.58/0.64 (~equalish(e_3, e_2)),
% 0.58/0.64 inference(modus_ponens,[status(thm)],[752, 751])).
% 0.58/0.64 tff(754,plain,
% 0.58/0.64 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_1, e_3, e_4)) | (~product(e_1, e_2, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_1, e_3, e_4)) | (~product(e_1, e_2, e_4)))),
% 0.58/0.64 inference(rewrite,[status(thm)],[])).
% 0.58/0.64 tff(755,plain,
% 0.58/0.64 ((equalish(e_3, e_2) | (~product(e_1, e_2, e_4)) | (~product(e_1, e_3, e_4))) <=> (equalish(e_3, e_2) | (~product(e_1, e_3, e_4)) | (~product(e_1, e_2, e_4)))),
% 0.58/0.64 inference(rewrite,[status(thm)],[])).
% 0.58/0.64 tff(756,plain,
% 0.58/0.64 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_1, e_2, e_4)) | (~product(e_1, e_3, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_1, e_3, e_4)) | (~product(e_1, e_2, e_4))))),
% 0.58/0.64 inference(monotonicity,[status(thm)],[755])).
% 0.58/0.64 tff(757,plain,
% 0.58/0.64 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_1, e_2, e_4)) | (~product(e_1, e_3, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_1, e_3, e_4)) | (~product(e_1, e_2, e_4)))),
% 0.58/0.64 inference(transitivity,[status(thm)],[756, 754])).
% 0.58/0.64 tff(758,plain,
% 0.58/0.64 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_1, e_2, e_4)) | (~product(e_1, e_3, e_4)))),
% 0.58/0.64 inference(quant_inst,[status(thm)],[])).
% 0.58/0.64 tff(759,plain,
% 0.58/0.64 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_1, e_3, e_4)) | (~product(e_1, e_2, e_4))),
% 0.58/0.64 inference(modus_ponens,[status(thm)],[758, 757])).
% 0.58/0.64 tff(760,plain,
% 0.58/0.64 ($false),
% 0.58/0.64 inference(unit_resolution,[status(thm)],[759, 753, 17, 395, 542])).
% 0.58/0.64 tff(761,plain,((~product(e_1, e_3, e_4)) | (~product(e_1, e_2, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.58/0.64 tff(762,plain,
% 0.58/0.64 (~product(e_1, e_3, e_4)),
% 0.58/0.64 inference(unit_resolution,[status(thm)],[761, 542])).
% 0.58/0.64 tff(763,plain,
% 0.58/0.64 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_2) | (~product(e_1, e_5, e_4)) | (~product(e_1, e_2, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_2) | (~product(e_1, e_5, e_4)) | (~product(e_1, e_2, e_4)))),
% 0.58/0.64 inference(rewrite,[status(thm)],[])).
% 0.58/0.64 tff(764,plain,
% 0.58/0.64 ((equalish(e_5, e_2) | (~product(e_1, e_2, e_4)) | (~product(e_1, e_5, e_4))) <=> (equalish(e_5, e_2) | (~product(e_1, e_5, e_4)) | (~product(e_1, e_2, e_4)))),
% 0.58/0.64 inference(rewrite,[status(thm)],[])).
% 0.58/0.64 tff(765,plain,
% 0.58/0.64 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_2) | (~product(e_1, e_2, e_4)) | (~product(e_1, e_5, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_2) | (~product(e_1, e_5, e_4)) | (~product(e_1, e_2, e_4))))),
% 0.58/0.64 inference(monotonicity,[status(thm)],[764])).
% 0.58/0.64 tff(766,plain,
% 0.58/0.64 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_2) | (~product(e_1, e_2, e_4)) | (~product(e_1, e_5, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_2) | (~product(e_1, e_5, e_4)) | (~product(e_1, e_2, e_4)))),
% 0.58/0.64 inference(transitivity,[status(thm)],[765, 763])).
% 0.58/0.64 tff(767,plain,
% 0.58/0.64 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_2) | (~product(e_1, e_2, e_4)) | (~product(e_1, e_5, e_4)))),
% 0.58/0.64 inference(quant_inst,[status(thm)],[])).
% 0.58/0.64 tff(768,plain,
% 0.58/0.64 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_2) | (~product(e_1, e_5, e_4)) | (~product(e_1, e_2, e_4))),
% 0.58/0.64 inference(modus_ponens,[status(thm)],[767, 766])).
% 0.58/0.64 tff(769,plain,
% 0.58/0.64 ($false),
% 0.58/0.64 inference(unit_resolution,[status(thm)],[768, 532, 17, 7, 542])).
% 0.58/0.64 tff(770,plain,((~product(e_1, e_5, e_4)) | (~product(e_1, e_2, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.58/0.64 tff(771,plain,
% 0.58/0.64 (~product(e_1, e_5, e_4)),
% 0.58/0.64 inference(unit_resolution,[status(thm)],[770, 542])).
% 0.58/0.64 tff(772,plain,
% 0.58/0.64 ((~equalish(e_4, e_5)) <=> (~equalish(e_4, e_5))),
% 0.58/0.64 inference(rewrite,[status(thm)],[])).
% 0.58/0.64 tff(773,axiom,(~equalish(e_4, e_5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_5')).
% 0.58/0.64 tff(774,plain,
% 0.58/0.64 (~equalish(e_4, e_5)),
% 0.58/0.64 inference(modus_ponens,[status(thm)],[773, 772])).
% 0.58/0.64 tff(775,plain,
% 0.58/0.64 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_5) | (~product(e_1, e_4, e_3)) | (~product(e_1, e_5, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_5) | (~product(e_1, e_4, e_3)) | (~product(e_1, e_5, e_3)))),
% 0.58/0.64 inference(rewrite,[status(thm)],[])).
% 0.58/0.64 tff(776,plain,
% 0.58/0.64 ((equalish(e_4, e_5) | (~product(e_1, e_5, e_3)) | (~product(e_1, e_4, e_3))) <=> (equalish(e_4, e_5) | (~product(e_1, e_4, e_3)) | (~product(e_1, e_5, e_3)))),
% 0.58/0.64 inference(rewrite,[status(thm)],[])).
% 0.58/0.64 tff(777,plain,
% 0.58/0.64 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_5) | (~product(e_1, e_5, e_3)) | (~product(e_1, e_4, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_5) | (~product(e_1, e_4, e_3)) | (~product(e_1, e_5, e_3))))),
% 0.58/0.64 inference(monotonicity,[status(thm)],[776])).
% 0.58/0.64 tff(778,plain,
% 0.58/0.64 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_5) | (~product(e_1, e_5, e_3)) | (~product(e_1, e_4, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_5) | (~product(e_1, e_4, e_3)) | (~product(e_1, e_5, e_3)))),
% 0.58/0.64 inference(transitivity,[status(thm)],[777, 775])).
% 0.58/0.64 tff(779,plain,
% 0.58/0.64 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_5) | (~product(e_1, e_5, e_3)) | (~product(e_1, e_4, e_3)))),
% 0.58/0.64 inference(quant_inst,[status(thm)],[])).
% 0.58/0.64 tff(780,plain,
% 0.58/0.64 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_5) | (~product(e_1, e_4, e_3)) | (~product(e_1, e_5, e_3))),
% 0.58/0.64 inference(modus_ponens,[status(thm)],[779, 778])).
% 0.58/0.64 tff(781,plain,
% 0.58/0.64 ($false),
% 0.58/0.64 inference(unit_resolution,[status(thm)],[780, 774, 17, 680, 197])).
% 0.58/0.64 tff(782,plain,((~product(e_1, e_4, e_3)) | (~product(e_1, e_5, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.58/0.64 tff(783,plain,
% 0.58/0.65 (~product(e_1, e_4, e_3)),
% 0.58/0.65 inference(unit_resolution,[status(thm)],[782, 680])).
% 0.58/0.65 tff(784,plain,
% 0.58/0.65 (product(e_1, e_4, e_5)),
% 0.58/0.65 inference(unit_resolution,[status(thm)],[286, 783, 744, 743, 4])).
% 0.58/0.65 tff(785,plain,
% 0.58/0.65 (~product(e_1, e_6, e_5)),
% 0.58/0.65 inference(unit_resolution,[status(thm)],[298, 784])).
% 0.58/0.65 tff(786,plain,
% 0.58/0.65 (~product(e_1, e_3, e_5)),
% 0.58/0.65 inference(unit_resolution,[status(thm)],[506, 784])).
% 0.58/0.65 tff(787,plain,
% 0.58/0.65 (product(e_1, e_3, e_6)),
% 0.58/0.65 inference(unit_resolution,[status(thm)],[492, 786, 749, 406, 405])).
% 0.58/0.65 tff(788,plain,
% 0.58/0.65 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_6) | (~product(e_1, e_6, e_6)) | (~product(e_1, e_3, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_6) | (~product(e_1, e_6, e_6)) | (~product(e_1, e_3, e_6)))),
% 0.58/0.65 inference(rewrite,[status(thm)],[])).
% 0.58/0.65 tff(789,plain,
% 0.58/0.65 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_6) | (~product(e_1, e_6, e_6)) | (~product(e_1, e_3, e_6)))),
% 0.58/0.65 inference(quant_inst,[status(thm)],[])).
% 0.58/0.65 tff(790,plain,
% 0.58/0.65 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_6) | (~product(e_1, e_6, e_6)) | (~product(e_1, e_3, e_6))),
% 0.58/0.65 inference(modus_ponens,[status(thm)],[789, 788])).
% 0.58/0.65 tff(791,plain,
% 0.58/0.65 ($false),
% 0.58/0.65 inference(unit_resolution,[status(thm)],[790, 398, 17, 157, 407])).
% 0.58/0.65 tff(792,plain,((~product(e_1, e_3, e_6)) | (~product(e_1, e_6, e_6))), inference(lemma,lemma(discharge,[]))).
% 0.58/0.65 tff(793,plain,
% 0.58/0.65 (~product(e_1, e_6, e_6)),
% 0.58/0.65 inference(unit_resolution,[status(thm)],[792, 787])).
% 0.58/0.65 tff(794,plain,
% 0.58/0.65 (product(e_1, e_6, e_3)),
% 0.58/0.65 inference(unit_resolution,[status(thm)],[391, 793, 750, 785, 745])).
% 0.58/0.65 tff(795,plain,
% 0.58/0.65 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_6, e_5) | (~product(e_1, e_5, e_3)) | (~product(e_1, e_6, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_6, e_5) | (~product(e_1, e_5, e_3)) | (~product(e_1, e_6, e_3)))),
% 0.58/0.65 inference(rewrite,[status(thm)],[])).
% 0.58/0.65 tff(796,plain,
% 0.58/0.65 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_6, e_5) | (~product(e_1, e_5, e_3)) | (~product(e_1, e_6, e_3)))),
% 0.58/0.65 inference(quant_inst,[status(thm)],[])).
% 0.58/0.65 tff(797,plain,
% 0.58/0.65 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_6, e_5) | (~product(e_1, e_5, e_3)) | (~product(e_1, e_6, e_3))),
% 0.58/0.65 inference(modus_ponens,[status(thm)],[796, 795])).
% 0.58/0.65 tff(798,plain,
% 0.58/0.65 ($false),
% 0.58/0.65 inference(unit_resolution,[status(thm)],[797, 160, 17, 680, 794])).
% 0.58/0.65 tff(799,plain,((~product(e_1, e_5, e_3)) | product(e_1, e_6, e_4) | product(e_1, e_6, e_2) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_4) | product(e_1, e_4, e_4) | product(e_1, e_4, e_6) | product(e_1, e_4, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.58/0.65 tff(800,plain,
% 0.58/0.65 (~product(e_1, e_5, e_3)),
% 0.58/0.65 inference(unit_resolution,[status(thm)],[799, 762, 745, 749, 406, 750, 744, 743, 4])).
% 0.58/0.65 tff(801,plain,
% 0.58/0.65 (product(e_1, e_5, e_6)),
% 0.58/0.65 inference(unit_resolution,[status(thm)],[450, 800, 771, 154, 742])).
% 0.58/0.65 tff(802,plain,
% 0.58/0.65 (~product(e_1, e_3, e_6)),
% 0.58/0.65 inference(unit_resolution,[status(thm)],[425, 801])).
% 0.58/0.65 tff(803,plain,
% 0.58/0.65 (product(e_1, e_3, e_5)),
% 0.58/0.65 inference(unit_resolution,[status(thm)],[492, 802, 749, 406, 762])).
% 0.58/0.65 tff(804,plain,
% 0.58/0.65 (~product(e_1, e_4, e_5)),
% 0.58/0.65 inference(unit_resolution,[status(thm)],[506, 803])).
% 0.58/0.65 tff(805,plain,
% 0.58/0.65 (product(e_1, e_4, e_3)),
% 0.58/0.65 inference(unit_resolution,[status(thm)],[286, 804, 744, 743, 4])).
% 0.58/0.65 tff(806,plain,
% 0.58/0.65 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_6, e_4) | (~product(e_1, e_4, e_3)) | (~product(e_1, e_6, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_6, e_4) | (~product(e_1, e_4, e_3)) | (~product(e_1, e_6, e_3)))),
% 0.58/0.65 inference(rewrite,[status(thm)],[])).
% 0.58/0.65 tff(807,plain,
% 0.58/0.65 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_6, e_4) | (~product(e_1, e_4, e_3)) | (~product(e_1, e_6, e_3)))),
% 0.58/0.65 inference(quant_inst,[status(thm)],[])).
% 0.58/0.65 tff(808,plain,
% 0.58/0.65 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_6, e_4) | (~product(e_1, e_4, e_3)) | (~product(e_1, e_6, e_3))),
% 0.58/0.65 inference(modus_ponens,[status(thm)],[807, 806])).
% 0.58/0.65 tff(809,plain,
% 0.58/0.65 ($false),
% 0.58/0.65 inference(unit_resolution,[status(thm)],[808, 635, 17, 197, 300])).
% 0.58/0.65 tff(810,plain,((~product(e_1, e_6, e_3)) | (~product(e_1, e_4, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.58/0.65 tff(811,plain,
% 0.58/0.65 (~product(e_1, e_6, e_3)),
% 0.58/0.65 inference(unit_resolution,[status(thm)],[810, 805])).
% 0.58/0.65 tff(812,plain,
% 0.58/0.65 (~product(e_1, e_6, e_6)),
% 0.58/0.65 inference(unit_resolution,[status(thm)],[168, 801])).
% 0.58/0.65 tff(813,plain,
% 0.58/0.65 (product(e_1, e_6, e_5)),
% 0.58/0.65 inference(unit_resolution,[status(thm)],[391, 812, 750, 811, 745])).
% 0.58/0.65 tff(814,plain,
% 0.58/0.65 ((~equalish(e_6, e_3)) <=> (~equalish(e_6, e_3))),
% 0.58/0.65 inference(rewrite,[status(thm)],[])).
% 0.58/0.65 tff(815,axiom,(~equalish(e_6, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_6_is_not_e_3')).
% 0.58/0.65 tff(816,plain,
% 0.58/0.65 (~equalish(e_6, e_3)),
% 0.58/0.65 inference(modus_ponens,[status(thm)],[815, 814])).
% 0.58/0.65 tff(817,plain,
% 0.58/0.65 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_6, e_3) | (~product(e_1, e_6, e_5)) | (~product(e_1, e_3, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_6, e_3) | (~product(e_1, e_6, e_5)) | (~product(e_1, e_3, e_5)))),
% 0.58/0.65 inference(rewrite,[status(thm)],[])).
% 0.58/0.65 tff(818,plain,
% 0.58/0.65 ((equalish(e_6, e_3) | (~product(e_1, e_3, e_5)) | (~product(e_1, e_6, e_5))) <=> (equalish(e_6, e_3) | (~product(e_1, e_6, e_5)) | (~product(e_1, e_3, e_5)))),
% 0.58/0.65 inference(rewrite,[status(thm)],[])).
% 0.58/0.65 tff(819,plain,
% 0.58/0.65 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_6, e_3) | (~product(e_1, e_3, e_5)) | (~product(e_1, e_6, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_6, e_3) | (~product(e_1, e_6, e_5)) | (~product(e_1, e_3, e_5))))),
% 0.58/0.65 inference(monotonicity,[status(thm)],[818])).
% 0.58/0.65 tff(820,plain,
% 0.58/0.65 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_6, e_3) | (~product(e_1, e_3, e_5)) | (~product(e_1, e_6, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_6, e_3) | (~product(e_1, e_6, e_5)) | (~product(e_1, e_3, e_5)))),
% 0.58/0.65 inference(transitivity,[status(thm)],[819, 817])).
% 0.58/0.65 tff(821,plain,
% 0.58/0.65 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_6, e_3) | (~product(e_1, e_3, e_5)) | (~product(e_1, e_6, e_5)))),
% 0.58/0.65 inference(quant_inst,[status(thm)],[])).
% 0.58/0.65 tff(822,plain,
% 0.58/0.65 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_6, e_3) | (~product(e_1, e_6, e_5)) | (~product(e_1, e_3, e_5))),
% 0.58/0.65 inference(modus_ponens,[status(thm)],[821, 820])).
% 0.58/0.65 tff(823,plain,
% 0.58/0.65 ($false),
% 0.58/0.65 inference(unit_resolution,[status(thm)],[822, 816, 17, 813, 803])).
% 0.58/0.65 tff(824,plain,((~product(e_1, e_2, e_4)) | product(e_1, e_6, e_4) | product(e_1, e_6, e_2) | product(e_1, e_4, e_4) | product(e_1, e_4, e_6) | product(e_1, e_4, e_2) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_5, e_2) | product(e_1, e_5, e_5)), inference(lemma,lemma(discharge,[]))).
% 0.58/0.65 tff(825,plain,
% 0.58/0.65 (~product(e_1, e_2, e_4)),
% 0.58/0.65 inference(unit_resolution,[status(thm)],[824, 750, 745, 744, 743, 4, 749, 406, 154, 742])).
% 0.58/0.65 tff(826,assumption,(~product(e_1, e_2, e_4)), introduced(assumption)).
% 0.58/0.65 tff(827,plain,
% 0.58/0.65 (~product(e_1, e_2, e_5)),
% 0.58/0.65 inference(unit_resolution,[status(thm)],[527, 290])).
% 0.58/0.65 tff(828,plain,
% 0.58/0.65 (product(e_1, e_2, e_6)),
% 0.58/0.65 inference(unit_resolution,[status(thm)],[575, 827, 748, 826, 747, 746])).
% 0.58/0.65 tff(829,plain,
% 0.58/0.65 (~product(e_1, e_6, e_5)),
% 0.58/0.65 inference(unit_resolution,[status(thm)],[298, 290])).
% 0.58/0.65 tff(830,plain,
% 0.58/0.65 (~product(e_1, e_3, e_5)),
% 0.58/0.65 inference(unit_resolution,[status(thm)],[506, 290])).
% 0.58/0.65 tff(831,plain,
% 0.58/0.65 (((~![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_6)) | (~product(e_1, e_2, e_6)))) <=> ((~![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_6)) | (~product(e_1, e_2, e_6)))),
% 0.58/0.65 inference(rewrite,[status(thm)],[])).
% 0.58/0.65 tff(832,plain,
% 0.58/0.65 ((~![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_6)) | (~product(e_1, e_2, e_6)))),
% 0.58/0.65 inference(quant_inst,[status(thm)],[])).
% 0.58/0.65 tff(833,plain,
% 0.58/0.65 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_3) | (~product(e_1, e_3, e_6)) | (~product(e_1, e_2, e_6))),
% 0.58/0.65 inference(modus_ponens,[status(thm)],[832, 831])).
% 0.58/0.65 tff(834,plain,
% 0.58/0.65 ($false),
% 0.58/0.65 inference(unit_resolution,[status(thm)],[833, 556, 17, 407, 529])).
% 0.58/0.65 tff(835,plain,((~product(e_1, e_2, e_6)) | (~product(e_1, e_3, e_6))), inference(lemma,lemma(discharge,[]))).
% 0.58/0.65 tff(836,plain,
% 0.58/0.65 (~product(e_1, e_3, e_6)),
% 0.58/0.65 inference(unit_resolution,[status(thm)],[835, 828])).
% 0.58/0.65 tff(837,plain,
% 0.58/0.65 (product(e_1, e_3, e_4)),
% 0.58/0.65 inference(unit_resolution,[status(thm)],[492, 836, 749, 406, 830])).
% 0.58/0.65 tff(838,plain,
% 0.58/0.65 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_5) | (~product(e_1, e_3, e_4)) | (~product(e_1, e_5, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_5) | (~product(e_1, e_3, e_4)) | (~product(e_1, e_5, e_4)))),
% 0.58/0.65 inference(rewrite,[status(thm)],[])).
% 0.58/0.65 tff(839,plain,
% 0.58/0.65 ((equalish(e_3, e_5) | (~product(e_1, e_5, e_4)) | (~product(e_1, e_3, e_4))) <=> (equalish(e_3, e_5) | (~product(e_1, e_3, e_4)) | (~product(e_1, e_5, e_4)))),
% 0.58/0.65 inference(rewrite,[status(thm)],[])).
% 0.58/0.65 tff(840,plain,
% 0.58/0.65 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_5) | (~product(e_1, e_5, e_4)) | (~product(e_1, e_3, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_5) | (~product(e_1, e_3, e_4)) | (~product(e_1, e_5, e_4))))),
% 0.58/0.65 inference(monotonicity,[status(thm)],[839])).
% 0.58/0.65 tff(841,plain,
% 0.58/0.65 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_5) | (~product(e_1, e_5, e_4)) | (~product(e_1, e_3, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_5) | (~product(e_1, e_3, e_4)) | (~product(e_1, e_5, e_4)))),
% 0.58/0.65 inference(transitivity,[status(thm)],[840, 838])).
% 0.58/0.65 tff(842,plain,
% 0.58/0.65 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_5) | (~product(e_1, e_5, e_4)) | (~product(e_1, e_3, e_4)))),
% 0.58/0.65 inference(quant_inst,[status(thm)],[])).
% 0.58/0.65 tff(843,plain,
% 0.58/0.65 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_5) | (~product(e_1, e_3, e_4)) | (~product(e_1, e_5, e_4))),
% 0.58/0.65 inference(modus_ponens,[status(thm)],[842, 841])).
% 0.58/0.65 tff(844,plain,
% 0.58/0.65 ($false),
% 0.58/0.65 inference(unit_resolution,[status(thm)],[843, 420, 17, 7, 395])).
% 0.58/0.65 tff(845,plain,((~product(e_1, e_3, e_4)) | (~product(e_1, e_5, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.58/0.65 tff(846,plain,
% 0.58/0.65 (~product(e_1, e_5, e_4)),
% 0.58/0.65 inference(unit_resolution,[status(thm)],[845, 837])).
% 0.58/0.65 tff(847,plain,
% 0.58/0.65 (~product(e_1, e_5, e_6)),
% 0.58/0.65 inference(unit_resolution,[status(thm)],[540, 828])).
% 0.58/0.65 tff(848,plain,
% 0.58/0.65 (product(e_1, e_5, e_3)),
% 0.58/0.65 inference(unit_resolution,[status(thm)],[450, 847, 846, 154, 742])).
% 0.58/0.65 tff(849,plain,
% 0.58/0.65 ($false),
% 0.58/0.65 inference(unit_resolution,[status(thm)],[797, 160, 17, 680, 300])).
% 0.58/0.65 tff(850,plain,((~product(e_1, e_6, e_3)) | (~product(e_1, e_5, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.58/0.65 tff(851,plain,
% 0.58/0.65 (~product(e_1, e_6, e_3)),
% 0.58/0.65 inference(unit_resolution,[status(thm)],[850, 848])).
% 0.58/0.65 tff(852,plain,
% 0.58/0.65 (product(e_1, e_6, e_6)),
% 0.58/0.65 inference(unit_resolution,[status(thm)],[391, 851, 750, 829, 745])).
% 0.58/0.65 tff(853,plain,
% 0.58/0.65 ((~equalish(e_6, e_2)) <=> (~equalish(e_6, e_2))),
% 0.58/0.65 inference(rewrite,[status(thm)],[])).
% 0.58/0.65 tff(854,axiom,(~equalish(e_6, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_6_is_not_e_2')).
% 0.58/0.65 tff(855,plain,
% 0.58/0.65 (~equalish(e_6, e_2)),
% 0.58/0.65 inference(modus_ponens,[status(thm)],[854, 853])).
% 0.58/0.65 tff(856,plain,
% 0.58/0.65 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_6, e_2) | (~product(e_1, e_6, e_6)) | (~product(e_1, e_2, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_6, e_2) | (~product(e_1, e_6, e_6)) | (~product(e_1, e_2, e_6)))),
% 0.58/0.65 inference(rewrite,[status(thm)],[])).
% 0.58/0.65 tff(857,plain,
% 0.58/0.65 ((equalish(e_6, e_2) | (~product(e_1, e_2, e_6)) | (~product(e_1, e_6, e_6))) <=> (equalish(e_6, e_2) | (~product(e_1, e_6, e_6)) | (~product(e_1, e_2, e_6)))),
% 0.58/0.65 inference(rewrite,[status(thm)],[])).
% 0.58/0.65 tff(858,plain,
% 0.58/0.65 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_6, e_2) | (~product(e_1, e_2, e_6)) | (~product(e_1, e_6, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_6, e_2) | (~product(e_1, e_6, e_6)) | (~product(e_1, e_2, e_6))))),
% 0.58/0.65 inference(monotonicity,[status(thm)],[857])).
% 0.58/0.65 tff(859,plain,
% 0.58/0.65 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_6, e_2) | (~product(e_1, e_2, e_6)) | (~product(e_1, e_6, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_6, e_2) | (~product(e_1, e_6, e_6)) | (~product(e_1, e_2, e_6)))),
% 0.58/0.65 inference(transitivity,[status(thm)],[858, 856])).
% 0.58/0.65 tff(860,plain,
% 0.58/0.65 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_6, e_2) | (~product(e_1, e_2, e_6)) | (~product(e_1, e_6, e_6)))),
% 0.58/0.65 inference(quant_inst,[status(thm)],[])).
% 0.58/0.65 tff(861,plain,
% 0.58/0.65 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_6, e_2) | (~product(e_1, e_6, e_6)) | (~product(e_1, e_2, e_6))),
% 0.58/0.65 inference(modus_ponens,[status(thm)],[860, 859])).
% 0.58/0.65 tff(862,plain,
% 0.58/0.65 ($false),
% 0.58/0.65 inference(unit_resolution,[status(thm)],[861, 855, 17, 852, 828])).
% 0.58/0.65 tff(863,plain,((~product(e_1, e_4, e_5)) | product(e_1, e_6, e_4) | product(e_1, e_6, e_2) | product(e_1, e_5, e_2) | product(e_1, e_5, e_5) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_2, e_3) | product(e_1, e_2, e_4) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.58/0.65 tff(864,plain,
% 0.58/0.65 (~product(e_1, e_4, e_5)),
% 0.58/0.65 inference(unit_resolution,[status(thm)],[863, 750, 745, 154, 742, 749, 406, 748, 825, 747, 746])).
% 0.58/0.65 tff(865,plain,
% 0.58/0.65 (product(e_1, e_4, e_3)),
% 0.58/0.65 inference(unit_resolution,[status(thm)],[286, 864, 744, 743, 4])).
% 0.58/0.65 tff(866,plain,
% 0.58/0.65 (~product(e_1, e_6, e_3)),
% 0.58/0.65 inference(unit_resolution,[status(thm)],[810, 865])).
% 0.58/0.65 tff(867,plain,
% 0.58/0.65 (~product(e_1, e_2, e_5)),
% 0.58/0.65 inference(unit_resolution,[status(thm)],[727, 495])).
% 0.58/0.65 tff(868,plain,
% 0.58/0.65 (product(e_1, e_2, e_6)),
% 0.58/0.65 inference(unit_resolution,[status(thm)],[575, 867, 748, 826, 747, 746])).
% 0.58/0.65 tff(869,assumption,(~product(e_1, e_6, e_3)), introduced(assumption)).
% 0.58/0.65 tff(870,plain,
% 0.58/0.65 ($false),
% 0.58/0.65 inference(unit_resolution,[status(thm)],[822, 816, 17, 289, 495])).
% 0.58/0.65 tff(871,plain,((~product(e_1, e_6, e_5)) | (~product(e_1, e_3, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.58/0.65 tff(872,plain,
% 0.58/0.65 (~product(e_1, e_6, e_5)),
% 0.58/0.65 inference(unit_resolution,[status(thm)],[871, 495])).
% 0.58/0.65 tff(873,plain,
% 0.58/0.65 (product(e_1, e_6, e_6)),
% 0.58/0.65 inference(unit_resolution,[status(thm)],[391, 872, 750, 869, 745])).
% 0.58/0.65 tff(874,plain,
% 0.58/0.65 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_6) | (~product(e_1, e_6, e_6)) | (~product(e_1, e_2, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_6) | (~product(e_1, e_6, e_6)) | (~product(e_1, e_2, e_6)))),
% 0.58/0.65 inference(rewrite,[status(thm)],[])).
% 0.58/0.65 tff(875,plain,
% 0.58/0.65 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_6) | (~product(e_1, e_6, e_6)) | (~product(e_1, e_2, e_6)))),
% 0.58/0.65 inference(quant_inst,[status(thm)],[])).
% 0.58/0.65 tff(876,plain,
% 0.58/0.65 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_6) | (~product(e_1, e_6, e_6)) | (~product(e_1, e_2, e_6))),
% 0.58/0.65 inference(modus_ponens,[status(thm)],[875, 874])).
% 0.58/0.65 tff(877,plain,
% 0.58/0.65 ($false),
% 0.58/0.65 inference(unit_resolution,[status(thm)],[876, 545, 17, 873, 868])).
% 0.58/0.65 tff(878,plain,((~product(e_1, e_3, e_5)) | product(e_1, e_2, e_3) | product(e_1, e_2, e_4) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | product(e_1, e_6, e_4) | product(e_1, e_6, e_3) | product(e_1, e_6, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.58/0.65 tff(879,plain,
% 0.58/0.65 (~product(e_1, e_3, e_5)),
% 0.58/0.65 inference(unit_resolution,[status(thm)],[878, 825, 748, 747, 746, 750, 866, 745])).
% 0.58/0.65 tff(880,plain,
% 0.58/0.65 (~product(e_1, e_5, e_3)),
% 0.58/0.65 inference(unit_resolution,[status(thm)],[782, 865])).
% 0.58/0.65 tff(881,assumption,(~product(e_1, e_3, e_5)), introduced(assumption)).
% 0.58/0.66 tff(882,plain,
% 0.58/0.66 (~product(e_1, e_3, e_6)),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[792, 157])).
% 0.58/0.66 tff(883,plain,
% 0.58/0.66 (product(e_1, e_3, e_4)),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[492, 882, 749, 406, 881])).
% 0.58/0.66 tff(884,plain,
% 0.58/0.66 (~product(e_1, e_5, e_6)),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[168, 157])).
% 0.58/0.66 tff(885,plain,
% 0.58/0.66 (product(e_1, e_5, e_4)),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[450, 884, 155, 154, 742])).
% 0.58/0.66 tff(886,plain,
% 0.58/0.66 ($false),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[845, 885, 883])).
% 0.58/0.66 tff(887,plain,((~product(e_1, e_6, e_6)) | product(e_1, e_5, e_3) | product(e_1, e_5, e_2) | product(e_1, e_5, e_5) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_5)), inference(lemma,lemma(discharge,[]))).
% 0.58/0.66 tff(888,plain,
% 0.58/0.66 (~product(e_1, e_6, e_6)),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[887, 880, 154, 742, 749, 406, 879])).
% 0.58/0.66 tff(889,plain,
% 0.58/0.66 (product(e_1, e_6, e_5)),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[391, 888, 750, 866, 745])).
% 0.58/0.66 tff(890,plain,
% 0.58/0.66 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_6) | (~product(e_1, e_6, e_5)) | (~product(e_1, e_2, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_6) | (~product(e_1, e_6, e_5)) | (~product(e_1, e_2, e_5)))),
% 0.58/0.66 inference(rewrite,[status(thm)],[])).
% 0.58/0.66 tff(891,plain,
% 0.58/0.66 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_6) | (~product(e_1, e_6, e_5)) | (~product(e_1, e_2, e_5)))),
% 0.58/0.66 inference(quant_inst,[status(thm)],[])).
% 0.58/0.66 tff(892,plain,
% 0.58/0.66 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_6) | (~product(e_1, e_6, e_5)) | (~product(e_1, e_2, e_5))),
% 0.58/0.66 inference(modus_ponens,[status(thm)],[891, 890])).
% 0.58/0.66 tff(893,plain,
% 0.58/0.66 ($false),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[892, 545, 17, 289, 519])).
% 0.58/0.66 tff(894,plain,((~product(e_1, e_2, e_5)) | (~product(e_1, e_6, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.58/0.66 tff(895,plain,
% 0.58/0.66 (~product(e_1, e_2, e_5)),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[894, 889])).
% 0.58/0.66 tff(896,plain,
% 0.58/0.66 (product(e_1, e_2, e_6)),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[575, 895, 748, 825, 747, 746])).
% 0.58/0.66 tff(897,plain,
% 0.58/0.66 (~product(e_1, e_3, e_6)),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[835, 896])).
% 0.58/0.66 tff(898,plain,
% 0.58/0.66 (product(e_1, e_3, e_4)),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[492, 897, 749, 406, 879])).
% 0.58/0.66 tff(899,plain,
% 0.58/0.66 (~product(e_1, e_5, e_6)),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[540, 896])).
% 0.58/0.66 tff(900,plain,
% 0.58/0.66 (product(e_1, e_5, e_4)),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[450, 899, 880, 154, 742])).
% 0.58/0.66 tff(901,plain,
% 0.58/0.66 ($false),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[845, 900, 898])).
% 0.58/0.66 tff(902,plain,(product(e_1, e_6, e_4) | product(e_1, e_5, e_2) | product(e_1, e_5, e_5) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | product(e_1, e_6, e_2) | product(e_1, e_4, e_4) | product(e_1, e_4, e_6) | product(e_1, e_4, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.58/0.66 tff(903,plain,
% 0.58/0.66 (product(e_1, e_6, e_4)),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[902, 742, 154, 749, 406, 748, 747, 746, 745, 744, 743, 4])).
% 0.58/0.66 tff(904,plain,
% 0.58/0.66 (~product(e_1, e_5, e_4)),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[25, 903])).
% 0.58/0.66 tff(905,plain,
% 0.58/0.66 (~product(e_1, e_3, e_4)),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[403, 903])).
% 0.58/0.66 tff(906,plain,
% 0.58/0.66 (~product(e_1, e_2, e_4)),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[550, 903])).
% 0.58/0.66 tff(907,plain,
% 0.58/0.66 (product(e_1, e_5, e_3)),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[450, 426, 153, 154, 742])).
% 0.58/0.66 tff(908,plain,
% 0.58/0.66 (~product(e_1, e_4, e_3)),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[782, 907])).
% 0.58/0.66 tff(909,plain,
% 0.58/0.66 (~product(e_1, e_2, e_6)),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[835, 407])).
% 0.58/0.66 tff(910,plain,
% 0.58/0.66 (product(e_1, e_2, e_5)),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[575, 909, 748, 826, 747, 746])).
% 0.58/0.66 tff(911,plain,
% 0.58/0.66 (~product(e_1, e_4, e_5)),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[527, 910])).
% 0.58/0.66 tff(912,plain,
% 0.58/0.66 ($false),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[286, 911, 908, 744, 743, 4])).
% 0.58/0.66 tff(913,plain,((~product(e_1, e_3, e_6)) | product(e_1, e_4, e_4) | product(e_1, e_4, e_6) | product(e_1, e_4, e_2) | product(e_1, e_2, e_3) | product(e_1, e_2, e_4) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | product(e_1, e_5, e_4) | product(e_1, e_5, e_2) | product(e_1, e_5, e_5)), inference(lemma,lemma(discharge,[]))).
% 0.58/0.66 tff(914,plain,
% 0.58/0.66 (~product(e_1, e_3, e_6)),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[913, 906, 743, 4, 748, 744, 747, 746, 904, 154, 742])).
% 0.58/0.66 tff(915,plain,
% 0.58/0.66 (product(e_1, e_3, e_5)),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[492, 914, 749, 406, 905])).
% 0.58/0.66 tff(916,plain,
% 0.58/0.66 (~product(e_1, e_4, e_5)),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[506, 915])).
% 0.58/0.66 tff(917,plain,
% 0.58/0.66 (product(e_1, e_4, e_3)),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[286, 916, 744, 743, 4])).
% 0.58/0.66 tff(918,plain,
% 0.58/0.66 (~product(e_1, e_5, e_3)),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[782, 917])).
% 0.58/0.66 tff(919,plain,
% 0.58/0.66 (~product(e_1, e_2, e_5)),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[727, 915])).
% 0.58/0.66 tff(920,plain,
% 0.58/0.66 (product(e_1, e_2, e_6)),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[575, 919, 748, 906, 747, 746])).
% 0.58/0.66 tff(921,plain,
% 0.58/0.66 (~product(e_1, e_5, e_6)),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[540, 920])).
% 0.58/0.66 tff(922,plain,
% 0.58/0.66 ($false),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[450, 921, 918, 904, 154, 742])).
% 0.58/0.66 tff(923,plain,(product(e_1, e_5, e_5) | product(e_1, e_5, e_2) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | product(e_1, e_4, e_4) | product(e_1, e_4, e_6) | product(e_1, e_4, e_2) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_6, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.58/0.66 tff(924,plain,
% 0.58/0.66 (product(e_1, e_5, e_5) | product(e_1, e_5, e_2) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_4, e_4) | product(e_1, e_4, e_6) | product(e_1, e_4, e_2) | product(e_1, e_3, e_2)),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[923, 568, 474, 374])).
% 0.58/0.66 tff(925,plain,
% 0.58/0.66 (product(e_1, e_5, e_5) | product(e_1, e_5, e_2) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_4, e_6) | product(e_1, e_4, e_2) | product(e_1, e_3, e_2)),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[924, 196])).
% 0.58/0.66 tff(926,plain,
% 0.58/0.66 (product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_4, e_6) | product(e_1, e_4, e_2) | product(e_1, e_3, e_2)),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[925, 152, 741])).
% 0.58/0.66 tff(927,plain,
% 0.58/0.66 (product(e_1, e_4, e_6)),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[926, 721, 703, 689, 4])).
% 0.58/0.66 tff(928,plain,
% 0.58/0.66 (~product(e_1, e_2, e_6)),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[667, 927])).
% 0.58/0.66 tff(929,plain,
% 0.58/0.66 ($false),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[576, 928, 728, 703, 690, 689])).
% 0.58/0.66 tff(930,plain,((~product(e_1, e_6, e_4)) | product(e_1, e_4, e_2) | product(e_1, e_3, e_6)), inference(lemma,lemma(discharge,[]))).
% 0.58/0.66 tff(931,plain,
% 0.58/0.66 (~product(e_1, e_6, e_4)),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[930, 5, 4])).
% 0.58/0.66 tff(932,plain,
% 0.58/0.66 ((~![X: $i] : product(X, X, X)) | product(e_6, e_6, e_6)),
% 0.58/0.66 inference(quant_inst,[status(thm)],[])).
% 0.58/0.66 tff(933,plain,
% 0.58/0.66 (product(e_6, e_6, e_6)),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[932, 75])).
% 0.58/0.66 tff(934,plain,
% 0.58/0.66 ((~equalish(e_1, e_6)) <=> (~equalish(e_1, e_6))),
% 0.58/0.66 inference(rewrite,[status(thm)],[])).
% 0.58/0.66 tff(935,axiom,(~equalish(e_1, e_6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_6')).
% 0.58/0.66 tff(936,plain,
% 0.58/0.66 (~equalish(e_1, e_6)),
% 0.58/0.66 inference(modus_ponens,[status(thm)],[935, 934])).
% 0.58/0.66 tff(937,plain,
% 0.58/0.66 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_6) | (~product(e_1, e_6, e_6)) | (~product(e_6, e_6, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_6) | (~product(e_1, e_6, e_6)) | (~product(e_6, e_6, e_6)))),
% 0.58/0.66 inference(rewrite,[status(thm)],[])).
% 0.58/0.66 tff(938,plain,
% 0.58/0.66 ((equalish(e_1, e_6) | (~product(e_6, e_6, e_6)) | (~product(e_1, e_6, e_6))) <=> (equalish(e_1, e_6) | (~product(e_1, e_6, e_6)) | (~product(e_6, e_6, e_6)))),
% 0.58/0.66 inference(rewrite,[status(thm)],[])).
% 0.58/0.66 tff(939,plain,
% 0.58/0.66 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_6) | (~product(e_6, e_6, e_6)) | (~product(e_1, e_6, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_6) | (~product(e_1, e_6, e_6)) | (~product(e_6, e_6, e_6))))),
% 0.58/0.66 inference(monotonicity,[status(thm)],[938])).
% 0.58/0.66 tff(940,plain,
% 0.58/0.66 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_6) | (~product(e_6, e_6, e_6)) | (~product(e_1, e_6, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_6) | (~product(e_1, e_6, e_6)) | (~product(e_6, e_6, e_6)))),
% 0.58/0.66 inference(transitivity,[status(thm)],[939, 937])).
% 0.58/0.66 tff(941,plain,
% 0.58/0.66 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_6) | (~product(e_6, e_6, e_6)) | (~product(e_1, e_6, e_6)))),
% 0.58/0.66 inference(quant_inst,[status(thm)],[])).
% 0.58/0.66 tff(942,plain,
% 0.58/0.66 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_6) | (~product(e_1, e_6, e_6)) | (~product(e_6, e_6, e_6))),
% 0.58/0.66 inference(modus_ponens,[status(thm)],[941, 940])).
% 0.58/0.66 tff(943,plain,
% 0.58/0.66 ($false),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[942, 936, 87, 157, 933])).
% 0.58/0.66 tff(944,plain,(~product(e_1, e_6, e_6)), inference(lemma,lemma(discharge,[]))).
% 0.58/0.66 tff(945,plain,
% 0.58/0.66 (product(e_1, e_6, e_5) | product(e_1, e_6, e_4)),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[393, 944])).
% 0.58/0.66 tff(946,plain,
% 0.58/0.66 (product(e_1, e_6, e_5)),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[945, 931])).
% 0.58/0.66 tff(947,plain,
% 0.58/0.66 (~product(e_1, e_4, e_5)),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[298, 946])).
% 0.58/0.66 tff(948,plain,
% 0.58/0.66 (product(e_1, e_4, e_6)),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[287, 947, 4])).
% 0.58/0.66 tff(949,plain,
% 0.58/0.66 (~product(e_1, e_2, e_6)),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[667, 948])).
% 0.58/0.66 tff(950,plain,
% 0.58/0.66 (~product(e_1, e_2, e_5)),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[894, 946])).
% 0.58/0.66 tff(951,plain,
% 0.58/0.66 (~product(e_1, e_3, e_5)),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[871, 946])).
% 0.58/0.66 tff(952,plain,
% 0.58/0.66 (product(e_1, e_3, e_4)),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[493, 406, 951, 5])).
% 0.58/0.66 tff(953,plain,
% 0.58/0.66 (~product(e_1, e_2, e_4)),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[761, 952])).
% 0.58/0.66 tff(954,plain,
% 0.58/0.66 (~product(e_1, e_5, e_6)),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[181, 948])).
% 0.58/0.66 tff(955,assumption,(~product(e_1, e_6, e_1)), introduced(assumption)).
% 0.58/0.66 tff(956,assumption,(~product(e_1, e_5, e_6)), introduced(assumption)).
% 0.58/0.66 tff(957,assumption,(~product(e_1, e_4, e_1)), introduced(assumption)).
% 0.58/0.66 tff(958,assumption,(~product(e_1, e_4, e_3)), introduced(assumption)).
% 0.58/0.66 tff(959,assumption,(~product(e_1, e_5, e_1)), introduced(assumption)).
% 0.58/0.66 tff(960,assumption,(~product(e_1, e_3, e_1)), introduced(assumption)).
% 0.58/0.66 tff(961,plain,
% 0.58/0.66 (~product(e_1, e_4, e_5)),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[298, 289])).
% 0.58/0.66 tff(962,plain,
% 0.58/0.66 (product(e_1, e_4, e_6) | product(e_1, e_4, e_5) | product(e_1, e_4, e_4) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2)),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[285, 135, 279, 129, 957])).
% 0.58/0.66 tff(963,plain,
% 0.58/0.66 (product(e_1, e_4, e_4)),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[962, 961, 743, 958, 4])).
% 0.58/0.66 tff(964,plain,
% 0.58/0.66 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_4) | (~product(e_1, e_4, e_4)) | (~product(e_1, e_5, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_4) | (~product(e_1, e_4, e_4)) | (~product(e_1, e_5, e_4)))),
% 0.58/0.66 inference(rewrite,[status(thm)],[])).
% 0.58/0.66 tff(965,plain,
% 0.58/0.66 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_4) | (~product(e_1, e_4, e_4)) | (~product(e_1, e_5, e_4)))),
% 0.58/0.66 inference(quant_inst,[status(thm)],[])).
% 0.58/0.66 tff(966,plain,
% 0.58/0.66 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_4) | (~product(e_1, e_4, e_4)) | (~product(e_1, e_5, e_4))),
% 0.58/0.66 inference(modus_ponens,[status(thm)],[965, 964])).
% 0.58/0.66 tff(967,plain,
% 0.58/0.66 ($false),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[966, 173, 17, 185, 7])).
% 0.58/0.66 tff(968,plain,((~product(e_1, e_5, e_4)) | (~product(e_1, e_4, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.58/0.66 tff(969,plain,
% 0.58/0.66 (~product(e_1, e_5, e_4)),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[968, 963])).
% 0.58/0.66 tff(970,plain,
% 0.58/0.66 (product(e_1, e_5, e_6) | product(e_1, e_5, e_5) | product(e_1, e_5, e_4) | product(e_1, e_5, e_3) | product(e_1, e_5, e_2)),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[449, 135, 443, 129, 959])).
% 0.58/0.66 tff(971,plain,
% 0.58/0.66 (product(e_1, e_5, e_5)),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[970, 969, 956, 155, 154])).
% 0.58/0.66 tff(972,plain,
% 0.58/0.66 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_6) | (~product(e_1, e_6, e_5)) | (~product(e_1, e_5, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_6) | (~product(e_1, e_6, e_5)) | (~product(e_1, e_5, e_5)))),
% 0.58/0.66 inference(rewrite,[status(thm)],[])).
% 0.58/0.66 tff(973,plain,
% 0.58/0.66 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_6) | (~product(e_1, e_6, e_5)) | (~product(e_1, e_5, e_5)))),
% 0.58/0.66 inference(quant_inst,[status(thm)],[])).
% 0.58/0.66 tff(974,plain,
% 0.58/0.66 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_6) | (~product(e_1, e_6, e_5)) | (~product(e_1, e_5, e_5))),
% 0.58/0.66 inference(modus_ponens,[status(thm)],[973, 972])).
% 0.58/0.66 tff(975,plain,
% 0.58/0.66 ($false),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[974, 20, 17, 971, 289])).
% 0.58/0.66 tff(976,plain,((~product(e_1, e_6, e_5)) | product(e_1, e_5, e_6) | product(e_1, e_5, e_3) | product(e_1, e_5, e_2) | product(e_1, e_5, e_1) | product(e_1, e_4, e_6) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.58/0.66 tff(977,plain,
% 0.58/0.66 (~product(e_1, e_6, e_5)),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[976, 743, 155, 154, 959, 956, 958, 4, 957])).
% 0.58/0.66 tff(978,plain,
% 0.58/0.66 (product(e_1, e_6, e_6) | product(e_1, e_6, e_5) | product(e_1, e_6, e_4) | product(e_1, e_6, e_3) | product(e_1, e_6, e_2)),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[390, 135, 384, 129, 955])).
% 0.58/0.66 tff(979,plain,
% 0.58/0.66 (product(e_1, e_6, e_6)),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[978, 977, 750, 869, 745])).
% 0.58/0.66 tff(980,plain,
% 0.58/0.66 (~product(e_1, e_3, e_6)),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[792, 979])).
% 0.58/0.66 tff(981,plain,
% 0.58/0.66 (product(e_1, e_3, e_6) | product(e_1, e_3, e_5) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3) | product(e_1, e_3, e_1)),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[491, 135, 253, 129, 406])).
% 0.58/0.66 tff(982,plain,
% 0.58/0.66 (product(e_1, e_3, e_4)),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[981, 980, 881, 749, 960])).
% 0.58/0.66 tff(983,plain,
% 0.58/0.66 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_3) | (~product(e_1, e_3, e_4)) | (~product(e_1, e_4, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_3) | (~product(e_1, e_3, e_4)) | (~product(e_1, e_4, e_4)))),
% 0.58/0.66 inference(rewrite,[status(thm)],[])).
% 0.58/0.66 tff(984,plain,
% 0.58/0.66 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_3) | (~product(e_1, e_3, e_4)) | (~product(e_1, e_4, e_4)))),
% 0.58/0.66 inference(quant_inst,[status(thm)],[])).
% 0.58/0.66 tff(985,plain,
% 0.58/0.66 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_3) | (~product(e_1, e_3, e_4)) | (~product(e_1, e_4, e_4))),
% 0.58/0.66 inference(modus_ponens,[status(thm)],[984, 983])).
% 0.58/0.66 tff(986,plain,
% 0.58/0.66 ($false),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[985, 498, 17, 185, 395])).
% 0.58/0.66 tff(987,plain,((~product(e_1, e_4, e_4)) | (~product(e_1, e_3, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.58/0.66 tff(988,plain,
% 0.58/0.66 (~product(e_1, e_4, e_4)),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[987, 982])).
% 0.58/0.66 tff(989,plain,
% 0.58/0.66 (product(e_1, e_4, e_5)),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[962, 988, 743, 958, 4])).
% 0.58/0.66 tff(990,plain,
% 0.58/0.66 (~product(e_1, e_5, e_5)),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[457, 989])).
% 0.58/0.66 tff(991,plain,
% 0.58/0.66 (product(e_1, e_5, e_4)),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[970, 990, 956, 155, 154])).
% 0.58/0.66 tff(992,plain,
% 0.58/0.66 ($false),
% 0.58/0.67 inference(unit_resolution,[status(thm)],[843, 420, 17, 991, 982])).
% 0.58/0.67 tff(993,plain,(product(e_1, e_4, e_6) | product(e_1, e_5, e_6) | product(e_1, e_5, e_3) | product(e_1, e_5, e_2) | product(e_1, e_5, e_1) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_1) | product(e_1, e_3, e_5) | product(e_1, e_3, e_3) | product(e_1, e_3, e_1) | product(e_1, e_3, e_2) | product(e_1, e_6, e_4) | product(e_1, e_6, e_3) | product(e_1, e_6, e_2) | product(e_1, e_6, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.58/0.67 tff(994,plain,
% 0.58/0.67 (product(e_1, e_4, e_6)),
% 0.58/0.67 inference(unit_resolution,[status(thm)],[993, 960, 155, 154, 959, 958, 4, 957, 881, 749, 956, 406, 750, 869, 745, 955])).
% 0.58/0.67 tff(995,plain,
% 0.58/0.67 (~product(e_1, e_6, e_6)),
% 0.58/0.67 inference(unit_resolution,[status(thm)],[643, 994])).
% 0.58/0.67 tff(996,plain,
% 0.58/0.67 (product(e_1, e_6, e_5)),
% 0.58/0.67 inference(unit_resolution,[status(thm)],[978, 995, 750, 869, 745])).
% 0.58/0.67 tff(997,plain,
% 0.58/0.67 (~product(e_1, e_3, e_6)),
% 0.58/0.67 inference(unit_resolution,[status(thm)],[415, 994])).
% 0.58/0.67 tff(998,plain,
% 0.58/0.67 (product(e_1, e_3, e_4)),
% 0.58/0.67 inference(unit_resolution,[status(thm)],[981, 997, 881, 749, 960])).
% 0.58/0.67 tff(999,plain,
% 0.58/0.67 (~product(e_1, e_5, e_4)),
% 0.58/0.67 inference(unit_resolution,[status(thm)],[845, 998])).
% 0.58/0.67 tff(1000,plain,
% 0.58/0.67 (product(e_1, e_5, e_5)),
% 0.58/0.67 inference(unit_resolution,[status(thm)],[970, 999, 956, 155, 154])).
% 0.58/0.67 tff(1001,plain,
% 0.58/0.67 ($false),
% 0.58/0.67 inference(unit_resolution,[status(thm)],[974, 20, 17, 1000, 996])).
% 0.58/0.67 tff(1002,plain,(product(e_1, e_3, e_1) | product(e_1, e_5, e_6) | product(e_1, e_5, e_3) | product(e_1, e_5, e_2) | product(e_1, e_5, e_1) | product(e_1, e_3, e_5) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_6, e_4) | product(e_1, e_6, e_3) | product(e_1, e_6, e_2) | product(e_1, e_6, e_1) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.58/0.67 tff(1003,plain,
% 0.58/0.67 (product(e_1, e_5, e_6) | product(e_1, e_5, e_3) | product(e_1, e_5, e_2) | product(e_1, e_3, e_5) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_6, e_4) | product(e_1, e_6, e_3) | product(e_1, e_6, e_2) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2)),
% 0.58/0.67 inference(unit_resolution,[status(thm)],[1002, 485, 276, 440, 381])).
% 0.58/0.67 tff(1004,plain,
% 0.58/0.67 (product(e_1, e_5, e_6) | product(e_1, e_5, e_3) | product(e_1, e_5, e_2) | product(e_1, e_3, e_5) | product(e_1, e_3, e_2) | product(e_1, e_6, e_4) | product(e_1, e_6, e_3) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2)),
% 0.58/0.67 inference(unit_resolution,[status(thm)],[1003, 474, 374])).
% 0.58/0.67 tff(1005,plain,
% 0.58/0.67 (product(e_1, e_5, e_6) | product(e_1, e_5, e_3) | product(e_1, e_5, e_2) | product(e_1, e_3, e_5) | product(e_1, e_3, e_2) | product(e_1, e_6, e_4) | product(e_1, e_4, e_2)),
% 0.58/0.67 inference(unit_resolution,[status(thm)],[1004, 348, 269])).
% 0.58/0.67 tff(1006,plain,
% 0.58/0.67 (product(e_1, e_5, e_6) | product(e_1, e_5, e_3) | product(e_1, e_3, e_5) | product(e_1, e_3, e_2) | product(e_1, e_6, e_4) | product(e_1, e_4, e_2)),
% 0.58/0.67 inference(unit_resolution,[status(thm)],[1005, 152])).
% 0.58/0.67 tff(1007,plain,
% 0.58/0.67 (product(e_1, e_5, e_3)),
% 0.58/0.67 inference(unit_resolution,[status(thm)],[1006, 406, 4, 931, 954, 951])).
% 0.58/0.67 tff(1008,plain,
% 0.58/0.67 (~product(e_1, e_2, e_3)),
% 0.58/0.67 inference(unit_resolution,[status(thm)],[688, 1007])).
% 0.58/0.67 tff(1009,plain,
% 0.58/0.67 ($false),
% 0.58/0.67 inference(unit_resolution,[status(thm)],[576, 1008, 953, 703, 950, 949])).
% 0.58/0.67 tff(1010,plain,(product(e_1, e_3, e_2) | product(e_1, e_4, e_2) | product(e_1, e_3, e_6)), inference(lemma,lemma(discharge,[]))).
% 0.58/0.67 tff(1011,plain,
% 0.58/0.67 (product(e_1, e_3, e_2)),
% 0.58/0.67 inference(unit_resolution,[status(thm)],[1010, 5, 4])).
% 0.58/0.67 tff(1012,plain,
% 0.58/0.67 (product(e_3, e_1, e_3)),
% 0.58/0.67 inference(unit_resolution,[status(thm)],[720, 1011])).
% 0.58/0.67 tff(1013,plain,
% 0.58/0.67 (~product(e_1, e_5, e_3)),
% 0.58/0.67 inference(unit_resolution,[status(thm)],[709, 1012])).
% 0.58/0.67 tff(1014,plain,
% 0.58/0.67 (product(e_1, e_5, e_4)),
% 0.58/0.67 inference(unit_resolution,[status(thm)],[678, 1013, 4])).
% 0.58/0.67 tff(1015,plain,
% 0.58/0.67 (~product(e_1, e_2, e_4)),
% 0.58/0.67 inference(unit_resolution,[status(thm)],[770, 1014])).
% 0.58/0.67 tff(1016,plain,
% 0.58/0.67 (product(e_1, e_2, e_3)),
% 0.58/0.67 inference(unit_resolution,[status(thm)],[576, 1015, 703, 950, 949])).
% 0.58/0.67 tff(1017,plain,
% 0.58/0.67 (~product(e_3, e_1, e_2)),
% 0.58/0.67 inference(unit_resolution,[status(thm)],[593, 1016])).
% 0.58/0.67 tff(1018,plain,
% 0.58/0.67 ($false),
% 0.58/0.67 inference(unit_resolution,[status(thm)],[598, 1017, 1016, 1012])).
% 0.58/0.67 tff(1019,plain,(product(e_1, e_3, e_6) | product(e_1, e_4, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.58/0.67 tff(1020,plain,
% 0.58/0.67 (product(e_1, e_3, e_6)),
% 0.58/0.67 inference(unit_resolution,[status(thm)],[1019, 4])).
% 0.58/0.67 tff(1021,plain,
% 0.58/0.67 (~product(e_1, e_2, e_6)),
% 0.58/0.67 inference(unit_resolution,[status(thm)],[835, 1020])).
% 0.58/0.67 tff(1022,plain,
% 0.58/0.67 (~product(e_1, e_4, e_6)),
% 0.58/0.67 inference(unit_resolution,[status(thm)],[415, 1020])).
% 0.58/0.67 tff(1023,plain,
% 0.58/0.67 (product(e_1, e_4, e_5)),
% 0.58/0.67 inference(unit_resolution,[status(thm)],[287, 1022, 4])).
% 0.58/0.67 tff(1024,plain,
% 0.58/0.67 (~product(e_1, e_2, e_5)),
% 0.58/0.67 inference(unit_resolution,[status(thm)],[527, 1023])).
% 0.58/0.67 tff(1025,plain,
% 0.58/0.67 (~product(e_1, e_6, e_5)),
% 0.58/0.67 inference(unit_resolution,[status(thm)],[298, 1023])).
% 0.58/0.67 tff(1026,plain,
% 0.58/0.67 (product(e_1, e_6, e_4)),
% 0.58/0.67 inference(unit_resolution,[status(thm)],[945, 1025])).
% 0.58/0.67 tff(1027,plain,
% 0.58/0.67 (~product(e_1, e_2, e_4)),
% 0.58/0.67 inference(unit_resolution,[status(thm)],[550, 1026])).
% 0.58/0.67 tff(1028,plain,
% 0.58/0.67 (product(e_1, e_2, e_3)),
% 0.58/0.67 inference(unit_resolution,[status(thm)],[576, 1027, 703, 1024, 1021])).
% 0.58/0.67 tff(1029,plain,
% 0.58/0.67 (~product(e_1, e_5, e_4)),
% 0.58/0.67 inference(unit_resolution,[status(thm)],[25, 1026])).
% 0.58/0.67 tff(1030,plain,
% 0.58/0.67 (product(e_1, e_5, e_3)),
% 0.58/0.67 inference(unit_resolution,[status(thm)],[678, 1029, 4])).
% 0.58/0.67 tff(1031,plain,
% 0.58/0.67 ($false),
% 0.58/0.67 inference(unit_resolution,[status(thm)],[688, 1030, 1028])).
% 0.58/0.67 tff(1032,plain,(product(e_1, e_4, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.58/0.67 tff(1033,plain,
% 0.58/0.67 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_4) | (~product(e_1, e_4, e_2)) | (~product(e_2, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_4) | (~product(e_1, e_4, e_2)) | (~product(e_2, e_1, e_3)))),
% 0.58/0.67 inference(rewrite,[status(thm)],[])).
% 0.58/0.67 tff(1034,plain,
% 0.58/0.67 ((product(e_3, e_1, e_4) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_4, e_2))) <=> (product(e_3, e_1, e_4) | (~product(e_1, e_4, e_2)) | (~product(e_2, e_1, e_3)))),
% 0.58/0.67 inference(rewrite,[status(thm)],[])).
% 0.58/0.67 tff(1035,plain,
% 0.58/0.67 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_4) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_4, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_4) | (~product(e_1, e_4, e_2)) | (~product(e_2, e_1, e_3))))),
% 0.58/0.67 inference(monotonicity,[status(thm)],[1034])).
% 0.58/0.67 tff(1036,plain,
% 0.58/0.67 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_4) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_4, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_4) | (~product(e_1, e_4, e_2)) | (~product(e_2, e_1, e_3)))),
% 0.58/0.67 inference(transitivity,[status(thm)],[1035, 1033])).
% 0.58/0.67 tff(1037,plain,
% 0.58/0.67 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_4) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_4, e_2)))),
% 0.58/0.67 inference(quant_inst,[status(thm)],[])).
% 0.58/0.67 tff(1038,plain,
% 0.58/0.67 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_4) | (~product(e_1, e_4, e_2)) | (~product(e_2, e_1, e_3))),
% 0.58/0.67 inference(modus_ponens,[status(thm)],[1037, 1036])).
% 0.58/0.67 tff(1039,plain,
% 0.58/0.67 (product(e_3, e_1, e_4) | (~product(e_1, e_4, e_2)) | (~product(e_2, e_1, e_3))),
% 0.58/0.67 inference(unit_resolution,[status(thm)],[1038, 58])).
% 0.58/0.67 tff(1040,plain,
% 0.58/0.67 (product(e_3, e_1, e_4) | (~product(e_1, e_4, e_2))),
% 0.58/0.67 inference(unit_resolution,[status(thm)],[1039, 719])).
% 0.58/0.67 tff(1041,plain,
% 0.58/0.67 (product(e_3, e_1, e_4)),
% 0.58/0.67 inference(unit_resolution,[status(thm)],[1040, 1032])).
% 0.58/0.67 tff(1042,plain,
% 0.58/0.67 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_1, e_5) | (~product(e_1, e_5, e_3)) | (~product(e_3, e_1, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_4, e_1, e_5) | (~product(e_1, e_5, e_3)) | (~product(e_3, e_1, e_4)))),
% 0.58/0.67 inference(rewrite,[status(thm)],[])).
% 0.58/0.67 tff(1043,plain,
% 0.58/0.67 ((product(e_4, e_1, e_5) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_5, e_3))) <=> (product(e_4, e_1, e_5) | (~product(e_1, e_5, e_3)) | (~product(e_3, e_1, e_4)))),
% 0.58/0.67 inference(rewrite,[status(thm)],[])).
% 0.58/0.67 tff(1044,plain,
% 0.58/0.67 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_1, e_5) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_5, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_1, e_5) | (~product(e_1, e_5, e_3)) | (~product(e_3, e_1, e_4))))),
% 0.58/0.67 inference(monotonicity,[status(thm)],[1043])).
% 0.58/0.67 tff(1045,plain,
% 0.58/0.67 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_1, e_5) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_5, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_4, e_1, e_5) | (~product(e_1, e_5, e_3)) | (~product(e_3, e_1, e_4)))),
% 0.58/0.67 inference(transitivity,[status(thm)],[1044, 1042])).
% 0.58/0.67 tff(1046,plain,
% 0.58/0.67 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_1, e_5) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_5, e_3)))),
% 0.58/0.67 inference(quant_inst,[status(thm)],[])).
% 0.58/0.67 tff(1047,plain,
% 0.58/0.67 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_4, e_1, e_5) | (~product(e_1, e_5, e_3)) | (~product(e_3, e_1, e_4))),
% 0.58/0.67 inference(modus_ponens,[status(thm)],[1046, 1045])).
% 0.58/0.67 tff(1048,plain,
% 0.58/0.67 ($false),
% 0.58/0.67 inference(unit_resolution,[status(thm)],[1047, 58, 234, 3, 680])).
% 0.58/0.67 tff(1049,plain,(product(e_4, e_1, e_5) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_5, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.58/0.67 tff(1050,plain,
% 0.58/0.67 (product(e_4, e_1, e_5) | (~product(e_1, e_5, e_3))),
% 0.58/0.67 inference(unit_resolution,[status(thm)],[1049, 1041])).
% 0.58/0.67 tff(1051,plain,
% 0.58/0.67 (~product(e_1, e_5, e_3)),
% 0.58/0.67 inference(unit_resolution,[status(thm)],[1050, 3])).
% 0.58/0.67 tff(1052,assumption,(product(e_4, e_1, e_1)), introduced(assumption)).
% 0.58/0.67 tff(1053,plain,
% 0.58/0.67 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_6) | (~product(e_1, e_6, e_4)) | (~product(e_4, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_6) | (~product(e_1, e_6, e_4)) | (~product(e_4, e_1, e_1)))),
% 0.58/0.67 inference(rewrite,[status(thm)],[])).
% 0.58/0.67 tff(1054,plain,
% 0.58/0.67 ((product(e_1, e_1, e_6) | (~product(e_4, e_1, e_1)) | (~product(e_1, e_6, e_4))) <=> (product(e_1, e_1, e_6) | (~product(e_1, e_6, e_4)) | (~product(e_4, e_1, e_1)))),
% 0.58/0.67 inference(rewrite,[status(thm)],[])).
% 0.58/0.67 tff(1055,plain,
% 0.58/0.67 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_6) | (~product(e_4, e_1, e_1)) | (~product(e_1, e_6, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_6) | (~product(e_1, e_6, e_4)) | (~product(e_4, e_1, e_1))))),
% 0.58/0.67 inference(monotonicity,[status(thm)],[1054])).
% 0.58/0.67 tff(1056,plain,
% 0.58/0.67 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_6) | (~product(e_4, e_1, e_1)) | (~product(e_1, e_6, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_6) | (~product(e_1, e_6, e_4)) | (~product(e_4, e_1, e_1)))),
% 0.58/0.67 inference(transitivity,[status(thm)],[1055, 1053])).
% 0.58/0.67 tff(1057,plain,
% 0.58/0.67 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_6) | (~product(e_4, e_1, e_1)) | (~product(e_1, e_6, e_4)))),
% 0.58/0.67 inference(quant_inst,[status(thm)],[])).
% 0.58/0.67 tff(1058,plain,
% 0.58/0.67 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_6) | (~product(e_1, e_6, e_4)) | (~product(e_4, e_1, e_1))),
% 0.58/0.67 inference(modus_ponens,[status(thm)],[1057, 1056])).
% 0.58/0.67 tff(1059,plain,
% 0.58/0.67 ($false),
% 0.58/0.67 inference(unit_resolution,[status(thm)],[1058, 58, 314, 1052, 6])).
% 0.58/0.67 tff(1060,plain,((~product(e_4, e_1, e_1)) | (~product(e_1, e_6, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.58/0.67 tff(1061,plain,
% 0.58/0.67 (~product(e_4, e_1, e_1)),
% 0.58/0.67 inference(unit_resolution,[status(thm)],[1060, 6])).
% 0.58/0.67 tff(1062,assumption,(product(e_4, e_1, e_2)), introduced(assumption)).
% 0.58/0.67 tff(1063,plain,
% 0.58/0.67 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_6) | (~product(e_1, e_6, e_4)) | (~product(e_4, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_6) | (~product(e_1, e_6, e_4)) | (~product(e_4, e_1, e_2)))),
% 0.58/0.67 inference(rewrite,[status(thm)],[])).
% 0.58/0.67 tff(1064,plain,
% 0.58/0.67 ((product(e_2, e_1, e_6) | (~product(e_4, e_1, e_2)) | (~product(e_1, e_6, e_4))) <=> (product(e_2, e_1, e_6) | (~product(e_1, e_6, e_4)) | (~product(e_4, e_1, e_2)))),
% 0.58/0.67 inference(rewrite,[status(thm)],[])).
% 0.58/0.67 tff(1065,plain,
% 0.58/0.67 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_6) | (~product(e_4, e_1, e_2)) | (~product(e_1, e_6, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_6) | (~product(e_1, e_6, e_4)) | (~product(e_4, e_1, e_2))))),
% 0.58/0.67 inference(monotonicity,[status(thm)],[1064])).
% 0.58/0.67 tff(1066,plain,
% 0.58/0.67 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_6) | (~product(e_4, e_1, e_2)) | (~product(e_1, e_6, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_6) | (~product(e_1, e_6, e_4)) | (~product(e_4, e_1, e_2)))),
% 0.58/0.67 inference(transitivity,[status(thm)],[1065, 1063])).
% 0.58/0.67 tff(1067,plain,
% 0.58/0.67 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_6) | (~product(e_4, e_1, e_2)) | (~product(e_1, e_6, e_4)))),
% 0.58/0.67 inference(quant_inst,[status(thm)],[])).
% 0.58/0.67 tff(1068,plain,
% 0.58/0.67 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_6) | (~product(e_1, e_6, e_4)) | (~product(e_4, e_1, e_2))),
% 0.58/0.67 inference(modus_ponens,[status(thm)],[1067, 1066])).
% 0.58/0.67 tff(1069,plain,
% 0.58/0.67 ($false),
% 0.58/0.67 inference(unit_resolution,[status(thm)],[1068, 58, 105, 1062, 6])).
% 0.58/0.67 tff(1070,plain,((~product(e_4, e_1, e_2)) | (~product(e_1, e_6, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.58/0.67 tff(1071,plain,
% 0.58/0.67 (~product(e_4, e_1, e_2)),
% 0.58/0.67 inference(unit_resolution,[status(thm)],[1070, 6])).
% 0.58/0.67 tff(1072,assumption,(product(e_4, e_1, e_3)), introduced(assumption)).
% 0.58/0.67 tff(1073,plain,
% 0.58/0.67 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_6) | (~product(e_1, e_6, e_4)) | (~product(e_4, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_6) | (~product(e_1, e_6, e_4)) | (~product(e_4, e_1, e_3)))),
% 0.58/0.67 inference(rewrite,[status(thm)],[])).
% 0.58/0.67 tff(1074,plain,
% 0.58/0.67 ((product(e_3, e_1, e_6) | (~product(e_4, e_1, e_3)) | (~product(e_1, e_6, e_4))) <=> (product(e_3, e_1, e_6) | (~product(e_1, e_6, e_4)) | (~product(e_4, e_1, e_3)))),
% 0.58/0.67 inference(rewrite,[status(thm)],[])).
% 0.58/0.67 tff(1075,plain,
% 0.58/0.67 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_6) | (~product(e_4, e_1, e_3)) | (~product(e_1, e_6, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_6) | (~product(e_1, e_6, e_4)) | (~product(e_4, e_1, e_3))))),
% 0.58/0.67 inference(monotonicity,[status(thm)],[1074])).
% 0.58/0.67 tff(1076,plain,
% 0.58/0.67 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_6) | (~product(e_4, e_1, e_3)) | (~product(e_1, e_6, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_6) | (~product(e_1, e_6, e_4)) | (~product(e_4, e_1, e_3)))),
% 0.58/0.67 inference(transitivity,[status(thm)],[1075, 1073])).
% 0.58/0.67 tff(1077,plain,
% 0.58/0.67 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_6) | (~product(e_4, e_1, e_3)) | (~product(e_1, e_6, e_4)))),
% 0.58/0.67 inference(quant_inst,[status(thm)],[])).
% 0.58/0.67 tff(1078,plain,
% 0.58/0.67 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_6) | (~product(e_1, e_6, e_4)) | (~product(e_4, e_1, e_3))),
% 0.58/0.67 inference(modus_ponens,[status(thm)],[1077, 1076])).
% 0.58/0.67 tff(1079,plain,
% 0.58/0.67 ($false),
% 0.58/0.67 inference(unit_resolution,[status(thm)],[1078, 58, 250, 1072, 6])).
% 0.58/0.67 tff(1080,plain,((~product(e_4, e_1, e_3)) | (~product(e_1, e_6, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.58/0.67 tff(1081,plain,
% 0.58/0.67 (~product(e_4, e_1, e_3)),
% 0.58/0.67 inference(unit_resolution,[status(thm)],[1080, 6])).
% 0.58/0.67 tff(1082,plain,
% 0.58/0.67 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_1, e_6) | (~group_element(e_1)) | product(e_4, e_1, e_5) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_4, e_1, e_6) | (~group_element(e_1)) | product(e_4, e_1, e_5) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | (~group_element(e_4)))),
% 0.58/0.67 inference(rewrite,[status(thm)],[])).
% 0.58/0.67 tff(1083,plain,
% 0.58/0.67 ((product(e_4, e_1, e_6) | product(e_4, e_1, e_5) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_4))) <=> (product(e_4, e_1, e_6) | (~group_element(e_1)) | product(e_4, e_1, e_5) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | (~group_element(e_4)))),
% 0.58/0.68 inference(rewrite,[status(thm)],[])).
% 0.58/0.68 tff(1084,plain,
% 0.58/0.68 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_1, e_6) | product(e_4, e_1, e_5) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_1, e_6) | (~group_element(e_1)) | product(e_4, e_1, e_5) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | (~group_element(e_4))))),
% 0.58/0.68 inference(monotonicity,[status(thm)],[1083])).
% 0.58/0.68 tff(1085,plain,
% 0.58/0.68 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_1, e_6) | product(e_4, e_1, e_5) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_4, e_1, e_6) | (~group_element(e_1)) | product(e_4, e_1, e_5) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | (~group_element(e_4)))),
% 0.58/0.68 inference(transitivity,[status(thm)],[1084, 1082])).
% 0.58/0.68 tff(1086,plain,
% 0.58/0.68 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_1, e_6) | product(e_4, e_1, e_5) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_4)))),
% 0.58/0.68 inference(quant_inst,[status(thm)],[])).
% 0.58/0.68 tff(1087,plain,
% 0.58/0.68 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_4, e_1, e_6) | (~group_element(e_1)) | product(e_4, e_1, e_5) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | (~group_element(e_4))),
% 0.58/0.68 inference(modus_ponens,[status(thm)],[1086, 1085])).
% 0.58/0.68 tff(1088,plain,
% 0.58/0.68 (product(e_4, e_1, e_5) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1)),
% 0.58/0.68 inference(unit_resolution,[status(thm)],[1087, 135, 279, 129, 330])).
% 0.58/0.68 tff(1089,plain,
% 0.58/0.68 (product(e_4, e_1, e_5) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1)),
% 0.58/0.68 inference(unit_resolution,[status(thm)],[1088, 233])).
% 0.58/0.68 tff(1090,plain,
% 0.58/0.68 ($false),
% 0.58/0.68 inference(unit_resolution,[status(thm)],[1089, 1081, 1071, 3, 1061])).
% 0.58/0.68 tff(1091,plain,((~product(e_1, e_6, e_4)) | product(e_4, e_1, e_5)), inference(lemma,lemma(discharge,[]))).
% 0.58/0.68 tff(1092,plain,
% 0.58/0.68 (~product(e_1, e_6, e_4)),
% 0.58/0.68 inference(unit_resolution,[status(thm)],[1091, 3])).
% 0.58/0.68 tff(1093,plain,
% 0.58/0.68 (product(e_1, e_6, e_5)),
% 0.58/0.68 inference(unit_resolution,[status(thm)],[945, 1092])).
% 0.58/0.68 tff(1094,plain,
% 0.58/0.68 (~product(e_1, e_2, e_5)),
% 0.58/0.68 inference(unit_resolution,[status(thm)],[894, 1093])).
% 0.58/0.68 tff(1095,assumption,(~product(e_1, e_2, e_5)), introduced(assumption)).
% 0.58/0.68 tff(1096,assumption,(product(e_4, e_5, e_5)), introduced(assumption)).
% 0.58/0.68 tff(1097,plain,
% 0.58/0.68 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_5) | (~product(e_4, e_5, e_5)) | (~product(e_5, e_5, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_5) | (~product(e_4, e_5, e_5)) | (~product(e_5, e_5, e_5)))),
% 0.58/0.68 inference(rewrite,[status(thm)],[])).
% 0.58/0.68 tff(1098,plain,
% 0.58/0.68 ((equalish(e_4, e_5) | (~product(e_5, e_5, e_5)) | (~product(e_4, e_5, e_5))) <=> (equalish(e_4, e_5) | (~product(e_4, e_5, e_5)) | (~product(e_5, e_5, e_5)))),
% 0.58/0.68 inference(rewrite,[status(thm)],[])).
% 0.58/0.68 tff(1099,plain,
% 0.58/0.68 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_5) | (~product(e_5, e_5, e_5)) | (~product(e_4, e_5, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_5) | (~product(e_4, e_5, e_5)) | (~product(e_5, e_5, e_5))))),
% 0.58/0.68 inference(monotonicity,[status(thm)],[1098])).
% 0.58/0.68 tff(1100,plain,
% 0.58/0.68 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_5) | (~product(e_5, e_5, e_5)) | (~product(e_4, e_5, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_5) | (~product(e_4, e_5, e_5)) | (~product(e_5, e_5, e_5)))),
% 0.58/0.68 inference(transitivity,[status(thm)],[1099, 1097])).
% 0.58/0.68 tff(1101,plain,
% 0.58/0.68 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_5) | (~product(e_5, e_5, e_5)) | (~product(e_4, e_5, e_5)))),
% 0.58/0.68 inference(quant_inst,[status(thm)],[])).
% 0.58/0.68 tff(1102,plain,
% 0.58/0.68 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_5) | (~product(e_4, e_5, e_5)) | (~product(e_5, e_5, e_5))),
% 0.58/0.68 inference(modus_ponens,[status(thm)],[1101, 1100])).
% 0.58/0.68 tff(1103,plain,
% 0.58/0.68 ($false),
% 0.58/0.68 inference(unit_resolution,[status(thm)],[1102, 774, 87, 1096, 730])).
% 0.58/0.68 tff(1104,plain,(~product(e_4, e_5, e_5)), inference(lemma,lemma(discharge,[]))).
% 0.58/0.68 tff(1105,assumption,(product(e_4, e_1, e_5)), introduced(assumption)).
% 0.58/0.68 tff(1106,assumption,(product(e_6, e_1, e_5)), introduced(assumption)).
% 0.58/0.68 tff(1107,plain,
% 0.58/0.68 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_4) | (~product(e_4, e_1, e_5)) | (~product(e_6, e_1, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_6, e_4) | (~product(e_4, e_1, e_5)) | (~product(e_6, e_1, e_5)))),
% 0.58/0.68 inference(rewrite,[status(thm)],[])).
% 0.58/0.68 tff(1108,plain,
% 0.58/0.68 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_4) | (~product(e_4, e_1, e_5)) | (~product(e_6, e_1, e_5)))),
% 0.58/0.68 inference(quant_inst,[status(thm)],[])).
% 0.58/0.68 tff(1109,plain,
% 0.58/0.68 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_6, e_4) | (~product(e_4, e_1, e_5)) | (~product(e_6, e_1, e_5))),
% 0.58/0.68 inference(modus_ponens,[status(thm)],[1108, 1107])).
% 0.58/0.68 tff(1110,plain,
% 0.58/0.68 ($false),
% 0.58/0.68 inference(unit_resolution,[status(thm)],[1109, 635, 87, 1105, 1106])).
% 0.58/0.68 tff(1111,plain,((~product(e_6, e_1, e_5)) | (~product(e_4, e_1, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.58/0.68 tff(1112,plain,
% 0.58/0.68 (~product(e_6, e_1, e_5)),
% 0.58/0.68 inference(unit_resolution,[status(thm)],[1111, 1105])).
% 0.58/0.68 tff(1113,assumption,(product(e_6, e_1, e_1)), introduced(assumption)).
% 0.58/0.68 tff(1114,plain,
% 0.58/0.68 ((~equalish(e_6, e_1)) <=> (~equalish(e_6, e_1))),
% 0.58/0.68 inference(rewrite,[status(thm)],[])).
% 0.58/0.68 tff(1115,axiom,(~equalish(e_6, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_6_is_not_e_1')).
% 0.58/0.68 tff(1116,plain,
% 0.58/0.68 (~equalish(e_6, e_1)),
% 0.58/0.68 inference(modus_ponens,[status(thm)],[1115, 1114])).
% 0.58/0.68 tff(1117,plain,
% 0.58/0.68 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_6, 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_6, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_6, e_1, e_1)))),
% 0.58/0.68 inference(rewrite,[status(thm)],[])).
% 0.58/0.68 tff(1118,plain,
% 0.58/0.68 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_6, e_1, e_1)))),
% 0.58/0.68 inference(quant_inst,[status(thm)],[])).
% 0.58/0.68 tff(1119,plain,
% 0.58/0.68 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_6, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_6, e_1, e_1))),
% 0.58/0.68 inference(modus_ponens,[status(thm)],[1118, 1117])).
% 0.58/0.68 tff(1120,plain,
% 0.58/0.68 ($false),
% 0.58/0.68 inference(unit_resolution,[status(thm)],[1119, 1116, 87, 77, 1113])).
% 0.58/0.68 tff(1121,plain,(~product(e_6, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.58/0.68 tff(1122,assumption,(product(e_6, e_1, e_4)), introduced(assumption)).
% 0.58/0.68 tff(1123,plain,
% 0.58/0.68 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_3) | (~product(e_3, e_1, e_4)) | (~product(e_6, e_1, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_6, e_3) | (~product(e_3, e_1, e_4)) | (~product(e_6, e_1, e_4)))),
% 0.58/0.68 inference(rewrite,[status(thm)],[])).
% 0.58/0.68 tff(1124,plain,
% 0.58/0.68 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_3) | (~product(e_3, e_1, e_4)) | (~product(e_6, e_1, e_4)))),
% 0.58/0.68 inference(quant_inst,[status(thm)],[])).
% 0.58/0.68 tff(1125,plain,
% 0.58/0.68 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_6, e_3) | (~product(e_3, e_1, e_4)) | (~product(e_6, e_1, e_4))),
% 0.58/0.68 inference(modus_ponens,[status(thm)],[1124, 1123])).
% 0.58/0.68 tff(1126,plain,
% 0.58/0.68 ($false),
% 0.58/0.68 inference(unit_resolution,[status(thm)],[1125, 816, 87, 234, 1122])).
% 0.58/0.68 tff(1127,plain,((~product(e_6, e_1, e_4)) | (~product(e_3, e_1, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.58/0.68 tff(1128,plain,
% 0.58/0.68 (~product(e_6, e_1, e_4)),
% 0.58/0.68 inference(unit_resolution,[status(thm)],[1127, 1041])).
% 0.58/0.68 tff(1129,assumption,(product(e_6, e_1, e_3)), introduced(assumption)).
% 0.58/0.68 tff(1130,plain,
% 0.58/0.68 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_6, 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_6, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_6, e_1, e_3)))),
% 0.58/0.68 inference(rewrite,[status(thm)],[])).
% 0.58/0.68 tff(1131,plain,
% 0.58/0.68 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_6, e_1, e_3)))),
% 0.58/0.68 inference(quant_inst,[status(thm)],[])).
% 0.58/0.68 tff(1132,plain,
% 0.58/0.68 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_6, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_6, e_1, e_3))),
% 0.58/0.68 inference(modus_ponens,[status(thm)],[1131, 1130])).
% 0.58/0.68 tff(1133,plain,
% 0.58/0.68 ($false),
% 0.58/0.68 inference(unit_resolution,[status(thm)],[1132, 855, 87, 28, 1129])).
% 0.58/0.68 tff(1134,plain,((~product(e_6, e_1, e_3)) | (~product(e_2, e_1, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.58/0.68 tff(1135,plain,
% 0.58/0.68 (~product(e_6, e_1, e_3)),
% 0.58/0.68 inference(unit_resolution,[status(thm)],[1134, 719])).
% 0.58/0.68 tff(1136,assumption,(product(e_6, e_1, e_6)), introduced(assumption)).
% 0.58/0.68 tff(1137,plain,
% 0.58/0.68 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_6) | (~product(e_6, e_1, e_6)) | (~product(e_6, e_6, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_6) | (~product(e_6, e_1, e_6)) | (~product(e_6, e_6, e_6)))),
% 0.58/0.68 inference(rewrite,[status(thm)],[])).
% 0.58/0.68 tff(1138,plain,
% 0.58/0.68 ((equalish(e_1, e_6) | (~product(e_6, e_6, e_6)) | (~product(e_6, e_1, e_6))) <=> (equalish(e_1, e_6) | (~product(e_6, e_1, e_6)) | (~product(e_6, e_6, e_6)))),
% 0.58/0.68 inference(rewrite,[status(thm)],[])).
% 0.58/0.68 tff(1139,plain,
% 0.58/0.68 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_6) | (~product(e_6, e_6, e_6)) | (~product(e_6, e_1, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_6) | (~product(e_6, e_1, e_6)) | (~product(e_6, e_6, e_6))))),
% 0.58/0.68 inference(monotonicity,[status(thm)],[1138])).
% 0.58/0.68 tff(1140,plain,
% 0.58/0.68 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_6) | (~product(e_6, e_6, e_6)) | (~product(e_6, e_1, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_6) | (~product(e_6, e_1, e_6)) | (~product(e_6, e_6, e_6)))),
% 0.58/0.68 inference(transitivity,[status(thm)],[1139, 1137])).
% 0.58/0.68 tff(1141,plain,
% 0.58/0.68 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_6) | (~product(e_6, e_6, e_6)) | (~product(e_6, e_1, e_6)))),
% 0.58/0.68 inference(quant_inst,[status(thm)],[])).
% 0.58/0.68 tff(1142,plain,
% 0.58/0.68 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_6) | (~product(e_6, e_1, e_6)) | (~product(e_6, e_6, e_6))),
% 0.58/0.68 inference(modus_ponens,[status(thm)],[1141, 1140])).
% 0.58/0.68 tff(1143,plain,
% 0.58/0.68 ($false),
% 0.58/0.68 inference(unit_resolution,[status(thm)],[1142, 936, 17, 1136, 933])).
% 0.58/0.68 tff(1144,plain,(~product(e_6, e_1, e_6)), inference(lemma,lemma(discharge,[]))).
% 0.58/0.68 tff(1145,plain,
% 0.58/0.68 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_1)) | (~group_element(e_6)) | product(e_6, e_1, e_6) | product(e_6, e_1, e_3) | product(e_6, e_1, e_4) | product(e_6, e_1, e_2) | product(e_6, e_1, e_1) | product(e_6, e_1, e_5))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | (~group_element(e_6)) | product(e_6, e_1, e_6) | product(e_6, e_1, e_3) | product(e_6, e_1, e_4) | product(e_6, e_1, e_2) | product(e_6, e_1, e_1) | product(e_6, e_1, e_5))),
% 0.58/0.68 inference(rewrite,[status(thm)],[])).
% 0.58/0.68 tff(1146,plain,
% 0.58/0.68 ((product(e_6, e_1, e_6) | product(e_6, e_1, e_5) | product(e_6, e_1, e_4) | product(e_6, e_1, e_3) | product(e_6, e_1, e_2) | product(e_6, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_6))) <=> ((~group_element(e_1)) | (~group_element(e_6)) | product(e_6, e_1, e_6) | product(e_6, e_1, e_3) | product(e_6, e_1, e_4) | product(e_6, e_1, e_2) | product(e_6, e_1, e_1) | product(e_6, e_1, e_5))),
% 0.58/0.68 inference(rewrite,[status(thm)],[])).
% 0.58/0.68 tff(1147,plain,
% 0.58/0.68 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_6, e_1, e_6) | product(e_6, e_1, e_5) | product(e_6, e_1, e_4) | product(e_6, e_1, e_3) | product(e_6, e_1, e_2) | product(e_6, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_6)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_1)) | (~group_element(e_6)) | product(e_6, e_1, e_6) | product(e_6, e_1, e_3) | product(e_6, e_1, e_4) | product(e_6, e_1, e_2) | product(e_6, e_1, e_1) | product(e_6, e_1, e_5)))),
% 0.58/0.68 inference(monotonicity,[status(thm)],[1146])).
% 0.58/0.68 tff(1148,plain,
% 0.58/0.68 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_6, e_1, e_6) | product(e_6, e_1, e_5) | product(e_6, e_1, e_4) | product(e_6, e_1, e_3) | product(e_6, e_1, e_2) | product(e_6, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_6)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | (~group_element(e_6)) | product(e_6, e_1, e_6) | product(e_6, e_1, e_3) | product(e_6, e_1, e_4) | product(e_6, e_1, e_2) | product(e_6, e_1, e_1) | product(e_6, e_1, e_5))),
% 0.58/0.69 inference(transitivity,[status(thm)],[1147, 1145])).
% 0.58/0.69 tff(1149,plain,
% 0.58/0.69 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_6, e_1, e_6) | product(e_6, e_1, e_5) | product(e_6, e_1, e_4) | product(e_6, e_1, e_3) | product(e_6, e_1, e_2) | product(e_6, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_6)))),
% 0.58/0.69 inference(quant_inst,[status(thm)],[])).
% 0.58/0.69 tff(1150,plain,
% 0.58/0.69 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | (~group_element(e_6)) | product(e_6, e_1, e_6) | product(e_6, e_1, e_3) | product(e_6, e_1, e_4) | product(e_6, e_1, e_2) | product(e_6, e_1, e_1) | product(e_6, e_1, e_5)),
% 0.58/0.69 inference(modus_ponens,[status(thm)],[1149, 1148])).
% 0.58/0.69 tff(1151,plain,
% 0.58/0.69 (product(e_6, e_1, e_6) | product(e_6, e_1, e_3) | product(e_6, e_1, e_4) | product(e_6, e_1, e_2) | product(e_6, e_1, e_1) | product(e_6, e_1, e_5)),
% 0.58/0.69 inference(unit_resolution,[status(thm)],[1150, 135, 384, 129])).
% 0.58/0.69 tff(1152,plain,
% 0.58/0.69 (product(e_6, e_1, e_3) | product(e_6, e_1, e_4) | product(e_6, e_1, e_2) | product(e_6, e_1, e_1) | product(e_6, e_1, e_5)),
% 0.58/0.69 inference(unit_resolution,[status(thm)],[1151, 1144])).
% 0.58/0.69 tff(1153,plain,
% 0.58/0.69 (product(e_6, e_1, e_4) | product(e_6, e_1, e_2) | product(e_6, e_1, e_1) | product(e_6, e_1, e_5)),
% 0.58/0.69 inference(unit_resolution,[status(thm)],[1152, 1135])).
% 0.58/0.69 tff(1154,plain,
% 0.58/0.69 (product(e_6, e_1, e_2) | product(e_6, e_1, e_1) | product(e_6, e_1, e_5)),
% 0.58/0.69 inference(unit_resolution,[status(thm)],[1153, 1128])).
% 0.58/0.69 tff(1155,plain,
% 0.58/0.69 (product(e_6, e_1, e_2) | product(e_6, e_1, e_5)),
% 0.58/0.69 inference(unit_resolution,[status(thm)],[1154, 1121])).
% 0.58/0.69 tff(1156,plain,
% 0.58/0.69 (product(e_6, e_1, e_2)),
% 0.58/0.69 inference(unit_resolution,[status(thm)],[1155, 1112])).
% 0.58/0.69 tff(1157,assumption,(product(e_6, e_1, e_2)), introduced(assumption)).
% 0.58/0.69 tff(1158,plain,
% 0.58/0.69 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_5) | (~product(e_1, e_5, e_6)) | (~product(e_6, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_5) | (~product(e_1, e_5, e_6)) | (~product(e_6, e_1, e_2)))),
% 0.58/0.69 inference(rewrite,[status(thm)],[])).
% 0.58/0.69 tff(1159,plain,
% 0.58/0.69 ((product(e_2, e_1, e_5) | (~product(e_6, e_1, e_2)) | (~product(e_1, e_5, e_6))) <=> (product(e_2, e_1, e_5) | (~product(e_1, e_5, e_6)) | (~product(e_6, e_1, e_2)))),
% 0.58/0.69 inference(rewrite,[status(thm)],[])).
% 0.58/0.69 tff(1160,plain,
% 0.58/0.69 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_5) | (~product(e_6, e_1, e_2)) | (~product(e_1, e_5, e_6)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_5) | (~product(e_1, e_5, e_6)) | (~product(e_6, e_1, e_2))))),
% 0.58/0.69 inference(monotonicity,[status(thm)],[1159])).
% 0.58/0.69 tff(1161,plain,
% 0.58/0.69 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_5) | (~product(e_6, e_1, e_2)) | (~product(e_1, e_5, e_6)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_5) | (~product(e_1, e_5, e_6)) | (~product(e_6, e_1, e_2)))),
% 0.58/0.69 inference(transitivity,[status(thm)],[1160, 1158])).
% 0.58/0.69 tff(1162,plain,
% 0.58/0.69 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_5) | (~product(e_6, e_1, e_2)) | (~product(e_1, e_5, e_6)))),
% 0.58/0.69 inference(quant_inst,[status(thm)],[])).
% 0.58/0.69 tff(1163,plain,
% 0.58/0.69 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_5) | (~product(e_1, e_5, e_6)) | (~product(e_6, e_1, e_2))),
% 0.58/0.69 inference(modus_ponens,[status(thm)],[1162, 1161])).
% 0.58/0.69 tff(1164,plain,
% 0.58/0.69 ($false),
% 0.58/0.69 inference(unit_resolution,[status(thm)],[1163, 58, 112, 156, 1157])).
% 0.58/0.69 tff(1165,plain,((~product(e_6, e_1, e_2)) | (~product(e_1, e_5, e_6))), inference(lemma,lemma(discharge,[]))).
% 0.58/0.69 tff(1166,plain,
% 0.58/0.69 (~product(e_1, e_5, e_6)),
% 0.58/0.69 inference(unit_resolution,[status(thm)],[1165, 1156])).
% 0.58/0.69 tff(1167,plain,
% 0.58/0.69 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_2) | (~product(e_1, e_2, e_6)) | (~product(e_6, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_2) | (~product(e_1, e_2, e_6)) | (~product(e_6, e_1, e_2)))),
% 0.58/0.69 inference(rewrite,[status(thm)],[])).
% 0.58/0.69 tff(1168,plain,
% 0.58/0.69 ((product(e_2, e_1, e_2) | (~product(e_6, e_1, e_2)) | (~product(e_1, e_2, e_6))) <=> (product(e_2, e_1, e_2) | (~product(e_1, e_2, e_6)) | (~product(e_6, e_1, e_2)))),
% 0.58/0.69 inference(rewrite,[status(thm)],[])).
% 0.58/0.69 tff(1169,plain,
% 0.58/0.69 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_2) | (~product(e_6, e_1, e_2)) | (~product(e_1, e_2, e_6)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_2) | (~product(e_1, e_2, e_6)) | (~product(e_6, e_1, e_2))))),
% 0.58/0.69 inference(monotonicity,[status(thm)],[1168])).
% 0.58/0.69 tff(1170,plain,
% 0.58/0.69 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_2) | (~product(e_6, e_1, e_2)) | (~product(e_1, e_2, e_6)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_2) | (~product(e_1, e_2, e_6)) | (~product(e_6, e_1, e_2)))),
% 0.58/0.69 inference(transitivity,[status(thm)],[1169, 1167])).
% 0.58/0.69 tff(1171,plain,
% 0.58/0.69 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_2) | (~product(e_6, e_1, e_2)) | (~product(e_1, e_2, e_6)))),
% 0.58/0.69 inference(quant_inst,[status(thm)],[])).
% 0.58/0.69 tff(1172,plain,
% 0.58/0.69 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_2) | (~product(e_1, e_2, e_6)) | (~product(e_6, e_1, e_2))),
% 0.58/0.69 inference(modus_ponens,[status(thm)],[1171, 1170])).
% 0.58/0.69 tff(1173,plain,
% 0.58/0.69 ($false),
% 0.58/0.69 inference(unit_resolution,[status(thm)],[1172, 58, 718, 529, 1157])).
% 0.58/0.69 tff(1174,plain,((~product(e_6, e_1, e_2)) | (~product(e_1, e_2, e_6))), inference(lemma,lemma(discharge,[]))).
% 0.58/0.69 tff(1175,plain,
% 0.58/0.69 (~product(e_1, e_2, e_6)),
% 0.58/0.69 inference(unit_resolution,[status(thm)],[1174, 1156])).
% 0.58/0.69 tff(1176,plain,
% 0.58/0.69 (product(e_1, e_2, e_6) | product(e_1, e_2, e_3) | product(e_1, e_2, e_5) | product(e_1, e_2, e_4)),
% 0.58/0.69 inference(unit_resolution,[status(thm)],[576, 703])).
% 0.58/0.69 tff(1177,plain,
% 0.58/0.69 (product(e_1, e_2, e_3)),
% 0.58/0.69 inference(unit_resolution,[status(thm)],[1176, 1175, 1095, 826])).
% 0.58/0.69 tff(1178,plain,
% 0.58/0.69 (~product(e_1, e_5, e_3)),
% 0.58/0.69 inference(unit_resolution,[status(thm)],[688, 1177])).
% 0.58/0.69 tff(1179,plain,
% 0.58/0.69 (product(e_1, e_5, e_6) | product(e_1, e_5, e_4) | product(e_1, e_5, e_3)),
% 0.58/0.69 inference(unit_resolution,[status(thm)],[450, 152, 741])).
% 0.58/0.69 tff(1180,plain,
% 0.58/0.69 (product(e_1, e_5, e_4)),
% 0.58/0.69 inference(unit_resolution,[status(thm)],[1179, 1178, 1166])).
% 0.58/0.69 tff(1181,plain,
% 0.58/0.69 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_5, e_5) | (~product(e_1, e_5, e_4)) | (~product(e_5, e_5, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_4, e_5, e_5) | (~product(e_1, e_5, e_4)) | (~product(e_5, e_5, e_1)))),
% 0.58/0.69 inference(rewrite,[status(thm)],[])).
% 0.58/0.69 tff(1182,plain,
% 0.58/0.69 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_5, e_5) | (~product(e_1, e_5, e_4)) | (~product(e_5, e_5, e_1)))),
% 0.58/0.69 inference(quant_inst,[status(thm)],[])).
% 0.58/0.69 tff(1183,plain,
% 0.58/0.69 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_4, e_5, e_5) | (~product(e_1, e_5, e_4)) | (~product(e_5, e_5, e_1))),
% 0.58/0.69 inference(modus_ponens,[status(thm)],[1182, 1181])).
% 0.58/0.69 tff(1184,plain,
% 0.58/0.69 (~product(e_5, e_5, e_1)),
% 0.58/0.69 inference(unit_resolution,[status(thm)],[1183, 58, 1180, 1104])).
% 0.58/0.69 tff(1185,plain,
% 0.58/0.69 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_5, e_5, e_5)) | product(e_5, e_5, e_1) | (~product(e_5, e_1, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_5, e_5, e_5)) | product(e_5, e_5, e_1) | (~product(e_5, e_1, e_5)))),
% 0.58/0.69 inference(rewrite,[status(thm)],[])).
% 0.58/0.69 tff(1186,plain,
% 0.58/0.69 ((product(e_5, e_5, e_1) | (~product(e_5, e_5, e_5)) | (~product(e_5, e_1, e_5))) <=> ((~product(e_5, e_5, e_5)) | product(e_5, e_5, e_1) | (~product(e_5, e_1, e_5)))),
% 0.58/0.69 inference(rewrite,[status(thm)],[])).
% 0.58/0.69 tff(1187,plain,
% 0.58/0.69 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_5, e_5, e_1) | (~product(e_5, e_5, e_5)) | (~product(e_5, e_1, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_5, e_5, e_5)) | product(e_5, e_5, e_1) | (~product(e_5, e_1, e_5))))),
% 0.58/0.69 inference(monotonicity,[status(thm)],[1186])).
% 0.58/0.69 tff(1188,plain,
% 0.58/0.69 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_5, e_5, e_1) | (~product(e_5, e_5, e_5)) | (~product(e_5, e_1, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_5, e_5, e_5)) | product(e_5, e_5, e_1) | (~product(e_5, e_1, e_5)))),
% 0.58/0.69 inference(transitivity,[status(thm)],[1187, 1185])).
% 0.58/0.69 tff(1189,plain,
% 0.58/0.69 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_5, e_5, e_1) | (~product(e_5, e_5, e_5)) | (~product(e_5, e_1, e_5)))),
% 0.58/0.69 inference(quant_inst,[status(thm)],[])).
% 0.58/0.69 tff(1190,plain,
% 0.58/0.69 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_5, e_5, e_5)) | product(e_5, e_5, e_1) | (~product(e_5, e_1, e_5))),
% 0.58/0.69 inference(modus_ponens,[status(thm)],[1189, 1188])).
% 0.58/0.69 tff(1191,plain,
% 0.58/0.69 (~product(e_5, e_1, e_5)),
% 0.58/0.69 inference(unit_resolution,[status(thm)],[1190, 58, 730, 1184])).
% 0.58/0.69 tff(1192,plain,
% 0.58/0.69 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_5, e_4)) | (~product(e_4, e_1, e_5)) | product(e_5, e_1, e_5))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_5, e_4)) | (~product(e_4, e_1, e_5)) | product(e_5, e_1, e_5))),
% 0.58/0.69 inference(rewrite,[status(thm)],[])).
% 0.58/0.69 tff(1193,plain,
% 0.58/0.69 ((product(e_5, e_1, e_5) | (~product(e_4, e_1, e_5)) | (~product(e_1, e_5, e_4))) <=> ((~product(e_1, e_5, e_4)) | (~product(e_4, e_1, e_5)) | product(e_5, e_1, e_5))),
% 0.58/0.69 inference(rewrite,[status(thm)],[])).
% 0.58/0.69 tff(1194,plain,
% 0.58/0.69 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_5, e_1, e_5) | (~product(e_4, e_1, e_5)) | (~product(e_1, e_5, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_5, e_4)) | (~product(e_4, e_1, e_5)) | product(e_5, e_1, e_5)))),
% 0.58/0.69 inference(monotonicity,[status(thm)],[1193])).
% 0.58/0.69 tff(1195,plain,
% 0.58/0.69 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_5, e_1, e_5) | (~product(e_4, e_1, e_5)) | (~product(e_1, e_5, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_5, e_4)) | (~product(e_4, e_1, e_5)) | product(e_5, e_1, e_5))),
% 0.58/0.69 inference(transitivity,[status(thm)],[1194, 1192])).
% 0.58/0.69 tff(1196,plain,
% 0.58/0.69 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_5, e_1, e_5) | (~product(e_4, e_1, e_5)) | (~product(e_1, e_5, e_4)))),
% 0.58/0.69 inference(quant_inst,[status(thm)],[])).
% 0.58/0.69 tff(1197,plain,
% 0.58/0.69 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_5, e_4)) | (~product(e_4, e_1, e_5)) | product(e_5, e_1, e_5)),
% 0.58/0.69 inference(modus_ponens,[status(thm)],[1196, 1195])).
% 0.58/0.69 tff(1198,plain,
% 0.58/0.69 ($false),
% 0.58/0.69 inference(unit_resolution,[status(thm)],[1197, 58, 1105, 1180, 1191])).
% 0.58/0.69 tff(1199,plain,((~product(e_4, e_1, e_5)) | product(e_1, e_2, e_5) | product(e_1, e_2, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.58/0.69 tff(1200,plain,
% 0.58/0.69 (~product(e_4, e_1, e_5)),
% 0.58/0.69 inference(unit_resolution,[status(thm)],[1199, 826, 1095])).
% 0.58/0.69 tff(1201,plain,
% 0.58/0.69 (~product(e_1, e_5, e_3)),
% 0.58/0.69 inference(unit_resolution,[status(thm)],[1050, 1200])).
% 0.58/0.69 tff(1202,plain,
% 0.58/0.69 (~product(e_1, e_3, e_5)),
% 0.58/0.69 inference(unit_resolution,[status(thm)],[871, 1093])).
% 0.58/0.69 tff(1203,plain,
% 0.58/0.69 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_3) | (~product(e_1, e_3, e_4)) | (~product(e_4, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_3) | (~product(e_1, e_3, e_4)) | (~product(e_4, e_1, e_1)))),
% 0.58/0.69 inference(rewrite,[status(thm)],[])).
% 0.58/0.69 tff(1204,plain,
% 0.58/0.69 ((product(e_1, e_1, e_3) | (~product(e_4, e_1, e_1)) | (~product(e_1, e_3, e_4))) <=> (product(e_1, e_1, e_3) | (~product(e_1, e_3, e_4)) | (~product(e_4, e_1, e_1)))),
% 0.58/0.69 inference(rewrite,[status(thm)],[])).
% 0.58/0.69 tff(1205,plain,
% 0.58/0.69 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_3) | (~product(e_4, e_1, e_1)) | (~product(e_1, e_3, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_3) | (~product(e_1, e_3, e_4)) | (~product(e_4, e_1, e_1))))),
% 0.58/0.69 inference(monotonicity,[status(thm)],[1204])).
% 0.58/0.69 tff(1206,plain,
% 0.58/0.69 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_3) | (~product(e_4, e_1, e_1)) | (~product(e_1, e_3, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_3) | (~product(e_1, e_3, e_4)) | (~product(e_4, e_1, e_1)))),
% 0.58/0.69 inference(transitivity,[status(thm)],[1205, 1203])).
% 0.58/0.69 tff(1207,plain,
% 0.58/0.69 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_3) | (~product(e_4, e_1, e_1)) | (~product(e_1, e_3, e_4)))),
% 0.58/0.69 inference(quant_inst,[status(thm)],[])).
% 0.58/0.69 tff(1208,plain,
% 0.58/0.69 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_3) | (~product(e_1, e_3, e_4)) | (~product(e_4, e_1, e_1))),
% 0.58/0.69 inference(modus_ponens,[status(thm)],[1207, 1206])).
% 0.58/0.69 tff(1209,plain,
% 0.58/0.69 ($false),
% 0.58/0.69 inference(unit_resolution,[status(thm)],[1208, 58, 481, 1052, 395])).
% 0.58/0.70 tff(1210,plain,((~product(e_4, e_1, e_1)) | (~product(e_1, e_3, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.58/0.70 tff(1211,plain,
% 0.58/0.70 (~product(e_1, e_3, e_4)),
% 0.58/0.70 inference(unit_resolution,[status(thm)],[1210, 1052])).
% 0.58/0.70 tff(1212,assumption,(product(e_1, e_4, e_2)), introduced(assumption)).
% 0.58/0.70 tff(1213,plain,
% 0.58/0.70 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_3) | (~product(e_1, e_3, e_2)) | (~product(e_1, e_4, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_3) | (~product(e_1, e_3, e_2)) | (~product(e_1, e_4, e_2)))),
% 0.58/0.70 inference(rewrite,[status(thm)],[])).
% 0.58/0.70 tff(1214,plain,
% 0.58/0.70 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_3) | (~product(e_1, e_3, e_2)) | (~product(e_1, e_4, e_2)))),
% 0.58/0.70 inference(quant_inst,[status(thm)],[])).
% 0.58/0.70 tff(1215,plain,
% 0.58/0.70 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_3) | (~product(e_1, e_3, e_2)) | (~product(e_1, e_4, e_2))),
% 0.58/0.70 inference(modus_ponens,[status(thm)],[1214, 1213])).
% 0.58/0.70 tff(1216,plain,
% 0.58/0.70 ($false),
% 0.58/0.70 inference(unit_resolution,[status(thm)],[1215, 498, 17, 1212, 553])).
% 0.58/0.70 tff(1217,plain,((~product(e_1, e_4, e_2)) | (~product(e_1, e_3, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.58/0.70 tff(1218,plain,
% 0.58/0.70 (~product(e_1, e_3, e_2)),
% 0.58/0.70 inference(unit_resolution,[status(thm)],[1217, 1032])).
% 0.58/0.70 tff(1219,plain,
% 0.58/0.70 (product(e_1, e_3, e_6) | product(e_1, e_3, e_5) | product(e_1, e_3, e_4)),
% 0.58/0.70 inference(unit_resolution,[status(thm)],[493, 1218])).
% 0.58/0.70 tff(1220,plain,
% 0.58/0.70 (product(e_1, e_3, e_6)),
% 0.58/0.70 inference(unit_resolution,[status(thm)],[1219, 1211, 881])).
% 0.58/0.70 tff(1221,plain,
% 0.58/0.70 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_5) | (~product(e_1, e_5, e_4)) | (~product(e_4, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_5) | (~product(e_1, e_5, e_4)) | (~product(e_4, e_1, e_1)))),
% 0.58/0.70 inference(rewrite,[status(thm)],[])).
% 0.58/0.70 tff(1222,plain,
% 0.58/0.70 ((product(e_1, e_1, e_5) | (~product(e_4, e_1, e_1)) | (~product(e_1, e_5, e_4))) <=> (product(e_1, e_1, e_5) | (~product(e_1, e_5, e_4)) | (~product(e_4, e_1, e_1)))),
% 0.58/0.70 inference(rewrite,[status(thm)],[])).
% 0.58/0.70 tff(1223,plain,
% 0.58/0.70 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_5) | (~product(e_4, e_1, e_1)) | (~product(e_1, e_5, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_5) | (~product(e_1, e_5, e_4)) | (~product(e_4, e_1, e_1))))),
% 0.58/0.70 inference(monotonicity,[status(thm)],[1222])).
% 0.58/0.70 tff(1224,plain,
% 0.58/0.70 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_5) | (~product(e_4, e_1, e_1)) | (~product(e_1, e_5, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_5) | (~product(e_1, e_5, e_4)) | (~product(e_4, e_1, e_1)))),
% 0.58/0.70 inference(transitivity,[status(thm)],[1223, 1221])).
% 0.58/0.70 tff(1225,plain,
% 0.58/0.70 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_5) | (~product(e_4, e_1, e_1)) | (~product(e_1, e_5, e_4)))),
% 0.58/0.70 inference(quant_inst,[status(thm)],[])).
% 0.58/0.70 tff(1226,plain,
% 0.58/0.70 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_5) | (~product(e_1, e_5, e_4)) | (~product(e_4, e_1, e_1))),
% 0.58/0.70 inference(modus_ponens,[status(thm)],[1225, 1224])).
% 0.58/0.70 tff(1227,plain,
% 0.58/0.70 ($false),
% 0.58/0.70 inference(unit_resolution,[status(thm)],[1226, 58, 433, 1052, 7])).
% 0.58/0.70 tff(1228,plain,((~product(e_4, e_1, e_1)) | (~product(e_1, e_5, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.58/0.70 tff(1229,plain,
% 0.58/0.70 (~product(e_1, e_5, e_4)),
% 0.58/0.70 inference(unit_resolution,[status(thm)],[1228, 1052])).
% 0.58/0.70 tff(1230,plain,
% 0.58/0.70 (product(e_1, e_5, e_6)),
% 0.58/0.70 inference(unit_resolution,[status(thm)],[1179, 1229, 155])).
% 0.58/0.70 tff(1231,plain,
% 0.58/0.70 ($false),
% 0.58/0.70 inference(unit_resolution,[status(thm)],[425, 1230, 1220])).
% 0.58/0.70 tff(1232,plain,((~product(e_4, e_1, e_1)) | product(e_1, e_5, e_3) | product(e_1, e_3, e_5)), inference(lemma,lemma(discharge,[]))).
% 0.58/0.70 tff(1233,plain,
% 0.58/0.70 (~product(e_4, e_1, e_1)),
% 0.58/0.70 inference(unit_resolution,[status(thm)],[1232, 1051, 1202])).
% 0.58/0.70 tff(1234,assumption,(~product(e_6, e_2, e_3)), introduced(assumption)).
% 0.58/0.70 tff(1235,assumption,(product(e_5, e_1, e_1)), introduced(assumption)).
% 0.58/0.70 tff(1236,plain,
% 0.58/0.70 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_6) | (~product(e_1, e_6, e_5)) | (~product(e_5, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_6) | (~product(e_1, e_6, e_5)) | (~product(e_5, e_1, e_1)))),
% 0.58/0.70 inference(rewrite,[status(thm)],[])).
% 0.58/0.70 tff(1237,plain,
% 0.58/0.70 ((product(e_1, e_1, e_6) | (~product(e_5, e_1, e_1)) | (~product(e_1, e_6, e_5))) <=> (product(e_1, e_1, e_6) | (~product(e_1, e_6, e_5)) | (~product(e_5, e_1, e_1)))),
% 0.58/0.70 inference(rewrite,[status(thm)],[])).
% 0.58/0.70 tff(1238,plain,
% 0.58/0.70 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_6) | (~product(e_5, e_1, e_1)) | (~product(e_1, e_6, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_6) | (~product(e_1, e_6, e_5)) | (~product(e_5, e_1, e_1))))),
% 0.58/0.70 inference(monotonicity,[status(thm)],[1237])).
% 0.58/0.70 tff(1239,plain,
% 0.58/0.70 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_6) | (~product(e_5, e_1, e_1)) | (~product(e_1, e_6, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_6) | (~product(e_1, e_6, e_5)) | (~product(e_5, e_1, e_1)))),
% 0.58/0.70 inference(transitivity,[status(thm)],[1238, 1236])).
% 0.58/0.70 tff(1240,plain,
% 0.58/0.70 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_6) | (~product(e_5, e_1, e_1)) | (~product(e_1, e_6, e_5)))),
% 0.58/0.70 inference(quant_inst,[status(thm)],[])).
% 0.58/0.70 tff(1241,plain,
% 0.58/0.70 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_6) | (~product(e_1, e_6, e_5)) | (~product(e_5, e_1, e_1))),
% 0.58/0.70 inference(modus_ponens,[status(thm)],[1240, 1239])).
% 0.58/0.70 tff(1242,plain,
% 0.58/0.70 ($false),
% 0.58/0.70 inference(unit_resolution,[status(thm)],[1241, 58, 314, 289, 1235])).
% 0.58/0.70 tff(1243,plain,((~product(e_5, e_1, e_1)) | (~product(e_1, e_6, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.58/0.70 tff(1244,plain,
% 0.58/0.70 (~product(e_5, e_1, e_1)),
% 0.58/0.70 inference(unit_resolution,[status(thm)],[1243, 289])).
% 0.58/0.70 tff(1245,assumption,(product(e_5, e_1, e_2)), introduced(assumption)).
% 0.58/0.70 tff(1246,plain,
% 0.58/0.70 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_6) | (~product(e_1, e_6, e_5)) | (~product(e_5, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_6) | (~product(e_1, e_6, e_5)) | (~product(e_5, e_1, e_2)))),
% 0.58/0.70 inference(rewrite,[status(thm)],[])).
% 0.58/0.70 tff(1247,plain,
% 0.58/0.70 ((product(e_2, e_1, e_6) | (~product(e_5, e_1, e_2)) | (~product(e_1, e_6, e_5))) <=> (product(e_2, e_1, e_6) | (~product(e_1, e_6, e_5)) | (~product(e_5, e_1, e_2)))),
% 0.58/0.70 inference(rewrite,[status(thm)],[])).
% 0.58/0.70 tff(1248,plain,
% 0.58/0.70 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_6) | (~product(e_5, e_1, e_2)) | (~product(e_1, e_6, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_6) | (~product(e_1, e_6, e_5)) | (~product(e_5, e_1, e_2))))),
% 0.58/0.70 inference(monotonicity,[status(thm)],[1247])).
% 0.58/0.70 tff(1249,plain,
% 0.58/0.70 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_6) | (~product(e_5, e_1, e_2)) | (~product(e_1, e_6, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_6) | (~product(e_1, e_6, e_5)) | (~product(e_5, e_1, e_2)))),
% 0.58/0.70 inference(transitivity,[status(thm)],[1248, 1246])).
% 0.58/0.70 tff(1250,plain,
% 0.58/0.70 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_6) | (~product(e_5, e_1, e_2)) | (~product(e_1, e_6, e_5)))),
% 0.58/0.70 inference(quant_inst,[status(thm)],[])).
% 0.58/0.70 tff(1251,plain,
% 0.58/0.70 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_6) | (~product(e_1, e_6, e_5)) | (~product(e_5, e_1, e_2))),
% 0.58/0.70 inference(modus_ponens,[status(thm)],[1250, 1249])).
% 0.58/0.70 tff(1252,plain,
% 0.58/0.70 ($false),
% 0.58/0.70 inference(unit_resolution,[status(thm)],[1251, 58, 105, 289, 1245])).
% 0.58/0.70 tff(1253,plain,((~product(e_5, e_1, e_2)) | (~product(e_1, e_6, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.58/0.70 tff(1254,plain,
% 0.58/0.70 (~product(e_5, e_1, e_2)),
% 0.58/0.70 inference(unit_resolution,[status(thm)],[1253, 289])).
% 0.58/0.70 tff(1255,assumption,(product(e_5, e_1, e_6)), introduced(assumption)).
% 0.58/0.70 tff(1256,plain,
% 0.58/0.70 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_6, e_5)) | product(e_6, e_1, e_6) | (~product(e_5, e_1, e_6)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_6, e_5)) | product(e_6, e_1, e_6) | (~product(e_5, e_1, e_6)))),
% 0.58/0.70 inference(rewrite,[status(thm)],[])).
% 0.58/0.70 tff(1257,plain,
% 0.58/0.70 ((product(e_6, e_1, e_6) | (~product(e_5, e_1, e_6)) | (~product(e_1, e_6, e_5))) <=> ((~product(e_1, e_6, e_5)) | product(e_6, e_1, e_6) | (~product(e_5, e_1, e_6)))),
% 0.58/0.70 inference(rewrite,[status(thm)],[])).
% 0.58/0.70 tff(1258,plain,
% 0.58/0.70 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_6, e_1, e_6) | (~product(e_5, e_1, e_6)) | (~product(e_1, e_6, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_6, e_5)) | product(e_6, e_1, e_6) | (~product(e_5, e_1, e_6))))),
% 0.58/0.70 inference(monotonicity,[status(thm)],[1257])).
% 0.58/0.70 tff(1259,plain,
% 0.58/0.70 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_6, e_1, e_6) | (~product(e_5, e_1, e_6)) | (~product(e_1, e_6, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_6, e_5)) | product(e_6, e_1, e_6) | (~product(e_5, e_1, e_6)))),
% 0.58/0.70 inference(transitivity,[status(thm)],[1258, 1256])).
% 0.58/0.70 tff(1260,plain,
% 0.58/0.70 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_6, e_1, e_6) | (~product(e_5, e_1, e_6)) | (~product(e_1, e_6, e_5)))),
% 0.58/0.70 inference(quant_inst,[status(thm)],[])).
% 0.58/0.70 tff(1261,plain,
% 0.58/0.70 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_6, e_5)) | product(e_6, e_1, e_6) | (~product(e_5, e_1, e_6))),
% 0.58/0.70 inference(modus_ponens,[status(thm)],[1260, 1259])).
% 0.58/0.70 tff(1262,plain,
% 0.58/0.70 ($false),
% 0.58/0.70 inference(unit_resolution,[status(thm)],[1261, 58, 289, 1144, 1255])).
% 0.58/0.70 tff(1263,plain,((~product(e_5, e_1, e_6)) | (~product(e_1, e_6, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.58/0.70 tff(1264,plain,
% 0.58/0.70 (~product(e_5, e_1, e_6)),
% 0.58/0.70 inference(unit_resolution,[status(thm)],[1263, 289])).
% 0.58/0.70 tff(1265,plain,
% 0.58/0.70 (~product(e_1, e_3, e_5)),
% 0.58/0.70 inference(unit_resolution,[status(thm)],[871, 289])).
% 0.58/0.70 tff(1266,plain,
% 0.58/0.70 (product(e_1, e_3, e_4)),
% 0.58/0.70 inference(unit_resolution,[status(thm)],[1219, 1265, 5])).
% 0.58/0.70 tff(1267,plain,
% 0.58/0.70 (~product(e_4, e_1, e_1)),
% 0.58/0.70 inference(unit_resolution,[status(thm)],[1210, 1266])).
% 0.58/0.70 tff(1268,plain,
% 0.58/0.70 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_3) | (~product(e_1, e_3, e_4)) | (~product(e_4, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_3) | (~product(e_1, e_3, e_4)) | (~product(e_4, e_1, e_3)))),
% 0.58/0.70 inference(rewrite,[status(thm)],[])).
% 0.58/0.70 tff(1269,plain,
% 0.58/0.70 ((product(e_3, e_1, e_3) | (~product(e_4, e_1, e_3)) | (~product(e_1, e_3, e_4))) <=> (product(e_3, e_1, e_3) | (~product(e_1, e_3, e_4)) | (~product(e_4, e_1, e_3)))),
% 0.58/0.70 inference(rewrite,[status(thm)],[])).
% 0.58/0.70 tff(1270,plain,
% 0.58/0.70 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_3) | (~product(e_4, e_1, e_3)) | (~product(e_1, e_3, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_3) | (~product(e_1, e_3, e_4)) | (~product(e_4, e_1, e_3))))),
% 0.58/0.70 inference(monotonicity,[status(thm)],[1269])).
% 0.58/0.70 tff(1271,plain,
% 0.58/0.70 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_3) | (~product(e_4, e_1, e_3)) | (~product(e_1, e_3, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_3) | (~product(e_1, e_3, e_4)) | (~product(e_4, e_1, e_3)))),
% 0.58/0.70 inference(transitivity,[status(thm)],[1270, 1268])).
% 0.58/0.70 tff(1272,plain,
% 0.58/0.70 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_3) | (~product(e_4, e_1, e_3)) | (~product(e_1, e_3, e_4)))),
% 0.58/0.70 inference(quant_inst,[status(thm)],[])).
% 0.58/0.70 tff(1273,plain,
% 0.58/0.70 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_3) | (~product(e_1, e_3, e_4)) | (~product(e_4, e_1, e_3))),
% 0.58/0.70 inference(modus_ponens,[status(thm)],[1272, 1271])).
% 0.58/0.70 tff(1274,plain,
% 0.58/0.70 ($false),
% 0.58/0.70 inference(unit_resolution,[status(thm)],[1273, 58, 600, 1072, 395])).
% 0.58/0.70 tff(1275,plain,((~product(e_4, e_1, e_3)) | product(e_3, e_1, e_3) | (~product(e_1, e_3, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.58/0.70 tff(1276,plain,
% 0.58/0.70 (~product(e_4, e_1, e_3)),
% 0.58/0.70 inference(unit_resolution,[status(thm)],[1275, 1266, 600])).
% 0.58/0.70 tff(1277,plain,
% 0.58/0.70 (product(e_4, e_1, e_2)),
% 0.58/0.70 inference(unit_resolution,[status(thm)],[1089, 1276, 3, 1267])).
% 0.58/0.70 tff(1278,assumption,(product(e_4, e_5, e_2)), introduced(assumption)).
% 0.58/0.70 tff(1279,plain,
% 0.58/0.70 ((~equalish(e_5, e_1)) <=> (~equalish(e_5, e_1))),
% 0.58/0.70 inference(rewrite,[status(thm)],[])).
% 0.58/0.70 tff(1280,axiom,(~equalish(e_5, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_5_is_not_e_1')).
% 0.58/0.70 tff(1281,plain,
% 0.58/0.70 (~equalish(e_5, e_1)),
% 0.58/0.70 inference(modus_ponens,[status(thm)],[1280, 1279])).
% 0.58/0.70 tff(1282,plain,
% 0.58/0.70 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_1) | (~product(e_4, e_1, e_2)) | (~product(e_4, e_5, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_1) | (~product(e_4, e_1, e_2)) | (~product(e_4, e_5, e_2)))),
% 0.58/0.70 inference(rewrite,[status(thm)],[])).
% 0.58/0.70 tff(1283,plain,
% 0.58/0.70 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_1) | (~product(e_4, e_1, e_2)) | (~product(e_4, e_5, e_2)))),
% 0.58/0.70 inference(quant_inst,[status(thm)],[])).
% 0.58/0.70 tff(1284,plain,
% 0.58/0.70 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_1) | (~product(e_4, e_1, e_2)) | (~product(e_4, e_5, e_2))),
% 0.58/0.71 inference(modus_ponens,[status(thm)],[1283, 1282])).
% 0.58/0.71 tff(1285,plain,
% 0.58/0.71 ($false),
% 0.58/0.71 inference(unit_resolution,[status(thm)],[1284, 1281, 17, 1062, 1278])).
% 0.58/0.71 tff(1286,plain,((~product(e_4, e_5, e_2)) | (~product(e_4, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.58/0.71 tff(1287,plain,
% 0.58/0.71 (~product(e_4, e_5, e_2)),
% 0.58/0.71 inference(unit_resolution,[status(thm)],[1286, 1277])).
% 0.58/0.71 tff(1288,plain,
% 0.58/0.71 (~product(e_1, e_5, e_4)),
% 0.58/0.71 inference(unit_resolution,[status(thm)],[845, 1266])).
% 0.58/0.71 tff(1289,plain,
% 0.58/0.71 (product(e_1, e_5, e_6)),
% 0.58/0.71 inference(unit_resolution,[status(thm)],[1179, 1288, 1051])).
% 0.58/0.71 tff(1290,assumption,(product(e_4, e_5, e_6)), introduced(assumption)).
% 0.58/0.71 tff(1291,plain,
% 0.58/0.71 ((~equalish(e_4, e_1)) <=> (~equalish(e_4, e_1))),
% 0.58/0.71 inference(rewrite,[status(thm)],[])).
% 0.58/0.71 tff(1292,axiom,(~equalish(e_4, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_1')).
% 0.58/0.71 tff(1293,plain,
% 0.58/0.71 (~equalish(e_4, e_1)),
% 0.58/0.71 inference(modus_ponens,[status(thm)],[1292, 1291])).
% 0.58/0.71 tff(1294,plain,
% 0.58/0.71 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_1) | (~product(e_1, e_5, e_6)) | (~product(e_4, e_5, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_1) | (~product(e_1, e_5, e_6)) | (~product(e_4, e_5, e_6)))),
% 0.58/0.71 inference(rewrite,[status(thm)],[])).
% 0.58/0.71 tff(1295,plain,
% 0.58/0.71 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_1) | (~product(e_1, e_5, e_6)) | (~product(e_4, e_5, e_6)))),
% 0.58/0.71 inference(quant_inst,[status(thm)],[])).
% 0.58/0.71 tff(1296,plain,
% 0.58/0.71 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_1) | (~product(e_1, e_5, e_6)) | (~product(e_4, e_5, e_6))),
% 0.58/0.71 inference(modus_ponens,[status(thm)],[1295, 1294])).
% 0.58/0.71 tff(1297,plain,
% 0.58/0.71 ($false),
% 0.58/0.71 inference(unit_resolution,[status(thm)],[1296, 1293, 87, 156, 1290])).
% 0.58/0.71 tff(1298,plain,((~product(e_4, e_5, e_6)) | (~product(e_1, e_5, e_6))), inference(lemma,lemma(discharge,[]))).
% 0.58/0.71 tff(1299,plain,
% 0.58/0.71 (~product(e_4, e_5, e_6)),
% 0.58/0.71 inference(unit_resolution,[status(thm)],[1298, 1289])).
% 0.58/0.71 tff(1300,assumption,(product(e_4, e_6, e_2)), introduced(assumption)).
% 0.58/0.71 tff(1301,plain,
% 0.58/0.71 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_6, e_1) | (~product(e_4, e_1, e_2)) | (~product(e_4, e_6, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_6, e_1) | (~product(e_4, e_1, e_2)) | (~product(e_4, e_6, e_2)))),
% 0.58/0.71 inference(rewrite,[status(thm)],[])).
% 0.58/0.71 tff(1302,plain,
% 0.58/0.71 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_6, e_1) | (~product(e_4, e_1, e_2)) | (~product(e_4, e_6, e_2)))),
% 0.58/0.71 inference(quant_inst,[status(thm)],[])).
% 0.58/0.71 tff(1303,plain,
% 0.58/0.71 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_6, e_1) | (~product(e_4, e_1, e_2)) | (~product(e_4, e_6, e_2))),
% 0.58/0.71 inference(modus_ponens,[status(thm)],[1302, 1301])).
% 0.58/0.71 tff(1304,plain,
% 0.58/0.71 ($false),
% 0.58/0.71 inference(unit_resolution,[status(thm)],[1303, 1116, 17, 1062, 1300])).
% 0.58/0.71 tff(1305,plain,((~product(e_4, e_6, e_2)) | (~product(e_4, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.58/0.71 tff(1306,plain,
% 0.58/0.71 (~product(e_4, e_6, e_2)),
% 0.58/0.71 inference(unit_resolution,[status(thm)],[1305, 1277])).
% 0.58/0.71 tff(1307,assumption,(product(e_4, e_6, e_5)), introduced(assumption)).
% 0.58/0.71 tff(1308,plain,
% 0.58/0.71 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_1) | (~product(e_1, e_6, e_5)) | (~product(e_4, e_6, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_1) | (~product(e_1, e_6, e_5)) | (~product(e_4, e_6, e_5)))),
% 0.58/0.71 inference(rewrite,[status(thm)],[])).
% 0.58/0.71 tff(1309,plain,
% 0.58/0.71 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_1) | (~product(e_1, e_6, e_5)) | (~product(e_4, e_6, e_5)))),
% 0.58/0.71 inference(quant_inst,[status(thm)],[])).
% 0.58/0.71 tff(1310,plain,
% 0.58/0.71 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_1) | (~product(e_1, e_6, e_5)) | (~product(e_4, e_6, e_5))),
% 0.58/0.71 inference(modus_ponens,[status(thm)],[1309, 1308])).
% 0.58/0.71 tff(1311,plain,
% 0.58/0.71 ($false),
% 0.58/0.71 inference(unit_resolution,[status(thm)],[1310, 1293, 87, 289, 1307])).
% 0.58/0.71 tff(1312,plain,((~product(e_4, e_6, e_5)) | (~product(e_1, e_6, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.58/0.71 tff(1313,plain,
% 0.58/0.71 (~product(e_4, e_6, e_5)),
% 0.58/0.71 inference(unit_resolution,[status(thm)],[1312, 289])).
% 0.58/0.71 tff(1314,plain,
% 0.58/0.71 (~product(e_6, e_1, e_2)),
% 0.58/0.71 inference(unit_resolution,[status(thm)],[1165, 1289])).
% 0.58/0.71 tff(1315,plain,
% 0.58/0.71 (product(e_6, e_1, e_5)),
% 0.58/0.71 inference(unit_resolution,[status(thm)],[1155, 1314])).
% 0.58/0.71 tff(1316,assumption,(product(e_6, e_2, e_5)), introduced(assumption)).
% 0.58/0.71 tff(1317,plain,
% 0.58/0.71 (((~![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_6, e_1, e_5)) | (~product(e_6, e_2, e_5)))) <=> ((~![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_6, e_1, e_5)) | (~product(e_6, e_2, e_5)))),
% 0.58/0.71 inference(rewrite,[status(thm)],[])).
% 0.58/0.71 tff(1318,plain,
% 0.58/0.71 ((~![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_6, e_1, e_5)) | (~product(e_6, e_2, e_5)))),
% 0.58/0.71 inference(quant_inst,[status(thm)],[])).
% 0.58/0.71 tff(1319,plain,
% 0.58/0.71 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_6, e_1, e_5)) | (~product(e_6, e_2, e_5))),
% 0.58/0.71 inference(modus_ponens,[status(thm)],[1318, 1317])).
% 0.58/0.71 tff(1320,plain,
% 0.58/0.71 ($false),
% 0.58/0.71 inference(unit_resolution,[status(thm)],[1319, 90, 17, 1106, 1316])).
% 0.58/0.71 tff(1321,plain,((~product(e_6, e_2, e_5)) | (~product(e_6, e_1, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.58/0.71 tff(1322,plain,
% 0.58/0.71 (~product(e_6, e_2, e_5)),
% 0.58/0.71 inference(unit_resolution,[status(thm)],[1321, 1315])).
% 0.58/0.71 tff(1323,assumption,(product(e_4, e_6, e_1)), introduced(assumption)).
% 0.58/0.71 tff(1324,assumption,(~product(e_2, e_4, e_6)), introduced(assumption)).
% 0.58/0.71 tff(1325,plain,
% 0.58/0.71 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_4, e_2)) | (~product(e_4, e_6, e_1)) | product(e_2, e_4, e_6))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_4, e_2)) | (~product(e_4, e_6, e_1)) | product(e_2, e_4, e_6))),
% 0.58/0.71 inference(rewrite,[status(thm)],[])).
% 0.58/0.71 tff(1326,plain,
% 0.58/0.71 ((product(e_2, e_4, e_6) | (~product(e_1, e_4, e_2)) | (~product(e_4, e_6, e_1))) <=> ((~product(e_1, e_4, e_2)) | (~product(e_4, e_6, e_1)) | product(e_2, e_4, e_6))),
% 0.58/0.71 inference(rewrite,[status(thm)],[])).
% 0.58/0.71 tff(1327,plain,
% 0.58/0.71 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_4, e_6) | (~product(e_1, e_4, e_2)) | (~product(e_4, e_6, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_4, e_2)) | (~product(e_4, e_6, e_1)) | product(e_2, e_4, e_6)))),
% 0.58/0.71 inference(monotonicity,[status(thm)],[1326])).
% 0.58/0.71 tff(1328,plain,
% 0.58/0.71 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_4, e_6) | (~product(e_1, e_4, e_2)) | (~product(e_4, e_6, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_4, e_2)) | (~product(e_4, e_6, e_1)) | product(e_2, e_4, e_6))),
% 0.58/0.71 inference(transitivity,[status(thm)],[1327, 1325])).
% 0.58/0.71 tff(1329,plain,
% 0.58/0.71 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_4, e_6) | (~product(e_1, e_4, e_2)) | (~product(e_4, e_6, e_1)))),
% 0.58/0.71 inference(quant_inst,[status(thm)],[])).
% 0.58/0.71 tff(1330,plain,
% 0.58/0.71 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_4, e_2)) | (~product(e_4, e_6, e_1)) | product(e_2, e_4, e_6)),
% 0.58/0.71 inference(modus_ponens,[status(thm)],[1329, 1328])).
% 0.58/0.71 tff(1331,plain,
% 0.58/0.71 ($false),
% 0.58/0.71 inference(unit_resolution,[status(thm)],[1330, 58, 1032, 1323, 1324])).
% 0.58/0.71 tff(1332,plain,(product(e_2, e_4, e_6) | (~product(e_4, e_6, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.58/0.71 tff(1333,plain,
% 0.58/0.71 (product(e_2, e_4, e_6)),
% 0.58/0.71 inference(unit_resolution,[status(thm)],[1332, 1323])).
% 0.58/0.71 tff(1334,plain,
% 0.58/0.71 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_6, e_2) | (~product(e_4, e_6, e_1)) | (~product(e_6, e_2, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_6, e_2) | (~product(e_4, e_6, e_1)) | (~product(e_6, e_2, e_4)))),
% 0.58/0.71 inference(rewrite,[status(thm)],[])).
% 0.58/0.71 tff(1335,plain,
% 0.58/0.71 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_6, e_2) | (~product(e_4, e_6, e_1)) | (~product(e_6, e_2, e_4)))),
% 0.58/0.71 inference(quant_inst,[status(thm)],[])).
% 0.58/0.71 tff(1336,plain,
% 0.58/0.71 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_6, e_2) | (~product(e_4, e_6, e_1)) | (~product(e_6, e_2, e_4))),
% 0.58/0.71 inference(modus_ponens,[status(thm)],[1335, 1334])).
% 0.58/0.71 tff(1337,plain,
% 0.58/0.71 (~product(e_6, e_2, e_4)),
% 0.58/0.71 inference(unit_resolution,[status(thm)],[1336, 58, 374, 1323])).
% 0.58/0.71 tff(1338,assumption,(~product(e_6, e_2, e_5)), introduced(assumption)).
% 0.58/0.71 tff(1339,assumption,(product(e_2, e_4, e_6)), introduced(assumption)).
% 0.58/0.71 tff(1340,assumption,(product(e_6, e_2, e_1)), introduced(assumption)).
% 0.58/0.71 tff(1341,plain,
% 0.58/0.71 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_4) | (~product(e_6, e_2, e_1)) | (~product(e_2, e_4, e_6)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_2, e_4) | (~product(e_6, e_2, e_1)) | (~product(e_2, e_4, e_6)))),
% 0.58/0.71 inference(rewrite,[status(thm)],[])).
% 0.58/0.71 tff(1342,plain,
% 0.58/0.71 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_4) | (~product(e_6, e_2, e_1)) | (~product(e_2, e_4, e_6)))),
% 0.58/0.71 inference(quant_inst,[status(thm)],[])).
% 0.58/0.71 tff(1343,plain,
% 0.58/0.71 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_2, e_4) | (~product(e_6, e_2, e_1)) | (~product(e_2, e_4, e_6))),
% 0.58/0.71 inference(modus_ponens,[status(thm)],[1342, 1341])).
% 0.58/0.71 tff(1344,plain,
% 0.58/0.71 ($false),
% 0.58/0.71 inference(unit_resolution,[status(thm)],[1343, 58, 826, 1340, 1339])).
% 0.58/0.71 tff(1345,plain,((~product(e_6, e_2, e_1)) | product(e_1, e_2, e_4) | (~product(e_2, e_4, e_6))), inference(lemma,lemma(discharge,[]))).
% 0.58/0.71 tff(1346,plain,
% 0.58/0.71 (~product(e_6, e_2, e_1)),
% 0.58/0.71 inference(unit_resolution,[status(thm)],[1345, 1333, 826])).
% 0.58/0.71 tff(1347,assumption,(product(e_6, e_2, e_2)), introduced(assumption)).
% 0.58/0.71 tff(1348,plain,
% 0.58/0.71 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_6, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_6, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_6, e_2, e_2)))),
% 0.58/0.71 inference(rewrite,[status(thm)],[])).
% 0.58/0.71 tff(1349,plain,
% 0.58/0.71 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_6, e_2, e_2)))),
% 0.58/0.71 inference(quant_inst,[status(thm)],[])).
% 0.58/0.71 tff(1350,plain,
% 0.58/0.71 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_6, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_6, e_2, e_2))),
% 0.58/0.71 inference(modus_ponens,[status(thm)],[1349, 1348])).
% 0.58/0.71 tff(1351,plain,
% 0.58/0.71 ($false),
% 0.58/0.71 inference(unit_resolution,[status(thm)],[1350, 855, 87, 692, 1347])).
% 0.58/0.71 tff(1352,plain,(~product(e_6, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.58/0.71 tff(1353,plain,
% 0.58/0.71 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_2)) | (~group_element(e_6)) | product(e_6, e_2, e_2) | product(e_6, e_2, e_6) | product(e_6, e_2, e_1) | product(e_6, e_2, e_5) | product(e_6, e_2, e_3) | product(e_6, e_2, e_4))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_2)) | (~group_element(e_6)) | product(e_6, e_2, e_2) | product(e_6, e_2, e_6) | product(e_6, e_2, e_1) | product(e_6, e_2, e_5) | product(e_6, e_2, e_3) | product(e_6, e_2, e_4))),
% 0.58/0.71 inference(rewrite,[status(thm)],[])).
% 0.58/0.71 tff(1354,plain,
% 0.58/0.71 ((product(e_6, e_2, e_6) | product(e_6, e_2, e_5) | product(e_6, e_2, e_4) | product(e_6, e_2, e_3) | product(e_6, e_2, e_2) | product(e_6, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_6))) <=> ((~group_element(e_2)) | (~group_element(e_6)) | product(e_6, e_2, e_2) | product(e_6, e_2, e_6) | product(e_6, e_2, e_1) | product(e_6, e_2, e_5) | product(e_6, e_2, e_3) | product(e_6, e_2, e_4))),
% 0.58/0.71 inference(rewrite,[status(thm)],[])).
% 0.58/0.71 tff(1355,plain,
% 0.58/0.71 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_6, e_2, e_6) | product(e_6, e_2, e_5) | product(e_6, e_2, e_4) | product(e_6, e_2, e_3) | product(e_6, e_2, e_2) | product(e_6, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_6)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_2)) | (~group_element(e_6)) | product(e_6, e_2, e_2) | product(e_6, e_2, e_6) | product(e_6, e_2, e_1) | product(e_6, e_2, e_5) | product(e_6, e_2, e_3) | product(e_6, e_2, e_4)))),
% 0.58/0.71 inference(monotonicity,[status(thm)],[1354])).
% 0.58/0.71 tff(1356,plain,
% 0.58/0.71 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_6, e_2, e_6) | product(e_6, e_2, e_5) | product(e_6, e_2, e_4) | product(e_6, e_2, e_3) | product(e_6, e_2, e_2) | product(e_6, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_6)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_2)) | (~group_element(e_6)) | product(e_6, e_2, e_2) | product(e_6, e_2, e_6) | product(e_6, e_2, e_1) | product(e_6, e_2, e_5) | product(e_6, e_2, e_3) | product(e_6, e_2, e_4))),
% 0.58/0.71 inference(transitivity,[status(thm)],[1355, 1353])).
% 0.58/0.71 tff(1357,plain,
% 0.58/0.71 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_6, e_2, e_6) | product(e_6, e_2, e_5) | product(e_6, e_2, e_4) | product(e_6, e_2, e_3) | product(e_6, e_2, e_2) | product(e_6, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_6)))),
% 0.58/0.71 inference(quant_inst,[status(thm)],[])).
% 0.58/0.71 tff(1358,plain,
% 0.58/0.71 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_2)) | (~group_element(e_6)) | product(e_6, e_2, e_2) | product(e_6, e_2, e_6) | product(e_6, e_2, e_1) | product(e_6, e_2, e_5) | product(e_6, e_2, e_3) | product(e_6, e_2, e_4)),
% 0.58/0.72 inference(modus_ponens,[status(thm)],[1357, 1356])).
% 0.58/0.72 tff(1359,plain,
% 0.58/0.72 (product(e_6, e_2, e_6) | product(e_6, e_2, e_1) | product(e_6, e_2, e_5) | product(e_6, e_2, e_3) | product(e_6, e_2, e_4)),
% 0.58/0.72 inference(unit_resolution,[status(thm)],[1358, 132, 384, 129, 1352])).
% 0.58/0.72 tff(1360,plain,
% 0.58/0.72 (product(e_6, e_2, e_6)),
% 0.58/0.72 inference(unit_resolution,[status(thm)],[1359, 1346, 1338, 1234, 1337])).
% 0.58/0.72 tff(1361,plain,
% 0.58/0.72 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_6, e_2, e_6)) | product(e_6, e_2, e_4) | (~product(e_2, e_4, e_6)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_6, e_2, e_6)) | product(e_6, e_2, e_4) | (~product(e_2, e_4, e_6)))),
% 0.58/0.72 inference(rewrite,[status(thm)],[])).
% 0.58/0.72 tff(1362,plain,
% 0.58/0.72 ((product(e_6, e_2, e_4) | (~product(e_6, e_2, e_6)) | (~product(e_2, e_4, e_6))) <=> ((~product(e_6, e_2, e_6)) | product(e_6, e_2, e_4) | (~product(e_2, e_4, e_6)))),
% 0.58/0.72 inference(rewrite,[status(thm)],[])).
% 0.58/0.72 tff(1363,plain,
% 0.58/0.72 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_6, e_2, e_4) | (~product(e_6, e_2, e_6)) | (~product(e_2, e_4, e_6)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_6, e_2, e_6)) | product(e_6, e_2, e_4) | (~product(e_2, e_4, e_6))))),
% 0.58/0.72 inference(monotonicity,[status(thm)],[1362])).
% 0.58/0.72 tff(1364,plain,
% 0.58/0.72 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_6, e_2, e_4) | (~product(e_6, e_2, e_6)) | (~product(e_2, e_4, e_6)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_6, e_2, e_6)) | product(e_6, e_2, e_4) | (~product(e_2, e_4, e_6)))),
% 0.58/0.72 inference(transitivity,[status(thm)],[1363, 1361])).
% 0.58/0.72 tff(1365,plain,
% 0.58/0.72 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_6, e_2, e_4) | (~product(e_6, e_2, e_6)) | (~product(e_2, e_4, e_6)))),
% 0.58/0.72 inference(quant_inst,[status(thm)],[])).
% 0.58/0.72 tff(1366,plain,
% 0.58/0.72 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_6, e_2, e_6)) | product(e_6, e_2, e_4) | (~product(e_2, e_4, e_6))),
% 0.58/0.72 inference(modus_ponens,[status(thm)],[1365, 1364])).
% 0.58/0.72 tff(1367,plain,
% 0.58/0.72 ($false),
% 0.58/0.72 inference(unit_resolution,[status(thm)],[1366, 58, 1360, 1337, 1333])).
% 0.58/0.72 tff(1368,plain,((~product(e_4, e_6, e_1)) | product(e_6, e_2, e_5) | product(e_6, e_2, e_3) | product(e_1, e_2, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.58/0.72 tff(1369,plain,
% 0.58/0.72 (~product(e_4, e_6, e_1)),
% 0.58/0.72 inference(unit_resolution,[status(thm)],[1368, 1322, 1234, 826])).
% 0.58/0.72 tff(1370,assumption,(product(e_4, e_6, e_4)), introduced(assumption)).
% 0.58/0.72 tff(1371,plain,
% 0.58/0.72 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_6, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_6, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_6, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_6, e_4)))),
% 0.58/0.72 inference(rewrite,[status(thm)],[])).
% 0.58/0.72 tff(1372,plain,
% 0.58/0.72 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_6, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_6, e_4)))),
% 0.58/0.72 inference(quant_inst,[status(thm)],[])).
% 0.58/0.72 tff(1373,plain,
% 0.58/0.72 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_6, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_6, e_4))),
% 0.67/0.72 inference(modus_ponens,[status(thm)],[1372, 1371])).
% 0.67/0.72 tff(1374,plain,
% 0.67/0.72 ($false),
% 0.67/0.72 inference(unit_resolution,[status(thm)],[1373, 635, 17, 1370, 184])).
% 0.67/0.72 tff(1375,plain,(~product(e_4, e_6, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.67/0.72 tff(1376,assumption,(product(e_4, e_6, e_6)), introduced(assumption)).
% 0.67/0.72 tff(1377,plain,
% 0.67/0.72 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_6) | (~product(e_4, e_6, e_6)) | (~product(e_6, e_6, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_6) | (~product(e_4, e_6, e_6)) | (~product(e_6, e_6, e_6)))),
% 0.67/0.72 inference(rewrite,[status(thm)],[])).
% 0.67/0.72 tff(1378,plain,
% 0.67/0.72 ((equalish(e_4, e_6) | (~product(e_6, e_6, e_6)) | (~product(e_4, e_6, e_6))) <=> (equalish(e_4, e_6) | (~product(e_4, e_6, e_6)) | (~product(e_6, e_6, e_6)))),
% 0.67/0.72 inference(rewrite,[status(thm)],[])).
% 0.67/0.72 tff(1379,plain,
% 0.67/0.72 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_6) | (~product(e_6, e_6, e_6)) | (~product(e_4, e_6, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_6) | (~product(e_4, e_6, e_6)) | (~product(e_6, e_6, e_6))))),
% 0.67/0.72 inference(monotonicity,[status(thm)],[1378])).
% 0.67/0.72 tff(1380,plain,
% 0.67/0.72 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_6) | (~product(e_6, e_6, e_6)) | (~product(e_4, e_6, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_6) | (~product(e_4, e_6, e_6)) | (~product(e_6, e_6, e_6)))),
% 0.67/0.72 inference(transitivity,[status(thm)],[1379, 1377])).
% 0.67/0.72 tff(1381,plain,
% 0.67/0.72 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_6) | (~product(e_6, e_6, e_6)) | (~product(e_4, e_6, e_6)))),
% 0.67/0.72 inference(quant_inst,[status(thm)],[])).
% 0.67/0.72 tff(1382,plain,
% 0.67/0.72 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_6) | (~product(e_4, e_6, e_6)) | (~product(e_6, e_6, e_6))),
% 0.67/0.72 inference(modus_ponens,[status(thm)],[1381, 1380])).
% 0.67/0.72 tff(1383,plain,
% 0.67/0.72 ($false),
% 0.67/0.72 inference(unit_resolution,[status(thm)],[1382, 293, 87, 1376, 933])).
% 0.67/0.72 tff(1384,plain,(~product(e_4, e_6, e_6)), inference(lemma,lemma(discharge,[]))).
% 0.67/0.72 tff(1385,plain,
% 0.67/0.72 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_4)) | (~group_element(e_6)) | product(e_4, e_6, e_6) | product(e_4, e_6, e_4) | product(e_4, e_6, e_3) | product(e_4, e_6, e_5) | product(e_4, e_6, e_2) | product(e_4, e_6, e_1))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_4)) | (~group_element(e_6)) | product(e_4, e_6, e_6) | product(e_4, e_6, e_4) | product(e_4, e_6, e_3) | product(e_4, e_6, e_5) | product(e_4, e_6, e_2) | product(e_4, e_6, e_1))),
% 0.67/0.72 inference(rewrite,[status(thm)],[])).
% 0.67/0.72 tff(1386,plain,
% 0.67/0.72 ((product(e_4, e_6, e_6) | product(e_4, e_6, e_5) | product(e_4, e_6, e_4) | product(e_4, e_6, e_3) | product(e_4, e_6, e_2) | product(e_4, e_6, e_1) | (~group_element(e_6)) | (~group_element(e_4))) <=> ((~group_element(e_4)) | (~group_element(e_6)) | product(e_4, e_6, e_6) | product(e_4, e_6, e_4) | product(e_4, e_6, e_3) | product(e_4, e_6, e_5) | product(e_4, e_6, e_2) | product(e_4, e_6, e_1))),
% 0.67/0.72 inference(rewrite,[status(thm)],[])).
% 0.67/0.72 tff(1387,plain,
% 0.67/0.72 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_6, e_6) | product(e_4, e_6, e_5) | product(e_4, e_6, e_4) | product(e_4, e_6, e_3) | product(e_4, e_6, e_2) | product(e_4, e_6, e_1) | (~group_element(e_6)) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_4)) | (~group_element(e_6)) | product(e_4, e_6, e_6) | product(e_4, e_6, e_4) | product(e_4, e_6, e_3) | product(e_4, e_6, e_5) | product(e_4, e_6, e_2) | product(e_4, e_6, e_1)))),
% 0.67/0.72 inference(monotonicity,[status(thm)],[1386])).
% 0.67/0.72 tff(1388,plain,
% 0.67/0.72 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_6, e_6) | product(e_4, e_6, e_5) | product(e_4, e_6, e_4) | product(e_4, e_6, e_3) | product(e_4, e_6, e_2) | product(e_4, e_6, e_1) | (~group_element(e_6)) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_4)) | (~group_element(e_6)) | product(e_4, e_6, e_6) | product(e_4, e_6, e_4) | product(e_4, e_6, e_3) | product(e_4, e_6, e_5) | product(e_4, e_6, e_2) | product(e_4, e_6, e_1))),
% 0.67/0.72 inference(transitivity,[status(thm)],[1387, 1385])).
% 0.67/0.72 tff(1389,plain,
% 0.67/0.72 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_6, e_6) | product(e_4, e_6, e_5) | product(e_4, e_6, e_4) | product(e_4, e_6, e_3) | product(e_4, e_6, e_2) | product(e_4, e_6, e_1) | (~group_element(e_6)) | (~group_element(e_4)))),
% 0.67/0.72 inference(quant_inst,[status(thm)],[])).
% 0.67/0.72 tff(1390,plain,
% 0.67/0.72 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_4)) | (~group_element(e_6)) | product(e_4, e_6, e_6) | product(e_4, e_6, e_4) | product(e_4, e_6, e_3) | product(e_4, e_6, e_5) | product(e_4, e_6, e_2) | product(e_4, e_6, e_1)),
% 0.67/0.72 inference(modus_ponens,[status(thm)],[1389, 1388])).
% 0.67/0.72 tff(1391,plain,
% 0.67/0.72 (product(e_4, e_6, e_6) | product(e_4, e_6, e_4) | product(e_4, e_6, e_3) | product(e_4, e_6, e_5) | product(e_4, e_6, e_2) | product(e_4, e_6, e_1)),
% 0.67/0.72 inference(unit_resolution,[status(thm)],[1390, 279, 384, 129])).
% 0.67/0.72 tff(1392,plain,
% 0.67/0.72 (product(e_4, e_6, e_4) | product(e_4, e_6, e_3) | product(e_4, e_6, e_5) | product(e_4, e_6, e_2) | product(e_4, e_6, e_1)),
% 0.67/0.72 inference(unit_resolution,[status(thm)],[1391, 1384])).
% 0.67/0.72 tff(1393,plain,
% 0.67/0.72 (product(e_4, e_6, e_3) | product(e_4, e_6, e_5) | product(e_4, e_6, e_2) | product(e_4, e_6, e_1)),
% 0.67/0.72 inference(unit_resolution,[status(thm)],[1392, 1375])).
% 0.67/0.72 tff(1394,plain,
% 0.67/0.72 (product(e_4, e_6, e_3)),
% 0.67/0.72 inference(unit_resolution,[status(thm)],[1393, 1369, 1313, 1306])).
% 0.67/0.72 tff(1395,assumption,(product(e_4, e_5, e_3)), introduced(assumption)).
% 0.67/0.72 tff(1396,assumption,(product(e_4, e_6, e_3)), introduced(assumption)).
% 0.67/0.72 tff(1397,plain,
% 0.67/0.72 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_6, e_5) | (~product(e_4, e_5, e_3)) | (~product(e_4, e_6, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_6, e_5) | (~product(e_4, e_5, e_3)) | (~product(e_4, e_6, e_3)))),
% 0.67/0.72 inference(rewrite,[status(thm)],[])).
% 0.67/0.72 tff(1398,plain,
% 0.67/0.72 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_6, e_5) | (~product(e_4, e_5, e_3)) | (~product(e_4, e_6, e_3)))),
% 0.67/0.72 inference(quant_inst,[status(thm)],[])).
% 0.67/0.72 tff(1399,plain,
% 0.67/0.72 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_6, e_5) | (~product(e_4, e_5, e_3)) | (~product(e_4, e_6, e_3))),
% 0.67/0.72 inference(modus_ponens,[status(thm)],[1398, 1397])).
% 0.67/0.72 tff(1400,plain,
% 0.67/0.72 ($false),
% 0.67/0.72 inference(unit_resolution,[status(thm)],[1399, 160, 17, 1396, 1395])).
% 0.67/0.72 tff(1401,plain,((~product(e_4, e_6, e_3)) | (~product(e_4, e_5, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.67/0.72 tff(1402,plain,
% 0.67/0.72 (~product(e_4, e_5, e_3)),
% 0.67/0.72 inference(unit_resolution,[status(thm)],[1401, 1394])).
% 0.67/0.72 tff(1403,assumption,(product(e_4, e_5, e_4)), introduced(assumption)).
% 0.67/0.72 tff(1404,plain,
% 0.67/0.72 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_5, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_5, e_4)))),
% 0.67/0.72 inference(rewrite,[status(thm)],[])).
% 0.67/0.72 tff(1405,plain,
% 0.67/0.72 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_5, e_4)))),
% 0.67/0.72 inference(quant_inst,[status(thm)],[])).
% 0.67/0.72 tff(1406,plain,
% 0.67/0.72 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_5, e_4))),
% 0.67/0.72 inference(modus_ponens,[status(thm)],[1405, 1404])).
% 0.67/0.72 tff(1407,plain,
% 0.67/0.72 ($false),
% 0.67/0.72 inference(unit_resolution,[status(thm)],[1406, 173, 17, 1403, 184])).
% 0.67/0.72 tff(1408,plain,(~product(e_4, e_5, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.67/0.72 tff(1409,plain,
% 0.67/0.72 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_4)) | (~group_element(e_5)) | product(e_4, e_5, e_5) | product(e_4, e_5, e_4) | product(e_4, e_5, e_6) | product(e_4, e_5, e_3) | product(e_4, e_5, e_1) | product(e_4, e_5, e_2))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_4)) | (~group_element(e_5)) | product(e_4, e_5, e_5) | product(e_4, e_5, e_4) | product(e_4, e_5, e_6) | product(e_4, e_5, e_3) | product(e_4, e_5, e_1) | product(e_4, e_5, e_2))),
% 0.67/0.72 inference(rewrite,[status(thm)],[])).
% 0.67/0.72 tff(1410,plain,
% 0.67/0.72 ((product(e_4, e_5, e_6) | product(e_4, e_5, e_5) | product(e_4, e_5, e_4) | product(e_4, e_5, e_3) | product(e_4, e_5, e_2) | product(e_4, e_5, e_1) | (~group_element(e_5)) | (~group_element(e_4))) <=> ((~group_element(e_4)) | (~group_element(e_5)) | product(e_4, e_5, e_5) | product(e_4, e_5, e_4) | product(e_4, e_5, e_6) | product(e_4, e_5, e_3) | product(e_4, e_5, e_1) | product(e_4, e_5, e_2))),
% 0.67/0.72 inference(rewrite,[status(thm)],[])).
% 0.67/0.72 tff(1411,plain,
% 0.67/0.72 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_5, e_6) | product(e_4, e_5, e_5) | product(e_4, e_5, e_4) | product(e_4, e_5, e_3) | product(e_4, e_5, e_2) | product(e_4, e_5, e_1) | (~group_element(e_5)) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_4)) | (~group_element(e_5)) | product(e_4, e_5, e_5) | product(e_4, e_5, e_4) | product(e_4, e_5, e_6) | product(e_4, e_5, e_3) | product(e_4, e_5, e_1) | product(e_4, e_5, e_2)))),
% 0.67/0.72 inference(monotonicity,[status(thm)],[1410])).
% 0.67/0.72 tff(1412,plain,
% 0.67/0.72 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_5, e_6) | product(e_4, e_5, e_5) | product(e_4, e_5, e_4) | product(e_4, e_5, e_3) | product(e_4, e_5, e_2) | product(e_4, e_5, e_1) | (~group_element(e_5)) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_4)) | (~group_element(e_5)) | product(e_4, e_5, e_5) | product(e_4, e_5, e_4) | product(e_4, e_5, e_6) | product(e_4, e_5, e_3) | product(e_4, e_5, e_1) | product(e_4, e_5, e_2))),
% 0.67/0.73 inference(transitivity,[status(thm)],[1411, 1409])).
% 0.67/0.73 tff(1413,plain,
% 0.67/0.73 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_5, e_6) | product(e_4, e_5, e_5) | product(e_4, e_5, e_4) | product(e_4, e_5, e_3) | product(e_4, e_5, e_2) | product(e_4, e_5, e_1) | (~group_element(e_5)) | (~group_element(e_4)))),
% 0.67/0.73 inference(quant_inst,[status(thm)],[])).
% 0.67/0.73 tff(1414,plain,
% 0.67/0.73 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_4)) | (~group_element(e_5)) | product(e_4, e_5, e_5) | product(e_4, e_5, e_4) | product(e_4, e_5, e_6) | product(e_4, e_5, e_3) | product(e_4, e_5, e_1) | product(e_4, e_5, e_2)),
% 0.67/0.73 inference(modus_ponens,[status(thm)],[1413, 1412])).
% 0.67/0.73 tff(1415,plain,
% 0.67/0.73 (product(e_4, e_5, e_5) | product(e_4, e_5, e_4) | product(e_4, e_5, e_6) | product(e_4, e_5, e_3) | product(e_4, e_5, e_1) | product(e_4, e_5, e_2)),
% 0.67/0.73 inference(unit_resolution,[status(thm)],[1414, 279, 443, 129])).
% 0.67/0.73 tff(1416,plain,
% 0.67/0.73 (product(e_4, e_5, e_5) | product(e_4, e_5, e_6) | product(e_4, e_5, e_3) | product(e_4, e_5, e_1) | product(e_4, e_5, e_2)),
% 0.67/0.73 inference(unit_resolution,[status(thm)],[1415, 1408])).
% 0.67/0.73 tff(1417,plain,
% 0.67/0.73 (product(e_4, e_5, e_6) | product(e_4, e_5, e_3) | product(e_4, e_5, e_1) | product(e_4, e_5, e_2)),
% 0.67/0.73 inference(unit_resolution,[status(thm)],[1416, 1104])).
% 0.67/0.73 tff(1418,plain,
% 0.67/0.73 (product(e_4, e_5, e_1)),
% 0.67/0.73 inference(unit_resolution,[status(thm)],[1417, 1402, 1299, 1287])).
% 0.67/0.73 tff(1419,plain,
% 0.67/0.73 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_5, e_1) | (~product(e_4, e_5, e_1)) | (~product(e_5, e_1, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_5, e_1) | (~product(e_4, e_5, e_1)) | (~product(e_5, e_1, e_4)))),
% 0.67/0.73 inference(rewrite,[status(thm)],[])).
% 0.67/0.73 tff(1420,plain,
% 0.67/0.73 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_5, e_1) | (~product(e_4, e_5, e_1)) | (~product(e_5, e_1, e_4)))),
% 0.67/0.73 inference(quant_inst,[status(thm)],[])).
% 0.67/0.73 tff(1421,plain,
% 0.67/0.73 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_5, e_1) | (~product(e_4, e_5, e_1)) | (~product(e_5, e_1, e_4))),
% 0.67/0.73 inference(modus_ponens,[status(thm)],[1420, 1419])).
% 0.67/0.73 tff(1422,plain,
% 0.67/0.73 (~product(e_5, e_1, e_4)),
% 0.67/0.73 inference(unit_resolution,[status(thm)],[1421, 58, 440, 1418])).
% 0.67/0.73 tff(1423,assumption,(product(e_5, e_1, e_3)), introduced(assumption)).
% 0.67/0.73 tff(1424,plain,
% 0.67/0.73 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_6) | (~product(e_1, e_6, e_5)) | (~product(e_5, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_6) | (~product(e_1, e_6, e_5)) | (~product(e_5, e_1, e_3)))),
% 0.67/0.73 inference(rewrite,[status(thm)],[])).
% 0.67/0.73 tff(1425,plain,
% 0.67/0.73 ((product(e_3, e_1, e_6) | (~product(e_5, e_1, e_3)) | (~product(e_1, e_6, e_5))) <=> (product(e_3, e_1, e_6) | (~product(e_1, e_6, e_5)) | (~product(e_5, e_1, e_3)))),
% 0.67/0.73 inference(rewrite,[status(thm)],[])).
% 0.67/0.73 tff(1426,plain,
% 0.67/0.73 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_6) | (~product(e_5, e_1, e_3)) | (~product(e_1, e_6, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_6) | (~product(e_1, e_6, e_5)) | (~product(e_5, e_1, e_3))))),
% 0.67/0.73 inference(monotonicity,[status(thm)],[1425])).
% 0.67/0.73 tff(1427,plain,
% 0.67/0.73 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_6) | (~product(e_5, e_1, e_3)) | (~product(e_1, e_6, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_6) | (~product(e_1, e_6, e_5)) | (~product(e_5, e_1, e_3)))),
% 0.67/0.73 inference(transitivity,[status(thm)],[1426, 1424])).
% 0.67/0.73 tff(1428,plain,
% 0.67/0.73 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_6) | (~product(e_5, e_1, e_3)) | (~product(e_1, e_6, e_5)))),
% 0.67/0.73 inference(quant_inst,[status(thm)],[])).
% 0.67/0.73 tff(1429,plain,
% 0.67/0.73 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_6) | (~product(e_1, e_6, e_5)) | (~product(e_5, e_1, e_3))),
% 0.67/0.73 inference(modus_ponens,[status(thm)],[1428, 1427])).
% 0.67/0.73 tff(1430,plain,
% 0.67/0.73 ($false),
% 0.67/0.73 inference(unit_resolution,[status(thm)],[1429, 58, 250, 289, 1423])).
% 0.67/0.73 tff(1431,plain,((~product(e_5, e_1, e_3)) | (~product(e_1, e_6, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.67/0.73 tff(1432,plain,
% 0.67/0.73 (~product(e_5, e_1, e_3)),
% 0.67/0.73 inference(unit_resolution,[status(thm)],[1431, 289])).
% 0.67/0.73 tff(1433,plain,
% 0.67/0.73 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_1)) | (~group_element(e_5)) | product(e_5, e_1, e_4) | product(e_5, e_1, e_3) | product(e_5, e_1, e_2) | product(e_5, e_1, e_5) | product(e_5, e_1, e_1) | product(e_5, e_1, e_6))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | (~group_element(e_5)) | product(e_5, e_1, e_4) | product(e_5, e_1, e_3) | product(e_5, e_1, e_2) | product(e_5, e_1, e_5) | product(e_5, e_1, e_1) | product(e_5, e_1, e_6))),
% 0.67/0.73 inference(rewrite,[status(thm)],[])).
% 0.67/0.73 tff(1434,plain,
% 0.67/0.73 ((product(e_5, e_1, e_6) | product(e_5, e_1, e_5) | product(e_5, e_1, e_4) | product(e_5, e_1, e_3) | product(e_5, e_1, e_2) | product(e_5, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_5))) <=> ((~group_element(e_1)) | (~group_element(e_5)) | product(e_5, e_1, e_4) | product(e_5, e_1, e_3) | product(e_5, e_1, e_2) | product(e_5, e_1, e_5) | product(e_5, e_1, e_1) | product(e_5, e_1, e_6))),
% 0.67/0.73 inference(rewrite,[status(thm)],[])).
% 0.67/0.73 tff(1435,plain,
% 0.67/0.73 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_5, e_1, e_6) | product(e_5, e_1, e_5) | product(e_5, e_1, e_4) | product(e_5, e_1, e_3) | product(e_5, e_1, e_2) | product(e_5, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_5)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_1)) | (~group_element(e_5)) | product(e_5, e_1, e_4) | product(e_5, e_1, e_3) | product(e_5, e_1, e_2) | product(e_5, e_1, e_5) | product(e_5, e_1, e_1) | product(e_5, e_1, e_6)))),
% 0.67/0.73 inference(monotonicity,[status(thm)],[1434])).
% 0.67/0.73 tff(1436,plain,
% 0.67/0.73 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_5, e_1, e_6) | product(e_5, e_1, e_5) | product(e_5, e_1, e_4) | product(e_5, e_1, e_3) | product(e_5, e_1, e_2) | product(e_5, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_5)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | (~group_element(e_5)) | product(e_5, e_1, e_4) | product(e_5, e_1, e_3) | product(e_5, e_1, e_2) | product(e_5, e_1, e_5) | product(e_5, e_1, e_1) | product(e_5, e_1, e_6))),
% 0.67/0.73 inference(transitivity,[status(thm)],[1435, 1433])).
% 0.67/0.73 tff(1437,plain,
% 0.67/0.73 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_5, e_1, e_6) | product(e_5, e_1, e_5) | product(e_5, e_1, e_4) | product(e_5, e_1, e_3) | product(e_5, e_1, e_2) | product(e_5, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_5)))),
% 0.67/0.73 inference(quant_inst,[status(thm)],[])).
% 0.67/0.73 tff(1438,plain,
% 0.67/0.73 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | (~group_element(e_5)) | product(e_5, e_1, e_4) | product(e_5, e_1, e_3) | product(e_5, e_1, e_2) | product(e_5, e_1, e_5) | product(e_5, e_1, e_1) | product(e_5, e_1, e_6)),
% 0.67/0.73 inference(modus_ponens,[status(thm)],[1437, 1436])).
% 0.67/0.73 tff(1439,plain,
% 0.67/0.73 (product(e_5, e_1, e_2) | product(e_5, e_1, e_5) | product(e_5, e_1, e_1) | product(e_5, e_1, e_6)),
% 0.67/0.73 inference(unit_resolution,[status(thm)],[1438, 135, 443, 129, 1432, 1422])).
% 0.67/0.73 tff(1440,plain,
% 0.67/0.73 (product(e_5, e_1, e_5)),
% 0.67/0.73 inference(unit_resolution,[status(thm)],[1439, 1264, 1254, 1244])).
% 0.67/0.73 tff(1441,plain,
% 0.67/0.73 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_6, e_5)) | product(e_5, e_1, e_6) | (~product(e_5, e_1, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_6, e_5)) | product(e_5, e_1, e_6) | (~product(e_5, e_1, e_5)))),
% 0.67/0.73 inference(rewrite,[status(thm)],[])).
% 0.67/0.73 tff(1442,plain,
% 0.67/0.73 ((product(e_5, e_1, e_6) | (~product(e_5, e_1, e_5)) | (~product(e_1, e_6, e_5))) <=> ((~product(e_1, e_6, e_5)) | product(e_5, e_1, e_6) | (~product(e_5, e_1, e_5)))),
% 0.67/0.73 inference(rewrite,[status(thm)],[])).
% 0.67/0.73 tff(1443,plain,
% 0.67/0.73 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_5, e_1, e_6) | (~product(e_5, e_1, e_5)) | (~product(e_1, e_6, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_6, e_5)) | product(e_5, e_1, e_6) | (~product(e_5, e_1, e_5))))),
% 0.67/0.73 inference(monotonicity,[status(thm)],[1442])).
% 0.67/0.73 tff(1444,plain,
% 0.67/0.73 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_5, e_1, e_6) | (~product(e_5, e_1, e_5)) | (~product(e_1, e_6, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_6, e_5)) | product(e_5, e_1, e_6) | (~product(e_5, e_1, e_5)))),
% 0.67/0.73 inference(transitivity,[status(thm)],[1443, 1441])).
% 0.67/0.73 tff(1445,plain,
% 0.67/0.73 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_5, e_1, e_6) | (~product(e_5, e_1, e_5)) | (~product(e_1, e_6, e_5)))),
% 0.67/0.73 inference(quant_inst,[status(thm)],[])).
% 0.67/0.73 tff(1446,plain,
% 0.67/0.73 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_6, e_5)) | product(e_5, e_1, e_6) | (~product(e_5, e_1, e_5))),
% 0.67/0.73 inference(modus_ponens,[status(thm)],[1445, 1444])).
% 0.67/0.73 tff(1447,plain,
% 0.67/0.73 ($false),
% 0.67/0.73 inference(unit_resolution,[status(thm)],[1446, 58, 289, 1264, 1440])).
% 0.67/0.73 tff(1448,plain,((~product(e_1, e_6, e_5)) | product(e_6, e_2, e_3) | product(e_1, e_2, e_4) | product(e_4, e_1, e_5) | product(e_3, e_1, e_3) | product(e_1, e_3, e_6)), inference(lemma,lemma(discharge,[]))).
% 0.67/0.73 tff(1449,plain,
% 0.67/0.73 (product(e_3, e_1, e_3)),
% 0.67/0.73 inference(unit_resolution,[status(thm)],[1448, 5, 826, 3, 1093, 1234])).
% 0.67/0.73 tff(1450,plain,
% 0.67/0.73 (product(e_1, e_3, e_4)),
% 0.67/0.73 inference(unit_resolution,[status(thm)],[1219, 5, 1202])).
% 0.67/0.73 tff(1451,plain,
% 0.67/0.73 (~product(e_1, e_5, e_4)),
% 0.67/0.73 inference(unit_resolution,[status(thm)],[845, 1450])).
% 0.67/0.73 tff(1452,plain,
% 0.67/0.73 (product(e_1, e_5, e_6)),
% 0.67/0.73 inference(unit_resolution,[status(thm)],[450, 155, 152, 741, 153])).
% 0.67/0.73 tff(1453,plain,
% 0.67/0.73 (~product(e_1, e_2, e_6)),
% 0.67/0.73 inference(unit_resolution,[status(thm)],[540, 1452])).
% 0.67/0.73 tff(1454,plain,
% 0.67/0.73 (product(e_1, e_4, e_2)),
% 0.67/0.73 inference(unit_resolution,[status(thm)],[677, 155, 152, 153])).
% 0.67/0.73 tff(1455,plain,
% 0.67/0.73 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_2) | (~product(e_1, e_4, 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_4, e_2) | (~product(e_1, e_4, e_2)) | (~product(e_1, e_2, e_2)))),
% 0.67/0.73 inference(rewrite,[status(thm)],[])).
% 0.67/0.73 tff(1456,plain,
% 0.67/0.73 ((equalish(e_4, e_2) | (~product(e_1, e_2, e_2)) | (~product(e_1, e_4, e_2))) <=> (equalish(e_4, e_2) | (~product(e_1, e_4, e_2)) | (~product(e_1, e_2, e_2)))),
% 0.67/0.73 inference(rewrite,[status(thm)],[])).
% 0.67/0.73 tff(1457,plain,
% 0.67/0.73 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_2) | (~product(e_1, e_2, e_2)) | (~product(e_1, e_4, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_2) | (~product(e_1, e_4, e_2)) | (~product(e_1, e_2, e_2))))),
% 0.67/0.73 inference(monotonicity,[status(thm)],[1456])).
% 0.67/0.73 tff(1458,plain,
% 0.67/0.73 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_2) | (~product(e_1, e_2, e_2)) | (~product(e_1, e_4, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_2) | (~product(e_1, e_4, e_2)) | (~product(e_1, e_2, e_2)))),
% 0.67/0.73 inference(transitivity,[status(thm)],[1457, 1455])).
% 0.67/0.73 tff(1459,plain,
% 0.67/0.73 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_2) | (~product(e_1, e_2, e_2)) | (~product(e_1, e_4, e_2)))),
% 0.67/0.73 inference(quant_inst,[status(thm)],[])).
% 0.67/0.73 tff(1460,plain,
% 0.67/0.73 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_2) | (~product(e_1, e_4, e_2)) | (~product(e_1, e_2, e_2))),
% 0.67/0.73 inference(modus_ponens,[status(thm)],[1459, 1458])).
% 0.67/0.73 tff(1461,plain,
% 0.67/0.73 ($false),
% 0.67/0.73 inference(unit_resolution,[status(thm)],[1460, 659, 17, 1212, 552])).
% 0.67/0.73 tff(1462,plain,((~product(e_1, e_4, e_2)) | (~product(e_1, e_2, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.67/0.73 tff(1463,plain,
% 0.67/0.73 (~product(e_1, e_2, e_2)),
% 0.67/0.73 inference(unit_resolution,[status(thm)],[1462, 1454])).
% 0.67/0.73 tff(1464,assumption,(~product(e_1, e_2, e_6)), introduced(assumption)).
% 0.67/0.73 tff(1465,plain,
% 0.67/0.73 (product(e_1, e_3, e_6)),
% 0.67/0.73 inference(unit_resolution,[status(thm)],[493, 881, 406, 405])).
% 0.67/0.73 tff(1466,plain,
% 0.67/0.73 (~product(e_1, e_5, e_6)),
% 0.67/0.73 inference(unit_resolution,[status(thm)],[425, 1465])).
% 0.67/0.73 tff(1467,plain,
% 0.67/0.73 (product(e_1, e_5, e_5)),
% 0.67/0.73 inference(unit_resolution,[status(thm)],[450, 1466, 153, 155, 154])).
% 0.67/0.73 tff(1468,plain,
% 0.67/0.73 (~product(e_1, e_2, e_5)),
% 0.67/0.73 inference(unit_resolution,[status(thm)],[655, 1467])).
% 0.67/0.73 tff(1469,plain,
% 0.67/0.73 (~product(e_1, e_6, e_5)),
% 0.67/0.73 inference(unit_resolution,[status(thm)],[629, 1467])).
% 0.67/0.73 tff(1470,plain,
% 0.67/0.73 (product(e_1, e_3, e_6)),
% 0.67/0.73 inference(unit_resolution,[status(thm)],[492, 762, 749, 406, 881])).
% 0.67/0.74 tff(1471,assumption,(~product(e_1, e_6, e_5)), introduced(assumption)).
% 0.67/0.74 tff(1472,plain,
% 0.67/0.74 (~product(e_1, e_6, e_4)),
% 0.67/0.74 inference(unit_resolution,[status(thm)],[550, 542])).
% 0.67/0.74 tff(1473,plain,
% 0.67/0.74 (product(e_1, e_6, e_6)),
% 0.67/0.74 inference(unit_resolution,[status(thm)],[391, 1472, 1471, 869, 745])).
% 0.67/0.74 tff(1474,plain,
% 0.67/0.74 ($false),
% 0.67/0.74 inference(unit_resolution,[status(thm)],[792, 1473, 1470])).
% 0.67/0.74 tff(1475,plain,((~product(e_1, e_2, e_4)) | product(e_1, e_6, e_5) | product(e_1, e_6, e_3) | product(e_1, e_6, e_2) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_5)), inference(lemma,lemma(discharge,[]))).
% 0.67/0.74 tff(1476,plain,
% 0.67/0.74 ((~product(e_1, e_2, e_4)) | product(e_1, e_6, e_5) | product(e_1, e_6, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_5)),
% 0.67/0.74 inference(unit_resolution,[status(thm)],[1475, 374, 474])).
% 0.67/0.74 tff(1477,plain,
% 0.67/0.74 (~product(e_1, e_2, e_4)),
% 0.67/0.74 inference(unit_resolution,[status(thm)],[1476, 1469, 869, 406, 881])).
% 0.67/0.74 tff(1478,plain,
% 0.67/0.74 ($false),
% 0.67/0.74 inference(unit_resolution,[status(thm)],[576, 1477, 1468, 748, 1464, 747])).
% 0.67/0.74 tff(1479,plain,(product(e_1, e_3, e_5) | product(e_1, e_2, e_3) | product(e_1, e_2, e_6) | product(e_1, e_2, e_2) | product(e_1, e_6, e_3) | product(e_1, e_3, e_2) | product(e_1, e_5, e_4) | product(e_1, e_5, e_3) | product(e_1, e_5, e_2) | product(e_1, e_3, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.67/0.74 tff(1480,plain,
% 0.67/0.74 (product(e_1, e_3, e_5)),
% 0.67/0.74 inference(unit_resolution,[status(thm)],[1479, 747, 1464, 748, 869, 406, 153, 155, 154, 405])).
% 0.67/0.74 tff(1481,plain,
% 0.67/0.74 (~product(e_1, e_6, e_5)),
% 0.67/0.74 inference(unit_resolution,[status(thm)],[871, 1480])).
% 0.67/0.74 tff(1482,plain,
% 0.67/0.74 (~product(e_1, e_2, e_5)),
% 0.67/0.74 inference(unit_resolution,[status(thm)],[727, 1480])).
% 0.67/0.74 tff(1483,plain,
% 0.67/0.74 (product(e_1, e_2, e_4)),
% 0.67/0.74 inference(unit_resolution,[status(thm)],[576, 1482, 748, 1464, 747])).
% 0.67/0.74 tff(1484,plain,
% 0.67/0.74 (~product(e_1, e_6, e_4)),
% 0.67/0.74 inference(unit_resolution,[status(thm)],[550, 1483])).
% 0.67/0.74 tff(1485,plain,
% 0.67/0.74 (~product(e_1, e_5, e_5)),
% 0.67/0.74 inference(unit_resolution,[status(thm)],[513, 1480])).
% 0.67/0.74 tff(1486,plain,
% 0.67/0.74 (product(e_1, e_5, e_6)),
% 0.67/0.74 inference(unit_resolution,[status(thm)],[450, 1485, 153, 155, 154])).
% 0.67/0.74 tff(1487,plain,
% 0.67/0.74 (~product(e_1, e_6, e_6)),
% 0.67/0.74 inference(unit_resolution,[status(thm)],[168, 1486])).
% 0.67/0.74 tff(1488,plain,
% 0.67/0.74 ($false),
% 0.67/0.74 inference(unit_resolution,[status(thm)],[392, 1487, 1484, 869, 1481])).
% 0.67/0.74 tff(1489,plain,(product(e_1, e_2, e_2) | product(e_1, e_6, e_3) | product(e_1, e_5, e_4) | product(e_1, e_5, e_3) | product(e_1, e_5, e_2) | product(e_1, e_2, e_3) | product(e_1, e_2, e_6) | product(e_1, e_3, e_2) | product(e_1, e_3, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.67/0.74 tff(1490,plain,
% 0.67/0.74 (product(e_1, e_2, e_2) | product(e_1, e_5, e_4) | product(e_1, e_5, e_3) | product(e_1, e_5, e_2) | product(e_1, e_2, e_3) | product(e_1, e_2, e_6) | product(e_1, e_3, e_2) | product(e_1, e_3, e_4)),
% 0.67/0.74 inference(unit_resolution,[status(thm)],[1489, 348])).
% 0.67/0.74 tff(1491,plain,
% 0.67/0.74 (product(e_1, e_3, e_4)),
% 0.67/0.74 inference(unit_resolution,[status(thm)],[1490, 748, 152, 153, 406, 155, 1463, 1453])).
% 0.67/0.74 tff(1492,plain,
% 0.67/0.74 (~product(e_1, e_2, e_4)),
% 0.67/0.74 inference(unit_resolution,[status(thm)],[761, 1491])).
% 0.67/0.74 tff(1493,plain,
% 0.67/0.74 (product(e_1, e_2, e_5)),
% 0.67/0.74 inference(unit_resolution,[status(thm)],[576, 1492, 1463, 1453, 748])).
% 0.67/0.74 tff(1494,plain,
% 0.67/0.74 (~product(e_1, e_6, e_6)),
% 0.67/0.74 inference(unit_resolution,[status(thm)],[168, 1452])).
% 0.67/0.74 tff(1495,plain,
% 0.67/0.74 (~product(e_1, e_6, e_4)),
% 0.67/0.74 inference(unit_resolution,[status(thm)],[403, 1491])).
% 0.67/0.74 tff(1496,plain,
% 0.67/0.74 (product(e_1, e_6, e_5)),
% 0.67/0.74 inference(unit_resolution,[status(thm)],[393, 1495, 1494])).
% 0.67/0.74 tff(1497,plain,
% 0.67/0.74 ($false),
% 0.67/0.74 inference(unit_resolution,[status(thm)],[894, 1496, 1493])).
% 0.67/0.74 tff(1498,plain,(product(e_1, e_2, e_3) | product(e_1, e_5, e_4) | product(e_1, e_3, e_2) | product(e_1, e_5, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.67/0.74 tff(1499,plain,
% 0.67/0.74 (product(e_1, e_2, e_3) | product(e_1, e_5, e_4) | product(e_1, e_5, e_3)),
% 0.67/0.74 inference(unit_resolution,[status(thm)],[1498, 1218])).
% 0.67/0.74 tff(1500,plain,
% 0.67/0.74 (product(e_1, e_2, e_3)),
% 0.67/0.74 inference(unit_resolution,[status(thm)],[1499, 1451, 1051])).
% 0.67/0.74 tff(1501,plain,
% 0.67/0.74 (~product(e_3, e_1, e_2)),
% 0.67/0.74 inference(unit_resolution,[status(thm)],[593, 1500])).
% 0.67/0.74 tff(1502,plain,
% 0.67/0.74 ($false),
% 0.67/0.74 inference(unit_resolution,[status(thm)],[598, 1501, 1500, 1449])).
% 0.67/0.74 tff(1503,plain,(product(e_1, e_3, e_6) | product(e_1, e_2, e_4) | product(e_4, e_1, e_5) | product(e_6, e_2, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.67/0.74 tff(1504,plain,
% 0.67/0.74 (product(e_1, e_3, e_6)),
% 0.67/0.74 inference(unit_resolution,[status(thm)],[1503, 3, 826, 1234])).
% 0.67/0.74 tff(1505,plain,
% 0.67/0.74 (~product(e_1, e_5, e_6)),
% 0.67/0.74 inference(unit_resolution,[status(thm)],[425, 1504])).
% 0.67/0.74 tff(1506,plain,
% 0.67/0.74 (product(e_1, e_5, e_4)),
% 0.67/0.74 inference(unit_resolution,[status(thm)],[1179, 1505, 1051])).
% 0.67/0.74 tff(1507,plain,
% 0.67/0.74 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_5) | (~product(e_1, e_5, e_4)) | (~product(e_4, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_5) | (~product(e_1, e_5, e_4)) | (~product(e_4, e_1, e_2)))),
% 0.67/0.74 inference(rewrite,[status(thm)],[])).
% 0.67/0.74 tff(1508,plain,
% 0.67/0.74 ((product(e_2, e_1, e_5) | (~product(e_4, e_1, e_2)) | (~product(e_1, e_5, e_4))) <=> (product(e_2, e_1, e_5) | (~product(e_1, e_5, e_4)) | (~product(e_4, e_1, e_2)))),
% 0.67/0.74 inference(rewrite,[status(thm)],[])).
% 0.67/0.74 tff(1509,plain,
% 0.67/0.74 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_5) | (~product(e_4, e_1, e_2)) | (~product(e_1, e_5, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_5) | (~product(e_1, e_5, e_4)) | (~product(e_4, e_1, e_2))))),
% 0.67/0.74 inference(monotonicity,[status(thm)],[1508])).
% 0.67/0.74 tff(1510,plain,
% 0.67/0.74 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_5) | (~product(e_4, e_1, e_2)) | (~product(e_1, e_5, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_5) | (~product(e_1, e_5, e_4)) | (~product(e_4, e_1, e_2)))),
% 0.67/0.74 inference(transitivity,[status(thm)],[1509, 1507])).
% 0.67/0.74 tff(1511,plain,
% 0.67/0.74 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_5) | (~product(e_4, e_1, e_2)) | (~product(e_1, e_5, e_4)))),
% 0.67/0.74 inference(quant_inst,[status(thm)],[])).
% 0.67/0.74 tff(1512,plain,
% 0.67/0.74 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_5) | (~product(e_1, e_5, e_4)) | (~product(e_4, e_1, e_2))),
% 0.67/0.74 inference(modus_ponens,[status(thm)],[1511, 1510])).
% 0.67/0.74 tff(1513,plain,
% 0.67/0.74 ($false),
% 0.67/0.74 inference(unit_resolution,[status(thm)],[1512, 58, 112, 1062, 7])).
% 0.67/0.74 tff(1514,plain,((~product(e_4, e_1, e_2)) | (~product(e_1, e_5, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.67/0.74 tff(1515,plain,
% 0.67/0.74 (~product(e_4, e_1, e_2)),
% 0.67/0.74 inference(unit_resolution,[status(thm)],[1514, 1506])).
% 0.67/0.74 tff(1516,plain,
% 0.67/0.74 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_5) | (~product(e_1, e_5, e_4)) | (~product(e_4, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_5) | (~product(e_1, e_5, e_4)) | (~product(e_4, e_1, e_3)))),
% 0.67/0.74 inference(rewrite,[status(thm)],[])).
% 0.67/0.74 tff(1517,plain,
% 0.67/0.74 ((product(e_3, e_1, e_5) | (~product(e_4, e_1, e_3)) | (~product(e_1, e_5, e_4))) <=> (product(e_3, e_1, e_5) | (~product(e_1, e_5, e_4)) | (~product(e_4, e_1, e_3)))),
% 0.67/0.74 inference(rewrite,[status(thm)],[])).
% 0.67/0.74 tff(1518,plain,
% 0.67/0.74 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_5) | (~product(e_4, e_1, e_3)) | (~product(e_1, e_5, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_5) | (~product(e_1, e_5, e_4)) | (~product(e_4, e_1, e_3))))),
% 0.67/0.74 inference(monotonicity,[status(thm)],[1517])).
% 0.67/0.74 tff(1519,plain,
% 0.67/0.74 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_5) | (~product(e_4, e_1, e_3)) | (~product(e_1, e_5, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_5) | (~product(e_1, e_5, e_4)) | (~product(e_4, e_1, e_3)))),
% 0.67/0.74 inference(transitivity,[status(thm)],[1518, 1516])).
% 0.67/0.74 tff(1520,plain,
% 0.67/0.74 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_5) | (~product(e_4, e_1, e_3)) | (~product(e_1, e_5, e_4)))),
% 0.67/0.74 inference(quant_inst,[status(thm)],[])).
% 0.67/0.74 tff(1521,plain,
% 0.67/0.74 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_5) | (~product(e_1, e_5, e_4)) | (~product(e_4, e_1, e_3))),
% 0.67/0.74 inference(modus_ponens,[status(thm)],[1520, 1519])).
% 0.67/0.74 tff(1522,plain,
% 0.67/0.74 ($false),
% 0.67/0.74 inference(unit_resolution,[status(thm)],[1521, 58, 48, 1072, 7])).
% 0.67/0.74 tff(1523,plain,((~product(e_4, e_1, e_3)) | (~product(e_1, e_5, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.67/0.74 tff(1524,plain,
% 0.67/0.74 (~product(e_4, e_1, e_3)),
% 0.67/0.74 inference(unit_resolution,[status(thm)],[1523, 1506])).
% 0.67/0.74 tff(1525,plain,
% 0.67/0.74 ($false),
% 0.67/0.74 inference(unit_resolution,[status(thm)],[1089, 1524, 1515, 3, 1233])).
% 0.67/0.74 tff(1526,plain,(product(e_4, e_1, e_5) | product(e_1, e_2, e_4) | product(e_6, e_2, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.67/0.74 tff(1527,plain,
% 0.67/0.74 (product(e_6, e_2, e_3)),
% 0.67/0.74 inference(unit_resolution,[status(thm)],[1526, 1200, 826])).
% 0.67/0.74 tff(1528,assumption,(product(e_6, e_2, e_3)), introduced(assumption)).
% 0.67/0.74 tff(1529,plain,
% 0.67/0.74 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_1) | (~product(e_1, e_2, e_3)) | (~product(e_6, 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_6, e_1) | (~product(e_1, e_2, e_3)) | (~product(e_6, e_2, e_3)))),
% 0.67/0.74 inference(rewrite,[status(thm)],[])).
% 0.67/0.74 tff(1530,plain,
% 0.67/0.74 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_1) | (~product(e_1, e_2, e_3)) | (~product(e_6, e_2, e_3)))),
% 0.67/0.74 inference(quant_inst,[status(thm)],[])).
% 0.67/0.74 tff(1531,plain,
% 0.67/0.74 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_6, e_1) | (~product(e_1, e_2, e_3)) | (~product(e_6, e_2, e_3))),
% 0.67/0.74 inference(modus_ponens,[status(thm)],[1530, 1529])).
% 0.67/0.74 tff(1532,plain,
% 0.67/0.74 ($false),
% 0.67/0.74 inference(unit_resolution,[status(thm)],[1531, 1116, 87, 578, 1528])).
% 0.67/0.74 tff(1533,plain,((~product(e_6, e_2, e_3)) | (~product(e_1, e_2, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.67/0.74 tff(1534,plain,
% 0.67/0.74 (~product(e_1, e_2, e_3)),
% 0.67/0.74 inference(unit_resolution,[status(thm)],[1533, 1527])).
% 0.67/0.74 tff(1535,plain,
% 0.67/0.74 (~product(e_1, e_6, e_4)),
% 0.67/0.74 inference(unit_resolution,[status(thm)],[1091, 1200])).
% 0.67/0.74 tff(1536,plain,
% 0.67/0.74 (product(e_1, e_6, e_5)),
% 0.67/0.74 inference(unit_resolution,[status(thm)],[945, 1535])).
% 0.67/0.74 tff(1537,plain,
% 0.67/0.74 (~product(e_1, e_3, e_5)),
% 0.67/0.74 inference(unit_resolution,[status(thm)],[871, 1536])).
% 0.67/0.74 tff(1538,plain,
% 0.67/0.74 (~product(e_1, e_3, e_4)),
% 0.67/0.74 inference(unit_resolution,[status(thm)],[845, 7])).
% 0.67/0.74 tff(1539,plain,
% 0.67/0.74 (product(e_1, e_3, e_6)),
% 0.67/0.74 inference(unit_resolution,[status(thm)],[492, 1538, 749, 406, 881])).
% 0.67/0.74 tff(1540,plain,
% 0.67/0.74 (~product(e_1, e_2, e_4)),
% 0.67/0.74 inference(unit_resolution,[status(thm)],[770, 7])).
% 0.67/0.74 tff(1541,plain,
% 0.67/0.74 (product(e_1, e_2, e_6)),
% 0.67/0.74 inference(unit_resolution,[status(thm)],[575, 1540, 748, 1095, 747, 746])).
% 0.67/0.74 tff(1542,plain,
% 0.67/0.74 ($false),
% 0.67/0.74 inference(unit_resolution,[status(thm)],[835, 1541, 1539])).
% 0.67/0.74 tff(1543,plain,((~product(e_1, e_5, e_4)) | product(e_1, e_2, e_3) | product(e_1, e_2, e_5) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_5)), inference(lemma,lemma(discharge,[]))).
% 0.67/0.74 tff(1544,plain,
% 0.67/0.74 ((~product(e_1, e_5, e_4)) | product(e_1, e_2, e_3) | product(e_1, e_2, e_5) | product(e_1, e_2, e_2) | product(e_1, e_3, e_2) | product(e_1, e_3, e_5)),
% 0.67/0.74 inference(unit_resolution,[status(thm)],[1543, 568, 474])).
% 0.67/0.74 tff(1545,plain,
% 0.67/0.74 ((~product(e_1, e_5, e_4)) | product(e_1, e_2, e_3) | product(e_1, e_2, e_5) | product(e_1, e_3, e_5)),
% 0.67/0.74 inference(unit_resolution,[status(thm)],[1544, 1218, 703])).
% 0.67/0.74 tff(1546,plain,
% 0.67/0.74 (~product(e_1, e_5, e_4)),
% 0.67/0.74 inference(unit_resolution,[status(thm)],[1545, 1534, 1095, 1537])).
% 0.67/0.74 tff(1547,plain,
% 0.67/0.74 ($false),
% 0.67/0.74 inference(unit_resolution,[status(thm)],[1499, 1546, 1534, 1201])).
% 0.67/0.74 tff(1548,plain,(product(e_1, e_2, e_4) | product(e_1, e_2, e_5)), inference(lemma,lemma(discharge,[]))).
% 0.67/0.74 tff(1549,plain,
% 0.67/0.74 (product(e_1, e_2, e_4)),
% 0.67/0.74 inference(unit_resolution,[status(thm)],[1548, 1094])).
% 0.67/0.74 tff(1550,plain,
% 0.67/0.74 (~product(e_1, e_5, e_4)),
% 0.67/0.74 inference(unit_resolution,[status(thm)],[770, 1549])).
% 0.67/0.74 tff(1551,plain,
% 0.67/0.74 (product(e_1, e_5, e_6)),
% 0.67/0.74 inference(unit_resolution,[status(thm)],[1179, 1550, 1051])).
% 0.67/0.74 tff(1552,plain,
% 0.67/0.74 (~product(e_1, e_3, e_4)),
% 0.67/0.74 inference(unit_resolution,[status(thm)],[761, 1549])).
% 0.67/0.74 tff(1553,plain,
% 0.67/0.74 (product(e_1, e_3, e_6)),
% 0.67/0.74 inference(unit_resolution,[status(thm)],[1219, 1552, 1202])).
% 0.67/0.74 tff(1554,plain,
% 0.67/0.74 ($false),
% 0.67/0.74 inference(unit_resolution,[status(thm)],[425, 1553, 1551])).
% 0.67/0.74 tff(1555,plain,(product(e_4, e_1, e_5)), inference(lemma,lemma(discharge,[]))).
% 0.67/0.74 tff(1556,plain,
% 0.67/0.74 (~product(e_6, e_1, e_5)),
% 0.67/0.74 inference(unit_resolution,[status(thm)],[1111, 1555])).
% 0.67/0.74 tff(1557,plain,
% 0.67/0.74 (product(e_6, e_1, e_2)),
% 0.67/0.74 inference(unit_resolution,[status(thm)],[1155, 1556])).
% 0.67/0.74 tff(1558,plain,
% 0.67/0.74 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_1, e_4, e_6)) | (~product(e_6, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_4) | (~product(e_1, e_4, e_6)) | (~product(e_6, e_1, e_2)))),
% 0.67/0.74 inference(rewrite,[status(thm)],[])).
% 0.67/0.74 tff(1559,plain,
% 0.67/0.74 ((product(e_2, e_1, e_4) | (~product(e_6, e_1, e_2)) | (~product(e_1, e_4, e_6))) <=> (product(e_2, e_1, e_4) | (~product(e_1, e_4, e_6)) | (~product(e_6, e_1, e_2)))),
% 0.67/0.74 inference(rewrite,[status(thm)],[])).
% 0.67/0.74 tff(1560,plain,
% 0.67/0.74 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_6, e_1, e_2)) | (~product(e_1, e_4, e_6)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_1, e_4, e_6)) | (~product(e_6, e_1, e_2))))),
% 0.67/0.74 inference(monotonicity,[status(thm)],[1559])).
% 0.67/0.74 tff(1561,plain,
% 0.67/0.74 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_6, e_1, e_2)) | (~product(e_1, e_4, e_6)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_4) | (~product(e_1, e_4, e_6)) | (~product(e_6, e_1, e_2)))),
% 0.67/0.74 inference(transitivity,[status(thm)],[1560, 1558])).
% 0.67/0.74 tff(1562,plain,
% 0.67/0.74 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_6, e_1, e_2)) | (~product(e_1, e_4, e_6)))),
% 0.67/0.74 inference(quant_inst,[status(thm)],[])).
% 0.67/0.74 tff(1563,plain,
% 0.67/0.74 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_4) | (~product(e_1, e_4, e_6)) | (~product(e_6, e_1, e_2))),
% 0.67/0.74 inference(modus_ponens,[status(thm)],[1562, 1561])).
% 0.67/0.74 tff(1564,plain,
% 0.67/0.74 (~product(e_1, e_4, e_6)),
% 0.67/0.74 inference(unit_resolution,[status(thm)],[1563, 58, 119, 1557])).
% 0.67/0.74 tff(1565,plain,
% 0.67/0.74 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_4, e_6) | (~product(e_4, e_6, e_3)) | (~product(e_3, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_4, e_6) | (~product(e_4, e_6, e_3)) | (~product(e_3, e_4, e_1)))),
% 0.67/0.74 inference(rewrite,[status(thm)],[])).
% 0.67/0.74 tff(1566,plain,
% 0.67/0.74 ((product(e_1, e_4, e_6) | (~product(e_3, e_4, e_1)) | (~product(e_4, e_6, e_3))) <=> (product(e_1, e_4, e_6) | (~product(e_4, e_6, e_3)) | (~product(e_3, e_4, e_1)))),
% 0.67/0.74 inference(rewrite,[status(thm)],[])).
% 0.67/0.74 tff(1567,plain,
% 0.67/0.74 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_4, e_6) | (~product(e_3, e_4, e_1)) | (~product(e_4, e_6, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_4, e_6) | (~product(e_4, e_6, e_3)) | (~product(e_3, e_4, e_1))))),
% 0.67/0.74 inference(monotonicity,[status(thm)],[1566])).
% 0.67/0.74 tff(1568,plain,
% 0.67/0.74 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_4, e_6) | (~product(e_3, e_4, e_1)) | (~product(e_4, e_6, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_4, e_6) | (~product(e_4, e_6, e_3)) | (~product(e_3, e_4, e_1)))),
% 0.67/0.74 inference(transitivity,[status(thm)],[1567, 1565])).
% 0.67/0.74 tff(1569,plain,
% 0.67/0.74 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_4, e_6) | (~product(e_3, e_4, e_1)) | (~product(e_4, e_6, e_3)))),
% 0.67/0.74 inference(quant_inst,[status(thm)],[])).
% 0.67/0.74 tff(1570,plain,
% 0.67/0.74 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_4, e_6) | (~product(e_4, e_6, e_3)) | (~product(e_3, e_4, e_1))),
% 0.67/0.74 inference(modus_ponens,[status(thm)],[1569, 1568])).
% 0.67/0.74 tff(1571,plain,
% 0.67/0.74 (~product(e_4, e_6, e_3)),
% 0.67/0.74 inference(unit_resolution,[status(thm)],[1570, 58, 1564, 2])).
% 0.67/0.74 tff(1572,plain,
% 0.67/0.74 (product(e_1, e_2, e_5) | product(e_1, e_2, e_4)),
% 0.67/0.74 inference(unit_resolution,[status(thm)],[1199, 1555])).
% 0.67/0.74 tff(1573,plain,
% 0.67/0.74 (product(e_1, e_2, e_5)),
% 0.67/0.74 inference(unit_resolution,[status(thm)],[1572, 690])).
% 0.67/0.74 tff(1574,plain,
% 0.67/0.74 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_1) | (~product(e_1, e_2, e_5)) | (~product(e_6, e_2, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_6, e_1) | (~product(e_1, e_2, e_5)) | (~product(e_6, e_2, e_5)))),
% 0.67/0.74 inference(rewrite,[status(thm)],[])).
% 0.67/0.74 tff(1575,plain,
% 0.67/0.74 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_1) | (~product(e_1, e_2, e_5)) | (~product(e_6, e_2, e_5)))),
% 0.67/0.74 inference(quant_inst,[status(thm)],[])).
% 0.67/0.74 tff(1576,plain,
% 0.67/0.74 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_6, e_1) | (~product(e_1, e_2, e_5)) | (~product(e_6, e_2, e_5))),
% 0.67/0.74 inference(modus_ponens,[status(thm)],[1575, 1574])).
% 0.67/0.74 tff(1577,plain,
% 0.67/0.74 ($false),
% 0.67/0.74 inference(unit_resolution,[status(thm)],[1576, 1116, 87, 519, 1316])).
% 0.67/0.74 tff(1578,plain,((~product(e_6, e_2, e_5)) | (~product(e_1, e_2, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.67/0.74 tff(1579,plain,
% 0.67/0.74 (~product(e_6, e_2, e_5)),
% 0.67/0.74 inference(unit_resolution,[status(thm)],[1578, 1573])).
% 0.67/0.74 tff(1580,plain,
% 0.67/0.74 (~product(e_1, e_3, e_5)),
% 0.67/0.74 inference(unit_resolution,[status(thm)],[727, 1573])).
% 0.67/0.74 tff(1581,plain,
% 0.67/0.74 (product(e_1, e_3, e_6)),
% 0.67/0.74 inference(unit_resolution,[status(thm)],[1219, 1580, 704])).
% 0.67/0.74 tff(1582,assumption,(product(e_4, e_3, e_6)), introduced(assumption)).
% 0.67/0.74 tff(1583,plain,
% 0.67/0.74 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_1) | (~product(e_1, e_3, e_6)) | (~product(e_4, e_3, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_1) | (~product(e_1, e_3, e_6)) | (~product(e_4, e_3, e_6)))),
% 0.67/0.75 inference(rewrite,[status(thm)],[])).
% 0.67/0.75 tff(1584,plain,
% 0.67/0.75 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_1) | (~product(e_1, e_3, e_6)) | (~product(e_4, e_3, e_6)))),
% 0.67/0.75 inference(quant_inst,[status(thm)],[])).
% 0.67/0.75 tff(1585,plain,
% 0.67/0.75 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_1) | (~product(e_1, e_3, e_6)) | (~product(e_4, e_3, e_6))),
% 0.67/0.75 inference(modus_ponens,[status(thm)],[1584, 1583])).
% 0.67/0.75 tff(1586,plain,
% 0.67/0.75 ($false),
% 0.67/0.75 inference(unit_resolution,[status(thm)],[1585, 1293, 87, 407, 1582])).
% 0.67/0.75 tff(1587,plain,((~product(e_4, e_3, e_6)) | (~product(e_1, e_3, e_6))), inference(lemma,lemma(discharge,[]))).
% 0.67/0.75 tff(1588,plain,
% 0.67/0.75 (~product(e_4, e_3, e_6)),
% 0.67/0.75 inference(unit_resolution,[status(thm)],[1587, 1581])).
% 0.67/0.75 tff(1589,assumption,(product(e_4, e_3, e_5)), introduced(assumption)).
% 0.67/0.75 tff(1590,plain,
% 0.67/0.75 ((~equalish(e_3, e_1)) <=> (~equalish(e_3, e_1))),
% 0.67/0.75 inference(rewrite,[status(thm)],[])).
% 0.67/0.75 tff(1591,axiom,(~equalish(e_3, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_1')).
% 0.67/0.75 tff(1592,plain,
% 0.67/0.75 (~equalish(e_3, e_1)),
% 0.67/0.75 inference(modus_ponens,[status(thm)],[1591, 1590])).
% 0.67/0.75 tff(1593,plain,
% 0.67/0.75 (((~![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_4, e_1, e_5)) | (~product(e_4, e_3, e_5)))) <=> ((~![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_4, e_1, e_5)) | (~product(e_4, e_3, e_5)))),
% 0.67/0.75 inference(rewrite,[status(thm)],[])).
% 0.67/0.75 tff(1594,plain,
% 0.67/0.75 ((~![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_4, e_1, e_5)) | (~product(e_4, e_3, e_5)))),
% 0.67/0.75 inference(quant_inst,[status(thm)],[])).
% 0.67/0.75 tff(1595,plain,
% 0.67/0.75 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_1) | (~product(e_4, e_1, e_5)) | (~product(e_4, e_3, e_5))),
% 0.67/0.75 inference(modus_ponens,[status(thm)],[1594, 1593])).
% 0.67/0.75 tff(1596,plain,
% 0.67/0.75 ($false),
% 0.67/0.75 inference(unit_resolution,[status(thm)],[1595, 1592, 17, 1105, 1589])).
% 0.67/0.75 tff(1597,plain,((~product(e_4, e_3, e_5)) | (~product(e_4, e_1, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.67/0.75 tff(1598,plain,
% 0.67/0.75 (~product(e_4, e_3, e_5)),
% 0.67/0.75 inference(unit_resolution,[status(thm)],[1597, 1555])).
% 0.67/0.75 tff(1599,assumption,(product(e_4, e_3, e_4)), introduced(assumption)).
% 0.67/0.75 tff(1600,assumption,(product(e_4, e_3, e_1)), introduced(assumption)).
% 0.67/0.75 tff(1601,plain,
% 0.67/0.75 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_3, e_1) | (~product(e_3, e_1, e_4)) | (~product(e_4, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_3, e_1) | (~product(e_3, e_1, e_4)) | (~product(e_4, e_3, e_1)))),
% 0.67/0.75 inference(rewrite,[status(thm)],[])).
% 0.67/0.75 tff(1602,plain,
% 0.67/0.75 ((product(e_1, e_3, e_1) | (~product(e_4, e_3, e_1)) | (~product(e_3, e_1, e_4))) <=> (product(e_1, e_3, e_1) | (~product(e_3, e_1, e_4)) | (~product(e_4, e_3, e_1)))),
% 0.67/0.75 inference(rewrite,[status(thm)],[])).
% 0.67/0.75 tff(1603,plain,
% 0.67/0.75 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_3, e_1) | (~product(e_4, e_3, e_1)) | (~product(e_3, e_1, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_3, e_1) | (~product(e_3, e_1, e_4)) | (~product(e_4, e_3, e_1))))),
% 0.67/0.75 inference(monotonicity,[status(thm)],[1602])).
% 0.67/0.75 tff(1604,plain,
% 0.67/0.75 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_3, e_1) | (~product(e_4, e_3, e_1)) | (~product(e_3, e_1, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_3, e_1) | (~product(e_3, e_1, e_4)) | (~product(e_4, e_3, e_1)))),
% 0.67/0.75 inference(transitivity,[status(thm)],[1603, 1601])).
% 0.67/0.75 tff(1605,plain,
% 0.67/0.75 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_3, e_1) | (~product(e_4, e_3, e_1)) | (~product(e_3, e_1, e_4)))),
% 0.67/0.75 inference(quant_inst,[status(thm)],[])).
% 0.67/0.75 tff(1606,plain,
% 0.67/0.75 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_3, e_1) | (~product(e_3, e_1, e_4)) | (~product(e_4, e_3, e_1))),
% 0.67/0.75 inference(modus_ponens,[status(thm)],[1605, 1604])).
% 0.67/0.75 tff(1607,plain,
% 0.67/0.75 ($false),
% 0.67/0.75 inference(unit_resolution,[status(thm)],[1606, 58, 234, 485, 1600])).
% 0.67/0.75 tff(1608,plain,((~product(e_4, e_3, e_1)) | (~product(e_3, e_1, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.67/0.75 tff(1609,plain,
% 0.67/0.75 (~product(e_4, e_3, e_1)),
% 0.67/0.75 inference(unit_resolution,[status(thm)],[1608, 234])).
% 0.67/0.75 tff(1610,plain,
% 0.67/0.75 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_3, e_1, e_4)) | product(e_4, e_3, e_1) | (~product(e_4, e_3, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_3, e_1, e_4)) | product(e_4, e_3, e_1) | (~product(e_4, e_3, e_4)))),
% 0.67/0.75 inference(rewrite,[status(thm)],[])).
% 0.67/0.75 tff(1611,plain,
% 0.67/0.75 ((product(e_4, e_3, e_1) | (~product(e_4, e_3, e_4)) | (~product(e_3, e_1, e_4))) <=> ((~product(e_3, e_1, e_4)) | product(e_4, e_3, e_1) | (~product(e_4, e_3, e_4)))),
% 0.67/0.75 inference(rewrite,[status(thm)],[])).
% 0.67/0.75 tff(1612,plain,
% 0.67/0.75 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_3, e_1) | (~product(e_4, e_3, e_4)) | (~product(e_3, e_1, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_3, e_1, e_4)) | product(e_4, e_3, e_1) | (~product(e_4, e_3, e_4))))),
% 0.67/0.75 inference(monotonicity,[status(thm)],[1611])).
% 0.67/0.75 tff(1613,plain,
% 0.67/0.75 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_3, e_1) | (~product(e_4, e_3, e_4)) | (~product(e_3, e_1, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_3, e_1, e_4)) | product(e_4, e_3, e_1) | (~product(e_4, e_3, e_4)))),
% 0.67/0.75 inference(transitivity,[status(thm)],[1612, 1610])).
% 0.67/0.75 tff(1614,plain,
% 0.67/0.75 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_3, e_1) | (~product(e_4, e_3, e_4)) | (~product(e_3, e_1, e_4)))),
% 0.67/0.75 inference(quant_inst,[status(thm)],[])).
% 0.67/0.75 tff(1615,plain,
% 0.67/0.75 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_3, e_1, e_4)) | product(e_4, e_3, e_1) | (~product(e_4, e_3, e_4))),
% 0.67/0.75 inference(modus_ponens,[status(thm)],[1614, 1613])).
% 0.67/0.75 tff(1616,plain,
% 0.67/0.75 ($false),
% 0.67/0.75 inference(unit_resolution,[status(thm)],[1615, 58, 234, 1609, 1599])).
% 0.67/0.75 tff(1617,plain,((~product(e_4, e_3, e_4)) | (~product(e_3, e_1, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.67/0.75 tff(1618,plain,
% 0.67/0.75 (~product(e_4, e_3, e_4)),
% 0.67/0.75 inference(unit_resolution,[status(thm)],[1617, 1041])).
% 0.67/0.75 tff(1619,plain,
% 0.67/0.75 (~product(e_4, e_3, e_1)),
% 0.67/0.75 inference(unit_resolution,[status(thm)],[1608, 1041])).
% 0.67/0.75 tff(1620,assumption,(product(e_4, e_3, e_3)), introduced(assumption)).
% 0.67/0.75 tff(1621,plain,
% 0.67/0.75 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_4, 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_4, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_4, e_3, e_3)))),
% 0.67/0.75 inference(rewrite,[status(thm)],[])).
% 0.67/0.75 tff(1622,plain,
% 0.67/0.75 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_4, e_3, e_3)))),
% 0.67/0.75 inference(quant_inst,[status(thm)],[])).
% 0.67/0.75 tff(1623,plain,
% 0.67/0.75 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_4, e_3, e_3))),
% 0.67/0.75 inference(modus_ponens,[status(thm)],[1622, 1621])).
% 0.67/0.75 tff(1624,plain,
% 0.67/0.75 ($false),
% 0.67/0.75 inference(unit_resolution,[status(thm)],[1623, 498, 87, 462, 1620])).
% 0.67/0.75 tff(1625,plain,(~product(e_4, e_3, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.67/0.75 tff(1626,plain,
% 0.67/0.75 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_3)) | (~group_element(e_4)) | product(e_4, e_3, e_2) | product(e_4, e_3, e_5) | product(e_4, e_3, e_1) | product(e_4, e_3, e_6) | product(e_4, e_3, e_4) | product(e_4, e_3, e_3))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_3)) | (~group_element(e_4)) | product(e_4, e_3, e_2) | product(e_4, e_3, e_5) | product(e_4, e_3, e_1) | product(e_4, e_3, e_6) | product(e_4, e_3, e_4) | product(e_4, e_3, e_3))),
% 0.67/0.75 inference(rewrite,[status(thm)],[])).
% 0.67/0.75 tff(1627,plain,
% 0.67/0.75 ((product(e_4, e_3, e_6) | product(e_4, e_3, e_5) | product(e_4, e_3, e_4) | product(e_4, e_3, e_3) | product(e_4, e_3, e_2) | product(e_4, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_4))) <=> ((~group_element(e_3)) | (~group_element(e_4)) | product(e_4, e_3, e_2) | product(e_4, e_3, e_5) | product(e_4, e_3, e_1) | product(e_4, e_3, e_6) | product(e_4, e_3, e_4) | product(e_4, e_3, e_3))),
% 0.67/0.75 inference(rewrite,[status(thm)],[])).
% 0.67/0.75 tff(1628,plain,
% 0.67/0.75 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_3, e_6) | product(e_4, e_3, e_5) | product(e_4, e_3, e_4) | product(e_4, e_3, e_3) | product(e_4, e_3, e_2) | product(e_4, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_3)) | (~group_element(e_4)) | product(e_4, e_3, e_2) | product(e_4, e_3, e_5) | product(e_4, e_3, e_1) | product(e_4, e_3, e_6) | product(e_4, e_3, e_4) | product(e_4, e_3, e_3)))),
% 0.67/0.75 inference(monotonicity,[status(thm)],[1627])).
% 0.67/0.75 tff(1629,plain,
% 0.67/0.75 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_3, e_6) | product(e_4, e_3, e_5) | product(e_4, e_3, e_4) | product(e_4, e_3, e_3) | product(e_4, e_3, e_2) | product(e_4, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_3)) | (~group_element(e_4)) | product(e_4, e_3, e_2) | product(e_4, e_3, e_5) | product(e_4, e_3, e_1) | product(e_4, e_3, e_6) | product(e_4, e_3, e_4) | product(e_4, e_3, e_3))),
% 0.67/0.75 inference(transitivity,[status(thm)],[1628, 1626])).
% 0.67/0.75 tff(1630,plain,
% 0.67/0.75 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_3, e_6) | product(e_4, e_3, e_5) | product(e_4, e_3, e_4) | product(e_4, e_3, e_3) | product(e_4, e_3, e_2) | product(e_4, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_4)))),
% 0.67/0.75 inference(quant_inst,[status(thm)],[])).
% 0.67/0.75 tff(1631,plain,
% 0.67/0.75 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_3)) | (~group_element(e_4)) | product(e_4, e_3, e_2) | product(e_4, e_3, e_5) | product(e_4, e_3, e_1) | product(e_4, e_3, e_6) | product(e_4, e_3, e_4) | product(e_4, e_3, e_3)),
% 0.67/0.75 inference(modus_ponens,[status(thm)],[1630, 1629])).
% 0.67/0.75 tff(1632,plain,
% 0.67/0.75 (product(e_4, e_3, e_2) | product(e_4, e_3, e_5) | product(e_4, e_3, e_1) | product(e_4, e_3, e_6) | product(e_4, e_3, e_4) | product(e_4, e_3, e_3)),
% 0.67/0.75 inference(unit_resolution,[status(thm)],[1631, 253, 279, 129])).
% 0.67/0.75 tff(1633,plain,
% 0.67/0.75 (product(e_4, e_3, e_2) | product(e_4, e_3, e_5) | product(e_4, e_3, e_1) | product(e_4, e_3, e_6) | product(e_4, e_3, e_4)),
% 0.67/0.75 inference(unit_resolution,[status(thm)],[1632, 1625])).
% 0.67/0.75 tff(1634,plain,
% 0.67/0.75 (product(e_4, e_3, e_2) | product(e_4, e_3, e_5) | product(e_4, e_3, e_6)),
% 0.67/0.75 inference(unit_resolution,[status(thm)],[1633, 1619, 1618])).
% 0.67/0.75 tff(1635,plain,
% 0.67/0.75 (product(e_4, e_3, e_2) | product(e_4, e_3, e_6)),
% 0.67/0.75 inference(unit_resolution,[status(thm)],[1634, 1598])).
% 0.67/0.75 tff(1636,plain,
% 0.67/0.75 (product(e_4, e_3, e_2)),
% 0.67/0.75 inference(unit_resolution,[status(thm)],[1635, 1588])).
% 0.67/0.75 tff(1637,assumption,(product(e_4, e_3, e_2)), introduced(assumption)).
% 0.67/0.75 tff(1638,plain,
% 0.67/0.75 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_6, e_3) | (~product(e_4, e_3, e_2)) | (~product(e_4, e_6, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_6, e_3) | (~product(e_4, e_3, e_2)) | (~product(e_4, e_6, e_2)))),
% 0.67/0.75 inference(rewrite,[status(thm)],[])).
% 0.67/0.75 tff(1639,plain,
% 0.67/0.75 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_6, e_3) | (~product(e_4, e_3, e_2)) | (~product(e_4, e_6, e_2)))),
% 0.67/0.75 inference(quant_inst,[status(thm)],[])).
% 0.67/0.75 tff(1640,plain,
% 0.67/0.75 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_6, e_3) | (~product(e_4, e_3, e_2)) | (~product(e_4, e_6, e_2))),
% 0.67/0.75 inference(modus_ponens,[status(thm)],[1639, 1638])).
% 0.67/0.75 tff(1641,plain,
% 0.67/0.75 ($false),
% 0.67/0.75 inference(unit_resolution,[status(thm)],[1640, 816, 17, 1300, 1637])).
% 0.67/0.75 tff(1642,plain,((~product(e_4, e_6, e_2)) | (~product(e_4, e_3, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.67/0.75 tff(1643,plain,
% 0.67/0.75 (~product(e_4, e_6, e_2)),
% 0.67/0.75 inference(unit_resolution,[status(thm)],[1642, 1636])).
% 0.67/0.75 tff(1644,plain,
% 0.67/0.75 ((~equalish(e_5, e_3)) <=> (~equalish(e_5, e_3))),
% 0.67/0.75 inference(rewrite,[status(thm)],[])).
% 0.67/0.75 tff(1645,axiom,(~equalish(e_5, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_5_is_not_e_3')).
% 0.67/0.75 tff(1646,plain,
% 0.67/0.75 (~equalish(e_5, e_3)),
% 0.67/0.75 inference(modus_ponens,[status(thm)],[1645, 1644])).
% 0.67/0.75 tff(1647,plain,
% 0.67/0.75 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_3) | (~product(e_4, e_3, e_2)) | (~product(e_4, e_5, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_3) | (~product(e_4, e_3, e_2)) | (~product(e_4, e_5, e_2)))),
% 0.67/0.75 inference(rewrite,[status(thm)],[])).
% 0.67/0.75 tff(1648,plain,
% 0.67/0.75 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_3) | (~product(e_4, e_3, e_2)) | (~product(e_4, e_5, e_2)))),
% 0.67/0.75 inference(quant_inst,[status(thm)],[])).
% 0.67/0.75 tff(1649,plain,
% 0.67/0.75 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_3) | (~product(e_4, e_3, e_2)) | (~product(e_4, e_5, e_2))),
% 0.67/0.76 inference(modus_ponens,[status(thm)],[1648, 1647])).
% 0.67/0.76 tff(1650,plain,
% 0.67/0.76 ($false),
% 0.67/0.76 inference(unit_resolution,[status(thm)],[1649, 1646, 17, 1278, 1637])).
% 0.67/0.76 tff(1651,plain,((~product(e_4, e_5, e_2)) | (~product(e_4, e_3, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.67/0.76 tff(1652,plain,
% 0.67/0.76 (~product(e_4, e_5, e_2)),
% 0.67/0.76 inference(unit_resolution,[status(thm)],[1651, 1636])).
% 0.67/0.76 tff(1653,plain,
% 0.67/0.76 (~product(e_1, e_5, e_6)),
% 0.67/0.76 inference(unit_resolution,[status(thm)],[1165, 1557])).
% 0.67/0.76 tff(1654,plain,
% 0.67/0.76 (product(e_1, e_5, e_4) | product(e_1, e_5, e_3)),
% 0.67/0.76 inference(unit_resolution,[status(thm)],[1179, 1653])).
% 0.67/0.76 tff(1655,plain,
% 0.67/0.76 (product(e_1, e_5, e_3)),
% 0.67/0.76 inference(unit_resolution,[status(thm)],[1654, 26])).
% 0.67/0.76 tff(1656,plain,
% 0.67/0.76 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_1) | (~product(e_1, e_5, e_3)) | (~product(e_4, e_5, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_1) | (~product(e_1, e_5, e_3)) | (~product(e_4, e_5, e_3)))),
% 0.67/0.76 inference(rewrite,[status(thm)],[])).
% 0.67/0.76 tff(1657,plain,
% 0.67/0.76 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_1) | (~product(e_1, e_5, e_3)) | (~product(e_4, e_5, e_3)))),
% 0.67/0.76 inference(quant_inst,[status(thm)],[])).
% 0.67/0.76 tff(1658,plain,
% 0.67/0.76 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_1) | (~product(e_1, e_5, e_3)) | (~product(e_4, e_5, e_3))),
% 0.67/0.76 inference(modus_ponens,[status(thm)],[1657, 1656])).
% 0.67/0.76 tff(1659,plain,
% 0.67/0.76 ($false),
% 0.67/0.76 inference(unit_resolution,[status(thm)],[1658, 1293, 87, 680, 1395])).
% 0.67/0.76 tff(1660,plain,((~product(e_4, e_5, e_3)) | (~product(e_1, e_5, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.67/0.76 tff(1661,plain,
% 0.67/0.76 (~product(e_4, e_5, e_3)),
% 0.67/0.76 inference(unit_resolution,[status(thm)],[1660, 1655])).
% 0.67/0.76 tff(1662,plain,
% 0.67/0.76 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_6, e_4)) | product(e_4, e_6, e_4) | (~product(e_6, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_6, e_4)) | product(e_4, e_6, e_4) | (~product(e_6, e_4, e_1)))),
% 0.67/0.76 inference(rewrite,[status(thm)],[])).
% 0.67/0.76 tff(1663,plain,
% 0.67/0.76 ((product(e_4, e_6, e_4) | (~product(e_1, e_6, e_4)) | (~product(e_6, e_4, e_1))) <=> ((~product(e_1, e_6, e_4)) | product(e_4, e_6, e_4) | (~product(e_6, e_4, e_1)))),
% 0.67/0.76 inference(rewrite,[status(thm)],[])).
% 0.67/0.76 tff(1664,plain,
% 0.67/0.76 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_6, e_4) | (~product(e_1, e_6, e_4)) | (~product(e_6, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_6, e_4)) | product(e_4, e_6, e_4) | (~product(e_6, e_4, e_1))))),
% 0.67/0.76 inference(monotonicity,[status(thm)],[1663])).
% 0.67/0.76 tff(1665,plain,
% 0.67/0.76 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_6, e_4) | (~product(e_1, e_6, e_4)) | (~product(e_6, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_6, e_4)) | product(e_4, e_6, e_4) | (~product(e_6, e_4, e_1)))),
% 0.67/0.76 inference(transitivity,[status(thm)],[1664, 1662])).
% 0.67/0.76 tff(1666,plain,
% 0.67/0.76 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_6, e_4) | (~product(e_1, e_6, e_4)) | (~product(e_6, e_4, e_1)))),
% 0.67/0.76 inference(quant_inst,[status(thm)],[])).
% 0.67/0.76 tff(1667,plain,
% 0.67/0.76 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_6, e_4)) | product(e_4, e_6, e_4) | (~product(e_6, e_4, e_1))),
% 0.67/0.76 inference(modus_ponens,[status(thm)],[1666, 1665])).
% 0.67/0.76 tff(1668,plain,
% 0.67/0.76 (~product(e_6, e_4, e_1)),
% 0.67/0.76 inference(unit_resolution,[status(thm)],[1667, 58, 6, 1375])).
% 0.67/0.76 tff(1669,assumption,(~product(e_4, e_5, e_2)), introduced(assumption)).
% 0.67/0.76 tff(1670,assumption,(~product(e_4, e_5, e_3)), introduced(assumption)).
% 0.67/0.76 tff(1671,assumption,(product(e_4, e_2, e_6)), introduced(assumption)).
% 0.67/0.76 tff(1672,plain,
% 0.67/0.76 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_5) | (~product(e_4, e_5, e_6)) | (~product(e_4, e_2, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_5) | (~product(e_4, e_5, e_6)) | (~product(e_4, e_2, e_6)))),
% 0.67/0.76 inference(rewrite,[status(thm)],[])).
% 0.67/0.76 tff(1673,plain,
% 0.67/0.76 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_5) | (~product(e_4, e_5, e_6)) | (~product(e_4, e_2, e_6)))),
% 0.67/0.76 inference(quant_inst,[status(thm)],[])).
% 0.67/0.76 tff(1674,plain,
% 0.67/0.76 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_5) | (~product(e_4, e_5, e_6)) | (~product(e_4, e_2, e_6))),
% 0.67/0.76 inference(modus_ponens,[status(thm)],[1673, 1672])).
% 0.67/0.76 tff(1675,plain,
% 0.67/0.76 ($false),
% 0.67/0.76 inference(unit_resolution,[status(thm)],[1674, 650, 17, 1290, 1671])).
% 0.67/0.76 tff(1676,plain,((~product(e_4, e_2, e_6)) | (~product(e_4, e_5, e_6))), inference(lemma,lemma(discharge,[]))).
% 0.67/0.76 tff(1677,plain,
% 0.67/0.76 (~product(e_4, e_5, e_6)),
% 0.67/0.76 inference(unit_resolution,[status(thm)],[1676, 1671])).
% 0.67/0.76 tff(1678,plain,
% 0.67/0.76 (product(e_4, e_5, e_1)),
% 0.67/0.76 inference(unit_resolution,[status(thm)],[1417, 1677, 1670, 1669])).
% 0.67/0.76 tff(1679,plain,
% 0.67/0.76 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_5, e_5) | (~product(e_4, e_5, e_1)) | (~product(e_5, e_5, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_5, e_5) | (~product(e_4, e_5, e_1)) | (~product(e_5, e_5, e_4)))),
% 0.67/0.76 inference(rewrite,[status(thm)],[])).
% 0.67/0.76 tff(1680,plain,
% 0.67/0.76 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_5, e_5) | (~product(e_4, e_5, e_1)) | (~product(e_5, e_5, e_4)))),
% 0.67/0.76 inference(quant_inst,[status(thm)],[])).
% 0.67/0.76 tff(1681,plain,
% 0.67/0.76 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_5, e_5) | (~product(e_4, e_5, e_1)) | (~product(e_5, e_5, e_4))),
% 0.67/0.76 inference(modus_ponens,[status(thm)],[1680, 1679])).
% 0.67/0.76 tff(1682,plain,
% 0.67/0.76 (~product(e_5, e_5, e_4)),
% 0.67/0.76 inference(unit_resolution,[status(thm)],[1681, 58, 741, 1678])).
% 0.67/0.76 tff(1683,plain,
% 0.67/0.76 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_5, e_5, e_4) | (~product(e_5, e_4, e_5)) | (~product(e_5, e_5, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_5, e_5, e_4) | (~product(e_5, e_4, e_5)) | (~product(e_5, e_5, e_5)))),
% 0.67/0.76 inference(rewrite,[status(thm)],[])).
% 0.67/0.76 tff(1684,plain,
% 0.67/0.76 ((product(e_5, e_5, e_4) | (~product(e_5, e_5, e_5)) | (~product(e_5, e_4, e_5))) <=> (product(e_5, e_5, e_4) | (~product(e_5, e_4, e_5)) | (~product(e_5, e_5, e_5)))),
% 0.67/0.76 inference(rewrite,[status(thm)],[])).
% 0.67/0.76 tff(1685,plain,
% 0.67/0.76 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_5, e_5, e_4) | (~product(e_5, e_5, e_5)) | (~product(e_5, e_4, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_5, e_5, e_4) | (~product(e_5, e_4, e_5)) | (~product(e_5, e_5, e_5))))),
% 0.67/0.76 inference(monotonicity,[status(thm)],[1684])).
% 0.67/0.76 tff(1686,plain,
% 0.67/0.76 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_5, e_5, e_4) | (~product(e_5, e_5, e_5)) | (~product(e_5, e_4, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_5, e_5, e_4) | (~product(e_5, e_4, e_5)) | (~product(e_5, e_5, e_5)))),
% 0.67/0.76 inference(transitivity,[status(thm)],[1685, 1683])).
% 0.67/0.76 tff(1687,plain,
% 0.67/0.76 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_5, e_5, e_4) | (~product(e_5, e_5, e_5)) | (~product(e_5, e_4, e_5)))),
% 0.67/0.76 inference(quant_inst,[status(thm)],[])).
% 0.67/0.76 tff(1688,plain,
% 0.67/0.76 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_5, e_5, e_4) | (~product(e_5, e_4, e_5)) | (~product(e_5, e_5, e_5))),
% 0.67/0.76 inference(modus_ponens,[status(thm)],[1687, 1686])).
% 0.67/0.76 tff(1689,plain,
% 0.67/0.76 (~product(e_5, e_4, e_5)),
% 0.67/0.76 inference(unit_resolution,[status(thm)],[1688, 58, 730, 1682])).
% 0.67/0.76 tff(1690,assumption,(~product(e_6, e_4, e_1)), introduced(assumption)).
% 0.67/0.76 tff(1691,assumption,(product(e_5, e_4, e_6)), introduced(assumption)).
% 0.67/0.76 tff(1692,plain,
% 0.67/0.76 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_4, e_1, e_5)) | product(e_6, e_4, e_1) | (~product(e_5, e_4, e_6)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_4, e_1, e_5)) | product(e_6, e_4, e_1) | (~product(e_5, e_4, e_6)))),
% 0.67/0.76 inference(rewrite,[status(thm)],[])).
% 0.67/0.76 tff(1693,plain,
% 0.67/0.76 ((product(e_6, e_4, e_1) | (~product(e_5, e_4, e_6)) | (~product(e_4, e_1, e_5))) <=> ((~product(e_4, e_1, e_5)) | product(e_6, e_4, e_1) | (~product(e_5, e_4, e_6)))),
% 0.67/0.76 inference(rewrite,[status(thm)],[])).
% 0.67/0.76 tff(1694,plain,
% 0.67/0.76 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_6, e_4, e_1) | (~product(e_5, e_4, e_6)) | (~product(e_4, e_1, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_4, e_1, e_5)) | product(e_6, e_4, e_1) | (~product(e_5, e_4, e_6))))),
% 0.67/0.76 inference(monotonicity,[status(thm)],[1693])).
% 0.67/0.76 tff(1695,plain,
% 0.67/0.76 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_6, e_4, e_1) | (~product(e_5, e_4, e_6)) | (~product(e_4, e_1, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_4, e_1, e_5)) | product(e_6, e_4, e_1) | (~product(e_5, e_4, e_6)))),
% 0.67/0.76 inference(transitivity,[status(thm)],[1694, 1692])).
% 0.67/0.76 tff(1696,plain,
% 0.67/0.76 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_6, e_4, e_1) | (~product(e_5, e_4, e_6)) | (~product(e_4, e_1, e_5)))),
% 0.67/0.76 inference(quant_inst,[status(thm)],[])).
% 0.67/0.76 tff(1697,plain,
% 0.67/0.76 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_4, e_1, e_5)) | product(e_6, e_4, e_1) | (~product(e_5, e_4, e_6))),
% 0.67/0.76 inference(modus_ponens,[status(thm)],[1696, 1695])).
% 0.67/0.76 tff(1698,plain,
% 0.67/0.76 ($false),
% 0.67/0.76 inference(unit_resolution,[status(thm)],[1697, 58, 1555, 1690, 1691])).
% 0.67/0.76 tff(1699,plain,((~product(e_5, e_4, e_6)) | product(e_6, e_4, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.67/0.76 tff(1700,plain,
% 0.67/0.76 (~product(e_5, e_4, e_6)),
% 0.67/0.76 inference(unit_resolution,[status(thm)],[1699, 1690])).
% 0.67/0.76 tff(1701,plain,
% 0.67/0.76 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_5, e_2) | (~product(e_4, e_5, e_1)) | (~product(e_5, e_2, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_5, e_2) | (~product(e_4, e_5, e_1)) | (~product(e_5, e_2, e_4)))),
% 0.67/0.76 inference(rewrite,[status(thm)],[])).
% 0.67/0.76 tff(1702,plain,
% 0.67/0.76 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_5, e_2) | (~product(e_4, e_5, e_1)) | (~product(e_5, e_2, e_4)))),
% 0.67/0.76 inference(quant_inst,[status(thm)],[])).
% 0.67/0.76 tff(1703,plain,
% 0.67/0.76 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_5, e_2) | (~product(e_4, e_5, e_1)) | (~product(e_5, e_2, e_4))),
% 0.67/0.76 inference(modus_ponens,[status(thm)],[1702, 1701])).
% 0.67/0.76 tff(1704,plain,
% 0.67/0.76 (~product(e_5, e_2, e_4)),
% 0.67/0.76 inference(unit_resolution,[status(thm)],[1703, 58, 152, 1678])).
% 0.67/0.76 tff(1705,plain,
% 0.67/0.76 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_2, e_5)) | product(e_5, e_2, e_4) | (~product(e_2, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_2, e_5)) | product(e_5, e_2, e_4) | (~product(e_2, e_4, e_1)))),
% 0.67/0.76 inference(rewrite,[status(thm)],[])).
% 0.67/0.76 tff(1706,plain,
% 0.67/0.76 ((product(e_5, e_2, e_4) | (~product(e_1, e_2, e_5)) | (~product(e_2, e_4, e_1))) <=> ((~product(e_1, e_2, e_5)) | product(e_5, e_2, e_4) | (~product(e_2, e_4, e_1)))),
% 0.67/0.76 inference(rewrite,[status(thm)],[])).
% 0.67/0.76 tff(1707,plain,
% 0.67/0.76 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_5, e_2, e_4) | (~product(e_1, e_2, e_5)) | (~product(e_2, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_2, e_5)) | product(e_5, e_2, e_4) | (~product(e_2, e_4, e_1))))),
% 0.67/0.76 inference(monotonicity,[status(thm)],[1706])).
% 0.67/0.76 tff(1708,plain,
% 0.67/0.76 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_5, e_2, e_4) | (~product(e_1, e_2, e_5)) | (~product(e_2, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_2, e_5)) | product(e_5, e_2, e_4) | (~product(e_2, e_4, e_1)))),
% 0.67/0.76 inference(transitivity,[status(thm)],[1707, 1705])).
% 0.67/0.76 tff(1709,plain,
% 0.67/0.76 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_5, e_2, e_4) | (~product(e_1, e_2, e_5)) | (~product(e_2, e_4, e_1)))),
% 0.67/0.76 inference(quant_inst,[status(thm)],[])).
% 0.67/0.76 tff(1710,plain,
% 0.67/0.76 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_2, e_5)) | product(e_5, e_2, e_4) | (~product(e_2, e_4, e_1))),
% 0.67/0.76 inference(modus_ponens,[status(thm)],[1709, 1708])).
% 0.67/0.76 tff(1711,plain,
% 0.67/0.76 (~product(e_2, e_4, e_1)),
% 0.67/0.76 inference(unit_resolution,[status(thm)],[1710, 58, 519, 1704])).
% 0.67/0.76 tff(1712,assumption,(product(e_5, e_4, e_2)), introduced(assumption)).
% 0.67/0.76 tff(1713,assumption,(~product(e_2, e_4, e_1)), introduced(assumption)).
% 0.67/0.76 tff(1714,plain,
% 0.67/0.76 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_4, e_1, e_5)) | product(e_2, e_4, e_1) | (~product(e_5, e_4, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_4, e_1, e_5)) | product(e_2, e_4, e_1) | (~product(e_5, e_4, e_2)))),
% 0.67/0.76 inference(rewrite,[status(thm)],[])).
% 0.67/0.76 tff(1715,plain,
% 0.67/0.76 ((product(e_2, e_4, e_1) | (~product(e_5, e_4, e_2)) | (~product(e_4, e_1, e_5))) <=> ((~product(e_4, e_1, e_5)) | product(e_2, e_4, e_1) | (~product(e_5, e_4, e_2)))),
% 0.67/0.76 inference(rewrite,[status(thm)],[])).
% 0.67/0.76 tff(1716,plain,
% 0.67/0.76 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_4, e_1) | (~product(e_5, e_4, e_2)) | (~product(e_4, e_1, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_4, e_1, e_5)) | product(e_2, e_4, e_1) | (~product(e_5, e_4, e_2))))),
% 0.67/0.76 inference(monotonicity,[status(thm)],[1715])).
% 0.67/0.76 tff(1717,plain,
% 0.67/0.76 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_4, e_1) | (~product(e_5, e_4, e_2)) | (~product(e_4, e_1, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_4, e_1, e_5)) | product(e_2, e_4, e_1) | (~product(e_5, e_4, e_2)))),
% 0.67/0.77 inference(transitivity,[status(thm)],[1716, 1714])).
% 0.67/0.77 tff(1718,plain,
% 0.67/0.77 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_4, e_1) | (~product(e_5, e_4, e_2)) | (~product(e_4, e_1, e_5)))),
% 0.67/0.77 inference(quant_inst,[status(thm)],[])).
% 0.67/0.77 tff(1719,plain,
% 0.67/0.77 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_4, e_1, e_5)) | product(e_2, e_4, e_1) | (~product(e_5, e_4, e_2))),
% 0.67/0.77 inference(modus_ponens,[status(thm)],[1718, 1717])).
% 0.67/0.77 tff(1720,plain,
% 0.67/0.77 ($false),
% 0.67/0.77 inference(unit_resolution,[status(thm)],[1719, 58, 1105, 1713, 1712])).
% 0.67/0.77 tff(1721,plain,((~product(e_5, e_4, e_2)) | (~product(e_4, e_1, e_5)) | product(e_2, e_4, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.67/0.77 tff(1722,plain,
% 0.67/0.77 ((~product(e_5, e_4, e_2)) | product(e_2, e_4, e_1)),
% 0.67/0.77 inference(unit_resolution,[status(thm)],[1721, 1555])).
% 0.67/0.77 tff(1723,plain,
% 0.67/0.77 (~product(e_5, e_4, e_2)),
% 0.67/0.77 inference(unit_resolution,[status(thm)],[1722, 1711])).
% 0.67/0.77 tff(1724,assumption,(product(e_5, e_4, e_1)), introduced(assumption)).
% 0.67/0.77 tff(1725,plain,
% 0.67/0.77 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_4, e_1) | (~product(e_5, e_4, e_1)) | (~product(e_4, e_1, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_4, e_1) | (~product(e_5, e_4, e_1)) | (~product(e_4, e_1, e_5)))),
% 0.67/0.77 inference(rewrite,[status(thm)],[])).
% 0.67/0.77 tff(1726,plain,
% 0.67/0.77 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_4, e_1) | (~product(e_5, e_4, e_1)) | (~product(e_4, e_1, e_5)))),
% 0.67/0.77 inference(quant_inst,[status(thm)],[])).
% 0.67/0.77 tff(1727,plain,
% 0.67/0.77 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_4, e_1) | (~product(e_5, e_4, e_1)) | (~product(e_4, e_1, e_5))),
% 0.67/0.77 inference(modus_ponens,[status(thm)],[1726, 1725])).
% 0.67/0.77 tff(1728,plain,
% 0.67/0.77 ($false),
% 0.67/0.77 inference(unit_resolution,[status(thm)],[1727, 58, 1555, 276, 1724])).
% 0.67/0.77 tff(1729,plain,(~product(e_5, e_4, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.67/0.77 tff(1730,assumption,(product(e_5, e_4, e_4)), introduced(assumption)).
% 0.67/0.77 tff(1731,plain,
% 0.67/0.77 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_5, e_4, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_5, e_4, e_4)))),
% 0.67/0.77 inference(rewrite,[status(thm)],[])).
% 0.67/0.77 tff(1732,plain,
% 0.67/0.77 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_5, e_4, e_4)))),
% 0.67/0.77 inference(quant_inst,[status(thm)],[])).
% 0.67/0.77 tff(1733,plain,
% 0.67/0.77 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_5, e_4, e_4))),
% 0.67/0.77 inference(modus_ponens,[status(thm)],[1732, 1731])).
% 0.67/0.77 tff(1734,plain,
% 0.67/0.77 ($false),
% 0.67/0.77 inference(unit_resolution,[status(thm)],[1733, 173, 87, 184, 1730])).
% 0.67/0.77 tff(1735,plain,(~product(e_5, e_4, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.67/0.77 tff(1736,plain,
% 0.67/0.77 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_4)) | (~group_element(e_5)) | product(e_5, e_4, e_4) | product(e_5, e_4, e_5) | product(e_5, e_4, e_2) | product(e_5, e_4, e_6) | product(e_5, e_4, e_3) | product(e_5, e_4, e_1))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_4)) | (~group_element(e_5)) | product(e_5, e_4, e_4) | product(e_5, e_4, e_5) | product(e_5, e_4, e_2) | product(e_5, e_4, e_6) | product(e_5, e_4, e_3) | product(e_5, e_4, e_1))),
% 0.67/0.77 inference(rewrite,[status(thm)],[])).
% 0.67/0.77 tff(1737,plain,
% 0.67/0.77 ((product(e_5, e_4, e_6) | product(e_5, e_4, e_5) | product(e_5, e_4, e_4) | product(e_5, e_4, e_3) | product(e_5, e_4, e_2) | product(e_5, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_5))) <=> ((~group_element(e_4)) | (~group_element(e_5)) | product(e_5, e_4, e_4) | product(e_5, e_4, e_5) | product(e_5, e_4, e_2) | product(e_5, e_4, e_6) | product(e_5, e_4, e_3) | product(e_5, e_4, e_1))),
% 0.67/0.77 inference(rewrite,[status(thm)],[])).
% 0.67/0.77 tff(1738,plain,
% 0.67/0.77 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_5, e_4, e_6) | product(e_5, e_4, e_5) | product(e_5, e_4, e_4) | product(e_5, e_4, e_3) | product(e_5, e_4, e_2) | product(e_5, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_5)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_4)) | (~group_element(e_5)) | product(e_5, e_4, e_4) | product(e_5, e_4, e_5) | product(e_5, e_4, e_2) | product(e_5, e_4, e_6) | product(e_5, e_4, e_3) | product(e_5, e_4, e_1)))),
% 0.67/0.77 inference(monotonicity,[status(thm)],[1737])).
% 0.67/0.77 tff(1739,plain,
% 0.67/0.77 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_5, e_4, e_6) | product(e_5, e_4, e_5) | product(e_5, e_4, e_4) | product(e_5, e_4, e_3) | product(e_5, e_4, e_2) | product(e_5, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_5)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_4)) | (~group_element(e_5)) | product(e_5, e_4, e_4) | product(e_5, e_4, e_5) | product(e_5, e_4, e_2) | product(e_5, e_4, e_6) | product(e_5, e_4, e_3) | product(e_5, e_4, e_1))),
% 0.67/0.77 inference(transitivity,[status(thm)],[1738, 1736])).
% 0.67/0.77 tff(1740,plain,
% 0.67/0.77 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_5, e_4, e_6) | product(e_5, e_4, e_5) | product(e_5, e_4, e_4) | product(e_5, e_4, e_3) | product(e_5, e_4, e_2) | product(e_5, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_5)))),
% 0.67/0.77 inference(quant_inst,[status(thm)],[])).
% 0.67/0.77 tff(1741,plain,
% 0.67/0.77 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_4)) | (~group_element(e_5)) | product(e_5, e_4, e_4) | product(e_5, e_4, e_5) | product(e_5, e_4, e_2) | product(e_5, e_4, e_6) | product(e_5, e_4, e_3) | product(e_5, e_4, e_1)),
% 0.67/0.77 inference(modus_ponens,[status(thm)],[1740, 1739])).
% 0.67/0.77 tff(1742,plain,
% 0.67/0.77 (product(e_5, e_4, e_5) | product(e_5, e_4, e_2) | product(e_5, e_4, e_6) | product(e_5, e_4, e_3) | product(e_5, e_4, e_1)),
% 0.67/0.77 inference(unit_resolution,[status(thm)],[1741, 279, 443, 129, 1735])).
% 0.67/0.77 tff(1743,plain,
% 0.67/0.77 (product(e_5, e_4, e_5) | product(e_5, e_4, e_2) | product(e_5, e_4, e_6) | product(e_5, e_4, e_3)),
% 0.67/0.77 inference(unit_resolution,[status(thm)],[1742, 1729])).
% 0.67/0.77 tff(1744,plain,
% 0.67/0.77 (product(e_5, e_4, e_3)),
% 0.67/0.77 inference(unit_resolution,[status(thm)],[1743, 1723, 1700, 1689])).
% 0.67/0.77 tff(1745,plain,
% 0.67/0.77 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_6, e_2, e_2) | (~product(e_2, e_2, e_4)) | (~product(e_4, e_2, e_6)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_6, e_2, e_2) | (~product(e_2, e_2, e_4)) | (~product(e_4, e_2, e_6)))),
% 0.67/0.77 inference(rewrite,[status(thm)],[])).
% 0.67/0.77 tff(1746,plain,
% 0.67/0.77 ((product(e_6, e_2, e_2) | (~product(e_4, e_2, e_6)) | (~product(e_2, e_2, e_4))) <=> (product(e_6, e_2, e_2) | (~product(e_2, e_2, e_4)) | (~product(e_4, e_2, e_6)))),
% 0.67/0.77 inference(rewrite,[status(thm)],[])).
% 0.67/0.77 tff(1747,plain,
% 0.67/0.77 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_6, e_2, e_2) | (~product(e_4, e_2, e_6)) | (~product(e_2, e_2, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_6, e_2, e_2) | (~product(e_2, e_2, e_4)) | (~product(e_4, e_2, e_6))))),
% 0.67/0.77 inference(monotonicity,[status(thm)],[1746])).
% 0.67/0.77 tff(1748,plain,
% 0.67/0.77 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_6, e_2, e_2) | (~product(e_4, e_2, e_6)) | (~product(e_2, e_2, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_6, e_2, e_2) | (~product(e_2, e_2, e_4)) | (~product(e_4, e_2, e_6)))),
% 0.67/0.77 inference(transitivity,[status(thm)],[1747, 1745])).
% 0.67/0.77 tff(1749,plain,
% 0.67/0.77 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_6, e_2, e_2) | (~product(e_4, e_2, e_6)) | (~product(e_2, e_2, e_4)))),
% 0.67/0.77 inference(quant_inst,[status(thm)],[])).
% 0.67/0.77 tff(1750,plain,
% 0.67/0.77 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_6, e_2, e_2) | (~product(e_2, e_2, e_4)) | (~product(e_4, e_2, e_6))),
% 0.67/0.77 inference(modus_ponens,[status(thm)],[1749, 1748])).
% 0.67/0.77 tff(1751,plain,
% 0.67/0.77 (~product(e_2, e_2, e_4)),
% 0.67/0.77 inference(unit_resolution,[status(thm)],[1750, 58, 1671, 1352])).
% 0.67/0.77 tff(1752,plain,
% 0.67/0.77 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_2, e_4) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_4, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_2, e_4) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_4, e_2)))),
% 0.67/0.77 inference(rewrite,[status(thm)],[])).
% 0.67/0.77 tff(1753,plain,
% 0.67/0.77 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_2, e_4) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_4, e_2)))),
% 0.67/0.77 inference(quant_inst,[status(thm)],[])).
% 0.67/0.77 tff(1754,plain,
% 0.67/0.77 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_2, e_4) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_4, e_2))),
% 0.67/0.77 inference(modus_ponens,[status(thm)],[1753, 1752])).
% 0.67/0.77 tff(1755,plain,
% 0.67/0.77 (~product(e_2, e_4, e_2)),
% 0.67/0.77 inference(unit_resolution,[status(thm)],[1754, 58, 692, 1751])).
% 0.67/0.77 tff(1756,assumption,(product(e_6, e_4, e_2)), introduced(assumption)).
% 0.67/0.77 tff(1757,plain,
% 0.67/0.77 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_4, e_2, e_6)) | product(e_2, e_4, e_2) | (~product(e_6, e_4, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_4, e_2, e_6)) | product(e_2, e_4, e_2) | (~product(e_6, e_4, e_2)))),
% 0.67/0.77 inference(rewrite,[status(thm)],[])).
% 0.67/0.77 tff(1758,plain,
% 0.67/0.77 ((product(e_2, e_4, e_2) | (~product(e_6, e_4, e_2)) | (~product(e_4, e_2, e_6))) <=> ((~product(e_4, e_2, e_6)) | product(e_2, e_4, e_2) | (~product(e_6, e_4, e_2)))),
% 0.67/0.77 inference(rewrite,[status(thm)],[])).
% 0.67/0.77 tff(1759,plain,
% 0.67/0.77 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_4, e_2) | (~product(e_6, e_4, e_2)) | (~product(e_4, e_2, e_6)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_4, e_2, e_6)) | product(e_2, e_4, e_2) | (~product(e_6, e_4, e_2))))),
% 0.67/0.77 inference(monotonicity,[status(thm)],[1758])).
% 0.67/0.77 tff(1760,plain,
% 0.67/0.77 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_4, e_2) | (~product(e_6, e_4, e_2)) | (~product(e_4, e_2, e_6)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_4, e_2, e_6)) | product(e_2, e_4, e_2) | (~product(e_6, e_4, e_2)))),
% 0.67/0.77 inference(transitivity,[status(thm)],[1759, 1757])).
% 0.67/0.77 tff(1761,plain,
% 0.67/0.77 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_4, e_2) | (~product(e_6, e_4, e_2)) | (~product(e_4, e_2, e_6)))),
% 0.67/0.77 inference(quant_inst,[status(thm)],[])).
% 0.67/0.77 tff(1762,plain,
% 0.67/0.77 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_4, e_2, e_6)) | product(e_2, e_4, e_2) | (~product(e_6, e_4, e_2))),
% 0.67/0.77 inference(modus_ponens,[status(thm)],[1761, 1760])).
% 0.67/0.77 tff(1763,plain,
% 0.67/0.77 ($false),
% 0.67/0.77 inference(unit_resolution,[status(thm)],[1762, 58, 1671, 1756, 1755])).
% 0.67/0.77 tff(1764,plain,((~product(e_6, e_4, e_2)) | (~product(e_4, e_2, e_6))), inference(lemma,lemma(discharge,[]))).
% 0.67/0.77 tff(1765,plain,
% 0.67/0.77 (~product(e_6, e_4, e_2)),
% 0.67/0.77 inference(unit_resolution,[status(thm)],[1764, 1671])).
% 0.67/0.77 tff(1766,assumption,(~product(e_5, e_4, e_2)), introduced(assumption)).
% 0.67/0.77 tff(1767,assumption,(product(e_6, e_4, e_5)), introduced(assumption)).
% 0.67/0.77 tff(1768,plain,
% 0.67/0.77 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_5, e_4, e_2) | (~product(e_4, e_2, e_6)) | (~product(e_6, e_4, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_5, e_4, e_2) | (~product(e_4, e_2, e_6)) | (~product(e_6, e_4, e_5)))),
% 0.67/0.77 inference(rewrite,[status(thm)],[])).
% 0.67/0.77 tff(1769,plain,
% 0.67/0.77 ((product(e_5, e_4, e_2) | (~product(e_6, e_4, e_5)) | (~product(e_4, e_2, e_6))) <=> (product(e_5, e_4, e_2) | (~product(e_4, e_2, e_6)) | (~product(e_6, e_4, e_5)))),
% 0.67/0.77 inference(rewrite,[status(thm)],[])).
% 0.67/0.77 tff(1770,plain,
% 0.67/0.77 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_5, e_4, e_2) | (~product(e_6, e_4, e_5)) | (~product(e_4, e_2, e_6)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_5, e_4, e_2) | (~product(e_4, e_2, e_6)) | (~product(e_6, e_4, e_5))))),
% 0.67/0.77 inference(monotonicity,[status(thm)],[1769])).
% 0.67/0.77 tff(1771,plain,
% 0.67/0.77 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_5, e_4, e_2) | (~product(e_6, e_4, e_5)) | (~product(e_4, e_2, e_6)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_5, e_4, e_2) | (~product(e_4, e_2, e_6)) | (~product(e_6, e_4, e_5)))),
% 0.67/0.77 inference(transitivity,[status(thm)],[1770, 1768])).
% 0.67/0.77 tff(1772,plain,
% 0.67/0.77 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_5, e_4, e_2) | (~product(e_6, e_4, e_5)) | (~product(e_4, e_2, e_6)))),
% 0.67/0.77 inference(quant_inst,[status(thm)],[])).
% 0.67/0.77 tff(1773,plain,
% 0.67/0.77 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_5, e_4, e_2) | (~product(e_4, e_2, e_6)) | (~product(e_6, e_4, e_5))),
% 0.67/0.77 inference(modus_ponens,[status(thm)],[1772, 1771])).
% 0.67/0.77 tff(1774,plain,
% 0.67/0.77 ($false),
% 0.67/0.77 inference(unit_resolution,[status(thm)],[1773, 58, 1671, 1767, 1766])).
% 0.67/0.78 tff(1775,plain,((~product(e_6, e_4, e_5)) | (~product(e_4, e_2, e_6)) | product(e_5, e_4, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.67/0.78 tff(1776,plain,
% 0.67/0.78 (~product(e_6, e_4, e_5)),
% 0.67/0.78 inference(unit_resolution,[status(thm)],[1775, 1723, 1671])).
% 0.67/0.78 tff(1777,assumption,(product(e_6, e_4, e_6)), introduced(assumption)).
% 0.67/0.78 tff(1778,plain,
% 0.67/0.78 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_6) | (~product(e_6, e_4, e_6)) | (~product(e_6, e_6, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_6) | (~product(e_6, e_4, e_6)) | (~product(e_6, e_6, e_6)))),
% 0.67/0.78 inference(rewrite,[status(thm)],[])).
% 0.67/0.78 tff(1779,plain,
% 0.67/0.78 ((equalish(e_4, e_6) | (~product(e_6, e_6, e_6)) | (~product(e_6, e_4, e_6))) <=> (equalish(e_4, e_6) | (~product(e_6, e_4, e_6)) | (~product(e_6, e_6, e_6)))),
% 0.67/0.78 inference(rewrite,[status(thm)],[])).
% 0.67/0.78 tff(1780,plain,
% 0.67/0.78 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_6) | (~product(e_6, e_6, e_6)) | (~product(e_6, e_4, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_6) | (~product(e_6, e_4, e_6)) | (~product(e_6, e_6, e_6))))),
% 0.67/0.78 inference(monotonicity,[status(thm)],[1779])).
% 0.67/0.78 tff(1781,plain,
% 0.67/0.78 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_6) | (~product(e_6, e_6, e_6)) | (~product(e_6, e_4, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_6) | (~product(e_6, e_4, e_6)) | (~product(e_6, e_6, e_6)))),
% 0.67/0.78 inference(transitivity,[status(thm)],[1780, 1778])).
% 0.67/0.78 tff(1782,plain,
% 0.67/0.78 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_6) | (~product(e_6, e_6, e_6)) | (~product(e_6, e_4, e_6)))),
% 0.67/0.78 inference(quant_inst,[status(thm)],[])).
% 0.67/0.78 tff(1783,plain,
% 0.67/0.78 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_6) | (~product(e_6, e_4, e_6)) | (~product(e_6, e_6, e_6))),
% 0.67/0.78 inference(modus_ponens,[status(thm)],[1782, 1781])).
% 0.67/0.78 tff(1784,plain,
% 0.67/0.78 ($false),
% 0.67/0.78 inference(unit_resolution,[status(thm)],[1783, 293, 17, 933, 1777])).
% 0.67/0.78 tff(1785,plain,(~product(e_6, e_4, e_6)), inference(lemma,lemma(discharge,[]))).
% 0.67/0.78 tff(1786,assumption,(product(e_6, e_4, e_4)), introduced(assumption)).
% 0.67/0.78 tff(1787,plain,
% 0.67/0.78 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_6, e_4, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_6, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_6, e_4, e_4)))),
% 0.67/0.78 inference(rewrite,[status(thm)],[])).
% 0.67/0.78 tff(1788,plain,
% 0.67/0.78 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_6, e_4, e_4)))),
% 0.67/0.78 inference(quant_inst,[status(thm)],[])).
% 0.67/0.78 tff(1789,plain,
% 0.67/0.78 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_6, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_6, e_4, e_4))),
% 0.67/0.78 inference(modus_ponens,[status(thm)],[1788, 1787])).
% 0.67/0.78 tff(1790,plain,
% 0.67/0.78 ($false),
% 0.67/0.78 inference(unit_resolution,[status(thm)],[1789, 635, 87, 184, 1786])).
% 0.67/0.78 tff(1791,plain,(~product(e_6, e_4, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.67/0.78 tff(1792,plain,
% 0.67/0.78 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_4)) | (~group_element(e_6)) | product(e_6, e_4, e_1) | product(e_6, e_4, e_4) | product(e_6, e_4, e_3) | product(e_6, e_4, e_2) | product(e_6, e_4, e_6) | product(e_6, e_4, e_5))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_4)) | (~group_element(e_6)) | product(e_6, e_4, e_1) | product(e_6, e_4, e_4) | product(e_6, e_4, e_3) | product(e_6, e_4, e_2) | product(e_6, e_4, e_6) | product(e_6, e_4, e_5))),
% 0.67/0.78 inference(rewrite,[status(thm)],[])).
% 0.67/0.78 tff(1793,plain,
% 0.67/0.78 ((product(e_6, e_4, e_6) | product(e_6, e_4, e_5) | product(e_6, e_4, e_4) | product(e_6, e_4, e_3) | product(e_6, e_4, e_2) | product(e_6, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_6))) <=> ((~group_element(e_4)) | (~group_element(e_6)) | product(e_6, e_4, e_1) | product(e_6, e_4, e_4) | product(e_6, e_4, e_3) | product(e_6, e_4, e_2) | product(e_6, e_4, e_6) | product(e_6, e_4, e_5))),
% 0.67/0.78 inference(rewrite,[status(thm)],[])).
% 0.67/0.78 tff(1794,plain,
% 0.67/0.78 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_6, e_4, e_6) | product(e_6, e_4, e_5) | product(e_6, e_4, e_4) | product(e_6, e_4, e_3) | product(e_6, e_4, e_2) | product(e_6, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_6)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_4)) | (~group_element(e_6)) | product(e_6, e_4, e_1) | product(e_6, e_4, e_4) | product(e_6, e_4, e_3) | product(e_6, e_4, e_2) | product(e_6, e_4, e_6) | product(e_6, e_4, e_5)))),
% 0.67/0.78 inference(monotonicity,[status(thm)],[1793])).
% 0.67/0.78 tff(1795,plain,
% 0.67/0.78 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_6, e_4, e_6) | product(e_6, e_4, e_5) | product(e_6, e_4, e_4) | product(e_6, e_4, e_3) | product(e_6, e_4, e_2) | product(e_6, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_6)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_4)) | (~group_element(e_6)) | product(e_6, e_4, e_1) | product(e_6, e_4, e_4) | product(e_6, e_4, e_3) | product(e_6, e_4, e_2) | product(e_6, e_4, e_6) | product(e_6, e_4, e_5))),
% 0.67/0.78 inference(transitivity,[status(thm)],[1794, 1792])).
% 0.67/0.78 tff(1796,plain,
% 0.67/0.78 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_6, e_4, e_6) | product(e_6, e_4, e_5) | product(e_6, e_4, e_4) | product(e_6, e_4, e_3) | product(e_6, e_4, e_2) | product(e_6, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_6)))),
% 0.67/0.78 inference(quant_inst,[status(thm)],[])).
% 0.67/0.78 tff(1797,plain,
% 0.67/0.78 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_4)) | (~group_element(e_6)) | product(e_6, e_4, e_1) | product(e_6, e_4, e_4) | product(e_6, e_4, e_3) | product(e_6, e_4, e_2) | product(e_6, e_4, e_6) | product(e_6, e_4, e_5)),
% 0.67/0.78 inference(modus_ponens,[status(thm)],[1796, 1795])).
% 0.67/0.78 tff(1798,plain,
% 0.67/0.78 (product(e_6, e_4, e_1) | product(e_6, e_4, e_3) | product(e_6, e_4, e_2) | product(e_6, e_4, e_6) | product(e_6, e_4, e_5)),
% 0.67/0.78 inference(unit_resolution,[status(thm)],[1797, 279, 384, 129, 1791])).
% 0.67/0.78 tff(1799,plain,
% 0.67/0.78 (product(e_6, e_4, e_1) | product(e_6, e_4, e_3) | product(e_6, e_4, e_2) | product(e_6, e_4, e_5)),
% 0.67/0.78 inference(unit_resolution,[status(thm)],[1798, 1785])).
% 0.67/0.78 tff(1800,plain,
% 0.67/0.78 (product(e_6, e_4, e_3)),
% 0.67/0.78 inference(unit_resolution,[status(thm)],[1799, 1776, 1690, 1765])).
% 0.67/0.78 tff(1801,plain,
% 0.67/0.78 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_6) | (~product(e_5, e_4, e_3)) | (~product(e_6, e_4, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_6) | (~product(e_5, e_4, e_3)) | (~product(e_6, e_4, e_3)))),
% 0.67/0.78 inference(rewrite,[status(thm)],[])).
% 0.67/0.78 tff(1802,plain,
% 0.67/0.78 ((equalish(e_5, e_6) | (~product(e_6, e_4, e_3)) | (~product(e_5, e_4, e_3))) <=> (equalish(e_5, e_6) | (~product(e_5, e_4, e_3)) | (~product(e_6, e_4, e_3)))),
% 0.67/0.78 inference(rewrite,[status(thm)],[])).
% 0.67/0.78 tff(1803,plain,
% 0.67/0.78 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_6) | (~product(e_6, e_4, e_3)) | (~product(e_5, e_4, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_6) | (~product(e_5, e_4, e_3)) | (~product(e_6, e_4, e_3))))),
% 0.67/0.78 inference(monotonicity,[status(thm)],[1802])).
% 0.67/0.78 tff(1804,plain,
% 0.67/0.78 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_6) | (~product(e_6, e_4, e_3)) | (~product(e_5, e_4, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_6) | (~product(e_5, e_4, e_3)) | (~product(e_6, e_4, e_3)))),
% 0.67/0.78 inference(transitivity,[status(thm)],[1803, 1801])).
% 0.67/0.78 tff(1805,plain,
% 0.67/0.78 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_6) | (~product(e_6, e_4, e_3)) | (~product(e_5, e_4, e_3)))),
% 0.67/0.78 inference(quant_inst,[status(thm)],[])).
% 0.67/0.78 tff(1806,plain,
% 0.67/0.78 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_6) | (~product(e_5, e_4, e_3)) | (~product(e_6, e_4, e_3))),
% 0.67/0.78 inference(modus_ponens,[status(thm)],[1805, 1804])).
% 0.67/0.78 tff(1807,plain,
% 0.67/0.78 ($false),
% 0.67/0.78 inference(unit_resolution,[status(thm)],[1806, 20, 87, 1800, 1744])).
% 0.67/0.78 tff(1808,plain,((~product(e_4, e_2, e_6)) | product(e_6, e_4, e_1) | (~product(e_1, e_2, e_5)) | product(e_4, e_5, e_3) | product(e_4, e_5, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.67/0.78 tff(1809,plain,
% 0.67/0.78 (~product(e_4, e_2, e_6)),
% 0.67/0.78 inference(unit_resolution,[status(thm)],[1808, 1668, 1573, 1661, 1652])).
% 0.67/0.78 tff(1810,assumption,(product(e_4, e_2, e_5)), introduced(assumption)).
% 0.67/0.78 tff(1811,plain,
% 0.67/0.78 (((~![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_4, e_1, e_5)) | (~product(e_4, e_2, e_5)))) <=> ((~![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_4, e_1, e_5)) | (~product(e_4, e_2, e_5)))),
% 0.67/0.78 inference(rewrite,[status(thm)],[])).
% 0.67/0.78 tff(1812,plain,
% 0.67/0.78 ((~![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_4, e_1, e_5)) | (~product(e_4, e_2, e_5)))),
% 0.67/0.78 inference(quant_inst,[status(thm)],[])).
% 0.67/0.78 tff(1813,plain,
% 0.67/0.78 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_4, e_1, e_5)) | (~product(e_4, e_2, e_5))),
% 0.67/0.78 inference(modus_ponens,[status(thm)],[1812, 1811])).
% 0.67/0.78 tff(1814,plain,
% 0.67/0.78 ($false),
% 0.67/0.78 inference(unit_resolution,[status(thm)],[1813, 90, 17, 1105, 1810])).
% 0.67/0.78 tff(1815,plain,((~product(e_4, e_2, e_5)) | (~product(e_4, e_1, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.67/0.78 tff(1816,plain,
% 0.67/0.78 (~product(e_4, e_2, e_5)),
% 0.67/0.78 inference(unit_resolution,[status(thm)],[1815, 1555])).
% 0.67/0.78 tff(1817,assumption,(product(e_4, e_2, e_1)), introduced(assumption)).
% 0.67/0.78 tff(1818,plain,
% 0.67/0.78 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_2) | (~product(e_4, e_2, e_1)) | (~product(e_2, e_2, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_2, e_2) | (~product(e_4, e_2, e_1)) | (~product(e_2, e_2, e_4)))),
% 0.67/0.78 inference(rewrite,[status(thm)],[])).
% 0.67/0.78 tff(1819,plain,
% 0.67/0.78 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_2) | (~product(e_4, e_2, e_1)) | (~product(e_2, e_2, e_4)))),
% 0.67/0.78 inference(quant_inst,[status(thm)],[])).
% 0.67/0.78 tff(1820,plain,
% 0.67/0.78 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_2, e_2) | (~product(e_4, e_2, e_1)) | (~product(e_2, e_2, e_4))),
% 0.67/0.78 inference(modus_ponens,[status(thm)],[1819, 1818])).
% 0.67/0.78 tff(1821,plain,
% 0.67/0.78 (~product(e_2, e_2, e_4)),
% 0.67/0.78 inference(unit_resolution,[status(thm)],[1820, 58, 703, 1817])).
% 0.67/0.78 tff(1822,plain,
% 0.67/0.78 (~product(e_2, e_4, e_2)),
% 0.67/0.78 inference(unit_resolution,[status(thm)],[1754, 58, 692, 1821])).
% 0.67/0.78 tff(1823,plain,
% 0.67/0.78 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_4, e_2)) | (~product(e_4, e_2, e_1)) | product(e_2, e_4, e_2))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_4, e_2)) | (~product(e_4, e_2, e_1)) | product(e_2, e_4, e_2))),
% 0.67/0.78 inference(rewrite,[status(thm)],[])).
% 0.67/0.78 tff(1824,plain,
% 0.67/0.78 ((product(e_2, e_4, e_2) | (~product(e_1, e_4, e_2)) | (~product(e_4, e_2, e_1))) <=> ((~product(e_1, e_4, e_2)) | (~product(e_4, e_2, e_1)) | product(e_2, e_4, e_2))),
% 0.67/0.78 inference(rewrite,[status(thm)],[])).
% 0.67/0.78 tff(1825,plain,
% 0.67/0.78 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_4, e_2) | (~product(e_1, e_4, e_2)) | (~product(e_4, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_4, e_2)) | (~product(e_4, e_2, e_1)) | product(e_2, e_4, e_2)))),
% 0.67/0.78 inference(monotonicity,[status(thm)],[1824])).
% 0.74/0.78 tff(1826,plain,
% 0.74/0.78 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_4, e_2) | (~product(e_1, e_4, e_2)) | (~product(e_4, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_4, e_2)) | (~product(e_4, e_2, e_1)) | product(e_2, e_4, e_2))),
% 0.74/0.78 inference(transitivity,[status(thm)],[1825, 1823])).
% 0.74/0.78 tff(1827,plain,
% 0.74/0.78 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_4, e_2) | (~product(e_1, e_4, e_2)) | (~product(e_4, e_2, e_1)))),
% 0.74/0.78 inference(quant_inst,[status(thm)],[])).
% 0.74/0.78 tff(1828,plain,
% 0.74/0.78 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_4, e_2)) | (~product(e_4, e_2, e_1)) | product(e_2, e_4, e_2)),
% 0.74/0.78 inference(modus_ponens,[status(thm)],[1827, 1826])).
% 0.74/0.78 tff(1829,plain,
% 0.74/0.78 ($false),
% 0.74/0.78 inference(unit_resolution,[status(thm)],[1828, 58, 1032, 1817, 1822])).
% 0.74/0.78 tff(1830,plain,(~product(e_4, e_2, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.74/0.78 tff(1831,assumption,(product(e_4, e_2, e_4)), introduced(assumption)).
% 0.74/0.78 tff(1832,plain,
% 0.74/0.78 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_2, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_2, e_4)))),
% 0.74/0.78 inference(rewrite,[status(thm)],[])).
% 0.74/0.78 tff(1833,plain,
% 0.74/0.78 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_2, e_4)))),
% 0.74/0.78 inference(quant_inst,[status(thm)],[])).
% 0.74/0.78 tff(1834,plain,
% 0.74/0.78 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_2, e_4))),
% 0.74/0.79 inference(modus_ponens,[status(thm)],[1833, 1832])).
% 0.74/0.79 tff(1835,plain,
% 0.74/0.79 ($false),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[1834, 522, 17, 184, 1831])).
% 0.74/0.79 tff(1836,plain,(~product(e_4, e_2, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.74/0.79 tff(1837,assumption,(product(e_4, e_2, e_2)), introduced(assumption)).
% 0.74/0.79 tff(1838,plain,
% 0.74/0.79 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_2) | (~product(e_4, e_2, e_2)) | (~product(e_2, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_2) | (~product(e_4, e_2, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.74/0.79 inference(rewrite,[status(thm)],[])).
% 0.74/0.79 tff(1839,plain,
% 0.74/0.79 ((equalish(e_4, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_4, e_2, e_2))) <=> (equalish(e_4, e_2) | (~product(e_4, e_2, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.74/0.79 inference(rewrite,[status(thm)],[])).
% 0.74/0.79 tff(1840,plain,
% 0.74/0.79 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_4, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_2) | (~product(e_4, e_2, e_2)) | (~product(e_2, e_2, e_2))))),
% 0.74/0.79 inference(monotonicity,[status(thm)],[1839])).
% 0.74/0.79 tff(1841,plain,
% 0.74/0.79 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_4, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_2) | (~product(e_4, e_2, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.74/0.79 inference(transitivity,[status(thm)],[1840, 1838])).
% 0.74/0.79 tff(1842,plain,
% 0.74/0.79 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_4, e_2, e_2)))),
% 0.74/0.79 inference(quant_inst,[status(thm)],[])).
% 0.74/0.79 tff(1843,plain,
% 0.74/0.79 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_2) | (~product(e_4, e_2, e_2)) | (~product(e_2, e_2, e_2))),
% 0.74/0.79 inference(modus_ponens,[status(thm)],[1842, 1841])).
% 0.74/0.79 tff(1844,plain,
% 0.74/0.79 ($false),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[1843, 659, 87, 1837, 692])).
% 0.74/0.79 tff(1845,plain,(~product(e_4, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.74/0.79 tff(1846,plain,
% 0.74/0.79 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_2)) | (~group_element(e_4)) | product(e_4, e_2, e_5) | product(e_4, e_2, e_2) | product(e_4, e_2, e_6) | product(e_4, e_2, e_4) | product(e_4, e_2, e_1) | product(e_4, e_2, e_3))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_2)) | (~group_element(e_4)) | product(e_4, e_2, e_5) | product(e_4, e_2, e_2) | product(e_4, e_2, e_6) | product(e_4, e_2, e_4) | product(e_4, e_2, e_1) | product(e_4, e_2, e_3))),
% 0.74/0.79 inference(rewrite,[status(thm)],[])).
% 0.74/0.79 tff(1847,plain,
% 0.74/0.79 ((product(e_4, e_2, e_6) | product(e_4, e_2, e_5) | product(e_4, e_2, e_4) | product(e_4, e_2, e_3) | product(e_4, e_2, e_2) | product(e_4, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_4))) <=> ((~group_element(e_2)) | (~group_element(e_4)) | product(e_4, e_2, e_5) | product(e_4, e_2, e_2) | product(e_4, e_2, e_6) | product(e_4, e_2, e_4) | product(e_4, e_2, e_1) | product(e_4, e_2, e_3))),
% 0.74/0.79 inference(rewrite,[status(thm)],[])).
% 0.74/0.79 tff(1848,plain,
% 0.74/0.79 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_2, e_6) | product(e_4, e_2, e_5) | product(e_4, e_2, e_4) | product(e_4, e_2, e_3) | product(e_4, e_2, e_2) | product(e_4, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_2)) | (~group_element(e_4)) | product(e_4, e_2, e_5) | product(e_4, e_2, e_2) | product(e_4, e_2, e_6) | product(e_4, e_2, e_4) | product(e_4, e_2, e_1) | product(e_4, e_2, e_3)))),
% 0.74/0.79 inference(monotonicity,[status(thm)],[1847])).
% 0.74/0.79 tff(1849,plain,
% 0.74/0.79 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_2, e_6) | product(e_4, e_2, e_5) | product(e_4, e_2, e_4) | product(e_4, e_2, e_3) | product(e_4, e_2, e_2) | product(e_4, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_2)) | (~group_element(e_4)) | product(e_4, e_2, e_5) | product(e_4, e_2, e_2) | product(e_4, e_2, e_6) | product(e_4, e_2, e_4) | product(e_4, e_2, e_1) | product(e_4, e_2, e_3))),
% 0.74/0.79 inference(transitivity,[status(thm)],[1848, 1846])).
% 0.74/0.79 tff(1850,plain,
% 0.74/0.79 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_2, e_6) | product(e_4, e_2, e_5) | product(e_4, e_2, e_4) | product(e_4, e_2, e_3) | product(e_4, e_2, e_2) | product(e_4, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_4)))),
% 0.74/0.79 inference(quant_inst,[status(thm)],[])).
% 0.74/0.79 tff(1851,plain,
% 0.74/0.79 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_2)) | (~group_element(e_4)) | product(e_4, e_2, e_5) | product(e_4, e_2, e_2) | product(e_4, e_2, e_6) | product(e_4, e_2, e_4) | product(e_4, e_2, e_1) | product(e_4, e_2, e_3)),
% 0.74/0.79 inference(modus_ponens,[status(thm)],[1850, 1849])).
% 0.74/0.79 tff(1852,plain,
% 0.74/0.79 (product(e_4, e_2, e_5) | product(e_4, e_2, e_2) | product(e_4, e_2, e_6) | product(e_4, e_2, e_4) | product(e_4, e_2, e_1) | product(e_4, e_2, e_3)),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[1851, 132, 279, 129])).
% 0.74/0.79 tff(1853,plain,
% 0.74/0.79 (product(e_4, e_2, e_5) | product(e_4, e_2, e_6) | product(e_4, e_2, e_4) | product(e_4, e_2, e_1) | product(e_4, e_2, e_3)),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[1852, 1845])).
% 0.74/0.79 tff(1854,plain,
% 0.74/0.79 (product(e_4, e_2, e_5) | product(e_4, e_2, e_6) | product(e_4, e_2, e_1) | product(e_4, e_2, e_3)),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[1853, 1836])).
% 0.74/0.79 tff(1855,plain,
% 0.74/0.79 (product(e_4, e_2, e_5) | product(e_4, e_2, e_6) | product(e_4, e_2, e_3)),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[1854, 1830])).
% 0.74/0.79 tff(1856,plain,
% 0.74/0.79 (product(e_4, e_2, e_6) | product(e_4, e_2, e_3)),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[1855, 1816])).
% 0.74/0.79 tff(1857,plain,
% 0.74/0.79 (product(e_4, e_2, e_3)),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[1856, 1809])).
% 0.74/0.79 tff(1858,assumption,(product(e_4, e_2, e_3)), introduced(assumption)).
% 0.74/0.79 tff(1859,plain,
% 0.74/0.79 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_6) | (~product(e_4, e_6, e_3)) | (~product(e_4, e_2, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_6) | (~product(e_4, e_6, e_3)) | (~product(e_4, e_2, e_3)))),
% 0.74/0.79 inference(rewrite,[status(thm)],[])).
% 0.74/0.79 tff(1860,plain,
% 0.74/0.79 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_6) | (~product(e_4, e_6, e_3)) | (~product(e_4, e_2, e_3)))),
% 0.74/0.79 inference(quant_inst,[status(thm)],[])).
% 0.74/0.79 tff(1861,plain,
% 0.74/0.79 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_6) | (~product(e_4, e_6, e_3)) | (~product(e_4, e_2, e_3))),
% 0.74/0.79 inference(modus_ponens,[status(thm)],[1860, 1859])).
% 0.74/0.79 tff(1862,plain,
% 0.74/0.79 ($false),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[1861, 545, 17, 1396, 1858])).
% 0.74/0.79 tff(1863,plain,((~product(e_4, e_2, e_3)) | (~product(e_4, e_6, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.79 tff(1864,plain,
% 0.74/0.79 (~product(e_4, e_6, e_3)),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[1863, 1857])).
% 0.74/0.79 tff(1865,plain,
% 0.74/0.79 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_6, e_1) | (~product(e_4, e_1, e_5)) | (~product(e_4, e_6, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_6, e_1) | (~product(e_4, e_1, e_5)) | (~product(e_4, e_6, e_5)))),
% 0.74/0.79 inference(rewrite,[status(thm)],[])).
% 0.74/0.79 tff(1866,plain,
% 0.74/0.79 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_6, e_1) | (~product(e_4, e_1, e_5)) | (~product(e_4, e_6, e_5)))),
% 0.74/0.79 inference(quant_inst,[status(thm)],[])).
% 0.74/0.79 tff(1867,plain,
% 0.74/0.79 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_6, e_1) | (~product(e_4, e_1, e_5)) | (~product(e_4, e_6, e_5))),
% 0.74/0.79 inference(modus_ponens,[status(thm)],[1866, 1865])).
% 0.74/0.79 tff(1868,plain,
% 0.74/0.79 ($false),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[1867, 1116, 17, 1105, 1307])).
% 0.74/0.79 tff(1869,plain,((~product(e_4, e_6, e_5)) | (~product(e_4, e_1, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.79 tff(1870,plain,
% 0.74/0.79 (~product(e_4, e_6, e_5)),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[1869, 1555])).
% 0.74/0.79 tff(1871,plain,
% 0.74/0.79 (product(e_4, e_6, e_3) | product(e_4, e_6, e_2) | product(e_4, e_6, e_1)),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[1393, 1870])).
% 0.74/0.79 tff(1872,plain,
% 0.74/0.79 (product(e_4, e_6, e_1)),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[1871, 1864, 1643])).
% 0.74/0.79 tff(1873,plain,
% 0.74/0.79 (product(e_6, e_2, e_3)),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[1368, 1872, 1579, 690])).
% 0.74/0.79 tff(1874,plain,
% 0.74/0.79 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_6) | (~product(e_6, e_2, e_3)) | (~product(e_4, 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_4, e_6) | (~product(e_6, e_2, e_3)) | (~product(e_4, e_2, e_3)))),
% 0.74/0.79 inference(rewrite,[status(thm)],[])).
% 0.74/0.79 tff(1875,plain,
% 0.74/0.79 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_6) | (~product(e_6, e_2, e_3)) | (~product(e_4, e_2, e_3)))),
% 0.74/0.79 inference(quant_inst,[status(thm)],[])).
% 0.74/0.79 tff(1876,plain,
% 0.74/0.79 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_6) | (~product(e_6, e_2, e_3)) | (~product(e_4, e_2, e_3))),
% 0.74/0.79 inference(modus_ponens,[status(thm)],[1875, 1874])).
% 0.74/0.79 tff(1877,plain,
% 0.74/0.79 ($false),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[1876, 293, 87, 1857, 1873])).
% 0.74/0.79 tff(1878,plain,(~product(e_1, e_6, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.74/0.79 tff(1879,plain,
% 0.74/0.79 (product(e_1, e_6, e_5)),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[945, 1878])).
% 0.74/0.79 tff(1880,plain,
% 0.74/0.79 (~product(e_1, e_3, e_5)),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[871, 1879])).
% 0.74/0.79 tff(1881,plain,
% 0.74/0.79 (~product(e_1, e_2, e_5)),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[894, 1879])).
% 0.74/0.79 tff(1882,plain,
% 0.74/0.79 (product(e_1, e_2, e_4)),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[1548, 1881])).
% 0.74/0.79 tff(1883,plain,
% 0.74/0.79 (~product(e_1, e_3, e_4)),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[761, 1882])).
% 0.74/0.79 tff(1884,plain,
% 0.74/0.79 (product(e_1, e_3, e_6)),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[1219, 1883, 1880])).
% 0.74/0.79 tff(1885,plain,
% 0.74/0.79 (~product(e_4, e_3, e_6)),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[1587, 1884])).
% 0.74/0.79 tff(1886,plain,
% 0.74/0.79 (product(e_4, e_3, e_2)),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[1635, 1885])).
% 0.74/0.79 tff(1887,plain,
% 0.74/0.79 (~product(e_4, e_6, e_2)),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[1642, 1886])).
% 0.74/0.79 tff(1888,plain,
% 0.74/0.79 (product(e_4, e_6, e_3) | product(e_4, e_6, e_1)),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[1871, 1887])).
% 0.74/0.79 tff(1889,plain,
% 0.74/0.79 (product(e_4, e_6, e_1)),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[1888, 1571])).
% 0.74/0.79 tff(1890,plain,
% 0.74/0.79 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_6, e_3) | (~product(e_4, e_6, e_1)) | (~product(e_6, e_3, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_6, e_3) | (~product(e_4, e_6, e_1)) | (~product(e_6, e_3, e_4)))),
% 0.74/0.79 inference(rewrite,[status(thm)],[])).
% 0.74/0.79 tff(1891,plain,
% 0.74/0.79 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_6, e_3) | (~product(e_4, e_6, e_1)) | (~product(e_6, e_3, e_4)))),
% 0.74/0.79 inference(quant_inst,[status(thm)],[])).
% 0.74/0.79 tff(1892,plain,
% 0.74/0.79 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_6, e_3) | (~product(e_4, e_6, e_1)) | (~product(e_6, e_3, e_4))),
% 0.74/0.79 inference(modus_ponens,[status(thm)],[1891, 1890])).
% 0.74/0.79 tff(1893,plain,
% 0.74/0.79 (~product(e_6, e_3, e_4)),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[1892, 58, 348, 1889])).
% 0.74/0.79 tff(1894,plain,
% 0.74/0.79 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_3, e_6)) | product(e_6, e_3, e_4) | (~product(e_3, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_3, e_6)) | product(e_6, e_3, e_4) | (~product(e_3, e_4, e_1)))),
% 0.74/0.79 inference(rewrite,[status(thm)],[])).
% 0.74/0.79 tff(1895,plain,
% 0.74/0.79 ((product(e_6, e_3, e_4) | (~product(e_1, e_3, e_6)) | (~product(e_3, e_4, e_1))) <=> ((~product(e_1, e_3, e_6)) | product(e_6, e_3, e_4) | (~product(e_3, e_4, e_1)))),
% 0.74/0.79 inference(rewrite,[status(thm)],[])).
% 0.74/0.79 tff(1896,plain,
% 0.74/0.79 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_6, e_3, e_4) | (~product(e_1, e_3, e_6)) | (~product(e_3, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_3, e_6)) | product(e_6, e_3, e_4) | (~product(e_3, e_4, e_1))))),
% 0.74/0.79 inference(monotonicity,[status(thm)],[1895])).
% 0.74/0.79 tff(1897,plain,
% 0.74/0.79 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_6, e_3, e_4) | (~product(e_1, e_3, e_6)) | (~product(e_3, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_3, e_6)) | product(e_6, e_3, e_4) | (~product(e_3, e_4, e_1)))),
% 0.74/0.79 inference(transitivity,[status(thm)],[1896, 1894])).
% 0.74/0.79 tff(1898,plain,
% 0.74/0.79 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_6, e_3, e_4) | (~product(e_1, e_3, e_6)) | (~product(e_3, e_4, e_1)))),
% 0.74/0.79 inference(quant_inst,[status(thm)],[])).
% 0.74/0.79 tff(1899,plain,
% 0.74/0.79 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_3, e_6)) | product(e_6, e_3, e_4) | (~product(e_3, e_4, e_1))),
% 0.74/0.79 inference(modus_ponens,[status(thm)],[1898, 1897])).
% 0.74/0.79 tff(1900,plain,
% 0.74/0.79 ($false),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[1899, 58, 1884, 2, 1893])).
% 0.74/0.79 tff(1901,plain,(~product(e_3, e_4, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.74/0.79 tff(1902,assumption,(~product(e_3, e_4, e_1)), introduced(assumption)).
% 0.74/0.79 tff(1903,assumption,(product(e_5, e_4, e_3)), introduced(assumption)).
% 0.74/0.79 tff(1904,plain,
% 0.74/0.79 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_4, e_1, e_5)) | (~product(e_5, e_4, e_3)) | product(e_3, e_4, e_1))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_4, e_1, e_5)) | (~product(e_5, e_4, e_3)) | product(e_3, e_4, e_1))),
% 0.74/0.80 inference(rewrite,[status(thm)],[])).
% 0.74/0.80 tff(1905,plain,
% 0.74/0.80 ((product(e_3, e_4, e_1) | (~product(e_5, e_4, e_3)) | (~product(e_4, e_1, e_5))) <=> ((~product(e_4, e_1, e_5)) | (~product(e_5, e_4, e_3)) | product(e_3, e_4, e_1))),
% 0.74/0.80 inference(rewrite,[status(thm)],[])).
% 0.74/0.80 tff(1906,plain,
% 0.74/0.80 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_4, e_1) | (~product(e_5, e_4, e_3)) | (~product(e_4, e_1, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_4, e_1, e_5)) | (~product(e_5, e_4, e_3)) | product(e_3, e_4, e_1)))),
% 0.74/0.80 inference(monotonicity,[status(thm)],[1905])).
% 0.74/0.80 tff(1907,plain,
% 0.74/0.80 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_4, e_1) | (~product(e_5, e_4, e_3)) | (~product(e_4, e_1, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_4, e_1, e_5)) | (~product(e_5, e_4, e_3)) | product(e_3, e_4, e_1))),
% 0.74/0.80 inference(transitivity,[status(thm)],[1906, 1904])).
% 0.74/0.80 tff(1908,plain,
% 0.74/0.80 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_4, e_1) | (~product(e_5, e_4, e_3)) | (~product(e_4, e_1, e_5)))),
% 0.74/0.80 inference(quant_inst,[status(thm)],[])).
% 0.74/0.80 tff(1909,plain,
% 0.74/0.80 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_4, e_1, e_5)) | (~product(e_5, e_4, e_3)) | product(e_3, e_4, e_1)),
% 0.74/0.80 inference(modus_ponens,[status(thm)],[1908, 1907])).
% 0.74/0.80 tff(1910,plain,
% 0.74/0.80 ($false),
% 0.74/0.80 inference(unit_resolution,[status(thm)],[1909, 58, 1555, 1903, 1902])).
% 0.74/0.80 tff(1911,plain,((~product(e_5, e_4, e_3)) | product(e_3, e_4, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.74/0.80 tff(1912,plain,
% 0.74/0.80 (~product(e_5, e_4, e_3)),
% 0.74/0.80 inference(unit_resolution,[status(thm)],[1911, 1901])).
% 0.74/0.80 tff(1913,assumption,(product(e_5, e_4, e_5)), introduced(assumption)).
% 0.74/0.80 tff(1914,plain,
% 0.74/0.80 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_5, e_4, e_1) | (~product(e_4, e_1, e_5)) | (~product(e_5, e_4, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_5, e_4, e_1) | (~product(e_4, e_1, e_5)) | (~product(e_5, e_4, e_5)))),
% 0.74/0.80 inference(rewrite,[status(thm)],[])).
% 0.74/0.80 tff(1915,plain,
% 0.74/0.80 ((product(e_5, e_4, e_1) | (~product(e_5, e_4, e_5)) | (~product(e_4, e_1, e_5))) <=> (product(e_5, e_4, e_1) | (~product(e_4, e_1, e_5)) | (~product(e_5, e_4, e_5)))),
% 0.74/0.80 inference(rewrite,[status(thm)],[])).
% 0.74/0.80 tff(1916,plain,
% 0.74/0.80 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_5, e_4, e_1) | (~product(e_5, e_4, e_5)) | (~product(e_4, e_1, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_5, e_4, e_1) | (~product(e_4, e_1, e_5)) | (~product(e_5, e_4, e_5))))),
% 0.74/0.80 inference(monotonicity,[status(thm)],[1915])).
% 0.74/0.80 tff(1917,plain,
% 0.74/0.80 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_5, e_4, e_1) | (~product(e_5, e_4, e_5)) | (~product(e_4, e_1, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_5, e_4, e_1) | (~product(e_4, e_1, e_5)) | (~product(e_5, e_4, e_5)))),
% 0.74/0.80 inference(transitivity,[status(thm)],[1916, 1914])).
% 0.74/0.80 tff(1918,plain,
% 0.74/0.80 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_5, e_4, e_1) | (~product(e_5, e_4, e_5)) | (~product(e_4, e_1, e_5)))),
% 0.74/0.80 inference(quant_inst,[status(thm)],[])).
% 0.74/0.80 tff(1919,plain,
% 0.74/0.80 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_5, e_4, e_1) | (~product(e_4, e_1, e_5)) | (~product(e_5, e_4, e_5))),
% 0.74/0.80 inference(modus_ponens,[status(thm)],[1918, 1917])).
% 0.74/0.80 tff(1920,plain,
% 0.74/0.80 ($false),
% 0.74/0.80 inference(unit_resolution,[status(thm)],[1919, 58, 1555, 1913, 1729])).
% 0.74/0.80 tff(1921,plain,(~product(e_5, e_4, e_5)), inference(lemma,lemma(discharge,[]))).
% 0.74/0.80 tff(1922,plain,
% 0.74/0.80 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_2, e_4) | (~product(e_1, e_2, e_4)) | (~product(e_2, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_4, e_2, e_4) | (~product(e_1, e_2, e_4)) | (~product(e_2, e_4, e_1)))),
% 0.74/0.80 inference(rewrite,[status(thm)],[])).
% 0.74/0.80 tff(1923,plain,
% 0.74/0.80 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_2, e_4) | (~product(e_1, e_2, e_4)) | (~product(e_2, e_4, e_1)))),
% 0.74/0.80 inference(quant_inst,[status(thm)],[])).
% 0.74/0.80 tff(1924,plain,
% 0.74/0.80 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_4, e_2, e_4) | (~product(e_1, e_2, e_4)) | (~product(e_2, e_4, e_1))),
% 0.74/0.80 inference(modus_ponens,[status(thm)],[1923, 1922])).
% 0.74/0.80 tff(1925,plain,
% 0.74/0.80 (~product(e_2, e_4, e_1)),
% 0.74/0.80 inference(unit_resolution,[status(thm)],[1924, 58, 1882, 1836])).
% 0.74/0.80 tff(1926,plain,
% 0.74/0.80 (~product(e_5, e_4, e_2)),
% 0.74/0.80 inference(unit_resolution,[status(thm)],[1722, 1925])).
% 0.74/0.80 tff(1927,plain,
% 0.74/0.80 (product(e_5, e_4, e_6) | product(e_5, e_4, e_3)),
% 0.74/0.80 inference(unit_resolution,[status(thm)],[1743, 1926, 1921])).
% 0.74/0.80 tff(1928,plain,
% 0.74/0.80 (product(e_5, e_4, e_6)),
% 0.74/0.80 inference(unit_resolution,[status(thm)],[1927, 1912])).
% 0.74/0.80 tff(1929,plain,
% 0.74/0.80 (product(e_6, e_4, e_1)),
% 0.74/0.80 inference(unit_resolution,[status(thm)],[1699, 1928])).
% 0.74/0.80 tff(1930,plain,
% 0.74/0.80 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_6, e_5)) | (~product(e_6, e_4, e_1)) | product(e_5, e_6, e_4))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_6, e_5)) | (~product(e_6, e_4, e_1)) | product(e_5, e_6, e_4))),
% 0.74/0.80 inference(rewrite,[status(thm)],[])).
% 0.74/0.80 tff(1931,plain,
% 0.74/0.80 ((product(e_5, e_6, e_4) | (~product(e_1, e_6, e_5)) | (~product(e_6, e_4, e_1))) <=> ((~product(e_1, e_6, e_5)) | (~product(e_6, e_4, e_1)) | product(e_5, e_6, e_4))),
% 0.74/0.80 inference(rewrite,[status(thm)],[])).
% 0.74/0.80 tff(1932,plain,
% 0.74/0.80 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_5, e_6, e_4) | (~product(e_1, e_6, e_5)) | (~product(e_6, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_6, e_5)) | (~product(e_6, e_4, e_1)) | product(e_5, e_6, e_4)))),
% 0.74/0.80 inference(monotonicity,[status(thm)],[1931])).
% 0.74/0.80 tff(1933,plain,
% 0.74/0.80 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_5, e_6, e_4) | (~product(e_1, e_6, e_5)) | (~product(e_6, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_6, e_5)) | (~product(e_6, e_4, e_1)) | product(e_5, e_6, e_4))),
% 0.74/0.80 inference(transitivity,[status(thm)],[1932, 1930])).
% 0.74/0.80 tff(1934,plain,
% 0.74/0.80 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_5, e_6, e_4) | (~product(e_1, e_6, e_5)) | (~product(e_6, e_4, e_1)))),
% 0.74/0.80 inference(quant_inst,[status(thm)],[])).
% 0.74/0.80 tff(1935,plain,
% 0.74/0.80 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_6, e_5)) | (~product(e_6, e_4, e_1)) | product(e_5, e_6, e_4)),
% 0.74/0.80 inference(modus_ponens,[status(thm)],[1934, 1933])).
% 0.74/0.80 tff(1936,plain,
% 0.74/0.80 ($false),
% 0.74/0.80 inference(unit_resolution,[status(thm)],[1935, 58, 1879, 1929, 1])).
% 0.74/0.80 tff(1937,plain,(product(e_5, e_6, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.74/0.80 tff(1938,assumption,(product(e_4, e_5, e_1)), introduced(assumption)).
% 0.74/0.80 tff(1939,plain,
% 0.74/0.80 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_5, e_6) | (~product(e_5, e_6, e_4)) | (~product(e_4, e_5, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_5, e_6) | (~product(e_5, e_6, e_4)) | (~product(e_4, e_5, e_1)))),
% 0.74/0.80 inference(rewrite,[status(thm)],[])).
% 0.74/0.80 tff(1940,plain,
% 0.74/0.80 ((product(e_1, e_5, e_6) | (~product(e_4, e_5, e_1)) | (~product(e_5, e_6, e_4))) <=> (product(e_1, e_5, e_6) | (~product(e_5, e_6, e_4)) | (~product(e_4, e_5, e_1)))),
% 0.74/0.80 inference(rewrite,[status(thm)],[])).
% 0.74/0.80 tff(1941,plain,
% 0.74/0.80 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_5, e_6) | (~product(e_4, e_5, e_1)) | (~product(e_5, e_6, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_5, e_6) | (~product(e_5, e_6, e_4)) | (~product(e_4, e_5, e_1))))),
% 0.74/0.80 inference(monotonicity,[status(thm)],[1940])).
% 0.74/0.80 tff(1942,plain,
% 0.74/0.80 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_5, e_6) | (~product(e_4, e_5, e_1)) | (~product(e_5, e_6, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_5, e_6) | (~product(e_5, e_6, e_4)) | (~product(e_4, e_5, e_1)))),
% 0.74/0.80 inference(transitivity,[status(thm)],[1941, 1939])).
% 0.74/0.80 tff(1943,plain,
% 0.74/0.80 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_5, e_6) | (~product(e_4, e_5, e_1)) | (~product(e_5, e_6, e_4)))),
% 0.74/0.80 inference(quant_inst,[status(thm)],[])).
% 0.74/0.80 tff(1944,plain,
% 0.74/0.80 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_5, e_6) | (~product(e_5, e_6, e_4)) | (~product(e_4, e_5, e_1))),
% 0.74/0.80 inference(modus_ponens,[status(thm)],[1943, 1942])).
% 0.74/0.80 tff(1945,plain,
% 0.74/0.80 ($false),
% 0.74/0.80 inference(unit_resolution,[status(thm)],[1944, 58, 1653, 1938, 1937])).
% 0.74/0.80 tff(1946,plain,(~product(e_4, e_5, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.74/0.80 tff(1947,plain,
% 0.74/0.80 (~product(e_4, e_5, e_2)),
% 0.74/0.80 inference(unit_resolution,[status(thm)],[1651, 1886])).
% 0.74/0.80 tff(1948,plain,
% 0.74/0.80 (~product(e_1, e_5, e_4)),
% 0.74/0.80 inference(unit_resolution,[status(thm)],[770, 1882])).
% 0.74/0.80 tff(1949,plain,
% 0.74/0.80 (product(e_1, e_5, e_3)),
% 0.74/0.80 inference(unit_resolution,[status(thm)],[1654, 1948])).
% 0.74/0.80 tff(1950,plain,
% 0.74/0.80 (~product(e_4, e_5, e_3)),
% 0.74/0.80 inference(unit_resolution,[status(thm)],[1660, 1949])).
% 0.74/0.80 tff(1951,plain,
% 0.74/0.80 (product(e_4, e_5, e_6) | product(e_4, e_5, e_1)),
% 0.74/0.80 inference(unit_resolution,[status(thm)],[1417, 1950, 1947])).
% 0.74/0.80 tff(1952,plain,
% 0.74/0.80 (product(e_4, e_5, e_6)),
% 0.74/0.80 inference(unit_resolution,[status(thm)],[1951, 1946])).
% 0.74/0.80 tff(1953,plain,
% 0.74/0.80 (~product(e_4, e_2, e_6)),
% 0.74/0.80 inference(unit_resolution,[status(thm)],[1676, 1952])).
% 0.74/0.80 tff(1954,plain,
% 0.74/0.80 (product(e_4, e_2, e_3)),
% 0.74/0.80 inference(unit_resolution,[status(thm)],[1856, 1953])).
% 0.74/0.80 tff(1955,plain,
% 0.74/0.80 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_4) | (~product(e_6, e_2, e_3)) | (~product(e_4, 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_6, e_4) | (~product(e_6, e_2, e_3)) | (~product(e_4, e_2, e_3)))),
% 0.74/0.80 inference(rewrite,[status(thm)],[])).
% 0.74/0.80 tff(1956,plain,
% 0.74/0.80 ((equalish(e_6, e_4) | (~product(e_4, e_2, e_3)) | (~product(e_6, e_2, e_3))) <=> (equalish(e_6, e_4) | (~product(e_6, e_2, e_3)) | (~product(e_4, e_2, e_3)))),
% 0.74/0.80 inference(rewrite,[status(thm)],[])).
% 0.74/0.80 tff(1957,plain,
% 0.74/0.80 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_4) | (~product(e_4, e_2, e_3)) | (~product(e_6, 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_6, e_4) | (~product(e_6, e_2, e_3)) | (~product(e_4, e_2, e_3))))),
% 0.74/0.80 inference(monotonicity,[status(thm)],[1956])).
% 0.74/0.80 tff(1958,plain,
% 0.74/0.80 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_4) | (~product(e_4, e_2, e_3)) | (~product(e_6, 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_6, e_4) | (~product(e_6, e_2, e_3)) | (~product(e_4, e_2, e_3)))),
% 0.74/0.80 inference(transitivity,[status(thm)],[1957, 1955])).
% 0.74/0.80 tff(1959,plain,
% 0.74/0.80 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_4) | (~product(e_4, e_2, e_3)) | (~product(e_6, e_2, e_3)))),
% 0.74/0.80 inference(quant_inst,[status(thm)],[])).
% 0.74/0.80 tff(1960,plain,
% 0.74/0.80 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_6, e_4) | (~product(e_6, e_2, e_3)) | (~product(e_4, e_2, e_3))),
% 0.74/0.80 inference(modus_ponens,[status(thm)],[1959, 1958])).
% 0.74/0.80 tff(1961,plain,
% 0.74/0.80 ($false),
% 0.74/0.80 inference(unit_resolution,[status(thm)],[1960, 635, 87, 1858, 1528])).
% 0.74/0.80 tff(1962,plain,((~product(e_6, e_2, e_3)) | (~product(e_4, e_2, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.80 tff(1963,plain,
% 0.74/0.80 (~product(e_6, e_2, e_3)),
% 0.74/0.80 inference(unit_resolution,[status(thm)],[1962, 1954])).
% 0.74/0.80 tff(1964,plain,
% 0.74/0.80 (~product(e_4, e_6, e_3)),
% 0.74/0.80 inference(unit_resolution,[status(thm)],[1863, 1954])).
% 0.74/0.80 tff(1965,plain,
% 0.74/0.80 (product(e_4, e_6, e_1)),
% 0.74/0.80 inference(unit_resolution,[status(thm)],[1888, 1964])).
% 0.74/0.80 tff(1966,plain,
% 0.74/0.80 (~product(e_6, e_3, e_4)),
% 0.74/0.80 inference(unit_resolution,[status(thm)],[1892, 58, 348, 1323])).
% 0.74/0.80 tff(1967,assumption,(product(e_6, e_3, e_1)), introduced(assumption)).
% 0.74/0.80 tff(1968,plain,
% 0.74/0.80 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_4) | (~product(e_6, e_4, e_1)) | (~product(e_6, e_3, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_4) | (~product(e_6, e_4, e_1)) | (~product(e_6, e_3, e_1)))),
% 0.74/0.80 inference(rewrite,[status(thm)],[])).
% 0.74/0.80 tff(1969,plain,
% 0.74/0.80 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_4) | (~product(e_6, e_4, e_1)) | (~product(e_6, e_3, e_1)))),
% 0.74/0.80 inference(quant_inst,[status(thm)],[])).
% 0.74/0.80 tff(1970,plain,
% 0.74/0.80 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_4) | (~product(e_6, e_4, e_1)) | (~product(e_6, e_3, e_1))),
% 0.74/0.80 inference(modus_ponens,[status(thm)],[1969, 1968])).
% 0.74/0.80 tff(1971,plain,
% 0.74/0.80 ($false),
% 0.74/0.80 inference(unit_resolution,[status(thm)],[1970, 410, 17, 1929, 1967])).
% 0.74/0.80 tff(1972,plain,(~product(e_6, e_3, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.74/0.80 tff(1973,assumption,(product(e_6, e_3, e_6)), introduced(assumption)).
% 0.74/0.80 tff(1974,plain,
% 0.74/0.80 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_1) | (~product(e_1, e_3, e_6)) | (~product(e_6, e_3, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_6, e_1) | (~product(e_1, e_3, e_6)) | (~product(e_6, e_3, e_6)))),
% 0.74/0.80 inference(rewrite,[status(thm)],[])).
% 0.74/0.80 tff(1975,plain,
% 0.74/0.80 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_1) | (~product(e_1, e_3, e_6)) | (~product(e_6, e_3, e_6)))),
% 0.74/0.80 inference(quant_inst,[status(thm)],[])).
% 0.74/0.81 tff(1976,plain,
% 0.74/0.81 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_6, e_1) | (~product(e_1, e_3, e_6)) | (~product(e_6, e_3, e_6))),
% 0.74/0.81 inference(modus_ponens,[status(thm)],[1975, 1974])).
% 0.74/0.81 tff(1977,plain,
% 0.74/0.81 ($false),
% 0.74/0.81 inference(unit_resolution,[status(thm)],[1976, 1116, 87, 1884, 1973])).
% 0.74/0.81 tff(1978,plain,(~product(e_6, e_3, e_6)), inference(lemma,lemma(discharge,[]))).
% 0.74/0.81 tff(1979,assumption,(product(e_6, e_3, e_2)), introduced(assumption)).
% 0.74/0.81 tff(1980,plain,
% 0.74/0.81 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_4) | (~product(e_4, e_3, e_2)) | (~product(e_6, 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_6, e_4) | (~product(e_4, e_3, e_2)) | (~product(e_6, e_3, e_2)))),
% 0.74/0.81 inference(rewrite,[status(thm)],[])).
% 0.74/0.81 tff(1981,plain,
% 0.74/0.81 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_4) | (~product(e_4, e_3, e_2)) | (~product(e_6, e_3, e_2)))),
% 0.74/0.81 inference(quant_inst,[status(thm)],[])).
% 0.74/0.81 tff(1982,plain,
% 0.74/0.81 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_6, e_4) | (~product(e_4, e_3, e_2)) | (~product(e_6, e_3, e_2))),
% 0.74/0.81 inference(modus_ponens,[status(thm)],[1981, 1980])).
% 0.74/0.81 tff(1983,plain,
% 0.74/0.81 ($false),
% 0.74/0.81 inference(unit_resolution,[status(thm)],[1982, 635, 87, 1886, 1979])).
% 0.74/0.81 tff(1984,plain,(~product(e_6, e_3, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.74/0.81 tff(1985,assumption,(product(e_6, e_3, e_3)), introduced(assumption)).
% 0.74/0.81 tff(1986,plain,
% 0.74/0.81 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_6, 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_6, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_6, e_3, e_3)))),
% 0.74/0.81 inference(rewrite,[status(thm)],[])).
% 0.74/0.81 tff(1987,plain,
% 0.74/0.81 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_6, e_3, e_3)))),
% 0.74/0.81 inference(quant_inst,[status(thm)],[])).
% 0.74/0.81 tff(1988,plain,
% 0.74/0.81 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_6, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_6, e_3, e_3))),
% 0.74/0.81 inference(modus_ponens,[status(thm)],[1987, 1986])).
% 0.74/0.81 tff(1989,plain,
% 0.74/0.81 ($false),
% 0.74/0.81 inference(unit_resolution,[status(thm)],[1988, 816, 87, 462, 1985])).
% 0.74/0.81 tff(1990,plain,(~product(e_6, e_3, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.74/0.81 tff(1991,plain,
% 0.74/0.81 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_3)) | (~group_element(e_6)) | product(e_6, e_3, e_4) | product(e_6, e_3, e_3) | product(e_6, e_3, e_6) | product(e_6, e_3, e_5) | product(e_6, e_3, e_2) | product(e_6, e_3, e_1))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_3)) | (~group_element(e_6)) | product(e_6, e_3, e_4) | product(e_6, e_3, e_3) | product(e_6, e_3, e_6) | product(e_6, e_3, e_5) | product(e_6, e_3, e_2) | product(e_6, e_3, e_1))),
% 0.74/0.81 inference(rewrite,[status(thm)],[])).
% 0.74/0.81 tff(1992,plain,
% 0.74/0.81 ((product(e_6, e_3, e_6) | product(e_6, e_3, e_5) | product(e_6, e_3, e_4) | product(e_6, e_3, e_3) | product(e_6, e_3, e_2) | product(e_6, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_6))) <=> ((~group_element(e_3)) | (~group_element(e_6)) | product(e_6, e_3, e_4) | product(e_6, e_3, e_3) | product(e_6, e_3, e_6) | product(e_6, e_3, e_5) | product(e_6, e_3, e_2) | product(e_6, e_3, e_1))),
% 0.74/0.81 inference(rewrite,[status(thm)],[])).
% 0.74/0.81 tff(1993,plain,
% 0.74/0.81 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_6, e_3, e_6) | product(e_6, e_3, e_5) | product(e_6, e_3, e_4) | product(e_6, e_3, e_3) | product(e_6, e_3, e_2) | product(e_6, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_6)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_3)) | (~group_element(e_6)) | product(e_6, e_3, e_4) | product(e_6, e_3, e_3) | product(e_6, e_3, e_6) | product(e_6, e_3, e_5) | product(e_6, e_3, e_2) | product(e_6, e_3, e_1)))),
% 0.74/0.81 inference(monotonicity,[status(thm)],[1992])).
% 0.74/0.81 tff(1994,plain,
% 0.74/0.81 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_6, e_3, e_6) | product(e_6, e_3, e_5) | product(e_6, e_3, e_4) | product(e_6, e_3, e_3) | product(e_6, e_3, e_2) | product(e_6, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_6)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_3)) | (~group_element(e_6)) | product(e_6, e_3, e_4) | product(e_6, e_3, e_3) | product(e_6, e_3, e_6) | product(e_6, e_3, e_5) | product(e_6, e_3, e_2) | product(e_6, e_3, e_1))),
% 0.74/0.81 inference(transitivity,[status(thm)],[1993, 1991])).
% 0.74/0.81 tff(1995,plain,
% 0.74/0.81 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_6, e_3, e_6) | product(e_6, e_3, e_5) | product(e_6, e_3, e_4) | product(e_6, e_3, e_3) | product(e_6, e_3, e_2) | product(e_6, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_6)))),
% 0.74/0.81 inference(quant_inst,[status(thm)],[])).
% 0.74/0.81 tff(1996,plain,
% 0.74/0.81 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_3)) | (~group_element(e_6)) | product(e_6, e_3, e_4) | product(e_6, e_3, e_3) | product(e_6, e_3, e_6) | product(e_6, e_3, e_5) | product(e_6, e_3, e_2) | product(e_6, e_3, e_1)),
% 0.74/0.81 inference(modus_ponens,[status(thm)],[1995, 1994])).
% 0.74/0.81 tff(1997,plain,
% 0.74/0.81 (product(e_6, e_3, e_4) | product(e_6, e_3, e_6) | product(e_6, e_3, e_5) | product(e_6, e_3, e_2) | product(e_6, e_3, e_1)),
% 0.74/0.81 inference(unit_resolution,[status(thm)],[1996, 253, 384, 129, 1990])).
% 0.74/0.81 tff(1998,plain,
% 0.74/0.81 (product(e_6, e_3, e_4) | product(e_6, e_3, e_6) | product(e_6, e_3, e_5) | product(e_6, e_3, e_1)),
% 0.74/0.81 inference(unit_resolution,[status(thm)],[1997, 1984])).
% 0.74/0.81 tff(1999,plain,
% 0.74/0.81 (product(e_6, e_3, e_4) | product(e_6, e_3, e_5)),
% 0.74/0.81 inference(unit_resolution,[status(thm)],[1998, 1978, 1972])).
% 0.74/0.81 tff(2000,plain,
% 0.74/0.81 (product(e_6, e_3, e_5)),
% 0.74/0.81 inference(unit_resolution,[status(thm)],[1999, 1966])).
% 0.74/0.81 tff(2001,assumption,(product(e_6, e_4, e_1)), introduced(assumption)).
% 0.74/0.81 tff(2002,plain,
% 0.74/0.81 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_4) | (~product(e_6, e_4, e_1)) | (~product(e_6, e_2, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_4) | (~product(e_6, e_4, e_1)) | (~product(e_6, e_2, e_1)))),
% 0.74/0.81 inference(rewrite,[status(thm)],[])).
% 0.74/0.81 tff(2003,plain,
% 0.74/0.81 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_4) | (~product(e_6, e_4, e_1)) | (~product(e_6, e_2, e_1)))),
% 0.74/0.81 inference(quant_inst,[status(thm)],[])).
% 0.74/0.81 tff(2004,plain,
% 0.74/0.81 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_4) | (~product(e_6, e_4, e_1)) | (~product(e_6, e_2, e_1))),
% 0.74/0.81 inference(modus_ponens,[status(thm)],[2003, 2002])).
% 0.74/0.81 tff(2005,plain,
% 0.74/0.81 ($false),
% 0.74/0.81 inference(unit_resolution,[status(thm)],[2004, 522, 17, 1340, 2001])).
% 0.74/0.81 tff(2006,plain,((~product(e_6, e_2, e_1)) | (~product(e_6, e_4, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.81 tff(2007,plain,
% 0.74/0.81 (~product(e_6, e_2, e_1)),
% 0.74/0.81 inference(unit_resolution,[status(thm)],[2006, 1929])).
% 0.74/0.81 tff(2008,assumption,(product(e_6, e_2, e_6)), introduced(assumption)).
% 0.74/0.81 tff(2009,plain,
% 0.74/0.81 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_6) | (~product(e_6, e_2, e_6)) | (~product(e_6, e_6, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_6) | (~product(e_6, e_2, e_6)) | (~product(e_6, e_6, e_6)))),
% 0.74/0.81 inference(rewrite,[status(thm)],[])).
% 0.74/0.81 tff(2010,plain,
% 0.74/0.81 ((equalish(e_2, e_6) | (~product(e_6, e_6, e_6)) | (~product(e_6, e_2, e_6))) <=> (equalish(e_2, e_6) | (~product(e_6, e_2, e_6)) | (~product(e_6, e_6, e_6)))),
% 0.74/0.81 inference(rewrite,[status(thm)],[])).
% 0.74/0.81 tff(2011,plain,
% 0.74/0.81 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_6) | (~product(e_6, e_6, e_6)) | (~product(e_6, e_2, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_6) | (~product(e_6, e_2, e_6)) | (~product(e_6, e_6, e_6))))),
% 0.74/0.81 inference(monotonicity,[status(thm)],[2010])).
% 0.74/0.81 tff(2012,plain,
% 0.74/0.81 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_6) | (~product(e_6, e_6, e_6)) | (~product(e_6, e_2, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_6) | (~product(e_6, e_2, e_6)) | (~product(e_6, e_6, e_6)))),
% 0.74/0.81 inference(transitivity,[status(thm)],[2011, 2009])).
% 0.74/0.81 tff(2013,plain,
% 0.74/0.81 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_6) | (~product(e_6, e_6, e_6)) | (~product(e_6, e_2, e_6)))),
% 0.74/0.81 inference(quant_inst,[status(thm)],[])).
% 0.74/0.81 tff(2014,plain,
% 0.74/0.81 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_6) | (~product(e_6, e_2, e_6)) | (~product(e_6, e_6, e_6))),
% 0.74/0.81 inference(modus_ponens,[status(thm)],[2013, 2012])).
% 0.74/0.81 tff(2015,plain,
% 0.74/0.81 ($false),
% 0.74/0.81 inference(unit_resolution,[status(thm)],[2014, 545, 17, 933, 2008])).
% 0.74/0.81 tff(2016,plain,(~product(e_6, e_2, e_6)), inference(lemma,lemma(discharge,[]))).
% 0.74/0.81 tff(2017,plain,
% 0.74/0.81 (product(e_6, e_2, e_1) | product(e_6, e_2, e_5) | product(e_6, e_2, e_3) | product(e_6, e_2, e_4)),
% 0.74/0.81 inference(unit_resolution,[status(thm)],[1359, 2016])).
% 0.74/0.81 tff(2018,plain,
% 0.74/0.81 (product(e_6, e_2, e_5) | product(e_6, e_2, e_3) | product(e_6, e_2, e_4)),
% 0.74/0.81 inference(unit_resolution,[status(thm)],[2017, 2007])).
% 0.74/0.81 tff(2019,plain,
% 0.74/0.81 (product(e_6, e_2, e_5)),
% 0.74/0.81 inference(unit_resolution,[status(thm)],[2018, 1337, 1234])).
% 0.74/0.81 tff(2020,assumption,(product(e_6, e_3, e_5)), introduced(assumption)).
% 0.74/0.81 tff(2021,plain,
% 0.74/0.81 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_6, e_2, e_5)) | (~product(e_6, e_3, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_6, e_2, e_5)) | (~product(e_6, e_3, e_5)))),
% 0.74/0.81 inference(rewrite,[status(thm)],[])).
% 0.74/0.81 tff(2022,plain,
% 0.74/0.81 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_6, e_2, e_5)) | (~product(e_6, e_3, e_5)))),
% 0.74/0.81 inference(quant_inst,[status(thm)],[])).
% 0.74/0.81 tff(2023,plain,
% 0.74/0.81 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_6, e_2, e_5)) | (~product(e_6, e_3, e_5))),
% 0.74/0.81 inference(modus_ponens,[status(thm)],[2022, 2021])).
% 0.74/0.81 tff(2024,plain,
% 0.74/0.81 ($false),
% 0.74/0.81 inference(unit_resolution,[status(thm)],[2023, 753, 17, 1316, 2020])).
% 0.74/0.81 tff(2025,plain,((~product(e_6, e_3, e_5)) | (~product(e_6, e_2, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.81 tff(2026,plain,
% 0.74/0.81 ($false),
% 0.74/0.81 inference(unit_resolution,[status(thm)],[2025, 2019, 2000])).
% 0.74/0.81 tff(2027,plain,((~product(e_4, e_6, e_1)) | product(e_6, e_2, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.74/0.81 tff(2028,plain,
% 0.74/0.81 ($false),
% 0.74/0.81 inference(unit_resolution,[status(thm)],[2027, 1965, 1963])).
% 0.74/0.81 % SZS output end Proof
%------------------------------------------------------------------------------